Finite Group Databasebeta

← #33293583

Subgroups — #33293583

Order 18688.

2146 conjugacy classes of subgroups.

The subgroup lattice has 1602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618216C211yesmaximal, characteristic, complemented
2#22618216C211yesmaximal, characteristic, complemented
3#22617872C211yesmaximal, characteristic, complemented
4#22617633C211yesmaximal, characteristic, complemented
5#22617626C211yesmaximal, characteristic, complemented
6#22617586C211yesmaximal, characteristic, complemented
7#22617584C211yesmaximal, characteristic, complemented
8#22617581C211yesmaximal, characteristic, complemented
9#22617572C211yesmaximal, characteristic, complemented
10#22617145C211yesmaximal, characteristic, complemented
11#22617138C211yesmaximal, characteristic, complemented
12#22616953C211yesmaximal, characteristic, complemented
13#22616945C211yesmaximal, characteristic, complemented
14#22616433C211yesmaximal, characteristic, complemented
15#22616432C211yesmaximal, characteristic, complemented
16#22616426C211yesmaximal, characteristic, complemented
17#22616420C211yesmaximal, characteristic, complemented
18#22616300C211yesmaximal, characteristic, complemented
19#22615736C211yesmaximal, characteristic, complemented
20#22613613C211yesmaximal, characteristic, complemented
21#22613611C211yesmaximal, characteristic, complemented
22#22613605C211yesmaximal, characteristic, complemented
23#22613603C211yesmaximal, characteristic, complemented
24#22613599C211yesmaximal, characteristic, complemented
25#22613596C211yesmaximal, characteristic, complemented
26#22613595C211yesmaximal, characteristic, complemented
27#22613594C211yesmaximal, characteristic, complemented
28#22612512C211yesmaximal, characteristic
29#22612507C211yesmaximal, characteristic
30C2×#17988464C211yesmaximal, characteristic
31C73×#2626C211yesmaximal, characteristic, complemented
32C23×C22⋊D73C2211yescharacteristic
33C24×Dic73C2211yescharacteristic
34C2×#14556571C2211yescharacteristic, complemented
35C2×#14556570C2211yescharacteristic
36C2×#14556569C2211yescharacteristic, complemented
37C2×#14556569C2211yescharacteristic, complemented
38C2×#14556568C2211yescharacteristic
39C2×#14556568C2211yescharacteristic
40C2×#14556568C2211yescharacteristic, complemented
41C2×#14556568C2211yescharacteristic, complemented
42C2×#14556568C2211yescharacteristic, complemented
43C2×#14556568C2211yescharacteristic, complemented
44C2×#14556567C2211yescharacteristic, complemented
45C2×#14556547C2211yescharacteristic
46C2×#14556547C2211yescharacteristic
47C22×#11924005C2211yescharacteristic
48C22×#11924005C2211yescharacteristic
49C2×C22⋊C4×D73C2211yescharacteristic
50C2×C22⋊C4×D73C2211yescharacteristic
51#17988528C2211yescharacteristic, complemented
52#17988528C2211yescharacteristic, complemented
53#17988527C2211yescharacteristic, complemented
54#17988525C2211yescharacteristic, complemented
55#17988524C2211yescharacteristic, complemented
56#17988523C2211yescharacteristic, complemented
57#17988523C2211yescharacteristic, complemented
58#17988522C2211yescharacteristic, complemented
59#17988522C2211yescharacteristic, complemented
60#17988522C2211yescharacteristic, complemented
61#17988521C2211yescharacteristic, complemented
62#17988521C2211yescharacteristic, complemented
63#17988520C2211yescharacteristic, complemented
64#17988520C2211yescharacteristic, complemented
65#17988518C2211yescharacteristic, complemented
66#17988518C2211yescharacteristic, complemented
67#17988517C2211yescharacteristic, complemented
68#17988517C2211yescharacteristic, complemented
69#17988511C2211yescharacteristic, complemented
70#17988511C2211yescharacteristic, complemented
71#17988510C2211yescharacteristic, complemented
72#17988510C2211yescharacteristic, complemented
73#17988510C2211yescharacteristic, complemented
74#17988510C2211yescharacteristic, complemented
75#17988509C2211yescharacteristic, complemented
76#17988509C2211yescharacteristic, complemented
77#17988509C2211yescharacteristic, complemented
78#17988509C2211yescharacteristic, complemented
79#17988509C2211yescharacteristic, complemented
80#17988509C2211yescharacteristic, complemented
81#17988508C2211yescharacteristic, complemented
82#17988507C2211yescharacteristic, complemented
83#17988507C2211yescharacteristic, complemented
84#17988506C2211yescharacteristic, complemented
85#17988500C2211yescharacteristic, complemented
86#17988500C2211yescharacteristic, complemented
87#17988500C2211yescharacteristic, complemented
88#17988499C2211yescharacteristic, complemented
89#17988499C2211yescharacteristic, complemented
90#17988498C2211yescharacteristic, complemented
91#17988494C2211yescharacteristic, complemented
92#17988492C2211yescharacteristic, complemented
93#17988491C2211yescharacteristic, complemented
94#17988491C2211yescharacteristic, complemented
95#17988487C2211yescharacteristic
96#17988487C2211yescharacteristic
97#17988487C2211yescharacteristic
98#17988487C2211yescharacteristic
99#17988487C2211yescharacteristic
100#17988487C2211yescharacteristic
