Finite Group Databasebeta

← #33300141

Subgroups — #33300141

Order 18688.

1994 conjugacy classes of subgroups.

The subgroup lattice has 1600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618259C211yesmaximal, characteristic, complemented
2#22618256C211yesmaximal, characteristic, complemented
3#22617781C211yesmaximal, characteristic, complemented
4#22617570C211yesmaximal, characteristic, complemented
5#22617566C211yesmaximal, characteristic, complemented
6#22617556C211yesmaximal, characteristic, complemented
7#22617448C211yesmaximal, characteristic, complemented
8#22617373C211yesmaximal, characteristic, complemented
9#22617214C211yesmaximal, characteristic, complemented
10#22617177C211yesmaximal, characteristic, complemented
11#22617168C211yesmaximal, characteristic, complemented
12#22617048C211yesmaximal, characteristic, complemented
13#22616978C211yesmaximal, characteristic, complemented
14#22616966C211yesmaximal, characteristic, complemented
15#22616561C211yesmaximal, characteristic, complemented
16#22616496C211yesmaximal, characteristic, complemented
17#22616483C211yesmaximal, characteristic, complemented
18#22616329C211yesmaximal, characteristic, complemented
19#22615859C211yesmaximal, characteristic, complemented
20#22614255C211yesmaximal, characteristic, complemented
21#22614189C211yesmaximal, characteristic, complemented
22#22613672C211yesmaximal, characteristic, complemented
23#22613596C211yesmaximal, characteristic, complemented
24#22613480C211yesmaximal, characteristic, complemented
25#22613325C211yesmaximal, characteristic, complemented
26#22613304C211yesmaximal, characteristic
27#22613257C211yesmaximal, characteristic, complemented
28#22612588C211yesmaximal, characteristic, complemented
29#22612505C211yesmaximal, characteristic, complemented
30C2×#17988479C211yesmaximal, characteristic, complemented
31C73×#2643C211yesmaximal, characteristic, complemented
32C22×D4×D73C2211yescharacteristic
33C2×#14556586C2211yescharacteristic, complemented
34C2×#14556575C2211yescharacteristic
35C2×#14556575C2211yescharacteristic, complemented
36C2×#14556573C2211yescharacteristic, complemented
37C2×#14556572C2211yescharacteristic
38C2×#14556570C2211yescharacteristic, complemented
39C2×#14556569C2211yescharacteristic, complemented
40C2×#14556565C2211yescharacteristic
41C2×#14556563C2211yescharacteristic
42C2×#14556561C2211yescharacteristic
43C2×#14556561C2211yescharacteristic
44C2×#14556551C2211yescharacteristic, complemented
45C22×C4⋊Dic73C2211yescharacteristic, complemented
46C22×#11924005C2211yescharacteristic
47C22×#11924005C2211yescharacteristic
48C22×#11924005C2211yescharacteristic
49C2×C22⋊C4×D73C2211yescharacteristic
50C22×C4×Dic73C2211yescharacteristic, complemented
51#17988529C2211yescharacteristic, complemented
52#17988529C2211yescharacteristic, complemented
53#17988528C2211yescharacteristic, complemented
54#17988527C2211yescharacteristic, complemented
55#17988527C2211yescharacteristic, complemented
56#17988526C2211yescharacteristic, complemented
57#17988523C2211yescharacteristic, complemented
58#17988522C2211yescharacteristic
59#17988521C2211yescharacteristic, complemented
60#17988519C2211yescharacteristic, complemented
61#17988515C2211yescharacteristic, complemented
62#17988514C2211yescharacteristic
63#17988514C2211yescharacteristic
64#17988514C2211yescharacteristic, complemented
65#17988514C2211yescharacteristic, complemented
66#17988514C2211yescharacteristic, complemented
67#17988514C2211yescharacteristic, complemented
68#17988514C2211yescharacteristic, complemented
69#17988511C2211yescharacteristic
70#17988509C2211yescharacteristic
71#17988509C2211yescharacteristic, complemented
72#17988509C2211yescharacteristic, complemented
73#17988505C2211yescharacteristic
74#17988505C2211yescharacteristic
75#17988505C2211yescharacteristic
76#17988505C2211yescharacteristic, complemented
77#17988505C2211yescharacteristic, complemented
78#17988504C2211yescharacteristic
79#17988504C2211yescharacteristic
80#17988504C2211yescharacteristic, complemented
81#17988503C2211yescharacteristic
82#17988503C2211yescharacteristic
83#17988503C2211yescharacteristic
84#17988503C2211yescharacteristic, complemented
85#17988500C2211yescharacteristic
86#17988500C2211yescharacteristic, complemented
87#17988500C2211yescharacteristic, complemented
88#17988499C2211yescharacteristic, complemented
89#17988497C2211yescharacteristic
90#17988496C2211yescharacteristic
91#17988491C2211yescharacteristic, complemented
92#17988488C2211yescharacteristic
93#17988488C2211yescharacteristic, complemented
