Finite Group Databasebeta

← C2×D61⋊(D4⋊C8) #30610374

Subgroups — C2×D61⋊(D4⋊C8) #30610374

Order 15616.

1886 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C2×C4×D61⋊C8C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal, complemented
4D61⋊(D4⋊C8)C218yesmaximal, direct product factor
5C2×D4⋊#92420C212yesmaximal, complemented
6C2×C4×D4×D61C211yesmaximal, characteristic
7C22×D61⋊C8—21no—
8C22×D61⋊C8—21no—
9C2×#14519844—21no—
10D61⋊(C4⋊C8)—22no—
11D61⋊(C4⋊C8)C2214yescomplemented
12C2×C4⋊#92420C2212yescomplemented
13C4×D61⋊C8—22no—
14C4×D61⋊C8C2214yescomplemented
15C2×C4×#92420—21no—
16C2×C4×#92420C2212yescomplemented
17#16840610C2218yescomplemented
18D4⋊#92420C2218yescomplemented
19C22×D4×D61C411yescharacteristic
20C23×C4×D61—21no—
21C2×C4×D244C411yescharacteristic
22C2×D4×Dic61C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×C4×C22⋊D61—21no—
25C2×#14519737—21no—
26C4×D4×D61—22no—
27C4×D4×D61—22no—
28C4×D4×D61C414yes—
29C4×D4×D61C2214yes—
30C2×C4⋊C4×D61C411yescharacteristic
31C2×C22⋊C4×D61—21no—
32C2×C42×D61C2211yescharacteristic
33C2×C4×D4×C61C411yescharacteristic
34C2×D61⋊C8—28no—
35C2×D61⋊C8—24no—
36C2×D61⋊C8—24no—
37C2×D61⋊C8—44no—
38C22×#92420—22no—
39C22×#92420—22no—
40#14519844—24no—
41C4⋊#92420—22no—
42C4⋊#92420C2314yescomplemented
43C4×#92420—24no—
44C4×#92420—22no—
45C4×#92420C2314yescomplemented
46C24×D61—21no—
47C22×D244C2×C411yescharacteristic
48C22×C22⋊D61—21no—
49C2×D4×D61—22no—
50C2×D4×D61—24no—
51C2×D4×D61C818yescomplemented
52C2×D4×D61C2×C414yes—
53C23×Dic61—21no—
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—24no—
58C22×C4×D61—24no—
59C22×C4×D61—44no—
60C22×C4×D61—44no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C4×D244—22no—
65C4×D244C2×C414yes—
66D4×Dic61—21no—
67D4×Dic61—21no—
68D4×Dic61C2×C412yes—
69D4×Dic61C2312yes—
70#14519739—21no—
71#14519739—21no—
72#14519739C2×C412yes—
73#14519739C2312yes—
74C4×C22⋊D61—24no—
75C4×C22⋊D61—24no—
76#14519737—24no—
77#14519737—24no—
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×#11758196—21no—
80C4⋊C4×D61—22no—
81C4⋊C4×D61C2×C414yes—
82C2×C22⋊Dic61—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C22⋊C4×D61—24no—
86C22⋊C4×D61—24no—
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90C42×D61C2×C412yes—
91C42×D61D412yes—
92C42×D61D412yes—
93C42×D61C2312yes—
94C22×D4×C61C2×C411yescharacteristic
95C23×C4×C61—21no—
96C4×D4×C61—22no—
97C4×D4×C61C2×C414yes—
98C2×C4⋊C4×C61C2×C411yescharacteristic
99C2×C22⋊C4×C61—21no—
100C2×C42×C61C2×C411yescharacteristic
101C24×C61—21no—
102C23×D61—21no—
103C23×D61—28no—
104C23×D61—24no—
105C23×D61—44no—
106C23×D61—44no—
107C23×D61C22⋊C411yescharacteristic
