Finite Group Databasebeta

← C41×#11478 #23787679

Subgroups — C41×#11478 #23787679

Order 10496.

428 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 134 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
1C4×C4⋊Q8×C41C211yesmaximal, characteristic
2C41×#1461C212yesmaximal
3C41×#1325C212yesmaximal
4C41×#1319C212yesmaximal
5C2×C4⋊Q8×C41C411yescharacteristic
6C2×C4×Q8×C41C411yescharacteristic
7C2×C4×Q8×C41C2211yescharacteristic
8C41×#431—22no—
9C41×#391C411yescharacteristic
10C41×#391C2211yescharacteristic
11C41×#389—22no—
12C41×#384C2211yescharacteristic
13C4×C4⋊C4×C41—22no—
14C43×C41C411yescharacteristic
15C41×#324—22no—
16C41×#324C2214yes—
17C22×Q8×C41C2×C411yescharacteristic
18C22×Q8×C41C2×C411yescharacteristic
19C4⋊Q8×C41—22no—
20C4⋊Q8×C41C814yescomplemented
21C4×Q8×C41—41no—
22C4×Q8×C41—41no—
23C4×Q8×C41—41no—
24C4×Q8×C41—41no—
25C2×C4⋊C4×C41—22no—
26C2×C4⋊C4×C41—21no—
27C2×C4⋊C4×C41—22no—
28C2×C4⋊C4×C41C2×C411yescharacteristic
29C2×C4⋊C4×C41D412yes—
30C2×C4⋊C4×C41C2311yescharacteristic
31C2×C42×C41—21no—
32C2×C42×C41—21no—
33C2×C42×C41—21no—
34C2×C42×C41C2×C411yescharacteristic
35C2×C42×C41C2×C411yescharacteristic
36C2×C42×C41C2×C411yescharacteristic
37C2×C42×C41D412yes—
38C4⋊C8×C41—42no—
39C22⋊C8×C41—24no—
40C4×C8×C41—42no—
41#95×C41—22no—
42#95×C41—22no—
43C2×Q8×C41—21no—
44C2×Q8×C41—41no—
45C2×Q8×C41—41no—
46C2×Q8×C41—41no—
47C2×Q8×C41—41no—
48C2×Q8×C41C2×C812yes—
49C2×Q8×C41C2×C812yes—
50C2×Q8×C41M1612yes—
51C22×C4×C41—21no—
52C22×C4×C41—21no—
53C22×C4×C41—21no—
54C22×C4×C41—21no—
55C22×C4×C41C22⋊C412yes—
56C22×C4×C41C22⋊C411yescharacteristic
57C22×C4×C41C22⋊C411yescharacteristic
58C22×C4×C41C22×C411yescharacteristic
59C22×C4×C41C2×D412yes—
60C2×C8×C41—44no—
61C4⋊C4×C41—28no—
62C4⋊C4×C41—42no—
63C4⋊C4×C41—41no—
64C4⋊C4×C41—41no—
65C4⋊C4×C41—44no—
66C4⋊C4×C41—42no—
67C42×C41—24no—
68C42×C41—22no—
69C42×C41—21no—
70C42×C41—22no—
71C42×C41—21no—
72C42×C41—21no—
73C42×C41—41no—
74C42×C41—42no—
75C42×C41—41no—
76C42×C41—41no—
77C42×C41C2×C812yes—
78C23×C41C2×C22⋊C411yescharacteristic
79Q8×C41—42no—
80Q8×C41—42no—
81Q8×C41—42no—
82Q8×C41—42no—
83C2×C4×C41—22no—
84C2×C4×C41—22no—
85C2×C4×C41—22no—
86C2×C4×C41—21no—
87C2×C4×C41—22no—
88C2×C4×C41—21no—
89C2×C4×C41—22no—
90C2×C4×C41—22no—
91C2×C4×C41—22no—
92C2×C4×C41—22no—
93C2×C4×C41—21no—
94C2×C4×C41—22no—
95C2×C4×C41—41no—
96C2×C4×C41—41no—
97C2×C4×C41—41no—
98C2×C4×C41—41no—
99C2×C4×C41—41no—
100C2×C4×C41—42no—
101C2×C4×C41—42no—
102C2×C4×C41—41no—
103C2×C4×C41C22⋊C814yes—
104C2×C4×C41#9911yescharacteristic
105C2×C4×C41#9911yescharacteristic
106C2×C4×C41C22×C811yescharacteristic
107C2×C4×C41C2×M1611yescharacteristic
108C8×C41—84no—
109#11478C4111yesmaximal, characteristic, direct product factor, Sylow
110C22×C41—21no—
111C22×C41—21no—
112C22×C41C2×C22⋊C811yescharacteristic
113C22×C41C2×#9911yescharacteristic
114C22×C41#41311yescharacteristic
115C4×C41—24no—
116C4×C41—21no—
117C4×C41—24no—
118C4×C41—21no—
119C4×C41—21no—
120C4×C41—42no—
121C4×C41—42no—
122C4×C41—41no—
123C4×C41—42no—