101#17988487C2211yescharacteristic
102#17988487C2211yescharacteristic
103#17988486C2211yescharacteristic, complemented
104#17988483C2211yescharacteristic, complemented
105#17988482C2211yescharacteristic, complemented
106#17988482C2211yescharacteristic, complemented
107#17988473C2211yescharacteristic, complemented
108#17988473C2211yescharacteristic, complemented
109#17988472C2211yescharacteristic, complemented
110#17988472C2211yescharacteristic, complemented
111#17988469C2211yescharacteristic, complemented
112#17988469C2211yescharacteristic, complemented
113#17988468C2211yescharacteristic, complemented
114#17988468C2211yescharacteristic, complemented
115#17988464C2211yescharacteristic
116#17988464C2211yescharacteristic
117#17988464C2211yescharacteristic
118#17988464C2211yescharacteristic
119#17988464C2211yescharacteristic
120#17988464C2211yescharacteristic
121#17988464C2211yescharacteristic
122#17988464C2211yescharacteristic
123#17988463C2211yescharacteristic
124#17988463C2211yescharacteristic
125#17988463C2211yescharacteristic
126#17988463C2211yescharacteristic
127#17988463C2211yescharacteristic
128#17988463C2211yescharacteristic
129#17988463C2211yescharacteristic
130#17988463C2211yescharacteristic
131#17988462C2211yescharacteristic
132#17988462C2211yescharacteristic
133#17988462C2211yescharacteristic, complemented
134#17988462C2211yescharacteristic, complemented
135#17988462C2211yescharacteristic, complemented
136#17988462C2211yescharacteristic, complemented
137#17988461C2211yescharacteristic, complemented
138#17988461C2211yescharacteristic, complemented
139#17988461C2211yescharacteristic, complemented
140#17988461C2211yescharacteristic, complemented
141#17988460C2211yescharacteristic
142#17988460C2211yescharacteristic
143#17988459C2211yescharacteristic
144#17988459C2211yescharacteristic
145#17988459C2211yescharacteristic, complemented
146#17988459C2211yescharacteristic, complemented
147#17988459C2211yescharacteristic, complemented
148#17988459C2211yescharacteristic, complemented
149#17988458C2211yescharacteristic, complemented
150#17988458C2211yescharacteristic, complemented
151#17988458C2211yescharacteristic, complemented
152#17988458C2211yescharacteristic, complemented
153#17988448C2211yescharacteristic
154#17988448C2211yescharacteristic
155#17988447C2211yescharacteristic
156#17988446C2211yescharacteristic, complemented
157#17988446C2211yescharacteristic, complemented
158#17988445C2211yescharacteristic
159#17988445C2211yescharacteristic
160#17988445C2211yescharacteristic, complemented
161#17988445C2211yescharacteristic, complemented
162#17988445C2211yescharacteristic, complemented
163#17988445C2211yescharacteristic, complemented
164#17988444C2211yescharacteristic, complemented
165#17988444C2211yescharacteristic, complemented
166#17988443C2211yescharacteristic
167#17988443C2211yescharacteristic
168#17988442C2211yescharacteristic
169#17988442C2211yescharacteristic
170C2×#14556498C2211yescharacteristic
171C2×#14556498C2211yescharacteristic
172C2×C22⋊Q8×C73C2211yescharacteristic
173C22×C22⋊C4×C73C2211yescharacteristic
174#399×C73C2211yescharacteristic, complemented
175#399×C73C2211yescharacteristic, complemented
176#396×C73C2211yescharacteristic, complemented
177#396×C73C2211yescharacteristic, complemented
178#396×C73C2211yescharacteristic, complemented
179#396×C73C2211yescharacteristic, complemented
180#393×C73C2211yescharacteristic, complemented
181#393×C73C2211yescharacteristic, complemented
182#385×C73C2211yescharacteristic
183#385×C73C2211yescharacteristic
184#380×C73C2211yescharacteristic
185#379×C73C2211yescharacteristic
186#379×C73C2211yescharacteristic
187C24×D73C2311yescharacteristic
188C22×Dic146C2311yescharacteristic
189C22×Dic146C2311yescharacteristic
190C22×Dic146C2311yescharacteristic
191C22×C22⋊D73—42no—
192C22×C22⋊D73—42no—
193C22×C22⋊D73Q818yescomplemented
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C22×C22⋊D73C2311yescharacteristic
197C22×C22⋊D73C2311yescharacteristic
198C23×Dic73—42no—
199C23×Dic73—42no—
200C23×Dic73—42no—
201C23×Dic73C2311yescharacteristic
202C23×Dic73C2311yescharacteristic
203C23×Dic73C2311yescharacteristic
204C23×Dic73C2311yescharacteristic
205C23×Dic73C2311yescharacteristic
206C23×Dic73C2311yescharacteristic
207C23×Dic73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211C22×C4×D73C2311yescharacteristic
212#14556571—42no—
213#14556570—42no—
214#14556569—42no—
215#14556569—42no—
216#14556568—42no—
217#14556568—42no—
218#14556568—42no—
219#14556568—42no—
220#14556568—42no—
221#14556568—42no—
222#14556567—42no—
223#14556547—42no—
224#14556547—42no—
225C2×C4⋊Dic73C2311yescharacteristic
226C2×C4⋊Dic73C2311yescharacteristic
227C2×C4⋊Dic73C2311yescharacteristic
228C2×C4⋊Dic73C2311yescharacteristic
229C2×C4⋊Dic73C2311yescharacteristic
230C2×C4⋊Dic73C2311yescharacteristic
231C2×C4⋊Dic73C2311yescharacteristic
232C2×C4⋊Dic73C2311yescharacteristic
233C2×C4⋊Dic73C2311yescharacteristic
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
239C2×#11924007C2311yescharacteristic
