Finite Group Databasebeta

← #29691348

Subgroups — #29691348

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×#16839895C211yesmaximal, characteristic
2#21448399C211yesmaximal, characteristic, complemented
3#21446694C211yesmaximal, characteristic, complemented
4#21446684C211yesmaximal, characteristic, complemented
5#21446515C211yesmaximal, characteristic, complemented
6#21446501C211yesmaximal, characteristic, complemented
7#21446446C211yesmaximal, characteristic, complemented
8#21446439C211yesmaximal, characteristic, complemented
9#21446167C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446142C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21445749C211yesmaximal, characteristic, complemented
14#21445585C211yesmaximal, characteristic, complemented
15C61×#2324C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16839895C418yescomplemented
21C2×#14519710C2211yescharacteristic, complemented
22C2×#14519708C2211yescharacteristic, complemented
23C2×#14519698C2211yescharacteristic, complemented
24C2×#14519698C2211yescharacteristic, complemented
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519688C2211yescharacteristic, complemented
34C2×C4×#92418C2211yescharacteristic, complemented
35#16839664C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839664C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839663—21no—
40#16839663—21no—
41#16839617—21no—
42#16839617—21no—
43#16839524C2211yescharacteristic, complemented
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839517C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49C2×#121×C61C2211yescharacteristic
50C2×C4×D4×C61C2211yescharacteristic, complemented
51C2×#117×C61C2211yescharacteristic
52C61×#390—21no—
53C61×#390C2211yescharacteristic, complemented
54C61×#389C2211yescharacteristic, complemented
55C61×#388—21no—
56C61×#386—21no—
57C61×#385—21no—
58C61×#380C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic, complemented
60C24×D61—21no—
61C22×D244—21no—
62C22×D244—22no—
63C22×D244—41no—
64C22×D244—41no—
65C22×D244—41no—
66C22×D244—41no—
67C22×D244C2×C414yescomplemented
68C22×D244C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C2×#11758199—41no—
71C2×#11758199—41no—
72C2×#11758199—41no—
73C2×#11758199—41no—
74C2×#11758199C2×C414yes—
75C2×#11758199C2×C414yes—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519736—41no—
81#14519736—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C22⋊Dic61—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×C4×Dic61—21no—
94#14519710—41no—
95#14519708—41no—
96#14519698—41no—
97#14519698—41no—
98#14519697—41no—
99#14519697—41no—
100#14519697—41no—
101#14519697—41no—
102#14519697C2×C414yescomplemented
103#14519697C2×C414yescomplemented
104C22⋊#92418—22no—
105C22⋊#92418C2×C414yescomplemented
106#14519688—41no—
107C4×#92418—41no—
108C22×D4×C61—21no—
109C22×D4×C61C2311yescharacteristic
110C23×C4×C61—21no—
111C23×C4×C61C2311yescharacteristic
112#121×C61—22no—
113#121×C61C2×C414yes—
114C4×D4×C61—41no—
115C4×D4×C61—41no—
116#117×C61—41no—
117#117×C61—41no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61D411yescharacteristic
120C2×C4⋊C4×C61D411yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
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×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61—21no—
132C2×C42×C61C2311yescharacteristic
133C2×C42×C61C2311yescharacteristic
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137C24×C61—21no—
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—81no—
145C23×D61—81no—
146C23×D61—81no—
147C23×D61—81no—
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—81no—
155C2×D4×C61—81no—
156C2×D4×C61C22×C412yes—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—42no—
165C22×C4×C61—81no—
166C22×C4×C61—81no—
167C22×C4×C61C22×C412yes—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61#4112yes—
174C22×C4×C61C2411yescharacteristic
175C22×Dic61—21no—
176C22×Dic61—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—24no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—44no—
189C2×D244—44no—
190C2×D244—42no—
191C2×D244—42no—
192C2×D244—44no—
193C2×D244—44no—
