Finite Group Databasebeta

← #29696294

Subgroups — #29696294

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840451C211yesmaximal, characteristic
2C2×#16839836C211yesmaximal, characteristic
3#21448715C211yesmaximal, characteristic
4#21446786C211yesmaximal, characteristic, complemented
5#21446775C211yesmaximal, characteristic, complemented
6#21446250C211yesmaximal, characteristic, complemented
7#21446241C211yesmaximal, characteristic, complemented
8#21446125C211yesmaximal, characteristic, complemented
9#21446124C211yesmaximal, characteristic, complemented
10#21445904C211yesmaximal, characteristic, complemented
11#21445823C211yesmaximal, characteristic, complemented
12#21445648C211yesmaximal, characteristic, complemented
13#21445540C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#1825C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840451—24no—
19#16840451C418yescomplemented
20C2×#14519770—21no—
21C2×#14519769—21no—
22C2×#14519768C2211yescharacteristic
23C2×#14519759—21no—
24C2×#14519757C2211yescharacteristic
25C2×#14519756C2211yescharacteristic
26C2×#14519742C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737—21no—
29C2×#14519734—21no—
30C22×C4⋊Dic61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C4⋊C4×D61C2211yescharacteristic
33#16839836—24no—
34C2×#14519706C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519687C2211yescharacteristic
41#16839659—21no—
42#16839636—21no—
43#16839634—21no—
44#16839631C2211yescharacteristic
45#16839619C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122C2311yescharacteristic
63C22×C22⋊D61D411yescharacteristic
64C23×Dic61—21no—
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61C2311yescharacteristic
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C2×C8×D61—22no—
74C2×C8×D61—22no—
75C2×C8×D61—41no—
76#14519770—28no—
77#14519769—28no—
78#14519768—22no—
79#14519768C2×C414yescomplemented
80#14519759—28no—
81#14519757—22no—
82#14519757C2×C414yescomplemented
83#14519756—22no—
84#14519756C2×C414yescomplemented
85#14519742—22no—
86#14519742C2×C414yescomplemented
87C4×C22⋊D61C2×C414yes—
88C4×C22⋊D61D414yes—
89#14519737—44no—
90#14519734—28no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—41no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196D411yescharacteristic
107C4⋊C4×D61—22no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—41no—
110C4⋊C4×D61C2×C414yescomplemented
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61D411yescharacteristic
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198D411yescharacteristic
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61C2311yescharacteristic
119#14519706—22no—
120#14519702—22no—
121#14519702—41no—
122#14519700—22no—
123#14519700—41no—
124#14519689—22no—
125#14519687—22no—
126#14519684—21no—
127#14519684—21no—
128C23×C4×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131#117×C61—22no—
132#117×C61C2×C414yescomplemented
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C42×C61—21no—
140C22⋊C8×C61—22no—
141#95×C61—21no—
142C24×C61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61C22⋊C414yes—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—42no—
164C22×Dic61—42no—
165C22×Dic61—81no—
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—24no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×C4×D61—42no—
178C2×C4×D61—81no—
179C2×C4×D61C22×C412yes—
180C2×C4×D61C2×D412yes—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122C22×C412yes—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61C22×C412yes—
200C4⋊C4×C61C22×C412yes—
201C22⋊C4×C61—24no—
202C22⋊C4×C61—42no—
203C42×C61—24no—
204C22⋊Dic61—24no—
205C22⋊Dic61C22⋊C414yes—
206#11758198—24no—
207#11758198—42no—
208#11758198C22⋊C414yes—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—24no—
212C4⋊Dic61—24no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—42no—
216C4⋊Dic61C22×C412yes—
217C4⋊Dic61#4112yes—
218#11758196—24no—
219#11758196—24no—
220#11758196—24no—
221#11758196—24no—
222#11758196—42no—
223#11758196—42no—
224#11758196—81no—
225#11758196C22⋊C414yes—
226C4×Dic61—24no—
227C4×Dic61—42no—
228C4×Dic61C22×C412yes—
229C4×Dic61C2×D412yes—
230#11758194—44no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418#4112yes—
