Finite Group Databasebeta

← #29646102

Subgroups — #29646102

Order 15616.

1386 conjugacy classes of subgroups.

The subgroup lattice has 784 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#407×D61C211yesmaximal, characteristic
4#21444184C211yesmaximal, characteristic, complemented
5#21444183C211yesmaximal, characteristic, complemented
6#21444182C211yesmaximal, characteristic, complemented
7#21444181C214yesmaximal, complemented
8#21444147C214yesmaximal, complemented
9C61×#1472C211yesmaximal, characteristic, complemented
10C22×Q8×D61C411yescharacteristic
11C23×C4×D61C2211yescharacteristic
12C22×#11758189—21no—
13C2×M16×D61—21no—
14C2×#14519757C411yescharacteristic
15C2×#14519756C2211yescharacteristic
16C2×#14519755C2212yes—
17C2×#14519754C412yes—
18C2×#14519753C411yescharacteristic
19C22⋊Q8×D61—21no—
20C22⋊Q8×D61—21no—
21C22⋊Q8×D61—21no—
22C22⋊Q8×D61—21no—
23C22⋊Q8×D61—21no—
24C22⋊Q8×D61—21no—
25C22⋊Q8×D61—21no—
26C22⋊Q8×D61—21no—
27C2×C4⋊C4×D61C411yescharacteristic
28C2×C4⋊C4×D61C2212yes—
29C2×C22⋊C4×D61C412yes—
30#16839726C2211yescharacteristic
31#16839725—21no—
32#16839724—21no—
33#16839724—21no—
34#16839724—21no—
35#16839724C2212yes—
36#16839724C2212yes—
37#16839724C2212yes—
38C2×C22⋊#92418C2211yescharacteristic
39C2×#14519689—21no—
40C22⋊C8×D61—21no—
41C22⋊C8×D61C2212yes—
42#16839488C2214yescomplemented
43#16839487C2214yescomplemented
44#16839487C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C61×#324C2214yescomplemented
49C24×D61C2×C411yescharacteristic
50C22×Dic122C2×C412yes—
51C22×Dic122C2×C411yescharacteristic
52C2×Q8×D61—21no—
53C2×Q8×D61—21no—
54C2×Q8×D61—21no—
55C2×Q8×D61—21no—
56C2×Q8×D61—44no—
57C23×Dic61C2×C411yescharacteristic
58C22×C4×D61—44no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C412yes—
61C22×C4×D61C2×C412yes—
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
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—
75C2×#11758189—22no—
76C2×#11758189—22no—
77C2×#11758189—44no—
78M16×D61—44no—
79C22×#92418—21no—
80C2×C8×D61—22no—
81#14519757—21no—
82#14519757—21no—
83#14519757—21no—
84#14519757—21no—
85#14519756—21no—
86#14519756—21no—
87#14519756—21no—
88#14519756—21no—
89#14519755—22no—
90#14519755—22no—
91#14519755—22no—
92#14519755—22no—
93#14519754—22no—
94#14519754—22no—
95#14519754—22no—
96#14519754—22no—
97#14519753—21no—
98#14519753—21no—
99#14519753—21no—
100#14519753—21no—
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×C4⋊Dic61C2×C412yes—
103C2×#11758196C2×C412yes—
104C2×#11758196C2×C412yes—
105C2×#11758196C2312yes—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—21no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61—22no—
113C4⋊C4×D61—22no—
114C2×C22⋊Dic61C2×C412yes—
115C2×#11758198C2×C412yes—
116C2×#11758198C2×C412yes—
117C22⋊C4×D61—22no—
118C22⋊C4×D61—22no—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C22⋊#92418—21no—
122C22⋊#92418—21no—
123C22⋊#92418C2312yes—
124C22⋊#92418C2312yes—
125#14519689—22no—
126#14519689—22no—
127#14519689—22no—
128#14519689—22no—
129C22×Q8×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C2×M16×C61—21no—
132C22×C8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2×C412yes—
140C22⋊C8×C61—21no—
141C22⋊C8×C61—21no—
142C22⋊C8×C61C2312yes—
143C22⋊C8×C61C2312yes—