108C2×D4×C61—21no—
109C2×D4×C61—22no—
110C2×D4×C61C2×C814yescomplemented
111C2×D4×C61C22×C412yes—
112C22×C4×C61—21no—
113C22×C4×C61—24no—
114C22×C4×C61—44no—
115C22×C4×C61C22⋊C411yescharacteristic
116C22×C4×C61C22⋊C411yescharacteristic
117C22×C4×C61C22×C411yescharacteristic
118C2×C22⋊D61—28no—
119C2×C22⋊D61—24no—
120C22×Dic61—21no—
121C22×Dic61—22no—
122C22×Dic61—22no—
123C22×Dic61—42no—
124C22×Dic61—42no—
125C22×Dic61C22⋊C411yescharacteristic
126C22×Dic61C2×D411yescharacteristic
127C22×Dic61C2×D411yescharacteristic
128D4×D61—216no—
129D4×D61—28no—
130D4×D61C2×C8116yescomplemented
131C2×D244—21no—
132C2×D244—22no—
133C2×D244C2×C814yescomplemented
134C2×D244C22×C412yes—
135C2×C4×D61—24no—
136C2×C4×D61—24no—
137C2×C4×D61—24no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—44no—
141C2×C4×D61—44no—
142C2×C4×D61—42no—
143C2×C4×D61—42no—
144C2×C4×D61—416no—
145C2×C4×D61—48no—
146C2×C4×D61—48no—
147C2×C4×D61C22⋊C412yes—
148C2×C4×D61C22⋊C412yes—
149C2×C4×D61C22⋊C412yes—
150C2×C4×D61C2×C814yes—
151C2×C4×D61M1614yes—
152C2×C4×D61D814yes—
153C2×C4×D61SD1614yes—
154C2×C4×D61C22×C412yes—
155C2×C4×D61C2×D412yes—
156C2×C4×D61C2×D412yes—
157C2×#92420—28no—
158C2×#92420—24no—
159C2×#92420—24no—
160C2×#92420—44no—
161D61⋊C8—216no—
162D61⋊C8—48no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61C22×C412yes—
165C22⋊C4×C61—24no—
166C42×C61C22⋊C412yes—
167C42×C61C22×C412yes—
168C22⋊Dic61—22no—
169C22⋊Dic61—22no—
170#11758198—24no—
171#11758198—22no—
172#11758198—22no—
173C4⋊Dic61—21no—
174C4⋊Dic61C22×C412yes—
175#11758196—24no—
176C4×Dic61C22⋊C412yes—
177C4×Dic61C22⋊C412yes—
178C4×Dic61C22×C411yescharacteristic
179C4×Dic61C2×D411yescharacteristic
180C4×Dic61C2×D412yes—
181C4×Dic61C2×D411yescharacteristic
182C4×Dic61C2×D412yes—
183C4×Dic61C2411yescharacteristic
184C23×C61—22no—
185C23×C61—24no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61C2×C22⋊C411yescharacteristic
189C22×D61—22no—
190C22×D61—24no—
191C22×D61—216no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—432no—
195C22×D61—48no—
196C22×D61—48no—
197C22×D61C22⋊C814yes—
198C22×D61#10214yes—
199C22×D61#10414yes—
200C22×D61C2×C22⋊C412yes—
201D4×C61—22no—
202D4×C61—24no—
203D4×C61C22×C814yescomplemented
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—42no—
207C2×C4×C61—48no—
208C2×C4×C61#10214yes—
209C2×C4×C61C2×C22⋊C412yes—
210C2×C4×C61C2×C22⋊C411yescharacteristic
211C2×C4×C61C2×C22⋊C412yes—
212C2×C4×C61C22×C812yes—
213C2×C4×C61C2×M1612yes—
214C2×C4×C61C23×C411yescharacteristic
215C22⋊D61—216no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61—42no—
221C2×Dic61—44no—
222C2×Dic61C22⋊C814yes—
