Finite Group Databasebeta

← #29698071

Subgroups — #29698071

Order 15616.

980 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839838C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic
3C2×#16839784C211yesmaximal, characteristic, complemented
4#21448256C211yesmaximal, characteristic
5#21446539C211yesmaximal, characteristic, complemented
6#21446534C211yesmaximal, characteristic, complemented
7#21446002C211yesmaximal, characteristic, complemented
8#21446000C211yesmaximal, characteristic, complemented
9#21446000C211yesmaximal, characteristic, complemented
10#21445997C211yesmaximal, characteristic, complemented
11#21445972C211yesmaximal, characteristic, complemented
12#21445803C211yesmaximal, characteristic, complemented
13#21445796C211yesmaximal, characteristic, complemented
14#21445678C211yesmaximal, characteristic, complemented
15C2×C61×#424C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×C42×D61C2211yescharacteristic
20#16839838—24no—
21#16839833—24no—
22#16839784—24no—
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839650C411yescharacteristic
38#16839650C411yescharacteristic
39#16839643C411yescharacteristic
40#16839643C411yescharacteristic
41#16839638C411yescharacteristic
42#16839638C411yescharacteristic
43#16839633C411yescharacteristic
44#16839633C411yescharacteristic
45C4×#11758196C2211yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×C22⋊Dic61C2211yescharacteristic
48#16839608C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×#117×C61C2211yescharacteristic
58C61×#424—24no—
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×C4⋊C8×C61C2211yescharacteristic
61C2×C4⋊C8×C61C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758189—22no—
68C2×#11758189—22no—
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189—41no—
72C2×#11758189—41no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C4×C22⋊D61D414yes—
78C4×C22⋊D61Q814yes—
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×C22⋊Dic61C2×C411yescharacteristic
83C2×C22⋊Dic61C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93C42×D61—22no—
94C42×D61—22no—
95C4⋊#92418—22no—
96C4⋊#92418—22no—
97#14519706—22no—
98#14519706—22no—
99#14519706—22no—
100#14519706—22no—
101#14519706—41no—
102#14519706—41no—
103C22⋊#92418—22no—
104C22⋊#92418—22no—
105#14519689—22no—
106#14519689—22no—
107#14519687—22no—
108C8×Dic61—22no—
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C2×M16×C61—22no—
121C2×M16×C61—22no—
122C2×M16×C61—41no—
123C22×C8×C61—22no—
124C22×C8×C61—22no—
125C22×C8×C61—41no—
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130#117×C61—22no—
131#117×C61—22no—
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—22no—
139C4⋊C8×C61—22no—
140C4⋊C8×C61—22no—
141C4⋊C8×C61D414yescomplemented
142C24×C61C22×C411yescharacteristic
143C23×D61C22×C411yescharacteristic
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×Q812yes—
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—41no—
157C2×C22⋊D61—41no—
158C2×C22⋊D61C4⋊C414yes—
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—41no—
174C2×C4×D61—41no—
175C2×C4×D61—41no—
176C2×C4×D61C2×D412yes—
177C2×C4×D61C2×Q812yes—
178M16×C61—44no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
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—44no—
190C2×C8×C61C2×D412yes—
191C2×C8×C61C2×D412yes—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C42×C61—21no—
197C42×C61—21no—
198C42×C61C2×D412yes—
199C42×C61#4112yes—
200C22⋊Dic61—22no—
201C22⋊Dic61—41no—
202C22⋊Dic61C4⋊C414yes—
203#11758198—41no—
204#11758198—41no—
205#11758198C4⋊C414yes—
206#11758196—22no—
207#11758196—41no—
208#11758196C4⋊C414yes—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61C2×D412yes—
216C4×Dic61C2×Q812yes—
217C2×#92418—21no—
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—
229#11758189—44no—
230#11758189—44no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61C2×C4⋊C412yes—
238C23×C61C23×C411yescharacteristic
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61C2×C4⋊C412yes—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
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×C4⋊C412yes—
