Finite Group Databasebeta

← #30610965

Subgroups — #30610965

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#21461218C212yesmaximal, complemented
4#21461216C212yesmaximal, complemented
5#21461207C214yesmaximal, complemented
6#21461196C214yesmaximal, complemented
7C2×#16840274C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9C22×C22⋊#6923—21no—
10C22×C4×#6923—21no—
11#16840734C2212yescomplemented
12#16840733—21no—
13#16840733C2212yes—
14#16840732—21no—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)C2212yescomplemented
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923C2212yes—
20C4×C22⋊#6923C2212yescomplemented
21C2×(C2×#6923)⋊C4C2212yescomplemented
22#16840615C2218yescomplemented
23#16840614C2218yescomplemented
24C22×#11758222C411yescharacteristic, complemented
25C23×C4×D61C2211yescharacteristic
26#16840274—21no—
27#16840274—21no—
28#16840274—21no—
29#16840274—21no—
30#16840274C412yescomplemented
31#16840274C412yescomplemented
32#16840274C2212yes—
33#16840274C2212yes—
34C2×#14519761—21no—
35C2×#14519757C411yescharacteristic, complemented
36C2×#14519757C2211yescharacteristic
37C2×#14519752C411yescharacteristic, complemented
38C2×#14519752C2211yescharacteristic
39C2×#14519747—21no—
40C2×C4×D244—21no—
41C2×C4×D244—21no—
42C2×#117×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
61C2×#11758222—21no—
62C2×#11758222—21no—
63C2×#11758222—44no—
64C2×#11758222C2×C412yes—
65C2×#11758222C2×C412yescomplemented
66C22×Dic122C2×C411yescharacteristic, complemented
67C22×D244—21no—
68C22×D244—21no—
69C22×D244C2×C411yescharacteristic, complemented
70C22×C22⋊D61—21no—
71C23×Dic61D411yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—44no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86#14519761—22no—
87#14519761—22no—
88#14519761—22no—
89#14519761—22no—
90#14519757—21no—
91#14519757—21no—
92#14519757—21no—
93#14519757—21no—
94#14519757C2×C412yes—
95#14519757C2×C412yescomplemented
96#14519757C2×C412yescomplemented
97#14519757C2312yes—
98#14519752—21no—
99#14519752—21no—
100#14519752—21no—
101#14519752—21no—
102#14519752C2×C412yes—
103#14519752C2×C412yescomplemented
104#14519752C2×C412yescomplemented
105#14519752C2312yes—
106#14519747—22no—
107#14519747—22no—
108#14519747—22no—
109#14519747—22no—
110C4×D244—22no—
111C4×D244—22no—
112C4×D244—22no—
113C4×D244—22no—
114C4×D244—22no—
115C4×D244—22no—
116C4×D244—22no—
117C4×D244—22no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C23×C4×C61C2×C411yescharacteristic
125#117×C61—21no—
126#117×C61—21no—
127#117×C61C2×C412yes—
128#117×C61C2×C412yescomplemented
129C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
131C2×C22⋊C4×C61—21no—
132C2×C42×C61—21no—
133C24×C61C22⋊C411yescharacteristic
134C23×D61—24no—
135C23×D61—21no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61C22⋊C411yescharacteristic
139C23×D61C22⋊C411yescharacteristic
140C23×D61C22⋊C411yescharacteristic
141C23×D61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C22×#6923—28no—
145C22×#6923—24no—
146C22×#6923—44no—
147C22×#6923—44no—
148C22×C4×C61—24no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61C22⋊C411yescharacteristic
152C22×C4×C61C22⋊C411yescharacteristic
153C22×C4×C61C22⋊C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—44no—
160C22×Dic61—21no—
161C22×Dic61—42no—
162C22×Dic61C22⋊C411yescharacteristic
163C22×Dic61C22⋊C411yescharacteristic
