Finite Group Databasebeta

← #29679842

Subgroups — #29679842

Order 15616.

1470 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic
3#21448200C211yesmaximal, characteristic
4#21445919C211yesmaximal, characteristic, complemented
5#21445918C211yesmaximal, characteristic, complemented
6#21445917C214yesmaximal, complemented
7#21445916C211yesmaximal, characteristic, complemented
8#21445527C214yesmaximal, complemented
9C61×#1826C211yesmaximal, characteristic, complemented
10C23×C4×D61C2211yescharacteristic
11C2×M16×D61C2212yes—
12C2×#14519736C2211yescharacteristic
13C2×#14519735C411yescharacteristic, complemented
14C2×#14519735C411yescharacteristic, complemented
15C2×#14519734—21no—
16C2×#14519734C2212yes—
17C2×#14519733—21no—
18#117×D61—21no—
19#117×D61—21no—
20#117×D61—21no—
21#117×D61—21no—
22#117×D61C412yescomplemented
23#117×D61C412yescomplemented
24#117×D61C2212yes—
25#117×D61C2212yes—
26C2×C4⋊C4×D61C411yescharacteristic, complemented
27C2×C4⋊C4×D61C411yescharacteristic, complemented
28C2×C22⋊C4×D61—21no—
29C2×C42×D61—21no—
30#16839726C2211yescharacteristic
31#16839725C2212yes—
32#16839724—21no—
33#16839724—21no—
34C22⋊C8×D61—21no—
35C22⋊C8×D61—21no—
36#16839624—21no—
37#16839621—21no—
38#16839620—21no—
39#16839617—21no—
40C4×#11758198C2212yes—
41C4×C22⋊Dic61C2211yescharacteristic
42#16839523C2214yescomplemented
43#16839522C2214yescomplemented
44#16839521C2214yescomplemented
45C2×#117×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#339C2214yescomplemented
49C24×D61D411yescharacteristic
50C23×Dic61D411yescharacteristic
51C22×C4×D61—28no—
52C22×C4×D61—21no—
53C22×C4×D61—21no—
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758194C2312yes—
67C2×#11758189—22no—
68M16×D61—28no—
69C2×C8×D61—22no—
70#14519736—21no—
71#14519736—21no—
72#14519736C2×C412yes—
73#14519736C2312yes—
74#14519735—21no—
75#14519735—21no—
76#14519735—21no—
77#14519735—21no—
78#14519735C2×C412yes—
79#14519735C2×C412yes—
80#14519735C2×C412yes—
81#14519735C2×C412yes—
82#14519734—22no—
83#14519734—22no—
84#14519734—22no—
85#14519734—22no—
86#14519734—28no—
87#14519733—22no—
88#14519733—22no—
89#14519733—22no—
90#14519733—22no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—22no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61C2×C412yes—
101C4⋊C4×D61C2×C412yes—
102C4⋊C4×D61C2×C412yes—
103C4⋊C4×D61C2×C412yes—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C22⋊C4×D61—22no—
111C22⋊C4×D61—22no—
112C22⋊C4×D61—22no—
113C22⋊C4×D61—22no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61C2312yes—
118C42×D61—22no—
119C42×D61—22no—
120C42×D61—22no—
121C42×D61—22no—
122C22⋊#92418—21no—
123C22⋊#92418—21no—
124#14519689—22no—
125#14519689—22no—
126#14519684—21no—
127#14519684—22no—
128C23×C4×C61C2311yescharacteristic
129C2×M16×C61C2312yes—
130#117×C61—21no—
131#117×C61—21no—
132#117×C61C2×C412yes—
133#117×C61C2312yes—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139C2×C42×C61C2312yes—
140C22⋊C8×C61—21no—
141C22⋊C8×C61—21no—
142#95×C61—21no—
143C24×C61C2×D411yescharacteristic
144C23×D61—24no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61C22⋊C411yescharacteristic
148C23×D61C22⋊C411yescharacteristic
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C2×D411yescharacteristic
152C23×D61C2×D411yescharacteristic
