Finite Group Databasebeta

← C31×#11813 #21468572

Subgroups — C31×#11813 #21468572

Order 7936.

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

normal subgroups only

This group has 382 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×#2628C211yesmaximal, characteristic
2C31×#1820C211yesmaximal, characteristic
3C31×#1464C211yesmaximal, characteristic
4C31×#1352C214yesmaximal
5C2×C31×C4⋊Q8C411yescharacteristic, complemented
6C2×C31×#117C2211yescharacteristic
7C31×#432—21no—
8C31×#400C412yescomplemented
9C31×#399C2212yes—
10C31×#395—21no—
11C31×#393—21no—
12C31×#389—21no—
13C31×#382C411yescharacteristic, complemented
14C31×#381—21no—
15C31×#380—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×#117—41no—
25C31×#117—41no—
26C2×C4⋊C4×C31—21no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31C2×C412yes—
30C2×C4⋊C4×C31C2×C411yescharacteristic
31C2×C4⋊C4×C31D411yescharacteristic
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31D411yescharacteristic
35C2×C22⋊C4×C31C2311yescharacteristic
36C2×C42×C31C2×C411yescharacteristic
37C2×C42×C31D411yescharacteristic
38C31×C4⋊C8—41no—
39C31×C22⋊C8—22no—
40C31×#97—41no—
41C31×#95—22no—
42C31×#95—21no—
43C31×#95—22no—
44C31×#95—41no—
45C31×#95—41no—
46C31×#95C2×C412yes—
47C24×C31C2×D411yescharacteristic
48C2×Q8×C31—42no—
49C2×Q8×C31—82no—
50C22×C4×C31—22no—
51C22×C4×C31—21no—
52C22×C4×C31—21no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—41no—
56C22×C4×C31—42no—
57C22×C4×C31C22⋊C411yescharacteristic
58C22×C4×C31C22⋊C411yescharacteristic
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22×C411yescharacteristic
62C22×C4×C31C2×D411yescharacteristic
63C2×C8×C31—42no—
64C4⋊C4×C31—41no—
65C4⋊C4×C31—41no—
66C4⋊C4×C31—42no—
67C4⋊C4×C31—42no—
68C4⋊C4×C31—41no—
69C4⋊C4×C31—41no—
70C4⋊C4×C31—82no—
71C22⋊C4×C31—41no—
72C22⋊C4×C31—41no—
73C22⋊C4×C31—42no—
74C22⋊C4×C31—42no—
75C22⋊C4×C31—82no—
76C42×C31—21no—
77C42×C31—21no—
78C42×C31—21no—
79C42×C31—21no—
80#11813C3111yesmaximal, characteristic, direct product factor, Sylow
81C23×C31—21no—
82C23×C31—21no—
83C23×C31—41no—
84C23×C31—41no—
85C23×C31C2×C22⋊C411yescharacteristic
86C23×C31#13712yes—
87Q8×C31—84no—
88C2×C4×C31—21no—
89C2×C4×C31—21no—
90C2×C4×C31—21no—
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—42no—
98C2×C4×C31—42no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—41no—
102C2×C4×C31—41no—
103C2×C4×C31—42no—
104C2×C4×C31—42no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—42no—
109C2×C4×C31—82no—
110C2×C4×C31—82no—
111C2×C4×C31—82no—
112C2×C4×C31#9911yescharacteristic
113C2×C4×C31#9911yescharacteristic
114C8×C31—82no—
115#2628C2×C3111yescharacteristic
116#1820C2×C3111yescharacteristic
117#1464C2×C3111yescharacteristic
118#1352C2×C3114yes—
119C22×C31—21no—
120C22×C31—21no—
121C22×C31—22no—
122C22×C31—42no—
123C22×C31—41no—
124C22×C31—41no—
125C22×C31—81no—
126C22×C31C2×#9911yescharacteristic
127C22×C31#41911yescharacteristic
128C22×C31#42111yescharacteristic
129C4×C31—21no—
130C4×C31—21no—
131C4×C31—41no—
132C4×C31—41no—
133C4×C31—41no—
134C4×C31—41no—
135C4×C31—41no—
136C4×C31—82no—
137C4×C31—82no—
138C4×C31—162no—
139C2×C4⋊Q8C4×C3111yescharacteristic, complemented
140C2×#117C22×C3111yescharacteristic
141#432—21no—
142#400C4×C3112yescomplemented
143#399C22×C3112yes—
144#395—21no—
145#393—21no—
146#389—21no—
147#382C4×C3111yescharacteristic, complemented
148#381—21no—
149#380—21no—
150#342—21no—
151#342C22×C3112yes—
152#324—21no—
153#323C22×C3112yes—
154C2×C31—21no—
155C2×C31—21no—
156C2×C31—42no—
157C2×C31#151111yescharacteristic
158C2×C31#212311yescharacteristic
159C2×C31#212811yescharacteristic
160C22×Q8—21no—
161C23×C4D4×C3111yescharacteristic
162C4⋊Q8—41no—
163C4⋊Q8—41no—
164#117—41no—
165#117—41no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4C2×C4×C3112yes—
170C2×C4⋊C4C2×C4×C3111yescharacteristic
171C2×C4⋊C4D4×C3111yescharacteristic
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4D4×C3111yescharacteristic
175C2×C22⋊C4C23×C3111yescharacteristic
176C2×C42C2×C4×C3111yescharacteristic
177C2×C42D4×C3111yescharacteristic
178C4⋊C8—41no—
179C22⋊C8—22no—
180#97—41no—
181#95—22no—
182#95—21no—
183#95—22no—
184#95—41no—
185#95—41no—
186#95C2×C4×C3112yes—
187C31#1181311yescharacteristic, direct product factor, Sylow
188C24C2×D4×C3111yescharacteristic
189C2×Q8—42no—
190C2×Q8—82no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4C22⋊C4×C3111yescharacteristic
199C22×C4C22⋊C4×C3111yescharacteristic
200C22×C4C22⋊C4×C3111yescharacteristic
201C22×C4C22⋊C4×C3111yescharacteristic
202C22×C4C22×C4×C3111yescharacteristic
203C22×C4C2×D4×C3111yescharacteristic
204C2×C8—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—82no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C23—21no—
222C23—21no—
223C23—41no—
224C23—41no—
225C23C2×C22⋊C4×C3111yescharacteristic
226C23C31×#13712yes—
227Q8—84no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4C31×#9911yescharacteristic
253C2×C4C31×#9911yescharacteristic
254C8—82no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—81no—
262C22C2×C31×#9911yescharacteristic
263C22C31×#41911yescharacteristic
264C22C31×#42111yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4—82no—
274C4—162no—
275C2—21no—
276C2—21no—
277C2—42no—
278C2C31×#151111yescharacteristic
279C2C31×#212311yescharacteristic
280C2C31×#212811yescharacteristic
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
8. C31×#400C4semidirect
13. C31×#382C4semidirect
80. #11813C31direct (N × H)
139. C2×C4⋊Q8C4×C31semidirect
142. #400C4×C31semidirect
147. #382C4×C31semidirect
187. C31#11813direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26282
C31×#18202
C31×#14642
C31×#13522
#1181331