Finite Group Databasebeta

← #29700776

Subgroups — #29700776

Order 15616.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455037C211yesmaximal, characteristic
2C2×#16839877C211yesmaximal, characteristic, complemented
3#21454540C211yesmaximal, characteristic, complemented
4C22×#14519704C211yesmaximal, characteristic, complemented
5#21446706C211yesmaximal, characteristic, complemented
6#21446526C211yesmaximal, characteristic, complemented
7#21446464C211yesmaximal, characteristic, complemented
8#21446260C211yesmaximal, characteristic, complemented
9#21446149C211yesmaximal, characteristic, complemented
10#21446146C211yesmaximal, characteristic, complemented
11#21446094C211yesmaximal, characteristic, complemented
12#21446023C211yesmaximal, characteristic, complemented
13#21445654C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic61C211yesmaximal, characteristic, complemented
15C61×#2880C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519783C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic
20#16840273C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839924C411yescharacteristic, complemented
23#16839924C411yescharacteristic, complemented
24#16839918C411yescharacteristic, complemented
25#16839913C411yescharacteristic, complemented
26#16839907C411yescharacteristic, complemented
27#16839907C411yescharacteristic, complemented
28#16839901C411yescharacteristic, complemented
29#16839896C411yescharacteristic, complemented
30#16839877—24no—
31#16839837—21no—
32#16839836—21no—
33#16839830—21no—
34#16839825—21no—
35C2×#14519712C2211yescharacteristic, complemented
36C2×#14519712C2211yescharacteristic, complemented
37#16839788C2211yescharacteristic, complemented
38C2×#14519704—24no—
39C2×#14519704C2211yescharacteristic
40C2×#14519704C2211yescharacteristic
41C2×#14519704C2211yescharacteristic
42C2×#14519704C2211yescharacteristic
43C2×#14519703C2211yescharacteristic, complemented
44C2×#14519703C2211yescharacteristic, complemented
45#16839758C2211yescharacteristic
46#16839758C2211yescharacteristic
47#16839728C2211yescharacteristic, complemented
48C2×C22⋊#92418C2211yescharacteristic
49#16839717C2211yescharacteristic, complemented
50C2×C8×Dic61C2211yescharacteristic, complemented
51C2×C8×Dic61C2211yescharacteristic, complemented
52#16839526C2211yescharacteristic, complemented
53#16839526C2211yescharacteristic, complemented
54#16839523C2211yescharacteristic, complemented
55#16839523C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57#16839516C2211yescharacteristic, complemented
58C22×#41×C61C2211yescharacteristic
59C2×#131×C61C2211yescharacteristic
60C2×#131×C61C2211yescharacteristic
61C61×#408—21no—
62C61×#408—21no—
63C61×#408C2211yescharacteristic
64C61×#408C2211yescharacteristic
65C61×#407—21no—
66C61×#407C2211yescharacteristic
67C2×C22⋊C8×C61—21no—
68C2×C22⋊C8×C61C2211yescharacteristic
69C2×#11758222C2311yescharacteristic
70C23×Dic61—21no—
71#14519797—22no—
72#14519797—22no—
73#14519797—41no—
74#14519797—41no—
75C2×#11758202C2×C411yescharacteristic, complemented
76C2×#11758202C2×C411yescharacteristic, complemented
77C2×#11758200C2×C411yescharacteristic, complemented
78C2×#11758200C2×C411yescharacteristic, complemented
79C2×#11758201C2×C411yescharacteristic, complemented
80C2×#11758201C2×C411yescharacteristic, complemented
81C2×#11758199C2×C411yescharacteristic, complemented
82C2×#11758199C2×C411yescharacteristic, complemented
83#14519783—22no—
84#14519783—41no—
85C2×#11758194—21no—
86C2×#11758194—22no—
87C2×#11758194—41no—
88C2×#11758194C2311yescharacteristic
89C2×#11758194C2311yescharacteristic
90C2×#11758189—21no—
91C22×#92418—21no—
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C2×C8×D61—21no—
95#14519760—21no—
