Finite Group Databasebeta

← #33112063

Subgroups — #33112063

Order 18688.

892 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613144C211yesmaximal, characteristic
2#22610727C211yesmaximal, characteristic, complemented
3#22610727C211yesmaximal, characteristic, complemented
4#22610723C211yesmaximal, characteristic, complemented
5#22610547C211yesmaximal, characteristic, complemented
6#22610547C211yesmaximal, characteristic, complemented
7#22610541C211yesmaximal, characteristic, complemented
8#22610541C211yesmaximal, characteristic, complemented
9#22610540C211yesmaximal, characteristic, complemented
10#22610534C211yesmaximal, characteristic, complemented
11#22610225C211yesmaximal, characteristic, complemented
12#22610225C211yesmaximal, characteristic, complemented
13#22610225C211yesmaximal, characteristic, complemented
14#22609843C211yesmaximal, characteristic, complemented
15C73×#1780C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C2×C4×C22⋊D73C2211yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556501C2211yescharacteristic
33C2×#14556501C2211yescharacteristic
34C2×C8×Dic73C2211yescharacteristic
35#17988506C411yescharacteristic
36#17988501C411yescharacteristic
37#17988501C411yescharacteristic
38#17988501C411yescharacteristic
39#17988498C411yescharacteristic
40#17988495C411yescharacteristic
41#17988495C411yescharacteristic
42#17988495C411yescharacteristic
43C4×C22⋊Dic73C2211yescharacteristic
44C4×C22⋊Dic73C2211yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C22×#41×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C22×C22⋊D73C2×C411yescharacteristic
60C22×C22⋊D73C2×C411yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C4×D73C2311yescharacteristic
63C2×#11924011—41no—
64C2×#11924011—41no—
65C2×#11924011—41no—
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C4×C22⋊D73—41no—
71C4×C22⋊D73—41no—
72C4×C22⋊D73—41no—
73C4×C22⋊D73—41no—
74C4×C22⋊D73—41no—
75C4×C22⋊D73—41no—
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×C22⋊Dic73C2×C411yescharacteristic
80C2×C22⋊Dic73C2×C411yescharacteristic
81C2×C22⋊Dic73C2×C411yescharacteristic
82C2×C22⋊Dic73C2×C411yescharacteristic
83C2×C22⋊Dic73C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×C4×Dic73C2311yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94#14556520—41no—
95#14556520—41no—
96#14556520—41no—
97C22⋊#10596831—41no—
98C22⋊#10596831—41no—
99C22⋊#10596831—41no—
100C22⋊#10596831—41no—
101C22⋊#10596831—41no—
102C22⋊#10596831—41no—
103#14556503—41no—
104#14556503—41no—
105#14556503—41no—
106#14556501—41no—
107#14556501—41no—
108C8×Dic73—41no—
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115C2×#41×C73—41no—
116C2×#41×C73—41no—
117C2×#41×C73—41no—
118C2×#41×C73—41no—
119C2×#41×C73—41no—
120C2×#41×C73—41no—
121C22×Q8×C73C2×C411yescharacteristic
122C22×D4×C73C2×C411yescharacteristic
123C22×D4×C73C2×C411yescharacteristic
124C22×D4×C73C2×C411yescharacteristic
125C23×C4×C73C2311yescharacteristic
126C23×C4×C73C2311yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132C22⋊C8×C73—41no—
133C22⋊C8×C73—41no—
134C22⋊C8×C73—41no—
135C22⋊C8×C73—41no—
136C22⋊C8×C73—41no—
137C22⋊C8×C73—41no—
138C23×D73C22×C411yescharacteristic
139C2×C22⋊D73—22no—
140C2×C22⋊D73—41no—
141C2×C22⋊D73—41no—
142C2×C22⋊D73—41no—
143C2×C22⋊D73—41no—
144C2×C22⋊D73—41no—
145C2×C22⋊D73—41no—
146C2×C22⋊D73—41no—
