Finite Group Databasebeta

← #29696394

Subgroups — #29696394

Order 15616.

1174 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×#16840470C211yesmaximal, characteristic
2C2×#16839836C211yesmaximal, characteristic
3#21448749C211yesmaximal, characteristic
4#21446790C211yesmaximal, characteristic, complemented
5#21446769C211yesmaximal, characteristic, complemented
6#21446253C211yesmaximal, characteristic, complemented
7#21446239C211yesmaximal, characteristic, complemented
8#21446123C211yesmaximal, characteristic, complemented
9#21445908C211yesmaximal, characteristic, complemented
10#21445906C211yesmaximal, characteristic, complemented
11#21445832C211yesmaximal, characteristic, complemented
12#21445651C211yesmaximal, characteristic, complemented
13#21445540C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#1873C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840470—24no—
19#16840470C418yescomplemented
20C2×#14519776C2211yescharacteristic
21C2×#14519767—21no—
22C2×#14519757—21no—
23C2×#14519754—21no—
24C2×#14519753C2211yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×C4×C22⋊D61C2211yescharacteristic
27C2×#14519737—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839836—24no—
32C2×#14519706C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519687C2211yescharacteristic
37#16839656—21no—
38#16839646—21no—
39#16839638—21no—
40#16839627C2211yescharacteristic
41#16839622C2211yescharacteristic
42#16839619C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44C4×#11758198—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122—21no—
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#14519776—22no—
77#14519776C2×C414yescomplemented
78#14519767—28no—
79#14519757—28no—
80#14519754—28no—
81#14519753—22no—
82#14519753C2×C414yes—
83Q8×Dic61—22no—
84Q8×Dic61C2×C414yescomplemented
85C4×C22⋊D61C2×C414yes—
86C4×C22⋊D61D414yes—
87#14519737—28no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2×C414yescomplemented
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196D411yescharacteristic
101C4⋊C4×D61—22no—
102C4⋊C4×D61—22no—
103C4⋊C4×D61—41no—
104C4⋊C4×D61C2×C414yes—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61D411yescharacteristic
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198D411yescharacteristic
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113#14519706—22no—
114#14519701—22no—
115#14519701—41no—
116#14519689—22no—
117#14519687—22no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C22×Q8×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22⋊Q8×C61—22no—
128C22⋊Q8×C61C2×C414yescomplemented
129#117×C61—22no—
130#117×C61—41no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C42×C61—21no—
138#103×C61—22no—
139#103×C61—41no—
140C22⋊C8×C61—22no—
141C24×C61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C22×C412yes—
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×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C22×C412yes—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61C22⋊C414yes—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—24no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—81no—
170C22×Dic61—81no—
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—24no—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61—81no—
182C2×C4×D61—81no—
183C2×C4×D61—81no—
184C2×C4×D61C22×C412yes—
185C2×C4×D61C2×D412yes—
186C2×Dic122—24no—
187C2×Dic122—81no—
188C2×Dic122—81no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C4⋊C4×C61—24no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61C22×C412yes—
201C4⋊C4×C61#4112yes—
202C22⋊C4×C61—24no—
203C22⋊C4×C61—42no—
204C42×C61—42no—
205C22⋊Dic61—81no—
206C22⋊Dic61C22⋊C414yes—
207#11758198—24no—
208#11758198—42no—
209#11758198C22⋊C414yes—