223C2×Dic61C2×C22⋊C411yescharacteristic
224C2×Dic61C2×C22⋊C412yes—
225C2×Dic61C2×C22⋊C411yescharacteristic
226C2×Dic61C2×D812yes—
227C2×Dic61C2×SD1612yes—
228C2×Dic61C22×D411yescharacteristic
229C2×Dic61C22×D411yescharacteristic
230D244—22no—
231D244—24no—
232D244C22×C814yescomplemented
233C4×D61—24no—
234C4×D61—24no—
235C4×D61—48no—
236C4×D61—48no—
237C4×D61—42no—
238C4×D61—42no—
239C4×D61—44no—
240C4×D61C22⋊C818yes—
241C4×D61#10218yes—
242C4×D61C22×C814yes—
243C4×D61C2×M1614yes—
244C4×D61C2×D814yes—
245C4×D61C2×SD1614yes—
246#92420—28no—
247#92420—44no—
248C22×D4⋊C8—611nomaximal, Sylow
249C22×C61—24no—
250C22×C61—42no—
251C22×C61—42no—
252C22×C61—48no—
253C22×C61C2×C22⋊C812yes—
254C22×C61C2×#10212yes—
255C22×C61C2×#10412yes—
256C22×C61C22×C22⋊C411yescharacteristic
257C2×D61—24no—
258C2×D61—42no—
259C2×D61—42no—
260C2×D61—48no—
261C2×D61—432no—
262C2×D61D4⋊C8116yescomplemented
263C2×D61C2×C22⋊C814yes—
264C2×D61C2×#10214yes—
265C2×D61C2×#10414yes—
266C4×C61—22no—
267C4×C61—42no—
268C4×C61C2×C22⋊C812yes—
269C4×C61C2×#10214yes—
270C4×C61C23×C811yescharacteristic
271C4×C61C22×M1611yescharacteristic
272Dic61—21no—
273Dic61—21no—
274Dic61—42no—
275Dic61C2×C22⋊C814yes—
276Dic61C2×#10212yes—
277Dic61C22×D811yescharacteristic
278Dic61C22×SD1611yescharacteristic
279C22×C4×D4—611no—
280C22×C4⋊C8—611no—
281C22×C4×C8—611no—
282C2×D4⋊C8—612no—
283C2×D4⋊C8—618no—
284C2×D4⋊C8—612no—
285C2×C61—44no—
286C2×C61C2×D4⋊C814yescomplemented
287C2×C61C22×C22⋊C811yescharacteristic
288C2×C61C22×#10211yescharacteristic
289C2×C61C22×#10411yescharacteristic
290D61—44no—
291D61C2×D4⋊C818yescomplemented
292C23×D4—611no—
293C24×C4—1221no—
294C23×C8—1221no—
295C23×C8—1221no—
296C2×C4×D4—611no—
297C2×C4×D4—614no—
298C2×C4×D4—614no—
299C2×C4×D4—611no—
300C2×C4×D4—611no—
301C2×C4×D4—1221no—
302C2×C4×D4—1222no—
303C2×C4×D4—1222no—
304C2×C4×D4—1221no—
305C2×C4×D4#692311yescharacteristic
306C22×C4⋊C4—611no—
307C22×C22⋊C4—1221no—
308C22×C42—611no—
309C2×C4⋊C8—612no—
310C2×C4⋊C8—614no—
311C2×C4⋊C8—1222no—
312C2×C4⋊C8—1221no—
313C2×C4×C8—612no—
314C2×C4×C8—614no—
315C2×C4×C8—1221no—
316C2×C4×C8—1222no—
317D4⋊C8—618no—
318D4⋊C8—618no—
319C61C22×D4⋊C811yescharacteristic, complemented, Sylow
320C25—1221no—
321C22×D4—618no—
322C22×D4—614no—
323C22×D4—611no—
324C22×D4—1222no—
325C22×D4—1224no—
326C22×D4—1221no—
327C22×D4C2×#692311yescharacteristic
328C23×C4—21no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—1221no—
333C23×C4—1224no—
334C23×C4—1224no—
335C23×C4—1221no—
336C23×C4—1221no—
337C23×C4—1221no—
338C23×C4—2444no—
339C23×C4—2444no—
340C22×C8—1222no—
341C22×C8—1224no—
342C22×C8—1228no—
343C22×C8—1222no—
