Finite Group Databasebeta

← C4⋊C42×C103 #39919078

Subgroups — C4⋊C42×C103 #39919078

Order 26368.

1838 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#384×C103C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C103C214yesmaximal
3C2×C4×C4⋊C4×C103C212yesmaximal
4C103×#1436C214yesmaximal
5C103×C4⋊#95C214yesmaximal
6C22×C4⋊C4×C103C2212yes—
7C22×C4⋊C4×C103C2214yes—
8C22×C4⋊C4×C103C2212yes—
9C22×C4⋊C4×C103C2212yes—
10C22×C42×C103C2214yes—
11C22×C42×C103C2214yes—
12C22×C42×C103C2211yescharacteristic
13#384×C103C418yescomplemented
14C4×C4⋊C4×C103—216no—
15C4×C4⋊C4×C103C4116yescomplemented
16C2×#95×C103C2218yes—
17C2×#95×C103C2214yes—
18C2×#95×C103C2214yes—
19C23×C4×C103C2314yes—
20C23×C4×C103C2314yes—
21C23×C4×C103C2311yescharacteristic
22C23×C4×C103C2314yes—
23C23×C4×C103C2312yes—
24C2×C4⋊C4×C103—28no—
25C2×C4⋊C4×C103—24no—
26C2×C4⋊C4×C103—24no—
27C2×C4⋊C4×C103—28no—
28C2×C4⋊C4×C103—42no—
29C2×C4⋊C4×C103—42no—
30C2×C4⋊C4×C103C2×C418yes—
31C2×C4⋊C4×C103C2×C4116yes—
32C2×C4⋊C4×C103C2×C418yes—
33C2×C4⋊C4×C103C2×C418yes—
34C2×C4⋊C4×C103D418yes—
35C2×C4⋊C4×C103Q818yes—
36C2×C42×C103—28no—
37C2×C42×C103—28no—
38C2×C42×C103—216no—
39C2×C42×C103—44no—
40C2×C42×C103C2×C4116yes—
41C2×C42×C103C2×C418yes—
42C2×C42×C103C2×C414yes—
43#95×C103—216no—
44#95×C103—44no—
45#95×C103C2×C4116yes—
46C24×C103C2411yescharacteristic
47C22×C4×C103—24no—
48C22×C4×C103—24no—
49C22×C4×C103—24no—
50C22×C4×C103—21no—
51C22×C4×C103—21no—
52C22×C4×C103—22no—
53C22×C4×C103—24no—
54C22×C4×C103—24no—
55C22×C4×C103—28no—
56C22×C4×C103—24no—
57C22×C4×C103—24no—
58C22×C4×C103—24no—
59C22×C4×C103—28no—
60C22×C4×C103—24no—
61C22×C4×C103—24no—
62C22×C4×C103—24no—
63C22×C4×C103—24no—
64C22×C4×C103C22×C418yes—
65C22×C4×C103C22×C418yes—
66C22×C4×C103C22×C414yes—
67C22×C4×C103C22×C412yes—
68C22×C4×C103C22×C418yes—
69C22×C4×C103C22×C414yes—
70C22×C4×C103C22×C414yes—
71C22×C4×C103C22×C414yes—
72C22×C4×C103C2×D418yes—
73C22×C4×C103C2×D414yes—
74C22×C4×C103C2×Q818yes—
75C22×C4×C103C2×Q814yes—
76C22×C4×C103#4114yes—
77C22×C4×C103#4114yes—
78C4⋊C4×C103—216no—
79C4⋊C4×C103—232no—
80C4⋊C4×C103—48no—
81C4⋊C4×C103C4⋊C4132yesdirect product factor
82C42×C103—232no—
83C42×C103—416no—
84C42×C103C42116yescomplemented
85C23×C103C23×C412yes—
86C23×C103C23×C411yescharacteristic
87C23×C103C22×D412yes—
88C23×C103C22×Q812yes—
89C23×C103C2×#4112yes—
90C23×C103C2×#4112yes—
91C23×C103H(5,𝔽2)11yescharacteristic
92C23×C103H(5,𝔽2)11yescharacteristic
93C23×C1032−1+412yes—
94C2×C4×C103—28no—
95C2×C4×C103—22no—
96C2×C4×C103—22no—
97C2×C4×C103—28no—
98C2×C4×C103—24no—
99C2×C4×C103—24no—
100C2×C4×C103—28no—
101C2×C4×C103—28no—
102C2×C4×C103—28no—
103C2×C4×C103—28no—
104C2×C4×C103—28no—
105C2×C4×C103—28no—
106C2×C4×C103—216no—
107C2×C4×C103—28no—
108C2×C4×C103—28no—
109C2×C4×C103—44no—
110C2×C4×C103—44no—
111C2×C4×C103—44no—