240C2×#11924007C2311yescharacteristic
241C2×#11924007C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×#11924007C2311yescharacteristic
245C2×#11924007C2311yescharacteristic
246C2×#11924007C2311yescharacteristic
247C2×#11924007C2311yescharacteristic
248C2×#11924007C2311yescharacteristic
249C2×#11924007C2311yescharacteristic
250C2×#11924007C2311yescharacteristic
251C2×#11924007C2311yescharacteristic
252C2×#11924007C2311yescharacteristic
253C2×#11924007C2311yescharacteristic
254C2×#11924007C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×C22⋊Dic73C2311yescharacteristic
257C2×C22⋊Dic73C2311yescharacteristic
258C2×C22⋊Dic73C2311yescharacteristic
259C2×C22⋊Dic73C2311yescharacteristic
260C2×C22⋊Dic73C2311yescharacteristic
261C2×C22⋊Dic73C2311yescharacteristic
262C2×C22⋊Dic73C2311yescharacteristic
263C2×C22⋊Dic73C2311yescharacteristic
264C2×C22⋊Dic73C2311yescharacteristic
265C2×C22⋊Dic73C2311yescharacteristic
266C2×C22⋊Dic73C2311yescharacteristic
267C2×C22⋊Dic73C2311yescharacteristic
268C2×#11924005—42no—
269C2×#11924005—42no—
270C2×#11924005C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×#11924005C2311yescharacteristic
274C2×#11924005C2311yescharacteristic
275C2×#11924005C2311yescharacteristic
276C2×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
289C2×#11924005C2311yescharacteristic
290C22⋊C4×D73—42no—
291C22⋊C4×D73—42no—
292C2×C4×Dic73C2311yescharacteristic
293C2×C4×Dic73C2311yescharacteristic
294C2×C4×Dic73C2311yescharacteristic
295C2×C4×Dic73C2311yescharacteristic
296#14556498C2311yescharacteristic
297#14556498C2311yescharacteristic
298#14556498C2311yescharacteristic
299#14556498C2311yescharacteristic
300#14556498C2311yescharacteristic
301#14556498C2311yescharacteristic
302#14556498C2311yescharacteristic
303#14556498C2311yescharacteristic
304#14556498C2311yescharacteristic
305#14556498C2311yescharacteristic
306#14556498C2311yescharacteristic
307#14556498C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330C25×C73C2311yescharacteristic
331C22×Q8×C73C2311yescharacteristic
332C23×C4×C73C2311yescharacteristic
333C23×C4×C73C2311yescharacteristic
334C22⋊Q8×C73—42no—
335C2×C4⋊C4×C73C2311yescharacteristic
336C2×C4⋊C4×C73C2311yescharacteristic
337C2×C4⋊C4×C73C2311yescharacteristic
338C2×C4⋊C4×C73C2311yescharacteristic
339C2×C4⋊C4×C73C2311yescharacteristic
340C2×C4⋊C4×C73C2311yescharacteristic
341C2×C4⋊C4×C73C2311yescharacteristic
342C2×C4⋊C4×C73C2311yescharacteristic
343C2×C4⋊C4×C73C2311yescharacteristic
344C2×C22⋊C4×C73—42no—
345C2×C22⋊C4×C73C2311yescharacteristic
346C2×C22⋊C4×C73C2311yescharacteristic
347C2×C22⋊C4×C73C2311yescharacteristic
348C2×C22⋊C4×C73C2311yescharacteristic
349C2×C22⋊C4×C73C2311yescharacteristic
350C2×C22⋊C4×C73C2311yescharacteristic
351C2×C22⋊C4×C73C2311yescharacteristic
352C2×C22⋊C4×C73C2311yescharacteristic
353C2×C22⋊C4×C73C2311yescharacteristic
354C2×C22⋊C4×C73C2311yescharacteristic
355C2×C22⋊C4×C73C2311yescharacteristic
356C2×C22⋊C4×C73C2311yescharacteristic
357C2×C22⋊C4×C73C2311yescharacteristic
358C2×C22⋊C4×C73C2311yescharacteristic
359C2×C22⋊C4×C73C2311yescharacteristic
360C2×C22⋊C4×C73C2311yescharacteristic
361#95×C73C2311yescharacteristic
362#95×C73C2311yescharacteristic
363#95×C73C2311yescharacteristic
364#95×C73C2311yescharacteristic
365#95×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367C23×D73—22no—
368C23×D73—22no—
369C23×D73—41no—
370C23×D73—41no—
371C23×D73—41no—
372C23×D73—41no—
373C23×D73C2×Q814yes—
374C23×D73C2411yescharacteristic
375C23×D73C2411yescharacteristic
376C2×Dic146—22no—
377C2×Dic146—22no—
378C2×Dic146—41no—
379C2×Dic146—41no—
380C2×Dic146—41no—
381C2×Dic146—41no—
382C2×Dic146—41no—
383C2×Dic146—41no—
384C2×Dic146—41no—
385C2×C22⋊D73—416no—
386C2×C22⋊D73—41no—
387C2×C22⋊D73—41no—
388C2×C22⋊D73—41no—
389C2×C22⋊D73—41no—
390C2×C22⋊D73—41no—
391C2×C22⋊D73—41no—
392C2×C22⋊D73—41no—
393C2×C22⋊D73—41no—
394C2×C22⋊D73C2×Q814yes—
395C2×C22⋊D73C2×Q814yes—
396C2×C22⋊D73C2×Q814yes—
397C2×C22⋊D73C2×Q814yes—
398C22×Dic73—22no—
399C22×Dic73—22no—
400C22×Dic73—22no—
401C22×Dic73—22no—
402C22×Dic73—22no—
403C22×Dic73—22no—
404C22×Dic73—22no—
405C22×Dic73—22no—
406C22×Dic73—22no—
407C22×Dic73—22no—
408C22×Dic73—41no—
409C22×Dic73—41no—
410C22×Dic73—41no—
411C22×Dic73—41no—
412C22×Dic73—41no—
413C22×Dic73—41no—
414C22×Dic73—41no—
415C22×Dic73—41no—
416C22×Dic73—41no—
417C22×Dic73—41no—
418C22×Dic73—416no—
419C22×Dic73C2×Q814yes—
420C22×Dic73C2411yescharacteristic
421C22×Dic73C2411yescharacteristic
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2411yescharacteristic
424C22×Dic73C2411yescharacteristic
425C22×Dic73C2411yescharacteristic
426C22×Dic73C2411yescharacteristic
427C22×Dic73C2411yescharacteristic
428C22×Dic73C2411yescharacteristic
429C22×Dic73C2411yescharacteristic
430C22×Dic73C2411yescharacteristic
431C22×Dic73C2411yescharacteristic
432C22×Dic73C2411yescharacteristic
433C22×Dic73C2411yescharacteristic
434C2×C4×D73—41no—
435C2×C4×D73—41no—
436C2×C4×D73—41no—
437C2×C4×D73—41no—
438C2×C4×D73—41no—
439C2×C4×D73—41no—
440C2×C4×D73—41no—