194C2×D244C22×C412yes—
195C2×D244C22×C412yes—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—41no—
202C4⋊C4×C61—41no—
203C4⋊C4×C61—81no—
204C4⋊C4×C61C22×C412yes—
205C22⋊C4×C61—24no—
206C22⋊C4×C61—41no—
207C22⋊C4×C61—41no—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C22⋊C4×C61—81no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—81no—
217C22⋊Dic61—42no—
218#11758199—44no—
219#11758199—44no—
220#11758198—81no—
221#11758198—81no—
222#11758198—81no—
223#11758198—81no—
224#11758198—81no—
225#11758198—81no—
226#11758198—81no—
227#11758198—81no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4×Dic61—42no—
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—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C4×D412yes—
259C23×C61C22×D411yescharacteristic
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—48no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61—84no—
278C22×D61—84no—
279C22×D61—84no—
280C22×D61—84no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—84no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
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—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—84no—
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
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327D244—22no—
328D244—22no—
329D244—22no—
330D244—22no—
331D244—48no—
332D244—41no—
333D244—41no—
334D244—41no—
335D244—41no—
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—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61C2×C4×D411yescharacteristic
356C22×C61#53411yescharacteristic
357C22×C61#53511yescharacteristic
358C22×C61#57611yescharacteristic
359C22×C61#57611yescharacteristic
360C22×C61#57611yescharacteristic
361C22×C61#57711yescharacteristic
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—816no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
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—42no—
383C4×C61—81no—
384C4×C61—81no—
385C4×C61#51811yescharacteristic
386C4×C61#51811yescharacteristic
387C4×C61#53811yescharacteristic
388C4×C61#53811yescharacteristic
389Dic61—81no—
390Dic61—81no—
391C2×#447—611no—
392#2324D6111yescharacteristic, complemented
393#2309—611no—
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#232111yescharacteristic
409C2×C61#294611yescharacteristic
410C2×C61#294811yescharacteristic
411C2×C61#319811yescharacteristic
412C2×C61#319911yescharacteristic
413C2×C61#322011yescharacteristic
414C2×C61#322411yescharacteristic
415D61—82no—
416D61—82no—
417C23×D4—611no—
418C22×D8—611no—
419C22×D8—611no—
420C2×#121C2×D6111yescharacteristic
421C2×C4×D4C2×D6111yescharacteristic, complemented
422C2×#117—611no—
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—611no—
441#390—611no—
442#390—611no—
443#390—611no—
444#390—1221no—
445#390—1221no—
446#390C2×D6111yescharacteristic, complemented
447#389C2×D6111yescharacteristic, complemented
448#388—21no—
449#386—21no—
450#385—21no—
451#380C2×D6111yescharacteristic
452#379—1221no—
453#379—1221no—
454C4×C4⋊C4C2×D6111yescharacteristic, complemented
455#340—611no—
456#340—611no—
457#340—611no—
458#340—611no—
459#336—611no—
460#336—611no—
461C61#2205611yescharacteristic, complemented, Sylow
462C25—1221no—
463C22×D4—21no—
464C22×D4—614no—
465C22×D4—611no—
466C22×D4—611no—
467C22×D4—1222no—
468C22×D4—1221no—
469C22×D4—2441no—
470C22×D4—2441no—
471C22×D4—2441no—
472C22×D4—2441no—
473C22×D4C22×D6111yescharacteristic
474C23×C4—21no—
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—22no—
487#121C4×D6114yes—
488C4×D4—41no—
489C4×D4—41no—
490#117—41no—
491#117—41no—
492#117—2441no—
493#117—2441no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4C22⋊D6111yescharacteristic
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—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
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—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—1224no—
541C24—1221no—
542C24—1221no—
543C24—4881no—
544C24—4881no—
545C24—4881no—
546C24—4881no—
547C24—2442no—
548C24—2442no—
549C24C2×C22⋊D6111yescharacteristic
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—612no—