164C22×Dic61C22⋊C411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168#11758222—44no—
169#11758222—44no—
170#11758222—44no—
171#11758222—44no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—21no—
177C2×D244—44no—
178C2×D244—44no—
179C2×D244—42no—
180C2×D244C22×C412yes—
181C2×C4×D61—24no—
182C2×C4×D61—24no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—44no—
196C2×C4×D61C22⋊C411yescharacteristic
197C2×C4×D61C22⋊C411yescharacteristic
198C2×C4×D61C22⋊C411yescharacteristic
199C2×C4×D61C22⋊C411yescharacteristic
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22×C411yescharacteristic
203C2×C4×D61C22×C411yescharacteristic
204C2×C4×D61C22×C411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122—42no—
214C2×Dic122C22×C412yes—
215C22⋊#6923—28no—
216C22⋊#6923—28no—
217#11758217—44no—
218C2×#92420—24no—
219C4×#6923—44no—
220C4×#6923—44no—
221#11758213—44no—
222D61⋊C8—44no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61C22×C412yes—
226C4⋊C4×C61C22×C412yes—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C42×C61—22no—
230C42×C61—22no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239C4⋊Dic61—22no—
240C4⋊Dic61—22no—
241C4⋊Dic61—22no—
242C4⋊Dic61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—41no—
246C23×C61C2×C22⋊C411yescharacteristic
247C23×C61C2×C22⋊C411yescharacteristic
248C23×C61C2×C22⋊C411yescharacteristic
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—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—416no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61#10414yes—
272C22×D61C2×C22⋊C411yescharacteristic
273C22×D61C2×C22⋊C411yescharacteristic
274C22×D61C2×C22⋊C411yescharacteristic
275C22×D61C22×D411yescharacteristic
276C2×#6923—28no—
277C2×#6923—44no—
278C2×#6923—416no—
279C2×#6923—44no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61#9914yes—
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C23×C411yescharacteristic
294C22⋊D61—44no—
295C22⋊D61—44no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—42no—
304C2×Dic61C2×C22⋊C411yescharacteristic
305C2×Dic61C2×C22⋊C411yescharacteristic
306C2×Dic61C2×C22⋊C411yescharacteristic
307C2×Dic61C22×D411yescharacteristic
308D244—42no—
309D244—44no—
310D244—44no—
311D244—44no—
312D244—44no—
313D244—42no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—41no—
323C4×D61—41no—
324C4×D61—41no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—44no—
331C4×D61—44no—
332Dic122—42no—
333Dic122—42no—
334#92420—44no—
335#17542—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—44no—
344C22×C61C2×#9912yes—
345C22×C61C2×#10412yes—
346C22×C61C22×C22⋊C411yescharacteristic
347C2×D61—28no—
348C2×D61—21no—
349C2×D61—21no—
350C2×D61—21no—
351C2×D61—21no—
352C2×D61—21no—
353C2×D61—21no—
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—44no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61—44no—
361C2×D61—44no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—84no—
366C2×D61C2×#10412yes—
367C2×D61C2×#10412yes—
368C2×D61#57512yes—
369#6923—48no—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—42no—
373C4×C61—42no—
374C4×C61C2×#9912yes—
375C4×C61C2×#9912yes—
376Dic61—21no—
377Dic61—21no—
378Dic61—21no—
379Dic61—21no—
380Dic61—42no—
381C2×#525—611no—
382C2×#407—611no—
383C2×C4×C22⋊C4—611no—
384#1508—612no—
385#1507—612no—
386#1504—614no—
387#1501—614no—
388C2×C61—22no—
389C2×C61—22no—
390C2×C61—41no—
391C2×C61C22×#9911yescharacteristic
392C2×C61#289611yescharacteristic
