Finite Group Databasebeta

← #29696567

Subgroups — #29696567

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic
2#21448698C211yesmaximal, characteristic, complemented
3#21448694C211yesmaximal, characteristic, complemented
4#21446805C211yesmaximal, characteristic, complemented
5#21446802C212yesmaximal, complemented
6#21446802C212yesmaximal, complemented
7#21445806C212yesmaximal
8#21445804C211yesmaximal, characteristic
9C4×#14519691C211yesmaximal, characteristic
10#21445606C212yesmaximal
11C61×#1996C211yesmaximal, characteristic, complemented
12#16840470—21no—
13#16840470—21no—
14#16840470—22no—
15#16840470—22no—
16#16840470—21no—
17#16840470—21no—
18C2×#14519776C411yescharacteristic, complemented
19C2×#14519767C412yescomplemented
20C2×#14519757C412yescomplemented
21C2×#14519754C2212yes—
22C2×#14519753C411yescharacteristic, complemented
23C2×Q8×Dic61C411yescharacteristic, complemented
24C2×C4×C22⋊D61C2211yescharacteristic
25C2×#14519737C2212yes—
26C22×C4⋊Dic61C2211yescharacteristic
27C2×C4⋊C4×D61C411yescharacteristic, complemented
28C2×#14519691C2212yes—
29C2×#14519691C2211yescharacteristic
30C2×#14519691C2211yescharacteristic
31#16839660—21no—
32#16839658—21no—
33#16839647—22no—
34#16839645—22no—
35#16839622C2211yescharacteristic
36#16839620C2212yes—
37#16839620C2212yes—
38C4⋊C4×Dic61—21no—
39C4×C4⋊Dic61—21no—
40C22⋊C4×Dic61C2212yes—
41C22⋊C4×Dic61C2212yes—
42C4×C22⋊Dic61C2211yescharacteristic
43#16839529C2212yes—
44#16839529C2212yes—
45#16839528C2212yes—
46#16839528C2211yescharacteristic
47#16839528C2211yescharacteristic
48C2×C22⋊Q8×C61C2211yescharacteristic
49C61×#380C2211yescharacteristic
50C4×C22⋊C4×C61C2211yescharacteristic
51C61×#342C2212yes—
52C61×#342C2212yes—
53C22×Dic122C2×C412yes—
54C22×C22⋊D61C2311yescharacteristic
55C23×Dic61C2312yes—
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C412yes—
58#14519776—22no—
59#14519776—21no—
60#14519776—21no—
61#14519767—22no—
62#14519767—22no—
63#14519767—22no—
64#14519767—22no—
65#14519757—22no—
66#14519757—22no—
67#14519757—22no—
68#14519757—22no—
69#14519754—22no—
70#14519754—22no—
71#14519754—22no—
72#14519754—22no—
73#14519753—22no—
74#14519753—21no—
75#14519753—21no—
76Q8×Dic61—22no—
77Q8×Dic61—21no—
78Q8×Dic61—21no—
79C4×C22⋊D61—21no—
80C4×C22⋊D61—21no—
81C4×C22⋊D61—21no—
82C4×C22⋊D61—21no—
83#14519737—22no—
84#14519737—22no—
85#14519737—22no—
86#14519737—22no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61C2×C412yes—
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×C4⋊Dic61C2×C412yes—
92C2×C4⋊Dic61D411yescharacteristic
93C2×C4⋊Dic61D411yescharacteristic
94C2×C4⋊Dic61D412yes—
95C2×C4⋊Dic61D412yes—
96C2×C4⋊Dic61D411yescharacteristic
97C2×C4⋊Dic61D411yescharacteristic
98C2×#11758196—22no—
99C2×#11758196—22no—
100C2×#11758196C2×C412yes—
101C2×#11758196C2×C412yes—
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C412yes—
104C4⋊C4×D61—22no—
105C4⋊C4×D61—21no—
106C4⋊C4×D61—21no—
107C2×C22⋊Dic61C2311yescharacteristic
108C2×C22⋊Dic61C2312yes—
109C2×C22⋊Dic61C2311yescharacteristic
110C2×C22⋊Dic61C2311yescharacteristic
111C2×#11758198C2×C412yes—
112C2×#11758198C2×C411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61C2×C412yes—
117C2×C4×Dic61C2×C411yescharacteristic
118#14519691—24no—
119#14519691—22no—
120#14519691Q814yescomplemented
121#14519684—21no—
122#14519684—21no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127C22×Q8×C61C2×C411yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C4⋊C4×C61C2×C412yes—
136C2×C22⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61C2312yes—
138C2×C22⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2311yescharacteristic
140C2×C42×C61—21no—
141#95×C61—21no—
142#95×C61—21no—
