Finite Group Databasebeta

← #30610284

Subgroups — #30610284

Order 15616.

1290 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462407C212yesmaximal, complemented
2#21461098C212yesmaximal, complemented
3#21461085C212yesmaximal, complemented
4#21461084C212yesmaximal, complemented
5#21461075C211yesmaximal, characteristic, complemented
6#21461068C211yesmaximal, characteristic, complemented
7#21461067C211yesmaximal, characteristic, complemented
8#21461055C211yesmaximal, characteristic, complemented
9D61⋊#324C211yesmaximal, characteristic, complemented
10C2×#16840607C211yesmaximal, characteristic, complemented
11C2×#16840412C211yesmaximal, characteristic
12C2×#14519864—22no—
13#16840736—22no—
14#16840735—22no—
15#16840735—22no—
16#16840733C2212yes—
17#16840732C2212yes—
18#16840732C2212yes—
19D61⋊(C22⋊C8)C2212yes—
20C2×C22⋊#92420C2212yes—
21C2×C22⋊#92420C2212yes—
22#16840608C2212yes—
23#16840608C2212yes—
24#16840607C2211yescharacteristic
25#16840607C2211yescharacteristic
26#16840607C2212yes—
27#16840607C2211yescharacteristic
28#16840607C2211yescharacteristic
29#16840607C2212yes—
30#16840605C2212yes—
31#16840605C2212yes—
32C22×#11758224C411yescharacteristic
33C22×#11758224C2211yescharacteristic
34#16840412—22no—
35#16840412—22no—
36#16840412—22no—
37#16840412—22no—
38C2×#14519776C411yescharacteristic
39C2×#14519759C411yescharacteristic
40C2×#14519759C2211yescharacteristic
41C2×#14519758C411yescharacteristic
42C2×#14519758C2211yescharacteristic
43C2×#14519754C411yescharacteristic
44C2×#14519754C2211yescharacteristic
45C2×#14519748C411yescharacteristic
46C2×D4×Dic61C2211yescharacteristic
47C2×C4×C22⋊D61C411yescharacteristic
48C22×C4⋊Dic61C2211yescharacteristic
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×#121×C61C411yescharacteristic
51#14519864—48no—
52C2×#11758213—22no—
53C2×#11758217—22no—
54C2×#11758217—22no—
55C2×D61⋊C8—22no—
56C22×#92420—22no—
57C22×#92420—22no—
58#14519834—22no—
59#14519834—22no—
60C22⋊#92420—22no—
61C22⋊#92420—22no—
62C22⋊#92420—22no—
63C22⋊#92420—22no—
64C22⋊#92420C2312yes—
65C22⋊#92420C2312yes—
66C22⋊#92420C2312yes—
67C22⋊#92420C2312yes—
68C2×#11758224—21no—
69C2×#11758224—21no—
70C2×#11758224—21no—
71C2×#11758224—21no—
72C2×#11758224—44no—
73C2×#11758224—44no—
74C2×#11758224D412yes—
75C2×#11758224D412yes—
76C2×#11758224D412yes—
77C2×#11758224D412yes—
78C22×Dic122C2×C411yescharacteristic
79C22×Dic122C2×C411yescharacteristic
80C22×C22⋊D61C2×C411yescharacteristic
81C22×C22⋊D61C2×C411yescharacteristic
82C22×C22⋊D61C2×C411yescharacteristic
83C23×Dic61C2×C411yescharacteristic
84C23×Dic61C2×C411yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C22×C4×D61C2×C411yescharacteristic
88C22×C4×D61C2×C411yescharacteristic
89C22×C4×D61C2311yescharacteristic
90#14519776—22no—
91#14519776—22no—
92#14519759—22no—
93#14519759—22no—
94#14519759—22no—
95#14519759—22no—
96#14519758—22no—
97#14519758—22no—
98#14519758—22no—
99#14519758—22no—
100#14519754—22no—
101#14519754—22no—
102#14519754—22no—
103#14519754—22no—
104#14519748—22no—
105#14519748—22no—
106D4×Dic61—22no—
107D4×Dic61—22no—
108C4×C22⋊D61—21no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111C4×C22⋊D61—21no—
112C2×C4⋊Dic61—22no—
113C2×C4⋊Dic61—22no—
114C2×C4⋊Dic61C2×C411yescharacteristic
115C2×C4⋊Dic61C2×C411yescharacteristic
116C2×C4⋊Dic61C2311yescharacteristic
117C2×C4⋊Dic61C2311yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758196C2311yescharacteristic
123C4⋊C4×D61—22no—
124C4⋊C4×D61—22no—
125C2×C22⋊Dic61C2×C411yescharacteristic
126C2×C22⋊Dic61C2×C411yescharacteristic
127C2×C22⋊Dic61C2×C411yescharacteristic
