Finite Group Databasebeta

← #29840865

Subgroups — #29840865

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×#16840294C211yesmaximal, characteristic
2#21448946C214yesmaximal, complemented
3#21448862C212yesmaximal
4#21448848C212yesmaximal, complemented
5#21448774C211yesmaximal, characteristic, complemented
6#21448769C212yesmaximal, complemented
7#21448750C212yesmaximal, complemented
8#21448731C211yesmaximal, characteristic, complemented
9D4×C4⋊Dic61C211yesmaximal, characteristic, complemented
10#21448616C214yesmaximal, complemented
11#21448426C212yesmaximal, complemented
12C4×#14519768C212yesmaximal, complemented
13#21448366C212yesmaximal, complemented
14#21448224C211yesmaximal, characteristic, complemented
15#21448175C212yesmaximal, complemented
16C4×#14519735C211yesmaximal, characteristic, complemented
17C61×#2354C211yesmaximal, characteristic, complemented
18#16840294C4116yescomplemented
19C2×#14519770C2212yes—
20C2×#14519768C2211yescharacteristic
21C2×#14519764C2211yescharacteristic
22C2×#14519759C2212yes—
23C2×#14519757C2211yescharacteristic
24C2×#14519748C2211yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519742C2212yes—
27C2×D4×Dic61C2212yes—
28C2×C4×C22⋊D61C2212yes—
29C2×#14519736C2212yes—
30C2×#14519735C2211yescharacteristic
31C2×#14519735C2211yescharacteristic
32C2×#14519735C2212yes—
33C22×C4⋊Dic61C2212yes—
34C2×C42×D61C2211yescharacteristic
35#16839668C2212yes—
36#16839662C2214yes—
37#16839661C2212yes—
38#16839658C2212yes—
39#16839657C2214yes—
40#16839656C2214yes—
41#16839654C2214yes—
42#16839653C2214yes—
43#16839650C2214yes—
44#16839650C2214yes—
45#16839649C2214yes—
46#16839649C2214yes—
47#16839647C2214yes—
48#16839645C2214yes—
49#16839639C2214yes—
50#16839637C2214yes—
51#16839632C2211yescharacteristic
52#16839631C2212yes—
53#16839627C2212yes—
54#16839627C2212yes—
55#16839622C2212yes—
56#16839619C2212yes—
57#16839619C2212yes—
58C4⋊C4×Dic61C2212yes—
59C4⋊C4×Dic61C2212yes—
60C4⋊C4×Dic61C2212yes—
61C4⋊C4×Dic61C2212yes—
62C4⋊C4×Dic61C2211yescharacteristic
63C4⋊C4×Dic61C2211yescharacteristic
64C4×#11758196C2214yes—
65C4×C4⋊Dic61C2211yescharacteristic
66C4×C4⋊Dic61C2212yes—
67C4×C4⋊Dic61C2214yes—
68C4×C4⋊Dic61C2214yes—
69C22⋊C4×Dic61C2214yes—
70C22⋊C4×Dic61C2214yes—
71C22⋊C4×Dic61C2214yes—
72C4×#11758198C2212yes—
73#16839609C2212yes—
74#16839607C2212yes—
75C42×Dic61C2212yes—
76C2×C4×D4×C61C2211yescharacteristic
77C2×#117×C61C2212yes—
78C61×#390C2212yes—
79C61×#388C2214yes—
80C61×#384C2211yescharacteristic
81C61×#380C2212yes—
82C4×C4⋊C4×C61C2211yescharacteristic
83C4×C4⋊C4×C61C2212yes—
84C22×Dic122C2311yescharacteristic
85C22×C22⋊D61C2312yes—
86C23×Dic61C2314yes—
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2311yescharacteristic
90#14519770C2×C4116yescomplemented
91#14519768C2×C418yescomplemented
92#14519764C2×C418yes—
93#14519759C2×C4116yescomplemented
94#14519757C2×C418yescomplemented
95#14519748C2×C418yes—
96C4×Dic122C2×C418yescomplemented
97#14519742—44no—
98D4×Dic61—44no—
99C4×C22⋊D61C2×C4116yescomplemented
100#14519736C2×C4116yescomplemented
101#14519735—24no—
102#14519735—24no—
103#14519735—44no—
104C2×C4⋊Dic61—28no—
105C2×C4⋊Dic61C2314yes—
