Finite Group Databasebeta

← D61×#2355 #29839365

Subgroups — D61×#2355 #29839365

Order 15616.

2638 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×C4×Q8×D61C211yesmaximal, characteristic
2#21448778C211yesmaximal, characteristic, complemented
3#21448777C212yesmaximal, complemented
4#21448776C211yesmaximal, characteristic, complemented
5#21448775C212yesmaximal, complemented
6#21448774C211yesmaximal, characteristic, complemented
7#21448773C214yesmaximal, complemented
8#21448772C212yesmaximal, complemented
9#21448771C212yesmaximal, complemented
10#391×D61C212yesmaximal
11#387×D61C214yesmaximal
12#384×D61C211yesmaximal, characteristic
13#382×D61C212yesmaximal
14C4×C4⋊C4×D61C211yesmaximal, characteristic
15C4×C4⋊C4×D61C212yesmaximal
16C4×C4⋊C4×D61C212yesmaximal
17C61×#2355C211yesmaximal, characteristic, complemented
18C22×Q8×D61C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×C4×Dic122C2212yes—
21C2×C4×Dic122C2211yescharacteristic
22C2×#14519742C2211yescharacteristic
23C2×#14519742C2212yes—
24C4×Q8×D61C4116yescomplemented
25C2×C4⋊C4×D61C2211yescharacteristic
26C2×C4⋊C4×D61C2212yes—
27C2×C4⋊C4×D61C2212yes—
28C2×C4⋊C4×D61C2212yes—
29C2×C4⋊C4×D61C2212yes—
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C42×D61C2212yes—
33C2×C42×D61C2214yes—
34C2×C42×D61C2212yes—
35C2×C42×D61C2211yescharacteristic
36#16839669C2212yes—
37#16839668C2212yes—
38#16839667C2212yes—
39#16839666C2214yes—
40#16839666C2214yes—
41#16839649C2214yes—
42#16839648C2214yes—
43#16839647C2214yes—
44#16839646C2214yes—
45#16839645C2214yes—
46#16839644C2214yes—
47#16839643C2214yes—
48#16839632C2211yescharacteristic
49#16839631C2212yes—
50#16839631C2212yes—
51#16839631C2212yes—
52#16839628C2212yes—
53#16839627C2212yes—
54#16839627C2212yes—
55#16839626C2214yes—
56#16839626C2214yes—
57C4⋊C4×Dic61C2211yescharacteristic
58C4⋊C4×Dic61C2212yes—
59C4⋊C4×Dic61C2212yes—
60C4⋊C4×Dic61C2212yes—
61C4⋊C4×Dic61C2212yes—
62C4⋊C4×Dic61C2211yescharacteristic
63C4×#11758196C2214yes—
64C4×#11758196C2212yes—
65C4×#11758196C2214yes—
66C4×C4⋊Dic61C2212yes—
67C4×C4⋊Dic61C2212yes—
68C4×C4⋊Dic61C2211yescharacteristic
69#16839613C2214yes—
70#16839613C2212yes—
71#16839613C2214yes—
72#95×D61C2214yes—
73#95×D61C2214yes—
74#95×D61C2212yes—
75#95×D61C2214yes—
76C2×C4×Q8×C61C2211yescharacteristic
77C61×#391C2212yes—
78C61×#387C2214yes—
79C61×#384C2211yescharacteristic
80C61×#382C2212yes—
81C4×C4⋊C4×C61C2212yes—
82C4×C4⋊C4×C61C2211yescharacteristic
83C4×C4⋊C4×C61C2212yes—
84C22×Dic122C2312yes—
85C22×Dic122C2311yescharacteristic
86C2×Q8×D61—24no—
87C2×Q8×D61—24no—
88C2×Q8×D61C2×C418yes—
89C22×C4×D61C2314yes—
90C22×C4×D61C2312yes—
91C22×C4×D61C2312yes—
92C22×C4×D61C2311yescharacteristic
93C22×C4×D61C2312yes—
94C22×C4×D61C2312yes—
95C22×C4×D61C2311yescharacteristic
96C22×C4×D61C2311yescharacteristic
