Finite Group Databasebeta

← #29647405

Subgroups — #29647405

Order 15616.

1418 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic
3#21448199C211yesmaximal, characteristic
4#21444389C214yesmaximal, complemented
5#21444353C211yesmaximal, characteristic, complemented
6#21444352C211yesmaximal, characteristic, complemented
7#21444351C211yesmaximal, characteristic, complemented
8#21444337C214yesmaximal, complemented
9C61×#1511C211yesmaximal, characteristic, complemented
10C22×Q8×D61C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61—21no—
13C2×#14519757C411yescharacteristic, complemented
14C2×#14519756C2211yescharacteristic
15C2×#14519755—21no—
16C2×#14519754—21no—
17C2×#14519753C411yescharacteristic, complemented
18C22⋊Q8×D61—21no—
19C22⋊Q8×D61—21no—
20C22⋊Q8×D61—21no—
21C22⋊Q8×D61—21no—
22C22⋊Q8×D61C412yescomplemented
23C22⋊Q8×D61C412yescomplemented
24C22⋊Q8×D61C2212yes—
25C22⋊Q8×D61C2212yes—
26C2×#14519733—21no—
27C2×C4⋊C4×D61—21no—
28C2×C4⋊C4×D61C411yescharacteristic, complemented
29C2×C22⋊C4×D61—21no—
30#16839726C2211yescharacteristic
31#16839725—21no—
32#16839724—21no—
33#16839724C2212yes—
34C22⋊C8×D61—21no—
35C22⋊C8×D61C2212yes—
36#16839625C2211yescharacteristic
37#16839621—21no—
38#16839621C2212yes—
39#16839617—21no—
40#16839609—21no—
41#16839609C2212yes—
42#16839500C2214yescomplemented
43#16839499C2214yescomplemented
44#16839498C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C61×#381C2211yescharacteristic
48C61×#328C2214yescomplemented
49C24×D61D411yescharacteristic
50C22×Dic122—21no—
51C22×Dic122C2×C411yescharacteristic
52C2×Q8×D61—21no—
53C2×Q8×D61—21no—
54C2×Q8×D61—44no—
55C2×Q8×D61C2×C412yes—
56C2×Q8×D61C2×C412yes—
57C23×Dic61D411yescharacteristic
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61—44no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×#11758194—21no—
74C2×#11758189—22no—
75M16×D61—44no—
76C2×C8×D61—22no—
77#14519757—21no—
78#14519757—21no—
79#14519757C2×C412yes—
80#14519757C2×C412yes—
81#14519756—21no—
82#14519756—21no—
83#14519756C2×C412yes—
84#14519756C2312yes—
85#14519755—22no—
86#14519755—22no—
87#14519755—22no—
88#14519755—22no—
89#14519754—22no—
90#14519754—22no—
91#14519754—22no—
92#14519754—22no—
93#14519753—21no—
94#14519753—21no—
95#14519753C2×C412yes—
96#14519753C2×C412yes—
97#14519733—44no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—22no—
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61C2×C412yes—
111C4⋊C4×D61C2×C412yes—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C22⋊C4×D61—22no—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C22⋊C4×D61—22no—
122C2×C4×Dic61—22no—
123C22⋊#92418—21no—
124C22⋊#92418C2312yes—
125#14519689—22no—
126#14519689—22no—
127#14519684—21no—
128#14519684C2312yes—
129C22×Q8×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C2×M16×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61C2×C412yes—
135C22⋊Q8×C61C2312yes—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C22⋊C8×C61—21no—
141C22⋊C8×C61C2312yes—
142#95×C61—21no—
143#95×C61C2312yes—
144C24×C61C2×D411yescharacteristic
145C23×D61—24no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61C22⋊C411yescharacteristic
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C2×D411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—42no—
156C2×Q8×C61C22×C412yes—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—22no—
160C22×C4×C61—42no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C22×Dic61—24no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61C22⋊C411yescharacteristic
172C22×Dic61C22⋊C411yescharacteristic
173C22×Dic61C22⋊C411yescharacteristic
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177Q8×D61—44no—
178Q8×D61—44no—
179Q8×D61—44no—
180Q8×D61—44no—
181C2×C4×D61—24no—
182C2×C4×D61—24no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
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×D61—44no—
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×D61C22×C411yescharacteristic
208C2×C4×D61C22×C411yescharacteristic
209C2×C4×D61C22×C411yescharacteristic
210C2×C4×D61C22×C411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×Dic122—21no—
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—44no—
219C2×Dic122—42no—
220C2×Dic122C22×C412yes—
221M16×C61—42no—
