Finite Group Databasebeta

← #29843047

Subgroups — #29843047

Order 15616.

2318 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840294C211yesmaximal, characteristic
2#21449006C214yesmaximal, complemented
3#21448840C212yesmaximal
4#21448826C212yesmaximal, complemented
5#21448774C211yesmaximal, characteristic, complemented
6#21448749C212yesmaximal, complemented
7#21448731C211yesmaximal, characteristic, complemented
8D4×C4⋊Dic61C211yesmaximal, characteristic, complemented
9#21448715C212yesmaximal, complemented
10#21448556C212yesmaximal, complemented
11#21448529C212yesmaximal, complemented
12#21448489C214yesmaximal, complemented
13#21448439C212yesmaximal, complemented
14#21448426C212yesmaximal, complemented
15#384×D61C211yesmaximal, characteristic, complemented
16#21448215C211yesmaximal, 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×#14519737C2214yes—
30C2×#14519736C2212yes—
31C22×C4⋊Dic61C2212yes—
32C2×C4⋊C4×D61C2212yes—
33C2×C4⋊C4×D61C2212yes—
34C2×C4⋊C4×D61C2212yes—
35C2×C42×D61C2211yescharacteristic
36#16839668C2212yes—
37#16839661C2212yes—
38#16839660C2214yes—
39#16839660C2214yes—
40#16839659C2214yes—
41#16839658C2212yes—
42#16839657C2214yes—
43#16839656C2214yes—
44#16839656C2214yes—
45#16839650C2214yes—
46#16839649C2214yes—
47#16839647C2214yes—
48#16839646C2214yes—
49#16839645C2214yes—
50#16839638C2214yes—
51#16839637C2214yes—
52#16839636C2214yes—
53#16839634C2214yes—
54#16839634C2214yes—
55#16839634C2214yes—
56#16839632C2211yescharacteristic
57#16839631C2212yes—
58#16839631C2212yes—
59#16839631C2212yes—
60#16839631C2212yes—
61#16839629C2212yes—
62#16839627C2211yescharacteristic
63#16839627C2211yescharacteristic
64#16839627C2212yes—
65#16839624C2212yes—
66#16839622C2212yes—
67#16839619C2211yescharacteristic
68#16839619C2211yescharacteristic
69C4⋊C4×Dic61C2212yes—
70C4⋊C4×Dic61C2212yes—
71C4×C4⋊Dic61C2211yescharacteristic
72C4×C4⋊Dic61C2212yes—
73C4×#11758198C2212yes—
74C4×#11758198C2214yes—
75#16839608C2212yes—
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
90C22×C4×D61C2314yes—
91#14519770C2×C4116yescomplemented
92#14519768C2×C418yescomplemented
93#14519764C2×C418yescomplemented
94#14519759C2×C4116yescomplemented
95#14519757C2×C418yescomplemented
96#14519748C2×C418yes—
97C4×Dic122C2×C418yescomplemented
98#14519742—44no—
99D4×Dic61—44no—
100C4×C22⋊D61C2×C4116yescomplemented
101#14519737—48no—
102#14519736C2×C4116yescomplemented
103C2×C4⋊Dic61—44no—
104C2×C4⋊Dic61C2312yes—
105C2×C4⋊Dic61C2312yes—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2312yes—
109C2×C4⋊Dic61C2314yes—
110C2×C4⋊Dic61C2312yes—
111C2×C4⋊Dic61C2312yes—
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196C2314yes—
114C2×#11758196C2314yes—
115C2×#11758196C2314yes—
116C2×#11758196C2314yes—
117C2×#11758196C2314yes—
118C2×#11758196C2312yes—
119C2×#11758196C2312yes—
120C4⋊C4×D61—44no—
121C4⋊C4×D61—44no—
122C4⋊C4×D61—44no—
123C2×C22⋊Dic61C2314yes—
124C2×C22⋊Dic61C2312yes—
125C2×C22⋊Dic61C2312yes—
126C2×C22⋊Dic61C2312yes—
127C2×#11758198C2312yes—
128C2×#11758198C2312yes—
129C2×#11758198C2312yes—
130C2×C4×Dic61C2312yes—
131C2×C4×Dic61C2314yes—
132C2×C4×Dic61C2314yes—