94#17988487C2211yescharacteristic, complemented
95#17988487C2211yescharacteristic, complemented
96#17988486C2211yescharacteristic, complemented
97#17988484C2211yescharacteristic, complemented
98#17988484C2211yescharacteristic, complemented
99#17988480C2211yescharacteristic, complemented
100#17988480C2211yescharacteristic, complemented
101#17988480C2211yescharacteristic, complemented
102#17988480C2211yescharacteristic, complemented
103#17988479C2211yescharacteristic
104#17988479C2211yescharacteristic
105#17988479C2211yescharacteristic
106#17988479C2211yescharacteristic
107#17988479C2211yescharacteristic, complemented
108#17988479C2211yescharacteristic, complemented
109#17988479C2211yescharacteristic, complemented
110#17988479C2211yescharacteristic, complemented
111#17988479C2211yescharacteristic, complemented
112#17988479C2211yescharacteristic, complemented
113#17988477C2211yescharacteristic
114#17988477C2211yescharacteristic, complemented
115#17988477C2211yescharacteristic, complemented
116#17988477C2211yescharacteristic, complemented
117#17988476C2211yescharacteristic
118#17988476C2211yescharacteristic, complemented
119#17988476C2211yescharacteristic, complemented
120#17988476C2211yescharacteristic, complemented
121#17988476C2211yescharacteristic, complemented
122#17988476C2211yescharacteristic, complemented
123#17988475C2211yescharacteristic, complemented
124#17988474C2211yescharacteristic, complemented
125#17988474C2211yescharacteristic, complemented
126#17988473C2211yescharacteristic, complemented
127#17988473C2211yescharacteristic, complemented
128#17988473C2211yescharacteristic, complemented
129#17988470C2211yescharacteristic, complemented
130#17988470C2211yescharacteristic, complemented
131#17988467C2211yescharacteristic
132#17988466C2211yescharacteristic
133#17988466C2211yescharacteristic
134#17988466C2211yescharacteristic, complemented
135#17988466C2211yescharacteristic, complemented
136#17988465C2211yescharacteristic
137#17988465C2211yescharacteristic
138#17988465C2211yescharacteristic
139#17988465C2211yescharacteristic
140#17988465C2211yescharacteristic, complemented
141#17988465C2211yescharacteristic, complemented
142#17988465C2211yescharacteristic, complemented
143#17988465C2211yescharacteristic, complemented
144#17988464C2211yescharacteristic
145#17988464C2211yescharacteristic
146#17988463C2211yescharacteristic
147#17988463C2211yescharacteristic
148#17988461C2211yescharacteristic
149#17988461C2211yescharacteristic
150#17988461C2211yescharacteristic
151#17988461C2211yescharacteristic, complemented
152#17988461C2211yescharacteristic, complemented
153#17988459C2211yescharacteristic, complemented
154#17988458C2211yescharacteristic, complemented
155#17988451C2211yescharacteristic, complemented
156#17988449C2211yescharacteristic
157#17988449C2211yescharacteristic
158#17988448C2211yescharacteristic, complemented
159#17988446C2211yescharacteristic, complemented
160#17988445C2211yescharacteristic, complemented
161#17988444C2211yescharacteristic, complemented
162#17988444C2211yescharacteristic, complemented
163#17988444C2211yescharacteristic, complemented
164#17988442C2211yescharacteristic
165#17988442C2211yescharacteristic
166#17988442C2211yescharacteristic
167#17988442C2211yescharacteristic
168#17988442C2211yescharacteristic
169#17988442C2211yescharacteristic
170C22⋊C4×Dic73C2211yescharacteristic, complemented
171C2×#14556498C2211yescharacteristic, complemented
172#401×C73C2211yescharacteristic, complemented
173#400×C73C2211yescharacteristic, complemented
174#400×C73C2211yescharacteristic, complemented
175#400×C73C2211yescharacteristic, complemented
176#397×C73C2211yescharacteristic, complemented
177#397×C73C2211yescharacteristic, complemented
178#397×C73C2211yescharacteristic, complemented
179#396×C73C2211yescharacteristic, complemented
180#386×C73C2211yescharacteristic
181#386×C73C2211yescharacteristic
182#386×C73C2211yescharacteristic
183#385×C73C2211yescharacteristic, complemented
184#385×C73C2211yescharacteristic, complemented
185#385×C73C2211yescharacteristic, complemented
186C2×#95×C73C2211yescharacteristic, complemented
187C24×D73C2311yescharacteristic
188C24×D73C2311yescharacteristic
189C22×Dic146C2311yescharacteristic
190C22×D292C2311yescharacteristic
191C22×D292C2311yescharacteristic
192C22×D292C2311yescharacteristic
193C22×D292C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C22×C22⋊D73C2311yescharacteristic
197C22×C22⋊D73C2311yescharacteristic
198C2×D4×D73—24no—
199C2×D4×D73—42no—
200C2×D4×D73—42no—
201C23×Dic73C2311yescharacteristic
202C23×Dic73C2311yescharacteristic