153C22×C4×C61—24no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—24no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61C22⋊C411yescharacteristic
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—24no—
176C2×C4×D61—24no—
177C2×C4×D61—24no—
178C2×C4×D61—24no—
179C2×C4×D61—24no—
180C2×C4×D61—24no—
181C2×C4×D61—24no—
182C2×C4×D61—24no—
183C2×C4×D61—24no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
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×D61C22×C411yescharacteristic
200C2×C4×D61C22×C411yescharacteristic
201C2×C4×D61C22×C411yescharacteristic
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2×D411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61#4118yes—
207M16×C61—24no—
208C2×C8×C61—22no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61C22×C412yes—
212C4⋊C4×C61C22×C412yes—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—42no—
216C42×C61—22no—
217C42×C61—22no—
218C42×C61—24no—
219C22⋊Dic61—22no—
220C22⋊Dic61—22no—
221C22⋊Dic61—42no—
222#11758198—22no—
223#11758198—22no—
224#11758198—22no—
225#11758198—22no—
226#11758198—44no—
227#11758198—44no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61C22×C412yes—
231C4⋊Dic61C22×C412yes—
232#11758196—22no—
233#11758196—22no—
234#11758196—22no—
235#11758196—22no—
236#11758196—44no—
237C4×Dic61—22no—
238C4×Dic61—22no—
239C4×Dic61—22no—
240C4×Dic61—22no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61—24no—
244#11758194—24no—
245C2×#92418—22no—
246#11758189—44no—
247C8×D61—44no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—41no—
251C23×C61C2×C22⋊C411yescharacteristic
252C23×C61C2×C22⋊C411yescharacteristic
253C23×C61C22×D411yescharacteristic
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
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—416no—
272C22×D61C2×C22⋊C411yescharacteristic
273C22×D61C2×C22⋊C411yescharacteristic
274C22×D61C2×C22⋊C411yescharacteristic
275C22×D61C2×C22⋊C411yescharacteristic
276C22×D61#12314yes—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61C2×C22⋊C411yescharacteristic
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C23×C411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C2×#4114yes—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61C2×C22⋊C411yescharacteristic
307C2×Dic61C2×C22⋊C411yescharacteristic
308C2×Dic61C2×C22⋊C411yescharacteristic
309C2×Dic61C2×C22⋊C411yescharacteristic
310C2×Dic61#12314yes—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
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—22no—
323C4×D61—44no—
324C4×D61—44no—
325C4×D61—44no—
326C4×D61—44no—
327C4×D61#11714yes—
328C4×D61#11714yes—
329C4×D61#12314yes—
330C4×D61#12314yes—
331C8×C61—42no—
332#92418—42no—
333#20705—611nomaximal, Sylow
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—44no—
342C22×C61#42112yes—
343C22×C61C22×C22⋊C411yescharacteristic
344C22×C61C2×#12312yes—
345C2×D61—28no—
346C2×D61—21no—
347C2×D61—21no—
348C2×D61—21no—
349C2×D61—21no—
350C2×D61—21no—
351C2×D61—21no—
352C2×D61—21no—
353C2×D61—21no—
354C2×D61—21no—
355C2×D61—44no—
356C2×D61—44no—
357C2×D61—44no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61#38112yes—
361C2×D61#38112yes—
362C2×D61#42112yes—
363C4×C61—21no—
364C4×C61—21no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61—82no—
368C4×C61C2×#11712yes—
369C4×C61C2×#12312yes—
