Finite Group Databasebeta

← D61×#2347 #29839270

Subgroups — D61×#2347 #29839270

Order 15616.

2790 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D61C211yesmaximal, characteristic
2#21448714C211yesmaximal, characteristic, complemented
3#21448713C212yesmaximal, complemented
4#21448712C211yesmaximal, characteristic, complemented
5#21448711C212yesmaximal, complemented
6#21448710C211yesmaximal, characteristic, complemented
7#21448709C214yesmaximal, complemented
8#21448708C212yesmaximal, complemented
9#21448707C212yesmaximal, complemented
10#389×D61C212yesmaximal, complemented
11#388×D61C214yesmaximal
12#383×D61C212yesmaximal, complemented
13#380×D61C211yesmaximal, characteristic
14C4×C4⋊C4×D61C212yesmaximal, complemented
15C4×C4⋊C4×D61C212yesmaximal, complemented
16C4×C22⋊C4×D61C211yesmaximal, characteristic
17C61×#2347C211yesmaximal, characteristic, complemented
18C23×C4×D61C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C2×#14519734C2212yes—
23C2×#14519733C2212yes—
24#117×D61C4116yescomplemented
25C2×C4⋊C4×D61C2214yes—
26C2×C4⋊C4×D61C2212yes—
27C2×C4⋊C4×D61C2211yescharacteristic
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C22⋊C4×D61C2212yes—
30C2×C22⋊C4×D61C2212yes—
31C2×C22⋊C4×D61C2212yes—
32C2×C42×D61C2212yes—
33C2×C42×D61C2214yes—
34C2×C42×D61C2212yes—
35#16839661C2212yescomplemented
36#16839660C2212yescomplemented
37#16839659C2214yescomplemented
38#16839658C2212yescomplemented
39#16839657C2214yescomplemented
40#16839656C2214yes—
41#16839655C2214yes—
42#16839654C2214yes—
43#16839653C2214yes—
44#16839652C2214yes—
45#16839651C2214yes—
46#16839650C2214yes—
47#16839630C2212yescomplemented
48#16839629C2212yescomplemented
49#16839629C2214yescomplemented
50#16839629C2214yescomplemented
51#16839629C2212yescomplemented
52#16839622C2211yescharacteristic
53#16839621C2212yes—
54#16839620C2212yes—
55#16839619C2212yes—
56C4⋊C4×Dic61C2212yescomplemented
57C4⋊C4×Dic61C2214yescomplemented
58C4⋊C4×Dic61C2212yescomplemented
59C4×#11758196C2214yescomplemented
60C4×#11758196C2214yescomplemented
61C4×C4⋊Dic61C2212yescomplemented
62C4×C4⋊Dic61C2212yescomplemented
63#16839613C2214yescomplemented
64#16839613C2212yescomplemented
65#16839613C2212yescomplemented
66C22⋊C4×Dic61C2212yes—
67C4×#11758198C2212yes—
68C4×C22⋊Dic61C2211yescharacteristic
69#16839609C2211yescharacteristic
70#16839609C2211yescharacteristic
71#95×D61C2211yescharacteristic
72#95×D61C2214yes—
73#95×D61C2214yes—
74#95×D61C2212yes—
75#95×D61C2211yescharacteristic
76C2×#117×C61C2211yescharacteristic
77C61×#389C2212yescomplemented
78C61×#388C2214yes—
79C61×#383C2212yescomplemented
80C61×#380C2211yescharacteristic
81C4×C4⋊C4×C61C2212yescomplemented
82C4×C4⋊C4×C61C2212yescomplemented
83C4×C22⋊C4×C61C2211yescharacteristic
84C24×D61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C22×C4×D61—28no—
87C22×C4×D61C2×C418yes—
