Finite Group Databasebeta

← #29700801

Subgroups — #29700801

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455033C211yesmaximal, characteristic
2C2×#16839879C211yesmaximal, characteristic, complemented
3#21454549C211yesmaximal, characteristic, complemented
4C2×#16839777C211yesmaximal, characteristic, complemented
5#21454266C211yesmaximal, characteristic, complemented
6#21446711C211yesmaximal, characteristic, complemented
7#21446521C211yesmaximal, characteristic, complemented
8#21446468C211yesmaximal, characteristic, complemented
9#21446264C211yesmaximal, characteristic, complemented
10#21446144C211yesmaximal, characteristic, complemented
11#21446092C211yesmaximal, characteristic, complemented
12#21446025C211yesmaximal, characteristic, complemented
13#21445661C211yesmaximal, characteristic, complemented
14#21445584C211yesmaximal, characteristic, complemented
15C61×#1876C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519784C2211yescharacteristic
19C2×#14519784C2211yescharacteristic, complemented
20C2×M16×D61C2211yescharacteristic
21#16840269C2211yescharacteristic
22C2×#14519734C2211yescharacteristic
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#16839879—24no—
32#16839837—21no—
33#16839836—21no—
34#16839830—21no—
35#16839825—21no—
36C2×#14519713C2211yescharacteristic, complemented
37C2×#14519712C2211yescharacteristic, complemented
38#16839790C2211yescharacteristic, complemented
39#16839777—24no—
40C2×#14519705C2211yescharacteristic
41C2×#14519704C2211yescharacteristic
42C2×#14519704C2211yescharacteristic, complemented
43C2×#14519703C2211yescharacteristic
44#16839759C2211yescharacteristic
45#16839758C2211yescharacteristic
46#16839730—21no—
47#16839730C2211yescharacteristic
48#16839728—21no—
49#16839728C2211yescharacteristic
50#16839725—21no—
51#16839725C2211yescharacteristic
52C2×#14519689—21no—
53C2×#14519689C2211yescharacteristic
54C2×#14519689C2211yescharacteristic
55#16839717C2211yescharacteristic, complemented
56C2×#14519687C2211yescharacteristic, complemented
57C2×C8×Dic61C2211yescharacteristic, complemented
58#16839526C2211yescharacteristic, complemented
59#16839523C2211yescharacteristic, complemented
60#16839522C2211yescharacteristic, complemented
61#16839517C2211yescharacteristic, complemented
62C2×#135×C61C2211yescharacteristic
63C2×#131×C61C2211yescharacteristic
64C2×#104×C61C2211yescharacteristic
65C2×#104×C61C2211yescharacteristic, complemented
66C61×#408C2211yescharacteristic, complemented
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×D61C2311yescharacteristic
83#14519797—41no—
84#14519797—41no—
85C2×#11758202C2×C411yescharacteristic
86C2×#11758200C2×C411yescharacteristic
87C2×#11758201C2×C411yescharacteristic
88C2×#11758199C2×C411yescharacteristic
89#14519784—22no—
90#14519784—22no—
91#14519784—41no—
92#14519784—41no—
93C2×#11758194—21no—
94C2×#11758194—21no—
95C2×#11758194C2311yescharacteristic
96C2×#11758194C2311yescharacteristic
97C2×#11758189—21no—
98M16×D61—22no—
99M16×D61—41no—
100C22×#92418—21no—
101C22×#92418—21no—
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104C2×C8×D61—21no—
105#14519758—21no—
106#14519753C2×C411yescharacteristic
107#14519753C2×C411yescharacteristic
108#14519748C2×C411yescharacteristic
109#14519748C2×C411yescharacteristic
110#14519745—21no—
111C4×C22⋊D61—21no—
112C4×C22⋊D61—21no—
113#14519736C2311yescharacteristic
114#14519734—22no—
115#14519734—41no—
116C2×#11758196—21no—
117C2×#11758198—21no—
118C2×C4×Dic61C2311yescharacteristic
119#14519713—22no—
120#14519712—41no—
121#14519706—21no—
122#14519706—21no—
123#14519705—22no—
124#14519704—22no—
125#14519704D414yescomplemented
126#14519703—22no—
127#14519702C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519701C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134#14519698C2×C411yescharacteristic
135#14519689—21no—
136#14519689—21no—
137#14519689—21no—
138#14519689—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—