112C2×C4×C103—48no—
113C2×C4×C103—44no—
114C2×C4×C103—44no—
115C2×C4×C103—44no—
116C2×C4×C103C2×C4214yes—
117C2×C4×C103C2×C4218yes—
118C2×C4×C103C2×C4⋊C4116yes—
119C2×C4×C103C2×C4⋊C418yes—
120C2×C4×C103#11718yes—
121C2×C4×C103C4×D418yes—
122C2×C4×C103C4×D418yes—
123C2×C4×C103C4×Q818yes—
124C2×C4×C103C4×Q818yes—
125C22×C103C22×C4211yescharacteristic
126C22×C103C22×C4⋊C412yes—
127C22×C103C2×#11712yes—
128C22×C103C2×C4×D412yes—
129C22×C103C2×C4×D412yes—
130C22×C103C2×C4×Q812yes—
131C22×C103C2×C4×Q812yes—
132C22×C103#51811yescharacteristic
133C22×C103#51911yescharacteristic
134C22×C103#52012yes—
135C22×C103#52012yes—
136C22×C103D4211yescharacteristic
137C22×C103#54712yes—
138C22×C103D4×Q812yes—
139C22×C103#55012yes—
140C22×C103#55412yes—
141C22×C103#55511yescharacteristic
142C22×C103#55612yes—
143C22×C103#55712yes—
144C22×C103Q8211yescharacteristic
145C22×C103#55911yescharacteristic
146C4×C103—216no—
147C4×C103—24no—
148C4×C103—48no—
149C4×C103—48no—
150C4×C103C4×C4⋊C4116yescomplemented
151C4⋊C42C10311yesmaximal, characteristic, direct product factor, Sylow
152C2×C103C2×C4×C4⋊C412yes—
153C2×C103#227411yescharacteristic
154C2×C103D4×C4⋊C412yes—
155C2×C103Q8×C4⋊C412yes—
156C2×C103#235412yes—
157C2×C103#235512yes—
158C2×C103#236512yes—
159C2×C103#236611yescharacteristic
160C2×C103#236911yescharacteristic
161C2×#384C2×C10311yescharacteristic
162C2×C4×C4⋊C4C2×C10314yes—
163C2×C4×C4⋊C4C2×C10312yes—
164#1436C2×C10314yes—
165C4⋊#95C2×C10314yes—
166C103C4⋊C4211yescharacteristic, direct product factor, Sylow
167C22×C4⋊C4C22×C10312yes—
168C22×C4⋊C4C22×C10314yes—
169C22×C4⋊C4C22×C10312yes—
170C22×C4⋊C4C22×C10312yes—
171C22×C42C22×C10314yes—
172C22×C42C22×C10314yes—
173C22×C42C22×C10311yescharacteristic
174#384C4×C10318yescomplemented
175C4×C4⋊C4—216no—
176C4×C4⋊C4C4×C103116yescomplemented
177C2×#95C22×C10318yes—
178C2×#95C22×C10314yes—
179C2×#95C22×C10314yes—
180C23×C4C23×C10314yes—
181C23×C4C23×C10314yes—
182C23×C4C23×C10311yescharacteristic
183C23×C4C23×C10314yes—
184C23×C4C23×C10312yes—
185C2×C4⋊C4—28no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—28no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4C2×C4×C10318yes—
192C2×C4⋊C4C2×C4×C103116yes—
193C2×C4⋊C4C2×C4×C10318yes—
194C2×C4⋊C4C2×C4×C10318yes—
195C2×C4⋊C4D4×C10318yes—
196C2×C4⋊C4Q8×C10318yes—
197C2×C42—28no—
198C2×C42—28no—
199C2×C42—216no—
200C2×C42—44no—
201C2×C42C2×C4×C103116yes—
202C2×C42C2×C4×C10318yes—
203C2×C42C2×C4×C10314yes—
204#95—216no—
205#95—44no—
206#95C2×C4×C103116yes—
207C24C24×C10311yescharacteristic
208C22×C4—24no—
209C22×C4—24no—
210C22×C4—24no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—28no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—28no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—24no—
225C22×C4C22×C4×C10318yes—
226C22×C4C22×C4×C10318yes—
227C22×C4C22×C4×C10314yes—
