Finite Group Databasebeta

← #29700779

Subgroups — #29700779

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#21455033C211yesmaximal, characteristic
2C2×#16839876C211yesmaximal, characteristic, complemented
3#21454549C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic, complemented
5#21454267C211yesmaximal, characteristic, complemented
6#21446520C211yesmaximal, characteristic, complemented
7#21446464C211yesmaximal, characteristic, complemented
8#21446259C211yesmaximal, characteristic, complemented
9#21446149C211yesmaximal, characteristic, complemented
10#21446148C211yesmaximal, characteristic, complemented
11#21446091C211yesmaximal, characteristic, complemented
12#21446022C211yesmaximal, characteristic, complemented
13#21445656C211yesmaximal, characteristic, complemented
14C4×#14519689C211yesmaximal, characteristic, complemented
15C61×#1974C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519785C2211yescharacteristic
19C2×#14519784C2211yescharacteristic, complemented
20C2×#14519783C2211yescharacteristic
21C2×M16×D61C2211yescharacteristic
22#16840269C2211yescharacteristic
23C2×C42×D61C2211yescharacteristic
24#16839923C411yescharacteristic, complemented
25#16839921C411yescharacteristic, complemented
26#16839916C411yescharacteristic, complemented
27#16839911C411yescharacteristic, complemented
28#16839906C411yescharacteristic, complemented
29#16839904C411yescharacteristic, complemented
30#16839899C411yescharacteristic, complemented
31#16839894C411yescharacteristic, complemented
32#16839876—24no—
33#16839837—21no—
34#16839836—21no—
35#16839830—21no—
36#16839825—21no—
37C2×#14519712C2211yescharacteristic, complemented
38#16839790C2211yescharacteristic, complemented
39C2×#14519705C2211yescharacteristic
40C2×#14519704C2211yescharacteristic
41C2×#14519704C2211yescharacteristic, complemented
42C2×#14519703C2211yescharacteristic
43#104×D61—24no—
44#16839759C2211yescharacteristic
45#16839758C2211yescharacteristic
46#16839729C2211yescharacteristic
47#16839727—21no—
48#16839727—21no—
49#16839725C2211yescharacteristic
50#16839724—21no—
51C2×#14519689C2211yescharacteristic
52C2×#14519689C2211yescharacteristic
53C22⋊C8×D61—21no—
54#16839717C2211yescharacteristic, complemented
55C2×C4×#92418C2211yescharacteristic, complemented
56#16839527C2211yescharacteristic, complemented
57#16839526C2211yescharacteristic, complemented
58#16839523C2211yescharacteristic, complemented
59#16839522C2211yescharacteristic, complemented
60#16839516C2211yescharacteristic, complemented
61#16839516C2211yescharacteristic, complemented
62C2×#135×C61C2211yescharacteristic
63C2×#108×C61C2211yescharacteristic, complemented
64C2×#104×C61C2211yescharacteristic
65C2×#104×C61C2211yescharacteristic, complemented
66C61×#408C2211yescharacteristic
67C61×#408C2211yescharacteristic, complemented
68C2×C4×C8×C61C2211yescharacteristic, complemented
69C2×#11758226C2×C411yescharacteristic
70C2×#11758222—21no—
71C2×#11758222C2311yescharacteristic
72C2×#11758224—21no—
73C2×#11758224C2×C411yescharacteristic
74#41×D61—22no—
75#41×D61—22no—
76#41×D61—41no—
77#41×D61—41no—
78C2×Q8×D61C2×C411yescharacteristic
79C2×D4×D61—21no—
80C2×D4×D61C2×C411yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84#14519797—22no—
85#14519797—22no—
86C2×#11758202C2×C411yescharacteristic, complemented
87C2×#11758200C2×C411yescharacteristic, complemented
88C2×#11758201C2×C411yescharacteristic, complemented
89C2×#11758199C2×C411yescharacteristic, complemented
90#14519785—22no—
91#14519785—41no—
92#14519784—22no—
93#14519784—41no—
94#14519783—22no—
95#14519783—41no—
96C2×#11758194—21no—
97C2×#11758194C2311yescharacteristic
98C2×#11758194C2311yescharacteristic
