Finite Group Databasebeta

← C31×#11801 #21468560

Subgroups — C31×#11801 #21468560

Order 7936.

402 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C31×#2621C211yesmaximal, characteristic
2C31×#1820C211yesmaximal, characteristic
3C31×#1464C211yesmaximal, characteristic
4C31×#1344C214yesmaximal
5C2×C31×C4⋊Q8C411yescharacteristic, complemented
6C2×C31×C22⋊Q8—21no—
7C2×C31×#117C2211yescharacteristic
8C31×#432—21no—
9C31×#398—21no—
10C31×#398C412yescomplemented
11C31×#397—21no—
12C31×#397C2212yes—
13C31×#391—21no—
14C31×#382C411yescharacteristic, complemented
15C31×#381—21no—
16C31×#342—21no—
17C31×#342C2212yes—
18C31×#324—21no—
19C31×#323C2212yes—
20C22×Q8×C31—21no—
21C23×C4×C31D411yescharacteristic
22C31×C4⋊Q8—41no—
23C31×C4⋊Q8—41no—
24C31×C22⋊Q8—44no—
25C31×#117—41no—
26C31×#117—41no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31C2×C412yes—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31D411yescharacteristic
36C2×C22⋊C4×C31C2311yescharacteristic
37C2×C42×C31C2×C411yescharacteristic
38C2×C42×C31D411yescharacteristic
39C31×C4⋊C8—41no—
40C31×C22⋊C8—22no—
41C31×#97—41no—
42C31×#95—21no—
43C31×#95—22no—
44C31×#95—22no—
45C31×#95—41no—
46C31×#95—41no—
47C31×#95C2×C412yes—
48C24×C31C2×D411yescharacteristic
49C2×Q8×C31—42no—
50C2×Q8×C31—42no—
51C2×Q8×C31—41no—
52C2×Q8×C31—41no—
53C22×C4×C31—22no—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—41no—
59C22×C4×C31—42no—
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31C22⋊C411yescharacteristic
64C22×C4×C31C22×C411yescharacteristic
65C22×C4×C31C2×D411yescharacteristic
66C2×C8×C31—42no—
67C4⋊C4×C31—41no—
68C4⋊C4×C31—41no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—44no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—42no—
73C22⋊C4×C31—41no—
74C22⋊C4×C31—41no—
75C22⋊C4×C31—44no—
76C22⋊C4×C31—42no—
77C22⋊C4×C31—42no—
78C42×C31—21no—
79C42×C31—21no—
80C42×C31—21no—
81C42×C31—21no—
82#11801C3111yesmaximal, characteristic, direct product factor, Sylow
83C23×C31—21no—
84C23×C31—21no—
85C23×C31—41no—
86C23×C31—41no—
87C23×C31C2×C22⋊C411yescharacteristic
88C23×C31AGL(1,ℤ/8)12yes—
89Q8×C31—82no—
90Q8×C31—82no—
91C2×C4×C31—21no—
92C2×C4×C31—21no—
93C2×C4×C31—21no—
94C2×C4×C31—21no—
95C2×C4×C31—21no—
96C2×C4×C31—21no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—42no—
101C2×C4×C31—42no—
102C2×C4×C31—41no—
103C2×C4×C31—41no—
104C2×C4×C31—41no—
105C2×C4×C31—41no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—42no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—82no—
113C2×C4×C31—82no—
114C2×C4×C31—82no—
115C2×C4×C31#9911yescharacteristic
116C2×C4×C31#9911yescharacteristic
117C8×C31—82no—
118#2621C2×C3111yescharacteristic
119#1820C2×C3111yescharacteristic
120#1464C2×C3111yescharacteristic
121#1344C2×C3114yes—
122C22×C31—21no—
123C22×C31—21no—
124C22×C31—22no—
125C22×C31—42no—
126C22×C31—41no—
127C22×C31—41no—
128C22×C31—81no—
129C22×C31C2×#9911yescharacteristic
130C22×C31#41811yescharacteristic
131C22×C31#42111yescharacteristic
132C4×C31—21no—
133C4×C31—21no—
134C4×C31—41no—
135C4×C31—41no—
136C4×C31—41no—
137C4×C31—41no—
138C4×C31—41no—
139C4×C31—82no—
140C4×C31—82no—
141C4×C31—162no—
142C2×C4⋊Q8C4×C3111yescharacteristic, complemented
143C2×C22⋊Q8—21no—
144C2×#117C22×C3111yescharacteristic
145#432—21no—
146#398—21no—
147#398C4×C3112yescomplemented
148#397—21no—
149#397C22×C3112yes—
150#391—21no—
151#382C4×C3111yescharacteristic, complemented
152#381—21no—
153#342—21no—
154#342C22×C3112yes—
155#324—21no—
156#323C22×C3112yes—
157C2×C31—21no—
158C2×C31—21no—
159C2×C31—42no—
160C2×C31#151011yescharacteristic
161C2×C31#212311yescharacteristic
162C2×C31#212911yescharacteristic
163C22×Q8—21no—
164C23×C4D4×C3111yescharacteristic
165C4⋊Q8—41no—
166C4⋊Q8—41no—
167C22⋊Q8—44no—
168#117—41no—
169#117—41no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C2×C4×C3112yes—
174C2×C4⋊C4C2×C4×C3111yescharacteristic
175C2×C4⋊C4D4×C3111yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4D4×C3111yescharacteristic
179C2×C22⋊C4C23×C3111yescharacteristic
180C2×C42C2×C4×C3111yescharacteristic
181C2×C42D4×C3111yescharacteristic
182C4⋊C8—41no—
183C22⋊C8—22no—
184#97—41no—
185#95—21no—
186#95—22no—
187#95—22no—
188#95—41no—
189#95—41no—
190#95C2×C4×C3112yes—
191C31#1180111yescharacteristic, direct product factor, Sylow
192C24C2×D4×C3111yescharacteristic
193C2×Q8—42no—
194C2×Q8—42no—
195C2×Q8—41no—
196C2×Q8—41no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—42no—
204C22×C4C22⋊C4×C3111yescharacteristic
205C22×C4C22⋊C4×C3111yescharacteristic
206C22×C4C22⋊C4×C3111yescharacteristic
207C22×C4C22⋊C4×C3111yescharacteristic
208C22×C4C22×C4×C3111yescharacteristic
209C22×C4C2×D4×C3111yescharacteristic
210C2×C8—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—44no—
216C4⋊C4—42no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23C2×C22⋊C4×C3111yescharacteristic
231C23C31×AGL(1,ℤ/8)12yes—
232Q8—82no—
233Q8—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4C31×#9911yescharacteristic
259C2×C4C31×#9911yescharacteristic
260C8—82no—
261C22—21no—
262C22—21no—
263C22—22no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—81no—
268C22C2×C31×#9911yescharacteristic
269C22C31×#41811yescharacteristic
270C22C31×#42111yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—82no—
279C4—82no—
280C4—162no—
281C2—21no—
282C2—21no—
283C2—42no—
284C2C31×#151011yescharacteristic
285C2C31×#212311yescharacteristic
286C2C31×#212911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C31×C4⋊Q8C4semidirect
10. C31×#398C4semidirect
14. C31×#382C4semidirect
82. #11801C31direct (N × H)
142. C2×C4⋊Q8C4×C31semidirect
147. #398C4×C31semidirect
151. #382C4×C31semidirect
191. C31#11801direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26212
C31×#18202
C31×#14642
C31×#13442
#1180131