559C2×D4—612no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1224no—
571C2×D4—2444no—
572C2×D4—2444no—
573C2×D4—2442no—
574C2×D4—2442no—
575C2×D4—2444no—
576C2×D4—2444no—
577C2×D4C2×C4×D6112yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—1221no—
589C22×C4—1221no—
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—21no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—81no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4C2×C4×D6112yes—
625C22⋊C4—24no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—4881no—
633C22⋊C4—4881no—
634C22⋊C4—4881no—
635C22⋊C4—4881no—
636C22⋊C4—4881no—
637C22⋊C4—4881no—
638C22⋊C4—4881no—
639C22⋊C4—4881no—
640C22⋊C4—2442no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—81no—
646C42—2442no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—1222no—
661C23—1222no—
662C23—4884no—
663C23—4884no—
664C23—4884no—
665C23—4884no—
666C23—4884no—
667C23—4884no—
668C23—2448no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23C4×C22⋊D6112yes—
682C23C22×C22⋊D6111yescharacteristic
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—1222no—
689D4—1222no—
690D4—1222no—
691D4—1222no—
692D4—2448no—
693D4—2441no—
694D4—2441no—
695D4—2441no—
696D4—2441no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
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—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
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#1451982311yescharacteristic
737C2×C4#1451982311yescharacteristic
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—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—48816no—
757C22—4881no—
758C22—4881no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22—4881no—
763C22—4881no—
764C22—4881no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22—2442no—
769C22—2442no—
770C22—2442no—
771C22C2×C4×C22⋊D6111yescharacteristic
772C22#1684032111yescharacteristic
773C22#1684032611yescharacteristic
774C22#1684056511yescharacteristic
775C22#1684056511yescharacteristic
776C22#1684056511yescharacteristic
777C22#1684057011yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—4881no—
787C4—4881no—
788C4#1684023411yescharacteristic
789C4#1684023411yescharacteristic
790C4#1684034511yescharacteristic
791C4#1684034511yescharacteristic
792C2—42no—
793C2—82no—
794C2—4882no—
795C2—4882no—
796C2#2144847311yescharacteristic
797C2#2145464711yescharacteristic
798C2#2145466911yescharacteristic
799C2#2145666511yescharacteristic
800C2#2145668011yescharacteristic
801C2#2145686311yescharacteristic
802C2#2145690711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2324C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
cosocleC22×C4×C61C24
hypercenter#2324D61
hypocenterC61#22056
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #21448399C2semidirect
3. #21446694C2semidirect
4. #21446684C2semidirect
5. #21446515C2semidirect
6. #21446501C2semidirect
7. #21446446C2semidirect
8. #21446439C2semidirect
9. #21446167C2semidirect
10. #21446167C2semidirect
11. #21446142C2semidirect
12. #21446016C2semidirect
13. #21445749C2semidirect
14. #21445585C2semidirect
15. C61×#2324C2semidirect
20. #16839895C4semidirect
21. C2×#14519710C22semidirect
22. C2×#14519708C22semidirect
23. C2×#14519698C22semidirect
24. C2×#14519698C22semidirect
33. C2×#14519688C22semidirect
34. C2×C4×#92418C22semidirect
43. #16839524C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839517C22semidirect
48. #16839517C22semidirect
50. C2×C4×D4×C61C22semidirect
53. C61×#390C22semidirect
54. C61×#389C22semidirect
59. C4×C4⋊C4×C61C22semidirect
67. C22×D244C2×C4semidirect
102. #14519697C2×C4semidirect
103. #14519697C2×C4semidirect
105. C22⋊#92418C2×C4semidirect
392. #2324D61semidirect
421. C2×C4×D4C2×D61semidirect
446. #390C2×D61semidirect
447. #389C2×D61semidirect
454. C4×C4⋊C4C2×D61semidirect
461. C61#22056semidirect

Maximal subgroups

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

subgroupindex
C2×#168398952
#214483992
#214466942
#214466842
#214465152
#214465012
#214464462
#214464392
#214461672
#214461422
#214460162
#214457492
#214455852
C61×#23242
#2205661