Finite Group Databasebeta

← D4×#14519840 #30620161

Subgroups — D4×#14519840 #30620161

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D61⋊C8C211yesmaximal, characteristic
2C22×#14519840C212yesmaximal, complemented
3D4×C4⋊#6923C211yesmaximal, characteristic
4#21461985C211yesmaximal, characteristic, complemented
5#21461946C211yesmaximal, characteristic, complemented
6#21461832C212yesmaximal, complemented
7#21461804C212yesmaximal, complemented
8#21461688C211yesmaximal, characteristic, complemented
9#21461658C212yesmaximal, complemented
10C4×#14519840C211yesmaximal, characteristic, complemented
11D4×Q8×D61C211yesmaximal, characteristic
12C22×D61⋊C8C2212yes—
13C2×D4×#6923—21no—
14C22×C4⋊#6923C2212yes—
15#16840790—21no—
16#16840789—22no—
17D4×#92420—21no—
18D61⋊(C4⋊C8)C2211yescharacteristic
19C2×#14519840—28no—
20C2×#14519840C2212yes—
21C2×#14519840C2212yes—
22C2×#14519840C2211yescharacteristic
23C2×#14519840C2212yes—
24C2×#14519840C2212yes—
25C2×#14519840C2212yes—
26C2×#14519840C2211yescharacteristic
27D61⋊(C22⋊C8)C2212yes—
28C4×D61⋊C8C2211yescharacteristic
29#16840713—21no—
30#16840709—22no—
31#16840708C2211yescharacteristic
32#16840704C2212yes—
33C4×C4⋊#6923C2211yescharacteristic
34#16840635C2211yescharacteristic
35#16840635C2212yes—
36#16840635C2211yescharacteristic
37C22×Q8×D61C2212yes—
38Q8×D244C411yescharacteristic, complemented
39D4×Dic122—21no—
40D4×Dic122C411yescharacteristic, complemented
41#16840427—21no—
42#16840427C411yescharacteristic, complemented
43Q8×C22⋊D61C412yescomplemented
44#16840425—22no—
45#16840425C412yescomplemented
46C4⋊Q8×D61—21no—
47C4⋊Q8×D61C2211yescharacteristic
48C22⋊Q8×D61—22no—
49C22⋊Q8×D61C2212yes—
50C4×Q8×D61C2211yescharacteristic
51C4×D4×D61—21no—
52C4×D4×D61C2211yescharacteristic
53D4×Q8×C61C411yescharacteristic, complemented
54C23×#6923—22no—
55C2×D61⋊C8—24no—
56C2×D61⋊C8—22no—
57C2×D61⋊C8—42no—
58C2×D61⋊C8C2311yescharacteristic
59C2×D61⋊C8C2312yes—
60C2×D61⋊C8C2311yescharacteristic
61C22×#92420—22no—
62D4×#6923—44no—
63C2×C4⋊#6923—24no—
64C2×C4⋊#6923—21no—
65C2×C4⋊#6923—22no—
66C2×C4⋊#6923—21no—
67C2×C4⋊#6923—42no—
68C2×C4⋊#6923C2311yescharacteristic
69C2×C4⋊#6923C2312yes—
70C2×C4⋊#6923C2311yescharacteristic
71C2×C22⋊#6923—22no—
72C2×C4×#6923—21no—
73#14519844—21no—
74C4⋊#92420—21no—
75#14519840—24no—
76#14519840—22no—
77#14519840—24no—
78#14519840—24no—
79#14519840—42no—
80#14519840—42no—
81#14519840D414yesdirect product factor
82#14519834—22no—
83C22⋊#92420—22no—
84C4×#92420—21no—
85C4×#92420—21no—
86(C2×#6923)⋊C4—22no—
87(C2×#6923)⋊C4—21no—
88C22×Dic122—22no—
89C22×Dic122C2×C412yescomplemented
90C2×Q8×D61—22no—
91C2×Q8×D61—22no—
92C2×Q8×D61—24no—
93C2×Q8×D61—24no—
94C2×Q8×D61—42no—
95C2×Q8×D61—42no—
96C2×Q8×D61C2×C412yescomplemented
97C2×Q8×D61C2×C412yescomplemented
98C2×Q8×D61C2312yes—
99C2×Q8×D61C2311yescharacteristic
100C2×D4×D61D411yescharacteristic
101C22×C4×D61—22no—
102C22×C4×D61C2312yes—
103#14519777—21no—
104#14519777C2×C411yescharacteristic, complemented
105#14519776—21no—
106#14519776—21no—
107#14519776—22no—
108#14519776—21no—
109#14519776—21no—