97Q8×Dic61C2×C418yescomplemented
98C4×Dic122C2×C4116yescomplemented
99C4×Dic122C2×C418yescomplemented
100#14519742C2×C418yescomplemented
101#14519742C2×C4116yescomplemented
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2312yes—
104C2×C4⋊Dic61C2312yes—
105C2×C4⋊Dic61C2312yes—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2312yes—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196C2312yes—
110C2×#11758196C2314yes—
111C2×#11758196C2314yes—
112C2×#11758196C2314yes—
113C2×#11758196C2312yes—
114C2×#11758196C2312yes—
115C2×#11758196C2312yes—
116C2×#11758196C2312yes—
117C4⋊C4×D61—28no—
118C4⋊C4×D61—24no—
119C4⋊C4×D61—28no—
120C4⋊C4×D61—44no—
121C4⋊C4×D61C2×C4116yes—
122C4⋊C4×D61C2×C418yes—
123C4⋊C4×D61Q818yescomplemented
124C2×C4×Dic61C2312yes—
125C2×C4×Dic61C2312yes—
126C2×C4×Dic61C2312yes—
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2311yescharacteristic
131C2×C4×Dic61C2312yes—
132C2×C4×Dic61C2312yes—
133C2×C4×Dic61C2311yescharacteristic
134C2×C4×Dic61C2312yes—
135C2×C4×Dic61C2311yescharacteristic
136C42×D61—28no—
137C42×D61—48no—
138C42×D61C2×C4116yes—
139C42×D61C2×C418yes—
140#14519684C2314yes—
141#14519684C2312yes—
142#14519684C2314yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146#14519684C2312yes—
147#14519684C2312yes—
148#14519684C2314yes—
149#14519684C2314yes—
150#14519684C2314yes—
151#14519684C2314yes—
152C22×Q8×C61C2311yescharacteristic
153C4×Q8×C61C2×C418yescomplemented
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2312yes—
156C2×C4⋊C4×C61C2312yes—
157C2×C4⋊C4×C61C2312yes—
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C4⋊C4×C61C2312yes—
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C42×C61C2312yes—
162C2×C42×C61C2314yes—
163C2×C42×C61C2312yes—
164C2×C42×C61C2311yescharacteristic
165#95×C61C2314yes—
166#95×C61C2312yes—
167#95×C61C2314yes—
168#95×C61C2314yes—
169C23×D61C2411yescharacteristic
170C2×Q8×C61—22no—
171C2×Q8×C61—22no—
172C2×Q8×C61C22×C414yes—
173C22×C4×C61C2412yes—
174C22×C4×C61C2414yes—
175C22×C4×C61C2412yes—
176C22×C4×C61C2412yes—
177C22×C4×C61C2411yescharacteristic
178C22×C4×C61C2412yes—
179C22×C4×C61C2411yescharacteristic
180C22×C4×C61C2411yescharacteristic
181C22×Dic61C2412yes—
182C22×Dic61C2414yes—
183C22×Dic61C2412yes—
184C22×Dic61C2412yes—
185C22×Dic61C2411yescharacteristic
186C22×Dic61C2412yes—
187C22×Dic61C2411yescharacteristic
188C22×Dic61C2411yescharacteristic
189Q8×D61—232no—
190C2×C4×D61—24no—
191C2×C4×D61—24no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—24no—
195C2×C4×D61—22no—
196C2×C4×D61—24no—
197C2×C4×D61—22no—
198C2×C4×D61—24no—
199C2×C4×D61—24no—
200C2×C4×D61—28no—
201C2×C4×D61—28no—
202C2×C4×D61—28no—
203C2×C4×D61—24no—
204C2×C4×D61C22×C418yes—
205C2×C4×D61C22×C418yes—
206C2×C4×D61C22×C414yes—
207C2×C4×D61C22×C414yes—
