Finite Group Databasebeta

← #29700783

Subgroups — #29700783

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×#16839877C211yesmaximal, characteristic, complemented
3#21454541C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic, complemented
5#21454267C211yesmaximal, characteristic, complemented
6#21446708C211yesmaximal, characteristic, complemented
7#21446526C211yesmaximal, characteristic, complemented
8#21446470C211yesmaximal, characteristic, complemented
9#21446259C211yesmaximal, characteristic, complemented
10#21446143C211yesmaximal, characteristic, complemented
11#21446097C211yesmaximal, characteristic, complemented
12#21446025C211yesmaximal, characteristic, complemented
13#21445655C211yesmaximal, characteristic, complemented
14#21445576C211yesmaximal, characteristic, complemented
15C61×#1876C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519785C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21#16840269C2211yescharacteristic
22C2×C42×D61C2211yescharacteristic
23#16839923C411yescharacteristic, complemented
24#16839921C411yescharacteristic, complemented
25#16839916C411yescharacteristic, complemented
26#16839911C411yescharacteristic, complemented
27#16839906C411yescharacteristic, complemented
28#16839904C411yescharacteristic, complemented
29#16839899C411yescharacteristic, complemented
30#16839894C411yescharacteristic, complemented
31#16839877—24no—
32#16839838—21no—
33#16839833—21no—
34#16839831—21no—
35C8×C22⋊D61—21no—
36C2×#14519713C2211yescharacteristic, complemented
37C2×#14519712C2211yescharacteristic, complemented
38#16839788C2211yescharacteristic, complemented
39C2×#14519705C2211yescharacteristic
40C2×#14519704C2211yescharacteristic
41C2×#14519704C2211yescharacteristic, complemented
42C2×#14519703C2211yescharacteristic
43#104×D61—24no—
44#16839759C2211yescharacteristic
45#16839758C2211yescharacteristic
46#16839729C2211yescharacteristic
47#16839729C2211yescharacteristic, complemented
48#16839727—21no—
49#16839727—21no—
50#16839725C2211yescharacteristic
51#16839724—21no—
52C2×#14519689C2211yescharacteristic
53C2×#14519689C2211yescharacteristic
54C22⋊C8×D61—21no—
55#16839720C2211yescharacteristic, complemented
56C2×C8×Dic61C2211yescharacteristic, complemented
57C2×C8×Dic61C2211yescharacteristic, complemented
58#16839526C2211yescharacteristic, complemented
59#16839523C2211yescharacteristic, complemented
60#16839522C2211yescharacteristic, complemented
61#16839517C2211yescharacteristic, complemented
62C2×#135×C61C2211yescharacteristic
63C2×#131×C61C2211yescharacteristic, complemented
64C2×#104×C61C2211yescharacteristic
65C2×#104×C61C2211yescharacteristic, complemented
66C61×#408C2211yescharacteristic
67C61×#341C2211yescharacteristic, complemented
68C61×#336C2211yescharacteristic, 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#14519783—22no—
93#14519783—41no—
94C2×#11758194C2311yescharacteristic
95C2×#11758194C2311yescharacteristic
96C2×#11758189—21no—
97C2×#11758189—21no—
98C2×#11758189—21no—
99M16×D61—22no—
100M16×D61—41no—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—21no—
104C2×C8×D61—21no—
105C2×C8×D61—21no—
106#14519758—21no—
107#14519753C2×C411yescharacteristic
108#14519753C2×C411yescharacteristic
109#14519748C2×C411yescharacteristic
110#14519748C2×C411yescharacteristic
111#14519745—21no—
112C4×C22⋊D61—21no—
113C4×C22⋊D61—21no—
114#14519736C2311yescharacteristic
115C2×C4×Dic61—21no—
116C2×C4×Dic61C2311yescharacteristic
117C42×D61—22no—
118C42×D61—41no—
119#14519713—41no—
120#14519712—22no—
121#14519706—21no—
122#14519706—21no—
123#14519705—22no—
124#14519704—22no—
125#14519704—22no—
126#14519703D414yescomplemented
127#14519702C2×C411yescharacteristic, complemented
128#14519702C2×C411yescharacteristic, complemented
129#14519701C2×C411yescharacteristic, complemented
