Finite Group Databasebeta

← #29696299

Subgroups — #29696299

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×#16840454C211yesmaximal, characteristic
2C2×#16839830C211yesmaximal, characteristic
3C4⋊C4×C22⋊D61C211yesmaximal, characteristic
4#21446786C211yesmaximal, characteristic, complemented
5#21446775C211yesmaximal, characteristic, complemented
6#21446249C211yesmaximal, characteristic, complemented
7#21446243C211yesmaximal, characteristic, complemented
8#21446123C211yesmaximal, characteristic, complemented
9#21445912C211yesmaximal, characteristic, complemented
10#21445906C211yesmaximal, characteristic, complemented
11#21445822C211yesmaximal, characteristic, complemented
12#21445651C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14C2×#16839524C211yesmaximal, characteristic, complemented
15C61×#1872C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18#16840454—24no—
19#16840454C418yescomplemented
20C2×#14519772—21no—
21C2×#14519768—21no—
22C2×#14519768C2211yescharacteristic
23C2×#14519761—21no—
24C2×#14519753C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×C4×C22⋊D61—21no—
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C2×#14519733—21no—
30C22×C4⋊Dic61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839830—24no—
33C2×#14519706C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38#16839657—21no—
39#16839635—21no—
40#16839633—21no—
41#16839631C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839619C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×C22⋊D61D411yescharacteristic
63C23×Dic61—21no—
64C22×C4×D61—21no—
65C22×C4×D61C2311yescharacteristic
66C2×#11758189—22no—
67C2×#11758189—22no—
68C2×#11758189—41no—
69C22×#92418—22no—
70C22×#92418—22no—
71C22×#92418—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519772—28no—
75#14519768—28no—
76#14519768—22no—
77#14519768C2×C414yescomplemented
78#14519761—28no—
79#14519753—22no—
80#14519753C2×C414yescomplemented
81Q8×Dic61—22no—
82Q8×Dic61C2×C414yescomplemented
83C4×C22⋊D61—44no—
84C4×C22⋊D61C2×C414yes—
85C4×C22⋊D61D414yes—
86#14519735—22no—
87#14519735C2×C414yescomplemented
88#14519733—28no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2×C414yescomplemented
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196D411yescharacteristic
104C4⋊C4×D61—22no—
105C4⋊C4×D61—41no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61D411yescharacteristic
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198D411yescharacteristic
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117#14519701—22no—
118#14519701—41no—
119#14519689—22no—
120#14519687—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124C22×Q8×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22⋊Q8×C61—22no—
130C22⋊Q8×C61C2×C414yescomplemented
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—41no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139#103×C61—22no—
140#103×C61—41no—
141C22⋊C8×C61—22no—
142C24×C61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C22×C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—81no—
161C22×C4×C61C22×C412yes—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2411yescharacteristic
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61C22⋊C414yes—
168C22×Dic61—24no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—42no—
174C22×Dic61—42no—
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—81no—
185C2×C4×D61C22×C412yes—
186C2×C4×D61C2×D412yes—
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—24no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—42no—
199C4⋊C4×C61C22×C412yes—
200C4⋊C4×C61#4112yes—
201C22⋊C4×C61—24no—
202C22⋊Dic61—42no—
203C22⋊Dic61C22⋊C414yes—
204#11758198—24no—
205#11758198—24no—
206#11758198—42no—
207#11758198C22⋊C414yes—
208C4⋊Dic61—24no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—24no—
212C4⋊Dic61—24no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61C22×C412yes—
218C4⋊Dic61C22×C412yes—
219#11758196—24no—
220#11758196—24no—
221#11758196—42no—
222#11758196—42no—
223#11758196—81no—
224#11758196C22⋊C414yes—
225C4×Dic61—24no—
226C4×Dic61—24no—
227C4×Dic61—42no—
228C4×Dic61C22×C412yes—
229C4×Dic61C2×D412yes—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—44no—
236C2×#92418#4112yes—
237#11758189—44no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61C2×C22⋊C412yes—
243C23×C61AGL(1,ℤ/8)12yes—
244C23×C61#13712yes—
245C23×C61C22×D411yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61C2×C22⋊C412yes—
253Q8×C61—22no—
254Q8×C61—22no—
255Q8×C61—41no—
256Q8×C61—41no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—84no—
276C2×C4×C61C2×C22⋊C412yes—
277C2×C4×C61C23×C411yescharacteristic
278C2×C4×C61C22×D411yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×C4×C61C2×#4111yescharacteristic
281C2×C4×C61H(5,𝔽2)11yescharacteristic
282C2×C4×C612−1+411yescharacteristic
283C22⋊D61—28no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—48no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61C2×C22⋊C412yes—
304C2×Dic61C2×C22⋊C412yes—
305C2×Dic61C2×C22⋊C412yes—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—84no—
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—22no—
320C22×C61—22no—
321C22×C61—22no—
322C22×C61#41714yes—
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—41no—
334C2×D61—41no—
335C2×D61—41no—
336C2×D61—41no—
337C4×C61—22no—
338C4×C61—42no—
339C4×C61—42no—
340C4×C61—42no—
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—81no—
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#1872D6111yescharacteristic, complemented
362#1825—611no—
363#1823—611no—
