Finite Group Databasebeta

← #33112061

Subgroups — #33112061

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#22613146C211yesmaximal, characteristic
2#22610730C211yesmaximal, characteristic, complemented
3#22610727C211yesmaximal, characteristic, complemented
4#22610723C211yesmaximal, characteristic, complemented
5#22610547C211yesmaximal, characteristic, complemented
6#22610545C211yesmaximal, characteristic, complemented
7#22610542C211yesmaximal, characteristic, complemented
8#22610542C211yesmaximal, characteristic, complemented
9#22610540C211yesmaximal, characteristic, complemented
10#22610538C211yesmaximal, characteristic, complemented
11#22610228C211yesmaximal, characteristic, complemented
12#22610228C211yesmaximal, characteristic, complemented
13#22609842C211yesmaximal, characteristic, complemented
14#22609842C211yesmaximal, characteristic, complemented
15C73×#1870C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C2×C4×C22⋊D73C2211yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×C22⋊#10596831C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556502C2211yescharacteristic
35C2×#14556501C2211yescharacteristic
36C2×C8×Dic73C2211yescharacteristic
37#17988507C411yescharacteristic
38#17988504C411yescharacteristic
39#17988502C411yescharacteristic
40#17988502C411yescharacteristic
41#17988499C411yescharacteristic
42#17988496C411yescharacteristic
43#17988495C411yescharacteristic
44#17988495C411yescharacteristic
45C4×#11924005C2211yescharacteristic
46C4×#11924005C2211yescharacteristic
47C4×C22⋊Dic73C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C22×M16×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C2×#11924028—41no—
60C2×#11924028—41no—
61C2×#11924028—41no—
62C2×#11924028—41no—
63C2×#11924028—41no—
64C2×#11924028—41no—
65C22×Dic146C2×C411yescharacteristic
66C22×D292C2×C411yescharacteristic
67C22×C22⋊D73C2×C411yescharacteristic
68C22×C22⋊D73C2×C411yescharacteristic
69C22×C22⋊D73C2×C411yescharacteristic
70C22×C22⋊D73C2×C411yescharacteristic
71C22×C4×D73C2311yescharacteristic
72C22×C4×D73C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C4×C22⋊D73—41no—
78C4×C22⋊D73—41no—
79C4×C22⋊D73—41no—
80C4×C22⋊D73—41no—
81C2×#11924007C2×C411yescharacteristic
82C2×#11924007C2×C411yescharacteristic
83C2×C22⋊Dic73C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C4⋊#10596831—41no—
96#14556520—41no—
97#14556520—41no—
98C22⋊#10596831—41no—
99C22⋊#10596831—41no—
100C22⋊#10596831—41no—
101C22⋊#10596831—41no—
102#14556503—41no—
103#14556503—41no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107#14556503—41no—
108#14556503—41no—
109#14556503—41no—
110#14556502—41no—
111#14556501—41no—
112C8×Dic73—41no—
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119C22×D4×C73C2×C411yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C2×M16×C73—41no—
123C2×M16×C73—41no—
124C2×M16×C73—41no—
125C22×C8×C73C2311yescharacteristic
126C22×C8×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C4×D4×C73—41no—
130C4×D4×C73—41no—
131C2×C4⋊C4×C73C2×C411yescharacteristic
132C2×C22⋊C4×C73C2×C411yescharacteristic
133C2×C22⋊C4×C73C2×C411yescharacteristic
134C2×C42×C73C2311yescharacteristic
135C22⋊C8×C73—41no—
136C22⋊C8×C73—41no—
137C22⋊C8×C73—41no—
138C23×D73C22×C411yescharacteristic
139C23×D73C22×C411yescharacteristic
140#11924028—44no—
141#11924028—44no—
142#11924028—44no—
143#11924028—44no—
144C2×Dic146—41no—
145C2×Dic146—41no—
146C2×Dic146—41no—
147C2×D292—41no—
148C2×D292—41no—
149C2×D292—41no—
150C2×C22⋊D73—22no—
151C2×C22⋊D73—41no—
152C2×C22⋊D73—41no—
153C2×C22⋊D73—41no—
154C2×C22⋊D73—41no—
155C2×C22⋊D73—41no—
156C2×C22⋊D73—41no—
157C2×C22⋊D73—41no—
158C2×C22⋊D73—41no—
159C2×C22⋊D73—41no—
160C2×C22⋊D73—41no—
161C2×C22⋊D73—41no—
162C22×Dic73C22×C411yescharacteristic
163C22×Dic73C22×C411yescharacteristic
164C22×Dic73C22×C411yescharacteristic
165C22×Dic73C22×C411yescharacteristic
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C2×C4×D73—21no—
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—21no—
179C2×C4×D73—21no—
180C2×#10596831—21no—
181C2×#10596831—21no—
