Finite Group Databasebeta

← C4×#16839922 #29685639

Subgroups — C4×#16839922 #29685639

Order 15616.

1480 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758222C211yesmaximal, characteristic
2C2×#16839922C211yesmaximal, characteristic
3C2×C4×#11758202C211yesmaximal, characteristic, complemented
4C2×C4×#11758201C211yesmaximal, characteristic, complemented
5#21446163C211yesmaximal, characteristic, complemented
6#21446156C211yesmaximal, characteristic, complemented
7#21446132C211yesmaximal, characteristic, complemented
8#21446086C211yesmaximal, characteristic, complemented
9#21446065C211yesmaximal, characteristic, complemented
10#21446016C211yesmaximal, characteristic, complemented
11#21445757C211yesmaximal, characteristic
12C4×#14519700C211yesmaximal, characteristic, complemented
13C4×#14519697C211yesmaximal, characteristic, complemented
14C4×C22⋊#92418C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C4×#11758222—24no—
20C4×#11758222—24no—
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×C22⋊D61—21no—
26C2×C4×C22⋊D61—21no—
27C2×#14519736C2211yescharacteristic
28C2×#14519734—21no—
29C2×C42×D61—21no—
30#16839922C418yesdirect product factor
31C4×#11758202—24no—
32C4×#11758201—24no—
33C2×#14519710C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×C4×#92418C2211yescharacteristic
46C2×C4×#92418C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839517C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C22×C42×C61C2211yescharacteristic
56C61×#391C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#387—21no—
59C61×#385—21no—
60C61×#380C2211yescharacteristic
61C4×C4⋊C4×C61—21no—
62C4×C4⋊C4×C61C2211yescharacteristic
63C4×C22⋊C4×C61—21no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222C2×C414yes—
70C22×Dic122C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C2×#11758202—22no—
77C2×#11758202—22no—
78C2×#11758202C2×C414yescomplemented
79C2×#11758201—22no—
80C2×#11758201—22no—
81C2×#11758201C2×C414yescomplemented
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C4×Dic122—22no—
87C4×Dic122—22no—
88C4×Dic122—22no—
89C4×Dic122D414yes—
90C4×D244—22no—
91C4×D244—22no—
92C4×D244—22no—
93C4×D244D414yes—
94C4×C22⋊D61—28no—
95C4×C22⋊D61—28no—
96#14519736—22no—
97#14519736—22no—
98#14519734—28no—
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C42×D61—28no—
110#14519710—22no—
111#14519708—22no—
112#14519701—22no—
113#14519701—22no—
114#14519700—22no—
115#14519700—22no—
116#14519700C2×C414yescomplemented
117#14519697—22no—
118#14519697—22no—
119#14519697C2×C414yescomplemented
120C22⋊#92418—22no—
121C22⋊#92418C2×C414yescomplemented
122C4×#92418—22no—
123C4×#92418—22no—
124C22×Q8×C61C2311yescharacteristic
125C23×C4×C61D411yescharacteristic
126C23×C4×C61D411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22⋊Q8×C61—22no—
129C22⋊Q8×C61C2×C414yescomplemented
130C4×Q8×C61—22no—
131C4×Q8×C61—22no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61—22no—
141C2×C42×C61—22no—
142C2×C42×C61—21no—
143C2×C42×C61—21no—
144C2×C42×C61D411yescharacteristic
145C2×C42×C61D411yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#95×C61—21no—
149#95×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C22×C412yes—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—41no—
175C22×C4×C61C22×C412yes—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61#4112yes—
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—24no—
184C2×C22⋊D61—24no—
185C2×C22⋊D61—24no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189#11758222—28no—
190#11758222—28no—
191#11758222—28no—
192#11758222—28no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244C22×C412yes—
197C2×D244C2×D412yes—
198C2×D244#4112yes—
199C2×C4×D61—24no—
200C2×C4×D61—24no—
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—24no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122C22×C412yes—
212C2×Dic122C2×D412yes—
213C2×Dic122#4112yes—
214C4⋊C4×C61—24no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—42no—
221C4⋊C4×C61—42no—
222C4⋊C4×C61C22×C412yes—
223C22⋊C4×C61—24no—
224C22⋊C4×C61—42no—
225C42×C61—22no—
226C42×C61—22no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—42no—
230C42×C61—42no—
231C42×C61C2×D412yes—
232C42×C61C2×D412yes—
233C22⋊Dic61—24no—
234#11758202—28no—
235#11758201—28no—
236#11758198—24no—
237#11758198—24no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61C2×D412yes—
241C4⋊Dic61C2×D412yes—
242#11758196—24no—
243#11758196—24no—
244C4×Dic61—24no—