203C23×Dic73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208#14556586—42no—
209#14556575—42no—
210#14556575—42no—
211#14556573—42no—
212#14556572—42no—
213#14556570—42no—
214#14556569—42no—
215#14556565—42no—
216#14556563—42no—
217#14556561—24no—
218#14556561—42no—
219#14556551—42no—
220C2×C4⋊Dic73—42no—
221C2×C4⋊Dic73C2311yescharacteristic
222C2×C4⋊Dic73C2311yescharacteristic
223C2×C4⋊Dic73C2311yescharacteristic
224C2×C4⋊Dic73C2311yescharacteristic
225C2×C4⋊Dic73C2311yescharacteristic
226C2×C4⋊Dic73C2311yescharacteristic
227C2×C4⋊Dic73C2311yescharacteristic
228C2×C4⋊Dic73C2311yescharacteristic
229C2×C4⋊Dic73C2311yescharacteristic
230C2×C4⋊Dic73C2311yescharacteristic
231C2×#11924007C2311yescharacteristic
232C2×#11924007C2311yescharacteristic
233C2×#11924007C2311yescharacteristic
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
239C2×#11924007C2311yescharacteristic
240C2×#11924007C2311yescharacteristic
241C2×C22⋊Dic73C2311yescharacteristic
242C2×C22⋊Dic73C2311yescharacteristic
243C2×C22⋊Dic73C2311yescharacteristic
244C2×C22⋊Dic73C2311yescharacteristic
245C2×C22⋊Dic73C2311yescharacteristic
246C2×C22⋊Dic73C2311yescharacteristic
247C2×C22⋊Dic73C2311yescharacteristic
248C2×#11924005—24no—
249C2×#11924005—42no—
250C2×#11924005—42no—
251C2×#11924005C2311yescharacteristic
252C2×#11924005C2311yescharacteristic
253C2×#11924005C2311yescharacteristic
254C2×#11924005C2311yescharacteristic
255C2×#11924005C2311yescharacteristic
256C2×#11924005C2311yescharacteristic
257C2×#11924005C2311yescharacteristic
258C2×#11924005C2311yescharacteristic
259C2×#11924005C2311yescharacteristic
260C2×#11924005C2311yescharacteristic
261C2×#11924005C2311yescharacteristic
262C2×#11924005C2311yescharacteristic
263C2×#11924005C2311yescharacteristic
264C2×#11924005C2311yescharacteristic
265C2×#11924005C2311yescharacteristic
266C2×#11924005C2311yescharacteristic
267C2×#11924005C2311yescharacteristic
268C2×#11924005C2311yescharacteristic
269C2×#11924005C2311yescharacteristic
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
290C2×#11924005C2311yescharacteristic
291C22⋊C4×D73—42no—
292C2×C4×Dic73—42no—
293C2×C4×Dic73C2311yescharacteristic
294C2×C4×Dic73C2311yescharacteristic
295C2×C4×Dic73C2311yescharacteristic
296C2×C4×Dic73C2311yescharacteristic
297C2×C4×Dic73C2311yescharacteristic
298C2×C4×Dic73C2311yescharacteristic
299C2×C4×Dic73C2311yescharacteristic
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
328C22×D4×C73C2311yescharacteristic
329C23×C4×C73C2311yescharacteristic
330C23×C4×C73C2311yescharacteristic
331C23×C4×C73C2311yescharacteristic
332C2×C4⋊C4×C73C2311yescharacteristic
333C2×C4⋊C4×C73C2311yescharacteristic
334C2×C4⋊C4×C73C2311yescharacteristic
335C2×C4⋊C4×C73C2311yescharacteristic
336C2×C4⋊C4×C73C2311yescharacteristic
337C2×C4⋊C4×C73C2311yescharacteristic
338C2×C22⋊C4×C73C2311yescharacteristic
339C2×C22⋊C4×C73C2311yescharacteristic
340C2×C22⋊C4×C73C2311yescharacteristic
341C2×C22⋊C4×C73C2311yescharacteristic
342C2×C22⋊C4×C73C2311yescharacteristic
343C2×C22⋊C4×C73C2311yescharacteristic
344C2×C22⋊C4×C73C2311yescharacteristic
345C2×C22⋊C4×C73C2311yescharacteristic
346C2×C22⋊C4×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×C73C2311yescharacteristic
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357#95×C73C2311yescharacteristic
358#95×C73C2311yescharacteristic
359#95×C73C2311yescharacteristic
360#95×C73C2311yescharacteristic
361#95×C73C2311yescharacteristic
362#95×C73C2311yescharacteristic
363C23×D73—22no—
364C23×D73—22no—
365C23×D73—22no—
366C23×D73—41no—
367C23×D73—41no—
368C23×D73—41no—
369C23×D73—41no—
370C23×D73—41no—
371C23×D73—41no—
372C23×D73—41no—
373C23×D73—41no—
374C23×D73—41no—
375C23×D73—41no—
376C23×D73#4114yes—
377C23×D73C2411yescharacteristic
378C23×D73C2411yescharacteristic
379C23×D73C2411yescharacteristic
380C23×D73C2411yescharacteristic
381C2×Dic146—41no—
382C2×Dic146—41no—
383C2×Dic146—41no—
384C2×D292—22no—
385C2×D292—22no—
386C2×D292—22no—
387C2×D292—41no—
388C2×D292—41no—
389C2×D292—41no—
390C2×D292—41no—
391C2×D292—41no—
392C2×D292—41no—
393C2×D292—41no—
394C2×D292—41no—
395C2×D292—41no—
396C2×C22⋊D73—22no—
397C2×C22⋊D73—22no—
398C2×C22⋊D73—22no—
399C2×C22⋊D73—22no—
400C2×C22⋊D73—22no—
401C2×C22⋊D73—22no—
402C2×C22⋊D73—22no—
403C2×C22⋊D73—22no—
404C2×C22⋊D73—41no—
405C2×C22⋊D73—41no—
406C2×C22⋊D73—41no—
407C2×C22⋊D73—41no—
408D4×D73—416no—
409C22×Dic73—22no—
410C22×Dic73—22no—
411C22×Dic73—22no—
412C22×Dic73—22no—
413C22×Dic73—22no—
414C22×Dic73—22no—
415C22×Dic73—41no—
416C22×Dic73—41no—
417C22×Dic73—41no—
418C22×Dic73C2411yescharacteristic
