Finite Group Databasebeta

← #29647407

Subgroups — #29647407

Order 15616.

1418 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic
3#21448201C211yesmaximal, characteristic
4#21444392C211yesmaximal, characteristic, complemented
5#21444391C211yesmaximal, characteristic, complemented
6#21444390C211yesmaximal, characteristic, complemented
7#21444350C214yesmaximal, complemented
8#21444337C214yesmaximal, complemented
9C61×#1520C211yesmaximal, characteristic, complemented
10C22×Q8×D61C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C22×#11758189—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×#14519735—21no—
27C2×C4⋊C4×D61—21no—
28C2×C4⋊C4×D61C411yescharacteristic, complemented
29C2×C22⋊C4×D61—21no—
30#16839724—21no—
31#16839724—21no—
32#16839724C2212yes—
33#16839724C2212yes—
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519689—21no—
36#16839624C2212yes—
37#16839622C2211yescharacteristic
38#16839619—21no—
39#16839617—21no—
40C22⋊C4×Dic61—21no—
41#16839609C2212yes—
42#16839500C2214yescomplemented
43#16839499C2214yescomplemented
44#16839498C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C61×#380C2211yescharacteristic
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×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189—44no—
76C22×#92418—21no—
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#14519735—44no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
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—22no—
128#14519684C2312yes—
129C22×Q8×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C22×C8×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×C61—21no—
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C22⋊C8×C61—21no—
142C22⋊C8×C61C2312yes—
143#95×C61C2312yes—
144C24×C61C2×D411yescharacteristic
145C23×D61—22no—
146C23×D61—22no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—42no—
157C2×Q8×C61C22×C412yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—22no—
161C22×C4×C61—42no—
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61—42no—
172C22×Dic61C22⋊C411yescharacteristic
173C22×Dic61C22⋊C411yescharacteristic
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178Q8×D61—44no—
179Q8×D61—44no—
180Q8×D61—44no—
181Q8×D61—44no—
182C2×C4×D61—24no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
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—42no—
198C2×C4×D61—44no—
199C2×C4×D61—44no—
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×D61C22×C411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×Dic122—21no—
217C2×Dic122—22no—
218C2×Dic122—22no—
219C2×Dic122—44no—
220C2×Dic122—42no—
221C2×Dic122C22×C412yes—
222C2×C8×C61—22no—
223C2×C8×C61—42no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—42no—
228C4⋊C4×C61C22×C412yes—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—42no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—42no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—44no—
240#11758198—44no—
241C4⋊Dic61—21no—
242C4⋊Dic61—22no—
243C4⋊Dic61—22no—
244C4⋊Dic61—42no—
245C4⋊Dic61C22×C412yes—
246#11758196—22no—
247#11758196—22no—
248#11758196—22no—
249#11758196—22no—
250#11758196—22no—
251#11758196—22no—
252C4×Dic61—44no—
253C2×#92418—22no—
254C2×#92418—42no—
255#11758189—44no—
256#11758189—44no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61C2×C22⋊C411yescharacteristic
260C23×C61C2×C22⋊C411yescharacteristic
261C23×C61#13712yes—
262C23×C61#13712yes—
263C23×C61C22×D411yescharacteristic
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—48no—
285C22×D61—48no—
286C22×D61C2×C22⋊C411yescharacteristic
287C22×D61C2×C22⋊C411yescharacteristic
288C22×D61C2×C22⋊C411yescharacteristic
289C22×D61C2×C22⋊C411yescharacteristic
290Q8×C61—42no—