106C2×C4⋊Dic61C2312yes—
107C2×C4⋊Dic61C2312yes—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2312yes—
110C2×C4⋊Dic61C2312yes—
111C2×C4⋊Dic61C2312yes—
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×#11758196C2314yes—
115C2×#11758196C2314yes—
116C2×#11758196C2312yes—
117C2×#11758196C2312yes—
118C2×C22⋊Dic61C2314yes—
119C2×C22⋊Dic61C2312yes—
120C2×C22⋊Dic61C2312yes—
121C2×C22⋊Dic61C2312yes—
122C2×#11758198C2312yes—
123C2×#11758198C2312yes—
124C2×#11758198C2314yes—
125C2×#11758198C2312yes—
126C2×C4×Dic61C2312yes—
127C2×C4×Dic61C2312yes—
128C2×C4×Dic61C2312yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131C2×C4×Dic61C2312yes—
132C2×C4×Dic61C2312yes—
133C2×C4×Dic61C2314yes—
134C2×C4×Dic61C2311yescharacteristic
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2311yescharacteristic
137C2×C4×Dic61C2312yes—
138C42×D61C2×C418yescomplemented
139#14519684C2312yes—
140#14519684C2312yes—
141#14519684C2312yes—
142#14519684C2314yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146#14519684C2314yes—
147#14519684C2314yes—
148#14519684C2314yes—
149C22×D4×C61C2311yescharacteristic
150C23×C4×C61C2312yes—
151C4×D4×C61C2×C418yes—
152#117×C61—28no—
153C2×C4⋊C4×C61C2312yes—
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2312yes—
156C2×C4⋊C4×C61C2312yes—
157C2×C4⋊C4×C61C2311yescharacteristic
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C22⋊C4×C61C2314yes—
160C2×C22⋊C4×C61C2314yes—
161C2×C22⋊C4×C61C2312yes—
162C2×C42×C61C2312yes—
163C2×C42×C61C2314yes—
164C2×C42×C61C2311yescharacteristic
165#95×C61C2314yes—
166#95×C61C2312yes—
167C24×C61C2412yes—
168C23×D61C2411yescharacteristic
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61C22×C414yes—
172C22×C4×C61—24no—
173C22×C4×C61—24no—
174C22×C4×C61C22×C418yes—
175C22×C4×C61C2412yes—
176C22×C4×C61C2414yes—
177C22×C4×C61C2411yescharacteristic
178C22×C4×C61C2412yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2411yescharacteristic
181C22×C4×C61C2411yescharacteristic
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61C22×C418yes—
185C22×Dic61—28no—
186C22×Dic61—44no—
187C22×Dic61—44no—
188C22×Dic61C2414yes—
189C22×Dic61C2412yes—
190C22×Dic61C2411yescharacteristic
191C22×Dic61C2411yescharacteristic
192C22×Dic61C2411yescharacteristic
193C22×Dic61C2412yes—
194C22×Dic61C2412yes—
195C22×Dic61C2412yes—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—41no—
201C2×C4×D61—41no—
202C2×C4×D61C22×C414yes—
203C2×C4×D61C22×C414yes—
204C2×C4×D61C22×C414yes—
205C2×Dic122—22no—
206C2×Dic122—22no—
207C2×Dic122C22×C414yes—
208C4⋊C4×C61—24no—
209C4⋊C4×C61—22no—
210C4⋊C4×C61—24no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61C22×C414yes—
213C4⋊C4×C61#4114yes—
214C22⋊C4×C61—28no—
215C22⋊C4×C61—44no—
216C22⋊C4×C61C22×C418yes—
217C42×C61—28no—
218C42×C61—24no—
219C42×C61C22×C414yes—
220C22⋊Dic61—44no—
221C22⋊Dic61C22×C418yes—
222C22⋊Dic61C22×C418yes—
223C22⋊Dic61C22×C418yes—
224#11758198—24no—
225#11758198—24no—
226#11758198—44no—
227#11758198C22×C418yes—
228C4⋊Dic61—24no—
229C4⋊Dic61—22no—
230C4⋊Dic61—24no—
231C4⋊Dic61—28no—
232C4⋊Dic61—42no—
233C4⋊Dic61C22×C418yes—
234C4⋊Dic61C22×C418yes—
235C4⋊Dic61C22×C414yes—
236C4⋊Dic61#4114yes—
