Finite Group Databasebeta

← #30615104

Subgroups — #30615104

Order 15616.

1542 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C2×#16840704C211yesmaximal, characteristic
3#21461724C214yesmaximal, complemented
4#21461723C212yesmaximal, complemented
5#21461722C212yesmaximal, complemented
6#21461508C214yesmaximal, complemented
7C2×#117×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C22×C4⋊#6923C2212yes—
10C22×C22⋊#6923—21no—
11#16840734—21no—
12#16840733—21no—
13#16840733—21no—
14#16840732—21no—
15D61⋊(C22⋊C8)C2212yes—
16D61⋊(C22⋊C8)C2212yes—
17#16840704—21no—
18#16840704—21no—
19#16840704C2212yes—
20#16840704C2212yes—
21C2×(C2×#6923)⋊C4—21no—
22#16840635C2218yescomplemented
23#16840635C2218yescomplemented
24C23×C4×D61C2211yescharacteristic
25C2×#14519736C411yescharacteristic, complemented
26C2×#14519735C411yescharacteristic, complemented
27C2×#14519735C411yescharacteristic, complemented
28C2×#14519734—21no—
29C2×#14519733—21no—
30#117×D61—21no—
31#117×D61—21no—
32#117×D61—21no—
33#117×D61—21no—
34#117×D61C412yescomplemented
35#117×D61C412yescomplemented
36#117×D61C2212yes—
37#117×D61C2212yes—
38C2×C4⋊C4×D61C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C22⋊C4×D61—21no—
41C2×C42×D61—21no—
42C2×#117×C61C411yescharacteristic, complemented
43C23×#6923—22no—
44C2×#11758213—22no—
45D61⋊M16—28no—
46C2×#11758217—22no—
47C2×D61⋊C8C2314yes—
48C2×C4⋊#6923—28no—
49C2×C4⋊#6923—22no—
50C2×C4⋊#6923C2314yes—
51C2×C22⋊#6923—22no—
52C2×C22⋊#6923—22no—
53C2×C22⋊#6923—44no—
54#14519834—22no—
55#14519834—22no—
56C22⋊#92420—22no—
57C22⋊#92420—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4—22no—
60C24×D61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62C22×C4×D61—28no—
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77#14519736—21no—
78#14519736—21no—
79#14519736C2×C412yes—
80#14519736C2×C412yescomplemented
81#14519735—21no—
82#14519735—21no—
83#14519735—21no—
84#14519735—21no—
85#14519735C2×C412yes—
86#14519735C2×C412yes—
87#14519735C2×C412yescomplemented
88#14519735C2×C412yescomplemented
89#14519734—22no—
90#14519734—22no—
91#14519734—22no—
92#14519734—22no—
93#14519733—22no—
94#14519733—22no—
95#14519733—22no—
96#14519733—22no—
97C2×C4⋊Dic61C2×C411yescharacteristic, complemented
98C2×C4⋊Dic61C2×C411yescharacteristic, complemented
99C2×#11758196—21no—
100C2×#11758196—21no—
101C4⋊C4×D61—21no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61—21no—
105C4⋊C4×D61C2×C412yescomplemented
106C4⋊C4×D61C2×C412yescomplemented
107C4⋊C4×D61C2312yes—
108C4⋊C4×D61C2312yes—
109C2×C22⋊Dic61—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C22⋊C4×D61—22no—
113C22⋊C4×D61—22no—
114C22⋊C4×D61—22no—
115C22⋊C4×D61—22no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C42×D61—22no—
120C42×D61—22no—
121C42×D61—22no—
122C42×D61—22no—
123C23×C4×C61C2×C411yescharacteristic
124#117×C61—21no—
125#117×C61—21no—
126#117×C61C2×C412yes—
127#117×C61C2×C412yescomplemented
128C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
129C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
130C2×C22⋊C4×C61—21no—
131C2×C42×C61—21no—
132C24×C61C22⋊C411yescharacteristic
133C23×D61—24no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—42no—
137C23×D61C22⋊C411yescharacteristic
138C23×D61C22⋊C411yescharacteristic
139C23×D61C22⋊C411yescharacteristic
140C23×D61C2×D411yescharacteristic
141C23×D61C2×D411yescharacteristic
142C23×D61C2×D411yescharacteristic
143C22×#6923—24no—
144C22×#6923—44no—
145C22×#6923—44no—
146C22×#6923—44no—
147C22×C4×C61—24no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C22⋊C411yescharacteristic
151C22×C4×C61C22⋊C411yescharacteristic