96#14519756C2×C411yescharacteristic
97#14519756C2×C411yescharacteristic
98#14519751C2×C411yescharacteristic
99#14519751C2×C411yescharacteristic
100#14519746—21no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—21no—
103#14519736C2311yescharacteristic
104C2×C4×Dic61—22no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—41no—
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109#14519712—22no—
110#14519712—41no—
111#14519706—21no—
112#14519706—21no—
113#14519704—22no—
114#14519704—22no—
115#14519704—22no—
116#14519704D414yescomplemented
117#14519703—22no—
118#14519703—41no—
119#14519701C2×C411yescharacteristic, complemented
120#14519701C2×C411yescharacteristic, complemented
121#14519701C2×C411yescharacteristic, complemented
122#14519701C2×C411yescharacteristic, complemented
123#14519698C2×C411yescharacteristic, complemented
124#14519698C2×C411yescharacteristic, complemented
125#14519698C2×C411yescharacteristic, complemented
126#14519698C2×C411yescharacteristic, complemented
127C22⋊#92418C2×C411yescharacteristic
128C22⋊#92418C2×C411yescharacteristic
129C22⋊#92418C2×C411yescharacteristic
130C22⋊#92418C2×C411yescharacteristic
131#14519689—21no—
132#14519689—21no—
133#14519687—21no—
134C8×Dic61—21no—
135C8×Dic61—22no—
136C8×Dic61—41no—
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—22no—
140C2×#41×C61—22no—
141C2×#41×C61—41no—
142C2×#41×C61—41no—
143C2×#41×C61C2×C411yescharacteristic
144C2×#41×C61C2×C411yescharacteristic
145C2×#41×C61C2311yescharacteristic
146C2×#41×C61C2311yescharacteristic
147C22×Q8×C61C2×C411yescharacteristic
148C22×D4×C61—21no—
149C22×D4×C61C2×C411yescharacteristic
150C23×C4×C61—21no—
151C23×C4×C61C2311yescharacteristic
152#131×C61—22no—
153#131×C61—22no—
154#131×C61—41no—
155#131×C61—41no—
156C2×M16×C61—21no—
157C2×M16×C61—21no—
158C2×M16×C61C2311yescharacteristic
159C2×M16×C61C2311yescharacteristic
160C22×C8×C61—21no—
161C22×C8×C61—21no—
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164C22⋊C8×C61—21no—
165C22⋊C8×C61—21no—
166C22⋊C8×C61—21no—
167C22⋊C8×C61—21no—
168C22⋊C8×C61—21no—
169C22⋊C8×C61—21no—
170C22⋊C8×C61D411yescharacteristic
171C22⋊C8×C61D411yescharacteristic
172C22⋊C8×C61D411yescharacteristic
173C22⋊C8×C61D411yescharacteristic
174C24×C61—21no—
175C24×C61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—22no—
179#41×C61—22no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61—21no—
183#41×C61—21no—
184#41×C61—42no—
185#41×C61—42no—
186#41×C61—41no—
187#41×C61—41no—
188#41×C61—42no—
189#41×C61—42no—
190#41×C61C2×D412yes—
191#41×C61#4112yes—
192C2×Q8×C61—21no—
193C2×Q8×C61—22no—
194C2×Q8×C61—41no—
195C2×Q8×C61C22×C411yescharacteristic
196C2×Q8×C61C22×C411yescharacteristic
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—41no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61C22×C411yescharacteristic
207C2×D4×C61C22×C411yescharacteristic
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—42no—
218C22×C4×C61—42no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61#4111yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C22×Dic61—21no—
229C22×Dic61—24no—
230C22×Dic61—21no—
231C22×Dic61—42no—
232C22×Dic61—42no—
233#11758222—21no—
234#11758222—21no—
235#11758222—21no—
236#11758222—21no—
237C2×D244C22×C411yescharacteristic
238C2×C4×D61—21no—
239C2×Dic122C22×C411yescharacteristic
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244M16×C61—42no—
245M16×C61—42no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—42no—
253C2×C8×C61—42no—
254C2×C8×C61C2×D411yescharacteristic
255C2×C8×C61C2×D411yescharacteristic
256C2×C8×C61C2×D411yescharacteristic
257C2×C8×C61C2×D411yescharacteristic
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261#11758202—22no—
262#11758202—41no—
