Finite Group Databasebeta

← #29698098

Subgroups — #29698098

Order 15616.

964 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×#16839834C211yesmaximal, characteristic
2C2×#16839790C211yesmaximal, characteristic, complemented
3C2×#16839788C211yesmaximal, characteristic, complemented
4#21448284C211yesmaximal, characteristic
5#21446542C211yesmaximal, characteristic, complemented
6#21446540C211yesmaximal, characteristic, complemented
7#21446002C211yesmaximal, characteristic, complemented
8#21446001C211yesmaximal, characteristic, complemented
9#21445997C211yesmaximal, characteristic, complemented
10#21445996C211yesmaximal, characteristic, complemented
11#21445970C211yesmaximal, characteristic, complemented
12#21445801C211yesmaximal, characteristic, complemented
13#21445801C211yesmaximal, characteristic, complemented
14#21445673C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16839834—24no—
21#16839790—24no—
22#16839788—24no—
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519706C2211yescharacteristic
33C2×#14519706C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37#16839665C411yescharacteristic
38#16839665C411yescharacteristic
39#16839661C411yescharacteristic
40#16839661C411yescharacteristic
41#16839655C411yescharacteristic
42#16839655C411yescharacteristic
43#16839655C411yescharacteristic
44#16839655C411yescharacteristic
45C4×C4⋊Dic61C2211yescharacteristic
46C4×C22⋊Dic61C2211yescharacteristic
47C4×C22⋊Dic61C2211yescharacteristic
48C42×Dic61C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#435—24no—
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C2×#11758194—22no—
64C2×#11758194—22no—
65C2×#11758194—41no—
66C22×#92418—22no—
67C22×#92418—22no—
68C22×#92418—41no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519736—22no—
74#14519736—22no—
75#14519736—22no—
76#14519736—22no—
77C2×C4⋊Dic61C2×C411yescharacteristic
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×C4⋊Dic61C2×C411yescharacteristic
80C2×C4⋊Dic61C2×C411yescharacteristic
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×C22⋊Dic61C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×C22⋊Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C4⋊#92418—22no—
100#14519706—22no—
101#14519706—22no—
102#14519706—22no—
103#14519706—22no—
104#14519706—22no—
105#14519706—22no—
106#14519706—22no—
107#14519706—41no—
108#14519706—41no—
109#14519706D414yescomplemented
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112#14519688—22no—
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119C22×D4×C61C2×C411yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C2×M16×C61—41no—
125C22×C8×C61—22no—
126C22×C8×C61—22no—
127C22×C8×C61—41no—
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C4×D4×C61D414yes—
133C4×D4×C61Q814yes—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—22no—
139C22⋊C8×C61—22no—
140C22⋊C8×C61—22no—
141#97×C61—22no—
142C24×C61C22×C411yescharacteristic
143C24×C61C22×C411yescharacteristic
144C2×D4×C61—41no—
145C2×D4×C61—41no—
146C2×D4×C61C4⋊C414yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×Q812yes—
162C22×C4×C61C2×Q812yes—
163C22×C4×C61C2411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172M16×C61—44no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—44no—
185C2×C8×C61C2×D412yes—
186C4⋊C4×C61C4⋊C414yes—
187C22⋊C4×C61C4⋊C414yes—
188C22⋊C4×C61C4⋊C414yes—
189C42×C61C2×D412yes—
190C42×C61C2×Q812yes—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—22no—
197C22⋊Dic61—41no—
198C22⋊Dic61—41no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61—41no—
204C4⋊Dic61—41no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—22no—
212C4×Dic61—41no—
213C4×Dic61—41no—
214C4×Dic61—41no—
215C4×Dic61C2×D412yes—
216C4×Dic61#4112yes—
217#11758194—44no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—44no—
230C2×#92418C2×D412yes—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61C2×C4⋊C412yes—
244C23×C61C2×C4⋊C412yes—
245C23×C61C23×C411yescharacteristic