263C2×C4×C61C4×D412yes—
264C2×C4×C61C4×D412yes—
265C2×C4×C61C22×D411yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61C22×Q811yescharacteristic
268C2×C4×C61C2×#4111yescharacteristic
269C2×C4×C61H(5,𝔽2)11yescharacteristic
270C2×C4×C612−1+411yescharacteristic
271C22⋊D61—44no—
272C2×Dic61—21no—
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×Dic61C2×C4⋊C412yes—
290C2×Dic61C2×C4⋊C412yes—
291C2×Dic61C2×C4⋊C412yes—
292C2×Dic61#13112yes—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—44no—
298C4×D61—44no—
299C8×C61—22no—
300C8×C61—22no—
301C8×C61—41no—
302C8×C61—41no—
303#92418—41no—
304#92418—41no—
305#92418—41no—
306#92418—41no—
307#22649—611nomaximal, Sylow
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61C22×C4⋊C411yescharacteristic
316C22×C61C2×C4×D411yescharacteristic
317C22×C61#52011yescharacteristic
318C22×C61C2×#13111yescharacteristic
319C22×C61#56811yescharacteristic
320C22×C61#56811yescharacteristic
321C22×C61#56811yescharacteristic
322C2×D61—22no—
323C2×D61—22no—
324C2×D61—22no—
325C2×D61—41no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61—41no—
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—41no—
333C4×C61—41no—
334C4×C61D4211yescharacteristic
335C4×C61#54711yescharacteristic
336C4×C61D4×Q811yescharacteristic
337C4×C61#55411yescharacteristic
338Dic61—22no—
339Dic61—22no—
340Dic61—22no—
341Dic61—22no—
342Dic61—41no—
343Dic61—41no—
344Dic61—41no—
345C2×#436—611no—
346C2×#435—611no—
347C2×#424D6111yescharacteristic, complemented
348C2×#423—611no—
349#2290—611no—
350#1940—611no—
351#1939—611no—
352#1851—611no—
353#1851—611no—
354#1851—611no—
355#1850—611no—
356#1843—611no—
357#1798—611no—
358#1797—611no—
359#1768—611no—
360C2×C61—42no—
361C2×C61D4×C4⋊C411yescharacteristic
362C2×C61#290511yescharacteristic
363C2×C61#290611yescharacteristic
364C2×C61#293011yescharacteristic
365C2×C61#293311yescharacteristic
366C2×C61#299311yescharacteristic
367C2×C61#299511yescharacteristic
368D61—42no—
369C22×M16—611no—
370C22×M16—611no—
371C22×M16C2×D6111yescharacteristic
372C23×C8C2×D6111yescharacteristic
373C2×C4×D4—611no—
374C2×#117C2×D6111yescharacteristic
375C22×C42—611no—
376#436—1224no—
377#435—1224no—
378#424—24no—
379#423—1224no—
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⋊C8C2×D6111yescharacteristic
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×C4×C8—611no—
398#388—611no—
399#388—611no—
400#387—611no—
401#387—611no—
402#386—611no—
403#386—611no—
404#385—611no—
405#385—611no—
406C4×C4⋊C4—611no—
407C4×C22⋊C4—611no—
408C4×C22⋊C4—611no—
409#376—611no—
410#336—611no—
411#336—611no—
412#336—611no—
413#336—611no—
414#336—611no—
415#336—611no—
416C61#2264911yescharacteristic, complemented, Sylow
417C22×D4—611no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4—611no—
421C23×C4C22×D6111yescharacteristic
422C2×M16—22no—
423C2×M16—22no—
424C2×M16—41no—
425C2×M16—1222no—
426C2×M16—1222no—
427C2×M16—1222no—
428C2×M16—1222no—
429C2×M16—2441no—
430C2×M16—2441no—
431C22×C8—22no—
432C22×C8—22no—
433C22×C8—41no—
434C22×C8—611no—
435C22×C8—611no—
436C22×C8—611no—
437C22×C8—611no—
438C22×C8C22×D6111yescharacteristic
439C22×C8C22×D6111yescharacteristic
440C22×C8C22×D6111yescharacteristic
441C22×C8C22×D6111yescharacteristic
442C4×D4—614no—
443C4×D4—614no—
444#117—22no—
445#117—22no—
446C2×C4⋊C4—611no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4C4×D6111yescharacteristic
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⋊C4C4×D6111yescharacteristic
458C2×C22⋊C4C4×D6111yescharacteristic
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—1222no—
465C2×C42—1222no—
466C2×C42C22×D6111yescharacteristic
467C2×C42C22×D6111yescharacteristic
468C4⋊C8—22no—
469C4⋊C8—22no—
470C4⋊C8—22no—
471C4⋊C8—1222no—
472C4⋊C8—1222no—
473C4⋊C8—1222no—
474C4⋊C8—1222no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477C4⋊C8—2441no—
478C4⋊C8—2441no—
479C4⋊C8C22⋊D6114yescomplemented
480C22⋊C8—1222no—
481C22⋊C8—1222no—
482C22⋊C8—1222no—
483C22⋊C8—1222no—
484#97—1222no—
485C4×C8—1222no—
486#95—611no—
487#95—611no—
488#95—611no—
489#95—611no—
