Finite Group Databasebeta

← #30611229

Subgroups — #30611229

Order 15616.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic, complemented
2C2×#16840704C211yesmaximal, characteristic, complemented
3#21461258C212yesmaximal, complemented
4#21461256C212yesmaximal, complemented
5#21461236C214yesmaximal, complemented
6#21461207C214yesmaximal, complemented
7C2×#16840274C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9C22×C4⋊#6923—21no—
10C22×C22⋊#6923—21no—
11#16840734C2212yescomplemented
12#16840733—21no—
13#16840733C2212yescomplemented
14#16840732—21no—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)C2212yes—
17#16840704—21no—
18#16840704—21no—
19#16840704C2212yes—
20#16840704C2212yescomplemented
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×C4⋊#6923—22no—
49C2×C4⋊#6923—22no—
50C2×C4⋊#6923—44no—
51C2×C22⋊#6923—22no—
52C2×C22⋊#6923—22no—
53C2×C22⋊#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—22no—
135C23×D61—22no—
136C23×D61—21no—
137C23×D61—42no—
138C23×D61—42no—
139C23×D61C22⋊C411yescharacteristic
140C23×D61C22⋊C411yescharacteristic
141C23×D61C22⋊C411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C23×D61C2×D411yescharacteristic
145C22×#6923—24no—
146C22×#6923—44no—
147C22×#6923—44no—
148C22×#6923—44no—
149C22×C4×C61—24no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22⋊C411yescharacteristic
153C22×C4×C61C22⋊C411yescharacteristic
154C22×C4×C61C22⋊C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—44no—
161C22×Dic61—21no—
162C22×Dic61—42no—
163C22×Dic61C22⋊C411yescharacteristic
164C22×Dic61C22⋊C411yescharacteristic
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169#11758222—44no—
170#11758222—44no—
171#11758222—44no—
172#11758222—44no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—21no—
178C2×D244—44no—
179C2×D244—42no—
180C2×D244—42no—
181C2×D244—42no—
182C2×D244C22×C412yes—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
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—42no—
196C2×C4×D61—42no—
197C2×C4×D61—44no—
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×D61C22×C411yescharacteristic
206C2×C4×D61C22×C411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2411yescharacteristic
214C2×Dic122—21no—
215C2×Dic122—42no—
216C2×Dic122C22×C412yes—
217C22⋊#6923—44no—
218C22⋊#6923—44no—
219#11758217—44no—
220C2×#92420—24no—
221C4⋊#6923—44no—
222C4⋊#6923—44no—
223#11758213—44no—
224D61⋊C8—44no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61C22×C412yes—
228C4⋊C4×C61C22×C412yes—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C42×C61—22no—
232C42×C61—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241C4⋊Dic61—22no—
242C4⋊Dic61—22no—
243C4⋊Dic61—22no—
244C4⋊Dic61—22no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—41no—
248C23×C61C2×C22⋊C411yescharacteristic
249C23×C61C2×C22⋊C411yescharacteristic
250C23×C61C2×C22⋊C411yescharacteristic
251C22×D61—22no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—48no—
272C22×D61—48no—
273C22×D61—42no—
274C22×D61—42no—
275C22×D61—42no—
276C22×D61C2×C22⋊C411yescharacteristic
277C22×D61C2×C22⋊C411yescharacteristic
278C22×D61C2×C22⋊C411yescharacteristic
279C22×D61AGL(1,ℤ/8)12yes—
280C22×D61#13712yes—
281C22×D61C22×D411yescharacteristic
282C2×#6923—44no—
283C2×#6923—44no—
284C2×#6923—44no—
285C2×#6923—88no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61#9914yes—
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C23×C411yescharacteristic
300C22⋊D61—44no—
301C22⋊D61—44no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—42no—
310C2×Dic61C2×C22⋊C411yescharacteristic
311C2×Dic61C2×C22⋊C411yescharacteristic
312C2×Dic61C2×C22⋊C411yescharacteristic
313C2×Dic61C22×D411yescharacteristic
314D244—42no—
315D244—44no—
316D244—42no—
317D244—42no—