88C22×C4×D61C2314yes—
89C22×C4×D61C2312yes—
90C22×C4×D61C2312yes—
91C22×C4×D61C2311yescharacteristic
92C22×C4×D61C2312yes—
93C22×C4×D61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2312yes—
96C22×C4×D61C2311yescharacteristic
97#14519736C2×C418yescomplemented
98#14519735C2×C418yescomplemented
99#14519735C2×C418yescomplemented
100#14519734C2×C4116yescomplemented
101#14519733C2×C4116yescomplemented
102C2×C4⋊Dic61C2312yes—
103C2×C4⋊Dic61C2314yes—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2312yes—
110C2×#11758196C2312yes—
111C4⋊C4×D61—216no—
112C4⋊C4×D61—28no—
113C4⋊C4×D61C2×C418yes—
114C4⋊C4×D61C2×C418yes—
115C2×C22⋊Dic61C2312yes—
116C2×C22⋊Dic61C2312yes—
117C2×C22⋊Dic61C2312yes—
118C2×#11758198C2312yes—
119C2×#11758198C2312yes—
120C2×#11758198C2314yes—
121C2×#11758198C2312yes—
122C2×#11758198C2312yes—
123C22⋊C4×D61—28no—
124C22⋊C4×D61—44no—
125C22⋊C4×D61C2×C4116yes—
126C2×C4×Dic61C2312yes—
127C2×C4×Dic61C2312yes—
128C2×C4×Dic61C2312yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131C2×C4×Dic61C2314yes—
132C2×C4×Dic61C2312yes—
133C2×C4×Dic61C2312yes—
134C2×C4×Dic61C2312yes—
135C42×D61—28no—
136C42×D61—48no—
137C42×D61C2×C4116yes—
138#14519684C2311yescharacteristic
139#14519684C2311yescharacteristic
140#14519684C2312yes—
141#14519684C2312yes—
142#14519684C2312yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146#14519684C2314yes—
147#14519684C2314yes—
148#14519684C2314yes—
149#14519684C2314yes—
150C23×C4×C61C2311yescharacteristic
151#117×C61C2×C418yescomplemented
152C2×C4⋊C4×C61C2312yes—
153C2×C4⋊C4×C61C2314yes—
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61C2312yes—
157C2×C22⋊C4×C61C2312yes—
158C2×C22⋊C4×C61C2312yes—
159C2×C42×C61C2312yes—
160C2×C42×C61C2314yes—
161C2×C42×C61C2312yes—
162#95×C61C2311yescharacteristic
163#95×C61C2311yescharacteristic
164#95×C61C2312yes—
165#95×C61C2314yes—
166#95×C61C2314yes—
167C24×C61C2411yescharacteristic
168C23×D61—24no—
169C23×D61—24no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61C22×C414yes—
173C23×D61C2411yescharacteristic
174C23×D61C2411yescharacteristic
175C22×C4×C61—24no—
176C22×C4×C61C22×C414yes—
177C22×C4×C61C2412yes—
178C22×C4×C61C2414yes—
179C22×C4×C61C2411yescharacteristic
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2411yescharacteristic
184C22×Dic61—24no—
185C22×Dic61C22×C414yes—
186C22×Dic61C2412yes—
187C22×Dic61C2414yes—
188C22×Dic61C2411yescharacteristic
189C22×Dic61C2412yes—
190C22×Dic61C2412yes—
191C22×Dic61C2412yes—
192C22×Dic61C2411yescharacteristic
193C2×C4×D61—24no—
194C2×C4×D61—24no—
195C2×C4×D61—28no—
196C2×C4×D61—24no—
197C2×C4×D61—24no—
198C2×C4×D61—24no—
199C2×C4×D61—24no—
200C2×C4×D61—24no—
201C2×C4×D61—232no—
202C2×C4×D61—24no—
203C2×C4×D61—24no—
204C2×C4×D61—28no—
205C2×C4×D61—28no—
206C2×C4×D61—28no—
207C2×C4×D61—24no—
208C2×C4×D61C22×C414yes—
209C2×C4×D61C22×C414yes—
210C2×C4×D61C22×C414yes—