237C8×D61—44no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61C2×C22⋊C412yes—
245C23×C61C22×D411yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61C2×C22⋊C412yes—
251C22×D61AGL(1,ℤ/8)12yes—
252C22×D61#13712yes—
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—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61C2×C22⋊C412yes—
272C2×C4×C61C23×C411yescharacteristic
273C2×C4×C61C22×D411yescharacteristic
274C2×C4×C61C2×#4111yescharacteristic
275C2×C4×C61C2×#4111yescharacteristic
276C2×C4×C61H(5,𝔽2)11yescharacteristic
277C2×C4×C612−1+411yescharacteristic
278C22⋊D61—28no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—84no—
298C2×Dic61C2×C22⋊C412yes—
299C2×Dic61C2×C22⋊C412yes—
300C2×Dic61C2×C22⋊C412yes—
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—48no—
306C4×D61—84no—
307Dic122—22no—
308Dic122—22no—
309Dic122—41no—
310Dic122—41no—
311C8×C61—41no—
312C8×C61—41no—
313#92418—22no—
314#92418—41no—
315#22491—611nomaximal, Sylow
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61C22×C22⋊C411yescharacteristic
324C22×C61#54611yescharacteristic
325C22×C61#54711yescharacteristic
326C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C61C2×#13711yescharacteristic
328C22×C61#57711yescharacteristic
329C22×C61#57811yescharacteristic
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—22no—
335C2×D61—22no—
336C2×D61#41714yes—
337C4×C61—22no—
338C4×C61—42no—
339C4×C61—42no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61C4×#4111yescharacteristic
343C4×C61#52011yescharacteristic
344C4×C61#54611yescharacteristic
345C4×C61#54711yescharacteristic
346Dic61—22no—
347Dic61—22no—
348Dic61—22no—
349Dic61—42no—
350Dic61—42no—
351Dic61—42no—
352Dic61—81no—
353C2×#552—611no—
354C2×#435—611no—
355D4×C4⋊C4—611no—
356#1992—611no—
357#1989—611no—
358#1894—611no—
359#1892—611no—
360#1872—611no—
361#1872—611no—
362#1825D6111yescharacteristic, complemented
363#1823—611no—
364#1803—611no—
365#1763—611no—
366#1736—611no—
367C2×#340—611no—
368C2×C61—42no—
369C2×C61#233911yescharacteristic
370C2×C61C2×#41711yescharacteristic
371C2×C61#289811yescharacteristic
372C2×C61#331011yescharacteristic
373C2×C61#331211yescharacteristic
374C2×C61#334311yescharacteristic
375C2×C61#334411yescharacteristic
376D61—24no—
377C22×M16—611no—
378C23×C8—611no—
379#552—618no—
380#552—1224no—
381C2×#126—1221no—
382C2×#125—611no—
383C2×#125—1221no—
384C2×#123—1221no—
385C2×C22⋊Q8—611no—
386C2×C22⋊Q8—611no—
387C2×C4×Q8—611no—
388C2×C4×D4—611no—
389C2×C4×D4—1221no—
390C2×#117—1221no—
391C2×#117C2×D6111yescharacteristic
392C22×C4⋊C4—611no—
393C22×C4⋊C4—611no—
394C22×C4⋊C4—611no—
395#435—1224no—
396C2×C4⋊C8—611no—
397C2×#103—611no—
398C2×#103—611no—
399C2×#103—611no—
400C2×#103—611no—
401C2×C22⋊C8—611no—
402C2×C22⋊C8C2×D6111yescharacteristic
403C2×#97—611no—
404#389—1221no—
405#385—1221no—
406#385—1221no—
407#384—611no—
408#380—611no—
409#380C2×D6111yescharacteristic
410C4×C4⋊C4—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419#340C2×D6111yescharacteristic
420#340C2×D6111yescharacteristic
421#340C2×D6111yescharacteristic
422#340C2×D6111yescharacteristic
423C61#2249111yescharacteristic, complemented, Sylow
424C22×Q8—611no—
425C22×D4—611no—
426C23×C4—611no—
427C23×C4—1221no—
428C23×C4—1221no—
429C23×C4—1221no—
430C23×C4C22×D6111yescharacteristic
431C2×M16—1222no—
432C2×M16—1222no—
433C2×M16—2441no—
434C22×C8—611no—
435C22×C8—611no—
436C22×C8—1222no—
437C22×C8—1222no—
438C22×C8—2441no—
439C22×C8C22×D6111yescharacteristic
440C22×C8C22×D6111yescharacteristic
441#126—1228no—
442#125—614no—
443#125—1228no—
444#125—1222no—
445#123—1228no—
446C22⋊Q8—614no—
447C22⋊Q8—614no—
448C22⋊Q8—1222no—
449C22⋊Q8—1222no—
450C4×Q8—614no—
451C4×Q8—1222no—
452C4×D4—614no—
453C4×D4—614no—
454C4×D4—2444no—
455#117—22no—
456#117—1228no—
457#117C4×D6114yescomplemented
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—614no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—1222no—
464C2×C4⋊C4—1222no—
465C2×C4⋊C4—1222no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—2441no—
477C2×C4⋊C4—2441no—
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C42—21no—
490C2×C42—611no—
491C2×C42—1221no—
492C2×C42—1221no—
