Finite Group Databasebeta

← #29700774

Subgroups — #29700774

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
2#21454541C211yesmaximal, characteristic, complemented
3C2×#104×D61C211yesmaximal, characteristic, complemented
4#21454266C211yesmaximal, characteristic, complemented
5#21446704C211yesmaximal, characteristic, complemented
6#21446523C211yesmaximal, characteristic, complemented
7#21446466C211yesmaximal, characteristic, complemented
8#21446259C211yesmaximal, characteristic, complemented
9#21446148C211yesmaximal, characteristic, complemented
10#21446146C211yesmaximal, characteristic, complemented
11#21446094C211yesmaximal, characteristic, complemented
12#21446022C211yesmaximal, characteristic, complemented
13#21445657C211yesmaximal, characteristic, complemented
14C4×#14519689C211yesmaximal, characteristic, complemented
15C2×C61×#443C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519784C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20#16840269C2211yescharacteristic
21C2×C42×D61C2211yescharacteristic
22#16839923C411yescharacteristic, complemented
23#16839921C411yescharacteristic, complemented
24#16839916C411yescharacteristic, complemented
25#16839911C411yescharacteristic, complemented
26#16839906C411yescharacteristic, complemented
27#16839904C411yescharacteristic, complemented
28#16839899C411yescharacteristic, complemented
29#16839894C411yescharacteristic, complemented
30#16839838—21no—
31#16839833—21no—
32#16839831—21no—
33C8×C22⋊D61—21no—
34C2×#14519712C2211yescharacteristic, complemented
35#16839788C2211yescharacteristic, complemented
36C2×#14519705C2211yescharacteristic
37C2×#14519704C2211yescharacteristic
38C2×#14519704C2211yescharacteristic, complemented
39C2×#14519703C2211yescharacteristic
40#104×D61—24no—
41#16839759C2211yescharacteristic
42#16839758C2211yescharacteristic
43#16839730—21no—
44#16839730C2211yescharacteristic
45#16839729C2211yescharacteristic, complemented
46#16839728—21no—
47#16839728C2211yescharacteristic
48#16839725—21no—
49#16839725C2211yescharacteristic
50C2×#14519689—21no—
51C2×#14519689C2211yescharacteristic
52C2×#14519689C2211yescharacteristic
53#16839720C2211yescharacteristic, complemented
54C2×C4×#92418C2211yescharacteristic, complemented
55#16839527C2211yescharacteristic, complemented
56#16839526C2211yescharacteristic, complemented
57#16839523C2211yescharacteristic, complemented
58#16839522C2211yescharacteristic, complemented
59#16839516C2211yescharacteristic, complemented
60#16839516C2211yescharacteristic, complemented
61C2×#135×C61C2211yescharacteristic
62C2×#131×C61C2211yescharacteristic
63C2×#131×C61C2211yescharacteristic, complemented
64C61×#443—24no—
65C2×#108×C61C2211yescharacteristic, complemented
66C2×#104×C61C2211yescharacteristic
67C2×#104×C61C2211yescharacteristic, 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—41no—
85#14519797—41no—
86C2×#11758202C2×C411yescharacteristic, complemented
87C2×#11758200C2×C411yescharacteristic, complemented
88C2×#11758201C2×C411yescharacteristic, complemented
89C2×#11758199C2×C411yescharacteristic, complemented
90#14519784—22no—
91#14519784—41no—
92C2×#11758194—21no—
93C2×#11758194C2311yescharacteristic
94C2×#11758194C2311yescharacteristic
95C2×#11758189—21no—
96M16×D61—22no—
97M16×D61—41no—
98C22×#92418—21no—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C2×C8×D61—21no—
102#14519758—21no—
103#14519753C2×C411yescharacteristic
104#14519753C2×C411yescharacteristic
105#14519748C2×C411yescharacteristic
106#14519748C2×C411yescharacteristic
107#14519745—21no—
108C4×C22⋊D61—21no—
109C4×C22⋊D61—21no—
110#14519736C2311yescharacteristic
