Finite Group Databasebeta

← #29730993

Subgroups — #29730993

Order 15616.

1034 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840018C211yesmaximal, characteristic, complemented
2C2×#16839989C211yesmaximal, characteristic, complemented
3C2×#16839981C211yesmaximal, characteristic, complemented
4C2×#16839834C211yesmaximal, characteristic, complemented
5#21450741C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446636C211yesmaximal, characteristic, complemented
11#21446582C211yesmaximal, characteristic, complemented
12#21446258C211yesmaximal, characteristic, complemented
13#21446243C211yesmaximal, characteristic, complemented
14#21445652C211yesmaximal, characteristic, complemented
15C61×#2540C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23#16840018—24no—
24#16839989—24no—
25#16839981—24no—
26#16839834—24no—
27C2×#14519708C2211yescharacteristic
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×#14519688C2211yescharacteristic
41#16839685—21no—
42#16839685—21no—
43#16839665—21no—
44#16839658—21no—
45#16839632C2211yescharacteristic
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—
70C2×#11758194—22no—
71C2×#11758194—22no—
72C2×#11758194—41no—
73C22×#92418—22no—
74C22×#92418—22no—
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⋊Dic61—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C4×Dic61—21no—
99#14519708—22no—
100#14519708—22no—
101C4⋊#92418D414yescomplemented
102#14519701—22no—
103#14519701—22no—
104#14519701—41no—
105#14519700—22no—
106#14519700D414yescomplemented
107#14519698—22no—
108#14519698—22no—
109#14519698—41no—
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112#14519688—22no—
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—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—41no—
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—81no—
225C22⋊Dic61—81no—
226#11758202—44no—
227#11758200—44no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—42no—
235C4⋊Dic61—81no—
236#11758196—42no—
237#11758196—42no—
238#11758196—42no—
239C4×Dic61—42no—
240#11758194—44no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—44no—
251C2×#92418C2×D412yes—
252C2×#92418C2×D412yes—
253C2×#92418C2×D412yes—
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—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61#13712yes—
275C23×C61C22×D411yescharacteristic
276Q8×C61—41no—
277Q8×C61—41no—
278Q8×C61—41no—
279Q8×C61—41no—
280D4×C61—44no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—84no—
286D4×C61—84no—
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—21no—
294C2×C4×C61—21no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
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—41no—
313C2×C4×C61—41no—
314C2×C4×C61#12112yes—
315C2×C4×C61#12112yes—
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
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—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334Dic122—22no—
335Dic122—22no—
336Dic122—41no—
337Dic122—41no—
338#92418—22no—
339#92418—22no—
340#92418—22no—
341#92418—41no—
342#25403—611nomaximal, Sylow
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—41no—
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—41no—
356C22×C61—41no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61C2×#12111yescharacteristic
365C22×C61D4211yescharacteristic
366C22×C61#54611yescharacteristic
367C22×C61C2×#13711yescharacteristic
368C22×C61#57511yescharacteristic
369C22×C61#57711yescharacteristic
370C22×C61#57711yescharacteristic
371C4×C61—22no—
372C4×C61—22no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61—81no—
378C4×C61#53211yescharacteristic
379C4×C61#54011yescharacteristic
380C4×C61D4211yescharacteristic
381C4×C61#55011yescharacteristic
382Dic61—42no—
383Dic61—81no—
384Dic61—81no—
385Dic61—81no—
386C2×#470—611no—
387C2×#465—611no—
388C2×#464—611no—
389C2×#435—611no—
390#2540D6111yescharacteristic
391#2538—611no—
392#2035—611no—
393#2034—611no—
394#2001—611no—
395#2000—611no—
396#1959—611no—
397#1948—611no—
398#1895—611no—
399#1892—611no—
400#1763—611no—
401C2×C61—42no—
402C2×C61—81no—
403C2×C61—161no—
404C2×C61#242811yescharacteristic
405C2×C61#305611yescharacteristic
406C2×C61#306011yescharacteristic
407C2×C61#326611yescharacteristic
408C2×C61#327111yescharacteristic
409C2×C61#331111yescharacteristic
410C2×C61#331611yescharacteristic
411C22×Q16—611no—
412C22×SD16—611no—
413C22×M16—611no—
414C23×C8—611no—
415C2×#124C2×D6111yescharacteristic
416C2×C22⋊Q8—611no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8C2×D6111yescharacteristic
419C2×C22⋊Q8C2×D6111yescharacteristic
420C2×#121C2×D6111yescharacteristic
421C2×#121C2×D6111yescharacteristic
422C2×C4×Q8—611no—
423C2×C4×D4C2×D6111yescharacteristic
424#470—1224no—
425#465—1224no—
426#464—1224no—
427#435—1224no—
428C2×#106—611no—
429C2×#106—611no—
430C2×C4⋊C8—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×#97—611no—
442#399—21no—
443#396—1221no—
444#396—1221no—
445#392—21no—
446#390—21no—
447#390—21no—
448#390—1221no—
449#389—1221no—
450#384—611no—