344C22×C8—1224no—
345C22×C8—2444no—
346C4×D4—22no—
347C4×D4—612no—
348C4×D4—612no—
349C4×D4—612no—
350C4×D4—612no—
351C4×D4—614no—
352C4×D4—1224no—
353C4×D4—1224no—
354C4×D4—1221no—
355C4×D4—1221no—
356C4×D4—1224no—
357C4×D4—1224no—
358C4×D4—1221no—
359C4×D4—1221no—
360C4×D4—1222no—
361C4×D4C2×#692314yes—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—614no—
364C2×C4⋊C4—1222no—
365C2×C4⋊C4—1221no—
366C2×C4⋊C4C2×#692311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—1224no—
369C2×C22⋊C4—1224no—
370C2×C22⋊C4—1221no—
371C2×C22⋊C4—1221no—
372C2×C22⋊C4—1221no—
373C2×C42—611no—
374C2×C42—611no—
375C2×C42—611no—
376C2×C42—612no—
377C2×C42—612no—
378C2×C42—612no—
379C2×C42—612no—
380C2×C42C2×#692311yescharacteristic
381C4⋊C8—614no—
382C4⋊C8—1222no—
383C4⋊C8—1224no—
384C4×C8—614no—
385C4×C8—1224no—
386C4×C8—1222no—
387C24—21no—
388C24—611no—
389C24—1224no—
390C24—1228no—
391C24—1221no—
392C24—2444no—
393C24—2444no—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—6116no—
397C2×D4—614no—
398C2×D4—612no—
399C2×D4—12216no—
400C2×D4—1228no—
401C2×D4—1224no—
402C2×D4—1228no—
403C2×D4—1221no—
404C2×D4—1222no—
405C2×D4D61⋊C814yescomplemented
406C2×D4C22×#692312yes—
407C22×C4—21no—
408C22×C4—24no—
409C22×C4—44no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—614no—
413C22×C4—614no—
414C22×C4—612no—
415C22×C4—612no—
416C22×C4—612no—
417C22×C4—614no—
418C22×C4—614no—
419C22×C4—612no—
420C22×C4—611no—
421C22×C4—612no—
422C22×C4—612no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—1224no—
426C22×C4—1224no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1221no—
430C22×C4—1224no—
431C22×C4—2442no—
432C22×C4—2442no—
433C22×C4—24416no—
434C22×C4—2448no—
435C22×C4—2448no—
436C22×C4—2444no—
437C22×C4—2442no—
438C22×C4—2442no—
439C22×C4—2444no—
440C22×C4C22⋊#692311yescharacteristic
441C22×C4C22⋊#692311yescharacteristic
442C22×C4C22×#692311yescharacteristic
443C2×C8—1224no—
444C2×C8—12216no—
445C2×C8—1228no—
446C2×C8—1224no—
447C2×C8—2448no—
448C2×C8—2444no—
449C4⋊C4—21no—
450C4⋊C4—612no—
451C4⋊C4—1224no—
452C4⋊C4—1221no—
453C4⋊C4C22×#692312yes—
454C22⋊C4—24no—
455C22⋊C4—1222no—
456C22⋊C4—1222no—
457C22⋊C4—1222no—
458C22⋊C4—1222no—
459C22⋊C4—1224no—
460C42—612no—
461C42—611no—
462C42—612no—
463C42—611no—
464C42—612no—
465C42—612no—
466C42—611no—
467C42—611no—
468C42C22⋊#692312yes—
469C42C22×#692312yes—
470C23—24no—
471C23—22no—
472C23—42no—
473C23—42no—
474C23—614no—
475C23—614no—
476C23—614no—
477C23—612no—
478C23—12216no—
479C23—1224no—
480C23—1222no—
481C23—2448no—
482C23—24432no—
483C23—2448no—
484C23—2442no—
485C23—2442no—
486C23C2×C22⋊#692311yescharacteristic
487D4—24no—