211C2×C4×D61C22×C418yes—
212C2×C4×D61C22×C418yes—
213C2×C4×D61C22×C414yes—
214C2×C4×D61#4118yes—
215C2×C4×D61#4118yes—
216C4⋊C4×C61—28no—
217C4⋊C4×C61—24no—
218C4⋊C4×C61C22×C414yes—
219C4⋊C4×C61C22×C414yes—
220C22⋊C4×C61—24no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61C22×C418yes—
223C42×C61—24no—
224C42×C61—44no—
225C42×C61C22×C418yes—
226C22⋊Dic61—24no—
227C22⋊Dic61—42no—
228C22⋊Dic61C22×C418yes—
229#11758198—24no—
230#11758198—24no—
231#11758198—44no—
232#11758198C22×C418yes—
233#11758198C22×C418yes—
234C4⋊Dic61—24no—
235C4⋊Dic61—28no—
236C4⋊Dic61C22×C414yes—
237C4⋊Dic61C22×C414yes—
238#11758196—28no—
239#11758196—28no—
240#11758196—28no—
241#11758196C22×C418yes—
242#11758196C22×C418yes—
243C4×Dic61—24no—
244C4×Dic61—24no—
245C4×Dic61—24no—
246C4×Dic61—44no—
247C4×Dic61—44no—
248C4×Dic61—44no—
249C4×Dic61C22×C418yes—
250C4×Dic61C22×C418yes—
251C4×Dic61C22×C418yes—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61C23×C412yes—
257C23×C61C2511yescharacteristic
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—28no—
263C22×D61—28no—
264C22×D61—28no—
265C22×D61—48no—
266C22×D61—48no—
267C22×D61C23×C412yes—
268C22×D61C23×C412yes—
269C22×D61C2×#4114yes—
270C22×D61C2×#4114yes—
271C22×D61H(5,𝔽2)12yes—
272C22×D612−1+412yes—
273C2×C4×C61—22no—
274C2×C4×C61—24no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—28no—
280C2×C4×C61—22no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—22no—
284C2×C4×C61—24no—
285C2×C4×C61—22no—
286C2×C4×C61C23×C412yes—
287C2×C4×C61C23×C414yes—
288C2×C4×C61C23×C414yes—
289C2×C4×C61C23×C412yes—
290C2×C4×C61C2×#4114yes—
291C2×C4×C61C2×#4114yes—
292C2×Dic61—22no—
293C2×Dic61—24no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—28no—
299C2×Dic61—22no—
300C2×Dic61—24no—
301C2×Dic61—24no—
302C2×Dic61—22no—
303C2×Dic61—24no—
304C2×Dic61—22no—
305C2×Dic61C23×C412yes—
306C2×Dic61C23×C414yes—
307C2×Dic61C23×C414yes—
308C2×Dic61C23×C412yes—
309C2×Dic61C2×#4114yes—
310C2×Dic61C2×#4114yes—
311C4×D61—28no—
312C4×D61—216no—
313C4×D61—216no—
314C4×D61—216no—
315C4×D61—28no—
316C4×D61—28no—
317C4×D61—416no—
318C4×D61—48no—
319C4×D61#117116yes—
320C2×#2347—611nomaximal, Sylow
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61C24×C411yescharacteristic
327C22×C61C22×#4112yes—
328C22×C61C22×#4112yes—
329C22×C61C2×H(5,𝔽2)11yescharacteristic
330C22×C61C2×2−1+411yescharacteristic
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—42no—
335C2×D61—42no—
336C2×D61—416no—
337C2×D61C2×#11714yes—
338C2×D61C4×#4114yes—
339C2×D61#52014yes—
340C2×D61#55318yes—
341C2×D61#55618yes—
342C4×C61—22no—
343C4×C61—24no—
344C4×C61—24no—
345C4×C61—24no—
346C4×C61—44no—
347C4×C61—42no—
348C4×C61C2×#11714yes—
349Dic61—22no—
350Dic61—24no—
351Dic61—24no—
352Dic61—24no—
353Dic61—44no—
354Dic61—42no—
355Dic61C2×#11714yes—
356C22×#117—611no—
357#2347—612no—
358#2347—614no—
