Finite Group Databasebeta

← #29700791

Subgroups — #29700791

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#21455037C211yesmaximal, characteristic
2C2×#16839877C211yesmaximal, characteristic, complemented
3#21454540C211yesmaximal, characteristic, complemented
4C2×#16839779C211yesmaximal, characteristic, complemented
5#21446711C211yesmaximal, characteristic, complemented
6#21446526C211yesmaximal, characteristic, complemented
7#21446464C211yesmaximal, characteristic, complemented
8#21446265C211yesmaximal, characteristic, complemented
9#21446149C211yesmaximal, characteristic, complemented
10#21446146C211yesmaximal, characteristic, complemented
11#21446094C211yesmaximal, characteristic, complemented
12#21446023C211yesmaximal, characteristic, complemented
13#21445661C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#2880C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519783C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic
20#16840273C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
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
38#16839779—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×#14519687C2211yescharacteristic, 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
70#14519797—22no—
71#14519797—22no—
72#14519797—41no—
73#14519797—41no—
74C2×#11758202C2×C411yescharacteristic
75C2×#11758202C2×C411yescharacteristic
76C2×#11758200C2×C411yescharacteristic
77C2×#11758200C2×C411yescharacteristic
78C2×#11758201C2×C411yescharacteristic
79C2×#11758201C2×C411yescharacteristic
80C2×#11758199C2×C411yescharacteristic
81C2×#11758199C2×C411yescharacteristic
82#14519783—22no—
83#14519783—41no—
84C2×#11758194—21no—
85C2×#11758194—22no—
86C2×#11758194—41no—
87C2×#11758194C2311yescharacteristic
88C2×#11758194C2311yescharacteristic
89C2×#11758189—21no—
90C22×#92418—21no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C2×C8×D61—21no—
94#14519760—21no—
95#14519756C2×C411yescharacteristic
96#14519756C2×C411yescharacteristic
97#14519751C2×C411yescharacteristic
98#14519751C2×C411yescharacteristic
99#14519746—21no—
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102#14519736—22no—
103#14519736—41no—
104#14519736C2311yescharacteristic
105C2×C4⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
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
120#14519701C2×C411yescharacteristic
121#14519701C2×C411yescharacteristic
122#14519701C2×C411yescharacteristic
123#14519698C2×C411yescharacteristic
124#14519698C2×C411yescharacteristic
125#14519698C2×C411yescharacteristic
126#14519698C2×C411yescharacteristic
127C22⋊#92418C2×C411yescharacteristic
128C22⋊#92418C2×C411yescharacteristic
129C22⋊#92418C2×C411yescharacteristic
130C22⋊#92418C2×C411yescharacteristic
131#14519689—21no—
132#14519689—21no—
133#14519687—21no—
134#14519687—41no—
135C8×Dic61—21no—
136C8×Dic61—22no—
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—21no—
230#11758222—21no—
231#11758222—21no—
232#11758222—21no—
233#11758222—21no—
234C2×D244C22×C411yescharacteristic
235C2×C4×D61—21no—
236C2×Dic122C22×C411yescharacteristic
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—21no—
241M16×C61—42no—
242M16×C61—42no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—42no—
250C2×C8×C61—42no—
251C2×C8×C61C2×D411yescharacteristic
252C2×C8×C61C2×D411yescharacteristic
253C2×C8×C61C2×D411yescharacteristic
254C2×C8×C61C2×D411yescharacteristic
255C22⋊Dic61—21no—
256C22⋊Dic61—21no—
257C22⋊Dic61—21no—
258C22⋊Dic61—42no—
259#11758202—22no—
260#11758202—41no—
261#11758201—22no—
262#11758201—41no—
263#11758200—22no—
264#11758200—41no—
265#11758199—22no—
266#11758199—41no—
267#11758198—21no—
268#11758198—21no—
269C4⋊Dic61—42no—
270C4⋊Dic61C22×C411yescharacteristic
271C4⋊Dic61C22×C411yescharacteristic
272#11758196—21no—
273#11758196—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61C2×D412yes—
279#11758194—21no—
280#11758194—21no—
281#11758194—21no—
282#11758194—42no—
283#11758194C2×D412yes—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—42no—
291C2×#92418C22×C411yescharacteristic
292C2×#92418C22×C411yescharacteristic
