Finite Group Databasebeta

← #29647406

Subgroups — #29647406

Order 15616.

1418 conjugacy classes of subgroups.

The subgroup lattice has 802 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#21448200C211yesmaximal, characteristic
4#21444389C214yesmaximal, complemented
5#21444350C214yesmaximal, complemented
6#21444340C211yesmaximal, characteristic, complemented
7#21444339C211yesmaximal, characteristic, complemented
8#21444338C211yesmaximal, characteristic, complemented
9C61×#1508C211yesmaximal, 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×#14519734—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#16839624C2212yes—
37#16839621C2212yes—
38#16839620—21no—
39#16839617—21no—
40C4×#11758198—21no—
41C4×C22⋊Dic61C2211yescharacteristic
42#16839500C2214yescomplemented
43#16839499C2214yescomplemented
44#16839498C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
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#14519734—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—21no—
123C22⋊#92418—21no—
124C22⋊#92418C2312yes—
125#14519689—22no—
126#14519689—22no—
127#14519684—22no—
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—
140C2×C42×C61—21no—
141C22⋊C8×C61—21no—
142C22⋊C8×C61C2312yes—
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—21no—
168C22×Dic61—21no—
169C22×Dic61—22no—
170C22×Dic61—42no—
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—24no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
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—
230C42×C61—42no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—42no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—44no—
239#11758198—44no—
240C4⋊Dic61—21no—
241C4⋊Dic61—22no—
242C4⋊Dic61—22no—
243C4⋊Dic61C22×C412yes—
244#11758196—22no—
245#11758196—22no—
246#11758196—22no—
247#11758196—22no—
248#11758196—22no—
249#11758196—22no—
250#11758196—44no—
251C4×Dic61—42no—
252#11758194—42no—
253C2×#92418—22no—
254#11758189—44no—
255C8×D61—44no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—41no—
259C23×C61C2×C22⋊C411yescharacteristic
260C23×C61C2×C22⋊C411yescharacteristic
261C23×C61C22×D411yescharacteristic
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—22no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—416no—
280C22×D61C2×C22⋊C411yescharacteristic
281C22×D61C2×C22⋊C411yescharacteristic
282C22×D61C2×C22⋊C411yescharacteristic
283C22×D61C2×C22⋊C411yescharacteristic
284C22×D61#13714yes—
285Q8×C61—42no—
286Q8×C61—42no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C2×C22⋊C411yescharacteristic
302C2×C4×C61C23×C411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61C2×C22⋊C411yescharacteristic
318C2×Dic61C2×C22⋊C411yescharacteristic
319C2×Dic61C2×C22⋊C411yescharacteristic
320C2×Dic61C2×C22⋊C411yescharacteristic
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—22no—
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—
340C4×D61#9914yes—
341Dic122—44no—
342Dic122—42no—
343Dic122—44no—
344Dic122—42no—
345C8×C61—42no—
346#92418—42no—
347#17578—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—44no—
356C22×C61#42112yes—
357C22×C61C22×C22⋊C411yescharacteristic
358C22×C61C2×#13712yes—
359C2×D61—28no—
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—21no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—44no—
372C2×D61—44no—
373C2×D61—44no—
374C2×D61C2×#9912yes—
375C2×D61#41912yes—
376C2×D61#41912yes—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—82no—
383C4×C61C2×#9912yes—
384Dic61—21no—
385Dic61—21no—
386Dic61—21no—
387Dic61—42no—
388Dic61—42no—
389Dic61—82no—
390Dic61C2×#9912yes—
391C22×C22⋊Q8—611no—
392C2×#407—611no—
393#2280—611no—
394#1520—614no—
395#1511—614no—
396#1508—611no—
397#1508—611no—
398#1508—611no—
399#1508D6111yescharacteristic, complemented
400C2×C61—22no—
401C2×C61—22no—
402C2×C61—41no—
403C2×C61C22×#9911yescharacteristic
404C2×C61C2×#41911yescharacteristic
405C2×C61C2×#42111yescharacteristic
406D61—22no—
407D61—22no—
408D61—22no—
409D61—41no—
410C23×Q8—611no—
411C24×C4—611no—
412C22×M16—1221no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8—612no—
416C2×C22⋊Q8—612no—
417C2×C22⋊Q8—612no—
418C2×C22⋊Q8—612no—
419C2×C22⋊Q8—611no—
420C2×C22⋊Q8—1221no—
421C2×C22⋊Q8—1221no—
422C2×C22⋊Q8—1221no—
423C2×C22⋊Q8—1221no—
424C2×C22⋊Q8—1221no—
425C2×C22⋊Q8—1221no—
426C2×C22⋊Q8C2×D6111yescharacteristic
427C2×#117—1221no—
428C22×C4⋊C4—611no—
429C22×C4⋊C4—1221no—
430C22×C22⋊C4—1221no—
431#407—611no—
432#407—612no—
433#407—1221no—
434#407—1221no—
435#407C2×D6111yescharacteristic
436C2×C22⋊C8—612no—
437C2×C22⋊C8—1221no—
438#381—612no—
439#380—612no—
440#380—1221no—
441#379—1221no—
442C4×C22⋊C4—611no—
443C4×C22⋊C4—1221no—
444C4×C22⋊C4C2×D6111yescharacteristic
445#328—614no—
446#328—614no—
447#328—614no—
448#328C2×D6114yescomplemented
449C61#1757811yescharacteristic, complemented, Sylow
450C25—611no—
451C22×Q8—612no—
452C22×Q8—612no—
453C22×Q8—611no—
454C22×Q8—1221no—
