Finite Group Databasebeta

← #29696763

Subgroups — #29696763

Order 15616.

1172 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840461C211yesmaximal, characteristic
2#21448691C212yesmaximal, complemented
3#21446654C212yesmaximal, complemented
4#21446653C212yesmaximal, complemented
5#21446653C212yesmaximal, complemented
6#21445806C211yesmaximal, characteristic, complemented
7#21445806C211yesmaximal, characteristic, complemented
8C4×#14519692C211yesmaximal, characteristic, complemented
9#21445606C211yesmaximal, characteristic, complemented
10#21445606C211yesmaximal, characteristic, complemented
11C61×#1799C211yesmaximal, characteristic, complemented
12#16840461—22no—
13#16840461—22no—
14#16840461—22no—
15#16840461—22no—
16C2×#14519771C411yescharacteristic, complemented
17C2×#14519770C411yescharacteristic, complemented
18C2×#14519767C411yescharacteristic, complemented
19C2×#14519762C411yescharacteristic, complemented
20C2×#14519760C411yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic
22C2×#14519750C411yescharacteristic, complemented
23C2×#14519749C2211yescharacteristic
24C2×#14519749C2211yescharacteristic
25C2×C4×C22⋊D61C411yescharacteristic, complemented
26C2×#14519737C2211yescharacteristic
27C2×#14519737C2211yescharacteristic
28C2×#14519734C411yescharacteristic, complemented
29C22×#11758196C2211yescharacteristic
30C2×#14519692C2212yes—
31C2×#14519691C2212yes—
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34C2×#14519691C2212yes—
35#16839657—22no—
36#16839644—22no—
37#16839643—22no—
38#16839620C2212yes—
39#16839620C2212yes—
40#16839613—22no—
41C22⋊C4×Dic61C2212yes—
42C22⋊C4×Dic61C2212yes—
43C4×C22⋊Dic61C2212yes—
44#16839529C2211yescharacteristic
45#16839529C2211yescharacteristic
46C2×C4×D4×C61C2211yescharacteristic
47C2×#99×C61C2212yes—
48C61×#380C2212yes—
49C61×#342C2211yescharacteristic
50C61×#342C2211yescharacteristic
51C22×D244C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C22⋊D61C2311yescharacteristic
55C22×C22⋊D61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60#14519771—22no—
61#14519771—22no—
62#14519770—22no—
63#14519770—22no—
64#14519767—22no—
65#14519767—22no—
66#14519762—22no—
67#14519762—22no—
68#14519760—22no—
69#14519760—22no—
70#14519751—22no—
71#14519751—22no—
72#14519750—22no—
73#14519750—22no—
74#14519749—22no—
75#14519749—22no—
76#14519749—22no—
77#14519749—22no—
78C4×C22⋊D61—21no—
79C4×C22⋊D61—21no—
80C4×C22⋊D61—21no—
81C4×C22⋊D61—21no—
82#14519737—22no—
83#14519737—22no—
84#14519737—22no—
85#14519737—22no—
86#14519734—21no—
87#14519734—21no—
88#14519734—21no—
89#14519734—21no—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196D412yes—
102C2×#11758196D412yes—
103C2×#11758196D412yes—
104C2×#11758196D412yes—
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2312yes—
108C2×C22⋊Dic61C2312yes—
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61C2×C411yescharacteristic
119C2×C4×Dic61C2×C411yescharacteristic
120#14519692—24no—
121#14519691—24no—
122#14519691—24no—
123#14519691—42no—
124#14519691—42no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130C22×D4×C61C2311yescharacteristic
131C23×C4×C61C2×C411yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C4×D4×C61—22no—
134C4×D4×C61—22no—
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2312yes—
140C2×C22⋊C4×C61C2311yescharacteristic
141C2×C42×C61C2×C411yescharacteristic
142#99×C61—42no—
143#95×C61—22no—
