Finite Group Databasebeta

← C2×#21461349 #30611815

Subgroups — C2×#21461349 #30611815

Order 15616.

1182 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840785C211yesmaximal, characteristic
2C2×#16840785C211yesmaximal, characteristic
3#21461349C218yesmaximal, direct product factor
4C2×#16840621C214yesmaximal, complemented
5C2×C4⋊Q8×D61C211yesmaximal, characteristic
6#16840785—22no—
7#16840785—22no—
8#16840785C2214yes—
9#16840785C2214yes—
10C2×#14519844C2212yes—
11C2×#14519844C2212yes—
12C2×#14519834—21no—
13C2×#14519834—21no—
14C2×#14519832—21no—
15C2×#14519832—21no—
16#16840621C22116yescomplemented
17C22×Q8×D61—21no—
18C2×#14519777C411yescharacteristic
19C2×#14519776—21no—
20C2×#14519776C2212yes—
21C2×#14519775—21no—
22C4⋊Q8×D61—22no—
23C4⋊Q8×D61—22no—
24C4⋊Q8×D61C414yes—
25C4⋊Q8×D61C2214yes—
26C2×C4⋊C4×D61—21no—
27C2×C4⋊C4×D61C412yes—
28C2×C42×D61C2211yescharacteristic
29C2×C4⋊Q8×C61C411yescharacteristic
30C22×#92420—22no—
31C22×#92420—22no—
32#14519844—22no—
33#14519844—22no—
34#14519844C2314yes—
35#14519844C2314yes—
36#14519834—24no—
37#14519834—24no—
38#14519832—24no—
39#14519832—24no—
40C22×Dic122—21no—
41C22×Dic122—22no—
42C2×Q8×D61—24no—
43C2×Q8×D61—24no—
44C2×Q8×D61—48no—
45C22×C4×D61—22no—
46C22×C4×D61C2×C411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×C4×D61D411yescharacteristic
49#14519777—22no—
50#14519777C2×C414yes—
51#14519776—24no—
52#14519776—22no—
53#14519776—22no—
54#14519776—24no—
55#14519776C2×C414yes—
56#14519776C2314yes—
57#14519775—24no—
58#14519775—24no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61C2×C412yes—
61C2×#11758196—22no—
62C2×#11758196—22no—
63C4⋊C4×D61—24no—
64C4⋊C4×D61—24no—
65C4⋊C4×D61—24no—
66C4⋊C4×D61C2×C418yes—
67C2×C4×Dic61D411yescharacteristic
68C2×C4×Dic61D411yescharacteristic
69C2×C4×Dic61C2311yescharacteristic
70C42×D61C2×C412yes—
71C42×D61D412yes—
72C42×D61D412yes—
73C42×D61C2312yes—
74C22×Q8×C61—21no—
75C4⋊Q8×C61—22no—
76C4⋊Q8×C61C2×C414yes—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61C2×C412yes—
79C2×C42×C61C2×C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C2×Q8×C61—24no—
82C2×Q8×C61—44no—
83C22×C4×C61—22no—
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22×C411yescharacteristic
87C22×Dic61—22no—
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91Q8×D61—416no—
92Q8×D61—416no—
93C2×C4×D61—24no—
94C2×C4×D61—24no—
95C2×C4×D61—24no—
96C2×C4×D61—28no—
97C2×C4×D61—48no—
98C2×C4×D61C22⋊C412yes—
99C2×C4×D61C22⋊C412yes—
100C2×C4×D61C22⋊C412yes—
101C2×C4×D61C22×C412yes—
102C2×C4×D61C2×D412yes—
103C2×C4×D61C2×D412yes—
104C2×Dic122—24no—
105C2×Dic122—24no—
106C2×Dic122—24no—
107C2×Dic122—44no—
108C2×Dic122—48no—
109C2×#92420—24no—
110C2×#92420—24no—
111C2×#92420—44no—
112C2×#92420—44no—
113C4⋊C4×C61—24no—
114C4⋊C4×C61—22no—
115C4⋊C4×C61C22×C414yes—
116C42×C61C22⋊C412yes—
117C42×C61C22×C412yes—
118C4⋊Dic61—24no—
119C4⋊Dic61—22no—