237#11758196—44no—
238#11758196—44no—
239#11758196C22×C418yes—
240#11758196C22×C418yes—
241C4×Dic61—24no—
242C4×Dic61—24no—
243C4×Dic61—24no—
244C4×Dic61—42no—
245C4×Dic61—42no—
246C4×Dic61—44no—
247C4×Dic61—44no—
248C4×Dic61—44no—
249C4×Dic61C22×C414yes—
250C4×Dic61C22×C414yes—
251C4×Dic61C22×C414yes—
252C4×Dic61C22×C418yes—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61C23×C414yes—
260C23×C61C2511yescharacteristic
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61C23×C412yes—
268D4×C61—28no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—216no—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—24no—
282C2×C4×C61C23×C412yes—
283C2×C4×C61C23×C414yes—
284C2×C4×C61C23×C412yes—
285C2×C4×C61C23×C412yes—
286C2×C4×C61C2×#4114yes—
287C2×C4×C61C2×#4112yes—
288C2×C4×C61C2×#4112yes—
289C2×C4×C61H(5,𝔽2)12yes—
290C2×C4×C612−1+412yes—
291C22⋊D61—48no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—22no—
295C2×Dic61—21no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—24no—
306C2×Dic61—22no—
307C2×Dic61—24no—
308C2×Dic61—22no—
309C2×Dic61—24no—
310C2×Dic61—88no—
311C2×Dic61C23×C412yes—
312C2×Dic61C23×C412yes—
313C2×Dic61C23×C412yes—
314C2×Dic61C23×C414yes—
315C2×Dic61C23×C414yes—
316C2×Dic61C2×#4114yes—
317C4×D61—28no—
318C4×D61—28no—
319C4×D61—44no—
320Dic122—28no—
321#34242—611nomaximal, Sylow
322C22×C61—24no—
323C22×C61—24no—
324C22×C61—24no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
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—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C4×C61—24no—
344C4×C61—22no—
345C4×C61—24no—
346C4×C61—44no—
347C4×C61—42no—
348C4×C61C4×#4114yes—
349C4×C61#52014yes—
350Dic61—22no—
351Dic61—24no—
352Dic61—22no—
353Dic61—22no—
354Dic61—24no—
355Dic61—24no—
356Dic61—44no—
357Dic61—42no—
358C2×#529—611no—
359#2373—614no—
360#2363—612no—
361#2362—612no—
362#2355—611no—
363#2354—612no—
364#2354D6111yescharacteristic, complemented
365#2352—612no—
366Q8×C4⋊C4—611no—
367D4×C4⋊C4—611no—
368#2335—614no—
369#2314—612no—
370C4×#125—612no—
371C4×#124—612no—
372#2285—611no—
373#2274—612no—
374C4×#117—611no—
375C2×C61—44no—
376C2×C61C2×C4×#4111yescharacteristic
377C2×C61C2×#52011yescharacteristic
378C2×C61#342811yescharacteristic
379C2×C61#351411yescharacteristic
380C2×C61#351511yescharacteristic
381C2×C61#351711yescharacteristic
382C2×C61#351811yescharacteristic
383D61—42no—
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×D4C2×D6111yescharacteristic
396C2×#117—612no—
397C2×#117—611no—
398C2×#117—611no—
399C2×#117—612no—
400C2×#117C2×D6112yes—
401C22×C4⋊C4—612no—
402C22×C42—611no—
403#391—612no—
404#390—614no—
405#390C2×D6112yes—
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#388C2×D6114yes—
415#387—614no—
416#387—614no—
417#387—614no—
418#387—614no—
419#386—614no—
420#385—614no—
421#384—612no—
422#384—611no—
423#384C2×D6111yescharacteristic
424#382—612no—
425#382—612no—
426#380—612no—
427#380—612no—
428#380—612no—
429#380C2×D6112yes—
430C4×C4⋊C4—611no—
431C4×C4⋊C4—612no—
432C4×C4⋊C4—612no—
433C4×C4⋊C4—612no—
434C4×C4⋊C4—612no—
435C4×C4⋊C4—611no—
436C4×C4⋊C4—614no—
437C4×C4⋊C4—614no—
438C4×C4⋊C4—612no—
439C4×C4⋊C4—611no—