144C24×C61C22×C411yescharacteristic
145C24×C61C2411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—81no—
157C22×C4×C61—81no—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D412yes—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—21no—
170C2×C22⋊D61—21no—
171C2×C22⋊D61—21no—
172C2×C22⋊D61—21no—
173C2×C22⋊D61—21no—
174C2×C22⋊D61—21no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—81no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—42no—
181C22×Dic61—81no—
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C2×D412yes—
189C22×Dic61C2×D412yes—
190C22×Dic61C2×D412yes—
191C22×Dic61C2×D412yes—
192C2×D244—22no—
193C2×D244—81no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—42no—
199C2×C4×D61—81no—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—82no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C42×C61—21no—
209C42×C61—21no—
210C22⋊Dic61—22no—
211C22⋊Dic61—21no—
212C22⋊Dic61—21no—
213C22⋊Dic61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61—22no—
216C22⋊Dic61#4114yes—
217#11758198—21no—
218#11758198—21no—
219#11758198—21no—
220#11758198—21no—
221#11758198—21no—
222#11758198—21no—
223#11758198—22no—
224#11758198—22no—
225#11758198—22no—
226C4⋊Dic61—22no—
227#11758196—21no—
228#11758196—21no—
229#11758196—22no—
230#11758196—22no—
231#11758196—22no—
232#11758196—44no—
233#11758196—82no—
234#11758196C22⋊C411yescharacteristic
235#11758196C22⋊C411yescharacteristic
236#11758196C22⋊C411yescharacteristic
237#11758196C22⋊C411yescharacteristic
238#11758196C22⋊C412yes—
239#11758196C22⋊C412yes—
240#11758196C22⋊C412yes—
241#11758196C22⋊C412yes—
242#11758196C22⋊C412yes—
243#11758196C22⋊C412yes—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61—44no—
249C4×Dic61—82no—
250C4×Dic61—82no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C23×C411yescharacteristic
259C23×C61C22×D412yes—
260C23×C61C2×#4112yes—
261C23×C61H(5,𝔽2)11yescharacteristic
262C23×C612−1+411yescharacteristic
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273D4×C61—42no—
274D4×C61—42no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—81no—
293C2×C4×C61—81no—
294C2×C4×C61C2×C22⋊C412yes—
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C22⋊D61—42no—
298C22⋊D61—42no—
299C22⋊D61—42no—
300C22⋊D61—42no—
301C22⋊D61—42no—
302C22⋊D61—42no—
303C22⋊D61—82no—
304C2×Dic61—24no—
305C2×Dic61—22no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—24no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—42no—
318C2×Dic61—41no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61C2×C22⋊C411yescharacteristic
325C2×Dic61C2×C22⋊C411yescharacteristic
326C2×Dic61C2×C22⋊C411yescharacteristic
327C2×Dic61C2×C22⋊C412yes—
328C2×Dic61C2×C22⋊C412yes—
329C2×Dic61C2×C22⋊C411yescharacteristic
330D244—82no—
331C4×D61—42no—
332C4×D61—42no—
333C4×D61—81no—
334C4×D61—81no—
335#22535—611nomaximal, Sylow
336C22×C61—22no—
337C22×C61—21no—
338C22×C61—22no—
339C22×C61—21no—
340C22×C61—42no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61C22×C22⋊C411yescharacteristic
349C22×C61C4×#4111yescharacteristic
350C22×C61#52011yescharacteristic
351C22×C61#54812yes—
352C22×C61#55012yes—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—81no—
363C4×C61—22no—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—82no—
370C4×C61—82no—
371Dic61—21no—
372Dic61—22no—
373Dic61—21no—
374Dic61—21no—
375Dic61—22no—
376Dic61—44no—
377Dic61—41no—
378Dic61—41no—
