Finite Group Databasebeta

← #29730799

Subgroups — #29730799

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840001C211yesmaximal, characteristic, complemented
2C2×#16839989C211yesmaximal, characteristic, complemented
3C2×#16839981C211yesmaximal, characteristic, complemented
4C2×D4×#92418C211yesmaximal, characteristic, complemented
5#21450728C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446631C211yesmaximal, characteristic, complemented
11#21446587C211yesmaximal, characteristic, complemented
12#21446248C211yesmaximal, characteristic, complemented
13#21446243C211yesmaximal, characteristic, complemented
14C4×#14519700C211yesmaximal, characteristic, complemented
15C61×#2540C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23#16840001—24no—
24#16839989—24no—
25#16839981—24no—
26D4×#92418—24no—
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
41#16839693—21no—
42#16839676—21no—
43#16839650—21no—
44#16839650—21no—
45#16839628C2211yescharacteristic
46#16839622C2211yescharacteristic
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×#124×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#399—21no—
59C61×#392—21no—
60C61×#390—21no—
61C61×#390—21no—
62C4×C4⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C2×#11758202—22no—
65C2×#11758202—22no—
66C2×#11758202—41no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—41no—
70C22×#92418—22no—
71C22×#92418—22no—
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418—41no—
75C22×#92418—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519756—22no—
81#14519756—22no—
82#14519756—41no—
83#14519756—41no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C4×Dic61—21no—
97#14519710—22no—
98#14519708—22no—
99C4⋊#92418D414yescomplemented
100#14519701—22no—
101#14519701—22no—
102#14519701—41no—
103#14519700—22no—
104#14519700D414yescomplemented
105#14519698—22no—
106#14519698—22no—
107#14519698—41no—
108C22⋊#92418—22no—
109C22⋊#92418—22no—
110C4×#92418—22no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C22×Q8×C61C2311yescharacteristic
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61D411yescharacteristic
119C22×D4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122#124×C61—22no—
123#124×C61—22no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127C22⋊Q8×C61—41no—
128#121×C61—22no—
129#121×C61—22no—
130#121×C61—41no—
131#121×C61—41no—
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61D411yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#95×C61—21no—
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152C24×C61C2×D411yescharacteristic
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—81no—
173C2×D4×C61—81no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122C2×D412yes—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61C2×D412yes—
210C4⋊C4×C61#4112yes—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C42×C61—81no—
220C42×C61C2×D412yes—
221C42×C61#4112yes—
222C22⋊Dic61—42no—
223C22⋊Dic61—42no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226#11758202—44no—
227#11758200—44no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234#11758196—42no—
235#11758196—42no—
236#11758196—42no—
237C4×Dic61—42no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—44no—
248C2×#92418—44no—
249C2×#92418C2×D412yes—
250C2×#92418C2×D412yes—
251C2×#92418C2×D412yes—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61#13512yes—
272C23×C61#13512yes—
273C23×C61C22×D411yescharacteristic
274Q8×C61—41no—
275Q8×C61—41no—
276Q8×C61—41no—
277Q8×C61—41no—
278D4×C61—28no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—84no—
284D4×C61—84no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
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#12112yes—
313C2×C4×C61#12112yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×Dic61—22no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332Dic122—22no—
333Dic122—22no—
334Dic122—41no—
335Dic122—41no—
336#92418—22no—
337#92418—22no—
338#92418—22no—
339#92418—41no—
340#25389—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61C2×#12111yescharacteristic
363C22×C61D4211yescharacteristic
364C22×C61#54611yescharacteristic
365C22×C61C2×#13511yescharacteristic
366C22×C61C2×#13511yescharacteristic
367C22×C61#57711yescharacteristic
368C22×C61#57811yescharacteristic
369C4×C61—22no—
370C4×C61—22no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61—81no—
376C4×C61#53211yescharacteristic
377C4×C61#54011yescharacteristic
378C4×C61D4211yescharacteristic
379C4×C61#55011yescharacteristic
380Dic61—42no—
381Dic61—81no—
382Dic61—81no—
383Dic61—81no—
384C2×#467—611no—
385C2×#465—611no—
386C2×#464—611no—
387C2×C8×D4—611no—
388#2540D6111yescharacteristic
389#2536—611no—
390#2035—611no—
391#2033—611no—
392#2001—611no—
393#2000—611no—
394#1958—611no—
395#1949—611no—
396#1893—611no—
397#1892—611no—
398C4×#103—611no—
399C2×C61—42no—
400C2×C61—42no—
401C2×C61—161no—
402C2×C61#242811yescharacteristic
403C2×C61#305011yescharacteristic
404C2×C61#306311yescharacteristic
405C2×C61#328211yescharacteristic
406C2×C61#328511yescharacteristic
407C2×C61#329611yescharacteristic
408C2×C61#330011yescharacteristic
409C22×Q16—611no—
410C22×SD16—611no—
411C23×C8—611no—
412C23×C8—611no—
413C2×#124C2×D6111yescharacteristic
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8C2×D6111yescharacteristic
417C2×C22⋊Q8C2×D6111yescharacteristic
418C2×#121C2×D6111yescharacteristic