370Dic61—21no—
371Dic61—21no—
372Dic61—42no—
373Dic61—42no—
374Dic61—82no—
375Dic61#38112yes—
376Dic61#38112yes—
377C22×#117—611no—
378C2×#407—611no—
379#2280—611no—
380#1826—611no—
381#1826—611no—
382#1826—614no—
383#1826—611no—
384#1826D6111yescharacteristic, complemented
385#1733—614no—
386C2×C61—22no—
387C2×C61—22no—
388C2×C61—41no—
389C2×C61C2×#38111yescharacteristic
390C2×C61C2×#42111yescharacteristic
391C2×C61C2×#42111yescharacteristic
392D61—22no—
393D61—22no—
394D61—22no—
395D61—41no—
396C24×C4—611no—
397C22×M16—612no—
398C2×#117—612no—
399C2×#117—611no—
400C2×#117—612no—
401C2×#117—612no—
402C2×#117—612no—
403C2×#117—612no—
404C2×#117—611no—
405C2×#117—611no—
406C2×#117—1221no—
407C2×#117—1221no—
408C2×#117—1221no—
409C2×#117—1221no—
410C2×#117—1221no—
411C2×#117—1221no—
412C2×#117C2×D6111yescharacteristic
413C22×C4⋊C4—611no—
414C22×C4⋊C4—611no—
415C22×C22⋊C4—1221no—
416C22×C42—1221no—
417#407—611no—
418#407—612no—
419#407—1221no—
420#407—1221no—
421#407C2×D6111yescharacteristic
422C2×C22⋊C8—1221no—
423C2×C22⋊C8—1221no—
424#381—1221no—
425#380—1221no—
426#380—1221no—
427#379—1221no—
428C4×C22⋊C4—611no—
429C4×C22⋊C4—612no—
430C4×C22⋊C4C2×D6111yescharacteristic
431#339—614no—
432#339—614no—
433#339—614no—
434#339C2×D6114yescomplemented
435C61#2070511yescharacteristic, complemented, Sylow
436C25—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—611no—
449C23×C4—611no—
450C23×C4—1228no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4C22×D6111yescharacteristic
454C2×M16—612no—
455C2×M16—1222no—
456C2×M16—1228no—
457C2×M16C22×D6112yes—
458C22×C8—1222no—
459#117—21no—
460#117—21no—
461#117—612no—
462#117—612no—
463#117—612no—
464#117—612no—
465#117—612no—
466#117—612no—
467#117—1222no—
468#117—1222no—
469#117—1222no—
470#117—1222no—
471#117—1228no—
472#117—1222no—
473#117—1222no—
474#117—1222no—
475#117—1222no—
476#117—1221no—
477#117—1221no—
478#117—1221no—
479#117—1221no—
480#117—1221no—
481#117—1221no—
482#117C4×D6112yes—
483#117C22×D6112yes—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—612no—
487C2×C4⋊C4—612no—
488C2×C4⋊C4—612no—
489C2×C4⋊C4—612no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1222no—
497C2×C4⋊C4C4×D6111yescharacteristic
498C2×C4⋊C4C4×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—1222no—
502C2×C22⋊C4—1222no—
503C2×C22⋊C4—1222no—
504C2×C22⋊C4—1222no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1222no—
509C2×C22⋊C4—1222no—
510C2×C22⋊C4—1221no—
511C2×C42—21no—
512C2×C42—612no—
513C2×C42—1222no—
514C2×C42—1222no—
515C2×C42—1222no—
516C2×C42—1222no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42C22×D6112yes—
521C22⋊C8—21no—
522C22⋊C8—21no—
523C22⋊C8—1222no—
524C22⋊C8—1222no—
525C22⋊C8—1221no—
526C22⋊C8—1221no—
527#95—21no—
528#95—1222no—
529#95—1221no—
530C24—611no—
531C24—611no—
532C24—611no—
533C24—611no—
534C24—611no—
535C24—611no—
536C24—1224no—
537C24—2442no—
538C24—2442no—
539C24D4×D6111yescharacteristic
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—618no—
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—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—1224no—
568C22×C4—1224no—
569C22×C4—1224no—
570C22×C4—1224no—
571C22×C4—1224no—
572C22×C4—1224no—
573C22×C4—1224no—
574C22×C4—1224no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—2444no—