263#11758201—22no—
264#11758201—41no—
265#11758200—22no—
266#11758200—41no—
267#11758199—22no—
268#11758199—41no—
269#11758198—21no—
270#11758198—21no—
271C4⋊Dic61C22×C411yescharacteristic
272C4⋊Dic61C22×C411yescharacteristic
273#11758196—21no—
274#11758196—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—42no—
280C4×Dic61C2×D412yes—
281#11758194—21no—
282#11758194—21no—
283#11758194—21no—
284#11758194—42no—
285#11758194C2×D412yes—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—42no—
293C2×#92418C22×C411yescharacteristic
294C2×#92418C22×C411yescharacteristic
295C2×#92418C22×C411yescharacteristic
296C2×#92418C22×C411yescharacteristic
297#11758189—42no—
298C8×D61—42no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—22no—
303C23×C61—21no—
304C23×C61—41no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—81no—
308C23×C61C4×D411yescharacteristic
309C23×C61C4×D411yescharacteristic
310C23×C61C2×#4111yescharacteristic
311C22×D61—21no—
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61—42no—
316Q8×C61C4×D412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—21no—
320D4×C61—21no—
321D4×C61—21no—
322D4×C61—42no—
323D4×C61—42no—
324D4×C61—42no—
325D4×C61—41no—
326D4×C61—41no—
327D4×C61C4×D412yes—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61C4×D411yescharacteristic
348C2×C4×C61C4×D411yescharacteristic
349C2×C4×C61C23×C411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C2×#4111yescharacteristic
353C2×C4×C61H(5,𝔽2)11yescharacteristic
354C2×C4×C61H(5,𝔽2)11yescharacteristic
355C22⋊D61—41no—
356C22⋊D61—41no—
357C22⋊D61—42no—
358C22⋊D61—81no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—48no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369D244—21no—
370D244—21no—
371C4×D61—41no—
372C4×D61—41no—
373Dic122—21no—
374Dic122—21no—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—21no—
378C8×C61—21no—
379C8×C61—41no—
380C8×C61—41no—
381#92418—21no—
382#92418—21no—
383#92418—21no—
384#92418—21no—
385#92418—22no—
386#92418—41no—
387#22888—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—22no—
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—84no—
404C22×C61#44312yescomplemented
405C22×C61C2×C4×D411yescharacteristic
406C22×C61#54611yescharacteristic
407C22×C61#55111yescharacteristic
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—22no—
414C4×C61—41no—
415C4×C61C2×C4×D411yescharacteristic
416C4×C61#51811yescharacteristic
417C4×C61D4211yescharacteristic
418C4×C61#54611yescharacteristic
419Dic61—24no—
420Dic61—42no—
421Dic61—41no—
422Dic61—41no—
423Dic61—41no—
424#3002—611no—
425C2×#443—611no—
426#2933—611no—
427C22×#104—611no—
428#2880D6111yescharacteristic, complemented
429#1974—611no—
430#1937—611no—
431#1929—611no—
432#1896—611no—
433#1876—611no—
434#1876—611no—
435#1866—611no—
436#1855—611no—
437#1764—611no—
438C4×C22⋊C8—611no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61—21no—
442C2×C61—41no—
443C2×C61—42no—
444C2×C61—81no—
445C2×C61#235811yescharacteristic
446C2×C61C2×#44311yescharacteristic
447C2×C61#295611yescharacteristic
448D61—81no—
449C22×#41C2×D6111yescharacteristic
450C2×#135—611no—
451C2×#135—611no—
452C2×#131—611no—
453C2×#131C2×D6111yescharacteristic
454C2×#131C2×D6111yescharacteristic
455C22×M16—611no—
456#525—611no—
457C22×C42—611no—
458#452—611no—
459#452—611no—
460#451—611no—
461#450—611no—
462#449—611no—
463#449—611no—
464#448—611no—
465#447—611no—
466#443—1224no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470C8×D4—1221no—
471C2×#108—611no—
472C2×#108—611no—
473#424—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478C2×#104—611no—
479C2×#104—611no—
480C2×#104—1224no—
481#416—611no—
482#416—611no—
483#408—21no—
484#408—21no—
485#408—611no—