152C22×C4×C61C22⋊C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×Dic61—24no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61C22⋊C411yescharacteristic
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C2×C4×D61—24no—
166C2×C4×D61—24no—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—24no—
172C2×C4×D61—24no—
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—24no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—44no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22×C411yescharacteristic
190C2×C4×D61C22×C411yescharacteristic
191C2×C4×D61C22×C411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61C2×D411yescharacteristic
197C2×C4×D61C2×D411yescharacteristic
198C2×C4×D61#4118yes—
199C2×C4×D61C2411yescharacteristic
200C22⋊#6923—44no—
201C22⋊#6923—44no—
202#11758217—44no—
203C2×#92420—24no—
204C4⋊#6923—28no—
205C4⋊#6923—44no—
206#11758213—44no—
207D61⋊C8—28no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61C22×C412yes—
211C4⋊C4×C61C22×C412yes—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C42×C61—22no—
215C42×C61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218#11758198—22no—
219#11758198—22no—
220#11758198—22no—
221#11758198—22no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61C22×C412yes—
225C4⋊Dic61C22×C412yes—
226#11758196—22no—
227#11758196—22no—
228#11758196—22no—
229#11758196—22no—
230C4×Dic61—22no—
231C4×Dic61—22no—
232C4×Dic61—22no—
233C4×Dic61—22no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236C23×C61—22no—
237C23×C61—22no—
238C23×C61—41no—
239C23×C61C2×C22⋊C411yescharacteristic
240C23×C61C2×C22⋊C411yescharacteristic
241C23×C61C2×C22⋊C411yescharacteristic
242C22×D61—22no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—48no—
261C22×D61—48no—
262C22×D61C2×C22⋊C411yescharacteristic
263C22×D61C2×C22⋊C411yescharacteristic
264C22×D61C2×C22⋊C411yescharacteristic
265C22×D61#12314yes—
266C22×D61AGL(1,ℤ/8)12yes—
267C22×D61#13712yes—
268C22×D61C22×D411yescharacteristic
269C2×#6923—44no—
270C2×#6923—44no—
271C2×#6923—44no—
272C2×#6923—88no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61C2×C22⋊C411yescharacteristic
283C2×C4×C61C2×C22⋊C411yescharacteristic
284C2×C4×C61C2×C22⋊C411yescharacteristic
285C2×C4×C61#11714yes—
286C2×C4×C61C23×C411yescharacteristic
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—42no—
295C2×Dic61—42no—
296C2×Dic61C2×C22⋊C411yescharacteristic
297C2×Dic61C2×C22⋊C411yescharacteristic
298C2×Dic61C2×C22⋊C411yescharacteristic
299C2×Dic61#12314yes—
300C2×Dic61C22×D411yescharacteristic
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
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—44no—
314C4×D61—42no—
315C4×D61—42no—
316C4×D61—44no—
317C4×D61—44no—
318C4×D61#11714yes—
319C4×D61#12314yes—
320C4×D61#12314yes—
321C4×D61C2×#4114yes—
322#92420—44no—
323#20702—611nomaximal, Sylow
324C22×C61—21no—
325C22×C61—21no—
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—21no—
331C22×C61—44no—
332C22×C61#38112yes—
333C22×C61#41712yes—
334C22×C61C22×C22⋊C411yescharacteristic
335C2×D61—21no—
336C2×D61—21no—
337C2×D61—21no—
338C2×D61—21no—
339C2×D61—24no—
340C2×D61—24no—
341C2×D61—24no—
342C2×D61—24no—
343C2×D61—21no—
344C2×D61—21no—
345C2×D61—21no—
346C2×D61—44no—
347C2×D61—44no—
348C2×D61—44no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61#38112yes—
352C2×D61#41712yes—
353C2×D61C2×#12312yes—
354C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
355C2×D61C2×#13711yescharacteristic
356C2×D61#57512yes—
357#6923—84no—
358C4×C61—21no—
359C4×C61—21no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61#38112yes—
363C4×C61C2×#11712yes—
364Dic61—21no—
365Dic61—21no—
366Dic61—42no—
367Dic61—42no—
368Dic61#38112yes—
