Finite Group Databasebeta

← D4×#14268634 #28402270

Subgroups — D4×#14268634 #28402270

Order 14464.

546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14268634C212yesmaximal, complemented
2D4×D452C211yesmaximal, characteristic
3#20298972C211yesmaximal, characteristic, complemented
4#20298829C212yesmaximal, complemented
5#20298800C211yesmaximal, characteristic, complemented
6#20298798C211yesmaximal, characteristic, complemented
7#20298748C212yesmaximal, complemented
8#20298737C212yesmaximal, complemented
9C4×#14268634C211yesmaximal, characteristic, complemented
10D4×#11744751C211yesmaximal, characteristic, complemented
11D4×Q8×C113C211yesmaximal, characteristic, complemented
12C22×D452C2212yes—
13C2×D4×D113—21no—
14C2×#14268634—28no—
15C2×#14268634C2212yes—
16C2×#14268634C2211yescharacteristic
17C2×#14268634C2212yescomplemented
18C2×#14268634C2212yescomplemented
19C2×#14268634C2212yescomplemented
20C22×#11744751C2212yescomplemented
21#16813619C2211yescharacteristic
22#16813597—21no—
23#16813596C2212yes—
24#16813592—22no—
25C4×D452C2211yescharacteristic
26#16813553C2211yescharacteristic, complemented
27C4⋊#11744751C2211yescharacteristic, complemented
28#16813546C2212yescomplemented
29#16813546C2211yescharacteristic, complemented
30#16813542C2211yescharacteristic
31#16813542C2212yescomplemented
32C22⋊#11744751C2212yescomplemented
33C4×#11744751C2211yescharacteristic, complemented
34C22×Q8×C113C2212yescomplemented
35C4⋊Q8×C113—21no—
36C4⋊Q8×C113C2211yescharacteristic, complemented
37C22⋊Q8×C113—22no—
38C22⋊Q8×C113C2212yescomplemented
39C4×Q8×C113C2211yescharacteristic, complemented
40C4×D4×C113—21no—
41C4×D4×C113C2211yescharacteristic
42C23×D113—22no—
43C2×D452—24no—
44C2×D452—22no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452—42no—
48C2×D452C2312yes—
49C2×D452C2311yescharacteristic
50C2×C22⋊D113—22no—
51D4×D113—44no—
52C2×C4×D113—21no—
53#14268634—24no—
54#14268634—24no—
55#14268634—24no—
56#14268634—42no—
57#14268634D414yesdirect product factor
58C2×#11744751—24no—
59C2×#11744751C2312yes—
60C2×#11744751C2311yescharacteristic
61C2×#11744751C2311yescharacteristic
62C4⋊Dic113C2311yescharacteristic
63#14268624—21no—
64#14268624—22no—
65C2×Q8×C113—22no—
66C2×Q8×C113—24no—
67C2×Q8×C113—42no—
68C2×Q8×C113C2312yes—
69C2×Q8×C113C2311yescharacteristic
70C2×D4×C113D411yescharacteristic
71C22×C4×C113—22no—
72C22×C4×C113C2312yes—
73C4⋊C4×C113—21no—
74C4⋊C4×C113—21no—
75C4⋊C4×C113—21no—
76C4⋊C4×C113—22no—
77C4⋊C4×C113D411yescharacteristic
78C4⋊C4×C113C2311yescharacteristic
79C22⋊C4×C113—22no—
80C22⋊C4×C113D412yes—
81C42×C113—21no—
82C42×C113C2311yescharacteristic
83C23×C113C2×D412yes—
84C22×D113—21no—
85C22×D113—22no—
86C22×D113—44no—
87C22×D113—44no—
88C22×D113—82no—
89Q8×C113—21no—
90Q8×C113—22no—
91Q8×C113—22no—