133C2×C4×Dic61C2311yescharacteristic
134C2×C4×Dic61C2311yescharacteristic
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2312yes—
137C42×D61C2×C418yescomplemented
138#14519684C2312yes—
139#14519684C2312yes—
140#14519684C2312yes—
141#14519684C2312yes—
142#14519684C2314yes—
143#14519684C2312yes—
144#14519684C2312yes—
145#14519684C2314yes—
146#14519684C2312yes—
147#14519684C2314yes—
148#14519684C2314yes—
149#14519684C2314yes—
150C22×D4×C61C2311yescharacteristic
151C23×C4×C61C2312yes—
152C4×D4×C61C2×C418yescomplemented
153#117×C61—44no—
154C2×C4⋊C4×C61C2312yes—
155C2×C4⋊C4×C61C2312yes—
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C4⋊C4×C61C2311yescharacteristic
158C2×C4⋊C4×C61C2312yes—
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C22⋊C4×C61C2314yes—
161C2×C22⋊C4×C61C2314yes—
162C2×C22⋊C4×C61C2312yes—
163C2×C42×C61C2312yes—
164C2×C42×C61C2314yes—
165C2×C42×C61C2311yescharacteristic
166#95×C61C2314yes—
167#95×C61C2312yes—
168C24×C61C2412yes—
169C23×D61C2411yescharacteristic
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61C22×C414yes—
173C22×C4×C61—24no—
174C22×C4×C61—24no—
175C22×C4×C61C22×C418yes—
176C22×C4×C61C2414yes—
177C22×C4×C61C2412yes—
178C22×C4×C61C2412yes—
179C22×C4×C61C2411yescharacteristic
180C22×C4×C61C2412yes—
181C22×C4×C61C2411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—24no—
184C2×C22⋊D61—24no—
185C2×C22⋊D61C22×C418yes—
186C22×Dic61—44no—
187C22×Dic61—44no—
188C22×Dic61—44no—
189C22×Dic61C2414yes—
190C22×Dic61C2412yes—
191C22×Dic61C2412yes—
192C22×Dic61C2411yescharacteristic
193C22×Dic61C2411yescharacteristic
194C22×Dic61C2411yescharacteristic
195C22×Dic61C2412yes—
196C22×Dic61C2412yes—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—28no—
204C2×C4×D61—44no—
205C2×C4×D61—44no—
206C2×C4×D61C22×C414yes—
207C2×C4×D61C22×C414yes—
208C2×C4×D61C22×C414yes—
209C2×Dic122—22no—
210C2×Dic122—22no—
211C2×Dic122C22×C414yes—
212C4⋊C4×C61—22no—
213C4⋊C4×C61—24no—
214C4⋊C4×C61—24no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—42no—
217C4⋊C4×C61C22×C414yes—
218C22⋊C4×C61—44no—
219C22⋊C4×C61—44no—
220C22⋊C4×C61C22×C418yes—
221C42×C61—24no—
222C42×C61—44no—
223C42×C61C22×C414yes—
224C22⋊Dic61—44no—
225C22⋊Dic61C22×C418yes—
226C22⋊Dic61C22×C418yes—
227C22⋊Dic61C22×C418yes—
228#11758198—24no—
229#11758198—24no—
230#11758198C22×C418yes—
231C4⋊Dic61—24no—
232C4⋊Dic61—24no—
233C4⋊Dic61—22no—
234C4⋊Dic61—22no—
235C4⋊Dic61—42no—
236C4⋊Dic61—44no—
237C4⋊Dic61C22×C418yes—
238C4⋊Dic61C22×C418yes—
239C4⋊Dic61C22×C414yes—
240#11758196—44no—
241#11758196—44no—
242#11758196—44no—
243#11758196—44no—
244#11758196—44no—
245#11758196C22×C418yes—
246#11758196C22×C418yes—
247C4×Dic61—24no—
248C4×Dic61—44no—
249C4×Dic61—44no—
250C4×Dic61C22×C414yes—
251C4×Dic61C22×C414yes—
252C4×Dic61C22×C414yes—
253C4×Dic61C22×C418yes—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61C23×C414yes—
261C23×C61C2511yescharacteristic
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61C23×C412yes—
267C22×D61H(5,𝔽2)12yes—
268C22×D612−1+412yes—
269D4×C61—28no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—216no—