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113C42×D61—22no—
114C42×D61—41no—
115#14519712—41no—
116#14519706—21no—
117#14519706—21no—
118#14519705—22no—
119#14519704—22no—
120#14519704—41no—
121#14519703—22no—
122#14519702C2×C411yescharacteristic, complemented
123#14519702C2×C411yescharacteristic, complemented
124#14519701C2×C411yescharacteristic, complemented
125#14519701C2×C411yescharacteristic, complemented
126#14519699C2×C411yescharacteristic, complemented
127#14519699C2×C411yescharacteristic, complemented
128#14519698C2×C411yescharacteristic, complemented
129#14519698C2×C411yescharacteristic, complemented
130C22⋊#92418—21no—
131C22⋊#92418—21no—
132#14519689—21no—
133#14519689—21no—
134#14519689—21no—
135#14519689—21no—
136#14519689—21no—
137#14519689—21no—
138#14519689C2×C411yescharacteristic
139#14519689C2×C411yescharacteristic
140#14519689C2×C411yescharacteristic
141#14519689C2×C411yescharacteristic
142#14519689D411yescharacteristic
143#14519689D411yescharacteristic
144#14519689D411yescharacteristic
145#14519689D411yescharacteristic
146#14519687—21no—
147C4×#92418—41no—
148C8×Dic61—21no—
149C2×#41×C61C2311yescharacteristic
150C2×#41×C61C2311yescharacteristic
151#135×C61—22no—
152#135×C61—22no—
153C2×Q16×C61C2×C411yescharacteristic, complemented
154C2×SD16×C61C2×C411yescharacteristic, complemented
155C2×SD16×C61C2×C411yescharacteristic, complemented
156C2×D8×C61C2×C411yescharacteristic, complemented
157#131×C61—22no—
158#131×C61—22no—
159#131×C61—41no—
160#131×C61—41no—
161C2×M16×C61—21no—
162C2×M16×C61—21no—
163C2×M16×C61C2311yescharacteristic
164C2×M16×C61C2311yescharacteristic
165C22×C8×C61—21no—
166C22×C8×C61—21no—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C2×C42×C61C2311yescharacteristic
170#108×C61—22no—
171#104×C61—22no—
172#104×C61D414yescomplemented
173C4×C8×C61—22no—
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×C61C2×D412yes—
183#41×C61#4112yes—
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—21no—
217#11758222—21no—
218#11758222—42no—
219#11758222—42no—
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—24no—
227C2×C4×D61—21no—
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—22no—
241SD16×C61—22no—
242SD16×C61—22no—
243D8×C61—22no—
244M16×C61—21no—
245M16×C61—21no—
246M16×C61—21no—
247M16×C61—42no—
248M16×C61—42no—
249M16×C61C2×D412yes—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—42no—
257C2×C8×C61—42no—
258C2×C8×C61C22×C411yescharacteristic
259C2×C8×C61C22×C411yescharacteristic
260C2×C8×C61C2×D411yescharacteristic
261C2×C8×C61C2×D411yescharacteristic
262C42×C61—21no—
263C42×C61C2×D412yes—
264C22⋊Dic61—21no—
265C22⋊Dic61—21no—
266C22⋊Dic61—21no—
267#11758202—41no—
268#11758201—41no—
269#11758200—41no—
270#11758199—41no—
271#11758198—21no—
272#11758198—21no—
273C4⋊Dic61C22×C411yescharacteristic
274C4⋊Dic61C22×C411yescharacteristic
275#11758196—21no—
276#11758196—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—21no—
280C4×Dic61—42no—
281#11758194—21no—
282#11758194—21no—
283#11758194—21no—
284#11758194—21no—
285#11758194—42no—
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×#92418C2×D411yescharacteristic
296C2×#92418C2×D411yescharacteristic
297#11758189—42no—
298C8×D61—42no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61C2×#4111yescharacteristic
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—22no—
305C22×D61—21no—
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×C61C4×D412yes—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—21no—
319D4×C61—21no—
320D4×C61—21no—
321D4×C61—41no—
322D4×C61—41no—