144C24×C61C22×C411yescharacteristic
145C23×D61—24no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61C22⋊C411yescharacteristic
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C412yes—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C22×Dic61—42no—
167C22×Dic61C22⋊C411yescharacteristic
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22×C412yes—
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C412yes—
174C22×Dic61C22×C411yescharacteristic
175Q8×D61—44no—
176Q8×D61—44no—
177Q8×D61—44no—
178Q8×D61—44no—
179C2×C4×D61—24no—
180C2×C4×D61—24no—
181C2×C4×D61—24no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—42no—
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—44no—
196C2×C4×D61—44no—
197C2×C4×D61C22⋊C411yescharacteristic
198C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—22no—
216C2×Dic122—22no—
217C2×Dic122—44no—
218C2×Dic122—42no—
219M16×C61—42no—
220C2×C8×C61—22no—
221C2×C8×C61—22no—
222C2×C8×C61—42no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—22no—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61—22no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—22no—
238C4⋊Dic61—22no—
239#11758196—22no—
240#11758196—22no—
241#11758196—22no—
242#11758196—22no—
243#11758196—22no—
244#11758196—22no—
245#11758194—42no—
246C2×#92418—22no—
247C2×#92418—22no—
248C2×#92418—42no—
249#11758189—44no—
250#11758189—44no—
251#11758189—44no—
252C8×D61—44no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61C2×C22⋊C411yescharacteristic
257C23×C61C2×C22⋊C411yescharacteristic
258C23×C61C23×C411yescharacteristic
259C22×D61—22no—
260C22×D61—22no—
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—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—416no—
277C22×D61#10114yes—
278C22×D61C2×C22⋊C411yescharacteristic
279C22×D61C2×C22⋊C411yescharacteristic
280C22×D61C2×C22⋊C411yescharacteristic
281C22×D61C2×C22⋊C411yescharacteristic
282Q8×C61—42no—
283Q8×C61—42no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—42no—
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C22×D411yescharacteristic
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—24no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—42no—
308C2×Dic61C2×C22⋊C411yescharacteristic
309C2×Dic61C2×C22⋊C411yescharacteristic
310C2×Dic61C2×C22⋊C411yescharacteristic
311C2×Dic61C2×C22⋊C411yescharacteristic
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—41no—
322C4×D61—41no—
323C4×D61—41no—
324C4×D61—41no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—44no—
328C4×D61—44no—
329C4×D61—44no—
330C4×D61—44no—
331C4×D61#9914yes—
332Dic122—44no—
333Dic122—42no—
334Dic122—42no—
335Dic122—44no—
336C8×C61—42no—
337C8×C61—42no—
338#92418—42no—
339#92418—42no—
340#17397—611nomaximal, Sylow
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—44no—
349C22×C61C2×#10112yes—
350C22×C61C22×C22⋊C411yescharacteristic
351C22×C61#56812yes—
352C2×D61—28no—
353C2×D61—21no—
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—44no—
363C2×D61—44no—
364C2×D61—44no—
365C2×D61—44no—
366C2×D61—44no—
367C2×D61C2×#9912yes—
368C2×D61C2×#10112yes—
369C2×D61C2×#10112yes—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61C2×#9912yes—
376Dic61—21no—
377Dic61—21no—
378Dic61—21no—
379Dic61—42no—
380Dic61—42no—
381Dic61C2×#9912yes—
