Finite Group Databasebeta

← #29696159

Subgroups — #29696159

Order 15616.

1132 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840447C211yesmaximal, characteristic
2#21448688C211yesmaximal, characteristic, complemented
3#21446804C211yesmaximal, characteristic, complemented
4#21446803C211yesmaximal, characteristic, complemented
5#21446277C212yesmaximal
6#21446275C212yesmaximal
7#21445894C212yesmaximal, complemented
8#21445804C211yesmaximal, characteristic
9C4×#14519691C211yesmaximal, characteristic
10#21445551C212yesmaximal, complemented
11C61×#2344C211yesmaximal, characteristic, complemented
12#16840447—21no—
13#16840447—22no—
14#16840447—21no—
15#16840447—21no—
16#16840447—22no—
17#16840447—21no—
18C2×#14519772C412yescomplemented
19C2×#14519768C411yescharacteristic, complemented
20C2×#14519767C412yescomplemented
21C2×#14519760C2212yes—
22C2×#14519757C411yescharacteristic, complemented
23C2×#14519756C2211yescharacteristic
24C2×#14519742C411yescharacteristic, complemented
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×#14519736C2212yes—
27C2×#14519736C2212yes—
28C2×#14519735C411yescharacteristic, complemented
29C2×#14519691C2211yescharacteristic
30C2×#14519691C2211yescharacteristic
31C2×#14519691C2212yes—
32#16839661—21no—
33#16839648—22no—
34#16839625C2212yes—
35#16839622C2211yescharacteristic
36C4⋊C4×Dic61—21no—
37C4×C22⋊Dic61C2211yescharacteristic
38#16839528C2211yescharacteristic
39#16839528C2212yes—
40#16839528C2212yes—
41#16839528C2212yes—
42#16839528C2212yes—
43#16839528C2212yes—
44#16839528C2211yescharacteristic
45C2×#117×C61C2212yes—
46C22×C4⋊C4×C61C2211yescharacteristic
47C61×#389—21no—
48C61×#387—22no—
49C61×#381C2212yes—
50C61×#380C2211yescharacteristic
51C4×C4⋊C4×C61—21no—
52C4×C22⋊C4×C61C2211yescharacteristic
53C22×Dic122C2×C411yescharacteristic
54C22×C22⋊D61C2311yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56#14519772—22no—
57#14519772—22no—
58#14519772—22no—
59#14519772—22no—
60#14519768—22no—
61#14519768—21no—
62#14519768—21no—
63#14519767—22no—
64#14519767—22no—
65#14519767—22no—
66#14519767—22no—
67#14519760—22no—
68#14519760—22no—
69#14519760—22no—
70#14519760—22no—
71#14519757—22no—
72#14519757—21no—
73#14519757—21no—
74#14519756—21no—
75#14519756—21no—
76#14519756—21no—
77#14519756—21no—
78#14519742—22no—
79#14519742—21no—
80#14519742—21no—
81C4×C22⋊D61—21no—
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84C4×C22⋊D61—21no—
85#14519736—22no—
86#14519736—22no—
87#14519736—22no—
88#14519736—22no—
89#14519736—24no—
90#14519736—42no—
91#14519735—22no—
92#14519735—21no—
93#14519735—21no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×C4⋊Dic61C2×C412yes—
98C2×C4⋊Dic61C2×C412yes—
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C412yes—
101C2×#11758196C2×C412yes—
102C2×#11758196C2×C412yes—
103C2×C22⋊Dic61C2312yes—
104C2×C22⋊Dic61C2311yescharacteristic
105C2×C22⋊Dic61C2311yescharacteristic
106C2×C22⋊Dic61C2312yes—
107C2×C22⋊Dic61C2311yescharacteristic
108C2×#11758198C2×C412yes—
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C412yes—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61C2×C412yes—
114C2×C4×Dic61C2×C412yes—
115C2×C4×Dic61C2×C411yescharacteristic
116#14519691—22no—
117#14519691—22no—
118#14519691—42no—
119#14519684—21no—
120#14519684—22no—
121#14519684—21no—
122#14519684—22no—
123C23×C4×C61C2312yes—
124C23×C4×C61C2311yescharacteristic
125#117×C61—24no—
126#117×C61—42no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—22no—
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C4⋊C4×C61C2×C412yes—
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C4⋊C4×C61D412yes—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61D411yescharacteristic
136C2×C4⋊C4×C61D412yes—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61C2312yes—