440C4×C4⋊C4—614no—
441C4×C4⋊C4C2×D6112yes—
442C4×C4⋊C4C2×D6111yescharacteristic
443C4×C22⋊C4—614no—
444C4×C22⋊C4—614no—
445C4×C22⋊C4—614no—
446C4×C22⋊C4—612no—
447C4×C22⋊C4—612no—
448#376—612no—
449C43—612no—
450C61#3424211yescharacteristic, complemented, Sylow
451C22×Q8—611no—
452C22×D4—612no—
453C22×D4C22×D6111yescharacteristic
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—614no—
458C23×C4C22×D6112yes—
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—2444no—
469C4×D4C4×D6118yes—
470#117—28no—
471#117—6116no—
472#117—1224no—
473#117—1224no—
474#117—2444no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—612no—
477C2×C4⋊C4—612no—
478C2×C4⋊C4—612no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—612no—
481C2×C4⋊C4—612no—
482C2×C4⋊C4—614no—
483C2×C4⋊C4—612no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—614no—
486C2×C4⋊C4—612no—
487C2×C4⋊C4—614no—
488C2×C4⋊C4—1228no—
489C2×C4⋊C4C22×D6112yes—
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6112yes—
492C2×C4⋊C4C22×D6112yes—
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C4⋊C4C22×D6111yescharacteristic
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—614no—
502C2×C22⋊C4—614no—
503C2×C22⋊C4C22×D6114yes—
504C2×C22⋊C4C22×D6114yes—
505C2×C22⋊C4C22×D6112yes—
506C2×C42—611no—
507C2×C42—612no—
508C2×C42—611no—
509C2×C42—611no—
510C2×C42—618no—
511C2×C42—612no—
512C2×C42—612no—
513C2×C42—612no—
514C2×C42—614no—
515C2×C42—614no—
516C2×C42—612no—
517C2×C42—612no—
518C2×C42—614no—
519C2×C42C22×D6114yes—
520C2×C42C22×D6112yes—
521C2×C42C22×D6111yescharacteristic
522#95—612no—
523#95—612no—
524#95—612no—
525#95—614no—
526#95—614no—
527#95—614no—
528#95—614no—
529#95—614no—
530#95—614no—
531#95—614no—
532#95C22×D6112yes—
533#95C22×D6114yes—
534C24—611no—
535C24C23×D6112yes—
536C2×Q8—614no—
537C2×Q8—1222no—
538C2×Q8—1222no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—618no—
542C2×D4—2442no—
543C2×D4—2442no—
544C2×D4C2×C4×D6114yes—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—614no—
554C22×C4—614no—
555C22×C4—614no—
556C22×C4—614no—
557C22×C4—612no—
558C22×C4—1228no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—2441no—
564C22×C4—2441no—
565C22×C4—2444no—
566C22×C4—2444no—
567C22×C4C2×C4×D6118yes—
568C22×C4C23×D6112yes—
569C22×C4C23×D6114yes—
570C22×C4C23×D6111yescharacteristic
571C22×C4C23×D6112yes—
572C22×C4C23×D6112yes—
573C22×C4C23×D6111yescharacteristic
574C22×C4C23×D6111yescharacteristic
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—42no—
579C4⋊C4—618no—
580C4⋊C4—618no—
581C4⋊C4—618no—
582C4⋊C4—618no—
583C4⋊C4—614no—
584C4⋊C4—614no—
585C4⋊C4—1228no—
586C4⋊C4—1224no—
587C4⋊C4—1222no—
588C4⋊C4—1224no—
589C4⋊C4—2444no—
590C4⋊C4—2444no—
591C4⋊C4—2442no—
592C4⋊C4C2×C4×D6114yes—
593C4⋊C4#1175822414yes—
594C22⋊C4—28no—
595C22⋊C4—44no—
596C22⋊C4—618no—
597C22⋊C4—618no—
598C22⋊C4—618no—
599C22⋊C4—618no—
600C22⋊C4—1224no—
601C22⋊C4—1224no—
602C22⋊C4—2444no—
603C22⋊C4—2444no—
604C22⋊C4C2×C4×D6118yes—
605C42—28no—
606C42—24no—
607C42—614no—
608C42—614no—
609C42—614no—
610C42—618no—
611C42—1224no—
612C42—1224no—
613C42—1224no—
614C42—2442no—
615C42—2444no—
616C42—2442no—