182C2×#10596831—21no—
183C2×#10596831—21no—
184C2×#10596831—21no—
185C2×#10596831—21no—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192#11924007—41no—
193#11924007—41no—
194C22⋊Dic73—22no—
195C22⋊Dic73—41no—
196C22⋊Dic73—41no—
197C22⋊Dic73—41no—
198#11924005—22no—
199#11924005—41no—
200#11924005—41no—
201#11924005—41no—
202#11924005—41no—
203#11924005—41no—
204C4×Dic73—21no—
205C4×Dic73—21no—
206C4×Dic73—21no—
207C4×Dic73—21no—
208C24×C73C22×C411yescharacteristic
209C24×C73C22×C411yescharacteristic
210C2×D4×C73—41no—
211C2×D4×C73—41no—
212C2×D4×C73—41no—
213C22×C4×C73—21no—
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×C73C22×C411yescharacteristic
226C22×C4×C73C22×C411yescharacteristic
227C22×C4×C73C22×C411yescharacteristic
228C22×C4×C73C22×C411yescharacteristic
229C22×C4×C73C2411yescharacteristic
230M16×C73—44no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
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—
243C4⋊C4×C73—41no—
244C22⋊C4×C73—41no—
245C22⋊C4×C73—41no—
246C42×C73—21no—
247C42×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×C73C23×C411yescharacteristic
263C22×D73—21no—
264C22×D73—21no—
265C22×D73—21no—
266C22×D73—21no—
267C22×D73—21no—
268C22×D73—21no—
269C22×D73—21no—
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277D4×C73—44no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
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×C73H(5,𝔽2)11yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×C4×C73H(5,𝔽2)11yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C22⋊D73—44no—
305C22⋊D73—44no—
306C22⋊D73—44no—
307C22⋊D73—44no—
308C2×Dic73—21no—
309C2×Dic73—21no—
310C2×Dic73—21no—
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#13112yes—
326D292—44no—
327C4×D73—41no—
328C4×D73—41no—
329C4×D73—41no—
330C4×D73—41no—
331C4×D73—41no—
332C4×D73—41no—
333C4×D73—41no—
334C4×D73—41no—
335Dic146—44no—
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#51811yescharacteristic
359C22×C73#51811yescharacteristic
360C22×C73#51811yescharacteristic
361C22×C73C2×#13111yescharacteristic
362C22×C73#56811yescharacteristic
363C22×C73#56811yescharacteristic
364C22×C73#56811yescharacteristic
365C2×D73—41no—
366C2×D73—41no—
367C2×D73—41no—
368C2×D73—41no—
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
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—41no—
383C4×C73#56011yescharacteristic
384C4×C73#56011yescharacteristic
385C4×C73#56011yescharacteristic
386C4×C73H(3,𝔽4)11yescharacteristic
387Dic73—22no—
388Dic73—41no—
389Dic73—41no—
390Dic73—41no—
391Dic73—41no—
392Dic73—41no—
393#23313—731nomaximal, Sylow
394C2×C73—81no—
395C2×C73—81no—
396C2×C73#237511yescharacteristic
397C2×C73#297611yescharacteristic
398C2×C73#297811yescharacteristic
399C2×C73#297811yescharacteristic
400C2×C73#298011yescharacteristic
401C2×C73#298111yescharacteristic
402C2×C73#298111yescharacteristic
403D73—81no—
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#1870D7311yescharacteristic, complemented
418#1780—731no—
419#1780—731no—
420C73#2331311yescharacteristic, complemented, Sylow
421C22×#41—731no—
422C22×M16C2×D7311yescharacteristic
423C2×C4×D4—731no—
424C2×C4×D4—731no—
425C2×C4×D4C2×D7311yescharacteristic
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⋊C8—731no—
439C2×C22⋊C8—731no—
440C2×C22⋊C8—731no—
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#336C2×D7311yescharacteristic
463#336C2×D7311yescharacteristic
464C2×#41—2921no—
465C2×#41—2921no—
466C2×#41—2921no—
467C2×#41—2921no—
468C2×#41—2921no—
469C2×#41—2921no—
470C22×Q8—731no—
471C22×D4—731no—
472C22×D4—731no—
473C22×D4—731no—
474C22×D4—731no—
475C22×D4—731no—
476C22×D4C4×D7311yescharacteristic
477C23×C4—731no—
478C23×C4—731no—
479C23×C4C22×D7311yescharacteristic
480C23×C4C22×D7311yescharacteristic
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—41no—
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—41no—
493C4×D4—41no—
494C4×D4—2921no—
495C4×D4—2921no—
496C4×D4—2921no—
497C4×D4—2921no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4C4×D7311yescharacteristic