140C2×C22⋊C4×C61C2311yescharacteristic
141C2×C42×C61—21no—
142C2×C42×C61—22no—
143#95×C61—21no—
144#95×C61—22no—
145#95×C61—21no—
146#95×C61—22no—
147C24×C61C2411yescharacteristic
148C23×D61C22×C411yescharacteristic
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—22no—
156C22×C4×C61—42no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C2×C22⋊D61—21no—
170C2×C22⋊D61—21no—
171C2×C22⋊D61—21no—
172C2×C22⋊D61—21no—
173C2×C22⋊D61—21no—
174C2×C22⋊D61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—22no—
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C412yes—
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C412yes—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—42no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—42no—
189C4⋊C4×C61—44no—
190C4⋊C4×C61—42no—
191C4⋊C4×C61C22⋊C412yes—
192C4⋊C4×C61C22⋊C411yescharacteristic
193C4⋊C4×C61C22⋊C411yescharacteristic
194C4⋊C4×C61C22⋊C412yes—
195C4⋊C4×C61C22⋊C411yescharacteristic
196C4⋊C4×C61C22⋊C411yescharacteristic
197C4⋊C4×C61C22⋊C412yes—
198C4⋊C4×C61C22⋊C412yes—
199C4⋊C4×C61C22⋊C412yes—
200C4⋊C4×C61C22⋊C412yes—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—21no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—21no—
206C22⋊C4×C61#4112yes—
207C42×C61—44no—
208C42×C61—42no—
209C22⋊Dic61—21no—
210C22⋊Dic61—21no—
211C22⋊Dic61—22no—
212C22⋊Dic61—22no—
213C22⋊Dic61—21no—
214C22⋊Dic61—21no—
215C22⋊Dic61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—21no—
218C22⋊Dic61#4112yes—
219#11758198—22no—
220#11758198—22no—
221#11758198—21no—
222#11758198—21no—
223#11758198—22no—
224#11758198—22no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—22no—
228C4⋊Dic61—22no—
229C4⋊Dic61—22no—
230C4⋊Dic61—22no—
231C4⋊Dic61—44no—
232C4⋊Dic61—42no—
233#11758196—21no—
234#11758196—21no—
235#11758196—22no—
236#11758196—22no—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61—22no—
244C4×Dic61—22no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—44no—
248C4×Dic61—42no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61C23×C411yescharacteristic
252C23×C61C22×D411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C23×C61C2×#4111yescharacteristic
255C23×C61C2×#4111yescharacteristic
256C23×C61H(5,𝔽2)11yescharacteristic
257C23×C612−1+411yescharacteristic
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—41no—
262C22×D61—41no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—42no—
286C2×C4×C61—41no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—41no—
290C2×C4×C61C2×C22⋊C412yes—
291C2×C4×C61C2×C22⋊C412yes—
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C412yes—
296C2×C4×C61C2×C22⋊C412yes—
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C22⋊D61—41no—
299C22⋊D61—41no—
300C22⋊D61—41no—
301C22⋊D61—41no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—42no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—42no—
316C2×Dic61—41no—
317C2×Dic61—42no—
318C2×Dic61—41no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—41no—
322C4×D61—42no—
323C4×D61—42no—
324Dic122—42no—
325Dic122—42no—
326#22478—611nomaximal, Sylow
327C22×C61—21no—
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—21no—
331C22×C61—21no—
332C22×C61—21no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61C22×C22⋊C411yescharacteristic
338C22×C61C4×#4111yescharacteristic
339C22×C61#52011yescharacteristic
340C22×C61#54611yescharacteristic
341C22×C61#54611yescharacteristic
342C22×C61#54711yescharacteristic
343C22×C61#54711yescharacteristic
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C2×D61—81no—
348C2×D61—81no—
349C4×C61—22no—
350C4×C61—22no—
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—42no—
357C4×C61—82no—
358C4×C61—81no—
359C4×C61#41012yes—
360Dic61—42no—
361Dic61—41no—
362Dic61—42no—
363Dic61—41no—
364Dic61—41no—
365Dic61—42no—