143C24×C61C2411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—42no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—42no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C2×C22⋊D61—21no—
161C2×C22⋊D61—21no—
162C2×C22⋊D61—21no—
163C2×C22⋊D61—21no—
164C2×C22⋊D61C2×Q812yes—
165C2×C22⋊D61#4112yes—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—22no—
169C22×Dic61—82no—
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C412yes—
174C22×Dic61C22×C412yes—
175C22×Dic61C2×D412yes—
176C22×Dic61C2×D412yes—
177C22×Dic61C2×D412yes—
178C22×Dic61C2×D412yes—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—42no—
184C2×C4×D61—82no—
185C2×Dic122—22no—
186C2×Dic122—22no—
187C2×Dic122—82no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—22no—
192C4⋊C4×C61—42no—
193C22⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—22no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—21no—
200C22⋊C4×C61C2×Q812yes—
201C42×C61—42no—
202C22⋊Dic61—21no—
203C22⋊Dic61—21no—
204C22⋊Dic61—21no—
205C22⋊Dic61—21no—
206C22⋊Dic61—22no—
207C22⋊Dic61—21no—
208C22⋊Dic61—22no—
209C22⋊Dic61C2×Q812yes—
210#11758198—21no—
211#11758198—21no—
212#11758198—22no—
213#11758198—22no—
214C4⋊Dic61—22no—
215C4⋊Dic61—22no—
216C4⋊Dic61—42no—
217C4⋊Dic61C22⋊C412yes—
218C4⋊Dic61C22⋊C411yescharacteristic
219C4⋊Dic61C22⋊C411yescharacteristic
220C4⋊Dic61C22⋊C412yes—
221C4⋊Dic61C22⋊C411yescharacteristic
222C4⋊Dic61C22⋊C411yescharacteristic
223C4⋊Dic61C22⋊C412yes—
224C4⋊Dic61C22⋊C412yes—
225C4⋊Dic61C22⋊C412yes—
226C4⋊Dic61C22⋊C412yes—
227#11758196—21no—
228#11758196—21no—
229#11758196—22no—
230#11758196—22no—
231#11758196—22no—
232#11758196—22no—
233#11758196—22no—
234#11758196—22no—
235#11758196—82no—
236#11758196—82no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—22no—
240C4×Dic61—22no—
241C4×Dic61—42no—
242C4×Dic61—82no—
243C4×Dic61—82no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61C23×C411yescharacteristic
247C23×C61C22×D411yescharacteristic
248C23×C61C22×D411yescharacteristic
249C23×C61C22×Q811yescharacteristic
250C23×C61C2×#4111yescharacteristic
251C23×C612−1+411yescharacteristic
252C23×C612−1+411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61C4×Q812yes—
258Q8×C61—42no—
259Q8×C61—42no—
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—42no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—41no—
279C2×C4×C61C2×C22⋊C411yescharacteristic
280C2×C4×C61C2×C22⋊C411yescharacteristic
281C2×C4×C61C2×C22⋊C411yescharacteristic
282C2×C4×C61C2×C22⋊C411yescharacteristic
283C22⋊D61—22no—
284C22⋊D61—22no—
285C22⋊D61—22no—
286C22⋊D61—22no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—22no—
292C2×Dic61—42no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61—42no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—42no—
304C2×Dic61—41no—
305C2×Dic61—42no—
306C2×Dic61—41no—
307C2×Dic61—42no—
308C2×Dic61C2×C22⋊C412yes—
309C2×Dic61C2×C22⋊C412yes—
310C2×Dic61C2×C22⋊C412yes—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C4×Q812yes—
313C4×D61—42no—
314C4×D61—42no—
315C4×D61—82no—
316C4×D61—82no—
317Dic122—82no—
318Dic122—82no—
319#22513—611nomaximal, Sylow
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—21no—
323C22×C61—21no—
324C22×C61—21no—
325C22×C61—21no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61C22×C22⋊C411yescharacteristic
331C22×C61C2×C4×Q811yescharacteristic
332C22×C61#51911yescharacteristic
333C22×C61#54811yescharacteristic
334C22×C61#54811yescharacteristic
335C22×C61D4×Q811yescharacteristic
336C22×C61D4×Q811yescharacteristic
337C2×D61—22no—
338C2×D61—42no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—42no—
342C4×C61—21no—
343C4×C61—21no—
344C4×C61—21no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61—42no—