150#14519687—41no—
151C8×Dic61—21no—
152C8×Dic61—22no—
153C2×#41×C61C2311yescharacteristic
154C2×#41×C61C2311yescharacteristic
155#135×C61—22no—
156#135×C61—22no—
157C2×Q16×C61C2×C411yescharacteristic
158C2×SD16×C61C2×C411yescharacteristic
159C2×SD16×C61C2×C411yescharacteristic
160C2×D8×C61C2×C411yescharacteristic
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×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—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61C22×C411yescharacteristic
232C2×C4×D61C22×C411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×Dic122—21no—
236C2×Dic122C22×C411yescharacteristic
237Q16×C61—22no—
238SD16×C61—22no—
239SD16×C61—22no—
240D8×C61—22no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244M16×C61—21no—
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×C61C22×C411yescharacteristic
254C2×C8×C61C22×C411yescharacteristic
255C2×C8×C61C2×D411yescharacteristic
256C2×C8×C61C2×D411yescharacteristic
257C42×C61—21no—
258C42×C61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262#11758202—41no—
263#11758201—41no—
264#11758200—41no—
265#11758199—41no—
266#11758198—21no—
267#11758198—21no—
268#11758198—42no—
269C4⋊Dic61C22×C411yescharacteristic
270C4⋊Dic61C22×C411yescharacteristic
271#11758196—21no—
272#11758196—21no—
273#11758196—42no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61C2×D412yes—
277#11758194—21no—
278#11758194—21no—
279#11758194—21no—
280#11758194—42no—
281#11758194—42no—
282#11758194C2×D412yes—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—42no—
290C2×#92418—42no—
291C2×#92418C22×C411yescharacteristic
292C2×#92418C22×C411yescharacteristic
293C2×#92418C2×D411yescharacteristic
294C2×#92418C2×D411yescharacteristic
295#11758189—42no—
296C8×D61—42no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61C2×#4111yescharacteristic
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—81no—
308C22×D61C4×D411yescharacteristic
309C22×D61C4×D411yescharacteristic
310Q8×C61—21no—
311Q8×C61—21no—
312Q8×C61—21no—
313Q8×C61C4×D412yes—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—21no—
317D4×C61—21no—
318D4×C61—21no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61C4×D412yes—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C22⋊D61—42no—
338C22⋊D61—42no—
339C22⋊D61—42no—
340C22⋊D61—41no—
341C22⋊D61—41no—
342C22⋊D61—81no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—22no—
349C2×Dic61—42no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61C4×D411yescharacteristic
353C2×Dic61C4×D411yescharacteristic
354D244—21no—
355D244—21no—
356D244—42no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—41no—
368C4×D61—41no—
369Dic122—21no—
370Dic122—21no—
371Dic122—42no—
372C8×C61—21no—
373C8×C61—21no—
374C8×C61—21no—
375C8×C61—21no—
376C8×C61—41no—
377C8×C61—41no—
378#92418—21no—
379#92418—21no—
380#92418—22no—
381#92418—21no—
382#92418—21no—
383#92418—41no—
384#22889—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—22no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61C2×C4×D411yescharacteristic
394C22×C61#54611yescharacteristic
395C22×C61#55111yescharacteristic
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—81no—
406C2×D61—81no—
407C2×D61—84no—
408C4×C61—22no—
409C4×C61—41no—
410C4×C61—81no—
411C4×C61C2×C4×D411yescharacteristic
412C4×C61#51811yescharacteristic
413C4×C61D4211yescharacteristic
414C4×C61#54611yescharacteristic
415Dic61—21no—
416Dic61—21no—
417Dic61—42no—
418Dic61—41no—
419Dic61—41no—
420Dic61—41no—
421#3002—611no—
422C2×#443—611no—
423#2933—611no—
424C2×#421—611no—
425#2880—611no—
426#1975—611no—
427#1937—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876D6111yescharacteristic, complemented
432#1866—611no—
433#1855—611no—
434#1765—611no—
435#1750—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—42no—
439C2×C61—81no—
440C2×C61#235811yescharacteristic
441C2×C61#295511yescharacteristic
442C2×C61#295711yescharacteristic
443D61—41no—
444D61—41no—
445D61—81no—