222C2×C8×C61—22no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61C22×C412yes—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—42no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—42no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—44no—
238#11758198—44no—
239C4⋊Dic61—21no—
240C4⋊Dic61—22no—
241C4⋊Dic61—22no—
242C4⋊Dic61C22×C412yes—
243#11758196—22no—
244#11758196—22no—
245#11758196—22no—
246#11758196—22no—
247#11758196—22no—
248#11758196—22no—
249#11758196—44no—
250C4×Dic61—44no—
251#11758194—42no—
252C2×#92418—22no—
253#11758189—44no—
254C8×D61—44no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—41no—
258C23×C61C2×C22⋊C411yescharacteristic
259C23×C61C2×C22⋊C411yescharacteristic
260C23×C61C22×D411yescharacteristic
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—416no—
279C22×D61C2×C22⋊C411yescharacteristic
280C22×D61C2×C22⋊C411yescharacteristic
281C22×D61C2×C22⋊C411yescharacteristic
282C22×D61C2×C22⋊C411yescharacteristic
283C22×D61#13714yes—
284Q8×C61—42no—
285Q8×C61—42no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C23×C411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61#9914yes—
316C2×Dic61C2×C22⋊C411yescharacteristic
317C2×Dic61C2×C22⋊C411yescharacteristic
318C2×Dic61C2×C22⋊C411yescharacteristic
319C2×Dic61C2×C22⋊C411yescharacteristic
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—44no—
337C4×D61—44no—
338C4×D61—44no—
339C4×D61—44no—
340Dic122—42no—
341Dic122—44no—
342Dic122—44no—
343Dic122—42no—
344C8×C61—42no—
345#92418—42no—
346#17578—611nomaximal, Sylow
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—44no—
355C22×C61C2×#9912yes—
356C22×C61C22×C22⋊C411yescharacteristic
357C22×C61C2×#13712yes—
358C2×D61—28no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—21no—
366C2×D61—21no—
367C2×D61—21no—
368C2×D61—44no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—44no—
372C2×D61—44no—
373C2×D61#41912yes—
374C2×D61#41912yes—
375C2×D61#42112yes—
376C4×C61—21no—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—82no—
383Dic61—21no—
384Dic61—21no—
385Dic61—42no—
386Dic61—42no—
387Dic61—82no—
388Dic61C2×#9912yes—
389Dic61C2×#9912yes—
390C22×C22⋊Q8—611no—
391C2×#407—611no—
392#2280—611no—
393#1520—614no—
394#1511—611no—
395#1511—611no—
396#1511—611no—
397#1511D6111yescharacteristic, complemented
398#1508—614no—
399C2×C61—22no—
400C2×C61—22no—
401C2×C61—41no—
402C2×C61C22×#9911yescharacteristic
403C2×C61C2×#41911yescharacteristic
404C2×C61C2×#42111yescharacteristic
405D61—22no—
406D61—22no—
407D61—22no—
408D61—41no—
409C23×Q8—611no—
410C24×C4—611no—
411C22×M16—1221no—
412C2×C22⋊Q8—611no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—612no—
415C2×C22⋊Q8—612no—
416C2×C22⋊Q8—612no—
417C2×C22⋊Q8—612no—
418C2×C22⋊Q8—611no—
419C2×C22⋊Q8—1221no—
420C2×C22⋊Q8—1221no—
421C2×C22⋊Q8—1221no—
422C2×C22⋊Q8—1221no—
423C2×C22⋊Q8—1221no—
424C2×C22⋊Q8—1221no—
425C2×C22⋊Q8C2×D6111yescharacteristic
426C2×#117—1221no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—1221no—
429C22×C22⋊C4—1221no—
430#407—611no—
431#407—612no—
432#407—1221no—
433#407—1221no—
434#407C2×D6111yescharacteristic
435C2×C22⋊C8—612no—
436C2×C22⋊C8—1221no—
437#381—611no—
438#381C2×D6111yescharacteristic
439#380—612no—
440#380—1221no—
441#379—1221no—
442C4×C22⋊C4—612no—
443C4×C22⋊C4—1221no—
444#328—614no—
445#328—614no—
446#328—614no—
447#328C2×D6114yescomplemented
448C61#1757811yescharacteristic, complemented, Sylow
449C25—611no—
450C22×Q8—612no—
451C22×Q8—612no—
452C22×Q8—611no—
453C22×Q8—1221no—
454C22×Q8—1221no—
455C22×Q8—1221no—
456C22×Q8—2444no—
457C22×Q8C4×D6111yescharacteristic
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—1221no—
473C23×C4—2444no—
474C23×C4C22×D6111yescharacteristic
475C2×M16—21no—
476C2×M16—1222no—
477C2×M16—1221no—
478C2×M16—2444no—
479C22×C8—1222no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—612no—
483C22⋊Q8—612no—
484C22⋊Q8—612no—
485C22⋊Q8—612no—
486C22⋊Q8—612no—
487C22⋊Q8—612no—
488C22⋊Q8—1222no—
489C22⋊Q8—1222no—
490C22⋊Q8—1222no—
491C22⋊Q8—1222no—
492C22⋊Q8—1222no—
493C22⋊Q8—1222no—
494C22⋊Q8—1222no—
495C22⋊Q8—1222no—
496C22⋊Q8—1221no—
497C22⋊Q8—1221no—
498C22⋊Q8—1221no—
499C22⋊Q8—1221no—
500C22⋊Q8—1221no—
501C22⋊Q8—1221no—
502C22⋊Q8C4×D6112yes—
503C22⋊Q8C22×D6112yes—
504#117—2444no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—612no—
508C2×C4⋊C4—612no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4C4×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1222no—