120C4⋊Dic61C22×C414yes—
121#11758196—24no—
122#11758196—28no—
123#11758196—24no—
124C4×Dic61C22⋊C412yes—
125C4×Dic61C22⋊C412yes—
126C4×Dic61C22×C411yescharacteristic
127C4×Dic61C2×D412yes—
128C4×Dic61C2×D412yes—
129C4×Dic61C2×D411yescharacteristic
130C4×Dic61C2×D411yescharacteristic
131C4×Dic61C2411yescharacteristic
132C23×C61C2×C22⋊C411yescharacteristic
133C22×D61—22no—
134C22×D61—22no—
135C22×D61#10114yes—
136C22×D61C2×C22⋊C412yes—
137Q8×C61—48no—
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—24no—
142C2×C4×C61—44no—
143C2×C4×C61C2×C22⋊C412yes—
144C2×C4×C61C2×C22⋊C412yes—
145C2×C4×C61C2×C22⋊C411yescharacteristic
146C2×C4×C61C23×C411yescharacteristic
147C2×Dic61—22no—
148C2×Dic61—24no—
149C2×Dic61—44no—
150C2×Dic61C2×C22⋊C412yes—
151C2×Dic61C2×C22⋊C411yescharacteristic
152C2×Dic61C2×C22⋊C411yescharacteristic
153C2×Dic61AGL(1,ℤ/8)14yes—
154C2×Dic61#13714yes—
155C2×Dic61C22×D411yescharacteristic
156C2×Dic61C22×D411yescharacteristic
157C4×D61—24no—
158C4×D61—24no—
159C4×D61—24no—
160C4×D61—24no—
161C4×D61—24no—
162C4×D61—24no—
163C4×D61—416no—
164Dic122—48no—
165Dic122—48no—
166Dic122—48no—
167#92420—44no—
168#92420—44no—
169C2×#1556—611nomaximal, Sylow
170C22×C61C2×#10112yes—
171C22×C61#41812yes—
172C22×C61#41912yes—
173C22×C61C22×C22⋊C411yescharacteristic
174C2×D61—28no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61C2×#10114yes—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—22no—
181C4×C61—22no—
182C4×C61—44no—
183Dic61—22no—
184Dic61—44no—
185Dic61#41812yes—
186Dic61#41912yes—
187Dic61C2×AGL(1,ℤ/8)12yes—
188Dic61C2×#13712yes—
189C22×C4⋊Q8—611no—
190C2×#432—611no—
191C2×#432—611no—
192#1556—618no—
193C2×#332—614no—
194C2×C61#155614yescomplemented
195C2×C61C22×#10111yescharacteristic
196C2×C61C2×#41811yescharacteristic
197C2×C61C2×#41911yescharacteristic
198D61—24no—
199C23×Q8—1221no—
200C2×C4⋊Q8—614no—
201C2×C4⋊Q8—614no—
202C2×C4⋊Q8—612no—
203C2×C4⋊Q8—611no—
204C2×C4⋊Q8—1221no—
205C2×C4⋊Q8—1222no—
206C2×C4⋊Q8—1222no—
207C2×C4⋊Q8—1221no—
208C2×C4⋊Q8#692311yescharacteristic
209C22×C4⋊C4—612no—
210C22×C4⋊C4—1221no—
211C22×C42—611no—
212#432—614no—
213#432—614no—
214#432—1222no—
215#432—1222no—
216C2×C4⋊C8—612no—
217C2×C4⋊C8—612no—
218C2×C22⋊C8—1221no—
219C2×C22⋊C8—1221no—
220C2×#97—1221no—
221C2×#97—1221no—
222#332—6116no—
223C61C2×#155611yescharacteristic, complemented, Sylow
224C22×Q8—21no—
225C22×Q8—1222no—
226C22×Q8—1224no—
227C22×Q8—1224no—
228C22×Q8—1221no—
229C22×Q8—2448no—
230C23×C4—611no—
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—1222no—
234C22×C8—1222no—
235C22×C8—1222no—
236C4⋊Q8—22no—
237C4⋊Q8—614no—
238C4⋊Q8—614no—
239C4⋊Q8—614no—
240C4⋊Q8—1224no—
241C4⋊Q8—1222no—
242C4⋊Q8—1222no—
243C4⋊Q8—1224no—
244C4⋊Q8—1224no—
245C4⋊Q8—1224no—
246C4⋊Q8—1222no—
247C4⋊Q8C2×#692314yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—612no—
250C2×C4⋊C4—618no—
251C2×C4⋊C4—1224no—