366Dic61—82no—
367Dic61—81no—
368C2×#552—611no—
369#2344—611no—
370#2344D6111yescharacteristic, complemented
371#1996—611no—
372#1996—611no—
373#1899—612no—
374#1899—612no—
375#1820—612no—
376#1799—611no—
377C4×#99—611no—
378#1740—612no—
379C2×C61—21no—
380C2×C61—21no—
381C2×C61—21no—
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61#233911yescharacteristic
386C2×C61C2×#41011yescharacteristic
387C2×C61#288411yescharacteristic
388D61—81no—
389#552—1221no—
390#552—1222no—
391#552—1221no—
392#552—1221no—
393#552—1222no—
394#552—1221no—
395C2×#126—612no—
396C2×#125—612no—
397C2×#125—611no—
398C2×#123—612no—
399C2×C22⋊Q8—611no—
400C2×C22⋊Q8—611no—
401C2×C4×Q8—611no—
402C2×C4×D4—611no—
403C2×#117—612no—
404C2×#117—611no—
405C2×#117—612no—
406C2×#117C2×D6112yes—
407C22×C4⋊C4C2×D6111yescharacteristic
408C2×#99—611no—
409C2×#99—611no—
410C2×#99—612no—
411#389—21no—
412#389—1221no—
413#387—22no—
414#387—1222no—
415#381—612no—
416#381C2×D6112yes—
417#380—611no—
418#380C2×D6111yescharacteristic
419C4×C4⋊C4—21no—
420C4×C4⋊C4—1221no—
421C4×C22⋊C4—611no—
422C4×C22⋊C4C2×D6111yescharacteristic
423#342—612no—
424#342—611no—
425#342—612no—
426#342—612no—
427#342—612no—
428#342—612no—
429#342—611no—
430C61#2247811yescharacteristic, complemented, Sylow
431C22×Q8—611no—
432C22×D4—611no—
433C23×C4—611no—
434C23×C4C22×D6112yes—
435C23×C4C22×D6111yescharacteristic
436#126—1222no—
437#126—1222no—
438#126—1222no—
439#126—1222no—
440#125—1222no—
441#125—1222no—
442#125—1222no—
443#125—1222no—
444#125—1222no—
445#125—1221no—
446#125—1221no—
447#123—1222no—
448#123—1222no—
449#123—1222no—
450#123—1222no—
451C22⋊Q8—1221no—
452C22⋊Q8—1221no—
453C22⋊Q8—1221no—
454C22⋊Q8—1221no—
455C22⋊Q8—1222no—
456C22⋊Q8—1221no—
457C22⋊Q8—1221no—
458C4×Q8—1222no—
459C4×Q8—1221no—
460C4×Q8—1221no—
461C4×D4—1221no—
462C4×D4—1221no—
463C4×D4—1221no—
464C4×D4—1221no—
465#117—24no—
466#117—42no—
467#117—1222no—
468#117—1222no—
469#117—1222no—
470#117—1222no—
471#117—1222no—
472#117—1221no—
473#117—1221no—
474#117—1224no—
475#117—2442no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—612no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—612no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—612no—
483C2×C4⋊C4—612no—
484C2×C4⋊C4—612no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4C4×D6111yescharacteristic
488C2×C4⋊C4C4×D6111yescharacteristic
489C2×C4⋊C4C4×D6112yes—
490C2×C4⋊C4D24411yescharacteristic
491C2×C4⋊C4D24412yes—
492C2×C4⋊C4D24411yescharacteristic
493C2×C4⋊C4C22⋊D6111yescharacteristic
494C2×C4⋊C4C22⋊D6112yes—
495C2×C4⋊C4C22⋊D6111yescharacteristic
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—612no—
499C2×C22⋊C4—612no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—612no—
502C2×C22⋊C4—612no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4C22×D6112yes—
505C2×C22⋊C4C22×D6111yescharacteristic
506C2×C22⋊C4C22×D6111yescharacteristic
507C2×C42—22no—
508C2×C42—21no—
509C2×C42—612no—
510C2×C42—612no—
511C2×C42—611no—
512C2×C42—1222no—
513C2×C42—1221no—
514#99—1222no—
515#99—1222no—
516#99—2442no—
517#95—21no—
518#95—22no—
519#95—21no—
520#95—22no—
521#95—1221no—
522#95—1222no—
523#95—1221no—
524#95—1222no—
525C24—611no—
526C24C23×D6111yescharacteristic
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—2442no—
530C2×D4—1221no—
531C2×D4—1221no—
532C2×D4—1221no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—42no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1222no—
554C22×C4—2442no—
555C22×C4C2×C4×D6112yes—
556C22×C4C2×C4×D6111yescharacteristic
557C22×C4C2×C4×D6112yes—
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4C2×D24412yes—
560C22×C4C2×D24412yes—
561C22×C4C2×D24411yescharacteristic
562C22×C4C2×D24411yescharacteristic
563C22×C4C2×C22⋊D6112yes—
564C22×C4C2×C22⋊D6112yes—
565C22×C4C2×C22⋊D6111yescharacteristic