524C2×C22⋊C4—1222no—
525C2×C22⋊C4—1222no—
526C2×C22⋊C4—1222no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1222no—
531C2×C22⋊C4—1222no—
532C2×C22⋊C4—1221no—
533C2×C42—1222no—
534C22⋊C8—21no—
535C22⋊C8—612no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C22⋊C8—1221no—
539C22⋊C8C22×D6112yes—
540#95—21no—
541#95—612no—
542#95—1221no—
543#95C22×D6112yes—
544C24—611no—
545C24—611no—
546C24—611no—
547C24—611no—
548C24—611no—
549C24—611no—
550C24—1224no—
551C24—2442no—
552C24—2442no—
553C24D4×D6111yescharacteristic
554C2×Q8—21no—
555C2×Q8—42no—
556C2×Q8—612no—
557C2×Q8—1222no—
558C2×Q8—1222no—
559C2×Q8—1221no—
560C2×Q8—2442no—
561C2×Q8—2444no—
562C2×Q8—2444no—
563C2×Q8—2444no—
564C2×Q8—2444no—
565C2×Q8—2444no—
566C2×Q8C2×C4×D6112yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—42no—
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—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—1224no—
594C22×C4—1224no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1224no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1222no—
603C22×C4—2442no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4—2442no—
609C22×C4—2442no—
610C22×C4—2442no—
611C22×C4—2442no—
612C22×C4—2442no—
613C22×C4—2444no—
614C22×C4—2444no—
615C22×C4C2×C4×D6111yescharacteristic
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4D4×D6111yescharacteristic
620C22×C4C23×D6111yescharacteristic
621M16—42no—
622M16—2444no—
623M16—2442no—
624C2×C8—22no—
625C2×C8—1222no—
626C2×C8—2444no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—612no—
631C4⋊C4—1222no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1221no—
639C4⋊C4—1222no—
640C4⋊C4—2444no—
641C4⋊C4C2×C4×D6112yes—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—2444no—
652C22⋊C4—2444no—
653C22⋊C4—2442no—
654C42—2444no—
655C23—22no—
656C23—22no—
657C23—41no—
658C23—611no—
659C23—611no—
660C23—611no—
661C23—614no—
662C23—611no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—24416no—
681C23C22⋊C4×D6111yescharacteristic
682C23C22⋊C4×D6111yescharacteristic
683C23C2×D4×D6111yescharacteristic
684Q8—42no—
685Q8—42no—
686Q8—2442no—
687Q8—2442no—
688Q8—2444no—
689Q8—2444no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—614no—
706C2×C4—611no—
707C2×C4—611no—
708C2×C4—1222no—
709C2×C4—1222no—
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—1222no—
722C2×C4—1222no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2444no—
732C2×C4—2444no—
733C2×C4—2444no—
734C2×C4—2444no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4C22⋊C4×D6111yescharacteristic
741C2×C4C22⋊C4×D6111yescharacteristic
742C2×C4C22×C4×D6111yescharacteristic
743C2×C4C2×D4×D6111yescharacteristic
744C8—42no—
745C8—2442no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—44no—
754C22—612no—
755C22—612no—
756C22—612no—
757C22—1228no—
758C22—1221no—
759C22—1221no—
760C22—1221no—
761C22—1221no—
762C22—1221no—
763C22—1221no—
764C22—1221no—
765C22—1221no—
766C22—1221no—
767C22—2444no—
768C22—2444no—
769C22—2444no—
770C22—2444no—
771C22—2444no—
772C22#99×D6112yes—
773C22C2×C22⋊C4×D6111yescharacteristic
774C22#137×D6112yes—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—612no—
783C4—612no—
784C4—1221no—
785C4—1221no—
786C4—4882no—
787C4—2442no—
788C4—2442no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—1222no—
793C2—1222no—
794C2—1222no—
795C2—2441no—
796C2C2×#99×D6111yescharacteristic
797C2#419×D6111yescharacteristic
798C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1511C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1511D61
hypocenterC61#17578
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
4. #21444389C2semidirect
5. #21444353C2semidirect
6. #21444352C2semidirect
7. #21444351C2semidirect
8. #21444337C2semidirect
9. C61×#1511C2semidirect
10. C22×Q8×D61C4semidirect
13. C2×#14519757C4semidirect
17. C2×#14519753C4semidirect
22. C22⋊Q8×D61C4semidirect
23. C22⋊Q8×D61C4semidirect
28. C2×C4⋊C4×D61C4semidirect
42. #16839500C22semidirect
43. #16839499C22semidirect
44. #16839498C22semidirect
48. C61×#328C22semidirect
397. #1511D61semidirect
447. #328C2×D61semidirect
448. C61#17578semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
#407×D612
#214481992
#214443892
#214443532
#214443522
#214443512
#214443372
C61×#15112
#1757861