419C22×Dic73C2411yescharacteristic
420C22×Dic73C2411yescharacteristic
421C22×Dic73C2411yescharacteristic
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2411yescharacteristic
424C22×Dic73C2411yescharacteristic
425C22×Dic73C2411yescharacteristic
426C22×Dic73C2411yescharacteristic
427C22×Dic73C2411yescharacteristic
428C22×Dic73C2411yescharacteristic
429C22×Dic73C2411yescharacteristic
430C2×C4×D73—22no—
431C2×C4×D73—41no—
432C2×C4×D73—41no—
433C2×C4×D73—41no—
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—
442C4⋊Dic73—22no—
443C4⋊Dic73—22no—
444C4⋊Dic73—41no—
445C4⋊Dic73—41no—
446C4⋊Dic73—41no—
447C4⋊Dic73—41no—
448C4⋊Dic73—41no—
449C4⋊Dic73—41no—
450C4⋊Dic73—41no—
451C4⋊Dic73—41no—
452#11924007—22no—
453#11924007—22no—
454#11924007—41no—
455#11924007—41no—
456#11924007—41no—
457#11924007—41no—
458#11924007—41no—
459#11924007—41no—
460#11924007—41no—
461#11924007—41no—
462C22⋊Dic73—22no—
463C22⋊Dic73—22no—
464C22⋊Dic73—41no—
465C22⋊Dic73—41no—
466C22⋊Dic73—41no—
467C22⋊Dic73—41no—
468C22⋊Dic73—41no—
469#11924005—22no—
470#11924005—22no—
471#11924005—22no—
472#11924005—22no—
473#11924005—22no—
474#11924005—22no—
475#11924005—22no—
476#11924005—22no—
477#11924005—22no—
478#11924005—41no—
479#11924005—41no—
480#11924005—41no—
481#11924005—41no—
482#11924005—41no—
483#11924005—41no—
484#11924005—41no—
485#11924005—41no—
486#11924005—41no—
487#11924005—41no—
488#11924005—41no—
489#11924005—41no—
490#11924005—41no—
491#11924005—41no—
492#11924005—41no—
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—
513C4×Dic73—41no—
514C4×Dic73—41no—
515C4×Dic73—41no—
516C24×C73C2411yescharacteristic
517C24×C73C2411yescharacteristic
518C2×D4×C73—22no—
519C2×D4×C73—22no—
520C2×D4×C73—22no—
521C22×C4×C73—22no—
522C22×C4×C73—22no—
523C22×C4×C73—22no—
524C22×C4×C73—41no—
525C22×C4×C73—41no—
526C22×C4×C73—41no—
527C22×C4×C73—41no—
528C22×C4×C73—41no—
529C22×C4×C73—41no—
530C22×C4×C73C2411yescharacteristic
531C22×C4×C73C2411yescharacteristic
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
543C4⋊C4×C73—41no—
544C4⋊C4×C73—41no—
545C4⋊C4×C73—41no—
546C4⋊C4×C73—41no—
547C4⋊C4×C73—41no—
548C4⋊C4×C73—41no—
549C22⋊C4×C73—22no—
550C22⋊C4×C73—22no—
551C22⋊C4×C73—22no—
552C22⋊C4×C73—41no—
553C22⋊C4×C73—41no—
554C22⋊C4×C73—41no—
555C22⋊C4×C73—41no—
556C22⋊C4×C73—41no—
557C22⋊C4×C73—41no—
558C23×C73—21no—
559C23×C73—21no—
560C23×C73—21no—
561C23×C73—21no—
562C23×C73—21no—
563C23×C73—21no—
564C23×C73—21no—
565C23×C73—21no—
566C23×C73—21no—
567C23×C73—21no—
568C23×C73—21no—
569C23×C73C2×#4112yes—
570C23×C73H(5,𝔽2)12yes—
571C23×C73H(5,𝔽2)12yes—
572C23×C73C2511yescharacteristic
573C22×D73—21no—
574C22×D73—21no—
575C22×D73—21no—
576C22×D73—21no—
577C22×D73—21no—
578C22×D73—21no—
579C22×D73—21no—
580C22×D73—21no—
581C22×D73—21no—
582C22×D73—21no—
583C22×D73—21no—
584C22×D73—21no—
585C22×D73—28no—
586C22×D73—21no—
587C22×D73—21no—
588C22×D73—21no—
589C22×D73—21no—
590C22×D73—21no—
591C22×D73—21no—
592C22×D73—21no—
593C22×D73—21no—
594C22×D73—21no—
595C22×D73—21no—
596C22×D73—21no—
597C22×D73—21no—
598C22×D73—21no—
599C22×D73—21no—
600C22×D73—44no—
601C22×D73—44no—
602C22×D73—44no—
603C22×D73—82no—
604C22×D73—82no—
605C22×D73—82no—
606C22×D73—82no—
607C22×D73—82no—
608C22×D73—82no—
609C22×D73—82no—
610C22×D73—82no—
611C22×D73—82no—
612C22×D73—82no—
613C22×D73C2×#4112yes—
614C22×D73C2×#4112yes—
615D4×C73—44no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
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—44no—
656C2×C4×C73—44no—
657C2×C4×C73—82no—
658C22⋊D73—44no—
659C22⋊D73—44no—
660C22⋊D73—44no—
661C22⋊D73—82no—
662C2×Dic73—21no—
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—44no—
698C2×Dic73—44no—
699C2×Dic73—82no—
700C2×Dic73H(5,𝔽2)12yes—
701D292—44no—
702D292—82no—
703D292—82no—
704D292—82no—
705C4×D73—44no—
706C4×D73—82no—
707C4×D73—82no—
708C4×D73—82no—
709Dic146—82no—
710C22×C73—22no—
711C22×C73—22no—
712C22×C73—22no—
713C22×C73—22no—
714C22×C73—22no—
715C22×C73—22no—
716C22×C73—41no—
717C22×C73—41no—
718C22×C73—41no—
719C22×C73—41no—
720C22×C73—41no—
721C22×C73—41no—
722C22×C73—41no—
723C22×C73#53814yes—
724C22×C73C22×#4111yescharacteristic
725C22×C73C2×H(5,𝔽2)11yescharacteristic
726C22×C73C2×H(5,𝔽2)11yescharacteristic
727C22×C73C2×H(5,𝔽2)11yescharacteristic
728C22×C73#58511yescharacteristic
729C22×C73#58511yescharacteristic
730C22×C73#58511yescharacteristic
731C2×D73—22no—
732C2×D73—22no—
733C2×D73—22no—
734C2×D73—22no—
735C2×D73—22no—
736C2×D73—22no—
737C2×D73—41no—
738C2×D73—41no—
739C2×D73—41no—
740C2×D73—41no—
741C2×D73—41no—
742C2×D73—41no—
743C2×D73—41no—
744C2×D73—41no—
745C2×D73—41no—
