Finite Group Databasebeta

← #29840856

Subgroups — #29840856

Order 15616.

2286 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840296C211yesmaximal, characteristic
2#21448935C214yesmaximal, complemented
3#21448857C212yesmaximal
4#21448846C212yesmaximal, complemented
5#21448778C211yesmaximal, characteristic, complemented
6#21448770C211yesmaximal, characteristic, complemented
7#21448763C212yesmaximal, complemented
8#21448741C212yesmaximal, complemented
9#21448731C211yesmaximal, characteristic, complemented
10#21448719C211yesmaximal, characteristic, complemented
11#21448605C214yesmaximal, complemented
12#21448424C212yesmaximal, complemented
13#21448374C212yesmaximal, complemented
14#21448358C212yesmaximal, complemented
15#21448173C212yesmaximal, complemented
16C4×#14519736C211yesmaximal, characteristic, complemented
17C61×#2285C211yesmaximal, characteristic, complemented
18#16840296C4116yescomplemented
19C2×#14519771C2212yes—
20C2×#14519769C2211yescharacteristic
21C2×#14519765C2211yescharacteristic
22C2×#14519760C2212yes—
23C2×#14519756C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519742C2212yes—
27C2×C4×D244C2211yescharacteristic
28C2×#14519739C2212yes—
29C2×C4×C22⋊D61C2212yes—
30C2×#14519736C2211yescharacteristic
31C2×#14519736C2211yescharacteristic
32C2×#14519735C2212yes—
33C2×#14519734C2212yes—
34C2×C4⋊C4×D61C2212yes—
35#16839667C2212yes—
36#16839663C2212yes—
37#16839662C2214yes—
38#16839658C2212yes—
39#16839658C2212yes—
40#16839657C2214yes—
41#16839656C2214yes—
42#16839653C2214yes—
43#16839652C2214yes—
44#16839651C2214yes—
45#16839651C2214yes—
46#16839650C2214yes—
47#16839646C2214yes—
48#16839644C2214yes—
49#16839644C2214yes—
50#16839643C2214yes—
51#16839638C2214yes—
52#16839633C2214yes—
53#16839631C2212yes—
54#16839627C2212yes—
55#16839619C2212yes—
56#16839619C2212yes—
57C4⋊C4×Dic61C2212yes—
58C4⋊C4×Dic61C2212yes—
59C4⋊C4×Dic61C2212yes—
60C4⋊C4×Dic61C2212yes—
61C4×#11758196C2214yes—
62C4×C4⋊Dic61C2211yescharacteristic
63C4×C4⋊Dic61C2211yescharacteristic
64C4×C4⋊Dic61C2211yescharacteristic
65C4×C4⋊Dic61C2211yescharacteristic
66#16839613C2214yes—
67#16839613C2214yes—
68C4×#11758198C2214yes—
69C4×C22⋊Dic61C2212yes—
70C4×C22⋊Dic61C2212yes—
71#16839609C2214yes—
72#16839609C2214yes—
73#16839608C2212yes—
74C42×Dic61C2212yes—
75C2×#117×C61C2212yes—
76C22×C42×C61C2211yescharacteristic
77C61×#384C2211yescharacteristic
78C61×#384C2211yescharacteristic
79C61×#382C2212yes—
80C61×#380C2212yes—
81C61×#380C2212yes—
82C4×C4⋊C4×C61C2212yes—
83C4×C4⋊C4×C61C2212yes—
84C22×Dic122C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C22⋊D61C2312yes—
87C22×C4×D61C2312yes—
88C22×C4×D61C2314yes—
89#14519771C2×C4116yescomplemented
90#14519769C2×C418yescomplemented
91#14519765C2×C418yes—
92#14519760C2×C4116yescomplemented
93#14519756C2×C418yescomplemented
94#14519751C2×C418yes—
95C4×Dic122C2×C418yescomplemented
96#14519742—44no—
97C4×D244C2×C418yes—
98#14519739—44no—
99C4×C22⋊D61C2×C4116yescomplemented
100#14519736—24no—
101#14519736—24no—
102#14519735—28no—
103#14519734C2×C4116yescomplemented
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196C2314yes—