359#2347—612no—
360#2347—611no—
361#2347—612no—
362#2347—612no—
363#2347—611no—
364#2347—611no—
365#2347D6111yescharacteristic, direct product factor
366C2×#389—612no—
367C2×#388—614no—
368C2×#383—612no—
369C2×#380—611no—
370C2×C4×C4⋊C4—612no—
371C2×C4×C4⋊C4—612no—
372C2×C4×C22⋊C4—611no—
373C2×C61—42no—
374C2×C61C22×#11711yescharacteristic
375C2×C61C2×C4×#4111yescharacteristic
376C2×C61C2×#52011yescharacteristic
377C2×C61C2×#55312yes—
378C2×C61C2×#55612yes—
379D61—42no—
380D61#234718yesdirect product factor
381C24×C4—611no—
382C2×#117—611no—
383C2×#117—6116no—
384C2×#117—611no—
385C2×#117—611no—
386C2×#117—612no—
387C2×#117—612no—
388C2×#117C2×D6111yescharacteristic
389C22×C4⋊C4—611no—
390C22×C4⋊C4—611no—
391C22×C4⋊C4—612no—
392C22×C4⋊C4—614no—
393C22×C22⋊C4—612no—
394C22×C22⋊C4—612no—
395C22×C22⋊C4—612no—
396C22×C42—612no—
397C22×C42—612no—
398C22×C42—614no—
399#389—614no—
400#389—612no—
401#389—612no—
402#389—612no—
403#389—614no—
404#389C2×D6112yescomplemented
405#388—614no—
406#388—614no—
407#388—614no—
408#388—614no—
409#388—614no—
410#388—614no—
411#388—614no—
412#388C2×D6114yes—
413#383—612no—
414#383—614no—
415#383—614no—
416#383—612no—
417#383—612no—
418#383C2×D6112yescomplemented
419#380—611no—
420#380—612no—
421#380—612no—
422#380—612no—
423#380C2×D6111yescharacteristic
424C4×C4⋊C4—614no—
425C4×C4⋊C4—612no—
426C4×C4⋊C4—612no—
427C4×C4⋊C4—612no—
428C4×C4⋊C4—612no—
429C4×C4⋊C4—614no—
430C4×C4⋊C4—614no—
431C4×C4⋊C4—612no—
432C4×C4⋊C4—612no—
433C4×C4⋊C4—614no—
434C4×C4⋊C4C2×D6112yescomplemented
435C4×C4⋊C4C2×D6112yescomplemented
436C4×C22⋊C4—611no—
437C4×C22⋊C4—612no—
438C4×C22⋊C4—612no—
439C4×C22⋊C4—611no—
440C4×C22⋊C4—611no—
441C4×C22⋊C4C2×D6111yescharacteristic
442C2×#95—611no—
443C2×#95—611no—
444C2×#95—612no—
445C2×#95—614no—
446C2×#95—614no—
447C61C2×#234711yescharacteristic, complemented, Sylow
448C25—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—618no—
452C23×C4—612no—
453C23×C4—612no—
454C23×C4—612no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—614no—
459C23×C4—612no—
460C23×C4—1228no—
461C23×C4C22×D6111yescharacteristic
462#117—618no—
463#117—618no—
464#117—618no—
465#117—6116no—
466#117—6116no—
467#117C4×D6118yescomplemented
468C2×C4⋊C4—612no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—612no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—618no—
473C2×C4⋊C4—618no—
474C2×C4⋊C4—614no—
475C2×C4⋊C4—612no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—1228no—
480C2×C4⋊C4—12216no—
481C2×C4⋊C4C22×D6112yes—
482C2×C4⋊C4C22×D6114yes—
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C22⋊C4—612no—
486C2×C22⋊C4—612no—
487C2×C22⋊C4—612no—
488C2×C22⋊C4—6116no—
489C2×C22⋊C4—612no—
490C2×C22⋊C4—612no—
491C2×C22⋊C4—612no—
492C2×C22⋊C4—612no—
493C2×C22⋊C4—614no—
494C2×C22⋊C4—1228no—
495C2×C22⋊C4—2444no—
496C2×C22⋊C4C22×D6112yes—
497C2×C22⋊C4C22×D6112yes—