208C2×C4×D61C22×C414yes—
209C2×C4×D61C2×Q818yes—
210C2×C4×D61C2×Q814yes—
211C2×C4×D61#4114yes—
212C2×C4×D61#4114yes—
213C2×C4×D61#4114yes—
214C2×Dic122—22no—
215C2×Dic122—22no—
216C2×Dic122—24no—
217C2×Dic122—24no—
218C2×Dic122C22×C414yes—
219C2×Dic122C22×C418yes—
220C4⋊C4×C61—24no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—24no—
223C4⋊C4×C61—42no—
224C4⋊C4×C61C22×C418yes—
225C4⋊C4×C61C22×C414yes—
226C4⋊C4×C61C2×Q814yescomplemented
227C42×C61—24no—
228C42×C61—44no—
229C42×C61C22×C418yes—
230C42×C61C22×C414yes—
231C4⋊Dic61—24no—
232C4⋊Dic61—22no—
233C4⋊Dic61—24no—
234C4⋊Dic61—42no—
235C4⋊Dic61C22×C418yes—
236C4⋊Dic61C22×C414yes—
237C4⋊Dic61C2×Q814yescomplemented
238#11758196—28no—
239#11758196—24no—
240#11758196—28no—
241#11758196—44no—
242#11758196C22×C418yes—
243#11758196C22×C418yes—
244#11758196C22×C418yes—
245#11758196C2×Q818yescomplemented
246C4×Dic61—24no—
247C4×Dic61—24no—
248C4×Dic61—24no—
249C4×Dic61—44no—
250C4×Dic61—44no—
251C4×Dic61—44no—
252C4×Dic61C22×C418yes—
253C4×Dic61C22×C414yes—
254C4×Dic61C22×C418yes—
255C4×Dic61C22×C414yes—
256C4×Dic61C22×C418yes—
257C4×Dic61C22×C414yes—
258C23×C61C2511yescharacteristic
259C22×D61C23×C412yes—
260C22×D61C22×Q812yes—
261C22×D61C2×#4112yes—
262C22×D61C2×#4112yes—
263C22×D61C2×#4112yes—
264C22×D61H(5,𝔽2)12yes—
265C22×D612−1+412yes—
266Q8×C61—28no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—24no—
280C2×C4×C61—22no—
281C2×C4×C61C23×C414yes—
282C2×C4×C61C23×C412yes—
283C2×C4×C61C23×C414yes—
284C2×C4×C61C23×C412yes—
285C2×C4×C61C23×C412yes—
286C2×C4×C61C22×Q814yes—
287C2×C4×C61C22×Q812yes—
288C2×C4×C61C2×#4112yes—
289C2×C4×C61C2×#4112yes—
290C2×C4×C61C2×#4112yes—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—21no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—24no—
302C2×Dic61—24no—
303C2×Dic61—24no—
304C2×Dic61—22no—
305C2×Dic61C23×C414yes—
306C2×Dic61C23×C412yes—
307C2×Dic61C23×C414yes—
308C2×Dic61C23×C412yes—
309C2×Dic61C23×C412yes—
310C2×Dic61C22×Q814yes—
311C2×Dic61C22×Q812yes—
312C2×Dic61C2×#4112yes—
313C2×Dic61C2×#4112yes—
314C2×Dic61C2×#4112yes—
315C4×D61—216no—
316C4×D61—216no—
317C4×D61—28no—
318C4×D61—216no—
319C4×D61—48no—
320C4×D61—416no—
321C4×D61#117116yes—
322C4×D61C4×Q8116yes—
323Dic122—28no—
324Dic122—216no—
325C2×#2355—611nomaximal, Sylow
326C22×C61C24×C411yescharacteristic
327C22×C61C23×Q811yescharacteristic
328C22×C61C22×#4111yescharacteristic
329C22×C61C22×#4111yescharacteristic
330C22×C61C22×#4111yescharacteristic
331C22×C61C2×H(5,𝔽2)11yescharacteristic
332C22×C61C2×2−1+411yescharacteristic
333C2×D61C2×#11714yes—
334C2×D61C2×C4×Q814yes—
335C2×D61#52014yes—
336C2×D61#55414yes—
337C2×D61#55614yes—
338C2×D61#55714yes—
339C2×D61#55914yes—
340C4×C61—24no—
341C4×C61—24no—
342C4×C61—22no—
343C4×C61—24no—
344C4×C61—42no—