128C2×C22⋊Dic61C2×C411yescharacteristic
129C2×C22⋊Dic61C2311yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×C4×Dic61C2×C411yescharacteristic
132C22×D4×C61C2×C411yescharacteristic
133C22×D4×C61C2×C411yescharacteristic
134C22×D4×C61C2×C411yescharacteristic
135C23×C4×C61C2×C411yescharacteristic
136#121×C61—22no—
137#121×C61—22no—
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C24×C61C22×C411yescharacteristic
142C24×C61C22×C411yescharacteristic
143C24×C61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C2×D4×C61—41no—
150C2×D4×C61—42no—
151C2×D4×C61—42no—
152C2×D4×C61C22⋊C412yes—
153C2×D4×C61C22⋊C412yes—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61—41no—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C2×C22⋊D61—24no—
163C2×C22⋊D61—21no—
164C2×C22⋊D61—21no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61C22⋊C411yescharacteristic
168C2×C22⋊D61C22⋊C411yescharacteristic
169C2×C22⋊D61C22⋊C411yescharacteristic
170C2×C22⋊D61C22⋊C412yes—
171C2×C22⋊D61C22⋊C412yes—
172C2×C22⋊D61C22⋊C411yescharacteristic
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—42no—
178C22×Dic61—42no—
179C22×Dic61—42no—
180C22×Dic61—42no—
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C2×D412yes—
188C22×Dic61C2×D412yes—
189C22×Dic61C2×D412yes—
190C22×Dic61C2×D412yes—
191C22×Dic61C2411yescharacteristic
192#11758224—28no—
193#11758224—44no—
194#11758224—44no—
195#11758224—44no—
196#11758224—44no—
197#11758224—44no—
198#11758224—44no—
199#11758224—44no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—22no—
205C2×C4×D61—42no—
206C2×C4×D61—41no—
207C2×C4×D61—42no—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D412yes—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—42no—
213C2×Dic122—42no—
214C2×Dic122C22⋊C412yes—
215C2×Dic122C22⋊C412yes—
216#11758217—44no—
217#11758217—44no—
218C2×#92420—22no—
219C2×#92420—22no—
220C2×#92420—22no—
221C2×#92420—22no—
222C2×#92420—44no—
223C2×#92420—44no—
224#11758213—44no—
225D61⋊C8—44no—
226C4⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊Dic61—21no—
230C22⋊Dic61—21no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235#11758198—21no—
236#11758198—21no—
237C4⋊Dic61—22no—
238C4⋊Dic61—22no—
239C4⋊Dic61—22no—
240C4⋊Dic61—22no—
241#11758196—22no—
242#11758196—22no—
243#11758196—21no—
244#11758196—21no—
245#11758196—22no—
246#11758196—22no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61C2×C22⋊C412yes—
263C23×C61C2×C22⋊C411yescharacteristic
264C23×C61C2×C22⋊C411yescharacteristic
265C23×C61C23×C411yescharacteristic
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—22no—
269C22×D61—41no—
270C22×D61C2×C22⋊C411yescharacteristic
271C22×D61C2×C22⋊C411yescharacteristic
272D4×C61—24no—
273D4×C61—42no—
274D4×C61—44no—
275D4×C61—42no—
276D4×C61—42no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—41no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—41no—
287C2×C4×C61C2×C22⋊C412yes—
288C2×C4×C61#13112yescomplemented
289C22⋊D61—22no—
290C22⋊D61—24no—
291C22⋊D61—22no—
292C22⋊D61—22no—
293C22⋊D61—42no—
294C22⋊D61—42no—
295C22⋊D61—42no—
296C22⋊D61#9914yes—
297C2×Dic61—24no—
298C2×Dic61—24no—
299C2×Dic61—22no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61C2×C22⋊C411yescharacteristic
318C2×Dic61C2×C22⋊C412yes—
319C2×Dic61C2×C22⋊C411yescharacteristic
320C2×Dic61C22×D412yes—
321C4×D61—24no—
322C4×D61—42no—
323C4×D61—42no—
324C4×D61—42no—
325C4×D61—42no—
326C4×D61—42no—
327Dic122—24no—
328Dic122—42no—
329Dic122—42no—
330Dic122—42no—
331#92420—42no—
332#92420—42no—
333#92420—42no—
334#92420—42no—