746C2×D73—41no—
747C2×D73—41no—
748C2×D73—41no—
749C2×D73—41no—
750C2×D73—41no—
751C2×D73—41no—
752C2×D73—41no—
753C2×D73—41no—
754C2×D73—41no—
755C2×D73—41no—
756C2×D73—41no—
757C2×D73—41no—
758C2×D73—41no—
759C2×D73—88no—
760C2×D73—88no—
761C4×C73—41no—
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—41no—
776Dic73—41no—
777Dic73—41no—
778Dic73—41no—
779Dic73—41no—
780Dic73—41no—
781Dic73—41no—
782Dic73—41no—
783Dic73—41no—
784Dic73—41no—
785Dic73—41no—
786#36986—731nomaximal, Sylow
787C2×C73—24no—
788C2×C73—81no—
789C2×C73C2×#53811yescharacteristic
790C2×C73#349111yescharacteristic
791C2×C73#350511yescharacteristic
792C2×C73#353311yescharacteristic
793C2×C73#353411yescharacteristic
794C2×C73#355811yescharacteristic
795C2×C73#356011yescharacteristic
796D73—42no—
797D73—42no—
798D73—81no—
799D73—81no—
800#2854—731no—
801#2853—731no—
802#2797—731no—
803#2779—731no—
804#2779—731no—
805#2778—731no—
806#2771—731no—
807#2765—731no—
808#2753—731no—
809#2751—731no—
810#2750—731no—
811#2741—731no—
812#2736—731no—
813#2735—731no—
814#2702—731no—
815#2697—731no—
816#2696—731no—
817#2685—731no—
818#2643D7311yescharacteristic, complemented
819#2639—731no—
820#2488—731no—
821#2481—731no—
822#2443—731no—
823#2437—731no—
824#2425—731no—
825#2412—731no—
826#2410—731no—
827#2405—731no—
828#2321—731no—
829#2308—731no—
830C2×#388—731no—
831C73#3698611yescharacteristic, complemented, Sylow
832C23×D4—731no—
833C2×#126—731no—
834C2×#123—731no—
835C2×#123—731no—
836C2×#123—731no—
837C2×#123—731no—
838C2×C22⋊Q8—731no—
839C2×C22⋊Q8—731no—
840C2×#121—731no—
841C2×#121—731no—
842C2×#120—731no—
843C2×#120—731no—
844C2×C4×D4—731no—
845C22×C4⋊C4—731no—
846C22×C22⋊C4—731no—
847C22×C22⋊C4—731no—
848C22×C22⋊C4—731no—
849C22×C22⋊C4—731no—
850C22×C42—731no—
851#401C2×D7311yescharacteristic, complemented
852#400—731no—
853#400—731no—
854#400—731no—
855#400—731no—
856#400—731no—
857#400—731no—
858#400C2×D7311yescharacteristic, complemented
859#400C2×D7311yescharacteristic, complemented
860#400C2×D7311yescharacteristic, complemented
861#399—731no—
862#399—731no—
863#398—731no—
864#398—731no—
865#397—731no—
866#397—731no—
867#397—731no—
868#397—731no—
869#397—731no—
870#397—731no—
871#397—731no—
872#397—731no—
873#397C2×D7311yescharacteristic, complemented
874#397C2×D7311yescharacteristic, complemented
875#397C2×D7311yescharacteristic, complemented
876#396—731no—
877#396—731no—
878#396—731no—
879#396—731no—
880#396C2×D7311yescharacteristic, complemented
881#394—731no—
882#394—731no—
883#394—731no—
884#394—731no—
885#394—731no—
886#394—731no—
887#394—731no—
888#394—731no—
889#394—731no—
890#394—731no—
891#394—731no—
892#394—731no—
893#393—731no—
894#393—731no—
895#393—731no—
896#393—731no—
897#392—731no—
898#392—731no—
899#391—731no—
900#390—731no—
901#390—731no—
902#390—731no—
903#390—731no—
904#389—731no—
905#389—731no—
906#389—731no—
907#388—731no—
908#388—731no—
909#388—731no—
910#388—731no—
911#388—731no—
912#388—731no—
913#388—731no—
914#388—731no—
915#388—731no—
916#388—731no—
917#388—731no—
918#388—731no—
919#388—731no—
920#388—731no—
921#388—731no—
922#388—731no—
923#388—731no—
924#388—731no—
925#388—731no—
926#388—731no—
927#388—731no—
928#388—731no—
929#388—731no—
930#388—731no—
931#388—731no—
932#387—731no—
933#387—731no—
934#387—731no—
935#387—731no—
936#387—731no—
937#387—731no—
938#387—731no—
939#386—731no—
940#386—731no—
941#386—731no—
942#386—731no—
943#386—731no—
944#386—731no—
945#386—731no—
946#386—731no—
947#386—731no—
948#386—731no—
949#386—731no—
950#386—731no—
951#386—731no—
952#386—731no—
953#386—731no—
954#386—731no—
955#386—731no—
956#386C2×D7311yescharacteristic
957#386C2×D7311yescharacteristic
958#386C2×D7311yescharacteristic
959#385—731no—
960#385—731no—
961#385—731no—
962#385—731no—
963#385—731no—
964#385—731no—
965#385—731no—
966#385C2×D7311yescharacteristic, complemented
967#385C2×D7311yescharacteristic, complemented
968#385C2×D7311yescharacteristic, complemented
969#382—731no—
970#381—731no—
971#381—731no—
972#381—731no—
973#380—731no—
974#380—731no—
975#380—731no—
976#380—731no—
977#380—731no—
978#379—731no—
979#379—731no—
980#379—731no—
981#379—731no—
982#379—731no—
983#379—731no—
984C4×C22⋊C4—731no—
985C2×#95—731no—
986C2×#95C2×D7311yescharacteristic, complemented
987C25—731no—
988C25—731no—
989C22×Q8—731no—
990C22×D4—2922no—
991C22×D4—2922no—
992C22×D4—731no—
993C22×D4—731no—
994C22×D4—731no—
995C22×D4—731no—
996C22×D4—731no—
997C22×D4—731no—
998C22×D4—731no—
999C22×D4—731no—
1000C22×D4—1464no—
1001C22×D4C22×D7311yescharacteristic
1002C23×C4—731no—
1003C23×C4—731no—
