Finite Group Databasebeta

← #29733071

Subgroups — #29733071

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic
2C2×#16840095C211yesmaximal, characteristic, complemented
3C2×#16840018C211yesmaximal, characteristic, complemented
4#21447157C211yesmaximal, characteristic, complemented
5#21447022C211yesmaximal, characteristic, complemented
6#21446970C211yesmaximal, characteristic, complemented
7#21446827C211yesmaximal, characteristic, complemented
8#21446163C211yesmaximal, characteristic, complemented
9#21446132C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21446117C211yesmaximal, characteristic
12#21446072C211yesmaximal, characteristic, complemented
13#21446016C211yesmaximal, characteristic, complemented
14#21445540C211yesmaximal, characteristic, complemented
15C61×#2415C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18#16840452—24no—
19#16840452—24no—
20C2×#14519770—21no—
21C2×#14519769C2211yescharacteristic
22C2×#14519767—21no—
23C2×#14519758—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519756C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28C2×#14519733—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30#16840095—24no—
31#16840018—24no—
32C2×#14519710C2211yescharacteristic
33C2×#14519710C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C61×#397—21no—
57C61×#394—21no—
58C61×#391C2211yescharacteristic
59C61×#389—21no—
60C61×#389C2211yescharacteristic
61C61×#388—21no—
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65C2×#11758202—22no—
66C2×#11758202—22no—
67C2×#11758202—41no—
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519770—28no—
76#14519769—22no—
77#14519769—22no—
78#14519767—28no—
79#14519758—28no—
80#14519756—22no—
81#14519756—22no—
82#14519756—22no—
83#14519756D414yes—
84C4×Dic122—22no—
85C4×Dic122—22no—
86#14519736—22no—
87#14519736—22no—
88#14519733—28no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61D414yes—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105#14519710—22no—
106#14519710—22no—
107#14519708—22no—
108#14519701—22no—
109#14519701—22no—
110#14519701—22no—
111#14519700—22no—
112#14519700—22no—
113#14519700—41no—
114C22⋊#92418—22no—
115C22⋊#92418—22no—
116C22⋊#92418—41no—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61D411yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61—22no—
123C22⋊Q8×C61—22no—
124C22⋊Q8×C61—41no—
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127#117×C61—22no—
128#117×C61—41no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61D411yescharacteristic
141C2×C22⋊C4×C61D411yescharacteristic
142C2×C42×C61—21no—
143C2×C42×C61C2311yescharacteristic
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×D4×C61—22no—
157C2×D4×C61—41no—
158C2×D4×C61—41no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D412yes—
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2411yescharacteristic
180C22×Dic61—24no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—42no—
186C22×Dic61—42no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122C2×D412yes—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—42no—
200C4⋊C4×C61—42no—
201C4⋊C4×C61—42no—
202C4⋊C4×C61#4112yes—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—42no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61—42no—
212C22⋊Dic61—24no—
213C22⋊Dic61—24no—
214C22⋊Dic61—24no—
215#11758202—44no—
216C4⋊Dic61—24no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61C2×D412yes—
221C4⋊Dic61C2×D412yes—
222C4⋊Dic61C2×D412yes—
223#11758196—24no—
224#11758196—24no—
225#11758196—24no—
226#11758196—24no—
227#11758196—24no—
228C4×Dic61—24no—
229C4×Dic61—24no—
230#11758194—44no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418#4112yes—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61#12012yes—