441C2×C4×D73—41no—
442C2×C4×D73—41no—
443C2×C4×D73—41no—
444C2×C4×D73—41no—
445C2×C4×D73—41no—
446C4⋊Dic73—22no—
447C4⋊Dic73—22no—
448C4⋊Dic73—41no—
449C4⋊Dic73—41no—
450C4⋊Dic73—41no—
451C4⋊Dic73—41no—
452C4⋊Dic73—41no—
453C4⋊Dic73—41no—
454C4⋊Dic73—41no—
455#11924007—22no—
456#11924007—22no—
457#11924007—22no—
458#11924007—22no—
459#11924007—41no—
460#11924007—41no—
461#11924007—41no—
462#11924007—41no—
463#11924007—41no—
464#11924007—41no—
465#11924007—41no—
466#11924007—41no—
467#11924007—41no—
468#11924007—41no—
469#11924007—41no—
470#11924007—41no—
471#11924007—41no—
472#11924007—41no—
473#11924007—41no—
474#11924007—41no—
475#11924007—41no—
476#11924007—41no—
477C22⋊Dic73—22no—
478C22⋊Dic73—22no—
479C22⋊Dic73—22no—
480C22⋊Dic73—22no—
481C22⋊Dic73—41no—
482C22⋊Dic73—41no—
483C22⋊Dic73—41no—
484C22⋊Dic73—41no—
485C22⋊Dic73—41no—
486C22⋊Dic73—41no—
487C22⋊Dic73—41no—
488C22⋊Dic73—41no—
489#11924005—22no—
490#11924005—22no—
491#11924005—22no—
492#11924005—22no—
493#11924005—41no—
494#11924005—41no—
495#11924005—41no—
496#11924005—41no—
497#11924005—41no—
498#11924005—41no—
499#11924005—41no—
500#11924005—41no—
501#11924005—41no—
502#11924005—41no—
503#11924005—41no—
504#11924005—41no—
505#11924005—41no—
506#11924005—41no—
507#11924005—41no—
508#11924005—41no—
509C4×Dic73—41no—
510C4×Dic73—41no—
511C4×Dic73—41no—
512C4×Dic73—41no—
513C24×C73—22no—
514C24×C73—22no—
515C24×C73—41no—
516C24×C73—41no—
517C24×C73—41no—
518C24×C73—41no—
519C24×C73C2×Q814yes—
520C24×C73C2411yescharacteristic
521C24×C73C2411yescharacteristic
522C24×C73C2411yescharacteristic
523C2×Q8×C73—41no—
524C2×Q8×C73—41no—
525C2×Q8×C73—41no—
526C22×C4×C73—22no—
527C22×C4×C73—22no—
528C22×C4×C73—41no—
529C22×C4×C73—41no—
530C22×C4×C73—41no—
531C22×C4×C73—41no—
532C22×C4×C73C2411yescharacteristic
533C22×C4×C73C2411yescharacteristic
534C22×C4×C73C2411yescharacteristic
535C22×C4×C73C2411yescharacteristic
536C22×C4×C73C2411yescharacteristic
537C22×C4×C73C2411yescharacteristic
538C22×C4×C73C2411yescharacteristic
539C22×C4×C73C2411yescharacteristic
540C22×C4×C73C2411yescharacteristic
541C22×C4×C73C2411yescharacteristic
542C22×C4×C73C2411yescharacteristic
543C22×C4×C73C2411yescharacteristic
544C4⋊C4×C73—41no—
545C4⋊C4×C73—41no—
546C4⋊C4×C73—41no—
547C4⋊C4×C73—41no—
548C4⋊C4×C73—41no—
549C4⋊C4×C73—41no—
550C4⋊C4×C73—41no—
551C4⋊C4×C73—41no—
552C4⋊C4×C73—41no—
553C22⋊C4×C73—22no—
554C22⋊C4×C73—22no—
555C22⋊C4×C73—22no—
556C22⋊C4×C73—22no—
557C22⋊C4×C73—41no—
558C22⋊C4×C73—41no—
559C22⋊C4×C73—41no—
560C22⋊C4×C73—41no—
561C22⋊C4×C73—41no—
562C22⋊C4×C73—41no—
563C22⋊C4×C73—41no—
564C22⋊C4×C73—41no—
565C22⋊C4×C73—41no—
566C22⋊C4×C73—41no—
567C22⋊C4×C73—41no—
568C22⋊C4×C73—41no—
569C23×C73—21no—
570C23×C73—21no—
571C23×C73—21no—
572C23×C73—21no—
573C23×C73—28no—
574C23×C73—21no—
575C23×C73—21no—
576C23×C73—21no—
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—44no—
587C23×C73—44no—
588C23×C73—44no—
589C23×C73—44no—
590C23×C73—44no—
591C23×C73—44no—
592C23×C73C22×Q812yes—
593C23×C73C22×Q812yes—
594C23×C73C22×Q812yes—
595C23×C73H(5,𝔽2)12yes—
596C23×C73H(5,𝔽2)12yes—
597C23×C73C2511yescharacteristic
598C22×D73—21no—
599C22×D73—21no—
600C22×D73—21no—
601C22×D73—21no—
602C22×D73—21no—
603C22×D73—21no—
604C22×D73—21no—
605C22×D73—21no—
606C22×D73—21no—
607C22×D73—21no—
608C22×D73—21no—
609C22×D73—21no—
610C22×D73—28no—
611C22×D73—44no—
612C22×D73—44no—
613C22×D73—82no—
614C22×D73—82no—
615C22×D73—82no—
616C22×D73—82no—
617C22×D73C22×Q812yes—
618C22×D73C22×Q812yes—
619Q8×C73—82no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—21no—
655C2×C4×C73—21no—
656C2×C4×C73—82no—
657C2×C4×C73—82no—
658C22⋊D73—44no—
659C22⋊D73—44no—
660C22⋊D73—44no—
661C22⋊D73—44no—
662C2×Dic73—28no—
663C2×Dic73—21no—
664C2×Dic73—21no—
665C2×Dic73—21no—
666C2×Dic73—21no—
667C2×Dic73—21no—
668C2×Dic73—21no—
669C2×Dic73—21no—
670C2×Dic73—21no—
671C2×Dic73—21no—
672C2×Dic73—21no—
673C2×Dic73—21no—
674C2×Dic73—21no—
675C2×Dic73—21no—
676C2×Dic73—21no—
677C2×Dic73—21no—
678C2×Dic73—21no—
679C2×Dic73—21no—
680C2×Dic73—21no—
681C2×Dic73—21no—
682C2×Dic73—21no—
683C2×Dic73—21no—
684C2×Dic73—21no—
685C2×Dic73—21no—
686C2×Dic73—21no—
687C2×Dic73—21no—
688C2×Dic73—21no—
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
695C2×Dic73—21no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—21no—
700C2×Dic73—21no—
701C2×Dic73—44no—
702C2×Dic73—44no—
703C2×Dic73—44no—
704C2×Dic73—44no—
705C2×Dic73—44no—
706C2×Dic73—44no—
707C2×Dic73C22×Q812yes—
708C2×Dic73C22×Q812yes—
709C2×Dic73H(5,𝔽2)12yes—
710C2×Dic73H(5,𝔽2)12yes—
711C4×D73—82no—
712C4×D73—82no—
713C4×D73—82no—
714C4×D73—82no—
715Dic146—82no—
716Dic146—82no—
717Dic146—82no—
718C22×C73—22no—
719C22×C73—22no—
720C22×C73—22no—
721C22×C73—22no—
722C22×C73—22no—
723C22×C73—22no—
724C22×C73—22no—
725C22×C73—22no—
726C22×C73—22no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—416no—
731C22×C73—41no—
732C22×C73—41no—
733C22×C73—41no—
734C22×C73—41no—
735C22×C73—41no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—41no—
739C22×C73#54314yes—