245C4×Dic61—24no—
246C4×Dic61—24no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418C22×C412yes—
258C2×#92418C22×C412yes—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61C4×D412yes—
266C23×C61C22×D411yescharacteristic
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—41no—
277Q8×C61—41no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—44no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—44no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61C4×D412yes—
306C2×C4×C61#12012yes—
307C2×C4×C61#12012yes—
308C2×C4×C61#13512yes—
309C2×C4×C61#13512yes—
310C2×C4×C61#13712yes—
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C22⋊D61—216no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327D244—22no—
328D244—22no—
329D244—22no—
330D244C4×D414yes—
331C4×D61—216no—
332C4×D61—48no—
333C4×D61—48no—
334Dic122—22no—
335Dic122—22no—
336Dic122—22no—
337Dic122C4×D414yes—
338#92418—22no—
339#92418—22no—
340#92418—41no—
341#92418—41no—
342C4×#452—611nomaximal, Sylow
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61C2×C4×D411yescharacteristic
351C22×C61C2×#12011yescharacteristic
352C22×C61#52511yescharacteristic
353C22×C61C2×#13511yescharacteristic
354C22×C61C2×#13511yescharacteristic
355C22×C61C2×#13711yescharacteristic
356C22×C61#57511yescharacteristic
357C2×D61—24no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—42no—
368C4×C61—41no—
369C4×C61—42no—
370C4×C61—81no—
371C4×C61—81no—
372C4×C61#45214yescomplemented
373C4×C61C2×C4×D411yescharacteristic
374C4×C61C2×C4×D411yescharacteristic
375C4×C61#52511yescharacteristic
376C4×C61#52511yescharacteristic
377Dic61—24no—
378Dic61—42no—
379Dic61—42no—
380C2×C4×#41—611no—
381C2×#452—611no—
382C2×C4×Q16—611no—
383C2×C4×SD16—611no—
384C4×C22⋊Q8D6111yescharacteristic, complemented
385#1878—611no—
386#1877—611no—
387#1873—611no—
388#1865—611no—
389#1862—611no—
390#1854—611no—
391#1788—611no—
392C4×#103—611no—
393C4×#102—611no—
394C4×C22⋊C8—611no—
395C2×C61—42no—
396C2×C61C4×#12011yescharacteristic
397C2×C61C4×#13511yescharacteristic
398C2×C61C4×#13711yescharacteristic
399C2×C61C2×#45211yescharacteristic
400C2×C61#300211yescharacteristic
401C2×C61#310211yescharacteristic
402C2×C61#310711yescharacteristic
403D61—44no—
404C22×#41—611no—
405C22×Q16—611no—
406C22×SD16—611no—
407C2×C22⋊Q8C2×D6111yescharacteristic
408C4×#41—1224no—
409C4×#41—1224no—
410C2×C4×Q8—611no—
411C2×C4×Q8—611no—
412C2×C4×Q8C2×D6111yescharacteristic
413C2×C4×D4—611no—
414C2×C4×D4—611no—
415C2×C4×D4—1221no—
416C2×C4×D4—1221no—
417C2×#117—611no—
418C2×#117—1221no—
419C22×C42—1221no—
420C22×C42C2×D6111yescharacteristic
421#452—618no—
422C4×Q16—1224no—
423C4×SD16—1224no—
424C2×#107—611no—
425C2×#106—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C4×C8—611no—
437C2×C4×C8—611no—
438#391C2×D6111yescharacteristic
439#389C2×D6111yescharacteristic
440#387—21no—
441#385—21no—
442#380C2×D6111yescharacteristic
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2×D6111yescharacteristic
445C4×C22⋊C4—21no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450#336—611no—
451#336—611no—
452C61C4×#45211yescharacteristic, complemented, Sylow
453C2×#41—614no—
454C2×#41—1222no—
455C2×#41—1222no—
456C2×#41—1222no—
457C2×#41—1222no—
458C2×#41—1222no—
459C22×Q8—611no—
460C22×Q8C22×D6111yescharacteristic
461C22×D4—611no—
462C22×D4—1221no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4—1221no—
466C23×C4C22⋊D6111yescharacteristic
467C23×C4C22⋊D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C2×Q16—614no—
470C2×Q16—1222no—
471C2×Q16—1222no—
472C2×SD16—614no—
473C2×SD16—1222no—
474C2×SD16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22⋊Q8—22no—
480C22⋊Q8C4×D6114yescomplemented
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—614no—
484C4×Q8—1222no—
485C4×Q8—1222no—
486C4×Q8—1222no—
487C4×D4—614no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1228no—
491C4×D4—1228no—
492C4×D4—1222no—
493#117—1228no—
494#117—1222no—
495#117—1222no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—1228no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42C22⋊D6111yescharacteristic
520C2×C42C22⋊D6111yescharacteristic
521C2×C42C22×D6111yescharacteristic
522C2×C42C22×D6111yescharacteristic
523#107—1222no—
524#106—1222no—
525#103—614no—
526#103—1222no—
527#103—1222no—
528#103—1222no—
529#103—1222no—
530#102—614no—
531#102—1222no—
532#102—1222no—
533C22⋊C8—614no—
534C22⋊C8—1222no—
535C4×C8—1222no—