257C23×C61C22×D411yescharacteristic
258Q8×C61—41no—
259Q8×C61—41no—
260Q8×C61—41no—
261Q8×C61—41no—
262D4×C61—44no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61#12012yes—
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C2×C4×C612−1+411yescharacteristic
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—48no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314Dic122—22no—
315Dic122—22no—
316Dic122—41no—
317Dic122—41no—
318#92418—22no—
319#92418—41no—
320#92418—41no—
321#92418—41no—
322#25557—611nomaximal, Sylow
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61C2×#12011yescharacteristic
338C22×C61#54611yescharacteristic
339C22×C61#54711yescharacteristic
340C22×C61#57511yescharacteristic
341C22×C61#57511yescharacteristic
342C22×C61#57811yescharacteristic
343C22×C61#57811yescharacteristic
344C4×C61—22no—
345C4×C61—41no—
346C4×C61—41no—
347C4×C61—41no—
348C4×C61—42no—
349C4×C61—81no—
350C4×C61—81no—
351C4×C61—81no—
352C4×C61#53211yescharacteristic
353C4×C61#53711yescharacteristic
354C4×C61#54611yescharacteristic
355C4×C61#54711yescharacteristic
356Dic61—42no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360C2×#552—611no—
361C2×#484—611no—
362C2×#470—611no—
363#2415D6111yescharacteristic
364#2059—611no—
365#2036—611no—
366#2026—611no—
367#2001—611no—
368#1878—611no—
369#1873—611no—
370#1873—611no—
371#1870—611no—
372#1863—611no—
373#1854—611no—
374#1736—611no—
375C2×C61—42no—
376C2×C61—81no—
377C2×C61#243011yescharacteristic
378C2×C61#300511yescharacteristic
379C2×C61#301111yescharacteristic
380C2×C61#331511yescharacteristic
381C2×C61#332711yescharacteristic
382C2×C61#334911yescharacteristic
383C2×C61#335211yescharacteristic
384C22×Q16—611no—
385C22×M16—611no—
386#552—1224no—
387#552—1224no—
388C2×#126—1221no—
389C2×#125—611no—
390C2×#125—1221no—
391C2×#123—1221no—
392C2×C22⋊Q8—611no—
393C2×C22⋊Q8—611no—
394C2×C22⋊Q8C2×D6111yescharacteristic
395C2×C22⋊Q8C2×D6111yescharacteristic
396C2×C4×Q8—611no—
397C2×C4×D4C2×D6111yescharacteristic
398C2×#117—611no—
399C2×#117—1221no—
400C2×#117C2×D6111yescharacteristic
401C22×C4⋊C4—611no—
402#484—1224no—
403#470—1224no—
404C2×#107—611no—
405C2×#107—611no—
406C2×#106—611no—
407C2×#103—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416#397—21no—
417#394—21no—
418#391C2×D6111yescharacteristic
419#389—21no—
420#389C2×D6111yescharacteristic
421#388—21no—
422#380C2×D6111yescharacteristic
423#340—611no—
424#340—611no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#336—611no—
430#336—611no—
431C61#2555711yescharacteristic, complemented, Sylow
432C22×Q8—611no—
433C22×Q8C22×D6111yescharacteristic
434C22×D4C22⋊D6111yescharacteristic
435C23×C4—1221no—
436C23×C4C22×D6111yescharacteristic
437C23×C4C22×D6111yescharacteristic
438C2×Q16—1222no—
439C2×Q16—1222no—
440C2×Q16—2441no—
441C2×M16—1222no—
442C2×M16—1222no—
443C2×M16—2441no—
444C22×C8—611no—
445C22×C8—611no—
446C22×C8—611no—
447C22×C8—611no—
448#126—1228no—
449#125—1222no—
450#125—1222no—
451#125—1228no—
452#123—1228no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456C22⋊Q8—41no—
457C22⋊Q8—614no—
458C22⋊Q8—1222no—
459C22⋊Q8—1222no—
460C22⋊Q8—1222no—
461C4×Q8—1222no—
462C4×Q8—1222no—
463C4×D4—22no—
464C4×D4—22no—
465#117—22no—
466#117—41no—
467#117—1228no—
468#117—1222no—
469#117—1222no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—614no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—1222no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4C22⋊D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4C22⋊D6111yescharacteristic
496C2×C22⋊C4C22⋊D6111yescharacteristic
