Finite Group Databasebeta

← #33300157

Subgroups — #33300157

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#22618252C211yesmaximal, characteristic, complemented
3#22617787C211yesmaximal, characteristic, complemented
4#22617571C211yesmaximal, characteristic, complemented
5#22617563C211yesmaximal, characteristic, complemented
6#22617551C211yesmaximal, characteristic, complemented
7#22617443C211yesmaximal, characteristic, complemented
8#22617371C211yesmaximal, characteristic, complemented
9#22617213C211yesmaximal, characteristic, complemented
10#22617183C211yesmaximal, characteristic, complemented
11#22617162C211yesmaximal, characteristic, complemented
12#22617053C211yesmaximal, characteristic, complemented
13#22616975C211yesmaximal, characteristic, complemented
14#22616971C211yesmaximal, characteristic, complemented
15#22616566C211yesmaximal, characteristic, complemented
16#22616497C211yesmaximal, characteristic, complemented
17#22616488C211yesmaximal, characteristic, complemented
18#22616324C211yesmaximal, characteristic, complemented
19#22615884C211yesmaximal, characteristic, complemented
20#22614263C211yesmaximal, characteristic, complemented
21#22614191C211yesmaximal, characteristic, complemented
22#22613664C211yesmaximal, characteristic, complemented
23#22613594C211yesmaximal, characteristic, complemented
24#22613488C211yesmaximal, characteristic, complemented
25#22613330C211yesmaximal, characteristic, complemented
26#22613302C211yesmaximal, characteristic
27#22613257C211yesmaximal, characteristic, complemented
28#22612594C211yesmaximal, characteristic, complemented
29#22612505C211yesmaximal, characteristic, complemented
30C2×#17988479C211yesmaximal, characteristic, complemented
31C73×#2639C211yesmaximal, characteristic, complemented
32C22×D4×D73C2211yescharacteristic
33C2×#14556584C2211yescharacteristic, complemented
34C2×#14556575C2211yescharacteristic
35C2×#14556575C2211yescharacteristic, complemented
36C2×#14556572C2211yescharacteristic
37C2×#14556572C2211yescharacteristic, complemented
38C2×#14556567C2211yescharacteristic, complemented
39C2×#14556563C2211yescharacteristic
40C2×#14556559C2211yescharacteristic
41C2×#14556559C2211yescharacteristic
42C2×D4×Dic73C2211yescharacteristic, complemented
43C22×C4⋊Dic73C2211yescharacteristic, complemented
44C22×#11924005C2211yescharacteristic
45C22×#11924005C2211yescharacteristic
46C22×#11924005C2211yescharacteristic
47C2×C22⋊C4×D73C2211yescharacteristic
48C22×C4×Dic73C2211yescharacteristic, complemented
49C73⋊#401C2211yescharacteristic, complemented
50#17988529C2211yescharacteristic, complemented
51#17988528C2211yescharacteristic, complemented
52#17988528C2211yescharacteristic, complemented
53#17988528C2211yescharacteristic, complemented
54#17988527C2211yescharacteristic, complemented
55#17988526C2211yescharacteristic, complemented
56#17988526C2211yescharacteristic, complemented
57#17988524C2211yescharacteristic, complemented
58#17988522C2211yescharacteristic
59#17988520C2211yescharacteristic, complemented
60#17988519C2211yescharacteristic, complemented
61#17988516C2211yescharacteristic
62#17988516C2211yescharacteristic
63#17988516C2211yescharacteristic, complemented
64#17988516C2211yescharacteristic, complemented
65#17988516C2211yescharacteristic, complemented
66#17988515C2211yescharacteristic, complemented
67#17988513C2211yescharacteristic, complemented
68#17988512C2211yescharacteristic, complemented
69#17988512C2211yescharacteristic, complemented
70#17988511C2211yescharacteristic, complemented
71#17988510C2211yescharacteristic, complemented
72#17988510C2211yescharacteristic, complemented