99C2×#11758189—21no—
100C2×#11758189—21no—
101C2×#11758189—21no—
102M16×D61—22no—
103M16×D61—41no—
104C22×#92418—21no—
105C22×#92418C2311yescharacteristic
106C22×#92418C2311yescharacteristic
107C2×C8×D61—21no—
108C2×C8×D61—21no—
109C2×C8×D61—21no—
110#14519758—21no—
111#14519753C2×C411yescharacteristic
112#14519753C2×C411yescharacteristic
113#14519748C2×C411yescharacteristic
114#14519748C2×C411yescharacteristic
115#14519745—21no—
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118#14519736C2311yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2311yescharacteristic
121C42×D61—22no—
122C42×D61—41no—
123#14519712—22no—
124#14519706—21no—
125#14519706—21no—
126#14519705D414yescomplemented
127#14519704—22no—
128#14519704—41no—
129#14519703—22no—
130#14519702C2×C411yescharacteristic, complemented
131#14519702C2×C411yescharacteristic, complemented
132#14519701C2×C411yescharacteristic, complemented
133#14519701C2×C411yescharacteristic, complemented
134#14519699C2×C411yescharacteristic, complemented
135#14519699C2×C411yescharacteristic, complemented
136#14519698C2×C411yescharacteristic, complemented
137#14519698C2×C411yescharacteristic, complemented
138C22⋊#92418—21no—
139C22⋊#92418—21no—
140#14519689—21no—
141#14519689—21no—
142#14519689C2×C411yescharacteristic
143#14519689C2×C411yescharacteristic
144#14519689C2×C411yescharacteristic
145#14519689C2×C411yescharacteristic
146#14519689D411yescharacteristic
147#14519689D411yescharacteristic
148#14519689D411yescharacteristic
149#14519689D411yescharacteristic
150#14519687—21no—
151C4×#92418—22no—
152C8×Dic61—21no—
153C2×#41×C61C2311yescharacteristic
154C2×#41×C61C2311yescharacteristic
155#135×C61—41no—
156#135×C61—41no—
157C2×Q16×C61C2×C411yescharacteristic, complemented
158C2×SD16×C61C2×C411yescharacteristic, complemented
159C2×SD16×C61C2×C411yescharacteristic, complemented
160C2×D8×C61C2×C411yescharacteristic, complemented
161C2×M16×C61C2311yescharacteristic
162C2×M16×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C2×C42×C61C2311yescharacteristic
166#108×C61—41no—
167#104×C61—22no—
168#104×C61—22no—
169C22⋊C8×C61—21no—
170C22⋊C8×C61—21no—
171C22⋊C8×C61—21no—
172C22⋊C8×C61—21no—
173C4×C8×C61—41no—
174C23×D61—21no—
175C23×D61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61—21no—
183#41×C61—21no—
184C2×Q8×C61C22×C411yescharacteristic
185C2×Q8×C61C22×C411yescharacteristic
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61C22×C411yescharacteristic
189C2×D4×C61C22×C411yescharacteristic
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61#4111yescharacteristic
202#11758226—22no—
203#11758226—41no—
204Q8×D61—22no—
205Q8×D61—41no—
206#11758224—22no—
207#11758224—41no—
208#11758224—42no—
209#11758224—42no—
210D4×D61—22no—
211D4×D61—41no—
212D4×D61—42no—
213D4×D61—42no—
214#11758222—21no—
215#11758222—21no—
216#11758222—42no—
217#11758222—42no—
218#11758222C2×D412yes—
219#11758222#4112yes—
220C2×D244—21no—
221C2×D244C22×C411yescharacteristic
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—24no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61C22×C411yescharacteristic
235C2×C4×D61C22×C411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×Dic122—21no—
239C2×Dic122C22×C411yescharacteristic
240Q16×C61—41no—
241SD16×C61—41no—
242SD16×C61—41no—
243D8×C61—41no—
244M16×C61—21no—
245M16×C61—21no—
246M16×C61—21no—
247M16×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61C22×C411yescharacteristic
255C2×C8×C61C22×C411yescharacteristic
256C2×C8×C61C2×D411yescharacteristic
257C2×C8×C61C2×D411yescharacteristic
258C42×C61—21no—
259C42×C61C2×D412yes—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263#11758202—22no—