566C22×C4C2×C22⋊D6111yescharacteristic
567C4⋊C4—44no—
568C4⋊C4—42no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1222no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C4⋊C4—1222no—
576C4⋊C4—1222no—
577C4⋊C4—1222no—
578C4⋊C4—1222no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1222no—
582C4⋊C4—1222no—
583C4⋊C4—2444no—
584C4⋊C4—2442no—
585C4⋊C4#1175819812yes—
586C4⋊C4#1175819811yescharacteristic
587C4⋊C4#1175819811yescharacteristic
588C4⋊C4#1175819812yes—
589C4⋊C4#1175819811yescharacteristic
590C4⋊C4#1175819811yescharacteristic
591C4⋊C4#1175819812yes—
592C4⋊C4#1175819812yes—
593C4⋊C4#1175819812yes—
594C4⋊C4#1175819812yes—
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—21no—
600C22⋊C4—612no—
601C22⋊C4—1221no—
602C22⋊C4—1222no—
603C22⋊C4—1221no—
604C22⋊C4—1222no—
605C22⋊C4—1221no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1221no—
609C22⋊C4—1221no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1221no—
614C22⋊C4—1222no—
615C22⋊C4—1221no—
616C22⋊C4#1175822412yes—
617C42—44no—
618C42—42no—
619C42—1222no—
620C42—1222no—
621C42—1222no—
622C42—1222no—
623C42—1221no—
624C42—1221no—
625C42—2444no—
626C42—2442no—
627C23—41no—
628C23—41no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—2441no—
633C23—2441no—
634C23C22×C4×D6111yescharacteristic
635C23C22×C22⋊D6111yescharacteristic
636C23C22×D24411yescharacteristic
637C23#41×D6111yescharacteristic
638C23C2×#1175822411yescharacteristic
639C23#1451982211yescharacteristic
640C23#1451982411yescharacteristic
641Q8—2442no—
642Q8—2442no—
643D4—2441no—
644D4—2441no—
645D4—2441no—
646D4—2441no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1222no—
682C2×C4—2442no—
683C2×C4—2441no—
684C2×C4—2442no—
685C2×C4—2441no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2442no—
692C2×C4—2441no—
693C2×C4—2442no—
694C2×C4—2441no—
695C2×C4—2442no—
696C2×C4C2×#1175819812yes—
697C2×C4C2×#1175819812yes—
698C2×C4C2×#1175819811yescharacteristic
699C2×C4C2×#1175819811yescharacteristic
700C2×C4C2×#1175819811yescharacteristic
701C2×C4C2×#1175819812yes—
702C2×C4C2×#1175819812yes—
703C2×C4C2×#1175819811yescharacteristic
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—4881no—
715C22—4881no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22C22×#1175819811yescharacteristic
720C22C4×#1175822411yescharacteristic
721C22#1684024111yescharacteristic
722C22#1684040611yescharacteristic
723C22#1684040711yescharacteristic
724C22#1684041111yescharacteristic
725C22#1684041611yescharacteristic
726C4—21no—
727C4—21no—
728C4—21no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—22no—
733C4—42no—
734C4—82no—
735C4—81no—
736C4—4882no—
737C4—4881no—
738C4—2442no—
739C4—2441no—
740C4—2442no—
741C4—2441no—
742C4—2441no—
743C4—2442no—
744C4#1683973512yes—
745C2—21no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—21no—
750C2—21no—
751C2—4881no—
752C2#2144864411yescharacteristic
753C2C2×#1683973511yescharacteristic
754C2#2145428211yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2344C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C23
cosocleC24×C61C24
hypercenter#2344D61
hypocenterC61#22478
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #21448688C2semidirect
3. #21446804C2semidirect
4. #21446803C2semidirect
7. #21445894C2semidirect
10. #21445551C2semidirect
11. C61×#2344C2semidirect
18. C2×#14519772C4semidirect
19. C2×#14519768C4semidirect
20. C2×#14519767C4semidirect
22. C2×#14519757C4semidirect
24. C2×#14519742C4semidirect
28. C2×#14519735C4semidirect
370. #2344D61semidirect
430. C61#22478semidirect

Maximal subgroups

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

subgroupindex
C2×#168404472
#214486882
#214468042
#214468032
#214462772
#214462752
#214458942
#214458042
C4×#145196912
#214455512
C61×#23442
#2247861