124C4×C41—81no—
125C4×C41#35612yes—
126C4×C4⋊Q8C2×C4111yescharacteristic
127#1461C2×C4112yes—
128#1325C2×C4112yes—
129#1319C2×C4112yes—
130C2×C41—21no—
131C2×C41—21no—
132C2×C41#145911yescharacteristic
133C2×C41#212611yescharacteristic
134C2×C41C2×#35611yescharacteristic
135C2×C4⋊Q8C4×C4111yescharacteristic
136C2×C4×Q8C4×C4111yescharacteristic
137C2×C4×Q8C22×C4111yescharacteristic
138#431—22no—
139#391C4×C4111yescharacteristic
140#391C22×C4111yescharacteristic
141#389—22no—
142#384C22×C4111yescharacteristic
143C4×C4⋊C4—22no—
144C43C4×C4111yescharacteristic
145#324—22no—
146#324C22×C4114yes—
147C41#1147811yescharacteristic, direct product factor, Sylow
148C22×Q8C2×C4×C4111yescharacteristic
149C22×Q8C2×C4×C4111yescharacteristic
150C4⋊Q8—22no—
151C4⋊Q8C8×C4114yescomplemented
152C4×Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C4×Q8—41no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4C2×C4×C4111yescharacteristic
160C2×C4⋊C4D4×C4112yes—
161C2×C4⋊C4C23×C4111yescharacteristic
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42C2×C4×C4111yescharacteristic
166C2×C42C2×C4×C4111yescharacteristic
167C2×C42C2×C4×C4111yescharacteristic
168C2×C42D4×C4112yes—
169C4⋊C8—42no—
170C22⋊C8—24no—
171C4×C8—42no—
172#95—22no—
173#95—22no—
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8C2×C8×C4112yes—
180C2×Q8C2×C8×C4112yes—
181C2×Q8M16×C4112yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4C22⋊C4×C4112yes—
187C22×C4C22⋊C4×C4111yescharacteristic
188C22×C4C22⋊C4×C4111yescharacteristic
189C22×C4C22×C4×C4111yescharacteristic
190C22×C4C2×D4×C4112yes—
191C2×C8—44no—
192C4⋊C4—28no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—44no—
198C42—24no—
199C42—22no—
200C42—22no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—41no—
205C42—42no—
206C42—41no—
207C42—41no—
208C42C2×C8×C4112yes—
209C23C2×C22⋊C4×C4111yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—42no—
213Q8—42no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4C22⋊C8×C4114yes—
235C2×C4#99×C4111yescharacteristic
236C2×C4#99×C4111yescharacteristic
237C2×C4C22×C8×C4111yescharacteristic
238C2×C4C2×M16×C4111yescharacteristic
239C8—84no—
240C22—21no—
241C22—21no—
242C22C2×C22⋊C8×C4111yescharacteristic
243C22C2×#99×C4111yescharacteristic
244C22C41×#41311yescharacteristic
245C4—24no—
246C4—21no—
247C4—24no—
248C4—21no—
249C4—21no—
250C4—42no—
251C4—42no—
252C4—41no—
253C4—42no—
254C4—81no—
255C4C41×#35612yes—
256C2—21no—
257C2—21no—
258C2C41×#145911yescharacteristic
259C2C41×#212611yescharacteristic
260C2C2×C41×#35611yescharacteristic
subgroupG/H
centerC2×C4×C41#99
commutatorC2×C4C22×C8×C41
Frattini, cosocleC2×C4⋊C4C23×C41
socleC22×C41C2×#99
prime radicalC23×C41C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C22×C4×C41 ◁ C2×C4×Q8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
20. C4⋊Q8×C41C8semidirect
109. #11478C41direct (N × H)
147. C41#11478direct (N × H)
151. C4⋊Q8C8×C41semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊Q8×C412
C41×#14612
C41×#13252
C41×#13192
#1147841