455C22×Q8—1221no—
456C22×Q8—1221no—
457C22×Q8—2444no—
458C22×Q8C4×D6111yescharacteristic
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—611no—
472C23×C4—1221no—
473C23×C4—1221no—
474C23×C4—2444no—
475C23×C4C22×D6111yescharacteristic
476C2×M16—21no—
477C2×M16—1222no—
478C2×M16—1221no—
479C2×M16—2444no—
480C22×C8—1222no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—612no—
484C22⋊Q8—612no—
485C22⋊Q8—612no—
486C22⋊Q8—612no—
487C22⋊Q8—612no—
488C22⋊Q8—612no—
489C22⋊Q8—1222no—
490C22⋊Q8—1222no—
491C22⋊Q8—1222no—
492C22⋊Q8—1222no—
493C22⋊Q8—1222no—
494C22⋊Q8—1222no—
495C22⋊Q8—1222no—
496C22⋊Q8—1222no—
497C22⋊Q8—1221no—
498C22⋊Q8—1221no—
499C22⋊Q8—1221no—
500C22⋊Q8—1221no—
501C22⋊Q8—1221no—
502C22⋊Q8—1221no—
503C22⋊Q8C4×D6112yes—
504C22⋊Q8C22×D6112yes—
505#117—2444no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—612no—
509C2×C4⋊C4—612no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4—1222no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1222no—
521C2×C4⋊C4C4×D6111yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1222no—
525C2×C22⋊C4—1222no—
526C2×C22⋊C4—1222no—
527C2×C22⋊C4—1222no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1222no—
532C2×C22⋊C4—1222no—
533C2×C22⋊C4—1221no—
534C2×C42—21no—
535C2×C42—1221no—
536C22⋊C8—21no—
537C22⋊C8—612no—
538C22⋊C8—1222no—
539C22⋊C8—1222no—
540C22⋊C8—1221no—
541C22⋊C8C22×D6112yes—
542#95—612no—
543#95—1222no—
544#95C22×D6112yes—
545C24—611no—
546C24—611no—
547C24—611no—
548C24—611no—
549C24—611no—
550C24—611no—
551C24—1224no—
552C24—2442no—
553C24—2442no—
554C24D4×D6111yescharacteristic
555C2×Q8—21no—
556C2×Q8—42no—
557C2×Q8—612no—
558C2×Q8—1222no—
559C2×Q8—1222no—
560C2×Q8—1221no—
561C2×Q8—2442no—
562C2×Q8—2444no—
563C2×Q8—2444no—
564C2×Q8—2444no—
565C2×Q8—2444no—
566C2×Q8—2444no—
567C2×Q8C2×C4×D6112yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—42no—
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—1224no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1222no—
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×C4—2442no—
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C2×C4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4D4×D6111yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4C23×D6111yescharacteristic
622M16—42no—
623M16—2444no—
624M16—2442no—
625C2×C8—22no—
626C2×C8—1222no—
627C2×C8—2444no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—21no—
631C4⋊C4—612no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C4⋊C4—1221no—
640C4⋊C4—1222no—
641C4⋊C4—2444no—
642C4⋊C4C2×C4×D6112yes—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—42no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—2444no—
653C22⋊C4—2444no—
654C22⋊C4—2442no—
655C42—42no—
656C42—2442no—
657C23—22no—
658C23—22no—
659C23—41no—
660C23—611no—
661C23—611no—
662C23—611no—
663C23—614no—
664C23—611no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—24416no—
683C23C22⋊C4×D6111yescharacteristic
684C23C22⋊C4×D6111yescharacteristic
685C23C2×D4×D6111yescharacteristic
686Q8—42no—
687Q8—42no—
688Q8—2442no—
689Q8—2444no—
690Q8—2444no—
691Q8—2442no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—611no—
706C2×C4—614no—
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—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2444no—
731C2×C4—2444no—
732C2×C4—2444no—
733C2×C4—2444no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4C22⋊C4×D6111yescharacteristic
743C2×C4C22⋊C4×D6111yescharacteristic
744C2×C4C22×C4×D6111yescharacteristic
745C2×C4C2×D4×D6111yescharacteristic
746C8—42no—
747C8—2442no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—44no—
756C22—612no—
757C22—612no—
758C22—612no—
759C22—1228no—
760C22—1221no—
761C22—1221no—
762C22—1221no—
763C22—1221no—
764C22—1221no—
765C22—1221no—
766C22—1221no—
767C22—1221no—
768C22—1221no—
769C22—2444no—
770C22—2444no—
771C22—2444no—
772C22—2444no—
773C22—2444no—
774C22#1683977712yes—
775C22C2×C22⋊C4×D6111yescharacteristic
776C22#137×D6112yes—
777C4—21no—
778C4—21no—
779C4—21no—
780C4—42no—
781C4—42no—
782C4—82no—
783C4—612no—
784C4—1221no—
785C4—1221no—
786C4—1221no—
787C4—4882no—
788C4—2442no—
789C4—2442no—
790C4#99×D6112yes—
791C2—22no—
792C2—22no—
793C2—41no—
794C2—1222no—
795C2—1222no—
796C2—1222no—
797C2—2441no—
798C2C2×#99×D6111yescharacteristic
799C2#419×D6111yescharacteristic
800C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1508C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1508D61
hypocenterC61#17578
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
4. #21444389C2semidirect
5. #21444350C2semidirect
6. #21444340C2semidirect
7. #21444339C2semidirect
8. #21444338C2semidirect
9. C61×#1508C2semidirect
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
399. #1508D61semidirect
448. #328C2×D61semidirect
449. 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
#214482002
#214443892
#214443502
#214443402
#214443392
#214443382
C61×#15082
#1757861