210C4⋊Dic61—24no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—24no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61C22×C412yes—
219C4⋊Dic61C22×C412yes—
220#11758196—24no—
221#11758196—24no—
222#11758196—24no—
223#11758196—42no—
224#11758196C22⋊C414yes—
225C4×Dic61—24no—
226C4×Dic61—81no—
227C4×Dic61C22×C412yes—
228C4×Dic61C2×D412yes—
229#11758194—44no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418#4112yes—
236C8×D61—44no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61C2×C22⋊C412yes—
244C23×C61C22×D411yescharacteristic
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61C2×C22⋊C412yes—
250C22×D61#13712yes—
251C22×D61#13712yes—
252Q8×C61—22no—
253Q8×C61—22no—
254Q8×C61—41no—
255Q8×C61—41no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—22no—
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—41no—
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×C61C2×C22⋊C412yes—
275C2×C4×C61C23×C411yescharacteristic
276C2×C4×C61C22×D411yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C2×C4×C612−1+411yescharacteristic
281C22⋊D61—28no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—84no—
301C2×Dic61C2×C22⋊C412yes—
302C2×Dic61C2×C22⋊C412yes—
303C2×Dic61C2×C22⋊C412yes—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—84no—
309C4×D61—84no—
310Dic122—84no—
311C8×C61—41no—
312C8×C61—41no—
313#92418—22no—
314#92418—41no—
315#22497—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×#13711yescharacteristic
327C22×C61C2×#13711yescharacteristic
328C22×C61#57611yescharacteristic
329C22×C61#57711yescharacteristic
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—22no—
335C2×D61—22no—
336C2×D61#41914yes—
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×#554—611no—
354C2×#435—611no—
355#2352—611no—
356#1993—611no—
357#1988—611no—
358#1894—611no—
359#1892—611no—
360#1873D6111yescharacteristic, complemented
361#1872—611no—
362#1824—611no—
363#1823—611no—
364#1805—611no—
365#1763—611no—
366#1736—611no—
367C2×#340—611no—
368C2×C61—42no—
369C2×C61#233911yescharacteristic
370C2×C61C2×#41911yescharacteristic
371C2×C61#289711yescharacteristic
372C2×C61#331411yescharacteristic
373C2×C61#331611yescharacteristic
374C2×C61#334411yescharacteristic
375C2×C61#334611yescharacteristic
376D61—24no—
377C22×M16—611no—
378C23×C8—611no—
379#554—618no—
380#554—1224no—
381C2×C4⋊Q8—611no—
382C2×#125—1221no—
383C2×C22⋊Q8—611no—
384C2×C22⋊Q8—1221no—
385C2×C22⋊Q8—1221no—
386C2×C22⋊Q8C2×D6111yescharacteristic
387C2×C4×Q8—611no—
388C2×C4×D4—611no—
389C2×C4×D4—1221no—
390C2×#117C2×D6111yescharacteristic
391C22×C4⋊C4—611no—
392C22×C4⋊C4—611no—
393C22×C4⋊C4—611no—
394#435—1224no—
395C2×C4⋊C8—611no—
396C2×#103—611no—
397C2×#103—611no—
398C2×#103C2×D6111yescharacteristic
399C2×#103C2×D6111yescharacteristic
400C2×C22⋊C8—611no—
401C2×C22⋊C8C2×D6111yescharacteristic
402C2×#97—611no—
403#388—1221no—
404#387—1221no—
405#386—1221no—
406#382—611no—
407#380—611no—
408#380—611no—
409C4×C4⋊C4—611no—
410C4×C22⋊C4—1221no—
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#2249711yescharacteristic, complemented, Sylow
424C22×Q8—1221no—
425C22×Q8C22×D6111yescharacteristic
426C22×D4—611no—
427C23×C4—611no—
428C23×C4—1221no—
429C23×C4—1221no—
430C23×C4—1221no—
431C23×C4C22×D6111yescharacteristic
432C2×M16—1222no—
433C2×M16—1222no—
434C2×M16—2441no—
435C22×C8—611no—
436C22×C8—611no—
437C22×C8—1222no—
438C22×C8—1222no—
439C22×C8—2441no—
440C22×C8C22×D6111yescharacteristic
441C22×C8C22×D6111yescharacteristic
442C4⋊Q8—614no—
443C4⋊Q8—1222no—
444#125—1228no—
445C22⋊Q8—22no—
446C22⋊Q8—614no—
447C22⋊Q8—1228no—
448C22⋊Q8—1228no—
449C22⋊Q8—1222no—
450C22⋊Q8C4×D6114yescomplemented
451C4×Q8—614no—
452C4×Q8—1222no—
453C4×D4—614no—
454C4×D4—614no—
455C4×D4—1228no—
456#117—22no—