587C22×C4—2444no—
588C22×C4C2×C4×D6111yescharacteristic
589C22×C4C2×C4×D6111yescharacteristic
590C22×C4D4×D6111yescharacteristic
591C22×C4D4×D6111yescharacteristic
592C22×C4D4×D6111yescharacteristic
593C22×C4C23×D6111yescharacteristic
594M16—24no—
595M16—1224no—
596M16—2444no—
597C2×C8—22no—
598C2×C8—1222no—
599C2×C8—2444no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—612no—
603C4⋊C4—612no—
604C4⋊C4—1222no—
605C4⋊C4—1222no—
606C4⋊C4—1222no—
607C4⋊C4—1222no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—2444no—
611C4⋊C4C2×C4×D6112yes—
612C4⋊C4C2×C4×D6112yes—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C22⋊C4—2444no—
623C22⋊C4—2444no—
624C22⋊C4—2442no—
625C42—22no—
626C42—22no—
627C42—24no—
628C42—1222no—
629C42—1222no—
630C42—1222no—
631C42—1222no—
632C42—1222no—
633C42—1222no—
634C42—1224no—
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—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23—24416no—
661C23C22⋊C4×D6111yescharacteristic
662C23C22⋊C4×D6111yescharacteristic
663C23C2×D4×D6111yescharacteristic
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—611no—
677C2×C4—611no—
678C2×C4—614no—
679C2×C4—614no—
680C2×C4—614no—
681C2×C4—614no—
682C2×C4—614no—
683C2×C4—611no—
684C2×C4—611no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
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—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—2444no—
705C2×C4—2444no—
706C2×C4—2444no—
707C2×C4—2444no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4C22⋊C4×D6111yescharacteristic
714C2×C4C22⋊C4×D6111yescharacteristic
715C2×C4C22×C4×D6111yescharacteristic
716C2×C4C2×D4×D6111yescharacteristic
717C2×C4#41×D6114yes—
718C8—42no—
719C8—2442no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—44no—
728C22—612no—
729C22—612no—
730C22—612no—
731C22—1228no—
732C22—1221no—
733C22—1221no—
734C22—1221no—
735C22—1221no—
736C22—1221no—
737C22—1221no—
738C22—1221no—
739C22—1221no—
740C22—1221no—
741C22—2444no—
742C22—2444no—
743C22—2444no—
744C22—2444no—
745C22—2444no—
746C22#1683977712yes—
747C22C2×C22⋊C4×D6111yescharacteristic
748C22#123×D6112yes—
749C4—21no—
750C4—21no—
751C4—42no—
752C4—42no—
753C4—82no—
754C4—612no—
755C4—612no—
756C4—1221no—
757C4—1221no—
758C4—4882no—
759C4—2442no—
760C4—2442no—
761C4#117×D6112yes—
762C4#123×D6112yes—
763C2—22no—
764C2—22no—
765C2—41no—
766C2—1222no—
767C2—1222no—
768C2—1222no—
769C2—2441no—
770C2#381×D6111yescharacteristic
771C2#421×D6111yescharacteristic
772C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1826C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1826D61
hypocenterC61#20705
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #21445919C2semidirect
5. #21445918C2semidirect
6. #21445917C2semidirect
7. #21445916C2semidirect
8. #21445527C2semidirect
9. C61×#1826C2semidirect
13. C2×#14519735C4semidirect
14. C2×#14519735C4semidirect
22. #117×D61C4semidirect
23. #117×D61C4semidirect
26. C2×C4⋊C4×D61C4semidirect
27. C2×C4⋊C4×D61C4semidirect
42. #16839523C22semidirect
43. #16839522C22semidirect
44. #16839521C22semidirect
48. C61×#339C22semidirect
384. #1826D61semidirect
434. #339C2×D61semidirect
435. C61#20705semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D612
#407×D612
#214482002
#214459192
#214459182
#214459172
#214459162
#214455272
C61×#18262
#2070561