130#14519701C2×C411yescharacteristic, complemented
131#14519699C2×C411yescharacteristic, complemented
132#14519699C2×C411yescharacteristic, complemented
133#14519698C2×C411yescharacteristic, complemented
134#14519698C2×C411yescharacteristic, complemented
135C22⋊#92418—21no—
136C22⋊#92418—21no—
137C22⋊#92418—21no—
138C22⋊#92418—21no—
139#14519689—21no—
140#14519689—21no—
141#14519689C2×C411yescharacteristic
142#14519689C2×C411yescharacteristic
143#14519689C2×C411yescharacteristic
144#14519689C2×C411yescharacteristic
145#14519689D411yescharacteristic
146#14519689D411yescharacteristic
147#14519689D411yescharacteristic
148#14519689D411yescharacteristic
149#14519687—21no—
150C8×Dic61—22no—
151C8×Dic61—21no—
152C8×Dic61—41no—
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
161#131×C61—22no—
162#131×C61—41no—
163C2×M16×C61—21no—
164C2×M16×C61C2311yescharacteristic
165C2×M16×C61C2311yescharacteristic
166C22×C8×C61—21no—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C2×C42×C61C2311yescharacteristic
170#104×C61—22no—
171#104×C61—41no—
172C22⋊C8×C61—21no—
173C22⋊C8×C61—21no—
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—42no—
248M16×C61C2×D412yes—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—42no—
256C2×C8×C61C22×C411yescharacteristic
257C2×C8×C61C22×C411yescharacteristic
258C2×C8×C61C2×D411yescharacteristic
259C2×C8×C61C2×D411yescharacteristic
260C42×C61—21no—
261C42×C61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265#11758202—22no—
266#11758201—22no—
267#11758200—22no—
268#11758199—22no—
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—42no—
278C4×Dic61C2×D412yes—
279#11758194—21no—
280#11758194—21no—
281#11758194—21no—
282#11758194—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
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—21no—
326C2×C4×C61—21no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
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—22no—
346C2×Dic61—22no—
347C2×Dic61—21no—
348C2×Dic61—22no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—42no—
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—22no—
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—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—42no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61C2×C4×D411yescharacteristic
415C4×C61#51811yescharacteristic
416C4×C61D4211yescharacteristic
417C4×C61#54611yescharacteristic
418Dic61—24no—
419Dic61—22no—
420Dic61—21no—
421Dic61—21no—
422Dic61—41no—
423Dic61—41no—
424#3002—611no—
425C2×#443—611no—
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#1876D6111yescharacteristic, complemented
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×#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—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—1224no—
479C2×#104C2×D6111yescharacteristic
480C2×#104C2×D6111yescharacteristic, complemented
481#416—611no—
482#416—611no—
483#408—611no—
484#408—611no—
485#408—1221no—
486#408—1221no—
487#408C2×D6111yescharacteristic
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×C8—611no—
496#341—611no—
497#341C2×D6111yescharacteristic, complemented
498#339—611no—
499#339—611no—
500#336—611no—
501#336C2×D6111yescharacteristic, complemented
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—22no—
533#131—41no—
534#131—1222no—
535#131—1222no—
536#131—2441no—
537#131—2441no—
538C2×M16—21no—
539C2×M16—611no—
540C2×M16—611no—
541C2×M16—1221no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1222no—
545C2×M16—2441no—
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—21no—
549C22×C8—611no—
550C22×C8—611no—
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—1222no—
571#108—2441no—
572C4⋊C8—1221no—
573C4⋊C8—1221no—
574#104—22no—
575#104—41no—
576#104—614no—
577#104—1222no—
578#104—1222no—