318D244—44no—
319D244—44no—
320D244—42no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—44no—
338C4×D61—44no—
339Dic122—42no—
340Dic122—42no—
341#92420—44no—
342#17592—611nomaximal, Sylow
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—44no—
351C22×C61C2×#9912yes—
352C22×C61#41712yes—
353C22×C61C22×C22⋊C411yescharacteristic
354C2×D61—24no—
355C2×D61—24no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—44no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—84no—
376C2×D61#41712yes—
377C2×D61#42112yes—
378C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
379C2×D61C2×#13711yescharacteristic
380#6923—84no—
381C4×C61—21no—
382C4×C61—21no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61C2×#9912yes—
386C4×C61C2×#9912yes—
387Dic61—21no—
388Dic61—21no—
389Dic61—21no—
390Dic61—21no—
391Dic61—42no—
392C2×#525—611no—
393C2×#407—611no—
394C2×#380—611no—
395#1520—612no—
396#1519—612no—
397#1513—614no—
398#1504—614no—
399C2×C61—22no—
400C2×C61—22no—
401C2×C61—41no—
402C2×C61C22×#9911yescharacteristic
403C2×C61C2×#41711yescharacteristic
404C2×C61C2×#42111yescharacteristic
405D61—21no—
406D61—21no—
407D61—22no—
408D61—22no—
409D61—41no—
410D61—82no—
411C22×#41—611no—
412C24×C4—611no—
413C22×M16—1221no—
414#525—612no—
415#525—612no—
416#525—612no—
417#525—612no—
418#525—1221no—
419#525—1221no—
420#525—1221no—
421#525—1221no—
422C2×#123—1221no—
423C2×C22⋊Q8—611no—
424C2×C22⋊Q8—611no—
425C2×#121—611no—
426C2×#121—611no—
427C2×#120—1221no—
428C2×C4×D4—1221no—
429C2×C4×D4—1221no—
430C2×#117#692311yescharacteristic, complemented
431C22×C4⋊C4—1221no—
432C22×C22⋊C4—1221no—
433#407—612no—
434#407—612no—
435#407—1221no—
436#407—1221no—
437C2×C22⋊C8—612no—
438C2×C22⋊C8—1221no—
439#380—612no—
440#380—612no—
441#380—1221no—
442#380—1221no—
443C2×#95—612no—
444#328—618no—
445#327—618no—
446C61#1759211yescharacteristic, complemented, Sylow
447C25—611no—
448C2×#41—612no—
449C2×#41—612no—
450C2×#41—1221no—
451C2×#41—1221no—
452C2×#41—2444no—
453C22×Q8—611no—
454C22×D4—611no—
455C22×D4—1221no—
456C22×D4—1221no—
457C22×D4—1221no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—1221no—
472C23×C4—1222no—
473C23×C4—2444no—
474C23×C4C2×#692311yescharacteristic
475C2×M16—1222no—
476C2×M16—1222no—
477C2×M16—2444no—
478C22×C8—1222no—
479#123—1222no—
480#123—1222no—
481#123—1222no—
482#123—1222no—
483C22⋊Q8—612no—
484C22⋊Q8—612no—
485C22⋊Q8—612no—
486C22⋊Q8—612no—
487C22⋊Q8—1221no—
488C22⋊Q8—1221no—
489C22⋊Q8—1221no—
490C22⋊Q8—1221no—
491#121—612no—
492#121—612no—
493#121—612no—
494#121—612no—
495#121—1221no—
496#121—1221no—
497#121—1221no—
498#121—1221no—
499#120—1222no—
500#120—1222no—
501#120—1222no—
502#120—1222no—
503C4×D4—1222no—
504C4×D4—1222no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—1222no—
511#117—21no—
512#117—21no—
513#117C2×#692312yes—
514#117C2×#692312yescomplemented
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—2444no—
520C2×C4⋊C4C2×#692311yescharacteristic, complemented
521C2×C4⋊C4C2×#692311yescharacteristic, complemented
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1222no—
528C2×C22⋊C4—1222no—
529C2×C22⋊C4—2444no—
530C2×C42—21no—
531C22⋊C8—614no—
532C22⋊C8—1222no—
533C22⋊C8—1222no—
534C22⋊C8—1222no—
535#95—614no—
536#95—1222no—
537C24—611no—
538C24—611no—
539C24—611no—
540C24—611no—
541C24—611no—
542C24—611no—
543C24—1222no—
544C24—1222no—
545C24—1221no—
546C24—2442no—
547C24—2442no—
548C24C22⋊#692311yescharacteristic
549#41—2444no—
550#41—2444no—
551#41—2444no—
552#41—2444no—
553C2×Q8—612no—
554C2×Q8—1221no—
555C2×Q8—2442no—
556C2×D4—612no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1221no—
564C2×D4—2442no—
565C2×D4—2442no—
566C2×D4—2442no—
567C2×D4—2444no—
568C2×D4—2444no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