110#14519775—22no—
111#14519775C2×C412yescomplemented
112#14519757—22no—
113#14519757C2×C412yescomplemented
114#14519756—22no—
115#14519756C2×C412yescomplemented
116#14519755—22no—
117#14519755—22no—
118#14519755—22no—
119#14519754—22no—
120#14519754—22no—
121#14519754—22no—
122#14519753—22no—
123#14519753C2×C412yescomplemented
124Q8×Dic61C2×C411yescharacteristic, complemented
125C4×Dic122—21no—
126C4×Dic122C2×C411yescharacteristic, complemented
127#14519742—21no—
128#14519742C2×C411yescharacteristic, complemented
129C4×D244—21no—
130C4×D244C2×C411yescharacteristic
131D4×Dic61—21no—
132D4×Dic61D411yescharacteristic
133#14519739—21no—
134#14519739D411yescharacteristic
135C4×C22⋊D61—22no—
136C4×C22⋊D61C2×C412yes—
137#14519737—22no—
138#14519737D412yes—
139C4⋊C4×D61—21no—
140C4⋊C4×D61—21no—
141C4⋊C4×D61—21no—
142C4⋊C4×D61—22no—
143C4⋊C4×D61D411yescharacteristic
144C4⋊C4×D61C2311yescharacteristic
145C22⋊C4×D61—22no—
146C22⋊C4×D61D412yes—
147C42×D61—21no—
148C42×D61C2311yescharacteristic
149C22×Q8×C61C2×C412yescomplemented
150C4⋊Q8×C61—21no—
151C4⋊Q8×C61C2×C411yescharacteristic, complemented
152C22⋊Q8×C61—22no—
153C22⋊Q8×C61C2×C412yescomplemented
154C4×Q8×C61C2×C411yescharacteristic, complemented
155C4×D4×C61—21no—
156C4×D4×C61C2×C411yescharacteristic
157C23×D61C2×D412yes—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—22no—
161C22×#6923—44no—
162C22×#6923—44no—
163C22×#6923—82no—
164C2×Q8×C61—22no—
165C2×Q8×C61—24no—
166C2×Q8×C61—42no—
167C2×Q8×C61C22×C412yes—
168C2×Q8×C61C22×C411yescharacteristic
169C2×D4×C61C22⋊C411yescharacteristic
170C22×C4×C61—22no—
171C22×C4×C61C22×C412yes—
172C2×C22⋊D61C22⋊C412yes—
173C22×Dic61—22no—
174C22×Dic61C2×D412yes—
175Q8×D61—21no—
176Q8×D61—21no—
177Q8×D61—24no—
178Q8×D61—22no—
179Q8×D61—22no—
180Q8×D61—22no—
181Q8×D61—22no—
182Q8×D61—24no—
183Q8×D61—42no—
184Q8×D61—42no—
185Q8×D61—44no—
186Q8×D61—44no—
187Q8×D61—44no—
188Q8×D61—44no—
189Q8×D61C2×D412yes—
190Q8×D61#4112yes—
191D4×D61SD1614yes—
192D4×D61Q1614yes—
193C2×D244C22⋊C411yescharacteristic
194C2×C4×D61—21no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—22no—
202C2×C4×D61—21no—
203C2×C4×D61—44no—
204C2×C4×D61—44no—
205C2×C4×D61C22×C412yes—
206C2×C4×D61C2×D412yes—
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2411yescharacteristic
211C2×Dic122—21no—
212C2×Dic122—24no—
213C2×Dic122—22no—
214C2×Dic122—22no—
215C2×Dic122—22no—
216C2×Dic122—22no—
217C2×Dic122—42no—
218C2×Dic122—44no—
219C2×Dic122—44no—
220C2×Dic122C22×C412yes—
221C2×Dic122C22×C411yescharacteristic
222C22⋊#6923—44no—
223C2×#92420—21no—
224C2×#92420—21no—
225C2×#92420—22no—
226C2×#92420—44no—
227C4⋊#6923—22no—
228C4⋊#6923—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—22no—
232C4⋊#6923—44no—
233C4⋊#6923—42no—
234C4⋊#6923—81no—
235C4⋊#6923C2×D412yes—
236C4×#6923—42no—
237D61⋊C8—21no—
238D61⋊C8—22no—
239D61⋊C8—21no—
240D61⋊C8—21no—
241D61⋊C8—22no—
242D61⋊C8—44no—
243D61⋊C8C2×D412yes—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—22no—
248C4⋊C4×C61C22⋊C411yescharacteristic
249C4⋊C4×C61C22×C411yescharacteristic
250C22⋊C4×C61—22no—