246D4×C61—44no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61C2×C4⋊C412yes—
264C2×C4×C61C2×C4⋊C412yes—
265C2×C4×C61C2×C4⋊C412yes—
266C2×C4×C61C2×C4⋊C412yes—
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×Q811yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61H(5,𝔽2)11yescharacteristic
272C2×C4×C612−1+411yescharacteristic
273C2×Dic61—21no—
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×Dic61—21no—
294C2×Dic61C4×D412yes—
295C2×Dic61C4×D412yes—
296C2×Dic61#13112yes—
297C8×C61—22no—
298C8×C61—41no—
299C8×C61—41no—
300C8×C61—41no—
301#92418—22no—
302#92418—41no—
303#92418—41no—
304#92418—41no—
305#22652—611nomaximal, Sylow
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61C22×C4⋊C411yescharacteristic
321C22×C61C2×C4×D411yescharacteristic
322C22×C61#52011yescharacteristic
323C22×C61C2×#13111yescharacteristic
324C22×C61#56811yescharacteristic
325C22×C61#56811yescharacteristic
326C22×C61#56811yescharacteristic
327C4×C61—22no—
328C4×C61—22no—
329C4×C61—22no—
330C4×C61—22no—
331C4×C61D4211yescharacteristic
332C4×C61#54711yescharacteristic
333C4×C61D4×Q811yescharacteristic
334C4×C61#55411yescharacteristic
335Dic61—22no—
336Dic61—22no—
337Dic61—22no—
338Dic61—41no—
339Dic61—41no—
340Dic61—41no—
341Dic61—41no—
342Dic61—41no—
343C2×#435—611no—
344C2×#435D6111yescharacteristic
345C2×#424—611no—
346C2×#424—611no—
347#2293—611no—
348#1940—611no—
349#1940—611no—
350#1851—611no—
351#1851—611no—
352#1850—611no—
353#1850—611no—
354#1842—611no—
355#1798—611no—
356#1798—611no—
357#1767—611no—
358C2×C61—42no—
359C2×C61—42no—
360C2×C61D4×C4⋊C411yescharacteristic
361C2×C61#290511yescharacteristic
362C2×C61#290611yescharacteristic
363C2×C61#293211yescharacteristic
364C2×C61#293511yescharacteristic
365C2×C61#299211yescharacteristic
366C2×C61#299511yescharacteristic
367C22×M16—611no—
368C22×M16C2×D6111yescharacteristic
369C23×C8—611no—
370C23×C8C2×D6111yescharacteristic
371C2×C4×D4C2×D6111yescharacteristic
372C2×#117—611no—
373C2×#117—611no—
374#435—24no—
375#435—1224no—
376#424—1224no—
377#424—1224no—
378C2×C4⋊C8—611no—
379C2×C4⋊C8—611no—
380C2×C4⋊C8—611no—
381C2×C4⋊C8—611no—
382C2×C4⋊C8—611no—
383C2×C4⋊C8—611no—
384C2×C4⋊C8—611no—
385C2×C4⋊C8—611no—
386C2×C4⋊C8—611no—
387C2×C4⋊C8—611no—
388C2×C4⋊C8—611no—
389C2×C4⋊C8C2×D6111yescharacteristic
390C2×C22⋊C8—611no—
391C2×C22⋊C8—611no—
392C2×C22⋊C8C2×D6111yescharacteristic
393C2×C22⋊C8C2×D6111yescharacteristic
394C2×#97—611no—
395C2×#97C2×D6111yescharacteristic
396#390—611no—
397#390—611no—
398#389—611no—
399#389—611no—
400#388—611no—
401#388—611no—
402#388—611no—
403#388—611no—
404C4×C4⋊C4—611no—
405C4×C22⋊C4—611no—
406C4×C22⋊C4—611no—
407C43—611no—
408#336—611no—
409#336—611no—
410#336—611no—
411#336—611no—
412#336—611no—
413#336—611no—
414C61#2265211yescharacteristic, complemented, Sylow
415C22×D4C4×D6111yescharacteristic
416C23×C4C22×D6111yescharacteristic
417C23×C4C22×D6111yescharacteristic
418C2×M16—22no—
419C2×M16—22no—
420C2×M16—41no—
421C2×M16—1222no—
422C2×M16—1222no—
423C2×M16—2441no—
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—41no—
427C22×C8—611no—
428C22×C8—611no—
429C22×C8—611no—
430C22×C8—611no—
431C22×C8—1222no—
432C22×C8—1222no—
433C22×C8—2441no—
434C22×C8C22×D6111yescharacteristic
435C22×C8C22×D6111yescharacteristic
436C22×C8C22×D6111yescharacteristic
437C22×C8C22×D6111yescharacteristic
438C4×D4Dic12214yes—
439C4×D4C22⋊D6114yes—
440#117—1222no—
441#117—1222no—
442#117—1222no—
443#117—1222no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4—611no—
446C2×C4⋊C4—611no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4C4×D6111yescharacteristic
451C2×C22⋊C4—611no—
452C2×C22⋊C4—611no—
453C2×C22⋊C4—611no—
454C2×C22⋊C4—611no—
455C2×C22⋊C4—611no—
456C2×C22⋊C4—611no—
457C2×C22⋊C4—611no—
458C2×C22⋊C4—611no—
459C2×C22⋊C4C4×D6111yescharacteristic
460C2×C22⋊C4C4×D6111yescharacteristic
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42—611no—
466C2×C42—611no—
467C2×C42—611no—
468C2×C42—611no—
469C2×C42C22×D6111yescharacteristic