369Dic61C2×#12312yes—
370C22×#117—611no—
371C2×#407—611no—
372C2×#380—611no—
373#1825—614no—
374#1824—612no—
375#1823—612no—
376#1736—614no—
377C2×C61—22no—
378C2×C61—22no—
379C2×C61—41no—
380C2×C61C2×#38111yescharacteristic
381C2×C61C2×#41711yescharacteristic
382C2×C61#289611yescharacteristic
383D61—22no—
384D61—22no—
385D61—41no—
386D61#309412yes—
387D61#309512yes—
388C24×C4—611no—
389C22×M16—612no—
390C2×#117—611no—
391C2×#117—612no—
392C2×#117—612no—
393C2×#117—612no—
394C2×#117—612no—
395C2×#117—611no—
396C2×#117—611no—
397C2×#117—1221no—
398C2×#117—1221no—
399C2×#117—1221no—
400C2×#117—1221no—
401C2×#117—1221no—
402C2×#117—1221no—
403C2×#117#692311yescharacteristic, complemented
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—612no—
407C22×C22⋊C4—1221no—
408C22×C22⋊C4—1221no—
409C22×C42—1221no—
410#407—1221no—
411#407—1221no—
412#407—1221no—
413#407—1221no—
414C2×C22⋊C8—612no—
415C2×C22⋊C8—612no—
416#380—612no—
417#380—612no—
418#380—1221no—
419#380—1221no—
420C2×#95—1221no—
421#340—618no—
422#340—618no—
423C61#2070211yescharacteristic, complemented, Sylow
424C25—611no—
425C23×C4—611no—
426C23×C4—611no—
427C23×C4—611no—
428C23×C4—611no—
429C23×C4—611no—
430C23×C4—611no—
431C23×C4—611no—
432C23×C4—611no—
433C23×C4—611no—
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—1228no—
439C23×C4—1221no—
440C23×C4—1221no—
441C23×C4—1222no—
442C23×C4C2×#692311yescharacteristic
443C2×M16—1222no—
444C2×M16—1228no—
445C2×M16—1222no—
446C22×C8—614no—
447#117—21no—
448#117—21no—
449#117—612no—
450#117—612no—
451#117—612no—
452#117—612no—
453#117—612no—
454#117—612no—
455#117—1222no—
456#117—1222no—
457#117—1222no—
458#117—1222no—
459#117—1222no—
460#117—1222no—
461#117—1222no—
462#117—1222no—
463#117—1221no—
464#117—1221no—
465#117—1221no—
466#117—1221no—
467#117—1221no—
468#117—1221no—
469#117C2×#692312yes—
470#117C2×#692312yescomplemented
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—612no—
474C2×C4⋊C4—612no—
475C2×C4⋊C4—612no—
476C2×C4⋊C4—612no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1228no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4C2×#692311yescharacteristic, complemented
487C2×C4⋊C4C2×#692311yescharacteristic, complemented
488C2×C22⋊C4—21no—
489C2×C22⋊C4—1222no—
490C2×C22⋊C4—1222no—
491C2×C22⋊C4—1222no—
492C2×C22⋊C4—1222no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1222no—
497C2×C22⋊C4—1222no—
498C2×C22⋊C4—2444no—
499C2×C42—21no—
500C2×C42—1222no—
501C2×C42—1222no—
502C2×C42—1222no—
503C2×C42—1222no—
504C2×C42—1221no—
505C2×C42—1221no—
506C2×C42—1221no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—1222no—
510C22⋊C8—1222no—
511#95—1222no—
512#95—1222no—
513C24—611no—
514C24—611no—
515C24—611no—
516C24—611no—
517C24—611no—
518C24—611no—
519C24—1222no—
520C24—1224no—
521C24—1222no—
522C24—2442no—
523C24C22⋊#692311yescharacteristic
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—618no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
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—1224no—
551C22×C4—1224no—
552C22×C4—1224no—
553C22×C4—1224no—
554C22×C4—1224no—
555C22×C4—1224no—
556C22×C4—1224no—
557C22×C4—1224no—
558C22×C4—1224no—
559C22×C4—1224no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1224no—
565C22×C4—1224no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1224no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2444no—
572C22×C4—2444no—
573C22×C4—2444no—
574C22×C4—2444no—
575C22×C4C22⋊#692311yescharacteristic
576C22×C4C22⋊#692311yescharacteristic
577C22×C4C22⋊#692311yescharacteristic
578C22×C4C22×#692311yescharacteristic
579C22×C4C22×#692311yescharacteristic
580C22×C4C22×#692311yescharacteristic
581M16—2444no—