740C22×C73C23×Q811yescharacteristic
741C22×C73C2×H(5,𝔽2)11yescharacteristic
742C22×C73C2×H(5,𝔽2)11yescharacteristic
743C22×C73C2×H(5,𝔽2)11yescharacteristic
744C22×C73C2×H(5,𝔽2)11yescharacteristic
745C22×C73#58511yescharacteristic
746C22×C73#58511yescharacteristic
747C2×D73—22no—
748C2×D73—22no—
749C2×D73—22no—
750C2×D73—22no—
751C2×D73—22no—
752C2×D73—22no—
753C2×D73—41no—
754C2×D73—41no—
755C2×D73—41no—
756C2×D73—41no—
757C2×D73—41no—
758C2×D73—41no—
759C2×D73—41no—
760C2×D73—41no—
761C2×D73—88no—
762C4×C73—41no—
763C4×C73—41no—
764C4×C73—41no—
765C4×C73—41no—
766C4×C73—41no—
767C4×C73—41no—
768C4×C73—41no—
769C4×C73—41no—
770C4×C73—41no—
771C4×C73—41no—
772C4×C73—41no—
773C4×C73—41no—
774Dic73—22no—
775Dic73—22no—
776Dic73—22no—
777Dic73—22no—
778Dic73—41no—
779Dic73—41no—
780Dic73—41no—
781Dic73—41no—
782Dic73—41no—
783Dic73—41no—
784Dic73—41no—
785Dic73—41no—
786Dic73—41no—
787Dic73—41no—
788#36747—731nomaximal, Sylow
789C2×C73—24no—
790C2×C73—42no—
791C2×C73—42no—
792C2×C73C2×#54311yescharacteristic
793C2×C73#350111yescharacteristic
794C2×C73#350111yescharacteristic
795C2×C73#353211yescharacteristic
796C2×C73#353311yescharacteristic
797C2×C73#354211yescharacteristic
798C2×C73#354211yescharacteristic
799D73—42no—
800D73—42no—
801#2848—731no—
802#2848—731no—
803#2804—731no—
804#2784—731no—
805#2784—731no—
806#2780—731no—
807#2780—731no—
808#2780—731no—
809#2780—731no—
810#2748—731no—
811#2748—731no—
812#2732—731no—
813#2732—731no—
814#2692—731no—
815#2692—731no—
816#2692—731no—
817#2692—731no—
818#2683—731no—
819#2626—731no—
820#2626D7311yescharacteristic, complemented
821#2438—731no—
822#2438—731no—
823#2438—731no—
824#2438—731no—
825#2437—731no—
826#2437—731no—
827#2437—731no—
828#2437—731no—
829#2309—731no—
830#2308—731no—
831C2×#386—731no—
832C73#3674711yescharacteristic, complemented, Sylow
833C23×D4—731no—
834C24×C4—731no—
835C2×C22⋊Q8—731no—
836C2×C22⋊Q8—731no—
837C2×C22⋊Q8—731no—
838C2×C22⋊Q8—731no—
839C2×C22⋊Q8—731no—
840C2×C22⋊Q8—731no—
841C2×C22⋊Q8—731no—
842C2×C22⋊Q8—731no—
843C2×C22⋊Q8—731no—
844C2×C22⋊Q8—731no—
845C2×C22⋊Q8—731no—
846C2×C22⋊Q8C2×D7311yescharacteristic
847C2×#117—731no—
848C2×#117—731no—
849C22×C22⋊C4—731no—
850C22×C22⋊C4—731no—
851C22×C22⋊C4—731no—
852C22×C22⋊C4—731no—
853C22×C22⋊C4C2×D7311yescharacteristic
854#400—731no—
855#400—731no—
856#400—731no—
857#400—731no—
858#399—731no—
859#399—731no—
860#399—731no—
861#399—731no—
862#399—731no—
863#399—731no—
864#399C2×D7311yescharacteristic, complemented
865#399C2×D7311yescharacteristic, complemented
866#398—731no—
867#398—731no—
868#398—731no—
869#398—731no—
870#398—731no—
871#398—731no—
872#398—731no—
873#398—731no—
874#396—731no—
875#396—731no—
876#396—731no—
877#396—731no—
878#396—731no—
879#396—731no—
880#396—731no—
881#396—731no—
882#396—731no—
883#396—731no—
884#396—731no—
885#396—731no—
886#396C2×D7311yescharacteristic, complemented
887#396C2×D7311yescharacteristic, complemented
888#396C2×D7311yescharacteristic, complemented
889#396C2×D7311yescharacteristic, complemented
890#395—731no—
891#395—731no—
892#395—731no—
893#395—731no—
894#393—731no—
895#393—731no—
896#393—731no—
897#393—731no—
898#393—731no—
899#393—731no—
900#393C2×D7311yescharacteristic, complemented
901#393C2×D7311yescharacteristic, complemented
902#391—731no—
903#391—731no—
904#391—731no—
905#391—731no—
906#390—731no—
907#390—731no—
908#390—731no—
909#390—731no—
910#390—731no—
911#390—731no—
912#390—731no—
913#390—731no—
914#389—731no—
915#389—731no—
916#389—731no—
917#389—731no—
918#387—731no—
919#387—731no—
920#387—731no—
921#387—731no—
922#387—731no—
923#387—731no—
924#387—731no—
925#387—731no—
926#386—731no—
927#386—731no—
928#386—731no—
929#386—731no—
930#386—731no—
931#386—731no—
932#386—731no—
933#386—731no—
934#386—731no—
935#386—731no—
936#386—731no—
937#386—731no—
938#386—731no—
939#386—731no—
940#386—731no—
941#386—731no—
942#385—731no—
943#385—731no—
944#385—731no—
945#385—731no—
946#385—731no—
947#385—731no—
948#385—731no—
949#385—731no—
950#385—731no—
951#385—731no—
952#385—731no—
953#385—731no—
954#385—731no—
955#385—731no—
956#385—731no—
957#385—731no—
958#385—731no—
959#385—731no—
960#385—731no—
961#385—731no—
962#385—731no—
963#385—731no—
964#385C2×D7311yescharacteristic
965#385C2×D7311yescharacteristic
966#381—731no—
967#381—731no—
968#380—731no—
969#380—731no—
970#380—731no—
971#380—731no—
972#380—731no—
973#380—731no—
974#380—731no—
975#380—731no—
976#380—731no—
977#380—731no—
978#380—731no—
979#380C2×D7311yescharacteristic
980#379—731no—
981#379—731no—
982#379—731no—
983#379—731no—
984#379C2×D7311yescharacteristic
985#379C2×D7311yescharacteristic
986C2×#95—731no—
987C2×#95—731no—
988C25—731no—
989C25C22×D7311yescharacteristic
990C22×Q8—731no—
991C22×Q8—731no—
992C22×Q8—731no—
993C22×Q8C22×D7311yescharacteristic
994C22×D4—2922no—
995C22×D4—2922no—
996C22×D4—738no—
997C22×D4—731no—
998C22×D4—731no—
999C22×D4—731no—
1000C22×D4—731no—
1001C23×C4—2922no—
1002C23×C4—2922no—
1003C23×C4—2922no—
1004C23×C4—731no—
1005C23×C4—731no—
1006C23×C4—731no—
1007C23×C4—731no—