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—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—1224no—
595C22×C4—1224no—
596C22×C4—1221no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1224no—
600C22×C4—2442no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4—2442no—
609C22×C4—2442no—
610C22×C4—2444no—
611C22×C4—2442no—
612C22×C4—2444no—
613C22×C4—2444no—
614C22×C4—2444no—
615C22×C4C22⋊#692311yescharacteristic
616C22×C4C22⋊#692311yescharacteristic
617C22×C4C22⋊#692311yescharacteristic
618C22×C4C22×#692311yescharacteristic
619C22×C4C22×#692311yescharacteristic
620C22×C4C22×#692311yescharacteristic
621M16—2444no—
622M16—2444no—
623C2×C8—1224no—
624C2×C8—2444no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—1222no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C4⋊C4—2444no—
632C4⋊C4—2444no—
633C4⋊C4C22×#692312yes—
634C4⋊C4C22×#692312yes—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—2444no—
646C22⋊C4—2444no—
647C42—22no—
648C42—22no—
649C23—22no—
650C23—22no—
651C23—41no—
652C23—611no—
653C23—611no—
654C23—611no—
655C23—612no—
656C23—612no—
657C23—611no—
658C23—1221no—
659C23—1222no—
660C23—1221no—
661C23—1221no—
662C23—1222no—
663C23—1222no—
664C23—1221no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2442no—
679C23—2442no—
680C23—2448no—
681C23—2448no—
682C23—2442no—
683C23C2×C22⋊#692311yescharacteristic
684C23C2×C22⋊#692311yescharacteristic
685C23C2×C22⋊#692311yescharacteristic
686Q8—2442no—
687Q8—2442no—
688D4—2442no—
689D4—2442no—
690D4—2442no—
691D4—2444no—
692D4—2444no—
693D4—2444no—
694D4—2444no—
695D4—2444no—
696D4—2442no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—611no—
709C2×C4—611no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—4888no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2444no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2444no—
736C2×C4—2444no—
737C2×C4—2444no—
738C2×C4—2442no—
739C2×C4—2444no—
740C2×C4#1451983614yes—
741C2×C4C2×C22⋊#692311yescharacteristic
742C2×C4C2×C22⋊#692311yescharacteristic
743C2×C4C2×C22⋊#692311yescharacteristic
744C2×C4C23×#692311yescharacteristic
745C8—2444no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—44no—
754C22—611no—
755C22—611no—
756C22—612no—
757C22—612no—
758C22—1224no—
759C22—1224no—
760C22—1221no—
761C22—1221no—
762C22—1221no—
763C22—1221no—
764C22—1221no—
765C22—1221no—
766C22—1221no—
767C22—1221no—
768C22—1221no—
769C22—4884no—
770C22—2442no—
771C22—2442no—
772C22—2444no—
773C22—2444no—
774C22—2444no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22—2442no—
779C22—2442no—
780C22C2×#1451983612yes—
781C22#1684075312yes—
782C22C22×C22⋊#692311yescharacteristic
783C4—21no—
784C4—21no—
785C4—42no—
786C4—42no—
787C4—1221no—
788C4—1221no—
789C4—1221no—
790C4—1221no—
791C4—4884no—
792C4—2442no—
793C4C2×#1451983612yes—
794C4C2×#1451983612yes—
795C2—22no—
796C2—22no—
797C2—41no—
798C2—1221no—
799C2—1221no—
800C2—1222no—
801C2—1222no—
802C2—4882no—
803C2—2441no—
804C2C22×#1451983611yescharacteristic
805C2C2×#1684075311yescharacteristic
806C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×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#17592
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. D61⋊#407C2semidirect
2. C2×#16840704C2semidirect
3. #21461258C2semidirect
4. #21461256C2semidirect
5. #21461236C2semidirect
6. #21461207C2semidirect
11. #16840734C22semidirect
13. #16840733C22semidirect
20. #16840704C22semidirect
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
430. C2×#117#6923semidirect
446. C61#17592semidirect
514. #117C2×#6923semidirect
520. C2×C4⋊C4C2×#6923semidirect
521. 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×#168407042
#214612582
#214612562
#214612362
#214612072
C2×#168402742
#1759261