73#17988509C2211yescharacteristic
74#17988509C2211yescharacteristic
75#17988505C2211yescharacteristic
76#17988505C2211yescharacteristic
77#17988504C2211yescharacteristic
78#17988503C2211yescharacteristic
79#17988503C2211yescharacteristic
80#17988503C2211yescharacteristic, complemented
81#17988502C2211yescharacteristic
82#17988502C2211yescharacteristic
83#17988502C2211yescharacteristic
84#17988501C2211yescharacteristic, complemented
85#17988498C2211yescharacteristic
86#17988498C2211yescharacteristic, complemented
87#17988496C2211yescharacteristic
88#17988495C2211yescharacteristic
89#17988494C2211yescharacteristic, complemented
90#17988487C2211yescharacteristic
91#17988487C2211yescharacteristic, complemented
92#17988487C2211yescharacteristic, complemented
93#17988487C2211yescharacteristic, complemented
94#17988484C2211yescharacteristic, complemented
95#17988484C2211yescharacteristic, complemented
96#17988482C2211yescharacteristic, complemented
97#17988481C2211yescharacteristic, complemented
98#17988481C2211yescharacteristic, complemented
99#17988481C2211yescharacteristic, complemented
100#17988480C2211yescharacteristic, complemented
101#17988480C2211yescharacteristic, complemented
102#17988480C2211yescharacteristic, complemented
103#17988480C2211yescharacteristic, complemented
104#17988480C2211yescharacteristic, complemented
105#17988479C2211yescharacteristic
106#17988479C2211yescharacteristic
107#17988479C2211yescharacteristic
108#17988479C2211yescharacteristic
109#17988479C2211yescharacteristic
110#17988479C2211yescharacteristic, complemented
111#17988479C2211yescharacteristic, complemented
112#17988479C2211yescharacteristic, complemented
113#17988479C2211yescharacteristic, complemented
114#17988479C2211yescharacteristic, complemented
115#17988479C2211yescharacteristic, complemented
116#17988477C2211yescharacteristic, complemented
117#17988477C2211yescharacteristic, complemented
118#17988476C2211yescharacteristic
119#17988476C2211yescharacteristic, complemented
120#17988476C2211yescharacteristic, complemented
121#17988476C2211yescharacteristic, complemented
122#17988474C2211yescharacteristic, complemented
123#17988472C2211yescharacteristic, complemented
124#17988472C2211yescharacteristic, complemented
125#17988470C2211yescharacteristic, complemented
126#17988470C2211yescharacteristic, complemented
127#17988469C2211yescharacteristic, complemented
128#17988469C2211yescharacteristic, complemented
129#17988467C2211yescharacteristic
130#17988467C2211yescharacteristic
131#17988467C2211yescharacteristic, complemented
132#17988466C2211yescharacteristic
133#17988466C2211yescharacteristic
134#17988466C2211yescharacteristic
135#17988465C2211yescharacteristic
136#17988465C2211yescharacteristic
137#17988464C2211yescharacteristic
138#17988464C2211yescharacteristic
139#17988464C2211yescharacteristic, complemented
140#17988463C2211yescharacteristic
141#17988463C2211yescharacteristic
142#17988463C2211yescharacteristic
143#17988463C2211yescharacteristic, complemented
144#17988463C2211yescharacteristic, complemented
145#17988462C2211yescharacteristic, complemented
146#17988462C2211yescharacteristic, complemented
147#17988461C2211yescharacteristic
148#17988461C2211yescharacteristic
149#17988460C2211yescharacteristic, complemented
150#17988460C2211yescharacteristic, complemented
151#17988460C2211yescharacteristic, complemented
152#17988458C2211yescharacteristic
153#17988458C2211yescharacteristic, complemented
154#17988458C2211yescharacteristic, complemented
155#17988452C2211yescharacteristic, complemented
156#17988449C2211yescharacteristic
157#17988449C2211yescharacteristic
