Finite Group Databasebeta

← D61⋊#1508 #30610928

Subgroups — D61⋊#1508 #30610928

Order 15616.

1554 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21461219C212yesmaximal, complemented
4#21461218C212yesmaximal, complemented
5#21461217C214yesmaximal, complemented
6D61⋊#328C214yesmaximal, complemented
7C2×C22⋊Q8×D61C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9C22×C22⋊#6923—21no—
10C22×C4×#6923—21no—
11#16840734C2212yes—
12#16840733—21no—
13#16840733C2212yes—
14#16840732—21no—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)C2212yes—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923C2212yes—
20C4×C22⋊#6923C2212yes—
21C2×(C2×#6923)⋊C4C2212yes—
22#16840616C2218yescomplemented
23#16840615C2218yescomplemented
24C22×Q8×D61C411yescharacteristic, complemented
25C23×C4×D61C2211yescharacteristic
26C2×#14519757C2211yescharacteristic
27C2×#14519756C411yescharacteristic, complemented
28C2×#14519755—21no—
29C2×#14519754—21no—
30C2×#14519753C2211yescharacteristic
31C22⋊Q8×D61—21no—
32C22⋊Q8×D61—21no—
33C22⋊Q8×D61—21no—
34C22⋊Q8×D61—21no—
35C22⋊Q8×D61C412yescomplemented
36C22⋊Q8×D61C412yescomplemented
37C22⋊Q8×D61C2212yes—
38C22⋊Q8×D61C2212yes—
39C2×C4⋊C4×D61—21no—
40C2×C4⋊C4×D61C411yescharacteristic, complemented
41C2×C22⋊C4×D61—21no—
42C2×C22⋊Q8×C61C411yescharacteristic, complemented
43C23×#6923—22no—
44C2×#11758213—22no—
45D61⋊M16—44no—
46C2×#11758217—22no—
47C2×D61⋊C8—22no—
48C2×C22⋊#6923—28no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923—22no—
51C2×C4×#6923—22no—
52C2×C4×#6923—22no—
53C2×C4×#6923—44no—
54#14519834—22no—
55#14519834C2314yes—
56C22⋊#92420—22no—
57C22⋊#92420—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4C2314yes—
60C24×D61D411yescharacteristic
61C22×Dic122—21no—
62C22×Dic122C2×C411yescharacteristic, complemented
63C2×Q8×D61—21no—
64C2×Q8×D61—21no—
65C2×Q8×D61—44no—
66C2×Q8×D61C2×C412yes—
67C2×Q8×D61C2×C412yescomplemented
68C23×Dic61D411yescharacteristic
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—44no—
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84#14519757—21no—
85#14519757—21no—
86#14519757C2×C412yescomplemented
87#14519757C2312yes—
88#14519756—21no—
89#14519756—21no—
90#14519756C2×C412yes—
91#14519756C2×C412yescomplemented
92#14519755—22no—
93#14519755—22no—
94#14519755—22no—
95#14519755—22no—
96#14519754—22no—
97#14519754—22no—
98#14519754—22no—
99#14519754—22no—
100#14519753—21no—
101#14519753—21no—
102#14519753C2×C412yescomplemented
103#14519753C2312yes—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61C2×C411yescharacteristic, complemented
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—21no—
112C4⋊C4×D61—21no—
113C4⋊C4×D61—22no—
114C4⋊C4×D61—22no—
115C4⋊C4×D61C2×C412yes—
116C4⋊C4×D61C2×C412yescomplemented
117C2×C22⋊Dic61—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C22⋊C4×D61—22no—
121C22⋊C4×D61—22no—
122C22⋊C4×D61—22no—
123C22⋊C4×D61—22no—
124C22×Q8×C61C2×C411yescharacteristic, complemented
125C23×C4×C61C2×C411yescharacteristic
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61C2×C412yes—
129C22⋊Q8×C61C2×C412yescomplemented
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
132C2×C22⋊C4×C61—21no—
133C24×C61C22⋊C411yescharacteristic
134C23×D61—24no—
135C23×D61—24no—
136C23×D61—42no—
137C23×D61C22⋊C411yescharacteristic
138C23×D61C22⋊C411yescharacteristic
139C23×D61C22⋊C411yescharacteristic
140C23×D61C2×D411yescharacteristic
141C23×D61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C22×#6923—28no—
144C22×#6923—24no—
145C22×#6923—44no—
146C22×#6923—44no—