498C2×C22⋊C4C22×D6112yes—
499C2×C42—612no—
500C2×C42—612no—
501C2×C42—612no—
502C2×C42—6116no—
503C2×C42—612no—
504C2×C42—612no—
505C2×C42—612no—
506C2×C42—614no—
507C2×C42—614no—
508C2×C42—614no—
509C2×C42—1228no—
510C2×C42—2448no—
511C2×C42C22×D6112yes—
512C2×C42C22×D6114yes—
513C2×C42C22×D6112yes—
514#95—612no—
515#95—611no—
516#95—612no—
517#95—611no—
518#95—614no—
519#95—612no—
520#95—614no—
521#95—614no—
522#95—614no—
523#95—614no—
524#95—614no—
525#95—614no—
526#95C22×D6111yescharacteristic
527#95C22×D6111yescharacteristic
528#95C22×D6112yes—
529#95C22×D6114yes—
530#95C22×D6114yes—
531C24—611no—
532C24—614no—
533C24—611no—
534C24—1224no—
535C24—1222no—
536C24—1224no—
537C24—1222no—
538C24C23×D6111yescharacteristic
539C22×C4—24no—
540C22×C4—611no—
541C22×C4—614no—
542C22×C4—618no—
543C22×C4—614no—
544C22×C4—611no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—614no—
549C22×C4—618no—
550C22×C4—618no—
551C22×C4—614no—
552C22×C4—614no—
553C22×C4—618no—
554C22×C4—612no—
555C22×C4—614no—
556C22×C4—1224no—
557C22×C4—12232no—
558C22×C4—1224no—
559C22×C4—1224no—
560C22×C4—1224no—
561C22×C4—1228no—
562C22×C4—1224no—
563C22×C4—1224no—
564C22×C4—1224no—
565C22×C4—1228no—
566C22×C4—1224no—
567C22×C4—1228no—
568C22×C4—1228no—
569C22×C4—1224no—
570C22×C4—1224no—
571C22×C4—1224no—
572C22×C4C2×C4×D6114yes—
573C22×C4C23×D6112yes—
574C22×C4C23×D6114yes—
575C22×C4C23×D6111yescharacteristic
576C22×C4C23×D6112yes—
577C22×C4C23×D6112yes—
578C22×C4C23×D6112yes—
579C22×C4C23×D6111yescharacteristic
580C4⋊C4—28no—
581C4⋊C4—24no—
582C4⋊C4—618no—
583C4⋊C4—618no—
584C4⋊C4—614no—
585C4⋊C4—614no—
586C4⋊C4—1228no—
587C4⋊C4—1228no—
588C4⋊C4—1228no—
589C4⋊C4—1228no—
590C4⋊C4—1224no—
591C4⋊C4C2×C4×D6114yes—
592C4⋊C4C2×C4×D6114yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—618no—
596C22⋊C4—618no—
597C22⋊C4—618no—
598C22⋊C4—1224no—
599C22⋊C4—1224no—
600C22⋊C4—1224no—
601C22⋊C4—2444no—
602C22⋊C4—2442no—
603C22⋊C4C2×C4×D6118yes—
604C42—24no—
605C42—44no—
606C42—618no—
607C42—618no—
608C42—618no—
609C42—1224no—
610C42—1224no—
611C42—1224no—
612C42—2444no—
613C42—2444no—
614C42—2444no—
615C42C2×C4×D6118yes—
616C23—22no—
617C23—22no—
618C23—21no—
619C23—21no—
620C23—612no—
621C23—614no—
622C23—614no—
623C23—612no—
624C23—612no—
625C23—612no—
626C23—1228no—
627C23—1228no—
628C23—1228no—
629C23—1222no—
630C23—1222no—
631C23—1221no—
632C23—1221no—
633C23—2448no—
634C23—2448no—
635C23C22×C4×D6112yes—
636C23C24×D6111yescharacteristic
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—612no—
651C2×C4—614no—
652C2×C4—6116no—
653C2×C4—612no—
654C2×C4—614no—
655C2×C4—614no—
656C2×C4—614no—
657C2×C4—1228no—
658C2×C4—12216no—
659C2×C4—12216no—
660C2×C4—12216no—
661C2×C4—1228no—
662C2×C4—1228no—
663C2×C4—1222no—
664C2×C4—1224no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1228no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1224no—