147C2×C22⋊D73—41no—
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C22×Dic73C22×C411yescharacteristic
154C22×Dic73C22×C411yescharacteristic
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161#11924011—44no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174#11924007—41no—
175#11924007—41no—
176#11924007—41no—
177C22⋊Dic73—22no—
178C22⋊Dic73—22no—
179C22⋊Dic73—41no—
180C22⋊Dic73—41no—
181C22⋊Dic73—41no—
182C22⋊Dic73—41no—
183C22⋊Dic73—41no—
184C22⋊Dic73—41no—
185C22⋊Dic73—41no—
186#11924005—41no—
187#11924005—41no—
188#11924005—41no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C24×C73C22×C411yescharacteristic
196C24×C73C22×C411yescharacteristic
197C24×C73C22×C411yescharacteristic
198#41×C73—44no—
199#41×C73—44no—
200#41×C73—44no—
201#41×C73—44no—
202C2×Q8×C73—41no—
203C2×Q8×C73—41no—
204C2×Q8×C73—41no—
205C2×D4×C73—41no—
206C2×D4×C73—41no—
207C2×D4×C73—41no—
208C2×D4×C73—41no—
209C2×D4×C73—41no—
210C2×D4×C73—41no—
211C2×D4×C73—41no—
212C2×D4×C73—41no—
213C2×D4×C73—41no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C2411yescharacteristic
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73C23×C411yescharacteristic
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277Q8×C73—44no—
278D4×C73—44no—
279D4×C73—44no—
280D4×C73—44no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C2×C4×C73H(5,𝔽2)11yescharacteristic
305C2×C4×C73H(5,𝔽2)11yescharacteristic
306C2×C4×C73H(5,𝔽2)11yescharacteristic
307C2×C4×C73H(5,𝔽2)11yescharacteristic
308C22⋊D73—44no—
309C22⋊D73—44no—
310C22⋊D73—44no—
311C2×Dic73—21no—
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—21no—
315C2×Dic73—21no—
316C2×Dic73—21no—
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73—21no—
326C2×Dic73—21no—
327C2×Dic73—21no—
328C2×Dic73—21no—
329C2×Dic73—21no—
330C2×Dic73—21no—
331C2×Dic73#13112yes—
332C4×D73—41no—
333C4×D73—41no—
334C4×D73—41no—
335C4×D73—41no—
336C8×C73—41no—
337C8×C73—41no—
338C8×C73—41no—
339C8×C73—41no—
340#10596831—41no—
341#10596831—41no—
342#10596831—41no—
343#10596831—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73#51811yescharacteristic
366C22×C73#51811yescharacteristic
367C22×C73#51811yescharacteristic
368C22×C73C2×#13111yescharacteristic
369C22×C73#56811yescharacteristic
370C22×C73#56811yescharacteristic
371C22×C73#56811yescharacteristic
372C2×D73—41no—
373C2×D73—41no—
374C2×D73—41no—
375C2×D73—41no—
376C2×D73—41no—
377C2×D73—41no—
378C2×D73—41no—
379C4×C73—41no—
380C4×C73—41no—
381C4×C73—41no—
382C4×C73#56011yescharacteristic
383C4×C73#56011yescharacteristic
384C4×C73#56011yescharacteristic
385C4×C73H(3,𝔽4)11yescharacteristic
386Dic73—22no—
387Dic73—41no—
388Dic73—41no—
389Dic73—41no—
390Dic73—41no—
391Dic73—41no—
392Dic73—41no—
393#23313—731nomaximal, Sylow
394C2×C73—81no—
395C2×C73—81no—
396C2×C73—81no—
397C2×C73#237511yescharacteristic
398C2×C73#297611yescharacteristic
399C2×C73#297811yescharacteristic
400C2×C73#297811yescharacteristic
401C2×C73#298011yescharacteristic
402C2×C73#298111yescharacteristic
403C2×C73#298111yescharacteristic
404D73—81no—
405#2388—731no—
406#1955—731no—
407#1955—731no—
408#1954—731no—
409#1924—731no—
410#1924—731no—
411#1924—731no—
412#1924—731no—
413#1923—731no—
414#1923—731no—
415#1870—731no—
416#1870—731no—
417#1870—731no—
418#1780—731no—
419#1780D7311yescharacteristic, complemented