490#95—611no—
491#95—611no—
492#95—611no—
493#95—611no—
494#95—611no—
495#95—611no—
496C24—611no—
497C24C2×C4×D6111yescharacteristic
498C2×D4—614no—
499C2×D4—2441no—
500C2×D4—2441no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—612no—
510C22×C4—612no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—1222no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1222no—
520C22×C4—1222no—
521C22×C4—2441no—
522C22×C4—2441no—
523C22×C4—2441no—
524C22×C4C2×C4×D6111yescharacteristic
525C22×C4C2×C4×D6111yescharacteristic
526C22×C4C2×C4×D6111yescharacteristic
527C22×C4C2×C4×D6111yescharacteristic
528C22×C4C2×C4×D6111yescharacteristic
529C22×C4D4×D6112yes—
530C22×C4Q8×D6112yes—
531C22×C4C23×D6111yescharacteristic
532M16—44no—
533M16—2444no—
534M16—2444no—
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—44no—
546C2×C8—1221no—
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×C8C2×C22⋊D6112yes—
559C2×C8C2×C22⋊D6112yes—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—614no—
563C4⋊C4—1222no—
564C4⋊C4—2441no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—614no—
568C22⋊C4—614no—
569C22⋊C4—1222no—
570C22⋊C4—2441no—
571C22⋊C4—2441no—
572C22⋊C4—2441no—
573C42—21no—
574C42—21no—
575C42—612no—
576C42—612no—
577C42—1221no—
578C42—1221no—
579C42—1221no—
580C42—1221no—
581C42—1222no—
582C42—1222no—
583C42#1175822212yes—
584C42C2×C22⋊D6112yes—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—612no—
592C23—1221no—
593C23—1221no—
594C23—1221no—
595C23—1221no—
596C23—1221no—
597C23—1221no—
598C23C4⋊C4×D6112yes—
599C23C22×C4×D6111yescharacteristic
600D4—2444no—
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—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—612no—
618C2×C4—612no—
619C2×C4—612no—
620C2×C4—612no—
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—1222no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—1222no—
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×C4C4⋊C4×D6112yes—
645C2×C4C4×C22⋊D6112yes—
646C2×C4C4×C22⋊D6112yes—
647C2×C4C2×D4×D6111yescharacteristic
648C2×C4C22×C22⋊D6111yescharacteristic
649C2×C4C2×Q8×D6111yescharacteristic
650C2×C4C2×#1175822211yescharacteristic
651C2×C4#1451982211yescharacteristic
652C2×C4#1451982511yescharacteristic
653C8—22no—
654C8—22no—
655C8—41no—
656C8—41no—
657C8—2441no—
658C8—2441no—
659C8—2441no—
660C8—2441no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—1222no—
669C22—1222no—
670C22—1222no—
671C22—2441no—
672C22—2441no—
673C22—2441no—
674C22—2441no—
675C22C2×C4⋊C4×D6111yescharacteristic
676C22C2×C4×C22⋊D6111yescharacteristic
677C22#1684024311yescharacteristic
678C22#131×D6111yescharacteristic
679C22#1684052711yescharacteristic
680C22#1684052711yescharacteristic
681C22#1684052711yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—41no—
686C4—41no—
687C4—1222no—
688C4—1222no—
689C4—1222no—
690C4—1222no—
691C4—2441no—
692C4—2441no—
693C4—2441no—
694C4D4×C22⋊D6111yescharacteristic
695C4#1684041311yescharacteristic
696C4Q8×C22⋊D6111yescharacteristic
697C4#1684046711yescharacteristic
698C2—42no—
699C2—2442no—
700C2C4⋊C4×C22⋊D6111yescharacteristic
701C2#2145438011yescharacteristic
702C2#2145438611yescharacteristic
703C2#2145452011yescharacteristic
704C2#2145454111yescharacteristic
705C2#2145496611yescharacteristic
706C2#2145498711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#424C2
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×#424D61
hypocenterC61#22649
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
3. C2×#16839784C2semidirect
5. #21446539C2semidirect
6. #21446534C2semidirect
7. #21446002C2semidirect
8. #21446000C2semidirect
9. #21446000C2semidirect
10. #21445997C2semidirect
11. #21445972C2semidirect
12. #21445803C2semidirect
13. #21445796C2semidirect
14. #21445678C2semidirect
15. C2×C61×#424C2semidirect
141. C4⋊C8×C61D4semidirect
347. C2×#424D61semidirect
416. C61#22649semidirect
479. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398382
C2×#168398332
C2×#168397842
#214482562
#214465392
#214465342
#214460022
#214460002
#214459972
#214459722
#214458032
#214457962
#214456782
C2×C61×#4242
#2264961