493C4⋊C8—1222no—
494#103—1222no—
495#103—1222no—
496#103—2441no—
497#103—2441no—
498C22⋊C8—22no—
499C22⋊C8—1222no—
500#97—1222no—
501#95—21no—
502#95—1221no—
503#95—1221no—
504C24—611no—
505C24D4×D6111yescharacteristic
506C2×Q8—612no—
507C2×Q8—1221no—
508C2×Q8—1221no—
509C2×Q8—1221no—
510C2×Q8—1221no—
511C2×Q8—1221no—
512C2×D4—614no—
513C2×D4—1222no—
514C2×D4—1222no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—612no—
527C22×C4—612no—
528C22×C4—1224no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—4881no—
538C22×C4—4881no—
539C22×C4—2442no—
540C22×C4—2442no—
541C22×C4—2442no—
542C22×C4—2442no—
543C22×C4—2442no—
544C22×C4—2442no—
545C22×C4C2×C4×D6112yes—
546C22×C4D4×D6112yes—
547C22×C4D4×D6111yescharacteristic
548C22×C4C23×D6111yescharacteristic
549M16—2444no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—612no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—2444no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—614no—
570C4⋊C4—612no—
571C4⋊C4—612no—
572C4⋊C4—1224no—
573C4⋊C4—1224no—
574C4⋊C4—1224no—
575C4⋊C4—1224no—
576C4⋊C4—1224no—
577C4⋊C4—1221no—
578C4⋊C4—1221no—
579C4⋊C4—1224no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—4881no—
583C4⋊C4—2442no—
584C4⋊C4—2442no—
585C4⋊C4—2442no—
586C4⋊C4C2×C4×D6112yes—
587C4⋊C4C2×C4×D6112yes—
588C22⋊C4—24no—
589C22⋊C4—42no—
590C22⋊C4—614no—
591C22⋊C4—614no—
592C22⋊C4—1224no—
593C22⋊C4—1224no—
594C22⋊C4—2442no—
595C42—24no—
596C42—612no—
597C42—612no—
598C42—1224no—
599C42—2442no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—612no—
607C23—612no—
608C23—612no—
609C23—1221no—
610C23—1221no—
611C23—1221no—
612C23—1221no—
613C23C22⋊C4×D6112yes—
614C23C2×D4×D6111yescharacteristic
615Q8—1222no—
616Q8—1222no—
617Q8—2441no—
618Q8—2441no—
619D4—1228no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—612no—
639C2×C4—612no—
640C2×C4—612no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—4884no—
655C2×C4—4884no—
656C2×C4—2448no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4C22⋊C4×D6112yes—
667C2×C4C22×C4×D6111yescharacteristic
668C2×C4C2×D4×D6111yescharacteristic
669C2×C4#41×D6111yescharacteristic
670C2×C4#41×D6111yescharacteristic
671C2×C4#1451982311yescharacteristic
672C2×C4#1451982411yescharacteristic
673C8—41no—
674C8—41no—
675C8—1222no—
676C8—2441no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—614no—
685C22—1222no—
686C22—1222no—
687C22—1222no—
688C22—1222no—
689C22—1222no—
690C22—1222no—
691C22C2×C22⋊C4×D6111yescharacteristic
692C22#1684040411yescharacteristic
693C22#1684041011yescharacteristic
694C22AGL(1,ℤ/8)×D6111yescharacteristic
695C22#137×D6111yescharacteristic
696C22#1684056911yescharacteristic
697C22#1684057611yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—1222no—
704C4—1222no—
705C4—1222no—
706C4—4881no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C4#1684023011yescharacteristic
711C4#1684024211yescharacteristic
712C4#1684040411yescharacteristic
713C4#1684041011yescharacteristic
714C2—42no—
715C2—1224no—
716C2#2144864311yescharacteristic
717C2#417×D6111yescharacteristic
718C2#2145434811yescharacteristic
719C2#2145784311yescharacteristic
720C2#2145787311yescharacteristic
721C2#2145825211yescharacteristic
722C2#2145826711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1825C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1825D61
hypocenterC61#22491
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. #21446786C2semidirect
5. #21446775C2semidirect
6. #21446250C2semidirect
7. #21446241C2semidirect
8. #21446125C2semidirect
9. #21446124C2semidirect
10. #21445904C2semidirect
11. #21445823C2semidirect
12. #21445648C2semidirect
13. #21445540C2semidirect
14. #340×D61C2semidirect
15. C61×#1825C2semidirect
19. #16840451C4semidirect
79. #14519768C2×C4semidirect
82. #14519757C2×C4semidirect
84. #14519756C2×C4semidirect
86. #14519742C2×C4semidirect
110. C4⋊C4×D61C2×C4semidirect
132. #117×C61C2×C4semidirect
362. #1825D61semidirect
423. C61#22491semidirect
457. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404512
C2×#168398362
#214487152
#214467862
#214467752
#214462502
#214462412
#214461252
#214461242
#214459042
#214458232
#214456482
#214455402
#340×D612
C61×#18252
#2249161