111C2×#11758196C2314yes—
112C2×#11758196C2314yes—
113C2×#11758196C2312yes—
114C2×#11758196C2312yes—
115C2×#11758196C2312yes—
116C2×#11758196C2312yes—
117C4⋊C4×D61—28no—
118C2×C22⋊Dic61C2312yes—
119C2×C22⋊Dic61C2312yes—
120C2×C22⋊Dic61C2312yes—
121C2×#11758198C2314yes—
122C2×#11758198C2314yes—
123C2×#11758198C2314yes—
124C2×#11758198C2312yes—
125C2×#11758198C2312yes—
126C2×#11758198C2312yes—
127C2×#11758198C2312yes—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2312yes—
130C2×C4×Dic61C2312yes—
131C2×C4×Dic61C2312yes—
132C2×C4×Dic61C2312yes—
133C2×C4×Dic61C2314yes—
134C2×C4×Dic61C2312yes—
135C2×C4×Dic61C2312yes—
136C2×C4×Dic61C2314yes—
137C2×C4×Dic61C2312yes—
138#14519684C2312yes—
139#14519684C2312yes—
140#14519684C2312yes—
141#14519684C2312yes—
142#14519684C2314yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146#14519684C2314yes—
147#14519684C2314yes—
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151#117×C61—44no—
152C2×C4⋊C4×C61C2312yes—
153C2×C4⋊C4×C61C2312yes—
154C2×C4⋊C4×C61C2312yes—
155C2×C4⋊C4×C61C2312yes—
156C2×C4⋊C4×C61C2312yes—
157C2×C4⋊C4×C61C2312yes—
158C2×C22⋊C4×C61C2314yes—
159C2×C42×C61C2×C418yescomplemented
160C2×C42×C61C2314yes—
161C2×C42×C61C2311yescharacteristic
162C2×C42×C61C2311yescharacteristic
163C2×C42×C61C2311yescharacteristic
164C2×C42×C61C2311yescharacteristic
165#95×C61C2314yes—
166#95×C61C2314yes—
167C24×C61C2411yescharacteristic
168C23×D61C2412yes—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—41no—
174C22×C4×C61—41no—
175C22×C4×C61C22×C414yes—
176C22×C4×C61C22×C414yes—
177C22×C4×C61C22×C414yes—
178C22×C4×C61C2414yes—
179C22×C4×C61C2414yes—
180C22×C4×C61C2411yescharacteristic
181C22×C4×C61C2411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C22×C4×C61C2411yescharacteristic
184C22×C4×C61C2411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—42no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61C22×C418yes—
189C22×Dic61C2412yes—
190C22×Dic61C2412yes—
191C22×Dic61C2412yes—
192C22×Dic61C2412yes—
193C22×Dic61C2412yes—
194C22×Dic61C2412yes—
195C22×Dic61C2412yes—
196C2×D244—22no—
197C2×D244—22no—
198C2×D244C22×C414yes—
199C2×C4×D61—24no—
200C2×C4×D61—24no—
201C2×C4×D61—28no—
202C2×C4×D61—44no—
203C2×C4×D61—44no—
204C2×C4×D61C22×C418yes—
205C2×Dic122—22no—
206C2×Dic122—22no—
207C2×Dic122C22×C414yes—
208C4⋊C4×C61—24no—
209C4⋊C4×C61—24no—
210C4⋊C4×C61—24no—
211C4⋊C4×C61—24no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—42no—
214C22⋊C4×C61—44no—
215C42×C61—44no—
216C42×C61C22×C414yes—
217C42×C61C22×C414yes—
218C42×C61C22×C414yes—
219C42×C61C22×C414yes—
220C22⋊Dic61—24no—
221C22⋊Dic61—24no—
222C22⋊Dic61C22×C418yes—
223#11758198—28no—
224#11758198—44no—
225#11758198—44no—
226#11758198C22×C418yes—
227#11758198C22×C418yes—
228#11758198C22×C418yes—
229#11758198C22×C418yes—
230C4⋊Dic61—22no—
231C4⋊Dic61—22no—
232C4⋊Dic61C22×C414yes—
233C4⋊Dic61C22×C414yes—
234C4⋊Dic61#4114yes—
235C4⋊Dic61#4114yes—
236#11758196—28no—
237#11758196—44no—
238#11758196—44no—
239#11758196C22×C418yes—
240#11758196C22×C418yes—
241#11758196C22×C418yes—
242#11758196C22×C418yes—
243C4×Dic61—24no—
244C4×Dic61—24no—