420C73#2331311yescharacteristic, complemented, Sylow
421C22×#41C2×D7311yescharacteristic
422C22×M16—731no—
423C2×C4×D4—731no—
424C2×C4×D4—731no—
425C2×C4×D4—731no—
426C2×C4⋊C8—731no—
427C2×C4⋊C8—731no—
428C2×C4⋊C8—731no—
429C2×C22⋊C8—731no—
430C2×C22⋊C8—731no—
431C2×C22⋊C8—731no—
432C2×C22⋊C8—731no—
433C2×C22⋊C8—731no—
434C2×C22⋊C8—731no—
435C2×C22⋊C8—731no—
436C2×C22⋊C8—731no—
437C2×C22⋊C8—731no—
438C2×C22⋊C8C2×D7311yescharacteristic
439C2×C22⋊C8C2×D7311yescharacteristic
440C2×C22⋊C8C2×D7311yescharacteristic
441C2×C22⋊C8C2×D7311yescharacteristic
442C2×C22⋊C8C2×D7311yescharacteristic
443C2×C22⋊C8C2×D7311yescharacteristic
444C2×#97—731no—
445C2×#97—731no—
446C2×C4×C8—731no—
447#395—731no—
448#394—731no—
449#394—731no—
450#394—731no—
451#393—731no—
452#392—731no—
453#392—731no—
454#392—731no—
455C4×C22⋊C4—731no—
456C4×C22⋊C4—731no—
457C4×C22⋊C4—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461#336—731no—
462#336—731no—
463#336—731no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41—41no—
469C2×#41—41no—
470C22×Q8C4×D7311yescharacteristic
471C22×D4—731no—
472C22×D4—731no—
473C22×D4—731no—
474C22×D4C4×D7311yescharacteristic
475C22×D4C4×D7311yescharacteristic
476C22×D4C4×D7311yescharacteristic
477C23×C4—731no—
478C23×C4C22×D7311yescharacteristic
479C23×C4C22×D7311yescharacteristic
480C23×C4C22×D7311yescharacteristic
481C2×M16—2921no—
482C2×M16—2921no—
483C2×M16—2921no—
484C22×C8—731no—
485C22×C8—731no—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490C22×C8C22×D7311yescharacteristic
491C22×C8C22×D7311yescharacteristic
492C4×D4—2921no—
493C4×D4—2921no—
494C4×D4—2921no—
495C4×D4—2921no—
496C4×D4—2921no—
497C4×D4—2921no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—731no—
501C2×C22⋊C4—731no—
502C2×C22⋊C4—731no—
503C2×C22⋊C4—731no—
504C2×C22⋊C4—731no—
505C2×C22⋊C4—731no—
506C2×C22⋊C4—731no—
507C2×C22⋊C4—731no—
508C2×C22⋊C4—731no—
509C2×C22⋊C4—731no—
510C2×C22⋊C4—731no—
511C2×C22⋊C4—731no—
512C2×C22⋊C4—731no—
513C2×C42—731no—
514C2×C42—731no—
515C2×C42—731no—
516C4⋊C8—2921no—
517C4⋊C8—2921no—
518C4⋊C8—2921no—
519C22⋊C8—41no—
520C22⋊C8—41no—
521C22⋊C8—41no—
522C22⋊C8—41no—
523C22⋊C8—41no—
524C22⋊C8—41no—
525C22⋊C8—2921no—
526C22⋊C8—2921no—
527C22⋊C8—2921no—
528C22⋊C8—2921no—
529C22⋊C8—2921no—
530C22⋊C8—2921no—
531C22⋊C8—2921no—
532C22⋊C8—2921no—
533C22⋊C8—2921no—
534#97—2921no—
535#97—2921no—
536C4×C8—2921no—
537#95—731no—
538#95—731no—
539#95—731no—
540#95—731no—
541#95—731no—
542#95—731no—
543C24—731no—
544C24C2×C4×D7311yescharacteristic
545C24C2×C4×D7311yescharacteristic
546C24C2×C4×D7311yescharacteristic
547#41—44no—
548#41—44no—
549#41—44no—
550#41—44no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—2921no—
564C2×D4—2921no—
565C2×D4—2921no—
566C2×D4—2921no—
567C2×D4—2921no—
568C2×D4—2921no—
569C2×D4—2921no—
570C2×D4—2921no—
571C2×D4—1462no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—731no—
591C22×C4—731no—
592C22×C4—731no—
593C22×C4—731no—
594C22×C4—731no—
595C22×C4—731no—
596C22×C4—731no—
597C22×C4—1461no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4C2×C4×D7311yescharacteristic
604C22×C4C2×C4×D7311yescharacteristic
605C22×C4C2×C4×D7311yescharacteristic
606C22×C4C23×D7311yescharacteristic
607M16—2924no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—1461no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8—1461no—
626C2×C8—1461no—