158#17988448C2211yescharacteristic, complemented
159#17988446C2211yescharacteristic, complemented
160#17988446C2211yescharacteristic, complemented
161#17988445C2211yescharacteristic, complemented
162#17988445C2211yescharacteristic, complemented
163#17988444C2211yescharacteristic, complemented
164#17988442C2211yescharacteristic
165#17988442C2211yescharacteristic
166#17988442C2211yescharacteristic
167#17988442C2211yescharacteristic
168#17988442C2211yescharacteristic
169#17988442C2211yescharacteristic
170C22⋊C4×Dic73C2211yescharacteristic, complemented
171C2×#14556498C2211yescharacteristic, complemented
172C2×C22⋊Q8×C73C2211yescharacteristic, complemented
173C2×#121×C73C2211yescharacteristic
174#400×C73C2211yescharacteristic, complemented
175#400×C73C2211yescharacteristic, complemented
176#397×C73C2211yescharacteristic, complemented
177#397×C73C2211yescharacteristic, complemented
178#394×C73C2211yescharacteristic, complemented
179#394×C73C2211yescharacteristic, complemented
180#393×C73C2211yescharacteristic, complemented
181#393×C73C2211yescharacteristic, complemented
182#386×C73C2211yescharacteristic
183#386×C73C2211yescharacteristic
184#386×C73C2211yescharacteristic, complemented
185#386×C73C2211yescharacteristic, complemented
186C2×#95×C73C2211yescharacteristic, complemented
187C24×D73C2311yescharacteristic
188C24×D73C2311yescharacteristic
189C22×D292C2311yescharacteristic
190C22×C22⋊D73C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C2×D4×D73—24no—
196C2×D4×D73—42no—
197C2×D4×D73—42no—
198C23×Dic73C2311yescharacteristic
199C23×Dic73C2311yescharacteristic
200C23×Dic73C2311yescharacteristic
201C23×Dic73C2311yescharacteristic
202C22×C4×D73C2311yescharacteristic
203C22×C4×D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205#14556584—42no—
206#14556575—42no—
207#14556575—42no—
208#14556572—42no—
209#14556572—42no—
210#14556567—42no—
211#14556563—42no—
212#14556559—24no—
213#14556559—42no—
214D4×Dic73—42no—
215C2×C4⋊Dic73—42no—
216C2×C4⋊Dic73C2311yescharacteristic
217C2×C4⋊Dic73C2311yescharacteristic
218C2×C4⋊Dic73C2311yescharacteristic
219C2×C4⋊Dic73C2311yescharacteristic
220C2×C4⋊Dic73C2311yescharacteristic
221C2×C4⋊Dic73C2311yescharacteristic
222C2×C4⋊Dic73C2311yescharacteristic
223C2×C4⋊Dic73C2311yescharacteristic
224C2×C4⋊Dic73C2311yescharacteristic
225C2×#11924007C2311yescharacteristic
226C2×#11924007C2311yescharacteristic
227C2×#11924007C2311yescharacteristic
228C2×#11924007C2311yescharacteristic
229C2×#11924007C2311yescharacteristic
230C2×#11924007C2311yescharacteristic
231C2×#11924007C2311yescharacteristic
232C2×#11924007C2311yescharacteristic
233C2×#11924007C2311yescharacteristic
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×C22⋊Dic73C2311yescharacteristic
239C2×C22⋊Dic73C2311yescharacteristic
240C2×C22⋊Dic73C2311yescharacteristic
241C2×C22⋊Dic73C2311yescharacteristic
242C2×C22⋊Dic73C2311yescharacteristic
243C2×C22⋊Dic73C2311yescharacteristic
244C2×C22⋊Dic73C2311yescharacteristic
245C2×C22⋊Dic73C2311yescharacteristic
246C2×C22⋊Dic73C2311yescharacteristic
247C2×C22⋊Dic73C2311yescharacteristic
248C2×C22⋊Dic73C2311yescharacteristic
249C2×C22⋊Dic73C2311yescharacteristic
250C2×C22⋊Dic73C2311yescharacteristic
251C2×#11924005—24no—
252C2×#11924005—42no—
253C2×#11924005—42no—
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
285C22⋊C4×D73—42no—
286C2×C4×Dic73—42no—
287C2×C4×Dic73C2311yescharacteristic
288C2×C4×Dic73C2311yescharacteristic
289C2×C4×Dic73C2311yescharacteristic
290C2×C4×Dic73C2311yescharacteristic
291C2×C4×Dic73C2311yescharacteristic
292C2×C4×Dic73C2311yescharacteristic
293C2×C4×Dic73C2311yescharacteristic
294#14556498C2311yescharacteristic