291Q8×C61—42no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C23×C411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C2×C22⋊C411yescharacteristic
325C2×Dic61C2×C22⋊C411yescharacteristic
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—44no—
342C4×D61—44no—
343C4×D61—44no—
344C4×D61—44no—
345C4×D61#9914yes—
346Dic122—44no—
347Dic122—42no—
348Dic122—44no—
349Dic122—42no—
350C8×C61—42no—
351#92418—42no—
352#17578—611nomaximal, Sylow
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61#41912yes—
362C22×C61#41912yes—
363C22×C61C22×C22⋊C411yescharacteristic
364C22×C61C2×#13711yescharacteristic
365C22×C61C2×#13711yescharacteristic
366C2×D61—28no—
367C2×D61—21no—
368C2×D61—21no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—44no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61C2×#9912yes—
385C2×D61#42112yes—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—82no—
392C4×C61C2×#9912yes—
393Dic61—21no—
394Dic61—21no—
395Dic61—21no—
396Dic61—42no—
397Dic61—42no—
398Dic61—82no—
399Dic61C2×#9912yes—
400C22×C22⋊Q8—611no—
401C2×#407—611no—
402#2280—611no—
403#1520—611no—
404#1520—611no—
405#1520—611no—
406#1520D6111yescharacteristic, complemented
407#1511—614no—
408#1508—614no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—22no—
412C2×C61—22no—
413C2×C61C22×#9911yescharacteristic
414C2×C61C2×#41911yescharacteristic
415C2×C61C2×#42111yescharacteristic
416D61—22no—
417D61—22no—
418D61—41no—
419D61—41no—
420C23×Q8—611no—
421C24×C4—611no—
422C22×M16—1221no—
423C2×C22⋊Q8—611no—
424C2×C22⋊Q8—611no—
425C2×C22⋊Q8—612no—
426C2×C22⋊Q8—612no—
427C2×C22⋊Q8—612no—
428C2×C22⋊Q8—612no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8—1221no—
431C2×C22⋊Q8—1221no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8—1221no—
434C2×C22⋊Q8—1221no—
435C2×C22⋊Q8—1221no—
436C2×C22⋊Q8C2×D6111yescharacteristic
437C2×#117—1221no—
438C22×C4⋊C4—611no—
439C22×C4⋊C4—1221no—
440C22×C22⋊C4—1221no—
441#407—612no—
442#407—612no—
443#407—1221no—
444#407—1221no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—1221no—
447C2×C22⋊C8C2×D6111yescharacteristic
448#381—612no—
449#380—611no—
450#380—1221no—
451#380C2×D6111yescharacteristic
452#379—1221no—
453C4×C22⋊C4—612no—
454C4×C22⋊C4—1221no—
455#328—614no—
456#328—614no—
457#328—614no—
458#328C2×D6114yescomplemented
459C61#1757811yescharacteristic, complemented, Sylow
460C25—611no—
461C22×Q8—612no—
462C22×Q8—612no—
463C22×Q8—611no—
464C22×Q8—1221no—
465C22×Q8—1221no—
466C22×Q8—1221no—
467C22×Q8—2444no—
468C22×Q8C4×D6111yescharacteristic
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—1221no—
483C23×C4—1221no—
484C23×C4—2444no—
485C23×C4C22×D6111yescharacteristic
486C2×M16—1222no—
487C2×M16—1222no—
488C2×M16—2444no—
489C22×C8—21no—
490C22×C8—1221no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—612no—
494C22⋊Q8—612no—
495C22⋊Q8—612no—
496C22⋊Q8—612no—
497C22⋊Q8—612no—
498C22⋊Q8—612no—
499C22⋊Q8—1222no—
500C22⋊Q8—1222no—
501C22⋊Q8—1222no—
502C22⋊Q8—1222no—
503C22⋊Q8—1222no—
504C22⋊Q8—1222no—
505C22⋊Q8—1222no—
506C22⋊Q8—1222no—
507C22⋊Q8—1221no—
508C22⋊Q8—1221no—
509C22⋊Q8—1221no—
510C22⋊Q8—1221no—
511C22⋊Q8—1221no—
512C22⋊Q8—1221no—
513C22⋊Q8C4×D6112yes—
514C22⋊Q8C22×D6112yes—
515#117—2444no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—612no—
520C2×C4⋊C4—612no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1222no—
524C2×C4⋊C4—1222no—
525C2×C4⋊C4—1222no—
526C2×C4⋊C4—1222no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4C4×D6111yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—1222no—
536C2×C22⋊C4—1222no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1222no—
543C2×C22⋊C4—1222no—
544C2×C22⋊C4—1221no—
545C2×C42—1222no—
546C22⋊C8—21no—
547C22⋊C8—612no—
548C22⋊C8—1222no—
549C22⋊C8—1222no—
550C22⋊C8—1221no—
551C22⋊C8C22×D6112yes—
552#95—612no—
553#95—1222no—
554#95C22×D6112yes—