264#11758201—22no—
265#11758200—22no—
266#11758199—22no—
267#11758198—21no—
268#11758198—21no—
269C4⋊Dic61C22×C411yescharacteristic
270C4⋊Dic61C22×C411yescharacteristic
271#11758196—21no—
272#11758196—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61—42no—
277#11758194—21no—
278#11758194—21no—
279#11758194—21no—
280#11758194—42no—
281#11758194C2×D412yes—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—42no—
289C2×#92418C22×C411yescharacteristic
290C2×#92418C22×C411yescharacteristic
291C2×#92418C2×D411yescharacteristic
292C2×#92418C2×D411yescharacteristic
293#11758189—42no—
294#11758189—42no—
295#11758189—42no—
296C8×D61—42no—
297C8×D61—42no—
298C8×D61—42no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61C2×#4111yescharacteristic
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—22no—
306C22×D61—41no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—81no—
310C22×D61C4×D411yescharacteristic
311C22×D61C4×D411yescharacteristic
312Q8×C61—21no—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61—21no—
316D4×C61—21no—
317D4×C61—21no—
318D4×C61—21no—
319D4×C61—21no—
320D4×C61—41no—
321D4×C61—41no—
322D4×C61—41no—
323D4×C61—41no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61C23×C411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61H(5,𝔽2)11yescharacteristic
338C2×C4×C61H(5,𝔽2)11yescharacteristic
339C22⋊D61—22no—
340C22⋊D61—22no—
341C22⋊D61—42no—
342C22⋊D61—42no—
343C22⋊D61—42no—
344C22⋊D61—81no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—22no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—42no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61C4×D411yescharacteristic
355C2×Dic61C4×D411yescharacteristic
356D244—21no—
357D244—42no—
358D244C4×D412yes—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—22no—
365C4×D61—21no—
366C4×D61—22no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—42no—
370C4×D61—42no—
371C4×D61—48no—
372Dic122—21no—
373Dic122—42no—
374Dic122C4×D412yes—
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—22no—
385#92418—21no—
386#92418—41no—
387#22888—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61C2×C4×D411yescharacteristic
397C22×C61#54611yescharacteristic
398C22×C61#55111yescharacteristic
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—22no—
403C2×D61—21no—
404C2×D61—21no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—84no—
410C2×D61#44312yescomplemented
411C4×C61—24no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61C2×C4×D411yescharacteristic
415C4×C61#51811yescharacteristic
416C4×C61D4211yescharacteristic
417C4×C61#54611yescharacteristic
418Dic61—22no—
419Dic61—21no—
420Dic61—21no—
421Dic61—42no—
422Dic61—41no—
423Dic61—41no—
424#3002—611no—
425C2×#443—611no—
426#2933—611no—
427C22×#104—611no—
428#2880—611no—
429#1974D6111yescharacteristic, complemented
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—21no—
441C2×C61—81no—
442C2×C61—81no—
443C2×C61#235811yescharacteristic
444C2×C61C2×#44311yescharacteristic
445C2×C61#295611yescharacteristic
446D61—22no—
447D61—41no—
448D61—42no—
449C22×#41—611no—
450C2×#135—611no—
451C2×#135C2×D6111yescharacteristic
452C2×#131—611no—
453C2×#131—611no—
454C2×#131—611no—
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×#108C2×D6111yescharacteristic, complemented
473#424—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478C2×#104—1224no—
479C2×#104C2×D6111yescharacteristic
480C2×#104C2×D6111yescharacteristic, complemented
481#416—611no—
482#416—611no—
483#408—611no—
484#408—1221no—
485#408—1221no—
486#408C2×D6111yescharacteristic
487#408C2×D6111yescharacteristic, complemented
488#407—611no—