295#14556498C2311yescharacteristic
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
326C22×Q8×C73C2311yescharacteristic
327C22×D4×C73C2311yescharacteristic
328C22×D4×C73C2311yescharacteristic
329C22×D4×C73C2311yescharacteristic
330C23×C4×C73C2311yescharacteristic
331C23×C4×C73C2311yescharacteristic
332C23×C4×C73C2311yescharacteristic
333C22⋊Q8×C73—42no—
334#121×C73—42no—
335C2×C4⋊C4×C73C2311yescharacteristic
336C2×C4⋊C4×C73C2311yescharacteristic
337C2×C4⋊C4×C73C2311yescharacteristic
338C2×C4⋊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
347C2×C22⋊C4×C73C2311yescharacteristic
348C2×C22⋊C4×C73C2311yescharacteristic
349C2×C22⋊C4×C73C2311yescharacteristic
350C2×C22⋊C4×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
380C2×D292—22no—
381C2×D292—41no—
382C2×D292—41no—
383C2×C22⋊D73—22no—
384C2×C22⋊D73—22no—
385C2×C22⋊D73—22no—
386C2×C22⋊D73—22no—
387C2×C22⋊D73—22no—
388C2×C22⋊D73—22no—
389C2×C22⋊D73—22no—
390C2×C22⋊D73—41no—
391C2×C22⋊D73—41no—
392C2×C22⋊D73—41no—
393C2×C22⋊D73—41no—
394C2×C22⋊D73—41no—
395C2×C22⋊D73—41no—
396C2×C22⋊D73—41no—
397C2×C22⋊D73—41no—
398D4×D73—416no—
399C22×Dic73—22no—
400C22×Dic73—22no—
401C22×Dic73—22no—
402C22×Dic73—22no—
403C22×Dic73—22no—
404C22×Dic73—22no—
405C22×Dic73—41no—
406C22×Dic73—41no—
407C22×Dic73—41no—
408C22×Dic73—41no—
409C22×Dic73—41no—
410C22×Dic73—41no—
411C22×Dic73C2411yescharacteristic
412C22×Dic73C2411yescharacteristic
413C22×Dic73C2411yescharacteristic
414C22×Dic73C2411yescharacteristic
415C22×Dic73C2411yescharacteristic
416C22×Dic73C2411yescharacteristic
417C22×Dic73C2411yescharacteristic
418C22×Dic73C2411yescharacteristic
419C22×Dic73C2411yescharacteristic
420C22×Dic73C2411yescharacteristic
421C22×Dic73C2411yescharacteristic
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2411yescharacteristic
424C2×C4×D73—22no—
425C2×C4×D73—41no—
426C2×C4×D73—41no—
427C2×C4×D73—41no—
428C2×C4×D73—41no—
429C2×C4×D73—41no—
430C2×C4×D73—41no—
431C2×C4×D73—41no—
432C2×C4×D73—41no—
433C4⋊Dic73—22no—
434C4⋊Dic73—22no—
435C4⋊Dic73—22no—
436C4⋊Dic73—41no—
437C4⋊Dic73—41no—
438C4⋊Dic73—41no—
439C4⋊Dic73—41no—
440C4⋊Dic73—41no—
441C4⋊Dic73—41no—
442#11924007—22no—
443#11924007—41no—
444#11924007—41no—
445#11924007—41no—
446#11924007—41no—
447#11924007—41no—
448#11924007—41no—
449#11924007—41no—
450#11924007—41no—
451#11924007—41no—
452#11924007—41no—
453#11924007—41no—
454#11924007—41no—
455C22⋊Dic73—22no—
456C22⋊Dic73—22no—
457C22⋊Dic73—22no—
458C22⋊Dic73—22no—
459C22⋊Dic73—41no—
460C22⋊Dic73—41no—
461C22⋊Dic73—41no—
462C22⋊Dic73—41no—
463C22⋊Dic73—41no—
464C22⋊Dic73—41no—
465C22⋊Dic73—41no—
466C22⋊Dic73—41no—
467C22⋊Dic73—41no—
468#11924005—22no—
469#11924005—22no—
470#11924005—22no—
471#11924005—22no—
472#11924005—22no—
473#11924005—22no—
474#11924005—22no—
475#11924005—22no—
476#11924005—41no—
477#11924005—41no—
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—
499C4×Dic73—41no—
500C4×Dic73—41no—
501C4×Dic73—41no—
502C4×Dic73—41no—
503C4×Dic73—41no—
504C4×Dic73—41no—
505C4×Dic73—41no—
506C24×C73C2411yescharacteristic
507C24×C73C2411yescharacteristic
508C24×C73C2411yescharacteristic
509C2×Q8×C73—41no—
510C2×Q8×C73—41no—
511C2×Q8×C73—41no—
512C2×D4×C73—22no—
513C2×D4×C73—22no—
514C2×D4×C73—22no—
515C2×D4×C73—22no—
516C2×D4×C73—22no—
517C2×D4×C73—22no—
518C2×D4×C73—41no—
519C2×D4×C73—41no—
520C2×D4×C73—41no—
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
542C4⋊C4×C73—41no—
543C4⋊C4×C73—41no—
544C4⋊C4×C73—41no—
545C4⋊C4×C73—41no—
546C22⋊C4×C73—22no—
547C22⋊C4×C73—22no—
548C22⋊C4×C73—41no—
549C22⋊C4×C73—41no—
550C22⋊C4×C73—41no—
551C22⋊C4×C73—41no—