364#1803—611no—
365#1763—611no—
366#1736—611no—
367C2×#340—611no—
368C2×C61—24no—
369C2×C61#233911yescharacteristic
370C2×C61C2×#41711yescharacteristic
371C2×C61#289811yescharacteristic
372C2×C61#331011yescharacteristic
373C2×C61#331211yescharacteristic
374C2×C61#334311yescharacteristic
375C2×C61#334411yescharacteristic
376D61—42no—
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⋊Q8C2×D6111yescharacteristic
387C2×C4×Q8—611no—
388C2×C4×D4—611no—
389C2×C4×D4—1221no—
390C2×#117—611no—
391C2×#117—1221no—
392C22×C4⋊C4—611no—
393C22×C4⋊C4—611no—
394C22×C4⋊C4C2×D6111yescharacteristic
395#435—1224no—
396C2×C4⋊C8—611no—
397C2×#103—611no—
398C2×#103—611no—
399C2×#103C2×D6111yescharacteristic
400C2×#103C2×D6111yescharacteristic
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#380—611no—
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#340—611no—
420#340—611no—
421#340C2×D6111yescharacteristic
422#340C2×D6111yescharacteristic
423C61#2249111yescharacteristic, complemented, Sylow
424C22×Q8C22×D6111yescharacteristic
425C22×D4—611no—
426C23×C4—21no—
427C23×C4—611no—
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—1222no—
444#125—1228no—
445#123—1228no—
446C22⋊Q8—22no—
447C22⋊Q8—614no—
448C22⋊Q8—1222no—
449C22⋊Q8C4×D6114yescomplemented
450C4×Q8—614no—
451C4×Q8—1222no—
452C4×D4—614no—
453C4×D4—614no—
454C4×D4—2444no—
455#117—614no—
456#117—1228no—
457#117—1222no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—614no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1222no—
474C2×C4⋊C4—1222no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—2441no—
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C42—611no—
490C2×C42—1221no—
491C2×C42—1221no—
492C2×C42—1221no—
493C4⋊C8—1222no—
494#103—22no—
495#103—41no—
496#103—1222no—
497#103—2441no—
498C22⋊C8—22no—
499C22⋊C8—1222no—
500#97—1222no—
501#95—1221no—
502#95—1221no—
503#95—1221no—
504C24—611no—
505C24D4×D6111yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8C2×C4×D6112yes—
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—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—612no—
530C22×C4—612no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1224no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—4881no—
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—24no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—614no—
570C4⋊C4—612no—
571C4⋊C4—612no—
572C4⋊C4—1224no—
573C4⋊C4—1224no—
574C4⋊C4—1224no—
575C4⋊C4—1224no—
576C4⋊C4—1221no—
577C4⋊C4—1221no—
578C4⋊C4—1224no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—4881no—
584C4⋊C4—2442no—
585C4⋊C4—2442no—
586C4⋊C4C2×C4×D6112yes—
587C4⋊C4#1175822412yes—
588C22⋊C4—24no—
589C22⋊C4—614no—
590C22⋊C4—614no—
591C22⋊C4—1224no—
592C22⋊C4—1224no—
593C22⋊C4—2442no—
594C22⋊C4—2442no—
595C42—612no—
596C42—612no—
597C42—1224no—
598C42—1224no—
599C42—2442no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—612no—
605C23—1221no—
606C23—1221no—
607C23—1221no—
608C23—1221no—
609C23—1221no—
610C23—1221no—
611C23C22⋊C4×D6112yes—
612C23#1451980412yes—
613C23#1451980912yes—
614C23C2×D4×D6111yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
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—22no—
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—84no—
639C2×C4—612no—
640C2×C4—612no—
641C2×C4—612no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—4884no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2448no—
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×C4C2×#1175822411yescharacteristic
671C2×C4#1451982211yescharacteristic
672C2×C4#1451982411yescharacteristic
673C8—41no—
674C8—41no—
675C8—1222no—
676C8—2441no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—1222no—
684C22—1222no—
685C22—1222no—
686C22—2441no—
687C22—2441no—
688C22—2441no—
689C22—2441no—
690C22#1683976214yes—
691C22C2×C22⋊C4×D6111yescharacteristic
692C22#1684039911yescharacteristic
693C22#1684041011yescharacteristic
694C22C2×#1451980411yescharacteristic
695C22C2×#1451980911yescharacteristic
696C22#1684057211yescharacteristic
697C22#1684057811yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—1222no—
704C4—1222no—
705C4—1222no—
706C4—4881no—
707C4—4881no—
708C4—2442no—
709C4—2442no—
710C4C4×#1175822411yescharacteristic
711C4#1684024111yescharacteristic
712C4#1684040111yescharacteristic
713C4#1684041211yescharacteristic
714C2—24no—
715C2—2442no—
716C2#2144864511yescharacteristic
717C2C2×#1683976211yescharacteristic
718C2#2145435011yescharacteristic
719C2#2145784411yescharacteristic
720C2#2145787411yescharacteristic
721C2#2145825711yescharacteristic
722C2#2145827211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1872C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1872D61
hypocenterC61#22491
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #21446786C2semidirect
5. #21446775C2semidirect
6. #21446249C2semidirect
7. #21446243C2semidirect
8. #21446123C2semidirect
9. #21445912C2semidirect
10. #21445906C2semidirect
11. #21445822C2semidirect
12. #21445651C2semidirect
13. #21445537C2semidirect
14. C2×#16839524C2semidirect
15. C61×#1872C2semidirect
19. #16840454C4semidirect
77. #14519768C2×C4semidirect
80. #14519753C2×C4semidirect
82. Q8×Dic61C2×C4semidirect
87. #14519735C2×C4semidirect
93. C2×C4⋊Dic61C2×C4semidirect
130. C22⋊Q8×C61C2×C4semidirect
361. #1872D61semidirect
423. C61#22491semidirect
449. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404542
C2×#168398302
C4⋊C4×C22⋊D612
#214467862
#214467752
#214462492
#214462432
#214461232
#214459122
#214459062
#214458222
#214456512
#214455372
C2×#168395242
C61×#18722
#2249161