Finite Group Databasebeta

← #29696550

Subgroups — #29696550

Order 15616.

1036 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2C2×#16839893C211yesmaximal, characteristic, complemented
3#21446759C211yesmaximal, characteristic, complemented
4#21446759C211yesmaximal, characteristic, complemented
5#21446758C211yesmaximal, characteristic, complemented
6#21446758C211yesmaximal, characteristic, complemented
7#21446755C211yesmaximal, characteristic, complemented
8#21446754C211yesmaximal, characteristic, complemented
9#21445800C211yesmaximal, characteristic
10#21445800C211yesmaximal, characteristic
11#21445796C211yesmaximal, characteristic
12#21445588C211yesmaximal, characteristic
13#21445586C211yesmaximal, characteristic
14#21445582C211yesmaximal, characteristic
15C2×C61×#446C211yesmaximal, characteristic, complemented
16#16840316—24no—
17#16840316—24no—
18C2×#14519776C411yescharacteristic
19C2×#14519775C411yescharacteristic
20C2×#14519767C411yescharacteristic
21C2×#14519767C411yescharacteristic
22C2×#14519757C411yescharacteristic
23C2×#14519755C411yescharacteristic
24C2×#14519755C411yescharacteristic
25C2×#14519753C411yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×Dic122C2211yescharacteristic
29C2×#14519734C2211yescharacteristic
30C2×#14519734C2211yescharacteristic
31C2×C42×D61C2211yescharacteristic
32#16839893—24no—
33C2×C4⋊#92418C2211yescharacteristic
34C2×C4⋊#92418C2211yescharacteristic
35C2×C4⋊#92418C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519688C2211yescharacteristic
41C2×#14519688C2211yescharacteristic
42C2×C4×#92418C2211yescharacteristic
43#16839516C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C61×#446—24no—
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C22×Dic122C2×C411yescharacteristic
64C22×Dic122C2×C411yescharacteristic
65C22×Dic122C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519776—24no—
74#14519775—24no—
75#14519767—24no—
76#14519767—24no—
77#14519757—24no—
78#14519755—24no—
79#14519755—24no—
80#14519753—24no—
81C4×Dic122—22no—
82C4×Dic122—22no—
83C4×Dic122—22no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C4×Dic122—22no—
87#14519734—22no—
88#14519734—22no—
89#14519734—22no—
90#14519734—22no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C42×D61—22no—
114C42×D61—22no—
115C4⋊#92418—22no—
116C4⋊#92418—22no—
117C4⋊#92418—22no—
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519689Q814yescomplemented
122#14519688—22no—
123#14519688—22no—
124C4×#92418—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C4×Q8×C61D414yes—
131C4×Q8×C61D414yes—
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—22no—
139C4⋊C8×C61—22no—
140C4⋊C8×C61—22no—
141#97×C61—22no—
142#97×C61—22no—
143C4×C8×C61—22no—
144C23×D61C22×C411yescharacteristic
145C2×Q8×C61—41no—
146C2×Q8×C61—41no—
147C2×Q8×C61C22⋊C414yes—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—41no—
170C2×C4×D61—41no—
171C2×C4×D61—41no—
172C2×C4×D61C2×Q812yes—
173C2×C4×D61#4112yes—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122—22no—
179C2×Dic122—41no—
180C2×Dic122—41no—
181C2×Dic122—41no—
182C2×Dic122—41no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61C2×Q812yes—
195C4⋊C4×C61C22⋊C414yes—
196C4⋊C4×C61C22⋊C414yes—
197C4⋊C4×C61C22⋊C414yes—
198C42×C61C2×D412yes—
199C42×C61C2×D412yes—
200C42×C61C2×D412yes—
201C42×C61C2×D412yes—
202C42×C61C2×D412yes—
203C42×C61C2×D412yes—
204#11758198—22no—
205#11758198—22no—
206#11758198—22no—
207#11758198—22no—
208C4⋊Dic61—22no—
209C4⋊Dic61—22no—
210C4⋊Dic61—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—22no—
214#11758196—22no—
215#11758196—22no—
216#11758196—22no—
217#11758196—22no—
218#11758196—22no—
219#11758196—22no—
220#11758196—22no—
221C4×Dic61—22no—
222C4×Dic61—22no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C2×#92418—21no—
230C2×#92418—21no—
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×#92418C2×Q812yes—
241C23×C61C23×C411yescharacteristic
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61C4×Q812yes—