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×C73—21no—
570C23×C73—21no—
571C23×C73—21no—
572C23×C73—21no—
573C23×C73—21no—
574C23×C73—21no—
575C23×C73—21no—
576C23×C73C2×#4112yes—
577C23×C73H(5,𝔽2)12yes—
578C23×C73H(5,𝔽2)12yes—
579C23×C73C2511yescharacteristic
580C22×D73—21no—
581C22×D73—21no—
582C22×D73—21no—
583C22×D73—21no—
584C22×D73—21no—
585C22×D73—21no—
586C22×D73—21no—
587C22×D73—21no—
588C22×D73—21no—
589C22×D73—21no—
590C22×D73—21no—
591C22×D73—21no—
592C22×D73—28no—
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—
615Q8×C73—82no—
616D4×C73—44no—
617D4×C73—44no—
618D4×C73—82no—
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—82no—
661C22⋊D73—82no—
662C22⋊D73—82no—
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—82no—
704C2×Dic73—82no—
705C2×Dic73H(5,𝔽2)12yes—
706D292—44no—
707C4×D73—44no—
708C4×D73—82no—
709C4×D73—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—41no—
724C22×C73—41no—
725C22×C73—41no—
726C22×C73—41no—
727C22×C73—41no—
728C22×C73—41no—
729C22×C73—41no—
730C22×C73#53814yes—
731C22×C73C22×#4111yescharacteristic
732C22×C73C2×H(5,𝔽2)11yescharacteristic
733C22×C73C2×H(5,𝔽2)11yescharacteristic
734C22×C73C2×H(5,𝔽2)11yescharacteristic
735C22×C73#58511yescharacteristic
736C22×C73#58511yescharacteristic
737C22×C73#58511yescharacteristic
738C2×D73—22no—
739C2×D73—22no—
740C2×D73—22no—
741C2×D73—22no—
742C2×D73—22no—
743C2×D73—22no—
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—
773Dic73—22no—
774Dic73—41no—
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×C73—81no—
790C2×C73C2×#53811yescharacteristic
791C2×C73#349111yescharacteristic
792C2×C73#350511yescharacteristic
793C2×C73#353311yescharacteristic
794C2×C73#353411yescharacteristic
795C2×C73#355811yescharacteristic
796C2×C73#356011yescharacteristic
797D73—42no—
798D73—42no—
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#2643—731no—
819#2639D7311yescharacteristic, complemented
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⋊Q8C2×D7311yescharacteristic, complemented
840C2×#121—731no—
841C2×#121C2×D7311yescharacteristic
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#401—731no—
852#400—731no—
853#400—731no—
854#400—731no—
855#400—731no—
856#400—731no—
857#400—731no—
858#400—731no—
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#397—731no—
874#397C2×D7311yescharacteristic, complemented
875#397C2×D7311yescharacteristic, complemented
876#396—731no—
877#396—731no—
878#396—731no—
879#396—731no—
880#396—731no—
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#394C2×D7311yescharacteristic, complemented
892#394C2×D7311yescharacteristic, complemented
893#393—731no—
894#393—731no—
895#393C2×D7311yescharacteristic, complemented
896#393C2×D7311yescharacteristic, complemented
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#386C2×D7311yescharacteristic
956#386C2×D7311yescharacteristic
957#386C2×D7311yescharacteristic, complemented
958#386C2×D7311yescharacteristic, complemented
959#385—731no—
960#385—731no—
961#385—731no—
962#385—731no—
963#385—731no—
964#385—731no—
965#385—731no—
966#385—731no—
967#385—731no—
968#385—731no—
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×Q8C22×D7311yescharacteristic
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—1464no—
999C22×D4C22×D7311yescharacteristic
1000C22×D4C22×D7311yescharacteristic
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—42no—
1018C22⋊Q8—2922no—
1019#121—42no—
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⋊C4—731no—
1046C2×C4⋊C4—731no—
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—1464no—
1099C2×C22⋊C4C22×D7311yescharacteristic
1100C2×C22⋊C4C22×D7311yescharacteristic
