Finite Group Databasebeta

← C31×#12802 #21469561

Subgroups — C31×#12802 #21469561

Order 7936.

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

normal subgroups only

This group has 468 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×C31×C4⋊Q8C211yesmaximal, characteristic
2C2×C31×#356C212yesmaximal
3C31×#1801C212yesmaximal
4C31×#1394C212yesmaximal
5C2×C31×C4⋊Q8C2211yescharacteristic
6C2×C4×Q8×C31C411yescharacteristic
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#423—22no—
9C2×C31×#101C2214yes—
10C31×#391C411yescharacteristic
11C31×#391C2211yescharacteristic
12C31×#389—22no—
13C31×#384C411yescharacteristic
14C4×C4⋊C4×C31—22no—
15C43×C31C411yescharacteristic
16C31×#356—24no—
17C31×#343—22no—
18C22×Q8×C31C2×C411yescharacteristic
19C22×Q8×C31C2311yescharacteristic
20C2×M16×C31—24no—
21C31×C4⋊Q8—22no—
22C31×C4⋊Q8D412yes—
23C31×C4⋊Q8Q812yes—
24C4×Q8×C31—41no—
25C4×Q8×C31—41no—
26C4×Q8×C31—41no—
27C4×Q8×C31—41no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31D412yes—
34C2×C42×C31—21no—
35C2×C42×C31—21no—
36C2×C42×C31—21no—
37C2×C42×C31C2×C411yescharacteristic
38C2×C42×C31C2×C411yescharacteristic
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31D412yes—
41C31×C4⋊C8—42no—
42C31×C4⋊C8—42no—
43C31×#101—24no—
44C31×#101—24no—
45C31×#95—22no—
46C31×#95—22no—
47C2×Q8×C31—21no—
48C2×Q8×C31—41no—
49C2×Q8×C31—41no—
50C2×Q8×C31—41no—
51C2×Q8×C31—41no—
52C2×Q8×C31C4⋊C412yes—
53C2×Q8×C31C2×D411yescharacteristic
54C2×Q8×C31C2×Q811yescharacteristic
55C2×Q8×C31#4112yes—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31C22⋊C412yes—
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31C22×C411yescharacteristic
64C22×C4×C31C2×D412yes—
65M16×C31—44no—
66M16×C31—44no—
67C2×C8×C31—44no—
68C4⋊C4×C31—24no—
69C4⋊C4×C31—24no—
70C4⋊C4×C31—41no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—44no—
73C4⋊C4×C31—42no—
74C4⋊C4×C31—41no—
75C42×C31—24no—
76C42×C31—22no—
77C42×C31—22no—
78C42×C31—21no—
79C42×C31—21no—
80C42×C31—21no—
81C42×C31—42no—
82C42×C31—41no—
83C42×C31—41no—
84C42×C31—41no—
85C42×C31C4⋊C412yes—
86#12802C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31C2×C22⋊C411yescharacteristic
88Q8×C31—41no—
89Q8×C31—41no—
90Q8×C31—42no—
91Q8×C31—42no—
92Q8×C31—42no—
93C2×C4×C31—22no—
94C2×C4×C31—22no—
95C2×C4×C31—22no—
96C2×C4×C31—21no—
97C2×C4×C31—22no—
98C2×C4×C31—21no—
99C2×C4×C31—22no—
100C2×C4×C31—22no—
101C2×C4×C31—22no—
102C2×C4×C31—22no—
103C2×C4×C31—21no—
104C2×C4×C31—22no—
105C2×C4×C31—41no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—41no—
113C2×C4×C31#9911yescharacteristic
114C2×C4×C31#9911yescharacteristic
115C2×C4×C31C2×C4⋊C411yescharacteristic
116C2×C4×C31#11711yescharacteristic
117C2×C4×C31#12112yes—
118C2×C4×C31C22⋊Q812yes—
119C8×C31—84no—
120C4×C4⋊Q8C2×C3111yescharacteristic
121C2×#356C2×C3112yes—
122#1801C2×C3112yes—
123#1394C2×C3112yes—
124C22×C31—21no—
125C22×C31—21no—
126C22×C31#38011yescharacteristic
127C22×C31C2×#9911yescharacteristic
128C22×C31#41011yescharacteristic
129C4×C31—24no—
130C4×C31—22no—
131C4×C31—21no—
132C4×C31—21no—
133C4×C31—22no—
134C4×C31—21no—