457#117—41no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—614no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—614no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—1222no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1222no—
473C2×C4⋊C4—1222no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—2441no—
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C42—21no—
487C2×C42—611no—
488C2×C42—1221no—
489C2×C42—1221no—
490C4⋊C8—1222no—
491#103—22no—
492#103—41no—
493#103—1222no—
494#103—2441no—
495C22⋊C8—22no—
496C22⋊C8—1222no—
497#97—1222no—
498#95—1221no—
499#95—1221no—
500#95—1221no—
501#95—1221no—
502#95—1221no—
503C24—611no—
504C24D4×D6111yescharacteristic
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—1224no—
511C2×Q8—4881no—
512C2×Q8—4881no—
513C2×Q8C2×C4×D6112yes—
514C2×D4—614no—
515C2×D4—1222no—
516C2×D4—1222no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—612no—
529C22×C4—612no—
530C22×C4—1224no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1224no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—4881no—
541C22×C4—4881no—
542C22×C4—4881no—
543C22×C4—4881no—
544C22×C4—4881no—
545C22×C4—2442no—
546C22×C4—2442no—
547C22×C4C2×C4×D6112yes—
548C22×C4D4×D6112yes—
549C22×C4D4×D6111yescharacteristic
550C22×C4C23×D6111yescharacteristic
551M16—2444no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—612no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—2444no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—614no—
571C4⋊C4—612no—
572C4⋊C4—612no—
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—1221no—
583C4⋊C4—1221no—
584C4⋊C4—2442no—
585C4⋊C4C2×C4×D6112yes—
586C4⋊C4#1175822412yes—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—614no—
590C22⋊C4—614no—
591C22⋊C4—1224no—
592C22⋊C4—4881no—
593C22⋊C4—2442no—
594C42—42no—
595C42—612no—
596C42—612no—
597C42—1224no—
598C42—4881no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—612no—
606C23—612no—
607C23—612no—
608C23—1221no—
609C23—1221no—
610C23—1221no—
611C23—1221no—
612C23C22⋊C4×D6112yes—
613C23C2×D4×D6111yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618Q8—4884no—
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—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—4884no—
654C2×C4—4884no—
655C2×C4—4884no—
656C2×C4—2441no—
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×C4C2×#1175822411yescharacteristic
671C2×C4#1451982211yescharacteristic
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#1684039911yescharacteristic
693C22#1684041011yescharacteristic
694C22#137×D6111yescharacteristic
695C22#137×D6111yescharacteristic
696C22#1684056411yescharacteristic
697C22#1684056911yescharacteristic
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—42no—
715C2—1224no—
716C2#2144864511yescharacteristic
717C2#419×D6111yescharacteristic
718C2#2145434111yescharacteristic
719C2#2145789311yescharacteristic
720C2#2145792311yescharacteristic
721C2#2145826711yescharacteristic
722C2#2145829711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1873C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1873D61
hypocenterC61#22497
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
4. #21446790C2semidirect
5. #21446769C2semidirect
6. #21446253C2semidirect
7. #21446239C2semidirect
8. #21446123C2semidirect
9. #21445908C2semidirect
10. #21445906C2semidirect
11. #21445832C2semidirect
12. #21445651C2semidirect
13. #21445540C2semidirect
14. #340×D61C2semidirect
15. C61×#1873C2semidirect
19. #16840470C4semidirect
77. #14519776C2×C4semidirect
84. Q8×Dic61C2×C4semidirect
91. C2×C4⋊Dic61C2×C4semidirect
128. C22⋊Q8×C61C2×C4semidirect
360. #1873D61semidirect
423. C61#22497semidirect
450. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168398362
#214487492
#214467902
#214467692
#214462532
#214462392
#214461232
#214459082
#214459062
#214458322
#214456512
#214455402
#340×D612
C61×#18732
#2249761