275C2×C4×C61—22no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61C23×C412yes—
285C2×C4×C61C23×C414yes—
286C2×C4×C61C23×C412yes—
287C2×C4×C61C23×C412yes—
288C2×C4×C61H(5,𝔽2)12yes—
289C2×C4×C61H(5,𝔽2)12yes—
290C2×C4×C612−1+412yes—
291C2×C4×C612−1+412yes—
292C22⋊D61—216no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—22no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—24no—
306C2×Dic61—22no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—88no—
313C2×Dic61C23×C412yes—
314C2×Dic61C23×C412yes—
315C2×Dic61C23×C412yes—
316C2×Dic61C23×C414yes—
317C2×Dic61C23×C414yes—
318C4×D61—28no—
319C4×D61—28no—
320C4×D61—28no—
321C4×D61—88no—
322Dic122—28no—
323#34384—611nomaximal, Sylow
324C22×C61—24no—
325C22×C61—24no—
326C22×C61—24no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61C24×C411yescharacteristic
332C22×C61C2×H(5,𝔽2)11yescharacteristic
333C22×C61C2×H(5,𝔽2)11yescharacteristic
334C22×C61C2×H(5,𝔽2)11yescharacteristic
335C22×C61C2×2−1+411yescharacteristic
336C22×C61C2×2−1+411yescharacteristic
337C22×C61C2×2−1+411yescharacteristic
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61#52014yes—
345C4×C61—22no—
346C4×C61—24no—
347C4×C61—44no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61#52014yes—
351C4×C61#52014yes—
352Dic61—24no—
353Dic61—22no—
354Dic61—22no—
355Dic61—22no—
356Dic61—24no—
357Dic61—44no—
358Dic61—42no—
359Dic61—42no—
360C2×#529—611no—
361#2383—614no—
362#2361—612no—
363#2360—612no—
364#2355—611no—
365#2354D6111yescharacteristic, complemented
366#2352—612no—
367Q8×C4⋊C4—611no—
368D4×C4⋊C4—612no—
369D4×C4⋊C4—611no—
370#2330—612no—
371#2326—612no—
372#2322—614no—
373#2317—612no—
374#2314—612no—
375C2×#384—611no—
376#2283—611no—
377C2×C61—44no—
378C2×C61C2×#52011yescharacteristic
379C2×C61C2×#52011yescharacteristic
380C2×C61C2×#52011yescharacteristic
381C2×C61#354311yescharacteristic
382C2×C61#354411yescharacteristic
383C2×C61#355211yescharacteristic
384C2×C61#355211yescharacteristic
385D61—24no—
386#529—6116no—
387C2×#126—612no—
388C2×#125—611no—
389C2×#124—611no—
390C2×#123—612no—
391C2×C22⋊Q8—611no—
392C2×#121—611no—
393C2×C4×Q8—612no—
394C2×C4×Q8—611no—
395C2×C4×D4—612no—
396C2×C4×D4—612no—
397C2×C4×D4—614no—
398C2×C4×D4C2×D6111yescharacteristic
399C2×#117—612no—
400C2×#117C2×D6112yes—
401C22×C4⋊C4—612no—
402C22×C4⋊C4—612no—
403C22×C4⋊C4—612no—
404C22×C4⋊C4—612no—
405C22×C42—611no—
406#391—612no—
407#390C2×D6112yes—
408#389—614no—
409#389—612no—
410#389—612no—
411#389—614no—
412#389—614no—
413#389—614no—
414#388—614no—
415#388—614no—
416#388—614no—
417#388C2×D6114yes—
418#387—614no—
419#387—614no—
420#387—614no—
421#387—614no—
422#386—614no—
423#385—614no—
424#385—614no—
425#385—614no—
426#385—614no—
427#385—614no—
428#384—612no—
429#384—612no—
430#384—612no—
431#384—612no—
432#384—611no—
433#384C2×D6111yescharacteristic
434#383—612no—
435#382—611no—
436#382—611no—
437#382—612no—
438#381—612no—
439#380—612no—
440#380—611no—
441#380—611no—
442#380C2×D6112yes—
443C4×C4⋊C4—612no—
444C4×C4⋊C4—612no—
445C4×C4⋊C4—612no—
446C4×C4⋊C4—611no—
447C4×C4⋊C4C2×D6112yes—
448C4×C4⋊C4C2×D6111yescharacteristic
449C4×C22⋊C4—614no—
450C4×C22⋊C4—612no—
451#376—612no—