1004C23×C4—731no—
1005C23×C4—731no—
1006C23×C4—731no—
1007C23×C4—731no—
1008C23×C4—731no—
1009C23×C4C22×D7311yescharacteristic
1010C23×C4C22×D7311yescharacteristic
1011C23×C4C22×D7311yescharacteristic
1012#126—2922no—
1013#123—2922no—
1014#123—2922no—
1015#123—2922no—
1016#123—2922no—
1017C22⋊Q8—2922no—
1018C22⋊Q8—2922no—
1019#121—2922no—
1020#121—2922no—
1021#120—2922no—
1022#120—1464no—
1023C4×D4—2922no—
1024C2×C4⋊C4—2922no—
1025C2×C4⋊C4—731no—
1026C2×C4⋊C4—731no—
1027C2×C4⋊C4—731no—
1028C2×C4⋊C4—731no—
1029C2×C4⋊C4—731no—
1030C2×C4⋊C4—731no—
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⋊C4C22×D7311yescharacteristic
1046C2×C4⋊C4C22×D7311yescharacteristic
1047C2×C4⋊C4C22×D7311yescharacteristic
1048C2×C4⋊C4C22×D7311yescharacteristic
1049C2×C4⋊C4C22×D7311yescharacteristic
1050C2×C4⋊C4C22×D7311yescharacteristic
1051C2×C22⋊C4—2922no—
1052C2×C22⋊C4—2922no—
1053C2×C22⋊C4—2922no—
1054C2×C22⋊C4—731no—
1055C2×C22⋊C4—731no—
1056C2×C22⋊C4—731no—
1057C2×C22⋊C4—731no—
1058C2×C22⋊C4—731no—
1059C2×C22⋊C4—731no—
1060C2×C22⋊C4—731no—
1061C2×C22⋊C4—731no—
1062C2×C22⋊C4—731no—
1063C2×C22⋊C4—731no—
1064C2×C22⋊C4—731no—
1065C2×C22⋊C4—731no—
1066C2×C22⋊C4—731no—
1067C2×C22⋊C4—731no—
1068C2×C22⋊C4—731no—
1069C2×C22⋊C4—731no—
1070C2×C22⋊C4—731no—
1071C2×C22⋊C4—731no—
1072C2×C22⋊C4—731no—
1073C2×C22⋊C4—731no—
1074C2×C22⋊C4—731no—
1075C2×C22⋊C4—731no—
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—1464no—
1102C2×C22⋊C4C22×D7311yescharacteristic
1103C2×C22⋊C4C22×D7311yescharacteristic
1104C2×C22⋊C4C22×D7311yescharacteristic
1105C2×C22⋊C4C22×D7311yescharacteristic
1106C2×C22⋊C4C22×D7311yescharacteristic
1107C2×C22⋊C4C22×D7311yescharacteristic
1108C2×C22⋊C4C22×D7311yescharacteristic
1109C2×C22⋊C4C22×D7311yescharacteristic
1110C2×C22⋊C4C22×D7311yescharacteristic
1111C2×C42—2922no—
1112C2×C42—731no—
1113C2×C42—731no—
1114C2×C42—731no—
1115C2×C42—731no—
1116C2×C42—731no—
1117C2×C42—731no—
1118C2×C42—731no—
1119#95—731no—
1120#95—731no—
1121#95—731no—
1122#95—731no—
1123#95—731no—
1124#95—731no—
1125#95—731no—
1126#95—731no—
1127#95—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#95C22×D7311yescharacteristic
1148#95C22×D7311yescharacteristic
1149#95C22×D7311yescharacteristic
1150#95C22×D7311yescharacteristic
1151#95C22×D7311yescharacteristic
1152#95C22×D7311yescharacteristic
1153#95C22×D7311yescharacteristic
1154#95C22×D7311yescharacteristic
1155#95C22×D7311yescharacteristic
1156#95C22×D7311yescharacteristic
1157#95C22×D7311yescharacteristic
1158#95C22×D7311yescharacteristic
1159#95C22×D7311yescharacteristic
1160#95C22×D7311yescharacteristic
1161#95C22×D7311yescharacteristic
1162#95C22×D7311yescharacteristic
1163C24—2921no—
1164C24—2921no—
1165C24—2921no—
1166C24—2921no—
1167C24—2921no—
1168C24—2921no—
1169C24—2921no—
1170C24—2921no—
1171C24—2921no—
1172C24—2921no—
1173C24—734no—
1174C24—731no—
1175C24—731no—
1176C24—731no—
1177C24—731no—
1178C24—1462no—
1179C24—1462no—
1180C24—1462no—
1181C24C23×D7311yescharacteristic
1182C24C23×D7311yescharacteristic
1183C2×Q8—2921no—
1184C2×Q8—2921no—
1185C2×Q8—2921no—
1186C2×D4—22no—
1187C2×D4—22no—
1188C2×D4—22no—
1189C2×D4—2921no—
1190C2×D4—2921no—
1191C2×D4—2921no—
1192C2×D4—2921no—
1193C2×D4—2921no—
1194C2×D4—2921no—
1195C2×D4—2921no—
1196C2×D4—2921no—
1197C2×D4—2921no—
1198C2×D4—29216no—
1199C2×D4—2921no—
1200C2×D4—2921no—
1201C2×D4—2921no—
1202C2×D4—2921no—
1203C2×D4—1462no—
1204C2×D4—1462no—
1205C2×D4—1462no—
1206C2×D4—1462no—
1207C2×D4—1462no—
1208C2×D4—1462no—
1209C2×D4—1462no—
1210C2×D4—1462no—
1211C2×D4—1462no—
1212C2×D4—1462no—
1213C2×D4—1462no—
1214C22×C4—22no—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—2921no—
1224C22×C4—2921no—
1225C22×C4—2921no—
1226C22×C4—2921no—
1227C22×C4—2921no—
1228C22×C4—2921no—
1229C22×C4—2921no—
1230C22×C4—2921no—
1231C22×C4—2921no—
1232C22×C4—2921no—
1233C22×C4—2921no—
1234C22×C4—2921no—
1235C22×C4—2921no—
1236C22×C4—2921no—
1237C22×C4—731no—
1238C22×C4—731no—
1239C22×C4—731no—
1240C22×C4—731no—
1241C22×C4—731no—
1242C22×C4—731no—
1243C22×C4—731no—
1244C22×C4—731no—
1245C22×C4—731no—
1246C22×C4—731no—
1247C22×C4—731no—
1248C22×C4—731no—
1249C22×C4—1462no—
1250C22×C4—1462no—
1251C22×C4—1462no—
1252C22×C4—1462no—
1253C22×C4—1462no—
1254C22×C4—1462no—
1255C22×C4—1462no—
1256C22×C4C23×D7311yescharacteristic
1257C22×C4C23×D7311yescharacteristic
1258C22×C4C23×D7311yescharacteristic
1259C22×C4C23×D7311yescharacteristic
1260C22×C4C23×D7311yescharacteristic
1261C22×C4C23×D7311yescharacteristic
1262C22×C4C23×D7311yescharacteristic
1263C22×C4C23×D7311yescharacteristic
1264C22×C4C23×D7311yescharacteristic