489#407—1221no—
490C2×C22⋊C8—611no—
491C2×C22⋊C8—611no—
492C2×C22⋊C8—1221no—
493#405—611no—
494C2×C4×C8—611no—
495C2×C4×C8C2×D6111yescharacteristic, complemented
496#341—611no—
497#341—611no—
498#339—611no—
499#339—611no—
500#336—611no—
501#336—611no—
502C61#2288811yescharacteristic, complemented, Sylow
503C2×#41—611no—
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—1221no—
507C2×#41—1221no—
508C2×#41—1222no—
509C2×#41—1222no—
510C2×#41—2441no—
511C2×#41—2441no—
512C2×#41C22×D6111yescharacteristic
513C2×#41C22×D6111yescharacteristic
514C22×Q8—611no—
515C22×D4—611no—
516C22×D4—1221no—
517C23×C4—611no—
518C23×C4—1221no—
519C23×C4—1221no—
520#135—41no—
521#135—41no—
522#135—1222no—
523#135—1222no—
524C2×Q16—611no—
525C2×Q16C4×D6111yescharacteristic, complemented
526C2×SD16—611no—
527C2×SD16—611no—
528C2×SD16C4×D6111yescharacteristic, complemented
529C2×SD16C4×D6111yescharacteristic, complemented
530C2×D8—611no—
531C2×D8C4×D6111yescharacteristic, complemented
532#131—1222no—
533#131—1222no—
534#131—1222no—
535#131—2441no—
536#131—2441no—
537#131—2441no—
538C2×M16—611no—
539C2×M16—611no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1222no—
545C2×M16—2441no—
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—611no—
549C22×C8—611no—
550C22×C8—1221no—
551C22×C8—1221no—
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—1222no—
567C2×C42—1221no—
568C2×C42—2441no—
569C2×C42C22×D6111yescharacteristic
570#108—41no—
571#108—1222no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—22no—
575#104—22no—
576#104—614no—
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—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—611no—
596C22⋊C8—611no—
597C22⋊C8—611no—
598C22⋊C8—611no—
599C22⋊C8—611no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8—1221no—
604#97—1221no—
605C4×C8—41no—
606C4×C8—1221no—
607C4×C8—1222no—
608C24—611no—
609C24—1221no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—612no—
619#41—612no—
620#41—1221no—
621#41—1221no—
622#41—1222no—
623#41—1222no—
624#41—2442no—
625#41—2442no—
626#41—2441no—
627#41—2442no—
628#41—2442no—
629#41—2441no—
630C2×Q8—611no—
631C2×Q8—1221no—
632C2×Q8—1222no—
633C2×Q8—2441no—
634C2×Q8C2×C4×D6111yescharacteristic
635C2×Q8C2×C4×D6111yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—611no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1222no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—2441no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4C2×C4×D6111yescharacteristic
650C2×D4C2×C4×D6111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1224no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—2442no—
670C22×C4—2442no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4C23×D6111yescharacteristic
674Q16—41no—
675Q16—1222no—
676SD16—41no—
677SD16—41no—
678SD16—1222no—
679SD16—1222no—
680D8—41no—
681D8—1222no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—612no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16—2442no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—611no—
701C2×C8—611no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—2442no—
711C2×C8—2442no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8C2×C4×D6111yescharacteristic
715C2×C8C2×C4×D6111yescharacteristic
716C2×C8D4×D6111yescharacteristic
717C2×C8D4×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—21no—
728C42—1221no—
729C42—1221no—
730C42—1221no—
731C42—2442no—
732C42D4×D6112yes—
733C23—21no—
734C23—21no—
735C23—611no—
736C23—611no—
737C23—1222no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—4881no—
742C23—2441no—
743C23—2442no—
744C23—2442no—
745C23#41×D6111yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—612no—