555C24—611no—
556C24—611no—
557C24—611no—
558C24—611no—
559C24—611no—
560C24—611no—
561C24—1222no—
562C24—1222no—
563C24—2442no—
564C24—2442no—
565C24D4×D6111yescharacteristic
566C2×Q8—21no—
567C2×Q8—42no—
568C2×Q8—612no—
569C2×Q8—1222no—
570C2×Q8—1222no—
571C2×Q8—1221no—
572C2×Q8—2442no—
573C2×Q8—2444no—
574C2×Q8—2444no—
575C2×Q8—2444no—
576C2×Q8—2444no—
577C2×Q8—2444no—
578C2×Q8C2×C4×D6112yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—42no—
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—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1222no—
615C22×C4—2442no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2444no—
625C22×C4—2444no—
626C22×C4—2442no—
627C22×C4C2×C4×D6111yescharacteristic
628C22×C4C2×C4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6111yescharacteristic
632C22×C4C23×D6111yescharacteristic
633M16—2444no—
634M16—2444no—
635C2×C8—22no—
636C2×C8—42no—
637C2×C8—1222no—
638C2×C8—2442no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—42no—
643C4⋊C4—612no—
644C4⋊C4—1222no—
645C4⋊C4—1222no—
646C4⋊C4—1222no—
647C4⋊C4—1222no—
648C4⋊C4—1222no—
649C4⋊C4—1222no—
650C4⋊C4—1222no—
651C4⋊C4—1221no—
652C4⋊C4—1222no—
653C4⋊C4—2442no—
654C4⋊C4C2×C4×D6112yes—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—1222no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—1222no—
663C22⋊C4—1222no—
664C22⋊C4—2444no—
665C22⋊C4—2444no—
666C22⋊C4—2442no—
667C42—2444no—
668C23—41no—
669C23—41no—
670C23—611no—
671C23—611no—
672C23—611no—
673C23—611no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—1222no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23—2448no—
695C23—2448no—
696C23C22⋊C4×D6111yescharacteristic
697C23C22⋊C4×D6111yescharacteristic
698C23#1451980612yes—
699C23#1451980912yes—
700C23C2×D4×D6111yescharacteristic
701Q8—42no—
702Q8—42no—
703Q8—2442no—
704Q8—2444no—
705Q8—2444no—
706Q8—2442no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—611no—
721C2×C4—614no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2444no—
746C2×C4—2444no—
747C2×C4—2444no—
748C2×C4—2444no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4C22⋊C4×D6111yescharacteristic
758C2×C4C22⋊C4×D6111yescharacteristic
759C2×C4C22×C4×D6111yescharacteristic
760C2×C4C2×D4×D6111yescharacteristic
761C8—42no—
762C8—2442no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—42no—
770C22—42no—
771C22—612no—
772C22—612no—
773C22—1228no—
774C22—1221no—
775C22—1221no—
776C22—1221no—
777C22—1221no—
778C22—1221no—
779C22—1221no—
780C22—1221no—
781C22—1221no—
782C22—1221no—
783C22—1221no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2444no—
789C22—2444no—
790C22—2444no—
791C22#1683976912yes—
792C22#1683976912yes—
793C22C2×C22⋊C4×D6111yescharacteristic
794C22C2×#1451980611yescharacteristic
795C22C2×#1451980911yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—42no—
800C4—42no—
801C4—82no—
802C4—612no—
803C4—1221no—
804C4—1221no—
805C4—1221no—
806C4—4882no—
807C4—2442no—
808C4—2442no—
809C4#99×D6112yes—
810C2—21no—
811C2—21no—
812C2—22no—
813C2—22no—
814C2—1222no—
815C2—1222no—
816C2—2441no—
817C2—2441no—
818C2C2×#99×D6111yescharacteristic
819C2C2×#1683976911yescharacteristic
820C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1520C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1520D61
hypocenterC61#17578
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
4. #21444392C2semidirect
5. #21444391C2semidirect
6. #21444390C2semidirect
7. #21444350C2semidirect
8. #21444337C2semidirect
9. C61×#1520C2semidirect
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
406. #1520D61semidirect
458. #328C2×D61semidirect
459. 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
C2×#168397242
#214482012
#214443922
#214443912
#214443902
#214443502
#214443372
C61×#15202
#1757861