393C2×C61C22×#10411yescharacteristic
394D61—22no—
395D61—22no—
396D61—22no—
397D61—41no—
398D61—82no—
399C22×#41—611no—
400C24×C4—611no—
401C22×M16—1221no—
402#525—612no—
403#525—612no—
404#525—612no—
405#525—612no—
406#525—1221no—
407#525—1221no—
408#525—1221no—
409#525—1221no—
410C2×#123—1221no—
411C2×C22⋊Q8—611no—
412C2×C22⋊Q8—611no—
413C2×#121—611no—
414C2×#121—611no—
415C2×#120—1221no—
416C2×C4×D4—1221no—
417C2×C4×D4—1221no—
418C2×#117#692311yescharacteristic, complemented
419C22×C22⋊C4—1221no—
420C22×C42—1221no—
421#407—612no—
422#407—612no—
423#407—1221no—
424#407—1221no—
425C2×C22⋊C8—612no—
426C2×C22⋊C8—1221no—
427C4×C22⋊C4—612no—
428C4×C22⋊C4—612no—
429C4×C22⋊C4—1221no—
430C4×C22⋊C4—1221no—
431C2×#95—612no—
432#328—618no—
433#327—618no—
434C61#1754211yescharacteristic, complemented, Sylow
435C25—611no—
436C2×#41—612no—
437C2×#41—612no—
438C2×#41—1221no—
439C2×#41—1221no—
440C2×#41—2444no—
441C22×Q8—611no—
442C22×D4—611no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4—1221no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—1222no—
460C23×C4—1221no—
461C23×C4—2444no—
462C23×C4C2×#692311yescharacteristic
463C2×M16—1222no—
464C2×M16—1222no—
465C2×M16—2444no—
466C22×C8—1222no—
467#123—1222no—
468#123—1222no—
469#123—1222no—
470#123—1222no—
471C22⋊Q8—612no—
472C22⋊Q8—612no—
473C22⋊Q8—612no—
474C22⋊Q8—612no—
475C22⋊Q8—1221no—
476C22⋊Q8—1221no—
477C22⋊Q8—1221no—
478C22⋊Q8—1221no—
479#121—612no—
480#121—612no—
481#121—612no—
482#121—612no—
483#121—1221no—
484#121—1221no—
485#121—1221no—
486#121—1221no—
487#120—1222no—
488#120—1222no—
489#120—1222no—
490#120—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499#117—21no—
500#117—21no—
501#117C2×#692312yes—
502#117C2×#692312yescomplemented
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4C2×#692311yescharacteristic, complemented
506C2×C4⋊C4C2×#692311yescharacteristic, complemented
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1222no—
513C2×C22⋊C4—1222no—
514C2×C22⋊C4—1228no—
515C2×C42—21no—
516C2×C42—1222no—
517C2×C42—1222no—
518C2×C42—2444no—
519C22⋊C8—614no—
520C22⋊C8—1222no—
521C22⋊C8—1222no—
522C22⋊C8—1222no—
523#95—614no—
524#95—1222no—
525C24—611no—
526C24—611no—
527C24—611no—
528C24—611no—
529C24—611no—
530C24—611no—
531C24—1224no—
532C24—1221no—
533C24—2442no—
534C24—2442no—
535C24C22⋊#692311yescharacteristic
536#41—2444no—
537#41—2444no—
538#41—2444no—
539#41—2444no—
540C2×Q8—612no—
541C2×Q8—1221no—
542C2×Q8—2442no—
543C2×D4—612no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1222no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1221no—
551C2×D4—2442no—
552C2×D4—2444no—
553C2×D4—2444no—
554C2×D4—2444no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—1224no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1228no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4—2442no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2444no—
598C22×C4—2442no—
599C22×C4—2444no—
600C22×C4—2444no—
601C22×C4C22⋊#692311yescharacteristic
602C22×C4C22⋊#692311yescharacteristic
603C22×C4C22⋊#692311yescharacteristic
604C22×C4C22×#692311yescharacteristic
605C22×C4C22×#692311yescharacteristic
606C22×C4C22×#692311yescharacteristic
607M16—2444no—
608M16—2444no—
609C2×C8—1224no—
610C2×C8—2444no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—1222no—
614C4⋊C4—1222no—
615C4⋊C4—1222no—
616C4⋊C4—1222no—
617C4⋊C4C22×#692312yes—