147C2×Q8×C61—21no—
148C2×Q8×C61—42no—
149C2×Q8×C61C22×C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—42no—
153C22×C4×C61C22⋊C411yescharacteristic
154C22×C4×C61C22⋊C411yescharacteristic
155C22×C4×C61C22⋊C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—42no—
162C22×Dic61C22⋊C411yescharacteristic
163C22×Dic61C22⋊C411yescharacteristic
164C22×Dic61C22⋊C411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168Q8×D61—44no—
169Q8×D61—44no—
170Q8×D61—44no—
171Q8×D61—44no—
172C2×C4×D61—24no—
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—44no—
189C2×C4×D61—44no—
190C2×C4×D61C22⋊C411yescharacteristic
191C2×C4×D61C22⋊C411yescharacteristic
192C2×C4×D61C22⋊C411yescharacteristic
193C2×C4×D61C22⋊C411yescharacteristic
194C2×C4×D61C22⋊C411yescharacteristic
195C2×C4×D61C22⋊C411yescharacteristic
196C2×C4×D61C22×C411yescharacteristic
197C2×C4×D61C22×C411yescharacteristic
198C2×C4×D61C22×C411yescharacteristic
199C2×C4×D61C2×D411yescharacteristic
200C2×C4×D61C2×D411yescharacteristic
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2×D411yescharacteristic
205C2×C4×D61C2411yescharacteristic
206C2×Dic122—21no—
207C2×Dic122—22no—
208C2×Dic122—22no—
209C2×Dic122—44no—
210C2×Dic122—42no—
211C2×Dic122C22×C412yes—
212C22⋊#6923—28no—
213C22⋊#6923—28no—
214#11758217—44no—
215C2×#92420—24no—
216C4×#6923—44no—
217C4×#6923—44no—
218#11758213—44no—
219D61⋊C8—44no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61C22×C412yes—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232C4⋊Dic61—21no—
233C4⋊Dic61—22no—
234C4⋊Dic61—22no—
235C4⋊Dic61C22×C412yes—
236#11758196—22no—
237#11758196—22no—
238#11758196—22no—
239#11758196—22no—
240#11758196—22no—
241#11758196—22no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—41no—
245C23×C61C2×C22⋊C411yescharacteristic
246C23×C61C2×C22⋊C411yescharacteristic
247C23×C61C2×C22⋊C411yescharacteristic
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—416no—
265C22×D61#10414yes—
266C22×D61C2×C22⋊C411yescharacteristic
267C22×D61C2×C22⋊C411yescharacteristic
268C22×D61C2×C22⋊C411yescharacteristic
269C22×D61#13714yes—
270C22×D61C22×D411yescharacteristic
271C2×#6923—28no—
272C2×#6923—44no—
273C2×#6923—416no—
274C2×#6923—44no—
275Q8×C61—42no—
276Q8×C61—42no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61C2×C22⋊C411yescharacteristic
288C2×C4×C61C2×C22⋊C411yescharacteristic
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C23×C411yescharacteristic
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61C2×C22⋊C411yescharacteristic
302C2×Dic61C2×C22⋊C411yescharacteristic
303C2×Dic61C2×C22⋊C411yescharacteristic
304C2×Dic61C22×D411yescharacteristic
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—44no—
321C4×D61—44no—
322C4×D61—44no—
323C4×D61—44no—
324C4×D61#9914yes—
325Dic122—44no—
326Dic122—42no—
327Dic122—44no—
328Dic122—42no—
329#92420—44no—
330C2×#1508—611nomaximal, Sylow
331C22×C61—21no—
332C22×C61—21no—
333C22×C61—21no—
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—44no—
339C22×C61#41912yes—
340C22×C61C2×#10412yes—
341C22×C61C22×C22⋊C411yescharacteristic
342C2×D61—21no—
343C2×D61—21no—
344C2×D61—21no—
345C2×D61—21no—
346C2×D61—28no—
347C2×D61—28no—
348C2×D61—21no—
349C2×D61—21no—
350C2×D61—21no—
351C2×D61—44no—
352C2×D61—44no—
353C2×D61—44no—
354C2×D61—44no—
355C2×D61C2×#9912yes—
356C2×D61#41912yes—
357C2×D61C2×#10412yes—
358C2×D61C2×#10412yes—
359C2×D61C2×#13712yes—
360#6923—48no—
361C4×C61—21no—
362C4×C61—21no—
363C4×C61—21no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61C2×#9912yes—
367Dic61—21no—