348C4×C61—81no—
349C4×C61—82no—
350C4×C61#41012yes—
351Dic61—22no—
352Dic61—22no—
353Dic61—22no—
354Dic61—22no—
355Dic61—22no—
356Dic61—42no—
357Dic61—41no—
358Dic61—41no—
359Dic61—82no—
360Dic61—81no—
361C2×#554—611no—
362#2345—611no—
363#2345—611no—
364#1996—612no—
365#1996—612no—
366#1996—611no—
367#1996D6111yescharacteristic, complemented
368#1799—611no—
369#1799—612no—
370C4×#99—611no—
371C4×#99—612no—
372C2×C61—21no—
373C2×C61—21no—
374C2×C61—21no—
375C2×C61—21no—
376C2×C61—21no—
377C2×C61—21no—
378C2×C61Q8×C22⋊C411yescharacteristic
379C2×C61C2×#41011yescharacteristic
380C2×C61#288311yescharacteristic
381D61—42no—
382#554—1221no—
383#554—1221no—
384#554—1222no—
385#554—1222no—
386#554—1221no—
387#554—1221no—
388C2×C4⋊Q8—611no—
389C2×#125—612no—
390C2×C22⋊Q8—611no—
391C2×C22⋊Q8—612no—
392C2×C22⋊Q8—612no—
393C2×C22⋊Q8C2×D6111yescharacteristic
394C2×C4×Q8—611no—
395C2×C4×D4—611no—
396C2×C4×D4—612no—
397C22×C4⋊C4—611no—
398C22×C4⋊C4—611no—
399C2×#99—611no—
400C2×#99—612no—
401C2×#99—611no—
402#389—1221no—
403#389—1221no—
404#387—1222no—
405#387—1222no—
406#380—611no—
407#380—612no—
408#380—612no—
409#380C2×D6111yescharacteristic
410C4×C4⋊C4—1221no—
411C4×C4⋊C4—1221no—
412C4×C22⋊C4—611no—
413C4×C22⋊C4—612no—
414C4×C22⋊C4—612no—
415C4×C22⋊C4C2×D6111yescharacteristic
416#342—612no—
417#342—612no—
418#342—611no—
419#342—611no—
420#342—612no—
421#342C2×D6112yes—
422#342C2×D6112yes—
423C61#2251311yescharacteristic, complemented, Sylow
424C22×Q8—612no—
425C22×Q8C4×D6111yescharacteristic
426C22×D4—611no—
427C23×C4—612no—
428C23×C4—612no—
429C23×C4—611no—
430C23×C4C22×D6111yescharacteristic
431C4⋊Q8—1222no—
432C4⋊Q8—1221no—
433C4⋊Q8—1221no—
434#125—1222no—
435#125—1222no—
436#125—1222no—
437#125—1222no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440C22⋊Q8—21no—
441C22⋊Q8—21no—
442C22⋊Q8—1222no—
443C22⋊Q8—1222no—
444C22⋊Q8—1222no—
445C22⋊Q8—1222no—
446C22⋊Q8—1222no—
447C22⋊Q8—1222no—
448C22⋊Q8—1222no—
449C22⋊Q8—1222no—
450C22⋊Q8—1222no—
451C22⋊Q8—1221no—
452C22⋊Q8—1221no—
453C4×Q8—1222no—
454C4×Q8—1221no—
455C4×Q8—1221no—
456C4×D4—1222no—
457C4×D4—1222no—
458C4×D4—1222no—
459C4×D4—1222no—
460C4×D4—1221no—
461C4×D4—1221no—
462C4×D4—1221no—
463C4×D4—1221no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—612no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—612no—
471C2×C4⋊C4—612no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—612no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—612no—
477C2×C4⋊C4—612no—
478C2×C4⋊C4—612no—
479C2×C4⋊C4—1222no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4C4×D6111yescharacteristic
486C2×C4⋊C4C4×D6112yes—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—612no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—612no—
493C2×C22⋊C4C22×D6112yes—
494C2×C22⋊C4C22×D6111yescharacteristic
495C2×C22⋊C4C22×D6112yes—
496C2×C22⋊C4C22×D6111yescharacteristic
497C2×C42—21no—
498C2×C42—612no—
499C2×C42—611no—
500C2×C42—1222no—
501C2×C42—1222no—
502C2×C42—1221no—
503#99—614no—
504#99—1224no—
505#99—1222no—
506#95—21no—
507#95—21no—
508#95—1222no—
509#95—1222no—
510#95—1222no—
511#95—1222no—
512#95—1221no—
513#95—1221no—
514C24—611no—
515C24C23×D6111yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—42no—
519C2×Q8—1222no—
520C2×Q8—1222no—
521C2×Q8—4882no—
522C2×D4—612no—
523C2×D4—612no—
524C2×D4—1221no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—1221no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—611no—
533C22×C4—612no—
534C22×C4—612no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1222no—
547C22×C4—1221no—
548C22×C4—4882no—
549C22×C4—4882no—
550C22×C4—2442no—
551C22×C4C2×C4×D6111yescharacteristic
552C22×C4C2×C4×D6112yes—
553C22×C4C2×C4×D6112yes—