452C61#3438411yescharacteristic, complemented, Sylow
453C22×Q8—611no—
454C22×D4—612no—
455C22×D4C22×D6111yescharacteristic
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—614no—
460C23×C4—614no—
461C23×C4C22×D6112yes—
462#126—6116no—
463#125—618no—
464#124—618no—
465#123—6116no—
466C22⋊Q8—618no—
467#121—618no—
468C4×Q8—618no—
469C4×Q8—2444no—
470C4×D4—6116no—
471C4×D4—2444no—
472C4×D4—2448no—
473C4×D4C4×D6118yescomplemented
474#117—44no—
475#117—6116no—
476C2×C4⋊C4—612no—
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—612no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—612no—
486C2×C4⋊C4—614no—
487C2×C4⋊C4—614no—
488C2×C4⋊C4—614no—
489C2×C4⋊C4—614no—
490C2×C4⋊C4—614no—
491C2×C4⋊C4—614no—
492C2×C4⋊C4—2444no—
493C2×C4⋊C4—2444no—
494C2×C4⋊C4—2444no—
495C2×C4⋊C4—2444no—
496C2×C4⋊C4C22×D6112yes—
497C2×C4⋊C4C22×D6112yes—
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C4⋊C4C22×D6111yescharacteristic
500C2×C4⋊C4C22×D6112yes—
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—612no—
503C2×C22⋊C4—612no—
504C2×C22⋊C4—612no—
505C2×C22⋊C4—612no—
506C2×C22⋊C4—612no—
507C2×C22⋊C4—612no—
508C2×C22⋊C4—614no—
509C2×C22⋊C4C22×D6114yes—
510C2×C22⋊C4C22×D6114yes—
511C2×C22⋊C4C22×D6112yes—
512C2×C42—611no—
513C2×C42—612no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—618no—
517C2×C42—612no—
518C2×C42—614no—
519C2×C42—614no—
520C2×C42C22×D6112yes—
521C2×C42C22×D6114yes—
522C2×C42C22×D6111yescharacteristic
523#95—612no—
524#95—612no—
525#95—612no—
526#95—612no—
527#95—614no—
528#95—612no—
529#95—612no—
530#95—614no—
531#95—612no—
532#95—614no—
533#95—614no—
534#95—614no—
535#95C22×D6114yes—
536#95C22×D6112yes—
537C24—611no—
538C24C23×D6112yes—
539C2×Q8—614no—
540C2×Q8—1222no—
541C2×Q8—1222no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—618no—
545C2×D4—1224no—
546C2×D4—1224no—
547C2×D4C2×C4×D6114yes—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—614no—
556C22×C4—614no—
557C22×C4—614no—
558C22×C4—612no—
559C22×C4—614no—
560C22×C4—612no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1228no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—2444no—
569C22×C4—2444no—
570C22×C4—2444no—
571C22×C4—2444no—
572C22×C4—2444no—
573C22×C4C2×C4×D6118yes—
574C22×C4C23×D6112yes—
575C22×C4C23×D6112yes—
576C22×C4C23×D6114yes—
577C22×C4C23×D6111yescharacteristic
578C22×C4C23×D6112yes—
579C22×C4C23×D6111yescharacteristic
580C22×C4C23×D6111yescharacteristic
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—42no—
586C4⋊C4—618no—
587C4⋊C4—618no—
588C4⋊C4—618no—
589C4⋊C4—618no—
590C4⋊C4—614no—
591C4⋊C4—1224no—
592C4⋊C4—1222no—
593C4⋊C4—1224no—
594C4⋊C4—1222no—
595C4⋊C4—2444no—
596C4⋊C4—2444no—
597C4⋊C4—2444no—
598C4⋊C4—2442no—
599C4⋊C4—2444no—
600C4⋊C4—2444no—
601C4⋊C4—2444no—
602C4⋊C4C2×C4×D6114yes—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—618no—
606C22⋊C4—618no—
607C22⋊C4—618no—
608C22⋊C4—618no—
609C22⋊C4—1224no—
610C22⋊C4—1224no—
611C22⋊C4—2444no—
612C22⋊C4C2×C4×D6118yes—
613C42—24no—
614C42—44no—
615C42—614no—
616C42—614no—
617C42—614no—
618C42—618no—
619C42—1224no—
620C42—2444no—
621C42—2444no—
622C42C2×C4×D6114yes—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—612no—