228C22×C4C22×C4×C10312yes—
229C22×C4C22×C4×C10318yes—
230C22×C4C22×C4×C10314yes—
231C22×C4C22×C4×C10314yes—
232C22×C4C22×C4×C10314yes—
233C22×C4C2×D4×C10318yes—
234C22×C4C2×D4×C10314yes—
235C22×C4C2×Q8×C10318yes—
236C22×C4C2×Q8×C10314yes—
237C22×C4#41×C10314yes—
238C22×C4#41×C10314yes—
239C4⋊C4—216no—
240C4⋊C4—232no—
241C4⋊C4—48no—
242C4⋊C4C4⋊C4×C103132yesdirect product factor
243C42—232no—
244C42—416no—
245C42C42×C103116yescomplemented
246C23C23×C4×C10312yes—
247C23C23×C4×C10311yescharacteristic
248C23C22×D4×C10312yes—
249C23C22×Q8×C10312yes—
250C23C2×#41×C10312yes—
251C23C2×#41×C10312yes—
252C23H(5,𝔽2)×C10311yescharacteristic
253C23H(5,𝔽2)×C10311yescharacteristic
254C232−1+4×C10312yes—
255C2×C4—28no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—24no—
259C2×C4—24no—
260C2×C4—28no—
261C2×C4—28no—
262C2×C4—28no—
263C2×C4—28no—
264C2×C4—28no—
265C2×C4—28no—
266C2×C4—28no—
267C2×C4—216no—
268C2×C4—28no—
269C2×C4—28no—
270C2×C4—44no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—48no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4C2×C42×C10314yes—
278C2×C4C2×C42×C10318yes—
279C2×C4C2×C4⋊C4×C103116yes—
280C2×C4C2×C4⋊C4×C10318yes—
281C2×C4#117×C10318yes—
282C2×C4C4×D4×C10318yes—
283C2×C4C4×D4×C10318yes—
284C2×C4C4×Q8×C10318yes—
285C2×C4C4×Q8×C10318yes—
286C22C22×C42×C10311yescharacteristic
287C22C22×C4⋊C4×C10312yes—
288C22C2×#117×C10312yes—
289C22C2×C4×D4×C10312yes—
290C22C2×C4×D4×C10312yes—
291C22C2×C4×Q8×C10312yes—
292C22C2×C4×Q8×C10312yes—
293C22#518×C10311yescharacteristic
294C22#519×C10311yescharacteristic
295C22#520×C10312yes—
296C22#520×C10312yes—
297C22D42×C10311yescharacteristic
298C22#547×C10312yes—
299C22D4×Q8×C10312yes—
300C22#550×C10312yes—
301C22#554×C10312yes—
302C22#555×C10311yescharacteristic
303C22#556×C10312yes—
304C22#557×C10312yes—
305C22Q82×C10311yescharacteristic
306C22#559×C10311yescharacteristic
307C4—24no—
308C4—216no—
309C4—48no—
310C4—48no—
311C4C4×C4⋊C4×C103116yescomplemented
312C2C2×C4×C4⋊C4×C10312yes—
313C2C103×#227411yescharacteristic
314C2D4×C4⋊C4×C10312yes—
315C2Q8×C4⋊C4×C10312yes—
316C2C103×#235412yes—
317C2C103×#235512yes—
318C2C103×#236512yes—
319C2C103×#236611yescharacteristic
320C2C103×#236911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C103C24
commutatorC22C22×C42×C103
Frattini, cosocleC24C24×C103
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
13. #384×C103C4semidirect
15. C4×C4⋊C4×C103C4semidirect
81. C4⋊C4×C103C4⋊C4direct (N × H)
84. C42×C103C42semidirect
150. C4×C103C4×C4⋊C4semidirect
151. C4⋊C42C103direct (N × H)
166. C103C4⋊C42direct (N × H)
174. #384C4×C103semidirect
176. C4×C4⋊C4C4×C103semidirect
242. C4⋊C4C4⋊C4×C103direct (N × H)
245. C42C42×C103semidirect
311. C4C4×C4⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#384×C1032
C2×C4×C4⋊C4×C1032
C103×#14362
C103×C4⋊#952
C4⋊C42103