451#380—611no—
452#380—611no—
453C4×C4⋊C4C2×D6111yescharacteristic
454#340—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458C61#2540311yescharacteristic, complemented, Sylow
459C22×Q8—611no—
460C22×Q8C22×D6111yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C22⋊D6111yescharacteristic
464C22×D4C22×D6111yescharacteristic
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C2×Q16—1222no—
468C2×Q16—1222no—
469C2×Q16—2441no—
470C2×SD16—1222no—
471C2×SD16—1222no—
472C2×SD16—2441no—
473C2×M16—1222no—
474C2×M16—1222no—
475C2×M16—2441no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—1222no—
481C22×C8—1222no—
482C22×C8—2441no—
483#124—22no—
484#124—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—41no—
488C22⋊Q8—41no—
489C22⋊Q8—1222no—
490C22⋊Q8—1222no—
491C22⋊Q8—2441no—
492C22⋊Q8—2441no—
493#121—22no—
494#121—22no—
495#121—41no—
496#121—41no—
497C4×Q8—1222no—
498C4×Q8—1222no—
499C4×D4—22no—
500C4×D4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22⋊D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4C22⋊D6111yescharacteristic
525C2×C22⋊C4C22⋊D6111yescharacteristic
526C2×C42—21no—
527C2×C42—1221no—
528C2×C42C22×D6111yescharacteristic
529#106—1222no—
530#106—1222no—
531C4⋊C8—614no—
532#103—614no—
533#103—1222no—
534#103—1222no—
535#103—1222no—
536#103—2441no—
537#102—1222no—
538#102—1222no—
539#102—2441no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542#97—1222no—
543#95—21no—
544#95—1221no—
545#95—1221no—
546C24—21no—
547C24C2×C22⋊D6111yescharacteristic
548C24C2×C22⋊D6111yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—612no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8—1221no—
560C2×Q8—1221no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—41no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—81no—
575C2×D4—81no—
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—21no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C23×D6111yescharacteristic
600Q16—2444no—
601SD16—2444no—
602M16—2444no—
603C2×C8—612no—
604C2×C8—612no—
605C2×C8—612no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—2444no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—22no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—4881no—
628C4⋊C4—2442no—
629C4⋊C4—2442no—
630C4⋊C4—2442no—
631C4⋊C4—2442no—
632C4⋊C4D4×D6112yes—
633C4⋊C4#1175822412yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—4881no—
643C22⋊C4—4881no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C42—81no—
647C42—2442no—
648C42D4×D6112yes—
649C42#1175822412yes—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23#1451980712yes—
671C23C22×C22⋊D6111yescharacteristic
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—1222no—
677Q8—1222no—
678Q8—2441no—
679Q8—2441no—
680D4—44no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—84no—
686D4—84no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
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—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—1222no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4#1451974912yes—
727C2×C4#1451974912yes—
728C2×C4C2×D4×D6111yescharacteristic
729C2×C4C2×D4×D6111yescharacteristic
730C2×C4C2×#1175822411yescharacteristic
731C2×C4C2×#1175822411yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982211yescharacteristic
734C8—1222no—
735C8—1222no—
736C8—1222no—
737C8—2441no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C2×#1451974911yescharacteristic
760C22D4×C22⋊D6111yescharacteristic
761C22#1684040611yescharacteristic
762C22C2×#1451980711yescharacteristic
763C22#1684056011yescharacteristic
764C22#1684057011yescharacteristic
765C22#1684057311yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—81no—
773C4—4881no—
774C4—4881no—
775C4—4881no—
776C4—2442no—
777C4#1684031011yescharacteristic
778C4#1684036611yescharacteristic
779C4#1684039711yescharacteristic
780C4#1684043211yescharacteristic
781C2—42no—
782C2—81no—
783C2—161no—
784C2#2144941011yescharacteristic
785C2#2145545111yescharacteristic
786C2#2145547811yescharacteristic
787C2#2145732511yescharacteristic
788C2#2145740511yescharacteristic
789C2#2145785511yescharacteristic
790C2#2145793011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2540C2
socleC23×C61C22×D4
hypercenter#2540D61
hypocenterC61#25403
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×#16840018C2semidirect
2. C2×#16839989C2semidirect
3. C2×#16839981C2semidirect
4. C2×#16839834C2semidirect
5. #21450741C2semidirect
6. #21447012C2semidirect
7. #21447005C2semidirect
8. #21446827C2semidirect
9. #21446822C2semidirect
10. #21446636C2semidirect
11. #21446582C2semidirect
12. #21446258C2semidirect
13. #21446243C2semidirect
14. #21445652C2semidirect
101. C4⋊#92418D4semidirect
106. #14519700D4semidirect
458. C61#25403semidirect

Maximal subgroups

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

subgroupindex
C2×#168400182
C2×#168399892
C2×#168399812
C2×#168398342
#214507412
#214470122
#214470052
#214468272
#214468222
#214466362
#214465822
#214462582
#214462432
#214456522
C61×#25402
#2540361