92Q8×C113—44no—
93Q8×C113C2×D412yescomplemented
94D4×C113SD1614yescomplemented
95C2×C4×C113—21no—
96C2×C4×C113—22no—
97C2×C4×C113—22no—
98C2×C4×C113—21no—
99C2×C4×C113—22no—
100C2×C4×C113—44no—
101C2×C4×C113C2×D411yescharacteristic
102C2×C4×C113C2×D412yes—
103C2×C4×C113C2×D411yescharacteristic
104C2×C4×C113C2411yescharacteristic
105C22⋊D113—44no—
106C2×Dic113—21no—
107D452—22no—
108D452—21no—
109D452—22no—
110D452—44no—
111D452—42no—
112D452—81no—
113D452C2×D412yes—
114C4×D113—42no—
115#11744751—22no—
116#11744751—21no—
117#11744751C2×D412yescomplemented
118C22×C113—22no—
119C22×C113—22no—
120C22×C113C2×SD1614yescomplemented
121C22×C113C22×D411yescharacteristic
122C2×D113—22no—
123C2×D113—41no—
124C2×D113—41no—
125C2×D113—42no—
126C2×D113—42no—
127C2×D113—42no—
128C2×D113—88no—
129C4×C113—22no—
130C4×C113—22no—
131C4×C113—21no—
132C4×C113—42no—
133C4×C113—41no—
134C4×C113C2×SD1612yescomplemented
135C4×C113C22×D411yescharacteristic
136C4×C113H(5,𝔽2)11yescharacteristic
137Dic113—41no—
138C2×C113—24no—
139C2×C113D4211yescharacteristic
140C2×C113C22×SD1611yescharacteristic
141C2×C113#57711yescharacteristic
142D113—42no—
143D113—82no—
144D4×SD16—1131nomaximal, Sylow
145C113D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—1132no—
147D4×Q8D11311yescharacteristic, complemented
148D42—1131no—
149#492—1131no—
150#465—1132no—
151#461—1131no—
152#460—1131no—
153#450—1132no—
154#448—1132no—
155C4×SD16—1131no—
156C8×D4—1131no—
157C22×Q8C2×D11312yescomplemented
158C22×D4—1132no—
159C22×D4—2261no—
160C2×SD16—1131no—
161C2×SD16—1132no—
162C2×SD16—1132no—
163C2×SD16—1132no—
164C2×SD16—1132no—
165C2×SD16—2268no—
166C22×C8—1132no—
167C4⋊Q8—21no—
168C4⋊Q8C2×D11311yescharacteristic, complemented
169#127—1131no—
170C22⋊Q8—22no—
171C22⋊Q8C2×D11312yescomplemented
172#121—1132no—
173#121—2261no—
174#120—2262no—
175C4×Q8C2×D11311yescharacteristic, complemented
176C4×D4—21no—
177C4×D4—1131no—
178C4×D4C2×D11311yescharacteristic
179#106—1131no—
180C4⋊C8—1131no—
181#103—1131no—
182#103—1132no—
183#102—1131no—
184#102—1132no—
185C22⋊C8—1132no—
186C4×C8—1131no—
187C24—2262no—
188C2×Q8—22no—
189C2×Q8—24no—
190C2×Q8—42no—
191C2×Q8C22×D11312yes—
192C2×Q8C22×D11311yescharacteristic
193C2×D4—1131no—
194C2×D4—1132no—
195C2×D4—4522no—
196C2×D4—4524no—
197C2×D4—2264no—
198C2×D4—2262no—
199C2×D4—2261no—
200C2×D4—2262no—
201C2×D4—2261no—
202C2×D4C22⋊D11311yescharacteristic
203C22×C4—22no—
204C22×C4—2261no—
205C22×C4C22×D11312yes—
206SD16—1134no—
207SD16—4522no—
208SD16—2264no—
209SD16—2264no—
210SD16—2264no—
211C2×C8—1131no—
212C2×C8—1131no—
213C2×C8—1132no—
214C2×C8—2264no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—22no—
219C4⋊C4—1131no—
220C4⋊C4C22⋊D11311yescharacteristic
221C4⋊C4C22×D11311yescharacteristic
222C22⋊C4—22no—
223C22⋊C4—2261no—