419C2×#121C2×D6111yescharacteristic
420C2×C4×Q8—611no—
421C2×C4×D4C2×D6111yescharacteristic
422#467—1224no—
423#465—1224no—
424#464—1224no—
425C8×D4—1224no—
426C2×#107—611no—
427C2×#106—611no—
428C2×C4⋊C8—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×C22⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C4×C8—611no—
440#399—21no—
441#398—1221no—
442#394—1221no—
443#392—21no—
444#390—21no—
445#390—21no—
446#388—1221no—
447#388—1221no—
448#382—611no—
449#380—611no—
450#380—611no—
451C4×C4⋊C4C2×D6111yescharacteristic
452#340—611no—
453#340—611no—
454#340—611no—
455#340—611no—
456C61#2538911yescharacteristic, complemented, Sylow
457C22×Q8—611no—
458C22×Q8C22×D6111yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C22⋊D6111yescharacteristic
462C22×D4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C2×Q16—1222no—
466C2×Q16—1222no—
467C2×Q16—2441no—
468C2×SD16—1222no—
469C2×SD16—1222no—
470C2×SD16—2441no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—1222no—
476C22×C8—1222no—
477C22×C8—1222no—
478C22×C8—1222no—
479C22×C8—2441no—
480C22×C8—2441no—
481#124—22no—
482#124—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—41no—
486C22⋊Q8—41no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—2441no—
490C22⋊Q8—2441no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×D4—22no—
498C4×D4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4C22⋊D6111yescharacteristic
508C2×C4⋊C4C22×D6111yescharacteristic
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4C22⋊D6111yescharacteristic
521C2×C22⋊C4C22⋊D6111yescharacteristic
522C2×C42—21no—
523C2×C42—1221no—
524C2×C42C22×D6111yescharacteristic
525#107—1222no—
526#106—1222no—
527C4⋊C8—614no—
528#103—614no—
529#103—1222no—
530#103—1222no—
531#103—1222no—
532#103—2441no—
533#102—1222no—
534#102—1222no—
535#102—2441no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C4×C8—1222no—
539#95—21no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543#95—1221no—
544C24—21no—
545C24C2×C22⋊D6111yescharacteristic
546C24C2×C22⋊D6111yescharacteristic
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—612no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
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—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C2×C22⋊D6111yescharacteristic
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598Q16—2444no—
599SD16—2444no—
600C2×C8—612no—
601C2×C8—612no—
602C2×C8—612no—
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—
612C2×C8—2444no—
613C2×C8—2444no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—22no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—2442no—
626C4⋊C4—2442no—
627C4⋊C4—2442no—
628C4⋊C4D4×D6112yes—
629C4⋊C4#1175822412yes—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—2442no—
639C22⋊C4—2442no—
640C22⋊C4—2442no—
641C22⋊C4—2442no—
642C42—81no—
643C42—2442no—
644C42D4×D6112yes—
645C42#1175822412yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23#1451979712yes—
666C23#1451979712yes—
667C23C22×C22⋊D6111yescharacteristic
668Q8—41no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—1222no—
673Q8—1222no—
674Q8—2441no—
675Q8—2441no—
676D4—28no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
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—1222no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4#1451974912yes—
723C2×C4#1451974912yes—
724C2×C4C2×D4×D6111yescharacteristic
725C2×C4C2×D4×D6111yescharacteristic
726C2×C4C2×#1175822411yescharacteristic
727C2×C4C2×#1175822411yescharacteristic
728C2×C4#1451982211yescharacteristic
729C2×C4#1451982211yescharacteristic
730C8—1222no—
731C8—1222no—
732C8—1222no—
733C8—2441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×#1451974911yescharacteristic
756C22D4×C22⋊D6111yescharacteristic
757C22#1684040611yescharacteristic
758C22C2×#1451979711yescharacteristic
759C22C2×#1451979711yescharacteristic
760C22#1684057311yescharacteristic
761C22#1684057711yescharacteristic
762C4—22no—
763C4—22no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—4881no—
770C4—4881no—
771C4—4881no—
772C4—2442no—
773C4#1684031011yescharacteristic
774C4#1684036611yescharacteristic
775C4#1684039711yescharacteristic
776C4#1684043211yescharacteristic
777C2—42no—
778C2—42no—
779C2—161no—
780C2#2144941011yescharacteristic
781C2#2145539711yescharacteristic
782C2#2145551211yescharacteristic
783C2#2145752211yescharacteristic
784C2#2145755611yescharacteristic
785C2#2145765411yescharacteristic
786C2#2145770611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2540C2
socleC23×C61C22×D4
hypercenter#2540D61
hypocenterC61#25389
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#16840001C2semidirect
2. C2×#16839989C2semidirect
3. C2×#16839981C2semidirect
4. C2×D4×#92418C2semidirect
5. #21450728C2semidirect
6. #21447012C2semidirect
7. #21446998C2semidirect
8. #21446827C2semidirect
9. #21446822C2semidirect
10. #21446631C2semidirect
11. #21446587C2semidirect
12. #21446248C2semidirect
13. #21446243C2semidirect
14. C4×#14519700C2semidirect
99. C4⋊#92418D4semidirect
104. #14519700D4semidirect
456. C61#25389semidirect

Maximal subgroups

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

subgroupindex
C2×#168400012
C2×#168399892
C2×#168399812
C2×D4×#924182
#214507282
#214470122
#214469982
#214468272
#214468222
#214466312
#214465872
#214462482
#214462432
C4×#145197002
C61×#25402
#2538961