Finite Group Databasebeta

← #29691354

Subgroups — #29691354

Order 15616.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839896C211yesmaximal, characteristic
2#21448512C211yesmaximal, characteristic, complemented
3#21446694C211yesmaximal, characteristic, complemented
4#21446684C211yesmaximal, characteristic, complemented
5#21446519C211yesmaximal, characteristic, complemented
6#21446505C211yesmaximal, characteristic, complemented
7#21446443C211yesmaximal, characteristic, complemented
8#21446436C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic, complemented
11#21446141C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#21445585C211yesmaximal, characteristic, complemented
15C61×#2309C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic, complemented
20#16839896C418yescomplemented
21C2×#14519710C2211yescharacteristic, complemented
22C2×#14519708C2211yescharacteristic, complemented
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519697C2211yescharacteristic, complemented
30C2×#14519697C2211yescharacteristic, complemented
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519688C2211yescharacteristic, complemented
34C2×C4×#92418C2211yescharacteristic, complemented
35#16839664C2211yescharacteristic, complemented
36#16839662—21no—
37#16839660C2211yescharacteristic, complemented
38#16839652—21no—
39#16839638—21no—
40#16839633—21no—
41#16839622C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic, complemented
43#16839524C2211yescharacteristic, complemented
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839517C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49C23×D4×C61C2211yescharacteristic
50C2×#117×C61C2211yescharacteristic
51C2×#117×C61C2211yescharacteristic
52C61×#390—21no—
53C61×#390—21no—
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#379—21no—
59C61×#379—21no—
60C22×D244C2311yescharacteristic
61C22×C22⋊D61—21no—
62C22×C4×D61—21no—
63C2×#11758199—41no—
64C2×#11758199—41no—
65C2×#11758199—41no—
66C2×#11758199—41no—
67C2×#11758199C2×C414yes—
68C2×#11758199C2×C414yes—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519751—22no—
74#14519751C2×C414yes—
75C4×D244—41no—
76C4×D244—41no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×C22⋊Dic61—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×C4×Dic61—21no—
87#14519710—41no—
88#14519708—41no—
89#14519698—41no—
90#14519698—41no—
91#14519698—41no—
92#14519698—41no—
93#14519698C2×C414yescomplemented
94#14519698C2×C414yescomplemented
95#14519697—41no—
96#14519697—41no—
97C22⋊#92418—22no—
98C22⋊#92418C2×C414yescomplemented
99#14519688—41no—
100C4×#92418—41no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104C25×C61—21no—
105C22×D4×C61—21no—
106C22×D4×C61—22no—
107C22×D4×C61—41no—
108C22×D4×C61—41no—
109C22×D4×C61—41no—
110C22×D4×C61—41no—
111C22×D4×C61C2×C414yescomplemented
112C22×D4×C61C2311yescharacteristic
113C22×D4×C61C2311yescharacteristic
114C23×C4×C61C2311yescharacteristic
115#117×C61—41no—
116#117×C61—41no—
117#117×C61—41no—
118#117×C61—41no—
119C2×C4⋊C4×C61D411yescharacteristic
120C2×C4⋊C4×C61D411yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—24no—
140C24×C61—42no—
141C24×C61—42no—
142C24×C61—81no—
143C24×C61—81no—
144C24×C61—81no—
145C24×C61—81no—
146C24×C61C2×D411yescharacteristic
147C23×D61—21no—
148C2×D4×C61—24no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—44no—
160C2×D4×C61—44no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—44no—
164C2×D4×C61—44no—
165C2×D4×C61C22×C412yes—
166C2×D4×C61C22×C412yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C22×C412yes—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61#4112yes—
180C22×C4×C61C2411yescharacteristic
181C2×C22⋊D61—24no—
182C2×C22⋊D61—81no—
183C2×C22⋊D61—81no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244C22×C412yes—
193C2×C4×D61—42no—
194C2×C4×D61—81no—
195C2×C4×D61—81no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—41no—
201C4⋊C4×C61—41no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—41no—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—81no—
206C22⋊C4×C61—81no—
207C22⋊C4×C61—81no—
208C22⋊C4×C61—81no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C22⋊C4×C61—81no—