1101C2×C22⋊C4C22×D7311yescharacteristic
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#95—731no—
1148#95—731no—
1149#95—731no—
1150#95—731no—
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—1462no—
1178C24—1462no—
1179C24—1462no—
1180C24C23×D7311yescharacteristic
1181C24C23×D7311yescharacteristic
1182C24C23×D7311yescharacteristic
1183C2×Q8—41no—
1184C2×Q8—41no—
1185C2×Q8—41no—
1186C2×D4—22no—
1187C2×D4—22no—
1188C2×D4—22no—
1189C2×D4—22no—
1190C2×D4—22no—
1191C2×D4—22no—
1192C2×D4—41no—
1193C2×D4—41no—
1194C2×D4—41no—
1195C2×D4—2921no—
1196C2×D4—2921no—
1197C2×D4—29216no—
1198C2×D4—2921no—
1199C2×D4—2921no—
1200C2×D4—2921no—
1201C2×D4—2921no—
1202C2×D4—2921no—
1203C2×D4—2921no—
1204C2×D4—2921no—
1205C2×D4—2921no—
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—731no—
1250C22×C4—1462no—
1251C22×C4—1462no—
1252C22×C4—1462no—
1253C22×C4—1462no—
1254C22×C4—1462no—
1255C22×C4—1462no—
1256C22×C4—1462no—
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—2921no—
1274C4⋊C4—2921no—
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—41no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—41no—
1305C22⋊C4—41no—
1306C22⋊C4—41no—
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—1462no—
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—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—21no—
1376C23—2924no—
1377C23—2924no—
1378C23—2924no—
1379C23—5842no—
1380C23—5842no—
1381C23—5842no—
1382C23—5842no—
1383C23—5842no—
1384C23—5842no—
1385C23—5842no—
1386C23—5842no—
1387C23—5842no—
1388C23—5842no—
1389C23—732no—
1390C23—732no—
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#1455663612yes—
1413C23#1455663712yes—
1414C23C24×D7311yescharacteristic
1415Q8—82no—
1416D4—44no—
1417D4—44no—
1418D4—82no—
1419D4—2924no—
1420D4—2924no—
1421D4—2924no—
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—44no—
1462C2×C4—44no—
1463C2×C4—82no—
1464C2×C4—2924no—
1465C2×C4—2924no—
1466C2×C4—2924no—
1467C2×C4—5842no—
1468C2×C4—5842no—
1469C2×C4—5842no—
1470C2×C4—5842no—
1471C2×C4—732no—
1472C2×C4—1461no—
1473C2×C4—1461no—
1474C2×C4—1461no—
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—41no—
1524C22—41no—
1525C22—41no—
1526C22—41no—
1527C22—41no—
1528C22—41no—
1529C22—41no—
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#1798917114yes—
1554C22C2×#41×D7311yescharacteristic
1555C22H(5,𝔽2)×D7311yescharacteristic
1556C22C2×#1455663611yescharacteristic
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—2921no—
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—81no—
1589C2—2922no—
1590C2—2922no—
1591C2—5841no—
1592C2C2×#1798917111yescharacteristic
1593C2#2262362511yescharacteristic
1594C2#2262376911yescharacteristic
1595C2#2262409911yescharacteristic
1596C2#2262411911yescharacteristic
1597C2#2262444311yescharacteristic
1598C2#2262448011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2639C2
prime radical#22613302C2
hypercenter#2639D73
hypocenterC73#36986
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2639

Complements

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

NH ≅ G/Ntype
1. #22618259C2semidirect
2. #22618252C2semidirect
3. #22617787C2semidirect
4. #22617571C2semidirect
5. #22617563C2semidirect
6. #22617551C2semidirect
7. #22617443C2semidirect
8. #22617371C2semidirect
9. #22617213C2semidirect
10. #22617183C2semidirect
11. #22617162C2semidirect
12. #22617053C2semidirect
13. #22616975C2semidirect
14. #22616971C2semidirect
15. #22616566C2semidirect
16. #22616497C2semidirect
17. #22616488C2semidirect
18. #22616324C2semidirect
19. #22615884C2semidirect
20. #22614263C2semidirect
21. #22614191C2semidirect