1008C23×C4—731no—
1009C23×C4—731no—
1010C23×C4—731no—
1011C23×C4—731no—
1012C23×C4—731no—
1013C23×C4—731no—
1014C23×C4—731no—
1015C23×C4C22×D7311yescharacteristic
1016C23×C4C22×D7311yescharacteristic
1017C22⋊Q8—42no—
1018C22⋊Q8—2922no—
1019C22⋊Q8—2922no—
1020C22⋊Q8—2922no—
1021C22⋊Q8—2922no—
1022C22⋊Q8—2922no—
1023C22⋊Q8—2922no—
1024C22⋊Q8—2922no—
1025C22⋊Q8—2922no—
1026C22⋊Q8—2922no—
1027C22⋊Q8—2922no—
1028C22⋊Q8—2922no—
1029#117—2922no—
1030#117—2922no—
1031C2×C4⋊C4—731no—
1032C2×C4⋊C4—731no—
1033C2×C4⋊C4—731no—
1034C2×C4⋊C4—731no—
1035C2×C4⋊C4—731no—
1036C2×C4⋊C4—731no—
1037C2×C4⋊C4—731no—
1038C2×C4⋊C4—731no—
1039C2×C4⋊C4—731no—
1040C2×C4⋊C4—731no—
1041C2×C4⋊C4—731no—
1042C2×C4⋊C4—731no—
1043C2×C4⋊C4—731no—
1044C2×C4⋊C4—731no—
1045C2×C4⋊C4—731no—
1046C2×C4⋊C4—731no—
1047C2×C4⋊C4—731no—
1048C2×C4⋊C4—731no—
1049C2×C4⋊C4—731no—
1050C2×C4⋊C4—731no—
1051C2×C4⋊C4—731no—
1052C2×C4⋊C4—731no—
1053C2×C4⋊C4—731no—
1054C2×C4⋊C4—731no—
1055C2×C4⋊C4—731no—
1056C2×C4⋊C4—731no—
1057C2×C4⋊C4—731no—
1058C2×C4⋊C4—731no—
1059C2×C4⋊C4—731no—
1060C2×C4⋊C4—731no—
1061C2×C4⋊C4—731no—
1062C2×C4⋊C4C22×D7311yescharacteristic
1063C2×C4⋊C4C22×D7311yescharacteristic
1064C2×C4⋊C4C22×D7311yescharacteristic
1065C2×C4⋊C4C22×D7311yescharacteristic
1066C2×C4⋊C4C22×D7311yescharacteristic
1067C2×C4⋊C4C22×D7311yescharacteristic
1068C2×C4⋊C4C22×D7311yescharacteristic
1069C2×C4⋊C4C22×D7311yescharacteristic
1070C2×C4⋊C4C22×D7311yescharacteristic
1071C2×C22⋊C4—42no—
1072C2×C22⋊C4—2922no—
1073C2×C22⋊C4—2922no—
1074C2×C22⋊C4—2922no—
1075C2×C22⋊C4—2922no—
1076C2×C22⋊C4—731no—
1077C2×C22⋊C4—731no—
1078C2×C22⋊C4—731no—
1079C2×C22⋊C4—731no—
1080C2×C22⋊C4—731no—
1081C2×C22⋊C4—731no—
1082C2×C22⋊C4—731no—
1083C2×C22⋊C4—731no—
1084C2×C22⋊C4—731no—
1085C2×C22⋊C4—731no—
1086C2×C22⋊C4—731no—
1087C2×C22⋊C4—731no—
1088C2×C22⋊C4—731no—
1089C2×C22⋊C4—731no—
1090C2×C22⋊C4—731no—
1091C2×C22⋊C4—731no—
1092C2×C22⋊C4—731no—
1093C2×C22⋊C4—731no—
1094C2×C22⋊C4—731no—
1095C2×C22⋊C4—731no—
1096C2×C22⋊C4—731no—
1097C2×C22⋊C4—731no—
1098C2×C22⋊C4—731no—
1099C2×C22⋊C4—731no—
1100C2×C22⋊C4—731no—
1101C2×C22⋊C4—731no—
1102C2×C22⋊C4—731no—
1103C2×C22⋊C4—731no—
1104C2×C22⋊C4—731no—
1105C2×C22⋊C4—731no—
1106C2×C22⋊C4—731no—
1107C2×C22⋊C4—731no—
1108C2×C22⋊C4C22×D7311yescharacteristic
1109C2×C22⋊C4C22×D7311yescharacteristic
1110C2×C22⋊C4C22×D7311yescharacteristic
1111C2×C22⋊C4C22×D7311yescharacteristic
1112C2×C22⋊C4C22×D7311yescharacteristic
1113C2×C22⋊C4C22×D7311yescharacteristic
1114C2×C22⋊C4C22×D7311yescharacteristic
1115C2×C22⋊C4C22×D7311yescharacteristic
1116C2×C22⋊C4C22×D7311yescharacteristic
1117C2×C22⋊C4C22×D7311yescharacteristic
1118C2×C22⋊C4C22×D7311yescharacteristic
1119C2×C22⋊C4C22×D7311yescharacteristic
1120C2×C22⋊C4C22×D7311yescharacteristic
1121C2×C22⋊C4C22×D7311yescharacteristic
1122C2×C22⋊C4C22×D7311yescharacteristic
1123C2×C22⋊C4C22×D7311yescharacteristic
1124C2×C42—731no—
1125C2×C42—731no—
1126C2×C42—731no—
1127C2×C42—731no—
1128#95—731no—
1129#95—731no—
1130#95—731no—
1131#95—731no—
1132#95—731no—
1133#95—731no—
1134#95—731no—
1135#95—731no—
1136#95—731no—
1137#95—731no—
1138#95—731no—
1139#95—731no—
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95—731no—
1144#95—731no—
1145#95—731no—
1146#95—731no—
1147#95—731no—
1148#95—731no—
1149#95—731no—
1150#95—731no—
1151#95—731no—
1152#95—731no—
1153#95—731no—
1154#95—731no—
1155#95—731no—
1156#95—731no—
1157#95—731no—
1158#95—731no—
1159#95—731no—
1160#95—731no—
1161#95—731no—
1162#95C22×D7311yescharacteristic
1163#95C22×D7311yescharacteristic
1164#95C22×D7311yescharacteristic
1165#95C22×D7311yescharacteristic
1166#95C22×D7311yescharacteristic
1167#95C22×D7311yescharacteristic
1168C24—22no—
1169C24—22no—
1170C24—41no—
1171C24—41no—
1172C24—41no—
1173C24—41no—
1174C24—2921no—
1175C24—2921no—
1176C24—2921no—
1177C24—2921no—
1178C24—734no—
1179C24—731no—
1180C24—731no—
1181C24—1462no—
1182C24—1462no—
1183C24Q8×D7314yes—
1184C24C23×D7311yescharacteristic
1185C24C23×D7311yescharacteristic
1186C24C23×D7311yescharacteristic
1187C2×Q8—41no—
1188C2×Q8—41no—
1189C2×Q8—41no—
1190C2×Q8—2921no—
1191C2×Q8—2921no—
1192C2×Q8—2921no—
1193C2×Q8—2921no—
1194C2×Q8—2921no—
1195C2×Q8—2921no—
1196C2×Q8—2921no—
1197C2×Q8—1462no—
1198C2×Q8—1462no—
1199C2×D4—2921no—
1200C2×D4—2921no—
1201C2×D4—2921no—
1202C2×D4—2921no—
1203C2×D4—2921no—
1204C2×D4—2921no—
1205C2×D4—2921no—
1206C2×D4—2921no—
1207C2×D4—29216no—
1208C2×D4—734no—
1209C2×D4—734no—
1210C2×D4—734no—
1211C2×D4—734no—
1212C22×C4—22no—
1213C22×C4—22no—
1214C22×C4—41no—
1215C22×C4—41no—
1216C22×C4—41no—
1217C22×C4—41no—
1218C22×C4—2921no—
1219C22×C4—2921no—
1220C22×C4—2921no—
1221C22×C4—2921no—
1222C22×C4—2921no—
1223C22×C4—2921no—
1224C22×C4—2921no—
1225C22×C4—2921no—
1226C22×C4—2921no—
1227C22×C4—2921no—
1228C22×C4—2921no—
1229C22×C4—2921no—
1230C22×C4—29216no—
1231C22×C4—2921no—
1232C22×C4—2921no—
1233C22×C4—2921no—
1234C22×C4—2921no—
1235C22×C4—2921no—
1236C22×C4—2921no—
1237C22×C4—2921no—
1238C22×C4—2921no—
1239C22×C4—2921no—
1240C22×C4—2921no—
1241C22×C4—734no—
1242C22×C4—731no—