251C22⋊C4×C61C22⋊C412yes—
252C42×C61—21no—
253C42×C61C22×C411yescharacteristic
254C22⋊Dic61—22no—
255C22⋊Dic61C22⋊C412yes—
256#11758198—22no—
257#11758198—22no—
258#11758198C22⋊C412yes—
259#11758198C22⋊C412yes—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—22no—
264C4⋊Dic61C22⋊C411yescharacteristic
265C4⋊Dic61C22×C411yescharacteristic
266#11758196—21no—
267#11758196—22no—
268#11758196—22no—
269#11758196—21no—
270#11758196—22no—
271#11758196—22no—
272#11758196—21no—
273#11758196C22⋊C412yes—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61C22×C411yescharacteristic
278C4×Dic61C2×D411yescharacteristic
279C4×Dic61C2×D411yescharacteristic
280C23×C61C2×C22⋊C412yes—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61C2×C22⋊C412yes—
286C22×D61C2×SD1614yes—
287C22×D61C2×Q1614yes—
288C22×D61C22×D411yescharacteristic
289C2×#6923—22no—
290C2×#6923—41no—
291C2×#6923—41no—
292C2×#6923—42no—
293C2×#6923—41no—
294C2×#6923—41no—
295C2×#6923—42no—
296C2×#6923—42no—
297C2×#6923—41no—
298C2×#6923—88no—
299Q8×C61—21no—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—44no—
303Q8×C61C4×D412yescomplemented
304D4×C61#10314yescomplemented
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—44no—
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C2×C22⋊C412yes—
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C23×C411yescharacteristic
315C22⋊D61#10318yescomplemented
316C2×Dic61—21no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—21no—
320C2×Dic61—22no—
321C2×Dic61—44no—
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C2×C22⋊C412yes—
324C2×Dic61C2×C22⋊C411yescharacteristic
325C2×Dic61C22×D411yescharacteristic
326D244#10314yescomplemented
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—21no—
332C4×D61—21no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—44no—
338C4×D61—44no—
339C4×D61—42no—
340C4×D61—42no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61C2×SD1612yes—
344C4×D61C2×Q1612yes—
345C4×D61C22×D411yescharacteristic
346C4×D61C2×#4111yescharacteristic
347C4×D61H(5,𝔽2)11yescharacteristic
348C4×D61H(5,𝔽2)11yescharacteristic
349Dic122—21no—
350Dic122—22no—
351Dic122—22no—
352Dic122—22no—
353Dic122—22no—
354Dic122—44no—
355Dic122—44no—
356Dic122—44no—
357Dic122—42no—
358Dic122—42no—
359Dic122C4×D412yescomplemented
360#92420—22no—
361#92420—42no—
362#92420—41no—
363D4×#103—611nomaximal, Sylow
364C22×C61—22no—
365C22×C61—22no—
366C22×C61C2×#10314yescomplemented
367C22×C61C22×C22⋊C411yescharacteristic
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—24no—
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—24no—
374C2×D61C2×#10314yescomplemented
375C2×D61D4211yescharacteristic
376C2×D61#54611yescharacteristic
377C2×D61C22×SD1611yescharacteristic
378C2×D61C22×Q1611yescharacteristic
379C2×D61#57711yescharacteristic
380C2×D61#57811yescharacteristic
381#6923—42no—
382#6923—82no—
383#6923—81no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—21no—
387C4×C61—42no—
388C4×C61—41no—
389C4×C61C2×#10312yescomplemented
390C4×C61C2×C4×D411yescharacteristic
391C4×C61#51811yescharacteristic