345C4×C61—44no—
346C4×C61C2×#11714yes—
347C4×C61C2×C4×Q814yes—
348Dic61—24no—
349Dic61—24no—
350Dic61—22no—
351Dic61—24no—
352Dic61—42no—
353Dic61—44no—
354Dic61C2×#11714yes—
355Dic61C2×C4×Q814yes—
356C22×C4×Q8—611no—
357#2355—612no—
358#2355—614no—
359#2355—611no—
360#2355—612no—
361#2355—612no—
362#2355—611no—
363#2355—612no—
364#2355—611no—
365#2355D6111yescharacteristic, direct product factor
366C2×#391—612no—
367C2×#387—614no—
368C2×#384—611no—
369C2×#382—612no—
370C2×C4×C4⋊C4—612no—
371C2×C4×C4⋊C4—611no—
372C2×C4×C4⋊C4—612no—
373C2×C61C22×#11711yescharacteristic
374C2×C61C22×C4×Q811yescharacteristic
375C2×C61C2×#52011yescharacteristic
376C2×C61C2×#55411yescharacteristic
377C2×C61C2×#55611yescharacteristic
378C2×C61C2×#55711yescharacteristic
379C2×C61C2×#55911yescharacteristic
380D61#235518yesdirect product factor
381C23×Q8—611no—
382C2×C4×Q8—611no—
383C2×C4×Q8—6116no—
384C2×C4×Q8—612no—
385C2×C4×Q8—611no—
386C2×C4×Q8—611no—
387C2×C4×Q8—612no—
388C2×C4×Q8C2×D6111yescharacteristic
389C22×C4⋊C4—611no—
390C22×C4⋊C4—612no—
391C22×C4⋊C4—611no—
392C22×C4⋊C4—611no—
393C22×C4⋊C4—612no—
394C22×C4⋊C4—612no—
395C22×C4⋊C4—612no—
396C22×C42—612no—
397C22×C42—611no—
398C22×C42—612no—
399C22×C42—614no—
400#391—612no—
401#391—612no—
402#391—612no—
403#391—614no—
404#391—614no—
405#391C2×D6112yes—
406#387—614no—
407#387—614no—
408#387—614no—
409#387—614no—
410#387—614no—
411#387—614no—
412#387—614no—
413#387C2×D6114yes—
414#384—612no—
415#384—612no—
416#384—612no—
417#384—611no—
418#384C2×D6111yescharacteristic
419#382—612no—
420#382—612no—
421#382—612no—
422#382—614no—
423#382—614no—
424#382C2×D6112yes—
425C4×C4⋊C4—612no—
426C4×C4⋊C4—612no—
427C4×C4⋊C4—611no—
428C4×C4⋊C4—611no—
429C4×C4⋊C4—612no—
430C4×C4⋊C4—612no—
431C4×C4⋊C4—612no—
432C4×C4⋊C4—611no—
433C4×C4⋊C4—612no—
434C4×C4⋊C4—614no—
435C4×C4⋊C4—612no—
436C4×C4⋊C4—614no—
437C4×C4⋊C4—614no—
438C4×C4⋊C4—612no—
439C4×C4⋊C4—614no—
440C4×C4⋊C4C2×D6112yes—
441C4×C4⋊C4C2×D6111yescharacteristic
442C4×C4⋊C4C2×D6112yes—
443C2×#95—614no—
444C2×#95—612no—
445C2×#95—614no—
446C2×#95—614no—
447C61C2×#235511yescharacteristic, complemented, Sylow
448C22×Q8—618no—
449C22×Q8—612no—
450C22×Q8—611no—
451C22×Q8—1224no—
452C22×Q8—1224no—
453C22×Q8C22×D6111yescharacteristic
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—612no—
458C23×C4—612no—
459C23×C4—612no—
460C23×C4—614no—
461C23×C4—612no—
462C4×Q8—618no—
463C4×Q8—6116no—
464C4×Q8—618no—
465C4×Q8—6116no—
466C4×Q8—618no—
467C4×Q8C4×D6118yescomplemented
468C2×C4⋊C4—612no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—612no—
471C2×C4⋊C4—612no—
472C2×C4⋊C4—612no—
473C2×C4⋊C4—612no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—618no—
476C2×C4⋊C4—6116no—
477C2×C4⋊C4—618no—
478C2×C4⋊C4—612no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—612no—