212C22⋊C4×C61—81no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—42no—
218C22⋊Dic61—81no—
219#11758199—44no—
220#11758199—44no—
221#11758198—24no—
222#11758198—42no—
223#11758198—81no—
224#11758198—81no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61C22×C412yes—
231#11758196—81no—
232C4×Dic61—81no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418C22×C412yes—
244C2×#92418C22×C412yes—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—48no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—84no—
267C23×C61—84no—
268C23×C61—84no—
269C23×C61—84no—
270C23×C61—84no—
271C23×C61—84no—
272C23×C61C4×D412yes—
273C23×C61C22×D411yescharacteristic
274C22×D61—22no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—48no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—41no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61C4×D412yes—
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C22⋊D61—84no—
322C2×Dic61—22no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331D244—22no—
332D244—22no—
333D244—41no—
334D244—41no—
335C4×D61—84no—
336#92418—22no—
337#92418—22no—
338#92418—41no—
339#92418—41no—
340#22056—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—816no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61C2×C4×D411yescharacteristic
364C22×C61#53411yescharacteristic
365C22×C61#53511yescharacteristic
366C22×C61#57611yescharacteristic
367C22×C61#57611yescharacteristic
368C22×C61#57611yescharacteristic
369C22×C61#57711yescharacteristic
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61—81no—
377C4×C61—22no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61—41no—
382C4×C61—81no—
383C4×C61—81no—
384C4×C61#51811yescharacteristic
385C4×C61#51811yescharacteristic
386C4×C61#53811yescharacteristic
387C4×C61#53811yescharacteristic
388Dic61—42no—
389Dic61—81no—
390Dic61—81no—
391C2×#447—611no—
392#2324—611no—
393#2309D6111yescharacteristic, complemented
394#1972—611no—
395#1970—611no—
396#1936—611no—
397#1934—611no—
398#1926—611no—
399#1925—611no—
400#1879—611no—
401#1879—611no—
402#1875—611no—
403#1854—611no—
404#1786—611no—
405#1750—611no—
406C2×C61—42no—
407C2×C61—82no—
408C2×C61—82no—
409C2×C61#232111yescharacteristic
410C2×C61#294611yescharacteristic
411C2×C61#294811yescharacteristic
412C2×C61#319811yescharacteristic
413C2×C61#319911yescharacteristic
414C2×C61#322011yescharacteristic
415C2×C61#322411yescharacteristic
416D61—82no—
417C23×D4C2×D6111yescharacteristic
418C22×D8—611no—
419C22×D8—611no—
420C2×#121—611no—
421C2×C4×D4—611no—
422C2×#117C2×D6111yescharacteristic
423C2×#117C2×D6111yescharacteristic
424#447—618no—
425C2×#107—611no—
426C2×#106—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×C22⋊C8—611no—
436C2×C22⋊C8—611no—
437C2×#97—611no—
438C2×C4×C8—611no—
439#390—21no—
440#390—21no—
441#390—611no—
442#390—1221no—
443#390C2×D6111yescharacteristic
444#390C2×D6111yescharacteristic
445#390C2×D6111yescharacteristic
446#390C2×D6111yescharacteristic
447#389—611no—
448#388—1221no—
449#386—1221no—
450#385—1221no—
451#380—611no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458#340—611no—
459#336—611no—
460#336—611no—
461C61#2205611yescharacteristic, complemented, Sylow
462C25—21no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—41no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—611no—
470C22×D4—1221no—
471C22×D4C4×D6114yescomplemented
472C22×D4C22×D6111yescharacteristic
473C22×D4C22×D6111yescharacteristic
474C23×C4—1221no—
475C23×C4C22×D6111yescharacteristic
476C2×D8—614no—
477C2×D8—614no—
478C2×D8—2441no—
479C2×D8—2441no—
480C2×D8—2441no—
481C2×D8—2441no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—611no—
486#121—614no—
487#121—1222no—
488C4×D4—2441no—
489C4×D4—2441no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4C22⋊D6111yescharacteristic
499C2×C4⋊C4C22⋊D6111yescharacteristic
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4C22⋊D6111yescharacteristic
517C2×C22⋊C4C22⋊D6111yescharacteristic
518C2×C42—21no—
519C2×C42—1221no—
520C2×C42C22×D6111yescharacteristic
521C2×C42C22×D6111yescharacteristic
522#107—2441no—
523#106—2441no—
524#102—614no—
525#102—614no—