335#17416—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—22no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61C2×#9912yes—
356C22×C61C22×C22⋊C411yescharacteristic
357C22×C61C2×#13111yescharacteristic
358C22×C61#56811yescharacteristic
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61C2×#9912yes—
367C4×C61—22no—
368C4×C61—22no—
369C4×C61—41no—
370C4×C61—41no—
371Dic61—22no—
372Dic61—22no—
373Dic61—21no—
374Dic61—41no—
375Dic61—41no—
376Dic61—41no—
377Dic61—41no—
378Dic61C2×#9912yes—
379C2×#547—611no—
380#2880—612no—
381#1472—612no—
382#1468—612no—
383#1468—612no—
384#1465—611no—
385#1463—611no—
386#1463—611no—
387#1459—611no—
388C2×#324—611no—
389C2×#324—611no—
390C2×C61—21no—
391C2×C61—21no—
392C2×C61—22no—
393C2×C61—41no—
394C2×C61—42no—
395C2×C61—81no—
396C2×C61#288011yescharacteristic
397C2×C61C22×#9911yescharacteristic
398C2×C61#288911yescharacteristic
399D61—22no—
400D61—41no—
401C22×#41—611no—
402C22×#41—611no—
403C2×#131—1222no—
404#547—1222no—
405#547—1222no—
406#547—1222no—
407#547—1222no—
408C2×C4⋊Q8—611no—
409C2×#123—611no—
410C2×#123—611no—
411C2×#123—611no—
412C2×#123—611no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×#121—611no—
416C2×#121#692311yescharacteristic
417C2×C4×D4—611no—
418C2×C4×D4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—611no—
421#408—1222no—
422#408—1222no—
423#408—1222no—
424#407—612no—
425#407—612no—
426#407—612no—
427C2×C22⋊C8—612no—
428C2×C22⋊C8—612no—
429C2×C22⋊C8—612no—
430#324—611no—
431#324—611no—
432#324—611no—
433#324—612no—
434#324—611no—
435#324—612no—
436#324—612no—
437#324—612no—
438#323—612no—
439#323—612no—
440C61#1741611yescharacteristic, complemented, Sylow
441C2×#41—612no—
442C2×#41—612no—
443C2×#41—612no—
444C2×#41—612no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41—1221no—
448C2×#41—1221no—
449C2×#41—2444no—
450C2×#41—2444no—
451C22×Q8—611no—
452C22×Q8—611no—
453C22×D4—611no—
454C22×D4—611no—
455C22×D4—611no—
456C22×D4C2×#692311yescharacteristic
457C22×D4C2×#692311yescharacteristic
458C22×D4C2×#692311yescharacteristic
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4C2×#692311yescharacteristic
467#131—2448no—
468C2×M16—1222no—
469C2×M16—1222no—
470C2×M16—1222no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8—1222no—
474C4⋊Q8—1222no—
475C4⋊Q8—1222no—
476#123—1222no—
477#123—1222no—
478#123—1222no—
479#123—1222no—
480#123—1222no—
481#123—1222no—
482#123—1222no—
483#123—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#121—22no—
489#121—22no—
490#121—1222no—
491#121—1222no—
492C4×D4—1221no—
493C4×D4—1221no—
494C4×D4—1221no—
495C4×D4—1221no—
496C4×D4—1222no—
497C4×D4—1222no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—1222no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4C2×#692311yescharacteristic
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4C2×#692311yescharacteristic
519C2×C22⋊C4C2×#692311yescharacteristic
520C2×C42—611no—
521C22⋊C8—612no—
522C22⋊C8—612no—
523C22⋊C8—612no—
524C22⋊C8—612no—
525C22⋊C8—1222no—
526C22⋊C8—1222no—
527C22⋊C8—1222no—
528C22⋊C8—1222no—
529C22⋊C8—1222no—
530C22⋊C8—1222no—
531C24—611no—
532C24C22×#692311yescharacteristic
533C24C22×#692311yescharacteristic
534C24C22×#692311yescharacteristic
535#41—1228no—
536#41—2444no—
537#41—2444no—
538#41—2444no—
539#41—2444no—
540#41—2444no—
541#41—2444no—
542#41—2444no—
543C2×Q8—612no—
544C2×Q8—612no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—2442no—
548C2×Q8—2442no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—611no—
557C2×D4—611no—
558C2×D4—611no—
559C2×D4—611no—
560C2×D4—612no—
561C2×D4—612no—