579#104—1222no—
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—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—611no—
596C22⋊C8—611no—
597C22⋊C8—611no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8—1221no—
604#97—1221no—
605C4×C8—1222no—
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—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—42no—
686M16—1221no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—2442no—
691M16—2442no—
692M16—2442no—
693M16D4×D6112yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—611no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
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—21no—
729C42—612no—
730C42—1221no—
731C42—1221no—
732C42—2442no—
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—21no—
772C2×C4—21no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—611no—
780C2×C4—611no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1221no—
784C2×C4—1222no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1222no—
793C2×C4—1221no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4—2448no—
802C2×C4—2442no—
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—22no—
814C8—41no—
815C8—1221no—
816C8—1221no—
817C8—1221no—
818C8—1221no—
819C8—2441no—
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#1684040911yescharacteristic
843C22#1684044011yescharacteristic
844C4—42no—
845C4—41no—
846C4—41no—
847C4—1224no—
848C4—1221no—
849C4—1221no—
850C4—1222no—
851C4—2441no—
852C4—2441no—
853C4C4×D4×D6111yescharacteristic
854C4#1684023511yescharacteristic
855C4#1684039411yescharacteristic
856C4#1684040911yescharacteristic
857C2—21no—
858C2—21no—
859C2—81no—
860C2—81no—
861C2—1222no—
862C2—2441no—
863C2—2442no—
864C2#2144880211yescharacteristic
865C2#443×D6111yescharacteristic
866C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1876C2
socleC22×C61C2×C4×D4
prime radical#21455033C2
cosocleC22×C4×C61C24
hypercenter#1876D61
hypocenterC61#22888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. C2×#16839877C2semidirect
3. #21454541C2semidirect
4. C2×#104×D61C2semidirect
5. #21454267C2semidirect
6. #21446708C2semidirect
7. #21446526C2semidirect
8. #21446470C2semidirect
9. #21446259C2semidirect
10. #21446143C2semidirect
11. #21446097C2semidirect
12. #21446025C2semidirect
13. #21445655C2semidirect
14. #21445576C2semidirect
15. C61×#1876C2semidirect
23. #16839923C4semidirect
24. #16839921C4semidirect
25. #16839916C4semidirect
26. #16839911C4semidirect
27. #16839906C4semidirect
28. #16839904C4semidirect
29. #16839899C4semidirect
30. #16839894C4semidirect
36. C2×#14519713C22semidirect
37. C2×#14519712C22semidirect
38. #16839788C22semidirect
41. C2×#14519704C22semidirect
47. #16839729C22semidirect
55. #16839720C22semidirect
56. C2×C8×Dic61C22semidirect
57. C2×C8×Dic61C22semidirect
58. #16839526C22semidirect
59. #16839523C22semidirect
60. #16839522C22semidirect
61. #16839517C22semidirect
63. C2×#131×C61C22semidirect
65. C2×#104×C61C22semidirect
67. C61×#341C22semidirect
68. C61×#336C22semidirect
86. C2×#11758202C2×C4semidirect
87. C2×#11758200C2×C4semidirect
88. C2×#11758201C2×C4semidirect
89. C2×#11758199C2×C4semidirect
126. #14519703D4semidirect
127. #14519702C2×C4semidirect
128. #14519702C2×C4semidirect
129. #14519701C2×C4semidirect
130. #14519701C2×C4semidirect
131. #14519699C2×C4semidirect
132. #14519699C2×C4semidirect
133. #14519698C2×C4semidirect
134. #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
434. #1876D61semidirect
454. C2×#131C2×D61semidirect
480. C2×#104C2×D61semidirect
497. #341C2×D61semidirect
501. #336C2×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×#168398772
#214545412
C2×#104×D612
#214542672
#214467082
#214465262
#214464702
#214462592
#214461432
#214460972
#214460252
#214456552
#214455762
C61×#18762
#2288861