368Dic61—21no—
369Dic61—21no—
370Dic61—42no—
371Dic61—42no—
372Dic61C2×#9912yes—
373C22×C22⋊Q8—611no—
374C2×#407—611no—
375C2×C4×C22⋊C4—611no—
376#1508—614no—
377#1508—612no—
378#1508—612no—
379C2×#328—614no—
380C2×C61—22no—
381C2×C61—22no—
382C2×C61—41no—
383C2×C61C22×#9911yescharacteristic
384C2×C61C2×#41911yescharacteristic
385C2×C61C22×#10411yescharacteristic
386D61—22no—
387D61—22no—
388D61—41no—
389D61#150814yescomplemented
390C23×Q8—611no—
391C24×C4—611no—
392C22×M16—1221no—
393C2×C22⋊Q8—611no—
394C2×C22⋊Q8—611no—
395C2×C22⋊Q8—612no—
396C2×C22⋊Q8—612no—
397C2×C22⋊Q8—612no—
398C2×C22⋊Q8—612no—
399C2×C22⋊Q8—611no—
400C2×C22⋊Q8—1221no—
401C2×C22⋊Q8—1221no—
402C2×C22⋊Q8—1221no—
403C2×C22⋊Q8—1221no—
404C2×C22⋊Q8—1221no—
405C2×C22⋊Q8—1221no—
406C2×C22⋊Q8#692311yescharacteristic, complemented
407C22×C4⋊C4—611no—
408C22×C4⋊C4—1221no—
409C22×C22⋊C4—1221no—
410C22×C22⋊C4—1221no—
411C22×C42—1221no—
412#407—612no—
413#407—612no—
414#407—1221no—
415#407—1221no—
416C2×C22⋊C8—612no—
417C2×C22⋊C8—1221no—
418C4×C22⋊C4—612no—
419C4×C22⋊C4—612no—
420C4×C22⋊C4—1221no—
421C4×C22⋊C4—1221no—
422C2×#95—612no—
423#328—618no—
424#328—618no—
425C61C2×#150811yescharacteristic, complemented, Sylow
426C25—611no—
427C22×Q8—612no—
428C22×Q8—612no—
429C22×Q8—611no—
430C22×Q8—1221no—
431C22×Q8—1221no—
432C22×Q8—1221no—
433C22×Q8—2444no—
434C22×Q8C2×#692311yescharacteristic, complemented
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—1221no—
449C23×C4—1221no—
450C23×C4—1222no—
451C23×C4—2444no—
452C23×C4C2×#692311yescharacteristic
453C2×M16—1222no—
454C2×M16—1222no—
455C2×M16—2444no—
456C22×C8—1222no—
457C22⋊Q8—21no—
458C22⋊Q8—21no—
459C22⋊Q8—612no—
460C22⋊Q8—612no—
461C22⋊Q8—612no—
462C22⋊Q8—612no—
463C22⋊Q8—612no—
464C22⋊Q8—612no—
465C22⋊Q8—1222no—
466C22⋊Q8—1222no—
467C22⋊Q8—1222no—
468C22⋊Q8—1222no—
469C22⋊Q8—1222no—
470C22⋊Q8—1222no—
471C22⋊Q8—1222no—
472C22⋊Q8—1222no—
473C22⋊Q8—1221no—
474C22⋊Q8—1221no—
475C22⋊Q8—1221no—
476C22⋊Q8—1221no—
477C22⋊Q8—1221no—
478C22⋊Q8—1221no—
479C22⋊Q8C2×#692312yes—
480C22⋊Q8C2×#692312yescomplemented
481C2×C4⋊C4—21no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—612no—
484C2×C4⋊C4—612no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1222no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4C2×#692311yescharacteristic, complemented
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1222no—
498C2×C22⋊C4—1222no—
499C2×C22⋊C4—1222no—
500C2×C22⋊C4—1222no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1222no—
504C2×C22⋊C4—1222no—
505C2×C22⋊C4—1228no—
506C2×C22⋊C4—1221no—
507C2×C42—1222no—
508C2×C42—1222no—
509C2×C42—2444no—
510C22⋊C8—614no—
511C22⋊C8—1222no—
512C22⋊C8—1222no—
513C22⋊C8—1222no—
514#95—614no—
515#95—1222no—
516C24—611no—
517C24—611no—
518C24—611no—
519C24—611no—
520C24—611no—
521C24—611no—
522C24—1224no—
523C24—1224no—
524C24—2442no—
525C24C22⋊#692311yescharacteristic
526C2×Q8—21no—
527C2×Q8—42no—
528C2×Q8—612no—
529C2×Q8—1222no—
530C2×Q8—1222no—
531C2×Q8—1221no—
532C2×Q8—2442no—
533C2×Q8—2444no—
534C2×Q8—2444no—
535C2×Q8—2444no—
536C2×Q8—2444no—
537C2×Q8—2444no—
538C2×Q8C22×#692312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—1224no—
565C22×C4—1224no—
566C22×C4—1224no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1224no—
572C22×C4—1228no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4—2444no—
585C22×C4—2444no—
586C22×C4—2442no—
587C22×C4—2444no—
588C22×C4—2444no—
589C22×C4C22⋊#692311yescharacteristic
590C22×C4C22⋊#692311yescharacteristic
591C22×C4C22⋊#692311yescharacteristic