392Dic61—22no—
393Dic61—22no—
394Dic61—21no—
395Dic61—42no—
396Dic61—41no—
397Dic61C2×#10312yescomplemented
398Dic61D4211yescharacteristic
399Dic61#54611yescharacteristic
400C2×D4×Q8—611no—
401C2×C8×D4—611no—
402C22×#103—612no—
403D4×C4⋊C4—611no—
404#1981—611no—
405#1956—611no—
406#1892—612no—
407#1872—612no—
408#1803—611no—
409#1787—612no—
410C4×#103—611no—
411C2×C61—24no—
412C2×C61D4×C22⋊C411yescharacteristic
413C2×C61C22×#10311yescharacteristic
414C2×C61#289811yescharacteristic
415D61—24no—
416D61D4×SD1611yescharacteristic
417D61D4×Q1611yescharacteristic
418D61#329811yescharacteristic
419D61#329911yescharacteristic
420C23×Q8—612no—
421C23×C8—612no—
422D4×Q8—612no—
423D4×Q8—611no—
424D4×Q8—612no—
425D4×Q8—611no—
426D4×Q8—611no—
427D4×Q8—1221no—
428D4×Q8—1222no—
429D4×Q8—1221no—
430D4×Q8#692311yescharacteristic, complemented
431C2×C4⋊Q8—611no—
432C2×C4⋊Q8—1221no—
433C2×C22⋊Q8—612no—
434C2×C22⋊Q8—1222no—
435C2×C4×Q8—611no—
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×C4×D4—1221no—
439C22×C4⋊C4—612no—
440C8×D4—1221no—
441C8×D4—1222no—
442C8×D4—1221no—
443C2×C4⋊C8—611no—
444C2×#103—611no—
445C2×#103—612no—
446C2×#103—612no—
447C2×#103—612no—
448C2×#103—611no—
449C2×#103—612no—
450C2×#103—612no—
451C2×#103—1228no—
452C2×C22⋊C8—612no—
453C2×C4×C8—611no—
454#389—1221no—
455#385—1222no—
456#384—611no—
457#380—612no—
458C4×C4⋊C4—611no—
459#340—612no—
460#340—611no—
461#340—611no—
462C61D4×#10311yescharacteristic, complemented, Sylow
463C22×Q8—611no—
464C22×Q8—612no—
465C22×Q8—612no—
466C22×Q8—612no—
467C22×Q8—612no—
468C22×Q8—1222no—
469C22×Q8—1222no—
470C22×Q8—1222no—
471C22×Q8—1224no—
472C22×Q8—1224no—
473C22×Q8—2442no—
474C22×Q8—2442no—
475C22×Q8C2×#692312yescomplemented
476C22×D4—611no—
477C23×C4—612no—
478C23×C4—1222no—
479C23×C4—1222no—
480C22×C8—611no—
481C22×C8—612no—
482C22×C8—611no—
483C22×C8—1224no—
484C22×C8—1222no—
485C22×C8—1222no—
486C22×C8—2442no—
487C4⋊Q8—21no—
488C4⋊Q8—612no—
489C4⋊Q8—611no—
490C4⋊Q8—1221no—
491C4⋊Q8—1221no—
492C4⋊Q8—1221no—
493C4⋊Q8—1222no—
494C4⋊Q8—1221no—
495C4⋊Q8—1222no—
496C4⋊Q8—1221no—
497C4⋊Q8C2×#692311yescharacteristic, complemented
498C22⋊Q8—22no—
499C22⋊Q8—612no—
500C22⋊Q8—612no—
501C22⋊Q8—612no—
502C22⋊Q8—1222no—
503C22⋊Q8—1222no—
504C22⋊Q8—1222no—
505C22⋊Q8—1222no—
506C22⋊Q8—1222no—
507C22⋊Q8—1222no—
508C22⋊Q8—1222no—
509C22⋊Q8—1222no—
510C22⋊Q8—1222no—
511C22⋊Q8C2×#692312yescomplemented
512C4×Q8—611no—
513C4×Q8—611no—
514C4×Q8—611no—
515C4×Q8—1221no—
516C4×Q8—1221no—
517C4×Q8C2×#692311yescharacteristic, complemented
518C4×D4—21no—
519C4×D4—611no—
520C4×D4—612no—
521C4×D4—611no—
522C4×D4—612no—
523C4×D4—611no—
524C4×D4—1221no—
525C4×D4—1222no—
526C4×D4—1221no—
527C4×D4—1222no—
528C4×D4—1221no—
529C4×D4—2444no—
530C4×D4C2×#692311yescharacteristic
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—612no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1222no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1224no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1222no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—2442no—
545C2×C22⋊C4—612no—