488D4—22no—
489D4—614no—
490D4—12216no—
491D4—1224no—
492D4—1222no—
493D4C2×D61⋊C814yescomplemented
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—42no—
497C2×C4—48no—
498C2×C4—614no—
499C2×C4—612no—
500C2×C4—612no—
501C2×C4—612no—
502C2×C4—611no—
503C2×C4—611no—
504C2×C4—618no—
505C2×C4—618no—
506C2×C4—614no—
507C2×C4—614no—
508C2×C4—614no—
509C2×C4—614no—
510C2×C4—611no—
511C2×C4—611no—
512C2×C4—1224no—
513C2×C4—1224no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4—2444no—
519C2×C4—2448no—
520C2×C4—2442no—
521C2×C4—2442no—
522C2×C4—2444no—
523C2×C4—2442no—
524C2×C4—2448no—
525C2×C4#1451983914yes—
526C2×C4C2×C22⋊#692312yes—
527C2×C4C2×C22⋊#692311yescharacteristic
528C2×C4C2×C22⋊#692312yes—
529C2×C4C2×D61⋊C812yes—
530C2×C4D61⋊M1612yes—
531C2×C4C23×#692311yescharacteristic
532C8—1228no—
533C8—2444no—
534C22—24no—
535C22—48no—
536C22—42no—
537C22—42no—
538C22—6116no—
539C22—614no—
540C22—614no—
541C22—614no—
542C22—1224no—
543C22—24432no—
544C22—2448no—
545C22—2442no—
546C22—2442no—
547C22D61⋊(C22⋊C8)12yes—
548C22C2×#1451983912yes—
549C22D61⋊#10412yes—
550C22C22×C22⋊#692311yescharacteristic
551C4—22no—
552C4—42no—
553C4—614no—
554C4—611no—
555C4—611no—
556C4—612no—
557C4—1221no—
558C4—1221no—
559C4—2442no—
560C4D61⋊(C22⋊C8)12yes—
561C4C2×#1451983914yes—
562C4C22×D61⋊C811yescharacteristic
563C4C2×D61⋊M1611yescharacteristic
564C2—44no—
565C2—618no—
566C2—2444no—
567C2D61⋊(D4⋊C8)14yesdirect product factor
568C2C2×D61⋊(C22⋊C8)11yescharacteristic
569C2C22×#1451983911yescharacteristic
570C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC4×C61C23×C8
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC4×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61C22×D4⋊C8
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊(C4⋊C8)C2semidirect
2. C2×C4×D61⋊C8C2semidirect
3. C2×#16840610C2semidirect
4. D61⋊(D4⋊C8)C2direct (N × H)
5. C2×D4⋊#92420C2semidirect
11. D61⋊(C4⋊C8)C22semidirect
12. C2×C4⋊#92420C22semidirect
14. C4×D61⋊C8C22semidirect
16. C2×C4×#92420C22semidirect
17. #16840610C22semidirect
18. D4⋊#92420C22semidirect
42. C4⋊#92420C23semidirect
45. C4×#92420C23semidirect
51. C2×D4×D61C8semidirect
110. C2×D4×C61C2×C8semidirect
130. D4×D61C2×C8semidirect
133. C2×D244C2×C8semidirect
203. D4×C61C22×C8semidirect
232. D244C22×C8semidirect
262. C2×D61D4⋊C8semidirect
286. C2×C61C2×D4⋊C8semidirect
291. D61C2×D4⋊C8semidirect
319. C61C22×D4⋊C8semidirect
405. C2×D4D61⋊C8semidirect
493. D4C2×D61⋊C8semidirect
567. C2D61⋊(D4⋊C8)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D61⋊(C4⋊C8)2
C2×C4×D61⋊C82
C2×#168406102
D61⋊(D4⋊C8)2
C2×D4⋊#924202
C2×C4×D4×D612
C22×D4⋊C861