1243C22×C4—731no—
1244C22×C4—731no—
1245C22×C4—731no—
1246C22×C4—731no—
1247C22×C4—731no—
1248C22×C4—731no—
1249C22×C4—731no—
1250C22×C4—731no—
1251C22×C4—731no—
1252C22×C4—731no—
1253C22×C4—731no—
1254C22×C4—731no—
1255C22×C4—731no—
1256C22×C4—1462no—
1257C22×C4—1462no—
1258C22×C4—1462no—
1259C22×C4—1462no—
1260C22×C4—1462no—
1261C22×C4—1462no—
1262C22×C4—1462no—
1263C22×C4—1462no—
1264C22×C4—1462no—
1265C22×C4—1462no—
1266C22×C4C23×D7311yescharacteristic
1267C22×C4C23×D7311yescharacteristic
1268C22×C4C23×D7311yescharacteristic
1269C22×C4C23×D7311yescharacteristic
1270C22×C4C23×D7311yescharacteristic
1271C22×C4C23×D7311yescharacteristic
1272C22×C4C23×D7311yescharacteristic
1273C22×C4C23×D7311yescharacteristic
1274C22×C4C23×D7311yescharacteristic
1275C22×C4C23×D7311yescharacteristic
1276C22×C4C23×D7311yescharacteristic
1277C22×C4C23×D7311yescharacteristic
1278C4⋊C4—41no—
1279C4⋊C4—41no—
1280C4⋊C4—41no—
1281C4⋊C4—41no—
1282C4⋊C4—41no—
1283C4⋊C4—41no—
1284C4⋊C4—41no—
1285C4⋊C4—41no—
1286C4⋊C4—41no—
1287C4⋊C4—2921no—
1288C4⋊C4—2921no—
1289C4⋊C4—2921no—
1290C4⋊C4—2921no—
1291C4⋊C4—2921no—
1292C4⋊C4—2921no—
1293C4⋊C4—2921no—
1294C4⋊C4—2921no—
1295C4⋊C4—2921no—
1296C4⋊C4—2921no—
1297C4⋊C4—2921no—
1298C4⋊C4—2921no—
1299C4⋊C4—2921no—
1300C4⋊C4—2921no—
1301C4⋊C4—2921no—
1302C4⋊C4—2921no—
1303C4⋊C4—2921no—
1304C4⋊C4—2921no—
1305C4⋊C4—2921no—
1306C4⋊C4—2921no—
1307C4⋊C4—2921no—
1308C4⋊C4—2921no—
1309C4⋊C4—2921no—
1310C4⋊C4—2921no—
1311C4⋊C4—2921no—
1312C4⋊C4—1462no—
1313C4⋊C4—1462no—
1314C4⋊C4—1462no—
1315C4⋊C4—1462no—
1316C4⋊C4—1462no—
1317C4⋊C4—1462no—
1318C22⋊C4—22no—
1319C22⋊C4—22no—
1320C22⋊C4—22no—
1321C22⋊C4—22no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—41no—
1328C22⋊C4—41no—
1329C22⋊C4—41no—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—2921no—
1335C22⋊C4—2921no—
1336C22⋊C4—2921no—
1337C22⋊C4—2921no—
1338C22⋊C4—2921no—
1339C22⋊C4—2921no—
1340C22⋊C4—2921no—
1341C22⋊C4—2921no—
1342C22⋊C4—2921no—
1343C22⋊C4—2921no—
1344C22⋊C4—2921no—
1345C22⋊C4—2921no—
1346C22⋊C4—2921no—
1347C22⋊C4—2921no—
1348C22⋊C4—2921no—
1349C22⋊C4—2921no—
1350C22⋊C4—2921no—
1351C22⋊C4—2921no—
1352C22⋊C4—2921no—
1353C22⋊C4—2921no—
1354C22⋊C4—2921no—
1355C22⋊C4—2921no—
1356C22⋊C4—2921no—
1357C22⋊C4—2921no—
1358C22⋊C4—1462no—
1359C22⋊C4—1462no—
1360C22⋊C4—1462no—
1361C22⋊C4—1462no—
1362C22⋊C4—1462no—
1363C22⋊C4—1462no—
1364C22⋊C4—1462no—
1365C22⋊C4—1462no—
1366C42—2921no—
1367C42—2921no—
1368C42—2921no—
1369C42—2921no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—21no—
1376C23—21no—
1377C23—21no—
1378C23—21no—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—28no—
1387C23—44no—
1388C23—44no—
1389C23—44no—
1390C23—44no—
1391C23—44no—
1392C23—44no—
1393C23—2924no—
1394C23—2924no—
1395C23—5842no—
1396C23—5842no—
1397C23—5842no—
1398C23—5842no—
1399C23—732no—
1400C23—732no—
1401C23—1461no—
1402C23—1461no—
1403C23—1461no—
1404C23—1461no—
1405C23—1461no—
1406C23—1461no—
1407C23—1461no—
1408C23—1461no—
1409C23—1461no—
1410C23—1461no—
1411C23—1461no—
1412C23—1461no—
1413C23—1468no—
1414C23C2×Q8×D7312yes—
1415C23C2×Q8×D7312yes—
1416C23C2×Q8×D7312yes—
1417C23#1455663612yes—
1418C23#1455663712yes—
1419C23C24×D7311yescharacteristic
1420Q8—82no—
1421Q8—5842no—
1422Q8—5842no—
1423Q8—5842no—
1424D4—2924no—
1425D4—2924no—
1426D4—2924no—
1427D4—2924no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—82no—
1465C2×C4—82no—
1466C2×C4—2924no—
1467C2×C4—2924no—
1468C2×C4—2924no—
1469C2×C4—2924no—
1470C2×C4—2924no—
1471C2×C4—2924no—
1472C2×C4—5842no—
1473C2×C4—5842no—
1474C2×C4—5842no—
1475C2×C4—5842no—
1476C2×C4—732no—
1477C2×C4—732no—
1478C2×C4—732no—
1479C2×C4—732no—
1480C2×C4—1461no—
1481C2×C4—1461no—
1482C2×C4—1461no—
1483C2×C4—1461no—
1484C2×C4—1461no—
1485C2×C4—1461no—
1486C2×C4—1461no—
1487C2×C4—1461no—
1488C2×C4—1461no—
1489C2×C4—1461no—
1490C2×C4—1461no—
1491C2×C4—1461no—
1492C2×C4—1461no—
1493C2×C4—1461no—
1494C2×C4—1461no—
1495C2×C4—1461no—
1496C2×C4—1461no—
1497C2×C4—1461no—
1498C2×C4—1461no—
1499C2×C4—1461no—
1500C2×C4—1461no—
1501C2×C4—1461no—
1502C2×C4—1461no—
1503C2×C4—1461no—
1504C2×C4—1461no—
1505C2×C4—1461no—
1506C2×C4—1461no—
1507C2×C4—1461no—
1508C2×C4—1461no—
1509C2×C4—1461no—
1510C2×C4—1461no—
1511C2×C4—1461no—
1512C2×C4—1461no—
1513C2×C4—1461no—
1514C2×C4—1461no—
1515C2×C4—1461no—
1516C2×C4—1461no—
1517C2×C4—1461no—
1518C2×C4—1468no—
1519C22—22no—
1520C22—22no—
1521C22—22no—
1522C22—22no—
1523C22—22no—
1524C22—22no—
1525C22—22no—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—416no—
1532C22—41no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—2921no—
1541C22—2921no—
1542C22—2921no—
1543C22—2921no—
1544C22—2921no—
1545C22—2921no—
1546C22—2921no—
1547C22—2921no—
1548C22—5848no—
1549C22—1462no—
1550C22—1462no—
1551C22—1462no—
1552C22—1462no—
1553C22—1462no—
1554C22—1462no—
1555C22#1798921214yes—
1556C22C22×Q8×D7311yescharacteristic
1557C22H(5,𝔽2)×D7311yescharacteristic
1558C22H(5,𝔽2)×D7311yescharacteristic
1559C22C2×#1455663611yescharacteristic
1560C22C2×#1455663711yescharacteristic
1561C22#1798942211yescharacteristic