486#408C2×D6111yescharacteristic
487#408C2×D6111yescharacteristic
488#407—21no—
489#407C2×D6111yescharacteristic
490C2×C22⋊C8—21no—
491C2×C22⋊C8—611no—
492C2×C22⋊C8C2×D6111yescharacteristic
493#405—611no—
494C2×C4×C8—611no—
495C2×C4×C8—611no—
496#341—611no—
497#341—611no—
498#339—611no—
499#339—611no—
500#336—611no—
501#336—611no—
502C61#2288811yescharacteristic, complemented, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—611no—
510C2×#41C4×D6111yescharacteristic
511C2×#41C4×D6111yescharacteristic
512C2×#41C22×D6111yescharacteristic
513C2×#41C22×D6111yescharacteristic
514C22×Q8C4×D6111yescharacteristic
515C22×D4—21no—
516C22×D4C4×D6111yescharacteristic
517C23×C4—21no—
518C23×C4—1221no—
519C23×C4C22×D6111yescharacteristic
520#135—1222no—
521#135—1222no—
522#135—2441no—
523#135—2441no—
524C2×Q16—611no—
525C2×Q16—611no—
526C2×SD16—611no—
527C2×SD16—611no—
528C2×SD16—611no—
529C2×SD16—611no—
530C2×D8—611no—
531C2×D8—611no—
532#131—22no—
533#131—22no—
534#131—41no—
535#131—41no—
536#131—1222no—
537#131—2441no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—611no—
541C2×M16—611no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1222no—
545C2×M16—2441no—
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—611no—
551C22×C8—611no—
552C22×C8—1221no—
553C22×C8—1221no—
554C22×C8C22×D6111yescharacteristic
555C22×C8C22×D6111yescharacteristic
556#123—1221no—
557C22⋊Q8—611no—
558C22⋊Q8—611no—
559#121—611no—
560#121—611no—
561#120—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564#117—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—1222no—
568C2×C42—1221no—
569C2×C42—2441no—
570#108—1222no—
571#108—2441no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—614no—
575#104—1222no—
576#104—1222no—
577#104—1222no—
578#104—1222no—
579#104—2441no—
580#103—611no—
581#103—611no—
582#103—611no—
583#103—611no—
584#102—611no—
585#102—611no—
586#102—611no—
587#102—611no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—611no—
595C22⋊C8—611no—
596C22⋊C8—611no—
597C22⋊C8—611no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8C22⋊D6111yescharacteristic
601C22⋊C8C22⋊D6111yescharacteristic
602C22⋊C8C22⋊D6111yescharacteristic
603C22⋊C8C22⋊D6111yescharacteristic
604#97—1221no—
605C4×C8—1222no—
606C4×C8—1221no—
607C4×C8—2441no—
608C24—21no—
609C24#1175822211yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—42no—
619#41—42no—
620#41—41no—
621#41—41no—
622#41—42no—
623#41—42no—
624#41—1221no—
625#41—1221no—
626#41—1221no—
627#41—1221no—
628#41D4×D6112yes—
629#41#1175822412yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8—611no—
634C2×Q8C2×C4×D6111yescharacteristic
635C2×Q8C2×C4×D6111yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—611no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4C2×C4×D6111yescharacteristic
650C2×D4C2×C4×D6111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—1221no—
663C22×C4—1224no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4C2×C4×D6111yescharacteristic
669C22×C4C2×C4×D6111yescharacteristic
670C22×C4#1175822211yescharacteristic
671C22×C4C2×C22⋊D6111yescharacteristic
672C22×C4C2×C22⋊D6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—1222no—
675Q16—2441no—
676SD16—1222no—
677SD16—1222no—
678SD16—2441no—
679SD16—2441no—
680D8—1222no—
681D8—2441no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—42no—
687M16—42no—
688M16—612no—
689M16—1221no—
690M16—1221no—
691M16—1221no—
692M16—2442no—
693M16—2442no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—611no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8C2×C22⋊D6111yescharacteristic
715C2×C8C2×C22⋊D6111yescharacteristic
716C2×C8C2×C22⋊D6111yescharacteristic
717C2×C8C2×C22⋊D6111yescharacteristic