546C2×C22⋊C4—1222no—
547C2×C22⋊C4—1222no—
548C2×C42—611no—
549C2×C42—1221no—
550C2×C42—1221no—
551C4⋊C8—1221no—
552C4⋊C8—1221no—
553#103—614no—
554#103—1224no—
555#103—1224no—
556#103—1222no—
557#103—1224no—
558#103—2442no—
559#103—2442no—
560C22⋊C8—1222no—
561C22⋊C8—1222no—
562C4×C8—1221no—
563C4×C8—1221no—
564#95—1221no—
565#95—1222no—
566C24—612no—
567C2×Q8—22no—
568C2×Q8—24no—
569C2×Q8—42no—
570C2×Q8—612no—
571C2×Q8—612no—
572C2×Q8—611no—
573C2×Q8—612no—
574C2×Q8—1221no—
575C2×Q8—1222no—
576C2×Q8—1222no—
577C2×Q8—1222no—
578C2×Q8—1224no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1222no—
582C2×Q8—1222no—
583C2×Q8—1222no—
584C2×Q8—1222no—
585C2×Q8—1222no—
586C2×Q8—1224no—
587C2×Q8—1224no—
588C2×Q8—2442no—
589C2×Q8—2444no—
590C2×Q8—2444no—
591C2×Q8—2444no—
592C2×Q8—2444no—
593C2×Q8—2442no—
594C2×Q8—2442no—
595C2×Q8—2444no—
596C2×Q8—2444no—
597C2×Q8C22×#692312yes—
598C2×Q8C22×#692311yescharacteristic
599C2×D4—612no—
600C2×D4—614no—
601C2×D4—614no—
602C2×D4—611no—
603C2×D4C22⋊#692311yescharacteristic
604C22×C4—22no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—612no—
608C22×C4—611no—
609C22×C4—612no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1221no—
622C22×C4—1222no—
623C22×C4—1221no—
624C22×C4—1222no—
625C22×C4—4882no—
626C22×C4—2444no—
627C22×C4—2444no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4C22×#692312yes—
631C2×C8—612no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1222no—
636C2×C8—1222no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1222no—
640C2×C8—2444no—
641C2×C8—2444no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—612no—
647C4⋊C4—611no—
648C4⋊C4—612no—
649C4⋊C4—611no—
650C4⋊C4—1221no—
651C4⋊C4—1222no—
652C4⋊C4—1221no—
653C4⋊C4—1222no—
654C4⋊C4—1222no—
655C4⋊C4—1221no—
656C4⋊C4—1222no—
657C4⋊C4—1221no—
658C4⋊C4—1222no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1222no—
662C4⋊C4—1221no—
663C4⋊C4—1222no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—4881no—
667C4⋊C4—2442no—
668C4⋊C4—2444no—
669C4⋊C4C22⋊#692311yescharacteristic
670C4⋊C4C22×#692311yescharacteristic
671C22⋊C4—22no—
672C22⋊C4—612no—
673C22⋊C4—612no—
674C22⋊C4—612no—
675C22⋊C4—1222no—
676C22⋊C4—1222no—
677C22⋊C4—1222no—
678C22⋊C4—2444no—
679C22⋊C4C22⋊#692312yes—
680C42—21no—
681C42—611no—
682C42—611no—
683C42—611no—
684C42—1221no—
685C42—1221no—
686C42—1221no—
687C42—2442no—
688C42C22×#692311yescharacteristic
689C23—611no—
690C23—614no—
691C23—614no—
692C23—612no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23C2×C22⋊#692312yes—
698Q8—21no—
699Q8—22no—
700Q8—22no—
701Q8—44no—
702Q8—612no—
703Q8—1222no—
704Q8—1222no—
705Q8—1221no—
706Q8—1222no—
707Q8—1222no—
708Q8—2444no—
709Q8—2444no—
710Q8—2442no—
711Q8—2442no—
712Q8—2444no—
713Q8D4×#692312yescomplemented
714D4—618no—
715D4—614no—
716D4#1451984014yesdirect product factor
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—44no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—612no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1221no—
736C2×C4—1222no—