630C23—612no—
631C23—612no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23C22×C4×D6114yes—
637C23C24×D6111yescharacteristic
638Q8—1228no—
639D4—28no—
640D4—12216no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—216no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—612no—
656C2×C4—612no—
657C2×C4—612no—
658C2×C4—614no—
659C2×C4—614no—
660C2×C4—1228no—
661C2×C4—1222no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1222no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1222no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1222no—
671C2×C4—1228no—
672C2×C4—1228no—
673C2×C4—1224no—
674C2×C4—1222no—
675C2×C4—1224no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1224no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—4888no—
683C2×C4—4888no—
684C2×C4C22×C4×D6112yes—
685C2×C4C22×C4×D6114yes—
686C2×C4C22×C4×D6112yes—
687C2×C4C22×C4×D6112yes—
688C2×C4#1451982212yes—
689C2×C4#1451982312yes—
690C2×C4#1451982412yes—
691C2×C4#1451982412yes—
692C22—24no—
693C22—24no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—614no—
700C22—1222no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—1222no—
705C22—1222no—
706C22C23×C4×D6111yescharacteristic
707C22H(5,𝔽2)×D6111yescharacteristic
708C22C2×#1451982211yescharacteristic
709C22C2×#1451982311yescharacteristic
710C222−1+4×D6111yescharacteristic
711C22C2×#1451982411yescharacteristic
712C22C2×#1451982411yescharacteristic
713C4—22no—
714C4—24no—
715C4—42no—
716C4—44no—
717C4—42no—
718C4—1222no—
719C4—1224no—
720C4—1222no—
721C4—1222no—
722C4—1224no—
723C4—2442no—
724C4—2444no—
725C4—2442no—
726C4#1684024114yes—
727C4#1684024214yes—
728C2—44no—
729C2—1224no—
730C2#520×D6111yescharacteristic
731C2C2×#1684024111yescharacteristic
732C2C2×#1684024211yescharacteristic
733C2#2146014311yescharacteristic
734C2#2146015411yescharacteristic
735C2#2146024911yescharacteristic
736C2#2146025711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2354C2
socle, cosocleC23×C61C25
prime radicalC2×#14519748C22
hypercenter#2354D61
hypocenterC61#34384
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #21449006C2semidirect
4. #21448826C2semidirect
5. #21448774C2semidirect
6. #21448749C2semidirect
7. #21448731C2semidirect
8. D4×C4⋊Dic61C2semidirect
9. #21448715C2semidirect
10. #21448556C2semidirect
11. #21448529C2semidirect
12. #21448489C2semidirect
13. #21448439C2semidirect
14. #21448426C2semidirect
15. #384×D61C2semidirect
16. #21448215C2semidirect
17. C61×#2354C2semidirect
18. #16840294C4semidirect
91. #14519770C2×C4semidirect
92. #14519768C2×C4semidirect
93. #14519764C2×C4semidirect
94. #14519759C2×C4semidirect
95. #14519757C2×C4semidirect
97. C4×Dic122C2×C4semidirect
100. C4×C22⋊D61C2×C4semidirect
102. #14519736C2×C4semidirect
137. C42×D61C2×C4semidirect
152. C4×D4×C61C2×C4semidirect
365. #2354D61semidirect
452. C61#34384semidirect
473. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402942
#214490062
#214488402
#214488262
#214487742
#214487492
#214487312
D4×C4⋊Dic612
#214487152
#214485562
#214485292
#214484892
#214484392
#214484262
#384×D612
#214482152
C61×#23542
#3438461