379Dic61—82no—
380Dic61#41012yes—
381C2×#553—611no—
382#2345—612no—
383#1964—612no—
384#1964—612no—
385#1964—612no—
386#1799—611no—
387#1799—611no—
388#1799D6111yescharacteristic, complemented
389C4×#99—611no—
390C4×#99—611no—
391C4×#99—611no—
392C2×C61—22no—
393C2×C61—22no—
394C2×C61—21no—
395C2×C61—21no—
396C2×C61—81no—
397C2×C61#234111yescharacteristic
398C2×C61C2×#41011yescharacteristic
399C2×C61#288311yescharacteristic
400D61—81no—
401D61—81no—
402#553—1222no—
403#553—1222no—
404#553—1222no—
405#553—1222no—
406C2×#126—611no—
407C2×#126—611no—
408C2×#125—611no—
409C2×#123—611no—
410C2×#123—611no—
411C2×#121—611no—
412C2×#121—611no—
413C2×#121—611no—
414C2×#121—611no—
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×C4×D4C2×D6111yescharacteristic
419C2×#117—611no—
420C22×C4⋊C4—611no—
421C2×#99—612no—
422C2×#99—612no—
423C2×#99—612no—
424C2×#99—612no—
425C2×#99—612no—
426C2×#99C2×D6112yes—
427#389—1222no—
428#387—1222no—
429#387—1222no—
430#380—612no—
431#380—612no—
432#380C2×D6112yes—
433C4×C4⋊C4—1222no—
434C4×C22⋊C4—612no—
435C4×C22⋊C4—612no—
436C4×C22⋊C4—612no—
437#342—611no—
438#342—611no—
439#342C2×D6111yescharacteristic
440#342C2×D6111yescharacteristic
441C61#2253511yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—611no—
444C22×D4—611no—
445C22×D4—611no—
446C22×D4—611no—
447C22×D4C22×D6111yescharacteristic
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4C4×D6111yescharacteristic
453C23×C4C22×D6111yescharacteristic
454#126—1222no—
455#126—1222no—
456#126—1222no—
457#126—1222no—
458#125—1222no—
459#125—1222no—
460#123—1222no—
461#123—1222no—
462#123—1222no—
463#123—1222no—
464#121—1222no—
465#121—1222no—
466#121—1222no—
467#121—1222no—
468#121—1222no—
469#121—1222no—
470#121—1222no—
471#121—1222no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—1222no—
475C4×D4—1222no—
476C4×D4—1222no—
477C4×D4—1222no—
478C4×D4—1221no—
479C4×D4—1221no—
480C4×D4—1221no—
481C4×D4—1221no—
482#117—1221no—
483#117—1221no—
484#117—1221no—
485#117—1221no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—612no—
492C2×C4⋊C4—612no—
493C2×C4⋊C4—612no—
494C2×C4⋊C4—612no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4—1222no—
502C2×C4⋊C4C4×D6111yescharacteristic
503C2×C22⋊C4—612no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4—612no—
513C2×C22⋊C4C4×D6111yescharacteristic
514C2×C22⋊C4C22×D6112yes—
515C2×C22⋊C4C22×D6112yes—
516C2×C22⋊C4C22×D6111yescharacteristic
517C2×C42—611no—
518C2×C42—611no—
519C2×C42—1222no—
520C2×C42—1222no—
521C2×C42—1222no—
522C2×C42C4×D6111yescharacteristic
523#99—42no—
524#99—1224no—
525#99—1224no—
526#99—1224no—
527#99—2442no—
528#99—2442no—
529#95—22no—
530#95—1222no—
531#95—1222no—
532#95—1222no—
533#95—1222no—
534#95—1222no—
535C24—611no—
536C24—611no—
537C24C2×C4×D6111yescharacteristic
538C24C23×D6111yescharacteristic
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—1222no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1222no—
547C2×D4—1222no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1222no—
555C2×D4—4881no—
556C2×D4—4881no—
557C2×D4—2442no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—611no—
565C22×C4—612no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—4881no—
581C22×C4—4881no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4C2×C4×D6111yescharacteristic
585C22×C4C2×C4×D6111yescharacteristic
586C22×C4C2×C4×D6111yescharacteristic