224C22⋊C4—2262no—
225C22⋊C4C22⋊D11312yes—
226C42—21no—
227C42C22×D11311yescharacteristic
228C23—9042no—
229C23—4524no—
230C23—4524no—
231C23—2262no—
232C23—2261no—
233C23C2×C22⋊D11312yes—
234Q8—21no—
235Q8—22no—
236Q8—22no—
237Q8—44no—
238Q8D4×D11312yescomplemented
239D4—1132no—
240D4—9041no—
241D4—4524no—
242D4—4524no—
243D4—4522no—
244D4—2262no—
245D4—2262no—
246D4—2261no—
247D4#1426863414yesdirect product factor
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—44no—
254C2×C4—4522no—
255C2×C4—2261no—
256C2×C4C2×C22⋊D11311yescharacteristic
257C2×C4C2×C22⋊D11312yes—
258C2×C4C2×C22⋊D11311yescharacteristic
259C2×C4C23×D11311yescharacteristic
260C8—1132no—
261C8—2262no—
262C8—2261no—
263C22—22no—
264C22—22no—
265C22—9048no—
266C22—4522no—
267C22—4522no—
268C22—4522no—
269C22—4521no—
270C22—4521no—
271C22—2262no—
272C22C2×#1426863414yescomplemented
273C22C22×C22⋊D11311yescharacteristic
274C4—21no—
275C4—22no—
276C4—22no—
277C4—41no—
278C4—42no—
279C4—4521no—
280C4C2×#1426863412yescomplemented
281C4C2×D4×D11311yescharacteristic
282C4#1681366711yescharacteristic
283C2—24no—
284C2—9042no—
285C2—4522no—
286C2D4×C22⋊D11311yescharacteristic
287C2C22×#1426863411yescharacteristic
288C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingD4×Q8×C113C2
socleC22×C113C22×D4
prime radicalD4×D452C2
hypercenterD4×Q8D113
hypocenterC113D4×SD16
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14268634C2semidirect
3. #20298972C2semidirect
4. #20298829C2semidirect
5. #20298800C2semidirect
6. #20298798C2semidirect
7. #20298748C2semidirect
8. #20298737C2semidirect
9. C4×#14268634C2semidirect
10. D4×#11744751C2semidirect
11. D4×Q8×C113C2semidirect
17. C2×#14268634C22semidirect
18. C2×#14268634C22semidirect
19. C2×#14268634C22semidirect
20. C22×#11744751C22semidirect
26. #16813553C22semidirect
27. C4⋊#11744751C22semidirect
28. #16813546C22semidirect
29. #16813546C22semidirect
31. #16813542C22semidirect
32. C22⋊#11744751C22semidirect
33. C4×#11744751C22semidirect
34. C22×Q8×C113C22semidirect
36. C4⋊Q8×C113C22semidirect
38. C22⋊Q8×C113C22semidirect
39. C4×Q8×C113C22semidirect
57. #14268634D4direct (N × H)
93. Q8×C113C2×D4semidirect
94. D4×C113SD16semidirect
117. #11744751C2×D4semidirect
120. C22×C113C2×SD16semidirect
134. C4×C113C2×SD16semidirect
145. C113D4×SD16semidirect
147. D4×Q8D113semidirect
157. C22×Q8C2×D113semidirect
168. C4⋊Q8C2×D113semidirect
171. C22⋊Q8C2×D113semidirect
175. C4×Q8C2×D113semidirect
238. Q8D4×D113semidirect
247. D4#14268634direct (N × H)
272. C22C2×#14268634semidirect
280. C4C2×#14268634semidirect

Maximal subgroups

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

subgroupindex
C22×#142686342
D4×D4522
#202989722
#202988292
#202988002
#202987982
#202987482
#202987372
C4×#142686342
D4×#117447512
D4×Q8×C1132
D4×SD16113