446C22×#41—611no—
447C2×#135—611no—
448C2×#135C2×D6111yescharacteristic
449C2×#131—611no—
450C2×#131—611no—
451C2×#131C2×D6111yescharacteristic
452C22×M16—611no—
453#525—611no—
454C2×#117—611no—
455#452—611no—
456#452—611no—
457#451—611no—
458#450—611no—
459#449—611no—
460#449—611no—
461#448—611no—
462#447—611no—
463#443—1224no—
464#436—1221no—
465#435—1221no—
466#435—1221no—
467C8×D4—1221no—
468C2×#108—611no—
469C2×#108—611no—
470#424—611no—
471#421—1224no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104C2×D6111yescharacteristic
477C2×#104C2×D6111yescharacteristic, complemented
478#416—611no—
479#416—611no—
480#408—611no—
481#408—611no—
482#408—1221no—
483#408—1221no—
484#408C2×D6111yescharacteristic, complemented
485#407—611no—
486#407—1221no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—611no—
489C2×C22⋊C8—1221no—
490#405—611no—
491C2×#97—611no—
492C2×C4×C8—611no—
493#341—611no—
494#341C2×D6111yescharacteristic, complemented
495#339—611no—
496#339—611no—
497#336—611no—
498#336C2×D6111yescharacteristic, complemented
499C61#2288911yescharacteristic, complemented, Sylow
500C2×#41—611no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—1221no—
504C2×#41—1221no—
505C2×#41—1222no—
506C2×#41—1222no—
507C2×#41—2441no—
508C2×#41—2441no—
509C2×#41C22×D6111yescharacteristic
510C2×#41C22×D6111yescharacteristic
511C22×Q8—611no—
512C22×D4—611no—
513C22×D4—1221no—
514C23×C4—611no—
515C23×C4—1221no—
516#135—22no—
517#135—22no—
518#135—2441no—
519#135—2441no—
520C2×Q16—611no—
521C2×Q16C4×D6111yescharacteristic
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16C4×D6111yescharacteristic
525C2×SD16C4×D6111yescharacteristic
526C2×D8—611no—
527C2×D8C4×D6111yescharacteristic
528#131—22no—
529#131—41no—
530#131—1222no—
531#131—1222no—
532#131—2441no—
533#131—2441no—
534C2×M16—21no—
535C2×M16—611no—
536C2×M16—611no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1222no—
541C2×M16—2441no—
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C22×C8—21no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—1221no—
548C22×C8—1221no—
549C22×C8—1221no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#123—1221no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555#121—611no—
556#121—611no—
557#120—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560#117—611no—
561#117—1222no—
562#117—2441no—
563C2×C4⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—611no—
566C2×C42C22×D6111yescharacteristic
567#108—1222no—
568#108—2441no—
569C4⋊C8—1221no—
570C4⋊C8—1221no—
571#104—22no—
572#104—41no—
573#104—614no—
574#104—1222no—
575#104—1222no—
576#104—1222no—
577#103—611no—
578#103—611no—
579#103—611no—
580#103—611no—
581#102—611no—
582#102—611no—
583#102—611no—
584#102—611no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—611no—
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601#97—1221no—
602#97—2441no—
603C4×C8—1222no—
604C4×C8—1221no—
605C24—611no—
606C24—1221no—
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—1222no—
614#41—1222no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—2442no—
620#41—2442no—
621#41—2441no—
622#41—2442no—
623#41—2442no—
624#41—2441no—
625#41D4×D6112yes—
626#41#1175822412yes—
627C2×Q8—611no—
628C2×Q8—1221no—
629C2×Q8—1222no—
630C2×Q8—2441no—
631C2×Q8C2×C4×D6111yescharacteristic
632C2×Q8C2×C4×D6111yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—611no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1222no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—2441no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4C2×C4×D6111yescharacteristic
647C2×D4C2×C4×D6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4C23×D6111yescharacteristic
668Q16—22no—
669Q16—2441no—
670SD16—22no—
671SD16—22no—
672SD16—2441no—
673SD16—2441no—
674D8—22no—
675D8—2441no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—42no—
681M16—612no—
682M16—1221no—
683M16—1221no—
684M16—1221no—
685M16—2442no—
686M16—2442no—