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C42—612no—
728C42—1221no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—2442no—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—1221no—
743C23C4×C22⋊D6111yescharacteristic
744C23C4×C22⋊D6111yescharacteristic
745C23C2×#1175822211yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—1221no—
751Q8—1221no—
752Q8#1451973712yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—1221no—
764D4—1221no—
765D4—4881no—
766D4—2442no—
767D4—2441no—
768D4—2441no—
769D4#1451973712yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—2448no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4C4×C22⋊D6111yescharacteristic
802C2×C4C4×C22⋊D6111yescharacteristic
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C22×C22⋊D6111yescharacteristic
806C2×C4C2×#1175822411yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982211yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—41no—
814C8—41no—
815C8—1221no—
816C8—1221no—
817C8—1221no—
818C8—1221no—
819C8—1222no—
820C8—2441no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22#1683987712yescomplemented
841C22C2×C4×C22⋊D6111yescharacteristic
842C22#1684040211yescharacteristic
843C22#1684043811yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—1224no—
849C4—2442no—
850C4—2441no—
851C4—2441no—
852C4—2441no—
853C4C2×#1451973711yescharacteristic
854C4#1684023511yescharacteristic
855C4D4×C22⋊D6111yescharacteristic
856C4#1684040611yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—4881no—
864C2#2144879811yescharacteristic
865C2C2×#1683987711yescharacteristic
866C2#2145472611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2880C2
socleC22×C61C2×C4×D4
prime radical#21455037C2
cosocleC22×C4×C61C24
hypercenter#2880D61
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#16839877C2semidirect
3. #21454540C2semidirect
4. C22×#14519704C2semidirect
5. #21446706C2semidirect
6. #21446526C2semidirect
7. #21446464C2semidirect
8. #21446260C2semidirect
9. #21446149C2semidirect
10. #21446146C2semidirect
11. #21446094C2semidirect
12. #21446023C2semidirect
13. #21445654C2semidirect
14. C22⋊C8×Dic61C2semidirect
15. C61×#2880C2semidirect
18. C2×#14519783C22semidirect
22. #16839924C4semidirect
23. #16839924C4semidirect
24. #16839918C4semidirect
25. #16839913C4semidirect
26. #16839907C4semidirect
27. #16839907C4semidirect
28. #16839901C4semidirect
29. #16839896C4semidirect
35. C2×#14519712C22semidirect
36. C2×#14519712C22semidirect
37. #16839788C22semidirect
43. C2×#14519703C22semidirect
44. C2×#14519703C22semidirect
47. #16839728C22semidirect
49. #16839717C22semidirect
50. C2×C8×Dic61C22semidirect
51. C2×C8×Dic61C22semidirect
52. #16839526C22semidirect
53. #16839526C22semidirect
54. #16839523C22semidirect
55. #16839523C22semidirect
56. #16839516C22semidirect
57. #16839516C22semidirect
75. C2×#11758202C2×C4semidirect
76. C2×#11758202C2×C4semidirect
77. C2×#11758200C2×C4semidirect
78. C2×#11758200C2×C4semidirect
79. C2×#11758201C2×C4semidirect
80. C2×#11758201C2×C4semidirect
81. C2×#11758199C2×C4semidirect
82. C2×#11758199C2×C4semidirect
116. #14519704D4semidirect
119. #14519701C2×C4semidirect
120. #14519701C2×C4semidirect
121. #14519701C2×C4semidirect
122. #14519701C2×C4semidirect
123. #14519698C2×C4semidirect
124. #14519698C2×C4semidirect
125. #14519698C2×C4semidirect
126. #14519698C2×C4semidirect
404. C22×C61#443semidirect
428. #2880D61semidirect
502. C61#22888semidirect
840. C22#16839877semidirect

Maximal subgroups

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

subgroupindex
#214550372
C2×#168398772
#214545402
C22×#145197042
#214467062
#214465262
#214464642
#214462602
#214461492
#214461462
#214460942
#214460232
#214456542
C22⋊C8×Dic612
C61×#28802
#2288861