1265C22×C4C23×D7311yescharacteristic
1266C22×C4C23×D7311yescharacteristic
1267C22×C4C23×D7311yescharacteristic
1268C22×C4C23×D7311yescharacteristic
1269C4⋊C4—41no—
1270C4⋊C4—41no—
1271C4⋊C4—41no—
1272C4⋊C4—41no—
1273C4⋊C4—41no—
1274C4⋊C4—41no—
1275C4⋊C4—2921no—
1276C4⋊C4—2921no—
1277C4⋊C4—2921no—
1278C4⋊C4—2921no—
1279C4⋊C4—2921no—
1280C4⋊C4—2921no—
1281C4⋊C4—2921no—
1282C4⋊C4—2921no—
1283C4⋊C4—2921no—
1284C4⋊C4—2921no—
1285C4⋊C4—2921no—
1286C4⋊C4—2921no—
1287C4⋊C4—2921no—
1288C4⋊C4—2921no—
1289C4⋊C4—2921no—
1290C4⋊C4—2921no—
1291C4⋊C4—1462no—
1292C4⋊C4—1462no—
1293C4⋊C4—1462no—
1294C4⋊C4—1462no—
1295C22⋊C4—22no—
1296C22⋊C4—22no—
1297C22⋊C4—22no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—2921no—
1305C22⋊C4—2921no—
1306C22⋊C4—2921no—
1307C22⋊C4—2921no—
1308C22⋊C4—2921no—
1309C22⋊C4—2921no—
1310C22⋊C4—2921no—
1311C22⋊C4—2921no—
1312C22⋊C4—2921no—
1313C22⋊C4—2921no—
1314C22⋊C4—2921no—
1315C22⋊C4—2921no—
1316C22⋊C4—2921no—
1317C22⋊C4—2921no—
1318C22⋊C4—2921no—
1319C22⋊C4—2921no—
1320C22⋊C4—2921no—
1321C22⋊C4—2921no—
1322C22⋊C4—2921no—
1323C22⋊C4—2921no—
1324C22⋊C4—2921no—
1325C22⋊C4—2921no—
1326C22⋊C4—2921no—
1327C22⋊C4—2921no—
1328C22⋊C4—2921no—
1329C22⋊C4—2921no—
1330C22⋊C4—2921no—
1331C22⋊C4—2921no—
1332C22⋊C4—2921no—
1333C22⋊C4—2921no—
1334C22⋊C4—2921no—
1335C22⋊C4—2921no—
1336C22⋊C4—2921no—
1337C22⋊C4—2921no—
1338C22⋊C4—2921no—
1339C22⋊C4—2921no—
1340C22⋊C4—1462no—
1341C22⋊C4—1462no—
1342C22⋊C4—1462no—
1343C22⋊C4—1462no—
1344C22⋊C4—1462no—
1345C22⋊C4—1462no—
1346C22⋊C4—1462no—
1347C22⋊C4—1462no—
1348C22⋊C4—1462no—
1349C22⋊C4—1462no—
1350C22⋊C4—1462no—
1351C42—2921no—
1352C42—2921no—
1353C42—2921no—
1354C42—2921no—
1355C42—2921no—
1356C42—2921no—
1357C42—2921no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—2924no—
1370C23—2924no—
1371C23—2924no—
1372C23—5842no—
1373C23—5842no—
1374C23—5842no—
1375C23—5842no—
1376C23—5842no—
1377C23—5842no—
1378C23—5842no—
1379C23—5842no—
1380C23—5842no—
1381C23—5842no—
1382C23—732no—
1383C23—732no—
1384C23—1461no—
1385C23—1461no—
1386C23—1461no—
1387C23—1461no—
1388C23—1461no—
1389C23—1461no—
1390C23—1461no—
1391C23—1461no—
1392C23—1461no—
1393C23—1461no—
1394C23—1461no—
1395C23—1461no—
1396C23—1461no—
1397C23—1461no—
1398C23—1461no—
1399C23—1461no—
1400C23—1461no—
1401C23—1461no—
1402C23—1461no—
1403C23—1461no—
1404C23—1461no—
1405C23—1461no—
1406C23—1461no—
1407C23—1461no—
1408C23—1461no—
1409C23—1461no—
1410C23—1468no—
1411C23#41×D7312yes—
1412C23#1455663712yes—
1413C23#1455663712yes—
1414C23C24×D7311yescharacteristic
1415Q8—5842no—
1416D4—44no—
1417D4—2924no—
1418D4—2924no—
1419D4—2924no—
1420D4—2924no—
1421D4—5842no—
1422D4—5842no—
1423D4—5842no—
1424D4—5842no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
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—44no—
1465C2×C4—44no—
1466C2×C4—82no—
1467C2×C4—2924no—
1468C2×C4—2924no—
1469C2×C4—2924no—
1470C2×C4—5842no—
1471C2×C4—5842no—
1472C2×C4—5842no—
1473C2×C4—5842no—
1474C2×C4—732no—
1475C2×C4—1461no—
1476C2×C4—1461no—
1477C2×C4—1461no—
1478C2×C4—1461no—
1479C2×C4—1461no—
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—
1510C22—22no—
1511C22—22no—
1512C22—22no—
1513C22—22no—
1514C22—22no—
1515C22—22no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—41no—
1522C22—41no—
1523C22—2921no—
1524C22—2921no—
1525C22—2921no—
1526C22—2921no—
1527C22—2921no—
1528C22—2921no—
1529C22—2921no—
1530C22—2921no—
1531C22—2921no—
1532C22—2921no—
1533C22—2921no—
1534C22—2921no—
1535C22—2921no—
1536C22—2921no—
1537C22—2921no—
1538C22—2921no—
1539C22—2921no—
1540C22—2921no—
1541C22—2921no—
1542C22—2921no—
1543C22—2921no—
1544C22—2921no—
1545C22—5848no—
1546C22—5848no—
1547C22—1462no—
1548C22—1462no—
1549C22—1462no—
1550C22—1462no—
1551C22—1462no—
1552C22—1462no—
1553C22#1798917614yes—
1554C22C2×#41×D7311yescharacteristic
1555C22H(5,𝔽2)×D7311yescharacteristic
1556C22C2×#1455663711yescharacteristic
1557C22C2×#1455663711yescharacteristic
1558C22#1798942211yescharacteristic
1559C22#1798942211yescharacteristic
1560C22#1798942411yescharacteristic
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—41no—
1565C4—41no—
1566C4—41no—
1567C4—41no—
1568C4—41no—
1569C4—41no—
1570C4—41no—
1571C4—41no—
1572C4—41no—
1573C4—41no—
1574C4—2921no—
1575C4—2921no—
1576C4—2921no—
1577C4—2921no—
1578C4—2921no—
1579C4—2921no—
1580C4—2921no—
1581C4—2921no—
1582C4—2921no—
1583C4—2921no—
1584C4—2921no—
1585C4—1462no—
1586C2—24no—
1587C2—81no—
1588C2—2922no—
1589C2—2922no—
1590C2—5841no—
1591C2—5841no—
1592C2C2×#1798917611yescharacteristic
1593C2#2262362511yescharacteristic
1594C2#2262376911yescharacteristic