252C2×C4⋊C4—1224no—
253C2×C4⋊C4—1224no—
254C2×C4⋊C4—1222no—
255C2×C4⋊C4—1222no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4C2×#692312yes—
258C2×C42—611no—
259C2×C42—611no—
260C2×C42—611no—
261C2×C42—612no—
262C2×C42—612no—
263C2×C42—612no—
264C2×C42—612no—
265C2×C42C2×#692311yescharacteristic
266C4⋊C8—614no—
267C4⋊C8—614no—
268C4⋊C8—1222no—
269C4⋊C8—1222no—
270C22⋊C8—1224no—
271C22⋊C8—1224no—
272#97—1224no—
273#97—1224no—
274C24—611no—
275C2×Q8—24no—
276C2×Q8—44no—
277C2×Q8—1224no—
278C2×Q8—1224no—
279C2×Q8—1224no—
280C2×Q8—2444no—
281C2×Q8—2448no—
282C2×Q8—24416no—
283C2×Q8—24416no—
284C22×C4—22no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—612no—
289C22×C4—612no—
290C22×C4—612no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—1224no—
295C22×C4—1224no—
296C22×C4—1224no—
297C22×C4—1228no—
298C22×C4—1222no—
299C22×C4—2448no—
300C22×C4C22⋊#692311yescharacteristic
301C22×C4C22⋊#692311yescharacteristic
302C22×C4C22×#692311yescharacteristic
303C2×C8—1224no—
304C2×C8—1224no—
305C2×C8—2444no—
306C2×C8—2444no—
307C4⋊C4—24no—
308C4⋊C4—22no—
309C4⋊C4—614no—
310C4⋊C4—1228no—
311C4⋊C4—1224no—
312C4⋊C4—1224no—
313C4⋊C4—1222no—
314C4⋊C4—1224no—
315C4⋊C4C22×#692314yes—
316C42—612no—
317C42—612no—
318C42—611no—
319C42—611no—
320C42—612no—
321C42—612no—
322C42—611no—
323C42—611no—
324C42C22⋊#692312yes—
325C42C22×#692312yes—
326C23—614no—
327C23—612no—
328C23—1222no—
329C23—1222no—
330C23C2×C22⋊#692311yescharacteristic
331Q8—48no—
332Q8—2448no—
333Q8—2448no—
334Q8—2448no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—44no—
340C2×C4—614no—
341C2×C4—614no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—612no—
347C2×C4—1224no—
348C2×C4—1224no—
349C2×C4—1224no—
350C2×C4—1224no—
351C2×C4—1224no—
352C2×C4—1224no—
353C2×C4—1222no—
354C2×C4—1224no—
355C2×C4—24416no—
356C2×C4—2444no—
357C2×C4C2×C22⋊#692311yescharacteristic
358C2×C4C2×C22⋊#692312yes—
359C2×C4C2×C22⋊#692312yes—
360C2×C4C23×#692311yescharacteristic
361C8—2444no—
362C8—2444no—
363C22—614no—
364C22—1228no—
365C22—1222no—
366C22—1222no—
367C22D61⋊#10112yes—
368C22#1684075412yes—
369C22#1684075512yes—
370C22C22×C22⋊#692311yescharacteristic
371C4—21no—
372C4—21no—
373C4—22no—
374C4—22no—
375C4—44no—
376C4—612no—
377C4—612no—
378C4—612no—
379C4—612no—
380C4—1222no—
381C4—2444no—
382C2—1224no—
383C2#2146134914yesdirect product factor
384C2C2×D61⋊#10111yescharacteristic
385C2C2×#1684075411yescharacteristic
386C2C2×#1684075511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC4×Dic61C24
hypercenterC2×C4⋊Q8#6923
hypocenterC61C2×#1556
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21461349C2direct (N × H)
4. C2×#16840621C2semidirect
16. #16840621C22semidirect
194. C2×C61#1556semidirect
223. C61C2×#1556semidirect
383. C2#21461349direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407852
#214613492
C2×#168406212
C2×C4⋊Q8×D612
C2×#155661