293C2×#92418C22×C411yescharacteristic
294C2×#92418C22×C411yescharacteristic
295#11758189—42no—
296C8×D61—42no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61—81no—
306C23×C61C4×D411yescharacteristic
307C23×C61C4×D411yescharacteristic
308C23×C61C2×#4111yescharacteristic
309C22×D61—21no—
310Q8×C61—21no—
311Q8×C61—21no—
312Q8×C61—21no—
313Q8×C61—42no—
314Q8×C61C4×D412yes—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—21no—
318D4×C61—21no—
319D4×C61—21no—
320D4×C61—42no—
321D4×C61—42no—
322D4×C61—42no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61C4×D412yes—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
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—22no—
336C2×C4×C61—22no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61C4×D411yescharacteristic
346C2×C4×C61C4×D411yescharacteristic
347C2×C4×C61C23×C411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C2×#4111yescharacteristic
351C2×C4×C61H(5,𝔽2)11yescharacteristic
352C2×C4×C61H(5,𝔽2)11yescharacteristic
353C22⋊D61—42no—
354C22⋊D61—41no—
355C22⋊D61—41no—
356C22⋊D61—81no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—22no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366D244—21no—
367D244—21no—
368C4×D61—41no—
369C4×D61—41no—
370Dic122—21no—
371Dic122—21no—
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—21no—
381#92418—21no—
382#92418—22no—
383#92418—41no—
384#22889—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—22no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61—84no—
402C22×C61C2×C4×D411yescharacteristic
403C22×C61#54611yescharacteristic
404C22×C61#55111yescharacteristic
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—22no—
411C4×C61—41no—
412C4×C61C2×C4×D411yescharacteristic
413C4×C61#51811yescharacteristic
414C4×C61D4211yescharacteristic
415C4×C61#54611yescharacteristic
416Dic61—42no—
417Dic61—41no—
418Dic61—41no—
419Dic61—41no—
420Dic61—81no—
421#3002—611no—
422C2×#443—611no—
423#2933—611no—
424C2×#421—611no—
425#2880D6111yescharacteristic, complemented
426#1975—611no—
427#1937—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876—611no—
432#1866—611no—
433#1855—611no—
434#1765—611no—
435#1750—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—41no—
439C2×C61—41no—
440C2×C61—42no—
441C2×C61—81no—
442C2×C61#235811yescharacteristic
443C2×C61#295511yescharacteristic
444C2×C61#295711yescharacteristic
445D61—81no—
446C22×#41C2×D6111yescharacteristic
447C2×#135—611no—
448C2×#135—611no—
449C2×#131—611no—
450C2×#131C2×D6111yescharacteristic
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×#104—611no—
477C2×#104—611no—
478#416—611no—
479#416—611no—
480#408—21no—
481#408—21no—
482#408—611no—
483#408C2×D6111yescharacteristic
484#408C2×D6111yescharacteristic
485#407—21no—
486#407C2×D6111yescharacteristic
487C2×C22⋊C8—21no—
488C2×C22⋊C8—611no—
489C2×C22⋊C8C2×D6111yescharacteristic
490#405—611no—
491C2×#97—611no—
492C2×C4×C8—611no—
493#341—611no—
494#341—611no—
495#339—611no—
496#339—611no—
497#336—611no—
498#336—611no—
499C61#2288911yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—611no—
507C2×#41C4×D6111yescharacteristic
508C2×#41C4×D6111yescharacteristic
509C2×#41C22×D6111yescharacteristic
510C2×#41C22×D6111yescharacteristic
511C22×Q8C4×D6111yescharacteristic
512C22×D4—21no—
513C22×D4C4×D6111yescharacteristic
514C23×C4—21no—
515C23×C4C22×D6111yescharacteristic
516#135—1222no—
517#135—1222no—
518#135—2441no—
519#135—2441no—
520C2×Q16—611no—
521C2×Q16—611no—
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16—611no—
525C2×SD16—611no—
526C2×D8—611no—
527C2×D8—611no—
528#131—22no—
529#131—22no—
530#131—41no—
531#131—41no—
532#131—1222no—
533#131—2441no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—611no—
537C2×M16—611no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1222no—
541C2×M16—2441no—
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—611no—
547C22×C8—611no—
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×C42—611no—
567#108—1222no—
568#108—2441no—
569C4⋊C8—1221no—
570C4⋊C8—1221no—
571#104—614no—
572#104—1222no—
573#104—1222no—
574#104—1222no—
575#104—1222no—