582M16—2444no—
583C2×C8—1224no—
584C2×C8—1228no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—612no—
588C4⋊C4—612no—
589C4⋊C4—1222no—
590C4⋊C4—1222no—
591C4⋊C4—1222no—
592C4⋊C4—1222no—
593C4⋊C4—1228no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—2444no—
597C4⋊C4C22×#692312yes—
598C4⋊C4C22×#692312yes—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—1222no—
602C22⋊C4—1222no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—2444no—
608C22⋊C4—2444no—
609C42—22no—
610C42—22no—
611C42—1222no—
612C42—1222no—
613C42—1222no—
614C42—1222no—
615C42—1222no—
616C42—1222no—
617C23—22no—
618C23—22no—
619C23—41no—
620C23—611no—
621C23—614no—
622C23—612no—
623C23—612no—
624C23—611no—
625C23—611no—
626C23—611no—
627C23—1222no—
628C23—1221no—
629C23—1222no—
630C23—1222no—
631C23—1221no—
632C23—1221no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—1222no—
637C23—1221no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2448no—
646C23—2448no—
647C23C2×C22⋊#692311yescharacteristic
648C23C2×C22⋊#692311yescharacteristic
649C23C2×C22⋊#692311yescharacteristic
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—614no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—614no—
663C2×C4—614no—
664C2×C4—614no—
665C2×C4—614no—
666C2×C4—611no—
667C2×C4—611no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
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—4888no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2444no—
691C2×C4—2444no—
692C2×C4—2444no—
693C2×C4—2444no—
694C2×C4—2444no—
695C2×C4—2444no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4C2×C22⋊#692311yescharacteristic
699C2×C4C2×C22⋊#692311yescharacteristic
700C2×C4C2×C22⋊#692311yescharacteristic
701C2×C4#1451985614yes—
702C2×C4C23×#692311yescharacteristic
703C8—2444no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—44no—
712C22—611no—
713C22—611no—
714C22—612no—
715C22—612no—
716C22—612no—
717C22—612no—
718C22—1224no—
719C22—1224no—
720C22—1224no—
721C22—1224no—
722C22—1221no—
723C22—1221no—
724C22—1221no—
725C22—1221no—
726C22—1221no—
727C22—1221no—
728C22—1221no—
729C22—2444no—
730C22—2444no—
731C22—2442no—
732C22—2442no—
733C22—2444no—
734C22#1684070512yes—
735C22#1684075312yes—
736C22C22×C22⋊#692311yescharacteristic
737C4—21no—
738C4—21no—
739C4—42no—
740C4—42no—
741C4—612no—
742C4—612no—
743C4—1221no—
744C4—1221no—
745C4—4884no—
746C4—2442no—
747C4—2442no—
748C4#1684070512yes—
749C4C2×#1451985612yes—
750C2—22no—
751C2—22no—
752C2—41no—
753C2—612no—
754C2—612no—
755C2—1222no—
756C2—1222no—
757C2—2441no—
758C2C2×#1684070511yescharacteristic
759C2C2×#1684075311yescharacteristic
760C2#2146243911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC2×C4×D61C24
hypercenterC2×#117#6923
hypocenterC61#20702
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #21461724C2semidirect
4. #21461723C2semidirect
5. #21461722C2semidirect
6. #21461508C2semidirect
22. #16840635C22semidirect
23. #16840635C22semidirect
25. C2×#14519736C4semidirect
26. C2×#14519735C4semidirect
27. C2×#14519735C4semidirect
34. #117×D61C4semidirect
35. #117×D61C4semidirect
42. C2×#117×C61C4semidirect
80. #14519736C2×C4semidirect
87. #14519735C2×C4semidirect
88. #14519735C2×C4semidirect
97. C2×C4⋊Dic61C2×C4semidirect
98. C2×C4⋊Dic61C2×C4semidirect
105. C4⋊C4×D61C2×C4semidirect
106. C4⋊C4×D61C2×C4semidirect
127. #117×C61C2×C4semidirect
128. C2×C4⋊C4×C61C2×C4semidirect
129. C2×C4⋊C4×C61C2×C4semidirect
403. C2×#117#6923semidirect
423. C61#20702semidirect
470. #117C2×#6923semidirect
486. C2×C4⋊C4C2×#6923semidirect
487. 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
#214617242
#214617232
#214617222
#214615082
C2×#117×D612
#2070261