470C4⋊C8—22no—
471C4⋊C8—614no—
472C4⋊C8—1222no—
473C4⋊C8—1222no—
474C4⋊C8—1222no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477C4⋊C8—1222no—
478C4⋊C8—1222no—
479C4⋊C8—1222no—
480C4⋊C8—2441no—
481C4⋊C8—2441no—
482C22⋊C8—22no—
483C22⋊C8—22no—
484C22⋊C8—1222no—
485C22⋊C8—1222no—
486#97—22no—
487#97—1222no—
488#95—611no—
489#95—611no—
490#95—611no—
491#95—611no—
492#95—611no—
493#95—611no—
494C24C2×C4×D6111yescharacteristic
495C24C2×C4×D6111yescharacteristic
496C2×D4—41no—
497C2×D4—41no—
498C2×D4#1175819614yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4C2×Dic12212yes—
516C22×C4C2×Dic12212yes—
517C22×C4C2×C4×D6111yescharacteristic
518C22×C4C2×C4×D6111yescharacteristic
519C22×C4C2×C4×D6111yescharacteristic
520C22×C4C2×C4×D6111yescharacteristic
521C22×C4C2×C22⋊D6112yes—
522C22×C4C2×C22⋊D6112yes—
523C22×C4C23×D6111yescharacteristic
524M16—44no—
525M16—2444no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—44no—
538C2×C8—612no—
539C2×C8—1221no—
540C2×C8—1221no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—2444no—
551C2×C8D4×D6112yes—
552C4⋊C4—1222no—
553C4⋊C4—1222no—
554C4⋊C4—1222no—
555C4⋊C4—1222no—
556C4⋊C4—2441no—
557C4⋊C4—2441no—
558C4⋊C4#1175819614yes—
559C22⋊C4—1222no—
560C22⋊C4—1222no—
561C22⋊C4—1222no—
562C22⋊C4—1222no—
563C22⋊C4—1222no—
564C22⋊C4—1222no—
565C22⋊C4—2441no—
566C22⋊C4—2441no—
567C22⋊C4#1175819614yes—
568C22⋊C4#1175819614yes—
569C42—612no—
570C42—612no—
571C42—1222no—
572C42—1221no—
573C42—1221no—
574C42—1221no—
575C42—1221no—
576C42—1221no—
577C42—1221no—
578C42—2441no—
579C42—2441no—
580C42—2441no—
581C42C2×Dic12212yes—
582C42C2×C22⋊D6112yes—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23C2×#1175819612yes—
596C23C2×#1175819612yes—
597C23C22×C4×D6111yescharacteristic
598D4—44no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—612no—
616C2×C4—612no—
617C2×C4—612no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
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×C4C2×#1175819612yes—
640C2×C4C2×#1175819612yes—
641C2×C4C2×#1175819612yes—
642C2×C4C2×#1175819612yes—
643C2×C4C2×D4×D6111yescharacteristic
644C2×C4C22×C22⋊D6111yescharacteristic
645C2×C4C22×Dic12211yescharacteristic
646C2×C4#41×D6111yescharacteristic
647C2×C4#1451982211yescharacteristic
648C2×C4#1451982411yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C8—1222no—
654C8—2441no—
655C8—2441no—
656C8—2441no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22C22×#1175819611yescharacteristic
672C22C4×D4×D6111yescharacteristic
673C22#1684024111yescharacteristic
674C22#131×D6111yescharacteristic
675C22#1684052711yescharacteristic
676C22#1684052811yescharacteristic
677C22#1684052811yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—1222no—
683C4—1222no—
684C4—1222no—
685C4—2441no—
686C4—2441no—
687C4—2441no—
688C4—2441no—
689C4—2441no—
690C4D4×C22⋊D6111yescharacteristic
691C4#1684041111yescharacteristic
692C4D4×Dic12211yescharacteristic
693C4#1684047111yescharacteristic
694C2—42no—
695C2—42no—
696C2D4×#1175819611yescharacteristic
697C2#2145438211yescharacteristic
698C2#2145438511yescharacteristic
699C2#2145453311yescharacteristic
700C2#2145456011yescharacteristic
701C2#2145495411yescharacteristic
702C2#2145498511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#435C2
prime radicalC22×D4×C61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22652
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#16839790C2semidirect
3. C2×#16839788C2semidirect
5. #21446542C2semidirect
6. #21446540C2semidirect
7. #21446002C2semidirect
8. #21446001C2semidirect
9. #21445997C2semidirect
10. #21445996C2semidirect
11. #21445970C2semidirect
12. #21445801C2semidirect
13. #21445801C2semidirect
14. #21445673C2semidirect
109. #14519706D4semidirect
414. C61#22652semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
C2×#168397902
C2×#168397882
#214482842
#214465422
#214465402
#214460022
#214460012
#214459972
#214459962
#214459702
#214458012
#214456732
C2×C61×#4352
#2265261