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⋊C4C4×D7311yescharacteristic
512C2×C22⋊C4C4×D7311yescharacteristic
513C2×C42—731no—
514C2×C42—731no—
515C2×C42C22×D7311yescharacteristic
516C4⋊C8—2921no—
517C4⋊C8—2921no—
518C4⋊C8—2921no—
519C22⋊C8—41no—
520C22⋊C8—41no—
521C22⋊C8—41no—
522C22⋊C8—2921no—
523C22⋊C8—2921no—
524C22⋊C8—2921no—
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—
544C24—731no—
545C24C2×C4×D7311yescharacteristic
546C24C2×C4×D7311yescharacteristic
547#41—2924no—
548#41—2924no—
549#41—2924no—
550#41—2924no—
551C2×Q8—2921no—
552C2×Q8—2921no—
553C2×Q8—2921no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—2921no—
558C2×D4—2921no—
559C2×D4—2921no—
560C2×D4—2921no—
561C2×D4—2921no—
562C2×D4—2921no—
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—731no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—731no—
588C22×C4—731no—
589C22×C4—731no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4—1461no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4C2×C4×D7311yescharacteristic
603C22×C4C2×C4×D7311yescharacteristic
604C22×C4C2×C4×D7311yescharacteristic
605C22×C4C2×C4×D7311yescharacteristic
606C22×C4C23×D7311yescharacteristic
607M16—44no—
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—41no—
633C4⋊C4—2921no—
634C4⋊C4—2921no—
635C22⋊C4—41no—
636C22⋊C4—41no—
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—21no—
648C42—21no—
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—1461no—
668C23—1461no—
669C23—1461no—
670C23—1461no—
671C23—1461no—
672C23—1461no—
673C23—1461no—
674C23—1461no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23—1461no—
679C23—1461no—
680C23—1461no—
681C23C22×C4×D7311yescharacteristic
682Q8—2924no—
683D4—44no—
684D4—2924no—
685D4—2924no—
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—21no—
699C2×C4—21no—
700C2×C4—21no—
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—2921no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—2921no—
713C2×C4—2921no—
714C2×C4—2921no—
715C2×C4—2921no—
716C2×C4—2921no—
717C2×C4—732no—
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#1455663711yescharacteristic
740C2×C4#1455663711yescharacteristic
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—2921no—
764C22—2921no—
765C22—2921no—
766C22—2921no—
767C22—2921no—
768C22—2921no—
769C22—2921no—
770C22—2921no—
771C22—2921no—
772C22—2921no—
773C22—2921no—
774C22—2921no—
775C22—2921no—
776C22—2921no—
777C22#1798905911yescharacteristic
778C22#1798905911yescharacteristic
779C22#1798906011yescharacteristic
780C22#131×D7311yescharacteristic
781C22#1798935211yescharacteristic
782C22#1798935311yescharacteristic
783C22#1798935311yescharacteristic
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—2921no—
789C4—2921no—
790C4—2921no—
791C4—2921no—
792C4—2921no—
793C4—1462no—
794C4#1798932511yescharacteristic
795C4#1798932511yescharacteristic
796C4#1798932711yescharacteristic
797C4#1798933011yescharacteristic
798C2—81no—
799C2—81no—
800C2—5841no—
801C2—5841no—
802C2#2261306911yescharacteristic
803C2#2261897511yescharacteristic
804C2#2261898811yescharacteristic
805C2#2261899111yescharacteristic
806C2#2261899911yescharacteristic
807C2#2261900311yescharacteristic
808C2#2261900411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1870C2
prime radical#22613146C2
cosocleC22×C4×C73C24
hypercenter#1870D73
hypocenterC73#23313
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #22610730C2semidirect
3. #22610727C2semidirect
4. #22610723C2semidirect
5. #22610547C2semidirect
6. #22610545C2semidirect
7. #22610542C2semidirect
8. #22610542C2semidirect
9. #22610540C2semidirect
10. #22610538C2semidirect
11. #22610228C2semidirect
12. #22610228C2semidirect
13. #22609842C2semidirect
14. #22609842C2semidirect
15. C73×#1870C2semidirect
417. #1870D73semidirect
420. C73#23313semidirect

Maximal subgroups

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

subgroupindex
#226131462
#226107302
#226107272
#226107232
#226105472
#226105452
#226105422
#226105402
#226105382
#226102282
#226098422
C73×#18702
#2331373