249Q8×C61—44no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61C2×C22⋊C412yes—
263C2×C4×C61C2×C22⋊C412yes—
264C2×C4×C61C2×C22⋊C412yes—
265C2×C4×C61C2×C22⋊C412yes—
266C2×C4×C61C2×C22⋊C412yes—
267C2×C4×C61C2×C22⋊C412yes—
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C22×Q811yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C612−1+411yescharacteristic
273C2×C4×C612−1+411yescharacteristic
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61C4×Q812yes—
294C2×Dic61#13112yes—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—44no—
300C4×D61—44no—
301Dic122—44no—
302Dic122—44no—
303Dic122—44no—
304C8×C61—22no—
305C8×C61—41no—
306C8×C61—41no—
307C8×C61—41no—
308#92418—22no—
309#92418—41no—
310#92418—41no—
311#92418—41no—
312#22511—611nomaximal, Sylow
313C22×C61C22×C22⋊C411yescharacteristic
314C22×C61C2×C4×Q811yescharacteristic
315C22×C61#51911yescharacteristic
316C22×C61C2×#13111yescharacteristic
317C22×C61#56811yescharacteristic
318C22×C61#56811yescharacteristic
319C22×C61#56811yescharacteristic
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—41no—
327C4×C61—22no—
328C4×C61—22no—
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—22no—
333C4×C61#54811yescharacteristic
334C4×C61#54811yescharacteristic
335C4×C61D4×Q811yescharacteristic
336C4×C61D4×Q811yescharacteristic
337Dic61—22no—
338Dic61—22no—
339Dic61—41no—
340Dic61—41no—
341Dic61—41no—
342Dic61—41no—
343Dic61—41no—
344C2×#533—611no—
345C2×#446—611no—
346C2×#446D6111yescharacteristic, complemented
347#1985—611no—
348#1985—611no—
349#1985—611no—
350#1985—611no—
351#1984—611no—
352#1984—611no—
353#1798—611no—
354#1798—611no—
355#1797—611no—
356#1750—611no—
357#1750—611no—
358#1749—611no—
359C2×C61Q8×C22⋊C411yescharacteristic
360C2×C61#287911yescharacteristic
361C2×C61#288011yescharacteristic
362C2×C61#296111yescharacteristic
363C2×C61#296211yescharacteristic
364C2×C61#298511yescharacteristic
365C2×C61#298711yescharacteristic
366D61—42no—
367#533—1224no—
368#533—1224no—
369C2×C4⋊Q8—611no—
370C2×C4⋊Q8—611no—
371C2×#125—611no—
372C2×#125—611no—
373C2×C22⋊Q8—611no—
374C2×C22⋊Q8—611no—
375C2×C22⋊Q8—611no—
376C2×C22⋊Q8—611no—
377C2×C4×Q8—611no—
378C2×C4×Q8—611no—
379C2×C4×Q8—611no—
380C2×C4×Q8C2×D6111yescharacteristic
381C2×#117—611no—
382C2×#117—611no—
383C22×C42—611no—
384#446—24no—
385#446—1224no—
386C2×C4⋊C8—611no—
387C2×C4⋊C8—611no—
388C2×C4⋊C8—611no—
389C2×C4⋊C8C2×D6111yescharacteristic
390C2×C4⋊C8C2×D6111yescharacteristic
391C2×C4⋊C8C2×D6111yescharacteristic
392C2×C22⋊C8—611no—
393C2×C22⋊C8—611no—
394C2×C22⋊C8—611no—
395C2×C22⋊C8—611no—
396C2×#97—611no—
397C2×#97—611no—
398C2×#97C2×D6111yescharacteristic
399C2×#97C2×D6111yescharacteristic
400C2×C4×C8—611no—
401C2×C4×C8C2×D6111yescharacteristic
402#336—611no—
403#336—611no—
404#336—611no—
405#336—611no—
406#336—611no—
407#336—611no—
408#336—611no—
409#336—611no—
410#336—611no—
411#336—611no—
412#336—611no—
413#336—611no—
414C61#2251111yescharacteristic, complemented, Sylow
415C22×Q8—611no—
416C22×Q8—611no—
417C22×Q8—611no—
418C22×Q8C4×D6111yescharacteristic
419C23×C4—611no—
420C23×C4—611no—
421C23×C4—611no—
422C22×C8—611no—
423C22×C8—611no—
424C22×C8—611no—
425C22×C8—611no—
426C22×C8C22×D6111yescharacteristic
427C22×C8C22×D6111yescharacteristic
428C22×C8C22×D6111yescharacteristic
429C22×C8C22×D6111yescharacteristic
430C4⋊Q8—1224no—
431C4⋊Q8—1224no—
432#125—1224no—
433#125—1224no—
434C22⋊Q8—1224no—
435C22⋊Q8—1224no—
436C22⋊Q8—1224no—
437C22⋊Q8—1224no—
438C4×Q8—1222no—
439C4×Q8—1222no—
440C4×Q8—1222no—
441C4×Q8—1222no—
442C4×Q8—1222no—
443C4×Q8—1222no—
444C4×Q8D24414yes—
445C4×Q8C22⋊D6114yes—
446#117—1222no—
447#117—1222no—
448#117—1222no—
449#117—1222no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4C4×D6111yescharacteristic
464C2×C4⋊C4C4×D6111yescharacteristic
465C2×C4⋊C4C4×D6111yescharacteristic
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—611no—
469C2×C22⋊C4—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—1222no—
476C2×C42—1222no—
477C2×C42C22×D6111yescharacteristic
478C2×C42C22×D6111yescharacteristic
479C2×C42C22×D6111yescharacteristic
