Finite Group Databasebeta

← C4⋊C4×C22⋊D113 #28393473

Subgroups — C4⋊C4×C22⋊D113 #28393473

Order 14464.

776 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D113C212yesmaximal
2C2×C4×C22⋊D113C211yesmaximal, characteristic
3C2×C4⋊C4×D113C211yesmaximal, characteristic, complemented
4#20298493C212yesmaximal, complemented
5#20298471C212yesmaximal, complemented
6#20298469C212yesmaximal, complemented
7#20298467C211yesmaximal, characteristic, complemented
8#20298458C211yesmaximal, characteristic, complemented
9#20298455C211yesmaximal, characteristic, complemented
10C4⋊C4×Dic113C211yesmaximal, characteristic, complemented
11C22×C4⋊C4×C113C211yesmaximal, characteristic, complemented
12C22×C22⋊D113C2211yescharacteristic
13C22×C4×D113C2212yes—
14C22×C4×D113C2211yescharacteristic
15C4×C22⋊D113—28no—
16C4×C22⋊D113C418yescomplemented
17C2×C4⋊Dic113C2211yescharacteristic
18C2×C4⋊Dic113C2211yescharacteristic
19C2×#14268626C2212yes—
20C2×#14268626C2212yes—
21C2×#14268626C2212yes—
22C2×#14268626C2211yescharacteristic
23C4⋊C4×D113—24no—
24C2×C22⋊Dic113C2212yes—
25C2×C22⋊Dic113C2211yescharacteristic
26C2×#14268624C2212yes—
27C2×#14268624C2211yescharacteristic
28C2×C4×Dic113C2212yes—
29C2×C4×Dic113C2211yescharacteristic
30#16813529C2212yes—
31#16813529C2212yes—
32#16813529C2212yes—
33C23×C4×C113C2212yes—
34C23×C4×C113C2211yescharacteristic
35C2×C4⋊C4×C113—24no—
36C2×C4⋊C4×C113C2211yescharacteristic
37C2×C4⋊C4×C113C2212yes—
38C2×C4⋊C4×C113C2211yescharacteristic
39C23×D113C2311yescharacteristic
40C2×C22⋊D113C2×C414yes—
41C2×C22⋊D113D414yes—
42C2×C22⋊D113Q814yes—
43C22×Dic113C2312yes—
44C22×Dic113C2312yes—
45C22×Dic113C2311yescharacteristic
46C22×Dic113C2311yescharacteristic
47C22×Dic113C2311yescharacteristic
48C2×C4×D113—22no—
49C2×C4×D113—22no—
50C2×C4×D113—24no—
51C2×C4×D113—24no—
52C2×C4×D113—42no—
53C2×C4×D113C2×C414yescomplemented
54C4⋊Dic113—22no—
55C4⋊Dic113—22no—
56#14268626—24no—
57#14268626—24no—
58#14268626—42no—
59#14268626C2×C414yescomplemented
60C22⋊Dic113—24no—
61C22⋊Dic113C2×C414yescomplemented
62#14268624—24no—
63#14268624C2×C414yescomplemented
64C4×Dic113—24no—
65C4×Dic113C2×C414yescomplemented
66C24×C113C2311yescharacteristic
67C22×C4×C113—22no—
68C22×C4×C113—22no—
69C22×C4×C113—24no—
70C22×C4×C113—24no—
71C22×C4×C113—42no—
72C22×C4×C113C2×C414yescomplemented
73C22×C4×C113C2312yes—
74C22×C4×C113C2311yescharacteristic
75C22×C4×C113C2312yes—
76C22×C4×C113C2311yescharacteristic
77C4⋊C4×C113—24no—
78C4⋊C4×C113—22no—
79C4⋊C4×C113D414yescomplemented
80C23×C113—21no—
81C23×C113—21no—
82C23×C113—21no—
83C23×C113—21no—
84C23×C113C22×C412yes—
85C23×C113C2×D412yes—
86C23×C113C2×Q812yes—
87C23×C113C2411yescharacteristic
88C22×D113—21no—
89C22×D113—21no—
90C22×D113—21no—
91C22×D113—21no—
92C22×D113C22×C412yes—
93C22×D113C2×D412yes—
94C22×D113C2×Q812yes—
95C2×C4×C113—21no—
96C2×C4×C113—22no—
97C2×C4×C113—21no—
98C2×C4×C113—22no—
99C2×C4×C113—28no—
100C2×C4×C113—22no—
101C2×C4×C113—22no—
102C2×C4×C113—22no—
103C2×C4×C113—48no—
104C2×C4×C113C22×C412yes—