22. #22613664C2semidirect
23. #22613594C2semidirect
24. #22613488C2semidirect
25. #22613330C2semidirect
27. #22613257C2semidirect
28. #22612594C2semidirect
29. #22612505C2semidirect
30. C2×#17988479C2semidirect
31. C73×#2639C2semidirect
33. C2×#14556584C22semidirect
35. C2×#14556575C22semidirect
37. C2×#14556572C22semidirect
38. C2×#14556567C22semidirect
42. C2×D4×Dic73C22semidirect
43. C22×C4⋊Dic73C22semidirect
48. C22×C4×Dic73C22semidirect
49. C73⋊#401C22semidirect
50. #17988529C22semidirect
51. #17988528C22semidirect
52. #17988528C22semidirect
53. #17988528C22semidirect
54. #17988527C22semidirect
55. #17988526C22semidirect
56. #17988526C22semidirect
57. #17988524C22semidirect
59. #17988520C22semidirect
60. #17988519C22semidirect
63. #17988516C22semidirect
64. #17988516C22semidirect
65. #17988516C22semidirect
66. #17988515C22semidirect
67. #17988513C22semidirect
68. #17988512C22semidirect
69. #17988512C22semidirect
70. #17988511C22semidirect
71. #17988510C22semidirect
72. #17988510C22semidirect
80. #17988503C22semidirect
84. #17988501C22semidirect
86. #17988498C22semidirect
89. #17988494C22semidirect
91. #17988487C22semidirect
92. #17988487C22semidirect
93. #17988487C22semidirect
94. #17988484C22semidirect
95. #17988484C22semidirect
96. #17988482C22semidirect
97. #17988481C22semidirect
98. #17988481C22semidirect
99. #17988481C22semidirect
100. #17988480C22semidirect
101. #17988480C22semidirect
102. #17988480C22semidirect
103. #17988480C22semidirect
104. #17988480C22semidirect
110. #17988479C22semidirect
111. #17988479C22semidirect
112. #17988479C22semidirect
113. #17988479C22semidirect
114. #17988479C22semidirect
115. #17988479C22semidirect
116. #17988477C22semidirect
117. #17988477C22semidirect
119. #17988476C22semidirect
120. #17988476C22semidirect
121. #17988476C22semidirect
122. #17988474C22semidirect
123. #17988472C22semidirect
124. #17988472C22semidirect
125. #17988470C22semidirect
126. #17988470C22semidirect
127. #17988469C22semidirect
128. #17988469C22semidirect
131. #17988467C22semidirect
139. #17988464C22semidirect
143. #17988463C22semidirect
144. #17988463C22semidirect
145. #17988462C22semidirect
146. #17988462C22semidirect
149. #17988460C22semidirect
150. #17988460C22semidirect
151. #17988460C22semidirect
153. #17988458C22semidirect
154. #17988458C22semidirect
155. #17988452C22semidirect
158. #17988448C22semidirect
159. #17988446C22semidirect
160. #17988446C22semidirect
161. #17988445C22semidirect
162. #17988445C22semidirect
163. #17988444C22semidirect
170. C22⋊C4×Dic73C22semidirect
171. C2×#14556498C22semidirect
172. C2×C22⋊Q8×C73C22semidirect
174. #400×C73C22semidirect
175. #400×C73C22semidirect
176. #397×C73C22semidirect
177. #397×C73C22semidirect
178. #394×C73C22semidirect
179. #394×C73C22semidirect
180. #393×C73C22semidirect
181. #393×C73C22semidirect
184. #386×C73C22semidirect
185. #386×C73C22semidirect
186. C2×#95×C73C22semidirect
819. #2639D73semidirect
831. C73#36986semidirect
839. C2×C22⋊Q8C2×D73semidirect
859. #400C2×D73semidirect
860. #400C2×D73semidirect
874. #397C2×D73semidirect
875. #397C2×D73semidirect
891. #394C2×D73semidirect
892. #394C2×D73semidirect
895. #393C2×D73semidirect
896. #393C2×D73semidirect
957. #386C2×D73semidirect
958. #386C2×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
#226182522
#226177872
#226175712
#226175632
#226175512
#226174432
#226173712
#226172132
#226171832
#226171622
#226170532
#226169752
#226169712
#226165662
#226164972
#226164882
#226163242
#226158842
#226142632
#226141912
#226136642
#226135942
#226134882
#226133302
#226133022
#226132572
#226125942
#226125052
C2×#179884792
C73×#26392
#3698673