592C22×C4C22×#692311yescharacteristic
593C22×C4C22×#692311yescharacteristic
594C22×C4C22×#692311yescharacteristic
595M16—2444no—
596M16—2444no—
597C2×C8—1224no—
598C2×C8—2444no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—612no—
603C4⋊C4—1222no—
604C4⋊C4—1222no—
605C4⋊C4—1222no—
606C4⋊C4—1222no—
607C4⋊C4—1222no—
608C4⋊C4—1222no—
609C4⋊C4—1221no—
610C4⋊C4—1222no—
611C4⋊C4—1222no—
612C4⋊C4C22×#692312yes—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1228no—
620C22⋊C4—1228no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C42—2444no—
624C42—2444no—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—611no—
629C23—614no—
630C23—614no—
631C23—611no—
632C23—611no—
633C23—611no—
634C23—1222no—
635C23—1222no—
636C23—1222no—
637C23—1222no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—1222no—
645C23—1222no—
646C23—1222no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—24416no—
651C23C2×C22⋊#692311yescharacteristic
652C23C2×C22⋊#692311yescharacteristic
653C23C2×C22⋊#692311yescharacteristic
654Q8—42no—
655Q8—42no—
656Q8—2442no—
657Q8—2444no—
658Q8—2444no—
659Q8—2442no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—611no—
671C2×C4—614no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—611no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1228no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2444no—
697C2×C4—2444no—
698C2×C4—2444no—
699C2×C4—2444no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2442no—
704C2×C4—2444no—
705C2×C4—2444no—
706C2×C4—24416no—
707C2×C4—2442no—
708C2×C4C2×C22⋊#692311yescharacteristic
709C2×C4C2×C22⋊#692311yescharacteristic
710C2×C4C2×C22⋊#692311yescharacteristic
711C2×C4C23×#692311yescharacteristic
712C8—2444no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—44no—
721C22—612no—
722C22—612no—
723C22—612no—
724C22—612no—
725C22—612no—
726C22—1228no—
727C22—1228no—
728C22—1221no—
729C22—1221no—
730C22—1221no—
731C22—1221no—
732C22—1221no—
733C22—1221no—
734C22—1221no—
735C22—2444no—
736C22—2444no—
737C22—2444no—
738C22—2444no—
739C22#1684075512yes—
740C22D61⋊#10412yes—
741C22C22×C22⋊#692311yescharacteristic
742C4—21no—
743C4—21no—
744C4—21no—
745C4—42no—
746C4—42no—
747C4—612no—
748C4—1221no—
749C4—1221no—
750C4—1221no—
751C4—2448no—
752C4—2442no—
753C4—2442no—
754C4D61⋊#9912yes—
755C2—22no—
756C2—22no—
757C2—41no—
758C2—614no—
759C2—1222no—
760C2—1222no—
761C2—2441no—
762C2C2×D61⋊#9911yescharacteristic
763C2C2×#1684075511yescharacteristic
764C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC2×C4×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61C2×#1508
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21461219C2semidirect
4. #21461218C2semidirect
5. #21461217C2semidirect
6. D61⋊#328C2semidirect
22. #16840616C22semidirect
23. #16840615C22semidirect
24. C22×Q8×D61C4semidirect
27. C2×#14519756C4semidirect
35. C22⋊Q8×D61C4semidirect
36. C22⋊Q8×D61C4semidirect
40. C2×C4⋊C4×D61C4semidirect
42. C2×C22⋊Q8×C61C4semidirect
62. C22×Dic122C2×C4semidirect
67. C2×Q8×D61C2×C4semidirect
86. #14519757C2×C4semidirect
91. #14519756C2×C4semidirect
102. #14519753C2×C4semidirect
105. C2×C4⋊Dic61C2×C4semidirect
116. C4⋊C4×D61C2×C4semidirect
124. C22×Q8×C61C2×C4semidirect
129. C22⋊Q8×C61C2×C4semidirect
131. C2×C4⋊C4×C61C2×C4semidirect
389. D61#1508semidirect
406. C2×C22⋊Q8#6923semidirect
425. C61C2×#1508semidirect
434. C22×Q8C2×#6923semidirect
480. C22⋊Q8C2×#6923semidirect
495. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×C4×C22⋊#69232
#214612192
#214612182
#214612172
D61⋊#3282
C2×C22⋊Q8×D612
C2×#150861