105C2×C4×C113C22×C412yes—
106C2×C4×C113C2×D414yes—
107C2×C4×C113C2×D412yes—
108C2×C4×C113#4112yes—
109C22⋊D113C4⋊C4116yesdirect product factor
110C2×Dic113—21no—
111C2×Dic113—21no—
112C2×Dic113—21no—
113C2×Dic113—21no—
114C2×Dic113—22no—
115C2×Dic113—22no—
116C2×Dic113—22no—
117C2×Dic113—22no—
118C2×Dic113—22no—
119C2×Dic113—22no—
120C2×Dic113C22×C412yes—
121C2×Dic113C22×C412yes—
122C2×Dic113C22×C412yes—
123C2×Dic113C2×D412yes—
124C2×Dic113C2×Q812yes—
125C4×D113—28no—
126C4×D113—48no—
127C22×C113—22no—
128C22×C113—22no—
129C22×C113—22no—
130C22×C113—22no—
131C22×C113—22no—
132C22×C113—22no—
133C22×C113C2×C4⋊C414yescomplemented
134C22×C113C23×C411yescharacteristic
135C22×C113C22×D411yescharacteristic
136C22×C113C22×D411yescharacteristic
137C22×C113C22×Q811yescharacteristic
138C22×C113C2×#4111yescharacteristic
139C22×C113H(5,𝔽2)11yescharacteristic
140C22×C1132−1+411yescharacteristic
141C2×D113—22no—
142C2×D113—22no—
143C2×D113—22no—
144C2×D113—22no—
145C2×D113—22no—
146C2×D113—22no—
147C2×D113C2×C4⋊C414yescomplemented
148C4×C113—22no—
149C4×C113—24no—
150C4×C113—42no—
151C4×C113C4×D414yescomplemented
152Dic113—22no—
153Dic113—22no—
154Dic113—42no—
155Dic113—42no—
156Dic113C2×C4⋊C414yescomplemented
157C2×C113—24no—
158C2×C113C22×C4⋊C411yescharacteristic
159C2×C113C2×C4×D411yescharacteristic
160C2×C113#52011yescharacteristic
161C2×C113D4211yescharacteristic
162C2×C113#54711yescharacteristic
163C2×C113D4×Q811yescharacteristic
164C2×C113#55411yescharacteristic
165D113—24no—
166D4×C4⋊C4—1131nomaximal, Sylow
167C113D4×C4⋊C411yescharacteristic, complemented, Sylow
168C2×C4×D4—1131no—
169C2×C4×D4—1132no—
170C22×C4⋊C4—1131no—
171C22×C4⋊C4D11311yescharacteristic, complemented
172#389—1132no—
173#385—1132no—
174#385—1132no—
175#384—1131no—
176#380—1131no—
177#380—1131no—
178C4×C4⋊C4—1131no—
179C22×D4—1131no—
180C23×C4—1131no—
181C23×C4—1132no—
182C23×C4C2×D11312yes—
183C23×C4C2×D11311yescharacteristic
184C4×D4—1138no—
185C4×D4—2268no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—1131no—
188C2×C4⋊C4—1132no—
189C2×C4⋊C4—1132no—
190C2×C4⋊C4—1131no—
191C2×C4⋊C4—1132no—
192C2×C4⋊C4—1131no—
193C2×C4⋊C4—2264no—
194C2×C4⋊C4C2×D11311yescharacteristic
195C2×C4⋊C4C2×D11312yes—
196C2×C4⋊C4C2×D11311yescharacteristic
197C2×C22⋊C4—1131no—
198C2×C22⋊C4—1131no—
199C2×C22⋊C4—1132no—
200C2×C22⋊C4—1132no—
201C2×C42—1131no—
202C2×C42—1132no—
203#95—1132no—
204#95—1132no—
205#95—1132no—
206C24—1131no—
207C24C22×D11311yescharacteristic
208C2×D4—1134no—
209C2×D4—1134no—
210C2×D4—1134no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—42no—
216C22×C4—1131no—
217C22×C4—1131no—
218C22×C4—1131no—
219C22×C4—1134no—
220C22×C4—1132no—
221C22×C4—1132no—
222C22×C4—4522no—
223C22×C4—2264no—
224C22×C4—2264no—
225C22×C4—2262no—
226C22×C4—2262no—
227C22×C4C4×D11314yescomplemented
228C22×C4C22×D11312yes—
229C22×C4C22×D11311yescharacteristic
230C22×C4C22×D11312yes—
231C22×C4C22×D11311yescharacteristic
232C4⋊C4—24no—
233C4⋊C4—22no—
234C4⋊C4—1134no—
235C4⋊C4—4522no—
236C4⋊C4—2264no—
237C4⋊C4—2264no—