497C2×C42—21no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42C22×D6111yescharacteristic
501#107—1222no—
502#107—1222no—
503#106—1222no—
504#103—1222no—
505#103—1222no—
506#103—1222no—
507#103—1222no—
508#103—1222no—
509#103—2441no—
510C22⋊C8—1222no—
511C22⋊C8—1222no—
512C22⋊C8—2441no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517C24C2×C22⋊D6111yescharacteristic
518C24C2×C22⋊D6111yescharacteristic
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—612no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×D4—22no—
532C2×D4—41no—
533C2×D4—41no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1224no—
553C22×C4—2442no—
554C22×C4—2442no—
555C22×C4D4×D6112yes—
556C22×C4D4×D6112yes—
557C22×C4C2×C22⋊D6111yescharacteristic
558C22×C4C2×C22⋊D6111yescharacteristic
559C22×C4C2×C22⋊D6111yescharacteristic
560C22×C4C2×C22⋊D6111yescharacteristic
561C22×C4C23×D6111yescharacteristic
562Q16—2444no—
563M16—2444no—
564C2×C8—612no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C4⋊C4—21no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—612no—
586C4⋊C4—612no—
587C4⋊C4—612no—
588C4⋊C4—1224no—
589C4⋊C4—1224no—
590C4⋊C4—1224no—
591C4⋊C4—1224no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1224no—
596C4⋊C4—1224no—
597C4⋊C4#1175822412yes—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—1224no—
605C22⋊C4—1224no—
606C22⋊C4—1224no—
607C42—21no—
608C42—21no—
609C42—42no—
610C42—1224no—
611C42—1224no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23#1451974512yes—
626C23C22×C22⋊D6111yescharacteristic
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—1222no—
632Q8—1222no—
633Q8—2441no—
634Q8—2441no—
635D4—44no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—2448no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4#1451974512yes—
681C2×C4C2×D4×D6111yescharacteristic
682C2×C4C2×D4×D6111yescharacteristic
683C2×C4#41×D6111yescharacteristic
684C2×C4C2×#1175822411yescharacteristic
685C2×C4#1451982211yescharacteristic
686C2×C4#1451982411yescharacteristic
687C8—1222no—
688C8—2441no—
689C8—2441no—
690C8—2441no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22C2×#1451974511yescharacteristic
706C22#1684040611yescharacteristic
707C22#1684041111yescharacteristic
708C22#1684056011yescharacteristic
709C22#1684056011yescharacteristic
710C22#1684057711yescharacteristic
711C22#1684057711yescharacteristic
712C4—22no—
713C4—41no—
714C4—41no—
715C4—41no—
716C4—42no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—2442no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4#1684030711yescharacteristic
725C4#1684033911yescharacteristic
726C4#1684040111yescharacteristic
727C4#1684041211yescharacteristic
728C2—42no—
729C2—81no—
730C2#2144942511yescharacteristic
731C2#2145505911yescharacteristic
732C2#2145511211yescharacteristic
733C2#2145791511yescharacteristic
734C2#2145808711yescharacteristic
735C2#2145834311yescharacteristic
736C2#2145838811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2415C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenter#2415D61
hypocenterC61#25557
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
2. C2×#16840095C2semidirect
3. C2×#16840018C2semidirect
4. #21447157C2semidirect
5. #21447022C2semidirect
6. #21446970C2semidirect
7. #21446827C2semidirect
8. #21446163C2semidirect
9. #21446132C2semidirect
10. #21446131C2semidirect
12. #21446072C2semidirect
13. #21446016C2semidirect
14. #21445540C2semidirect
431. C61#25557semidirect

Maximal subgroups

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

subgroupindex
C2×#168404522
C2×#168400952
C2×#168400182
#214471572
#214470222
#214469702
#214468272
#214461632
#214461322
#214461312
#214461172
#214460722
#214460162
#214455402
C61×#24152
#2555761