617C42—2444no—
618C42—2444no—
619C42C2×C4×D6114yes—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—612no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23C22×C4×D6114yes—
634C23C24×D6111yescharacteristic
635Q8—1228no—
636D4—28no—
637D4—2448no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—216no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—612no—
654C2×C4—614no—
655C2×C4—614no—
656C2×C4—614no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1222no—
660C2×C4—1221no—
661C2×C4—1222no—
662C2×C4—1221no—
663C2×C4—1222no—
664C2×C4—1221no—
665C2×C4—1222no—
666C2×C4—1221no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1228no—
670C2×C4—1228no—
671C2×C4—1224no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1224no—
675C2×C4—1222no—
676C2×C4—1224no—
677C2×C4—4888no—
678C2×C4—2444no—
679C2×C4C22×C4×D6112yes—
680C2×C4C22×C4×D6114yes—
681C2×C4C22×C4×D6112yes—
682C2×C4C22×C4×D6112yes—
683C2×C4#41×D6112yes—
684C2×C4C2×#1175822414yes—
685C2×C4C2×#1175822412yes—
686C2×C4#1451982312yes—
687C2×C4#1451982412yes—
688C22—24no—
689C22—24no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—1222no—
696C22—1222no—
697C22—1222no—
698C22—2441no—
699C22—2441no—
700C22—2441no—
701C22—2441no—
702C22C23×C4×D6111yescharacteristic
703C22C2×#41×D6111yescharacteristic
704C22C22×#1175822411yescharacteristic
705C22C2×#1451982311yescharacteristic
706C22C2×#1451982411yescharacteristic
707C22#1684059711yescharacteristic
708C22#1684059911yescharacteristic
709C4—24no—
710C4—22no—
711C4—24no—
712C4—44no—
713C4—42no—
714C4—1222no—
715C4—1222no—
716C4—1224no—
717C4—1224no—
718C4—1222no—
719C4—1224no—
720C4—2444no—
721C4—2442no—
722C4C4×#1175822414yes—
723C4#1684024214yes—
724C2—44no—
725C2—2442no—
726C2C2×C4×#1175822411yescharacteristic
727C2C2×#1684024211yescharacteristic
728C2#2145901911yescharacteristic
729C2#2145978311yescharacteristic
730C2#2145978811yescharacteristic
731C2#2145982011yescharacteristic
732C2#2145983511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2354C2
socle, cosocleC23×C61C25
prime radicalC2×#14519748C22
hypercenter#2354D61
hypocenterC61#34242
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #21448946C2semidirect
4. #21448848C2semidirect
5. #21448774C2semidirect
6. #21448769C2semidirect
7. #21448750C2semidirect
8. #21448731C2semidirect
9. D4×C4⋊Dic61C2semidirect
10. #21448616C2semidirect
11. #21448426C2semidirect
12. C4×#14519768C2semidirect
13. #21448366C2semidirect
14. #21448224C2semidirect
15. #21448175C2semidirect
16. C4×#14519735C2semidirect
17. C61×#2354C2semidirect
18. #16840294C4semidirect
90. #14519770C2×C4semidirect
91. #14519768C2×C4semidirect
93. #14519759C2×C4semidirect
94. #14519757C2×C4semidirect
96. C4×Dic122C2×C4semidirect
99. C4×C22⋊D61C2×C4semidirect
100. #14519736C2×C4semidirect
138. C42×D61C2×C4semidirect
364. #2354D61semidirect
450. C61#34242semidirect

Maximal subgroups

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

subgroupindex
C2×#168402942
#214489462
#214488622
#214488482
#214487742
#214487692
#214487502
#214487312
D4×C4⋊Dic612
#214486162
#214484262
C4×#145197682
#214483662
#214482242
#214481752
C4×#145197352
C61×#23542
#3424261