1595C2#2262409911yescharacteristic
1596C2#2262411911yescharacteristic
1597C2#2262445211yescharacteristic
1598C2#2262448811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2643C2
prime radical#22613304C2
hypercenter#2643D73
hypocenterC73#36986
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2643

Complements

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

NH ≅ G/Ntype
1. #22618259C2semidirect
2. #22618256C2semidirect
3. #22617781C2semidirect
4. #22617570C2semidirect
5. #22617566C2semidirect
6. #22617556C2semidirect
7. #22617448C2semidirect
8. #22617373C2semidirect
9. #22617214C2semidirect
10. #22617177C2semidirect
11. #22617168C2semidirect
12. #22617048C2semidirect
13. #22616978C2semidirect
14. #22616966C2semidirect
15. #22616561C2semidirect
16. #22616496C2semidirect
17. #22616483C2semidirect
18. #22616329C2semidirect
19. #22615859C2semidirect
20. #22614255C2semidirect
21. #22614189C2semidirect
22. #22613672C2semidirect
23. #22613596C2semidirect
24. #22613480C2semidirect
25. #22613325C2semidirect
27. #22613257C2semidirect
28. #22612588C2semidirect
29. #22612505C2semidirect
30. C2×#17988479C2semidirect
31. C73×#2643C2semidirect
33. C2×#14556586C22semidirect
35. C2×#14556575C22semidirect
36. C2×#14556573C22semidirect
38. C2×#14556570C22semidirect
39. C2×#14556569C22semidirect
44. C2×#14556551C22semidirect
45. C22×C4⋊Dic73C22semidirect
50. C22×C4×Dic73C22semidirect
51. #17988529C22semidirect
52. #17988529C22semidirect
53. #17988528C22semidirect
54. #17988527C22semidirect
55. #17988527C22semidirect
56. #17988526C22semidirect
57. #17988523C22semidirect
59. #17988521C22semidirect
60. #17988519C22semidirect
61. #17988515C22semidirect
64. #17988514C22semidirect
65. #17988514C22semidirect
66. #17988514C22semidirect
67. #17988514C22semidirect
68. #17988514C22semidirect
71. #17988509C22semidirect
72. #17988509C22semidirect
76. #17988505C22semidirect
77. #17988505C22semidirect
80. #17988504C22semidirect
84. #17988503C22semidirect
86. #17988500C22semidirect
87. #17988500C22semidirect
88. #17988499C22semidirect
91. #17988491C22semidirect
93. #17988488C22semidirect
94. #17988487C22semidirect
95. #17988487C22semidirect
96. #17988486C22semidirect
97. #17988484C22semidirect
98. #17988484C22semidirect
99. #17988480C22semidirect
100. #17988480C22semidirect
101. #17988480C22semidirect
102. #17988480C22semidirect
107. #17988479C22semidirect
108. #17988479C22semidirect
109. #17988479C22semidirect
110. #17988479C22semidirect
111. #17988479C22semidirect
112. #17988479C22semidirect
114. #17988477C22semidirect
115. #17988477C22semidirect
116. #17988477C22semidirect
118. #17988476C22semidirect
119. #17988476C22semidirect
120. #17988476C22semidirect
121. #17988476C22semidirect
122. #17988476C22semidirect
123. #17988475C22semidirect
124. #17988474C22semidirect
125. #17988474C22semidirect
126. #17988473C22semidirect
127. #17988473C22semidirect
128. #17988473C22semidirect
129. #17988470C22semidirect
130. #17988470C22semidirect
134. #17988466C22semidirect
135. #17988466C22semidirect
140. #17988465C22semidirect
141. #17988465C22semidirect
142. #17988465C22semidirect
143. #17988465C22semidirect
151. #17988461C22semidirect
152. #17988461C22semidirect
153. #17988459C22semidirect
154. #17988458C22semidirect
155. #17988451C22semidirect
158. #17988448C22semidirect
159. #17988446C22semidirect
160. #17988445C22semidirect
161. #17988444C22semidirect
162. #17988444C22semidirect
163. #17988444C22semidirect
170. C22⋊C4×Dic73C22semidirect
171. C2×#14556498C22semidirect
172. #401×C73C22semidirect
173. #400×C73C22semidirect
174. #400×C73C22semidirect
175. #400×C73C22semidirect
176. #397×C73C22semidirect
177. #397×C73C22semidirect
178. #397×C73C22semidirect
179. #396×C73C22semidirect
183. #385×C73C22semidirect
184. #385×C73C22semidirect
185. #385×C73C22semidirect
186. C2×#95×C73C22semidirect
818. #2643D73semidirect
831. C73#36986semidirect
851. #401C2×D73semidirect
858. #400C2×D73semidirect
859. #400C2×D73semidirect
860. #400C2×D73semidirect
873. #397C2×D73semidirect
874. #397C2×D73semidirect
875. #397C2×D73semidirect
880. #396C2×D73semidirect
966. #385C2×D73semidirect
967. #385C2×D73semidirect
968. #385C2×D73semidirect
986. C2×#95C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226182592
#226182562
#226177812
#226175702
#226175662
#226175562
#226174482
#226173732
#226172142
#226171772
#226171682
#226170482
#226169782
#226169662
#226165612
#226164962
#226164832
#226163292
#226158592
#226142552
#226141892
#226136722
#226135962
#226134802
#226133252
#226133042
#226132572
#226125882
#226125052
C2×#179884792
C73×#26432
#3698673