526#102—2441no—
527#102—2441no—
528#102—2441no—
529#102—2441no—
530#102—2441no—
531#102—2441no—
532C22⋊C8—614no—
533C22⋊C8—1222no—
534#97—2441no—
535C4×C8—2441no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—1221no—
549C24C2×C22⋊D6111yescharacteristic
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—24no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—612no—
568C2×D4—1224no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—4881no—
575C2×D4—4881no—
576C2×D4C2×C4×D6112yes—
577C2×D4C2×C4×D6112yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—4881no—
588C22×C4—4881no—
589C22×C4—2442no—
590C22×C4C2×C4×D6112yes—
591C22×C4#1175822212yes—
592C22×C4C2×C22⋊D6111yescharacteristic
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598D8—2444no—
599D8—2444no—
600C2×C8—612no—
601C2×C8—612no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—612no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—4881no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—1224no—
637C22⋊C4—4881no—
638C22⋊C4—4881no—
639C22⋊C4—4881no—
640C22⋊C4—2442no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—4881no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—1222no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23C4×C22⋊D6112yes—
682C23C22×C22⋊D6111yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—1222no—
693D4—1222no—
694D4—4884no—
695D4—2441no—
696D4—2441no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—1222no—
722C2×C4—4884no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4C4×C22⋊D6112yes—
732C2×C4C22×C4×D6111yescharacteristic
733C2×C4C2×#1175822211yescharacteristic
734C2×C4#1451982211yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982211yescharacteristic
737C2×C4#1451982211yescharacteristic
738C8—1222no—
739C8—1222no—
740C8—2441no—
741C8—2441no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—816no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—4881no—
765C22—4881no—
766C22—4881no—
767C22—4881no—
768C22—2442no—
769C22—2442no—
770C22—2442no—
771C22C2×C4×C22⋊D6111yescharacteristic
772C22#1684032111yescharacteristic
773C22#1684032911yescharacteristic
774C22#1684056511yescharacteristic
775C22#1684056511yescharacteristic
776C22#1684056511yescharacteristic
777C22#1684057311yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—4881no—
786C4—4881no—
787C4—2442no—
788C4#1684023511yescharacteristic
789C4#1684023511yescharacteristic
790C4#1684035011yescharacteristic
791C4#1684035011yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—4882no—
796C2#2144847711yescharacteristic
797C2#2145465111yescharacteristic
798C2#2145466911yescharacteristic
799C2#2145667111yescharacteristic
800C2#2145668011yescharacteristic
801C2#2145686911yescharacteristic
802C2#2145691311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2309C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
cosocleC22×C4×C61C24
hypercenter#2309D61
hypocenterC61#22056
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #21448512C2semidirect
3. #21446694C2semidirect
4. #21446684C2semidirect
5. #21446519C2semidirect
6. #21446505C2semidirect
7. #21446443C2semidirect
8. #21446436C2semidirect
9. #21446170C2semidirect
10. #21446170C2semidirect
11. #21446141C2semidirect
12. #21446018C2semidirect
13. #21445750C2semidirect
14. #21445585C2semidirect
15. C61×#2309C2semidirect
19. C2×C4×D244C22semidirect
20. #16839896C4semidirect
21. C2×#14519710C22semidirect
22. C2×#14519708C22semidirect
29. C2×#14519697C22semidirect
30. C2×#14519697C22semidirect
33. C2×#14519688C22semidirect
34. C2×C4×#92418C22semidirect
35. #16839664C22semidirect
37. #16839660C22semidirect
42. C4×C4⋊Dic61C22semidirect
43. #16839524C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839517C22semidirect
48. #16839517C22semidirect
93. #14519698C2×C4semidirect
94. #14519698C2×C4semidirect
98. C22⋊#92418C2×C4semidirect
111. C22×D4×C61C2×C4semidirect
393. #2309D61semidirect
461. C61#22056semidirect
471. C22×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398962
#214485122
#214466942
#214466842
#214465192
#214465052
#214464432
#214464362
#214461702
#214461412
#214460182
#214457502
#214455852
C61×#23092
#2205661