382C22×C22⋊Q8—611no—
383C2×#407—611no—
384C2×#407—611no—
385#1472—611no—
386#1472—611no—
387#1472—614no—
388#1472—611no—
389#1472D6111yescharacteristic, complemented
390#1463—614no—
391C2×C61—22no—
392C2×C61—22no—
393C2×C61—41no—
394C2×C61#287911yescharacteristic
395C2×C61C22×#9911yescharacteristic
396C2×C61C22×#10111yescharacteristic
397D61—22no—
398D61—22no—
399D61—22no—
400D61—41no—
401C23×Q8—611no—
402C24×C4—611no—
403C22×M16—1221no—
404C22×M16—1221no—
405C2×C22⋊Q8—611no—
406C2×C22⋊Q8—611no—
407C2×C22⋊Q8—611no—
408C2×C22⋊Q8—612no—
409C2×C22⋊Q8—612no—
410C2×C22⋊Q8—1221no—
411C2×C22⋊Q8—1221no—
412C2×C22⋊Q8—1221no—
413C2×C22⋊Q8—1221no—
414C2×C22⋊Q8—1221no—
415C2×C22⋊Q8—1221no—
416C2×C22⋊Q8—1221no—
417C2×C22⋊Q8—1221no—
418C2×C22⋊Q8C2×D6111yescharacteristic
419C22×C4⋊C4—611no—
420C22×C4⋊C4—612no—
421C22×C22⋊C4—612no—
422#407—611no—
423#407—612no—
424#407—612no—
425#407—612no—
426#407—1221no—
427#407—1221no—
428#407—1221no—
429#407—1221no—
430#407C2×D6111yescharacteristic
431C2×C22⋊C8—611no—
432C2×C22⋊C8—612no—
433C2×C22⋊C8—1221no—
434C2×C22⋊C8—1221no—
435C2×C22⋊C8C2×D6111yescharacteristic
436#324—614no—
437#324—614no—
438#324—614no—
439#324C2×D6114yescomplemented
440C61#1739711yescharacteristic, complemented, Sylow
441C25—611no—
442C22×Q8—612no—
443C22×Q8—611no—
444C22×Q8—1221no—
445C22×Q8—1221no—
446C22×Q8—1221no—
447C22×Q8—1221no—
448C22×Q8—2444no—
449C22×Q8C4×D6111yescharacteristic
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—612no—
464C23×C4—612no—
465C23×C4—2444no—
466C23×C4C22×D6111yescharacteristic
467C2×M16—21no—
468C2×M16—1222no—
469C2×M16—1222no—
470C2×M16—1222no—
471C2×M16—1221no—
472C2×M16—2444no—
473C2×M16—2444no—
474C22×C8—21no—
475C22×C8—1222no—
476C22×C8—1221no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—1222no—
482C22⋊Q8—1222no—
483C22⋊Q8—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—1221no—
490C22⋊Q8—1221no—
491C22⋊Q8—1221no—
492C22⋊Q8—1221no—
493C22⋊Q8—1221no—
494C22⋊Q8—1221no—
495C22⋊Q8—1221no—
496C22⋊Q8—1221no—
497C22⋊Q8—1221no—
498C22⋊Q8—1221no—
499C22⋊Q8—1221no—
500C22⋊Q8—1221no—
501C2×C4⋊C4—612no—
502C2×C4⋊C4—612no—
503C2×C4⋊C4—612no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—612no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1222no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4C4×D6111yescharacteristic
515C2×C4⋊C4C22×D6112yes—
516C2×C22⋊C4—612no—
517C2×C22⋊C4—612no—
518C2×C22⋊C4—612no—
519C2×C22⋊C4—1222no—
520C2×C22⋊C4—1222no—
521C2×C22⋊C4—1222no—
522C2×C22⋊C4—1222no—
523C2×C22⋊C4C4×D6112yes—
524C22⋊C8—21no—
525C22⋊C8—21no—
526C22⋊C8—612no—
527C22⋊C8—612no—
528C22⋊C8—1222no—
529C22⋊C8—1222no—
530C22⋊C8—1222no—
531C22⋊C8—1222no—
532C22⋊C8—1221no—
533C22⋊C8—1221no—
534C22⋊C8C22×D6112yes—
535C22⋊C8C22×D6112yes—
536C24—611no—
537C24—611no—
538C24—611no—
539C24—611no—
540C24—611no—
541C24—611no—
542C24—1224no—
543C24—2442no—
544C24—2442no—
545C24C2×C4×D6111yescharacteristic
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—42no—
549C2×Q8—1222no—
550C2×Q8—1222no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—2442no—
554C2×Q8—2444no—
555C2×Q8—2444no—
556C2×Q8—2444no—
557C2×Q8—2444no—
558C2×Q8—2444no—
559C22×C4—42no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
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—612no—