627C2×C8—1461no—
628C2×C8—1461no—
629C2×C8—1461no—
630C2×C8—1461no—
631C2×C8—1461no—
632C4⋊C4—2921no—
633C4⋊C4—2921no—
634C4⋊C4—2921no—
635C22⋊C4—2921no—
636C22⋊C4—2921no—
637C22⋊C4—2921no—
638C22⋊C4—2921no—
639C22⋊C4—2921no—
640C22⋊C4—2921no—
641C22⋊C4—2921no—
642C22⋊C4—2921no—
643C22⋊C4—2921no—
644C22⋊C4—2921no—
645C22⋊C4—1462no—
646C22⋊C4—1462no—
647C42—1461no—
648C42—1461no—
649C42—1461no—
650C42—1461no—
651C42—1461no—
652C42—1461no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—1461no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23—1461no—
679C23—1461no—
680C23—1461no—
681C23C22×C4×D7311yescharacteristic
682Q8—44no—
683D4—44no—
684D4—44no—
685D4—44no—
686D4—2924no—
687D4—2924no—
688D4—2924no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—2921no—
713C2×C4—2921no—
714C2×C4—732no—
715C2×C4—1461no—
716C2×C4—1461no—
717C2×C4—1461no—
718C2×C4—1461no—
719C2×C4—1461no—
720C2×C4—1461no—
721C2×C4—1461no—
722C2×C4—1461no—
723C2×C4—1461no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4—1461no—
727C2×C4—1461no—
728C2×C4—1461no—
729C2×C4—1461no—
730C2×C4—1461no—
731C2×C4—1461no—
732C2×C4—1461no—
733C2×C4—1461no—
734C2×C4—1461no—
735C2×C4#1455663611yescharacteristic
736C2×C4#1455663611yescharacteristic
737C2×C4#1455663611yescharacteristic
738C2×C4#1455663611yescharacteristic
739C2×C4#1455663611yescharacteristic
740C2×C4#1455663611yescharacteristic
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—2921no—
746C8—2921no—
747C8—2921no—
748C8—2921no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—2921no—
771C22—2921no—
772C22—2921no—
773C22—2921no—
774C22—2921no—
775C22—2921no—
776C22—2921no—
777C22#1798906011yescharacteristic
778C22#1798906011yescharacteristic
779C22#1798906011yescharacteristic
780C22#131×D7311yescharacteristic
781C22#1798935211yescharacteristic
782C22#1798935211yescharacteristic
783C22#1798935211yescharacteristic
784C4—41no—
785C4—41no—
786C4—41no—
787C4—2921no—
788C4—2921no—
789C4—2921no—
790C4—2921no—
791C4—2921no—
792C4—2921no—
793C4—1462no—
794C4#1798932611yescharacteristic
795C4#1798932611yescharacteristic
796C4#1798932611yescharacteristic
797C4#1798933011yescharacteristic
798C2—81no—
799C2—81no—
800C2—81no—
801C2—5841no—
802C2#2261307011yescharacteristic
803C2#2261897411yescharacteristic
804C2#2261898911yescharacteristic
805C2#2261898911yescharacteristic
806C2#2261900011yescharacteristic
807C2#2261900411yescharacteristic
808C2#2261900411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1780C2
prime radical#22613144C2
cosocleC22×C4×C73C24
hypercenter#1780D73
hypocenterC73#23313
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1780

Complements

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

NH ≅ G/Ntype
2. #22610727C2semidirect
3. #22610727C2semidirect
4. #22610723C2semidirect
5. #22610547C2semidirect
6. #22610547C2semidirect
7. #22610541C2semidirect
8. #22610541C2semidirect
9. #22610540C2semidirect
10. #22610534C2semidirect
11. #22610225C2semidirect
12. #22610225C2semidirect
13. #22610225C2semidirect
14. #22609843C2semidirect
15. C73×#1780C2semidirect
419. #1780D73semidirect
420. C73#23313semidirect

Maximal subgroups

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

subgroupindex
#226131442
#226107272
#226107232
#226105472
#226105412
#226105402
#226105342
#226102252
#226098432
C73×#17802
#2331373