576#104—2441no—
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—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8C22⋊D6111yescharacteristic
598C22⋊C8C22⋊D6111yescharacteristic
599C22⋊C8C22⋊D6111yescharacteristic
600C22⋊C8C22⋊D6111yescharacteristic
601#97—1221no—
602#97—2441no—
603C4×C8—1222no—
604C4×C8—1221no—
605C24—21no—
606C24#1175822211yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—1221no—
622#41—1221no—
623#41—1221no—
624#41—1221no—
625#41D4×D6112yes—
626#41#1175822412yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—611no—
631C2×Q8C2×C4×D6111yescharacteristic
632C2×Q8C2×C4×D6111yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—611no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4C2×C4×D6111yescharacteristic
647C2×D4C2×C4×D6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4C2×C4×D6111yescharacteristic
664C22×C4#1175822211yescharacteristic
665C22×C4C2×C22⋊D6111yescharacteristic
666C22×C4C2×C22⋊D6111yescharacteristic
667C22×C4C23×D6111yescharacteristic
668Q16—1222no—
669Q16—2441no—
670SD16—1222no—
671SD16—1222no—
672SD16—2441no—
673SD16—2441no—
674D8—1222no—
675D8—2441no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—42no—
681M16—42no—
682M16—612no—
683M16—1221no—
684M16—1221no—
685M16—1221no—
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—42no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—611no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—2442no—
707C2×C8—2442no—
708C2×C8C2×C22⋊D6111yescharacteristic
709C2×C8C2×C22⋊D6111yescharacteristic
710C2×C8C2×C22⋊D6111yescharacteristic
711C2×C8C2×C22⋊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—612no—
724C42—1221no—
725C42—1221no—
726C42—1221no—
727C42—1221no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—1221no—
738C23C4×C22⋊D6111yescharacteristic
739C23C4×C22⋊D6111yescharacteristic
740C23C2×#1175822211yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—1221no—
746Q8—1221no—
747Q8#1451973712yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—1221no—
759D4—1221no—
760D4—4881no—
761D4—2442no—
762D4—2441no—
763D4—2441no—
764D4#1451973712yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1222no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4C4×C22⋊D6111yescharacteristic
796C2×C4C4×C22⋊D6111yescharacteristic
797C2×C4C22×C4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C22×C22⋊D6111yescharacteristic
800C2×C4C2×#1175822411yescharacteristic
801C2×C4#1451982211yescharacteristic
802C2×C4#1451982211yescharacteristic
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—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C2×C4×C22⋊D6111yescharacteristic
836C22#1684040211yescharacteristic
837C22#1684043811yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—4881no—
843C4—2442no—
844C4—2441no—
845C4—2441no—
846C4—2441no—
847C4C2×#1451973711yescharacteristic
848C4#1684023511yescharacteristic
849C4D4×C22⋊D6111yescharacteristic
850C4#1684040611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—4881no—
858C2#2144879811yescharacteristic
859C2#2145472011yescharacteristic
860C2#2145473411yescharacteristic
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#22889
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. C2×#16839779C2semidirect
5. #21446711C2semidirect
6. #21446526C2semidirect
7. #21446464C2semidirect
8. #21446265C2semidirect
9. #21446149C2semidirect
10. #21446146C2semidirect
11. #21446094C2semidirect
12. #21446023C2semidirect
13. #21445661C2semidirect
14. #21445587C2semidirect
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×#14519687C22semidirect
51. C2×C8×Dic61C22semidirect
52. #16839526C22semidirect
53. #16839526C22semidirect
54. #16839523C22semidirect
55. #16839523C22semidirect
56. #16839516C22semidirect
57. #16839516C22semidirect
116. #14519704D4semidirect
425. #2880D61semidirect
499. C61#22889semidirect

Maximal subgroups

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

subgroupindex
#214550372
C2×#168398772
#214545402
C2×#168397792
#214467112
#214465262
#214464642
#214462652
#214461492
#214461462
#214460942
#214460232
#214456612
#214455872
C61×#28802
#2288961