673C2×C4—1224no—
674C2×C4—1224no—
675C2×C4—1222no—
676C2×C4—24416no—
677C2×C4—2448no—
678C2×C4C22×C4×D6112yes—
679C2×C4C22×C4×D6114yes—
680C2×C4C22×C4×D6114yes—
681C2×C4C22×C4×D6112yes—
682C2×C4#41×D6114yes—
683C2×C4#41×D6114yes—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—42no—
688C22—42no—
689C22—614no—
690C22—614no—
691C22—614no—
692C22—618no—
693C22—618no—
694C22—1222no—
695C22—1222no—
696C22—1222no—
697C22—24416no—
698C22—2442no—
699C22—2442no—
700C22C23×C4×D6111yescharacteristic
701C22C2×#41×D6112yes—
702C22C2×#41×D6112yes—
703C22H(5,𝔽2)×D6111yescharacteristic
704C222−1+4×D6111yescharacteristic
705C4—22no—
706C4—24no—
707C4—24no—
708C4—24no—
709C4—44no—
710C4—42no—
711C4—614no—
712C4—1222no—
713C4—1224no—
714C4—1224no—
715C4—1224no—
716C4—2444no—
717C4—2442no—
718C4#117×D6114yes—
719C2—42no—
720C2—618no—
721C2—2442no—
722C2C2×#117×D6111yescharacteristic
723C2C4×#41×D6111yescharacteristic
724C2#520×D6111yescharacteristic
725C2#553×D6112yes—
726C2#556×D6112yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2347C2
socle, cosocleC23×C61C25
prime radicalC24×D61C23
hypercenter#2347D61
hypocenterC61C2×#2347
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #21448714C2semidirect
3. #21448713C2semidirect
4. #21448712C2semidirect
5. #21448711C2semidirect
6. #21448710C2semidirect
7. #21448709C2semidirect
8. #21448708C2semidirect
9. #21448707C2semidirect
10. #389×D61C2semidirect
12. #383×D61C2semidirect
14. C4×C4⋊C4×D61C2semidirect
15. C4×C4⋊C4×D61C2semidirect
17. C61×#2347C2semidirect
24. #117×D61C4semidirect
35. #16839661C22semidirect
36. #16839660C22semidirect
37. #16839659C22semidirect
38. #16839658C22semidirect
39. #16839657C22semidirect
47. #16839630C22semidirect
48. #16839629C22semidirect
49. #16839629C22semidirect
50. #16839629C22semidirect
51. #16839629C22semidirect
56. C4⋊C4×Dic61C22semidirect
57. C4⋊C4×Dic61C22semidirect
58. C4⋊C4×Dic61C22semidirect
59. C4×#11758196C22semidirect
60. C4×#11758196C22semidirect
61. C4×C4⋊Dic61C22semidirect
62. C4×C4⋊Dic61C22semidirect
63. #16839613C22semidirect
64. #16839613C22semidirect
65. #16839613C22semidirect
77. C61×#389C22semidirect
79. C61×#383C22semidirect
81. C4×C4⋊C4×C61C22semidirect
82. C4×C4⋊C4×C61C22semidirect
97. #14519736C2×C4semidirect
98. #14519735C2×C4semidirect
99. #14519735C2×C4semidirect
100. #14519734C2×C4semidirect
101. #14519733C2×C4semidirect
151. #117×C61C2×C4semidirect
365. #2347D61direct (N × H)
380. D61#2347direct (N × H)
404. #389C2×D61semidirect
418. #383C2×D61semidirect
434. C4×C4⋊C4C2×D61semidirect
435. C4×C4⋊C4C2×D61semidirect
447. C61C2×#2347semidirect
467. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D612
#214487142
#214487132
#214487122
#214487112
#214487102
#214487092
#214487082
#214487072
#389×D612
#388×D612
#383×D612
#380×D612
C4×C4⋊C4×D612
C4×C22⋊C4×D612
C61×#23472
C2×#234761