583C22×C4—612no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1224no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4—2444no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4—2444no—
602C22×C4—2442no—
603C22×C4C2×C4×D6112yes—
604C22×C4C2×C4×D6111yescharacteristic
605C22×C4C2×C4×D6112yes—
606C22×C4D4×D6111yescharacteristic
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4D4×D6111yescharacteristic
610C22×C4C23×D6111yescharacteristic
611M16—42no—
612M16—2444no—
613M16—2444no—
614M16—2444no—
615M16—2442no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—42no—
619C2×C8—1222no—
620C2×C8—1222no—
621C2×C8—2444no—
622C2×C8—2442no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—1222no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C4⋊C4—1222no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1222no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—611no—
649C23—611no—
650C23—611no—
651C23—614no—
652C23—611no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—24416no—
671C23C22⋊C4×D6111yescharacteristic
672C23C22⋊C4×D6111yescharacteristic
673C23C22×C4×D6111yescharacteristic
674Q8—42no—
675Q8—42no—
676Q8—2442no—
677Q8—2444no—
678Q8—2444no—
679Q8—2442no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—611no—
691C2×C4—614no—
692C2×C4—611no—
693C2×C4—611no—
694C2×C4—611no—
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—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1224no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2444no—
717C2×C4—2444no—
718C2×C4—2444no—
719C2×C4—2444no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2442no—
724C2×C4C22⋊C4×D6111yescharacteristic
725C2×C4C22⋊C4×D6111yescharacteristic
726C2×C4C2×D4×D6111yescharacteristic
727C2×C4C2×D4×D6111yescharacteristic
728C8—42no—
729C8—42no—
730C8—2442no—
731C8—2442no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—44no—
740C22—612no—
741C22—612no—
742C22—612no—
743C22—1228no—
744C22—1221no—
745C22—1221no—
746C22—1221no—
747C22—1221no—
748C22—1221no—
749C22—1221no—
750C22—1221no—
751C22—1221no—
752C22—1221no—
753C22—2444no—
754C22—2444no—
755C22—2444no—
756C22—2444no—
757C22—2444no—
758C22#101×D6112yes—
759C22C2×C22⋊C4×D6111yescharacteristic
760C22#1684052712yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—42no—
765C4—42no—
766C4—612no—
767C4—1221no—
768C4—1221no—
769C4—1221no—
770C4—2442no—
771C4—2442no—
772C4#99×D6112yes—
773C2—22no—
774C2—22no—
775C2—41no—
776C2—1222no—
777C2—1222no—
778C2—1222no—
779C2—2441no—
780C2#2145426111yescharacteristic
781C2C2×#99×D6111yescharacteristic
782C2C2×#101×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1472C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1472D61
hypocenterC61#17397
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
4. #21444184C2semidirect
5. #21444183C2semidirect
6. #21444182C2semidirect
7. #21444181C2semidirect
8. #21444147C2semidirect
9. C61×#1472C2semidirect
42. #16839488C22semidirect
43. #16839487C22semidirect
44. #16839487C22semidirect
48. C61×#324C22semidirect
389. #1472D61semidirect
439. #324C2×D61semidirect
440. C61#17397semidirect

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
#407×D612
#214441842
#214441832
#214441822
#214441812
#214441472
C61×#14722
#1739761