1562C22#1798942211yescharacteristic
1563C4—41no—
1564C4—41no—
1565C4—41no—
1566C4—41no—
1567C4—41no—
1568C4—41no—
1569C4—41no—
1570C4—41no—
1571C4—41no—
1572C4—41no—
1573C4—41no—
1574C4—41no—
1575C4—2921no—
1576C4—2921no—
1577C4—2921no—
1578C4—2921no—
1579C4—2921no—
1580C4—2921no—
1581C4—2921no—
1582C4—2921no—
1583C4—2921no—
1584C4—2921no—
1585C4—1462no—
1586C4—1462no—
1587C4—1462no—
1588C4—1462no—
1589C2—24no—
1590C2—42no—
1591C2—42no—
1592C2—2922no—
1593C2—2922no—
1594C2C2×#1798921211yescharacteristic
1595C2#2262373111yescharacteristic
1596C2#2262373111yescharacteristic
1597C2#2262408211yescharacteristic
1598C2#2262409911yescharacteristic
1599C2#2262423411yescharacteristic
1600C2#2262424211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2626C2
prime radicalC23×C22⋊D73C22
hypercenter#2626D73
hypocenterC73#36747
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2626

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22618216C2semidirect
2. #22618216C2semidirect
3. #22617872C2semidirect
4. #22617633C2semidirect
5. #22617626C2semidirect
6. #22617586C2semidirect
7. #22617584C2semidirect
8. #22617581C2semidirect
9. #22617572C2semidirect
10. #22617145C2semidirect
11. #22617138C2semidirect
12. #22616953C2semidirect
13. #22616945C2semidirect
14. #22616433C2semidirect
15. #22616432C2semidirect
16. #22616426C2semidirect
17. #22616420C2semidirect
18. #22616300C2semidirect
19. #22615736C2semidirect
20. #22613613C2semidirect
21. #22613611C2semidirect
22. #22613605C2semidirect
23. #22613603C2semidirect
24. #22613599C2semidirect
25. #22613596C2semidirect
26. #22613595C2semidirect
27. #22613594C2semidirect
31. C73×#2626C2semidirect
34. C2×#14556571C22semidirect
36. C2×#14556569C22semidirect
37. C2×#14556569C22semidirect
40. C2×#14556568C22semidirect
41. C2×#14556568C22semidirect
42. C2×#14556568C22semidirect
43. C2×#14556568C22semidirect
44. C2×#14556567C22semidirect
51. #17988528C22semidirect
52. #17988528C22semidirect
53. #17988527C22semidirect
54. #17988525C22semidirect
55. #17988524C22semidirect
56. #17988523C22semidirect
57. #17988523C22semidirect
58. #17988522C22semidirect
59. #17988522C22semidirect
60. #17988522C22semidirect
61. #17988521C22semidirect
62. #17988521C22semidirect
63. #17988520C22semidirect
64. #17988520C22semidirect
65. #17988518C22semidirect
66. #17988518C22semidirect
67. #17988517C22semidirect
68. #17988517C22semidirect
69. #17988511C22semidirect
70. #17988511C22semidirect
71. #17988510C22semidirect
72. #17988510C22semidirect
73. #17988510C22semidirect
74. #17988510C22semidirect
75. #17988509C22semidirect
76. #17988509C22semidirect
77. #17988509C22semidirect
78. #17988509C22semidirect
79. #17988509C22semidirect
80. #17988509C22semidirect
81. #17988508C22semidirect
82. #17988507C22semidirect
83. #17988507C22semidirect
84. #17988506C22semidirect
85. #17988500C22semidirect
86. #17988500C22semidirect
87. #17988500C22semidirect
88. #17988499C22semidirect
89. #17988499C22semidirect
90. #17988498C22semidirect
91. #17988494C22semidirect
92. #17988492C22semidirect
93. #17988491C22semidirect
94. #17988491C22semidirect
103. #17988486C22semidirect
104. #17988483C22semidirect
105. #17988482C22semidirect
106. #17988482C22semidirect
107. #17988473C22semidirect
108. #17988473C22semidirect
109. #17988472C22semidirect
110. #17988472C22semidirect
111. #17988469C22semidirect
112. #17988469C22semidirect
113. #17988468C22semidirect
114. #17988468C22semidirect
133. #17988462C22semidirect
134. #17988462C22semidirect
135. #17988462C22semidirect
136. #17988462C22semidirect
137. #17988461C22semidirect
138. #17988461C22semidirect
139. #17988461C22semidirect
140. #17988461C22semidirect
145. #17988459C22semidirect
146. #17988459C22semidirect
147. #17988459C22semidirect
148. #17988459C22semidirect
149. #17988458C22semidirect
150. #17988458C22semidirect
151. #17988458C22semidirect
152. #17988458C22semidirect
156. #17988446C22semidirect
157. #17988446C22semidirect
160. #17988445C22semidirect
161. #17988445C22semidirect
162. #17988445C22semidirect
163. #17988445C22semidirect
164. #17988444C22semidirect
165. #17988444C22semidirect
174. #399×C73C22semidirect
175. #399×C73C22semidirect
176. #396×C73C22semidirect
177. #396×C73C22semidirect
178. #396×C73C22semidirect
179. #396×C73C22semidirect
180. #393×C73C22semidirect
181. #393×C73C22semidirect
193. C22×C22⋊D73Q8semidirect
820. #2626D73semidirect
832. C73#36747semidirect
864. #399C2×D73semidirect
865. #399C2×D73semidirect
886. #396C2×D73semidirect
887. #396C2×D73semidirect
888. #396C2×D73semidirect
889. #396C2×D73semidirect
900. #393C2×D73semidirect
901. #393C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
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#226176332
#226176262
#226175862
#226175842
#226175812
#226175722
#226171452
#226171382
#226169532
#226169452
#226164332
#226164322
#226164262
#226164202
#226163002
#226157362
#226136132
#226136112
#226136052
#226136032
#226135992
#226135962
#226135952
#226135942
#226125122
#226125072
C2×#179884642
C73×#26262
#3674773