245C4×Dic61—28no—
246C4×Dic61—24no—
247C4×Dic61—24no—
248C4×Dic61—44no—
249C4×Dic61—42no—
250C4×Dic61—42no—
251C4×Dic61—44no—
252C4×Dic61C22×C418yes—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61C23×C412yes—
260C23×C61C2511yescharacteristic
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61C23×C414yes—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—28no—
277C2×C4×C61—28no—
278C2×C4×C61—24no—
279C2×C4×C61—24no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—44no—
285C2×C4×C61C23×C412yes—
286C2×C4×C61C23×C412yes—
287C2×C4×C61C23×C412yes—
288C2×C4×C61C23×C412yes—
289C2×C4×C61C23×C412yes—
290C2×C4×C61C23×C412yes—
291C2×C4×C61C2×#4112yes—
292C2×C4×C61C2×#4112yes—
293C2×C4×C61H(5,𝔽2)12yes—
294C2×C4×C612−1+412yes—
295C22⋊D61—48no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61C23×C414yes—
313C2×Dic61C23×C414yes—
314C2×Dic61C23×C414yes—
315C2×Dic61C2×#4114yes—
316C2×Dic61C2×#4114yes—
317D244—28no—
318C4×D61—216no—
319C4×D61—88no—
320Dic122—28no—
321#34242—611nomaximal, Sylow
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61C24×C411yescharacteristic
330C22×C61C22×#4111yescharacteristic
331C22×C61C22×#4111yescharacteristic
332C22×C61C2×H(5,𝔽2)11yescharacteristic
333C22×C61C2×2−1+411yescharacteristic
334C22×C61#58511yescharacteristic
335C22×C61#58511yescharacteristic
336C2×D61—24no—
337C2×D61—24no—
338C2×D61—24no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—44no—
348C4×C61—44no—
349C4×C61C4×#4114yes—
350C4×C61#52014yes—
351Dic61—24no—
352Dic61—24no—
353Dic61—24no—
354Dic61—24no—
355Dic61—24no—
356Dic61—42no—
357Dic61—42no—
358C2×#529—611no—
359#2373—614no—
360#2363—612no—
361#2362—612no—
362#2355—611no—
363#2354—611no—
364#2354—612no—
365#2352—612no—
366Q8×C4⋊C4—611no—
367D4×C4⋊C4—611no—
368#2335—614no—
369#2314—612no—
370C4×#125—612no—
371C4×#124—612no—
372#2285D6111yescharacteristic, complemented
373#2274—612no—
374C4×#117—611no—
375C2×C61—42no—
376C2×C61C2×C4×#4111yescharacteristic
377C2×C61C2×#52011yescharacteristic
378C2×C61#342811yescharacteristic
379C2×C61#351411yescharacteristic
380C2×C61#351511yescharacteristic
381C2×C61#351711yescharacteristic
382C2×C61#351811yescharacteristic
383D61—44no—
384#529—6116no—
385C2×#126—612no—
386C2×#125—611no—
387C2×#124—611no—
388C2×#123—612no—
389C2×C22⋊Q8—611no—
390C2×#121—611no—
391C2×C4×Q8—612no—
392C2×C4×Q8—611no—
393C2×C4×D4—612no—
394C2×C4×D4—612no—
395C2×C4×D4—611no—
396C2×#117—611no—
397C2×#117—611no—
398C2×#117—612no—
399C2×#117—612no—
400C2×#117C2×D6112yes—
401C22×C4⋊C4—612no—
402C22×C42C2×D6111yescharacteristic
403#391—612no—
404#390—612no—
405#390—614no—
406#389—612no—
407#389—612no—
408#389—614no—
409#388—614no—
410#388—614no—
411#388—614no—
412#388—614no—
413#388—614no—
414#388—614no—
415#387—614no—
416#387—614no—
417#387—614no—
418#387—614no—
419#386—614no—
420#385—614no—
421#384—612no—
422#384C2×D6111yescharacteristic
423#384C2×D6111yescharacteristic
424#382—612no—
425#382C2×D6112yes—
426#380—612no—
427#380—612no—
428#380C2×D6112yes—
429#380C2×D6112yes—
430C4×C4⋊C4—612no—
431C4×C4⋊C4—612no—
432C4×C4⋊C4—612no—
433C4×C4⋊C4—612no—
434C4×C4⋊C4—611no—