482C2×C4⋊C4—614no—
483C2×C4⋊C4—612no—
484C2×C4⋊C4—614no—
485C2×C4⋊C4—612no—
486C2×C4⋊C4—1224no—
487C2×C4⋊C4—1228no—
488C2×C4⋊C4—1228no—
489C2×C4⋊C4—2444no—
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6112yes—
492C2×C4⋊C4C22×D6112yes—
493C2×C4⋊C4C22×D6112yes—
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6112yes—
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C42—612no—
498C2×C42—612no—
499C2×C42—612no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—611no—
503C2×C42—618no—
504C2×C42—6116no—
505C2×C42—612no—
506C2×C42—612no—
507C2×C42—612no—
508C2×C42—614no—
509C2×C42—614no—
510C2×C42—614no—
511C2×C42—1228no—
512C2×C42—2448no—
513C2×C42C22×D6112yes—
514C2×C42C22×D6114yes—
515C2×C42C22×D6112yes—
516C2×C42C22×D6111yescharacteristic
517#95—614no—
518#95—614no—
519#95—614no—
520#95—612no—
521#95—612no—
522#95—612no—
523#95—614no—
524#95—614no—
525#95—614no—
526#95—614no—
527#95—614no—
528#95—614no—
529#95C22×D6114yes—
530#95C22×D6112yes—
531#95C22×D6114yes—
532#95C22×D6114yes—
533C24—611no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—618no—
537C2×Q8—614no—
538C2×Q8—1224no—
539C2×Q8—1224no—
540C2×Q8—12232no—
541C2×Q8—1222no—
542C2×Q8—1222no—
543C2×Q8C2×C4×D6114yes—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—614no—
547C22×C4—614no—
548C22×C4—614no—
549C22×C4—614no—
550C22×C4—614no—
551C22×C4—614no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—611no—
556C22×C4—614no—
557C22×C4—618no—
558C22×C4—618no—
559C22×C4—618no—
560C22×C4—612no—
561C22×C4—614no—
562C22×C4—1224no—
563C22×C4—1224no—
564C22×C4—1224no—
565C22×C4—1222no—
566C22×C4—1224no—
567C22×C4—1224no—
568C22×C4—1222no—
569C22×C4—1224no—
570C22×C4—1224no—
571C22×C4—1228no—
572C22×C4—1228no—
573C22×C4—1228no—
574C22×C4—1224no—
575C22×C4—1224no—
576C22×C4C23×D6112yes—
577C22×C4C23×D6114yes—
578C22×C4C23×D6112yes—
579C22×C4C23×D6112yes—
580C22×C4C23×D6111yescharacteristic
581C22×C4C23×D6112yes—
582C22×C4C23×D6111yescharacteristic
583C22×C4C23×D6111yescharacteristic
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—24no—
587C4⋊C4—42no—
588C4⋊C4—618no—
589C4⋊C4—618no—
590C4⋊C4—618no—
591C4⋊C4—618no—
592C4⋊C4—614no—
593C4⋊C4—618no—
594C4⋊C4—614no—
595C4⋊C4—1224no—
596C4⋊C4—1228no—
597C4⋊C4—1228no—
598C4⋊C4—1224no—
599C4⋊C4—1222no—
600C4⋊C4—1224no—
601C4⋊C4—2444no—
602C4⋊C4—2442no—
603C4⋊C4C2×C4×D6118yes—
604C4⋊C4C2×C4×D6114yes—
605C4⋊C4Q8×D6114yescomplemented
606C42—24no—
607C42—44no—
608C42—614no—
609C42—618no—
610C42—614no—
611C42—618no—
612C42—614no—
613C42—618no—
614C42—1224no—
615C42—1224no—
616C42—1224no—
617C42—2444no—
618C42—2444no—
619C42—2444no—
620C42C2×C4×D6118yes—
621C42C2×C4×D6114yes—
622C23—612no—
623C23—612no—
624C23—612no—
625C23—612no—
626C23—612no—
627C23—612no—
628C23—612no—