751Q8—1221no—
752Q8—2442no—
753D4—21no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—612no—
762D4—1222no—
763D4—1222no—
764D4—1221no—
765D4—4881no—
766D4—2442no—
767D4—2442no—
768D4—2442no—
769D4—2442no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—611no—
780C2×C4—611no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1222no—
790C2×C4—1221no—
791C2×C4—1222no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—2448no—
798C2×C4—2442no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4#41×D6111yescharacteristic
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—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—612no—
830C22—1221no—
831C22—1221no—
832C22—1221no—
833C22—1222no—
834C22—1221no—
835C22—1221no—
836C22—4884no—
837C22—2442no—
838C22—2442no—
839C22—2441no—
840C22—2441no—
841C22C4×D4×D6111yescharacteristic
842C22#1684040111yescharacteristic
843C22#1684044211yescharacteristic
844C4—24no—
845C4—41no—
846C4—41no—
847C4—1221no—
848C4—1221no—
849C4—1222no—
850C4—2442no—
851C4—2441no—
852C4—2441no—
853C4C4×D4×D6111yescharacteristic
854C4#1684023511yescharacteristic
855C4#1684039711yescharacteristic
856C4#1684040111yescharacteristic
857C2—21no—
858C2—21no—
859C2—81no—
860C2—81no—
861C2—1222no—
862C2—2441no—
863C2—2442no—
864C2#2144880011yescharacteristic
865C2#443×D6111yescharacteristic
866C2#2145472411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1974C2
socleC22×C61C2×C4×D4
prime radical#21455033C2
cosocleC22×C4×C61C24
hypercenter#1974D61
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C2×#16839876C2semidirect
3. #21454549C2semidirect
4. C2×#104×D61C2semidirect
5. #21454267C2semidirect
6. #21446520C2semidirect
7. #21446464C2semidirect
8. #21446259C2semidirect
9. #21446149C2semidirect
10. #21446148C2semidirect
11. #21446091C2semidirect
12. #21446022C2semidirect
13. #21445656C2semidirect
14. C4×#14519689C2semidirect
15. C61×#1974C2semidirect
19. C2×#14519784C22semidirect
24. #16839923C4semidirect
25. #16839921C4semidirect
26. #16839916C4semidirect
27. #16839911C4semidirect
28. #16839906C4semidirect
29. #16839904C4semidirect
30. #16839899C4semidirect
31. #16839894C4semidirect
37. C2×#14519712C22semidirect
38. #16839790C22semidirect
41. C2×#14519704C22semidirect
54. #16839717C22semidirect
55. C2×C4×#92418C22semidirect
56. #16839527C22semidirect
57. #16839526C22semidirect
58. #16839523C22semidirect
59. #16839522C22semidirect
60. #16839516C22semidirect
61. #16839516C22semidirect
63. C2×#108×C61C22semidirect
65. C2×#104×C61C22semidirect
67. C61×#408C22semidirect
68. C2×C4×C8×C61C22semidirect
86. C2×#11758202C2×C4semidirect
87. C2×#11758200C2×C4semidirect
88. C2×#11758201C2×C4semidirect
89. C2×#11758199C2×C4semidirect
126. #14519705D4semidirect
130. #14519702C2×C4semidirect
131. #14519702C2×C4semidirect
132. #14519701C2×C4semidirect
133. #14519701C2×C4semidirect
134. #14519699C2×C4semidirect
135. #14519699C2×C4semidirect
136. #14519698C2×C4semidirect
137. #14519698C2×C4semidirect
157. C2×Q16×C61C2×C4semidirect
158. C2×SD16×C61C2×C4semidirect
159. C2×SD16×C61C2×C4semidirect
160. C2×D8×C61C2×C4semidirect
410. C2×D61#443semidirect
429. #1974D61semidirect
472. C2×#108C2×D61semidirect
480. C2×#104C2×D61semidirect
487. #408C2×D61semidirect
495. C2×C4×C8C2×D61semidirect
502. C61#22888semidirect
525. C2×Q16C4×D61semidirect
528. C2×SD16C4×D61semidirect
529. C2×SD16C4×D61semidirect
531. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214550332
C2×#168398762
#214545492
C2×#104×D612
#214542672
#214465202
#214464642
#214462592
#214461492
#214461482
#214460912
#214460222
#214456562
C4×#145196892
C61×#19742
#2288861