562C2×D4—1224no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—2442no—
566C2×D4—2442no—
567C2×D4C22⋊#692312yes—
568C2×D4C22⋊#692312yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—41no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—611no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1222no—
595C22×C4—2441no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4—2442no—
602C22×C4C22×#692311yescharacteristic
603C22×C4C22×#692311yescharacteristic
604C22×C4C22×#692311yescharacteristic
605C22×C4C22×#692311yescharacteristic
606M16—2444no—
607M16—2444no—
608M16—2444no—
609C2×C8—1222no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8—1222no—
613C2×C8—2444no—
614C2×C8—2444no—
615C2×C8—2444no—
616C4⋊C4—22no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1222no—
621C4⋊C4—1222no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1222no—
625C4⋊C4—1222no—
626C4⋊C4—1222no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—1221no—
630C22⋊C4—1221no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C22⋊C4—1221no—
634C22⋊C4—1221no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C42—1221no—
638C42—1221no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—611no—
653C23—611no—
654C23—1222no—
655C23—1221no—
656C23—1221no—
657C23—2441no—
658C23C2×C22⋊#692312yes—
659C23C2×C22⋊#692311yescharacteristic
660C23C2×C22⋊#692311yescharacteristic
661C23C23×#692311yescharacteristic
662Q8—1224no—
663Q8—2442no—
664Q8—2442no—
665Q8—2442no—
666D4—24no—
667D4—42no—
668D4—44no—
669D4—42no—
670D4—42no—
671D4—614no—
672D4—1222no—
673D4—1222no—
674D4—1224no—
675D4—1222no—
676D4—2442no—
677D4—2442no—
678D4—2442no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—611no—
690C2×C4—611no—
691C2×C4—612no—
692C2×C4—612no—
693C2×C4—1224no—
694C2×C4—1224no—
695C2×C4—1222no—
696C2×C4—1224no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4C2×C22⋊#692312yes—
720C2×C4#1451986412yescomplemented
721C8—2442no—
722C8—2442no—
723C8—2442no—
724C8—2442no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—22no—
731C22—22no—
732C22—21no—
733C22—21no—
734C22—22no—
735C22—42no—
736C22—42no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—612no—
745C22—1221no—
746C22—1221no—
747C22—1221no—
748C22—1221no—
749C22—1221no—
750C22—2442no—
751C22—2442no—
752C22D61⋊#9912yes—
753C22C22×C22⋊#692311yescharacteristic
754C22C2×#1451986411yescharacteristic
755C22#1684084011yescharacteristic
756C4—22no—
757C4—22no—
758C4—41no—
759C4—41no—
760C4—612no—
761C4—1222no—
762C4—1221no—
763C4—1222no—
764C4—2441no—
765C4—2441no—
766C4—2441no—
767C4—2441no—
768C2—21no—
769C2—21no—
770C2—22no—
771C2—41no—
772C2—42no—
773C2—81no—
774C2—1222no—
775C2—2441no—
776C2#2146240711yescharacteristic
777C2C2×D61⋊#9911yescharacteristic
778C2#2146243111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#121×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840412C2
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#17416
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×D4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21462407C2semidirect
2. #21461098C2semidirect
3. #21461085C2semidirect
4. #21461084C2semidirect
5. #21461075C2semidirect
6. #21461068C2semidirect
7. #21461067C2semidirect
8. #21461055C2semidirect
9. D61⋊#324C2semidirect
10. C2×#16840607C2semidirect
288. C2×C4×C61#131semidirect
440. C61#17416semidirect
720. C2×C4#14519864semidirect

Maximal subgroups

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

subgroupindex
#214624072
#214610982
#214610852
#214610842
#214610752
#214610682
#214610672
#214610552
D61⋊#3242
C2×#168406072
C2×#168404122
#1741661