135C4×C31—42no—
136C4×C31—42no—
137C4×C31—41no—
138C4×C31—42no—
139C4×C31—81no—
140C4×C31#35612yescomplemented
141C2×C4⋊Q8C22×C3111yescharacteristic
142C2×C4×Q8C4×C3111yescharacteristic
143C2×C4×Q8C22×C3111yescharacteristic
144#423—22no—
145C2×#101C22×C3114yes—
146#391C4×C3111yescharacteristic
147#391C22×C3111yescharacteristic
148#389—22no—
149#384C4×C3111yescharacteristic
150C4×C4⋊C4—22no—
151C43C4×C3111yescharacteristic
152#356—24no—
153#343—22no—
154C2×C31—21no—
155C2×C31—21no—
156C2×C31#179911yescharacteristic
157C2×C31C2×#35611yescharacteristic
158C2×C31#213211yescharacteristic
159C22×Q8C2×C4×C3111yescharacteristic
160C22×Q8C23×C3111yescharacteristic
161C2×M16—24no—
162C4⋊Q8—22no—
163C4⋊Q8D4×C3112yes—
164C4⋊Q8Q8×C3112yes—
165C4×Q8—41no—
166C4×Q8—41no—
167C4×Q8—41no—
168C4×Q8—41no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4C2×C4×C3111yescharacteristic
173C2×C4⋊C4C2×C4×C3111yescharacteristic
174C2×C4⋊C4D4×C3112yes—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42C2×C4×C3111yescharacteristic
179C2×C42C2×C4×C3111yescharacteristic
180C2×C42C2×C4×C3111yescharacteristic
181C2×C42D4×C3112yes—
182C4⋊C8—42no—
183C4⋊C8—42no—
184#101—24no—
185#101—24no—
186#95—22no—
187#95—22no—
188C31#1280211yescharacteristic, direct product factor, Sylow
189C2×Q8—21no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8C4⋊C4×C3112yes—
195C2×Q8C2×D4×C3111yescharacteristic
196C2×Q8C2×Q8×C3111yescharacteristic
197C2×Q8#41×C3112yes—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4C22⋊C4×C3111yescharacteristic
203C22×C4C22⋊C4×C3112yes—
204C22×C4C22⋊C4×C3111yescharacteristic
205C22×C4C22×C4×C3111yescharacteristic
206C22×C4C2×D4×C3112yes—
207M16—44no—
208M16—44no—
209C2×C8—44no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—41no—
215C4⋊C4—44no—
216C4⋊C4—42no—
217C42—24no—
218C42—22no—
219C42—22no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—41no—
224C42—42no—
225C42—41no—
226C42—41no—
227C42C4⋊C4×C3112yes—
228C23C2×C22⋊C4×C3111yescharacteristic
229Q8—41no—
230Q8—41no—
231Q8—42no—
232Q8—42no—
233Q8—42no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4C31×#9911yescharacteristic
255C2×C4C31×#9911yescharacteristic
256C2×C4C2×C4⋊C4×C3111yescharacteristic
257C2×C4C31×#11711yescharacteristic
258C2×C4C31×#12112yes—
259C2×C4C31×C22⋊Q812yes—
260C8—84no—
261C22—21no—
262C22—21no—
263C22C31×#38011yescharacteristic
264C22C2×C31×#9911yescharacteristic
265C22C31×#41011yescharacteristic
266C4—24no—
267C4—22no—
268C4—21no—
269C4—21no—
270C4—22no—
271C4—21no—
272C4—42no—
273C4—42no—
274C4—41no—
275C4—42no—
276C4—81no—
277C4C31×#35612yescomplemented
278C2—21no—
279C2—21no—
280C2C31×#179911yescharacteristic
281C2C2×C31×#35611yescharacteristic
282C2C31×#213211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC22×Q8C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
86. #12802C31direct (N × H)
140. C4×C31#356semidirect
188. C31#12802direct (N × H)
277. C4C31×#356semidirect

Maximal subgroups

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

subgroupindex
C4×C31×C4⋊Q82
C2×C31×#3562
C31×#18012
C31×#13942
#1280231