536C4×C8—1222no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542C24—1221no—
543C24C2×C22⋊D6111yescharacteristic
544#41—1228no—
545#41—1228no—
546#41—1228no—
547#41—1228no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—612no—
554C2×Q8—612no—
555C2×Q8—612no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8C2×C4×D6112yes—
560C2×D4—612no—
561C2×D4—612no—
562C2×D4—612no—
563C2×D4—1224no—
564C2×D4—1224no—
565C2×D4—1224no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—41no—
583C22×C4—1224no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1221no—
587C22×C4—1224no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1224no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4—2442no—
595C22×C4C2×C4×D6112yes—
596C22×C4#1175822212yes—
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603Q16—1228no—
604SD16—1228no—
605C2×C8—612no—
606C2×C8—612no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C4⋊C4—21no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—612no—
626C4⋊C4—612no—
627C4⋊C4—1224no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1224no—
631C4⋊C4C2×C4×D6112yes—
632C22⋊C4—24no—
633C22⋊C4—42no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C42—21no—
638C42—21no—
639C42—22no—
640C42—22no—
641C42—42no—
642C42—42no—
643C42—1224no—
644C42—1224no—
645C42—1224no—
646C42D4×D6112yes—
647C42D4×D6112yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23C4×C22⋊D6112yes—
662C23C22×C22⋊D6111yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—41no—
666Q8—41no—
667Q8—614no—
668Q8—1222no—
669Q8—1222no—
670Q8—1222no—
671D4—614no—
672D4—12216no—
673D4—1222no—
674D4—1222no—
675D4—1222no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—44no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—44no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—12216no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—2448no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2448no—
715C2×C4C4×C22⋊D6112yes—
716C2×C4#1451974512yes—
717C2×C4#1451974512yes—
718C2×C4#1451979712yes—
719C2×C4#1451979712yes—
720C2×C4#1451980812yes—
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×D4×D6111yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C2×C4#41×D6111yescharacteristic
726C2×C4C2×#1175822211yescharacteristic
727C8—1222no—
728C8—1222no—
729C8—2441no—
730C8—2441no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—1224no—
739C22—2442no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22—2442no—
744C22—2442no—
745C22C2×C4×C22⋊D6111yescharacteristic
746C22C2×#1451974511yescharacteristic
747C22#1684026911yescharacteristic
748C22C2×#1451979711yescharacteristic
749C22C2×#1451979711yescharacteristic
750C22C2×#1451980811yescharacteristic
751C22#1684056011yescharacteristic
752C4—22no—
753C4—22no—
754C4—22no—
755C4—42no—
756C4—41no—
757C4—42no—
758C4—81no—
759C4—81no—
760C4—1224no—
761C4—2442no—
762C4—2442no—
763C4#1683992214yesdirect product factor
764C4C4×D4×D6111yescharacteristic
765C4C4×D4×D6111yescharacteristic
766C4#1684027111yescharacteristic
767C4#1684027111yescharacteristic
768C2—42no—
769C2—2444no—
770C2C4×#1451974511yescharacteristic
771C2C4×#1451979711yescharacteristic
772C2C4×#1451980811yescharacteristic
773C2C2×#1683992211yescharacteristic
774C2#2145503511yescharacteristic
775C2#2145583111yescharacteristic
776C2#2145588411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×C22⋊Q8×C61C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC4×C22⋊Q8D61
hypocenterC61C4×#452
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758202C2semidirect
4. C2×C4×#11758201C2semidirect
5. #21446163C2semidirect
6. #21446156C2semidirect
7. #21446132C2semidirect
8. #21446086C2semidirect
9. #21446065C2semidirect
10. #21446016C2semidirect
12. C4×#14519700C2semidirect
13. C4×#14519697C2semidirect
14. C4×C22⋊#92418C2semidirect
15. C4×C22⋊Q8×C61C2semidirect
30. #16839922C4direct (N × H)
78. C2×#11758202C2×C4semidirect
81. C2×#11758201C2×C4semidirect
116. #14519700C2×C4semidirect
119. #14519697C2×C4semidirect
121. C22⋊#92418C2×C4semidirect
129. C22⋊Q8×C61C2×C4semidirect
372. C4×C61#452semidirect
384. C4×C22⋊Q8D61semidirect
452. C61C4×#452semidirect
480. C22⋊Q8C4×D61semidirect
763. C4#16839922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#117582222
C2×#168399222
C2×C4×#117582022
C2×C4×#117582012
#214461632
#214461562
#214461322
#214460862
#214460652
#214460162
#214457572
C4×#145197002
C4×#145196972
C4×C22⋊#924182
C4×C22⋊Q8×C612
C4×#45261