435C4×C4⋊C4—611no—
436C4×C4⋊C4—611no—
437C4×C4⋊C4—614no—
438C4×C4⋊C4—611no—
439C4×C4⋊C4—614no—
440C4×C4⋊C4—614no—
441C4×C4⋊C4C2×D6112yes—
442C4×C4⋊C4C2×D6112yes—
443C4×C22⋊C4—612no—
444C4×C22⋊C4—612no—
445C4×C22⋊C4—614no—
446C4×C22⋊C4—614no—
447C4×C22⋊C4—614no—
448#376—612no—
449C43—612no—
450C61#3424211yescharacteristic, complemented, Sylow
451C22×Q8—611no—
452C22×D4—612no—
453C22×D4—611no—
454C23×C4—612no—
455C23×C4—614no—
456C23×C4C22×D6111yescharacteristic
457C23×C4C22×D6111yescharacteristic
458C23×C4C22×D6111yescharacteristic
459#126—6116no—
460#125—618no—
461#124—618no—
462#123—6116no—
463C22⋊Q8—618no—
464#121—618no—
465C4×Q8—618no—
466C4×Q8—2444no—
467C4×D4—6116no—
468C4×D4—618no—
469C4×D4—2444no—
470#117—44no—
471#117—6116no—
472#117—1228no—
473#117—1224no—
474#117—1224no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—612no—
478C2×C4⋊C4—612no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—612no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—612no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—614no—
487C2×C4⋊C4—614no—
488C2×C4⋊C4—1228no—
489C2×C4⋊C4C22×D6112yes—
490C2×C4⋊C4C22×D6112yes—
491C2×C4⋊C4C22×D6112yes—
492C2×C4⋊C4C22×D6112yes—
493C2×C4⋊C4C22×D6112yes—
494C2×C4⋊C4C22×D6112yes—
495C2×C22⋊C4—612no—
496C2×C22⋊C4—612no—
497C2×C22⋊C4—612no—
498C2×C22⋊C4—612no—
499C2×C22⋊C4—612no—
500C2×C22⋊C4—612no—
501C2×C22⋊C4—612no—
502C2×C22⋊C4—614no—
503C2×C22⋊C4—614no—
504C2×C22⋊C4—614no—
505C2×C22⋊C4C22×D6114yes—
506C2×C42—612no—
507C2×C42—612no—
508C2×C42—612no—
509C2×C42—614no—
510C2×C42—612no—
511C2×C42—612no—
512C2×C42—614no—
513C2×C42—612no—
514C2×C42—612no—
515C2×C42—614no—
516C2×C42C4×D6118yescomplemented
517C2×C42C22×D6114yes—
518C2×C42C22×D6111yescharacteristic
519C2×C42C22×D6111yescharacteristic
520C2×C42C22×D6111yescharacteristic
521C2×C42C22×D6111yescharacteristic
522#95—612no—
523#95—612no—
524#95—612no—
525#95—612no—
526#95—614no—
527#95—614no—
528#95—614no—
529#95—614no—
530#95—614no—
531#95—614no—
532#95C22×D6114yes—
533#95C22×D6114yes—
534C24—612no—
535C24C23×D6111yescharacteristic
536C2×Q8—614no—
537C2×Q8—1222no—
538C2×Q8—1222no—
539C2×D4—618no—
540C2×D4—614no—
541C2×D4—1222no—
542C2×D4—1222no—
543C2×D4—2442no—
544C2×D4—2442no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—618no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—1228no—
560C22×C4—1224no—
561C22×C4—1224no—
562C22×C4—2444no—
563C22×C4—2444no—
564C22×C4C2×C4×D6114yes—
565C22×C4C2×C4×D6114yes—
566C22×C4C2×C4×D6114yes—
567C22×C4C23×D6114yes—
568C22×C4C23×D6114yes—
569C22×C4C23×D6111yescharacteristic
570C22×C4C23×D6111yescharacteristic
571C22×C4C23×D6111yescharacteristic
572C22×C4C23×D6111yescharacteristic
573C22×C4C23×D6111yescharacteristic
574C22×C4C23×D6111yescharacteristic
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—618no—
582C4⋊C4—618no—
583C4⋊C4—618no—
584C4⋊C4—618no—
585C4⋊C4—614no—
586C4⋊C4—614no—
587C4⋊C4—614no—
588C4⋊C4—614no—
589C4⋊C4—1228no—
590C4⋊C4—1222no—
591C4⋊C4—1222no—
592C4⋊C4—2444no—
593C4⋊C4—2444no—
594C22⋊C4—44no—
595C22⋊C4—618no—
596C22⋊C4—618no—
597C22⋊C4—618no—
598C22⋊C4—618no—
599C22⋊C4—618no—