618C4⋊C4C22×#692312yes—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—1228no—
630C22⋊C4—1228no—
631C42—22no—
632C42—22no—
633C42—2444no—
634C42—2444no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—611no—
639C23—611no—
640C23—611no—
641C23—614no—
642C23—611no—
643C23—1222no—
644C23—1222no—
645C23—1222no—
646C23—1222no—
647C23—1222no—
648C23—1222no—
649C23—1222no—
650C23—1222no—
651C23—1222no—
652C23—1222no—
653C23—1222no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23—2442no—
662C23—2442no—
663C23—24416no—
664C23—2442no—
665C23C2×C22⋊#692311yescharacteristic
666C23C2×C22⋊#692311yescharacteristic
667C23C2×C22⋊#692311yescharacteristic
668Q8—2442no—
669Q8—2442no—
670D4—2442no—
671D4—2444no—
672D4—2444no—
673D4—2444no—
674D4—2444no—
675D4—2444no—
676D4—2444no—
677D4—2442no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—611no—
688C2×C4—611no—
689C2×C4—611no—
690C2×C4—611no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1228no—
702C2×C4—1222no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2444no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2442no—
717C2×C4—2444no—
718C2×C4—2444no—
719C2×C4—24416no—
720C2×C4—2444no—
721C2×C4#1451983614yes—
722C2×C4C2×C22⋊#692311yescharacteristic
723C2×C4C2×C22⋊#692311yescharacteristic
724C2×C4C2×C22⋊#692311yescharacteristic
725C2×C4C23×#692311yescharacteristic
726C8—2444no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—44no—
735C22—612no—
736C22—612no—
737C22—612no—
738C22—1228no—
739C22—1221no—
740C22—1221no—
741C22—1221no—
742C22—1221no—
743C22—1221no—
744C22—1221no—
745C22—1221no—
746C22—1221no—
747C22—1221no—
748C22—4884no—
749C22—2444no—
750C22—2444no—
751C22—2444no—
752C22—2444no—
753C22—2444no—
754C22—2442no—
755C22—2442no—
756C22—2442no—
757C22C2×#1451983612yes—
758C22D61⋊#10412yes—
759C22C22×C22⋊#692311yescharacteristic
760C4—21no—
761C4—21no—
762C4—42no—
763C4—42no—
764C4—1221no—
765C4—1221no—
766C4—1221no—
767C4—1221no—
768C4—2448no—
769C4—2442no—
770C4C2×#1451983612yes—
771C4C2×#1451983612yes—
772C2—22no—
773C2—22no—
774C2—41no—
775C2—1222no—
776C2—1222no—
777C2—1222no—
778C2—4882no—
779C2—2441no—
780C2C22×#1451983611yescharacteristic
781C2#2146243911yescharacteristic
782C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840274C2
cosocleC2×C4×D61C24
hypercenterC2×#117#6923
hypocenterC61#17542
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. D61⋊#407C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21461218C2semidirect
4. #21461216C2semidirect
5. #21461207C2semidirect
6. #21461196C2semidirect
11. #16840734C22semidirect
16. D61⋊(C22⋊C8)C22semidirect
20. C4×C22⋊#6923C22semidirect
21. C2×(C2×#6923)⋊C4C22semidirect
22. #16840615C22semidirect
23. #16840614C22semidirect
24. C22×#11758222C4semidirect
30. #16840274C4semidirect
31. #16840274C4semidirect
35. C2×#14519757C4semidirect
37. C2×#14519752C4semidirect
42. C2×#117×C61C4semidirect
65. C2×#11758222C2×C4semidirect
66. C22×Dic122C2×C4semidirect
69. C22×D244C2×C4semidirect
95. #14519757C2×C4semidirect
96. #14519757C2×C4semidirect
103. #14519752C2×C4semidirect
104. #14519752C2×C4semidirect
128. #117×C61C2×C4semidirect
129. C2×C4⋊C4×C61C2×C4semidirect
130. C2×C4⋊C4×C61C2×C4semidirect
418. C2×#117#6923semidirect
434. C61#17542semidirect
502. #117C2×#6923semidirect
505. C2×C4⋊C4C2×#6923semidirect
506. 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
#214612182
#214612162
#214612072
#214611962
C2×#168402742
#1754261