238C4⋊C4—2262no—
239C4⋊C4—2262no—
240C4⋊C4C22⋊D11314yesdirect product factor
241C22⋊C4—1134no—
242C22⋊C4—1134no—
243C22⋊C4—2264no—
244C22⋊C4—2264no—
245C42—1134no—
246C42—2264no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—1132no—
252C23—1132no—
253C23—1132no—
254C23—2261no—
255C23—2261no—
256C23—2261no—
257C23—2261no—
258C23C2×C4×D11312yes—
259C23D4×D11312yes—
260C23Q8×D11312yes—
261C23C23×D11311yescharacteristic
262D4—11316no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—28no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—48no—
272C2×C4—1132no—
273C2×C4—1132no—
274C2×C4—1132no—
275C2×C4—1132no—
276C2×C4—1132no—
277C2×C4—4528no—
278C2×C4—2262no—
279C2×C4—2262no—
280C2×C4—2262no—
281C2×C4—2262no—
282C2×C4—2262no—
283C2×C4—2262no—
284C2×C4—2261no—
285C2×C4—2261no—
286C2×C4—2261no—
287C2×C4—2261no—
288C2×C4—2268no—
289C2×C4C2×C4×D11312yes—
290C2×C4C2×C4×D11312yes—
291C2×C4C2×C22⋊D11314yes—
292C2×C4C2×C22⋊D11312yes—
293C2×C4#1426864712yes—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—1134no—
301C22—2262no—
302C22—2262no—
303C22—2262no—
304C22—2262no—
305C22—2262no—
306C22—2262no—
307C22C4⋊C4×D11314yescomplemented
308C22C22×C4×D11311yescharacteristic
309C22C2×D4×D11311yescharacteristic
310C22C22×C22⋊D11311yescharacteristic
311C22C2×Q8×D11311yescharacteristic
312C22C2×#1426864711yescharacteristic
313C22#1681366711yescharacteristic
314C22#1681367011yescharacteristic
315C4—22no—
316C4—24no—
317C4—42no—
318C4—1134no—
319C4—4522no—
320C4—4522no—
321C4—2262no—
322C4—2262no—
323C4C4×C22⋊D11314yescomplemented
324C2—24no—
325C2—2264no—
326C2C2×C4⋊C4×D11311yescharacteristic
327C2C2×C4×C22⋊D11311yescharacteristic
328C2#2029907911yescharacteristic
329C2D4×C22⋊D11311yescharacteristic
330C2#2029924911yescharacteristic
331C2Q8×C22⋊D11311yescharacteristic
332C2#2029930311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
FittingC22×C4⋊C4×C113C2
socle, cosocleC23×C113C24
prime radicalC22×C22⋊D113C22
hypercenterC22×C4⋊C4D113
hypocenterC113D4×C4⋊C4
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D113C2semidirect
4. #20298493C2semidirect
5. #20298471C2semidirect
6. #20298469C2semidirect
7. #20298467C2semidirect
8. #20298458C2semidirect
9. #20298455C2semidirect
10. C4⋊C4×Dic113C2semidirect
11. C22×C4⋊C4×C113C2semidirect
16. C4×C22⋊D113C4semidirect
53. C2×C4×D113C2×C4semidirect
59. #14268626C2×C4semidirect
61. C22⋊Dic113C2×C4semidirect
63. #14268624C2×C4semidirect
65. C4×Dic113C2×C4semidirect
72. C22×C4×C113C2×C4semidirect
79. C4⋊C4×C113D4semidirect
109. C22⋊D113C4⋊C4direct (N × H)
133. C22×C113C2×C4⋊C4semidirect
147. C2×D113C2×C4⋊C4semidirect
151. C4×C113C4×D4semidirect
156. Dic113C2×C4⋊C4semidirect
167. C113D4×C4⋊C4semidirect
171. C22×C4⋊C4D113semidirect
227. C22×C4C4×D113semidirect
240. C4⋊C4C22⋊D113direct (N × H)
307. C22C4⋊C4×D113semidirect
323. C4C4×C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1132
C2×C4⋊C4×D1132
#202984932
#202984712
#202984692
#202984672
#202984582
#202984552
C4⋊C4×Dic1132
C22×C4⋊C4×C1132
D4×C4⋊C4113