687M16—2442no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—611no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—2442no—
706C2×C8—2442no—
707C2×C8—2442no—
708C2×C8C2×C4×D6111yescharacteristic
709C2×C8C2×C4×D6111yescharacteristic
710C2×C8D4×D6111yescharacteristic
711C2×C8D4×D6111yescharacteristic
712C4⋊C4—611no—
713C4⋊C4—611no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—2442no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—2442no—
723C42—21no—
724C42—21no—
725C42—612no—
726C42—1221no—
727C42—1221no—
728C23—21no—
729C23—21no—
730C23—611no—
731C23—611no—
732C23—1221no—
733C23—1221no—
734C23—1221no—
735C23—4881no—
736C23—2441no—
737C23—2441no—
738C23—2442no—
739C23—2442no—
740C23#41×D6111yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—1221no—
745Q8—1221no—
746Q8—2442no—
747Q8#1451973712yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—41no—
754D4—41no—
755D4—1221no—
756D4—1221no—
757D4—4881no—
758D4—2442no—
759D4—2442no—
760D4—2442no—
761D4—2442no—
762D4—2441no—
763D4—2441no—
764D4#1451973712yes—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
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—2442no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4C22×C4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C2×D4×D6111yescharacteristic
800C2×C4C2×#1175822411yescharacteristic
801C2×C4#1451982211yescharacteristic
802C2×C4#1451982311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—1221no—
810C8—1221no—
811C8—1221no—
812C8—1221no—
813C8—1222no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—22no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—1221no—
824C22—1221no—
825C22—1221no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—4881no—
830C22—4881no—
831C22—4884no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C4×D4×D6111yescharacteristic
836C22#1684040111yescharacteristic
837C22#1684043511yescharacteristic
838C4—22no—
839C4—41no—
840C4—81no—
841C4—1221no—
842C4—1221no—
843C4—2442no—
844C4—2441no—
845C4—2441no—
846C4—2441no—
847C4C2×#1451973711yescharacteristic
848C4#1684023411yescharacteristic
849C4#1684039611yescharacteristic
850C4#1684039911yescharacteristic
851C2—21no—
852C2—21no—
853C2—42no—
854C2—81no—
855C2—4881no—
856C2—2441no—
857C2—2441no—
858C2#2144879911yescharacteristic
859C2#2145471911yescharacteristic
860C2#2145473111yescharacteristic
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#22889
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×#16839879C2semidirect
3. #21454549C2semidirect
4. C2×#16839777C2semidirect
5. #21454266C2semidirect
6. #21446711C2semidirect
7. #21446521C2semidirect
8. #21446468C2semidirect
9. #21446264C2semidirect
10. #21446144C2semidirect
11. #21446092C2semidirect
12. #21446025C2semidirect
13. #21445661C2semidirect
14. #21445584C2semidirect
15. C61×#1876C2semidirect
19. C2×#14519784C22semidirect
23. #16839923C4semidirect
24. #16839921C4semidirect
25. #16839916C4semidirect
26. #16839911C4semidirect
27. #16839906C4semidirect
28. #16839904C4semidirect
29. #16839899C4semidirect
30. #16839894C4semidirect
36. C2×#14519713C22semidirect
37. C2×#14519712C22semidirect
38. #16839790C22semidirect
42. C2×#14519704C22semidirect
55. #16839717C22semidirect
56. C2×#14519687C22semidirect
57. C2×C8×Dic61C22semidirect
58. #16839526C22semidirect
59. #16839523C22semidirect
60. #16839522C22semidirect
61. #16839517C22semidirect
65. C2×#104×C61C22semidirect
66. C61×#408C22semidirect
67. C61×#341C22semidirect
68. C61×#336C22semidirect
125. #14519704D4semidirect
431. #1876D61semidirect
477. C2×#104C2×D61semidirect
484. #408C2×D61semidirect
494. #341C2×D61semidirect
498. #336C2×D61semidirect
499. C61#22889semidirect

Maximal subgroups

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

subgroupindex
#214550332
C2×#168398792
#214545492
C2×#168397772
#214542662
#214467112
#214465212
#214464682
#214462642
#214461442
#214460922
#214460252
#214456612
#214455842
C61×#18762
#2288961