480C4⋊C8—22no—
481C4⋊C8—22no—
482C4⋊C8—22no—
483C4⋊C8—1222no—
484C4⋊C8—1222no—
485C4⋊C8—1222no—
486C22⋊C8—614no—
487C22⋊C8—1222no—
488C22⋊C8—1222no—
489C22⋊C8—1222no—
490#97—22no—
491#97—22no—
492#97—1222no—
493#97—1222no—
494C4×C8—22no—
495C4×C8—1222no—
496C24—611no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—1222no—
500C2×Q8—1222no—
501C2×Q8—1222no—
502C2×Q8—1222no—
503C2×Q8—1222no—
504C2×Q8—2441no—
505C2×Q8—2441no—
506C2×Q8—2441no—
507C2×Q8—2441no—
508C2×Q8#1175819814yes—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—612no—
512C22×C4—612no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—1222no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—2441no—
526C22×C4—2441no—
527C22×C4—2441no—
528C22×C4C2×C4×D6111yescharacteristic
529C22×C4C2×C4×D6111yescharacteristic
530C22×C4C2×C4×D6111yescharacteristic
531C22×C4C2×C4×D6111yescharacteristic
532C22×C4C2×C4×D6111yescharacteristic
533C22×C4C2×C4×D6111yescharacteristic
534C22×C4C23×D6111yescharacteristic
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—612no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8Q8×D6112yes—
559C4⋊C4—1222no—
560C4⋊C4—1222no—
561C4⋊C4—1222no—
562C4⋊C4—1222no—
563C4⋊C4—1222no—
564C4⋊C4—1222no—
565C4⋊C4—1222no—
566C4⋊C4—1222no—
567C4⋊C4—1222no—
568C4⋊C4—1222no—
569C4⋊C4—1222no—
570C4⋊C4—1222no—
571C4⋊C4—1222no—
572C4⋊C4#1175819814yes—
573C4⋊C4#1175819814yes—
574C4⋊C4#1175819814yes—
575C22⋊C4—1222no—
576C22⋊C4—1222no—
577C22⋊C4—1222no—
578C22⋊C4—1222no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42—1221no—
583C42—1221no—
584C42—1221no—
585C42—1222no—
586C42—1222no—
587C42C2×D24412yes—
588C42C2×D24412yes—
589C42C2×D24412yes—
590C42C2×C22⋊D6112yes—
591C42C2×C22⋊D6112yes—
592C42C2×C22⋊D6112yes—
593C23—612no—
594C23—1221no—
595C23—1221no—
596C23—1221no—
597C23—1221no—
598C23—1221no—
599C23—1221no—
600C23C22×C4×D6111yescharacteristic
601Q8—44no—
602Q8—2444no—
603Q8—2444no—
604Q8—2444no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—2444no—
643C2×C4—2444no—
644C2×C4C2×#1175819812yes—
645C2×C4C2×#1175819812yes—
646C2×C4C2×#1175819812yes—
647C2×C4C2×#1175819812yes—
648C2×C4C2×#1175819812yes—
649C2×C4C2×#1175819812yes—
650C2×C4C22×C22⋊D6111yescharacteristic
651C2×C4C22×D24411yescharacteristic
652C2×C4C2×Q8×D6111yescharacteristic
653C2×C4#41×D6111yescharacteristic
654C2×C4#1451982411yescharacteristic
655C2×C4#1451982511yescharacteristic
656C8—22no—
657C8—41no—
658C8—41no—
659C8—41no—
660C8—1222no—
661C8—2441no—
662C8—2441no—
663C8—2441no—
664C22—1222no—
665C22—1222no—
666C22—1222no—
667C22—2441no—
668C22—2441no—
669C22—2441no—
670C22—2441no—
671C22C22×#1175819811yescharacteristic
672C22C4×Q8×D6111yescharacteristic
673C22#1684023811yescharacteristic
674C22#131×D6111yescharacteristic
675C22#1684052711yescharacteristic
676C22#1684052811yescharacteristic
677C22#1684052811yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—1222no—
685C4—1222no—
686C4—2441no—
687C4—2441no—
688C4—2441no—
689C4—2441no—
690C4—2441no—
691C4#1684041911yescharacteristic
692C4#1684042411yescharacteristic
693C4Q8×C22⋊D6111yescharacteristic
694C4Q8×D24411yescharacteristic
695C2—2442no—
696C2Q8×#1175819811yescharacteristic
697C2#2145426311yescharacteristic
698C2#2145426611yescharacteristic
699C2#2145475511yescharacteristic
700C2#2145476411yescharacteristic
701C2#2145491211yescharacteristic
702C2#2145492211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#446C2
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenterC2×#446D61
hypocenterC61#22511
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#16839893C2semidirect
3. #21446759C2semidirect
4. #21446759C2semidirect
5. #21446758C2semidirect
6. #21446758C2semidirect
7. #21446755C2semidirect
8. #21446754C2semidirect
15. C2×C61×#446C2semidirect
121. #14519689Q8semidirect
346. C2×#446D61semidirect
414. C61#22511semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
C2×#168398932
#214467592
#214467582
#214467552
#214467542
#214458002
#214457962
#214455882
#214455862
#214455822
C2×C61×#4462
#2251161