554C22×C4C2×C4×D6111yescharacteristic
555C22×C4D4×D6111yescharacteristic
556C22×C4D4×D6111yescharacteristic
557C22×C4D4×D6111yescharacteristic
558C22×C4D4×D6111yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—42no—
564C4⋊C4—612no—
565C4⋊C4—611no—
566C4⋊C4—611no—
567C4⋊C4—612no—
568C4⋊C4—612no—
569C4⋊C4—612no—
570C4⋊C4—612no—
571C4⋊C4—612no—
572C4⋊C4—611no—
573C4⋊C4—611no—
574C4⋊C4—1222no—
575C4⋊C4—1222no—
576C4⋊C4—1222no—
577C4⋊C4—1222no—
578C4⋊C4—1222no—
579C4⋊C4—1222no—
580C4⋊C4—1222no—
581C4⋊C4—1222no—
582C4⋊C4—1221no—
583C4⋊C4—1221no—
584C4⋊C4—4882no—
585C4⋊C4—4882no—
586C4⋊C4—2442no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—21no—
590C22⋊C4—22no—
591C22⋊C4—21no—
592C22⋊C4—22no—
593C22⋊C4—21no—
594C22⋊C4—612no—
595C22⋊C4—1222no—
596C22⋊C4—1222no—
597C22⋊C4—1221no—
598C22⋊C4—1221no—
599C22⋊C4—1221no—
600C22⋊C4—1221no—
601C22⋊C4—1221no—
602C22⋊C4—1221no—
603C22⋊C4—1222no—
604C22⋊C4—1221no—
605C22⋊C4—1222no—
606C22⋊C4Q8×D6112yes—
607C42—42no—
608C42—1222no—
609C42—1222no—
610C42—1221no—
611C42—1221no—
612C42—4882no—
613C42—4882no—
614C42—2442no—
615C23—41no—
616C23—41no—
617C23—612no—
618C23—1221no—
619C23—1221no—
620C23—2441no—
621C23—2441no—
622C23C22×C4×D6111yescharacteristic
623C23C2×D4×D6111yescharacteristic
624C23C2×D4×D6111yescharacteristic
625C23C2×Q8×D6111yescharacteristic
626C23#41×D6111yescharacteristic
627C23#1451982411yescharacteristic
628C23#1451982511yescharacteristic
629Q8—42no—
630Q8—42no—
631Q8—4882no—
632Q8—4882no—
633D4—1222no—
634D4—1222no—
635D4—1222no—
636D4—1222no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—612no—
657C2×C4—612no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1222no—
666C2×C4—4882no—
667C2×C4—4882no—
668C2×C4—2442no—
669C2×C4—2442no—
670C2×C4—2442no—
671C2×C4—2442no—
672C2×C4—2442no—
673C2×C4—2442no—
674C2×C4—2442no—
675C2×C4—2442no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2442no—
679C2×C4—2441no—
680C2×C4—2442no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2442no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4C22⋊C4×D6111yescharacteristic
687C2×C4C22⋊C4×D6111yescharacteristic
688C2×C4C22⋊C4×D6111yescharacteristic
689C2×C4C22⋊C4×D6111yescharacteristic
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—1222no—
701C22—2442no—
702C22—2442no—
703C22—2441no—
704C22—2441no—
705C22C2×C22⋊C4×D6111yescharacteristic
706C22C4×Q8×D6111yescharacteristic
707C22#1684023811yescharacteristic
708C22#1684042011yescharacteristic
709C22#1684042211yescharacteristic
710C22#1684042511yescharacteristic
711C22#1684042711yescharacteristic
712C4—21no—
713C4—21no—
714C4—21no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—82no—
719C4—81no—
720C4—1222no—
721C4—1222no—
722C4—1222no—
723C4—1222no—
724C4—1222no—
725C4—4881no—
726C4—4882no—
727C4—2442no—
728C4—2441no—
729C4—2441no—
730C4#1683973412yes—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—2442no—
738C2#2144865311yescharacteristic
739C2C2×#1683973411yescharacteristic
740C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C23
cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61#22513
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #21448698C2semidirect
3. #21448694C2semidirect
4. #21446805C2semidirect
5. #21446802C2semidirect
6. #21446802C2semidirect
11. C61×#1996C2semidirect
18. C2×#14519776C4semidirect
19. C2×#14519767C4semidirect
20. C2×#14519757C4semidirect
22. C2×#14519753C4semidirect
23. C2×Q8×Dic61C4semidirect
27. C2×C4⋊C4×D61C4semidirect
120. #14519691Q8semidirect
367. #1996D61semidirect
423. C61#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
#214486982
#214486942
#214468052
#214468022
#214458062
#214458042
C4×#145196912
#214456062
C61×#19962
#2251361