587C22×C4C2×C4×D6111yescharacteristic
588C22×C4C2×C4×D6111yescharacteristic
589C22×C4D4×D6112yes—
590C22×C4D4×D6112yes—
591C4⋊C4—22no—
592C4⋊C4—82no—
593C4⋊C4—611no—
594C4⋊C4—611no—
595C4⋊C4—611no—
596C4⋊C4—611no—
597C4⋊C4—612no—
598C4⋊C4—612no—
599C4⋊C4—612no—
600C4⋊C4—612no—
601C4⋊C4—612no—
602C4⋊C4—612no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1222no—
606C4⋊C4—1222no—
607C4⋊C4—1222no—
608C4⋊C4—1222no—
609C4⋊C4—4882no—
610C4⋊C4—2444no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—614no—
618C22⋊C4—1221no—
619C22⋊C4—1221no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1221no—
624C22⋊C4—1221no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1221no—
628C22⋊C4—1221no—
629C22⋊C4—1221no—
630C22⋊C4—1221no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C42—21no—
634C42—21no—
635C42—1221no—
636C42—1221no—
637C42—1221no—
638C42—1221no—
639C42—4882no—
640C42—4882no—
641C42—2444no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23C22×C4×D6111yescharacteristic
660C23C2×D4×D6112yes—
661C23#41×D6112yes—
662C23#1451982211yescharacteristic
663C23#1451982511yescharacteristic
664D4—42no—
665D4—42no—
666D4—4882no—
667D4—4882no—
668D4—2442no—
669D4—2442no—
670D4—2442no—
671D4—2442no—
672D4—2442no—
673D4—2442no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—611no—
694C2×C4—611no—
695C2×C4—611no—
696C2×C4—611no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—1224no—
700C2×C4—1222no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1224no—
708C2×C4—4881no—
709C2×C4—4881no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4C22⋊C4×D6111yescharacteristic
724C2×C4C22⋊C4×D6111yescharacteristic
725C2×C4C22⋊C4×D6112yes—
726C22—22no—
727C22—21no—
728C22—22no—
729C22—21no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—81no—
737C22—81no—
738C22—4881no—
739C22—4881no—
740C22—4881no—
741C22—4881no—
742C22—2441no—
743C22—2441no—
744C22—2441no—
745C22—2441no—
746C22—2441no—
747C22—2441no—
748C22C2×C22⋊C4×D6111yescharacteristic
749C22#1684023011yescharacteristic
750C22#1684024311yescharacteristic
751C22#1684042212yes—
752C22#1684043012yes—
753C4—21no—
754C4—21no—
755C4—22no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—82no—
760C4—82no—
761C4—612no—
762C4—1222no—
763C4—1221no—
764C4—1221no—
765C4—1221no—
766C4—1222no—
767C4—4882no—
768C4—2444no—
769C4—2441no—
770C4—2441no—
771C2—22no—
772C2—22no—
773C2—21no—
774C2—21no—
775C2—81no—
776C2—4881no—
777C2—4881no—
778C2#2144865611yescharacteristic
779C2#410×D6111yescharacteristic
780C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1799C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840461C2
cosocleC24×C61C24
hypercenter#1799D61
hypocenterC61#22535
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21448691C2semidirect
3. #21446654C2semidirect
4. #21446653C2semidirect
5. #21446653C2semidirect
6. #21445806C2semidirect
7. #21445806C2semidirect
8. C4×#14519692C2semidirect
9. #21445606C2semidirect
10. #21445606C2semidirect
11. C61×#1799C2semidirect
16. C2×#14519771C4semidirect
17. C2×#14519770C4semidirect
18. C2×#14519767C4semidirect
19. C2×#14519762C4semidirect
20. C2×#14519760C4semidirect
22. C2×#14519750C4semidirect
25. C2×C4×C22⋊D61C4semidirect
28. C2×#14519734C4semidirect
388. #1799D61semidirect
441. C61#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#168404612
#214486912
#214466542
#214466532
#214458062
C4×#145196922
#214456062
C61×#17992
#2253561