629C23C24×D6111yescharacteristic
630Q8—28no—
631Q8—12216no—
632Q8—1228no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—612no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—612no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—6116no—
654C2×C4—6116no—
655C2×C4—614no—
656C2×C4—612no—
657C2×C4—614no—
658C2×C4—614no—
659C2×C4—12216no—
660C2×C4—1228no—
661C2×C4—12216no—
662C2×C4—12216no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1221no—
669C2×C4—1222no—
670C2×C4—1221no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1224no—
674C2×C4—1224no—
675C2×C4—1224no—
676C2×C4—1222no—
677C2×C4—2448no—
678C2×C4—24416no—
679C2×C4C22×C4×D6114yes—
680C2×C4C22×C4×D6112yes—
681C2×C4C22×C4×D6114yes—
682C2×C4C22×C4×D6112yes—
683C2×C4C22×C4×D6112yes—
684C2×C4C2×Q8×D6114yes—
685C2×C4C2×Q8×D6112yes—
686C2×C4#41×D6112yes—
687C2×C4#41×D6112yes—
688C2×C4#41×D6112yes—
689C22—614no—
690C22—614no—
691C22—614no—
692C22—614no—
693C22—614no—
694C22—614no—
695C22—614no—
696C22C23×C4×D6111yescharacteristic
697C22C22×Q8×D6111yescharacteristic
698C22C2×#41×D6111yescharacteristic
699C22C2×#41×D6111yescharacteristic
700C22C2×#41×D6111yescharacteristic
701C22H(5,𝔽2)×D6111yescharacteristic
702C222−1+4×D6111yescharacteristic
703C4—24no—
704C4—24no—
705C4—22no—
706C4—24no—
707C4—42no—
708C4—44no—
709C4—614no—
710C4—614no—
711C4—1224no—
712C4—1224no—
713C4—1222no—
714C4—1224no—
715C4—2442no—
716C4—2444no—
717C4#117×D6114yes—
718C4C4×Q8×D6114yes—
719C2—618no—
720C2C2×#117×D6111yescharacteristic
721C2C2×C4×Q8×D6111yescharacteristic
722C2#520×D6111yescharacteristic
723C2#554×D6111yescharacteristic
724C2#556×D6111yescharacteristic
725C2#557×D6111yescharacteristic
726C2#559×D6111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2355C2
socle, cosocleC23×C61C25
prime radicalC23×D61C24
hypercenter#2355D61
hypocenterC61C2×#2355
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. #21448778C2semidirect
3. #21448777C2semidirect
4. #21448776C2semidirect
5. #21448775C2semidirect
6. #21448774C2semidirect
7. #21448773C2semidirect
8. #21448772C2semidirect
9. #21448771C2semidirect
17. C61×#2355C2semidirect
24. C4×Q8×D61C4semidirect
97. Q8×Dic61C2×C4semidirect
98. C4×Dic122C2×C4semidirect
99. C4×Dic122C2×C4semidirect
100. #14519742C2×C4semidirect
101. #14519742C2×C4semidirect
123. C4⋊C4×D61Q8semidirect
153. C4×Q8×C61C2×C4semidirect
226. C4⋊C4×C61C2×Q8semidirect
237. C4⋊Dic61C2×Q8semidirect
245. #11758196C2×Q8semidirect
365. #2355D61direct (N × H)
380. D61#2355direct (N × H)
447. C61C2×#2355semidirect
467. C4×Q8C4×D61semidirect
605. C4⋊C4Q8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D612
#214487782
#214487772
#214487762
#214487752
#214487742
#214487732
#214487722
#214487712
#391×D612
#387×D612
#384×D612
#382×D612
C4×C4⋊C4×D612
C61×#23552
C2×#235561