600C22⋊C4—1228no—
601C22⋊C4—1224no—
602C22⋊C4—1224no—
603C22⋊C4—2444no—
604C22⋊C4—2444no—
605C42—44no—
606C42—618no—
607C42—1224no—
608C42—1224no—
609C42—1228no—
610C42—1224no—
611C42—1224no—
612C42—2442no—
613C42—2442no—
614C42—2444no—
615C42—2444no—
616C42C2×C4×D6114yes—
617C42C2×C4×D6114yes—
618C42C2×C4×D6114yes—
619C42C2×C4×D6114yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—614no—
627C23—1222no—
628C23—1222no—
629C23—1222no—
630C23—1222no—
631C23—1222no—
632C23—1222no—
633C23C22×C4×D6112yes—
634C23C24×D6111yescharacteristic
635Q8—1228no—
636D4—1228no—
637D4—2448no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—44no—
655C2×C4—614no—
656C2×C4—614no—
657C2×C4—614no—
658C2×C4—614no—
659C2×C4—614no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—12216no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—4888no—
678C2×C4C22×C4×D6112yes—
679C2×C4C22×C4×D6112yes—
680C2×C4C22×C4×D6112yes—
681C2×C4C22×C4×D6112yes—
682C2×C4C22×C4×D6112yes—
683C2×C4C22×C4×D6112yes—
684C2×C4#41×D6112yes—
685C2×C4#41×D6112yes—
686C2×C4#1451982212yes—
687C2×C4#1451982512yes—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—1224no—
696C22—1224no—
697C22—1224no—
698C22—2442no—
699C22—2442no—
700C22—2442no—
701C22—2442no—
702C22C23×C4×D6111yescharacteristic
703C22C2×#41×D6111yescharacteristic
704C22C2×#41×D6111yescharacteristic
705C22C2×#1451982211yescharacteristic
706C22C2×#1451982511yescharacteristic
707C22#1684059811yescharacteristic
708C22#1684059811yescharacteristic
709C4—22no—
710C4—22no—
711C4—22no—
712C4—22no—
713C4—44no—
714C4—44no—
715C4—1224no—
716C4—1224no—
717C4—1224no—
718C4—1224no—
719C4—1224no—
720C4—2442no—
721C4—2442no—
722C4#1684023014yes—
723C4#1684024314yes—
724C2—42no—
725C2—2444no—
726C2C2×#1684023011yescharacteristic
727C2C2×#1684024311yescharacteristic
728C2#2145902011yescharacteristic
729C2#2145977511yescharacteristic
730C2#2145979211yescharacteristic
731C2#2145981711yescharacteristic
732C2#2145982811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2285C2
socle, cosocleC23×C61C25
prime radicalC2×#14519751C22
hypercenter#2285D61
hypocenterC61#34242
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #21448935C2semidirect
4. #21448846C2semidirect
5. #21448778C2semidirect
6. #21448770C2semidirect
7. #21448763C2semidirect
8. #21448741C2semidirect
9. #21448731C2semidirect
10. #21448719C2semidirect
11. #21448605C2semidirect
12. #21448424C2semidirect
13. #21448374C2semidirect
14. #21448358C2semidirect
15. #21448173C2semidirect
16. C4×#14519736C2semidirect
17. C61×#2285C2semidirect
18. #16840296C4semidirect
89. #14519771C2×C4semidirect
90. #14519769C2×C4semidirect
92. #14519760C2×C4semidirect
93. #14519756C2×C4semidirect
95. C4×Dic122C2×C4semidirect
99. C4×C22⋊D61C2×C4semidirect
103. #14519734C2×C4semidirect
159. C2×C42×C61C2×C4semidirect
372. #2285D61semidirect
450. C61#34242semidirect
516. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402962
#214489352
#214488572
#214488462
#214487782
#214487702
#214487632
#214487412
#214487312
#214487192
#214486052
#214484242
#214483742
#214483582
#214481732
C4×#145197362
C61×#22852
#3424261