323D4×C61C4×D412yes—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—21no—
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—42no—
340C22⋊D61—42no—
341C22⋊D61—41no—
342C22⋊D61—41no—
343C22⋊D61—42no—
344C22⋊D61—81no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—22no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—42no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61C4×D411yescharacteristic
355C2×Dic61C4×D411yescharacteristic
356D244—21no—
357D244—21no—
358D244—42no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—42no—
368C4×D61—42no—
369C4×D61—48no—
370C4×D61—41no—
371C4×D61—41no—
372Dic122—21no—
373Dic122—21no—
374Dic122—42no—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—22no—
378C8×C61—21no—
379C8×C61—21no—
380C8×C61—41no—
381#92418—21no—
382#92418—21no—
383#92418—21no—
384#92418—21no—
385#92418—41no—
386#92418—41no—
387#22888—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—22no—
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—21no—
403C2×D61—21no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—84no—
410C2×D61#44312yescomplemented
411C4×C61—24no—
412C4×C61—22no—
413C4×C61—41no—
414C4×C61C2×C4×D411yescharacteristic
415C4×C61#51811yescharacteristic
416C4×C61D4211yescharacteristic
417C4×C61#54611yescharacteristic
418Dic61—21no—
419Dic61—21no—
420Dic61—42no—
421Dic61—41no—
422Dic61—41no—
423Dic61—41no—
424#3002—611no—
425C2×#443D6111yescharacteristic, complemented
426#2933—611no—
427C22×#104—611no—
428#2880—611no—
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—21no—
441C2×C61—42no—
442C2×C61—81no—
443C2×C61#235811yescharacteristic
444C2×C61C2×#44311yescharacteristic
445C2×C61#295611yescharacteristic
446D61—22no—
447D61—41no—
448D61—81no—
449C22×#41—611no—
450C2×#135—611no—
451C2×#135C2×D6111yescharacteristic
452C2×#131—611no—
453C2×#131C2×D6111yescharacteristic
454C2×#131C2×D6111yescharacteristic, complemented
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—24no—
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—611no—
485#408—611no—
486#408—1221no—
487#408—1221no—
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—22no—
521#135—22no—
522#135—2441no—
523#135—2441no—
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—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—1222no—
567C2×C42—1221no—
568C2×C42—2441no—
569C2×C42C22×D6111yescharacteristic
570#108—22no—
571#108—2441no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—22no—
575#104—1222no—
576#104—1222no—
577#104—1222no—
578#104—2441no—
579#104C22⋊D6114yescomplemented
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—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—611no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8—1221no—
604#97—1221no—
605C4×C8—22no—
606C4×C8—1221no—
607C4×C8—2441no—
608C24—611no—
609C24—1221no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—1222no—
617#41—1222no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—1221no—
622#41—2442no—
623#41—2442no—
624#41—2441no—
625#41—2442no—
626#41—2442no—
627#41—2441no—
628#41#1175822212yes—
629#41C2×C22⋊D6112yes—
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—22no—
675Q16—2441no—
676SD16—22no—
677SD16—22no—
678SD16—2441no—
679SD16—2441no—
680D8—22no—
681D8—2441no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—1221no—
691M16—2442no—
692M16—2442no—
693M16C2×C22⋊D6112yes—
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×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—
732C42C2×C22⋊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—1221no—
750Q8—1221no—
751Q8—2442no—
752Q8C4×C22⋊D6112yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—41no—