737C2×C4—1221no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1221no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1221no—
748C2×C4—1222no—
749C2×C4—4888no—
750C2×C4—2444no—
751C2×C4—2444no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2444no—
757C2×C4—2441no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2441no—
761C2×C4—2442no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4C2×C22⋊#692311yescharacteristic
766C2×C4C2×C22⋊#692312yes—
767C2×C4C2×C22⋊#692311yescharacteristic
768C2×C4C23×#692311yescharacteristic
769C8—1222no—
770C8—2441no—
771C8—2442no—
772C22—22no—
773C22—22no—
774C22—611no—
775C22—611no—
776C22—611no—
777C22—611no—
778C22—611no—
779C22—611no—
780C22—614no—
781C22—1224no—
782C22—1224no—
783C22—1224no—
784C22—1224no—
785C22—1222no—
786C22—1222no—
787C22C2×#1451984014yescomplemented
788C22C22×C22⋊#692311yescharacteristic
789C4—22no—
790C4—22no—
791C4—21no—
792C4—42no—
793C4—41no—
794C4—611no—
795C4—611no—
796C4—612no—
797C4—1222no—
798C4—1222no—
799C4—1221no—
800C4—4882no—
801C4—4881no—
802C4—2442no—
803C4—2442no—
804C4—2441no—
805C4C2×#1451984012yescomplemented
806C4C2×D4×#692311yescharacteristic
807C4#1684082911yescharacteristic
808C2—24no—
809C2—611no—
810C2—611no—
811C2—611no—
812C2—611no—
813C2—1224no—
814C2D4×C22⋊#692311yescharacteristic
815C2C22×#1451984011yescharacteristic
816C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×D4×D61D4
cosocleC2×C4×D61C24
hypercenterD4×Q8#6923
hypocenterC61D4×#103
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#14519840C2semidirect
4. #21461985C2semidirect
5. #21461946C2semidirect
6. #21461832C2semidirect
7. #21461804C2semidirect
8. #21461688C2semidirect
9. #21461658C2semidirect
10. C4×#14519840C2semidirect
38. Q8×D244C4semidirect
40. D4×Dic122C4semidirect
42. #16840427C4semidirect
43. Q8×C22⋊D61C4semidirect
45. #16840425C4semidirect
53. D4×Q8×C61C4semidirect
81. #14519840D4direct (N × H)
89. C22×Dic122C2×C4semidirect
96. C2×Q8×D61C2×C4semidirect
97. C2×Q8×D61C2×C4semidirect
104. #14519777C2×C4semidirect
111. #14519775C2×C4semidirect
113. #14519757C2×C4semidirect
115. #14519756C2×C4semidirect
123. #14519753C2×C4semidirect
124. Q8×Dic61C2×C4semidirect
126. C4×Dic122C2×C4semidirect
128. #14519742C2×C4semidirect
149. C22×Q8×C61C2×C4semidirect
151. C4⋊Q8×C61C2×C4semidirect
153. C22⋊Q8×C61C2×C4semidirect
154. C4×Q8×C61C2×C4semidirect
303. Q8×C61C4×D4semidirect
304. D4×C61#103semidirect
315. C22⋊D61#103semidirect
326. D244#103semidirect
359. Dic122C4×D4semidirect
366. C22×C61C2×#103semidirect
374. C2×D61C2×#103semidirect
389. C4×C61C2×#103semidirect
397. Dic61C2×#103semidirect
430. D4×Q8#6923semidirect
462. C61D4×#103semidirect
475. C22×Q8C2×#6923semidirect
497. C4⋊Q8C2×#6923semidirect
511. C22⋊Q8C2×#6923semidirect
517. C4×Q8C2×#6923semidirect
713. Q8D4×#6923semidirect
716. D4#14519840direct (N × H)
787. C22C2×#14519840semidirect
805. C4C2×#14519840semidirect

Maximal subgroups

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

subgroupindex
D4×D61⋊C82
C22×#145198402
D4×C4⋊#69232
#214619852
#214619462
#214618322
#214618042
#214616882
#214616582
C4×#145198402
D4×Q8×D612
D4×#10361