759D4—41no—
760D4—1221no—
761D4—1221no—
762D4—4881no—
763D4—2442no—
764D4—2442no—
765D4—2442no—
766D4—2442no—
767D4—2441no—
768D4—2441no—
769D4C4×C22⋊D6112yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
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—1221no—
790C2×C4—1221no—
791C2×C4—1222no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4—2448no—
798C2×C4—2442no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C22×C22⋊D6111yescharacteristic
806C2×C4C2×#1175822211yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—22no—
814C8—41no—
815C8—1221no—
816C8—1221no—
817C8—1221no—
818C8—1221no—
819C8—2441no—
820C8—2441no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—612no—
830C22—1221no—
831C22—1221no—
832C22—1221no—
833C22—1221no—
834C22—1221no—
835C22—4884no—
836C22—2442no—
837C22—2442no—
838C22—2441no—
839C22—2441no—
840C22—2441no—
841C22C4×D4×D6111yescharacteristic
842C22#1684040011yescharacteristic
843C22#1684044111yescharacteristic
844C4—24no—
845C4—22no—
846C4—41no—
847C4—1221no—
848C4—1221no—
849C4—2442no—
850C4—2441no—
851C4—2441no—
852C4—2441no—
853C4C2×C4×C22⋊D6111yescharacteristic
854C4#1684023411yescharacteristic
855C4D4×C22⋊D6111yescharacteristic
856C4#1684040811yescharacteristic
857C2—21no—
858C2—21no—
859C2—42no—
860C2—81no—
861C2—1222no—
862C2—4881no—
863C2—2441no—
864C2#2144879611yescharacteristic
865C2#443×D6111yescharacteristic
866C2#2145472411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#443C2
socleC22×C61C2×C4×D4
prime radical#21455033C2
cosocleC22×C4×C61C24
hypercenterC2×#443D61
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. #21454541C2semidirect
3. C2×#104×D61C2semidirect
4. #21454266C2semidirect
5. #21446704C2semidirect
6. #21446523C2semidirect
7. #21446466C2semidirect
8. #21446259C2semidirect
9. #21446148C2semidirect
10. #21446146C2semidirect
11. #21446094C2semidirect
12. #21446022C2semidirect
13. #21445657C2semidirect
14. C4×#14519689C2semidirect
15. C2×C61×#443C2semidirect
22. #16839923C4semidirect
23. #16839921C4semidirect
24. #16839916C4semidirect
25. #16839911C4semidirect
26. #16839906C4semidirect
27. #16839904C4semidirect
28. #16839899C4semidirect
29. #16839894C4semidirect
34. C2×#14519712C22semidirect
35. #16839788C22semidirect
38. C2×#14519704C22semidirect
45. #16839729C22semidirect
53. #16839720C22semidirect
54. C2×C4×#92418C22semidirect
55. #16839527C22semidirect
56. #16839526C22semidirect
57. #16839523C22semidirect
58. #16839522C22semidirect
59. #16839516C22semidirect
60. #16839516C22semidirect
63. C2×#131×C61C22semidirect
65. C2×#108×C61C22semidirect
67. C2×#104×C61C22semidirect
68. C2×C4×C8×C61C22semidirect
86. C2×#11758202C2×C4semidirect
87. C2×#11758200C2×C4semidirect
88. C2×#11758201C2×C4semidirect
89. C2×#11758199C2×C4semidirect
122. #14519702C2×C4semidirect
123. #14519702C2×C4semidirect
124. #14519701C2×C4semidirect
125. #14519701C2×C4semidirect
126. #14519699C2×C4semidirect
127. #14519699C2×C4semidirect
128. #14519698C2×C4semidirect
129. #14519698C2×C4semidirect
153. C2×Q16×C61C2×C4semidirect
154. C2×SD16×C61C2×C4semidirect
155. C2×SD16×C61C2×C4semidirect
156. C2×D8×C61C2×C4semidirect
172. #104×C61D4semidirect
410. C2×D61#443semidirect
425. C2×#443D61semidirect
454. C2×#131C2×D61semidirect
472. C2×#108C2×D61semidirect
480. C2×#104C2×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
579. #104C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214550332
#214545412
C2×#104×D612
#214542662
#214467042
#214465232
#214464662
#214462592
#214461482
#214461462
#214460942
#214460222
#214456572
C4×#145196892
C2×C61×#4432
#2288861