Finite Group Databasebeta

← C31×#13301 #21470060

Subgroups — C31×#13301 #21470060

Order 7936.

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2568C211yesmaximal, characteristic
2C31×#1801C211yesmaximal, characteristic
3C4×C31×#101C211yesmaximal, characteristic
4C31×#1394C214yesmaximal
5C2×C31×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C31C2211yescharacteristic
7C31×#423—21no—
8C2×C31×#101C2212yes—
9C2×C31×#101C2212yes—
10C4×M16×C31—21no—
11C31×#400—21no—
12C31×#400—21no—
13C31×#391—21no—
14C31×#391—21no—
15C31×#391C2212yes—
16C31×#382C412yes—
17C4×C4⋊C4×C31C411yescharacteristic
18C31×#343—21no—
19C31×#343—21no—
20C22×Q8×C31—21no—
21C22×Q8×C31C2311yescharacteristic
22C2×M16×C31—22no—
23C2×M16×C31—22no—
24C31×C4⋊Q8—41no—
25C31×C4⋊Q8—41no—
26C4×Q8×C31—41no—
27C4×Q8×C31—41no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31C2×C412yes—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C4⋊C4×C31D411yescharacteristic
34C2×C42×C31C2×C411yescharacteristic
35C2×C42×C31C2×C412yes—
36C2×C42×C31D411yescharacteristic
37C2×C42×C31D411yescharacteristic
38C31×C4⋊C8—41no—
39C31×C4⋊C8—41no—
40C31×#101—22no—
41C31×#101—24no—
42C31×#101Q814yescomplemented
43C31×#97—41no—
44C4×C8×C31—41no—
45C31×#95—21no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—22no—
49C31×#95—22no—
50C2×Q8×C31—41no—
51C2×Q8×C31—41no—
52C2×Q8×C31—44no—
53C2×Q8×C31—41no—
54C2×Q8×C31—41no—
55C2×Q8×C31C2×Q812yes—
56C2×Q8×C31#4112yes—
57C22×C4×C31—22no—
58C22×C4×C31—22no—
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31C22×C411yescharacteristic
64C22×C4×C31C2×D411yescharacteristic
65C22×C4×C31C2×D411yescharacteristic
66M16×C31—24no—
67M16×C31—42no—
68M16×C31—42no—
69M16×C31—42no—
70C2×C8×C31—42no—
71C2×C8×C31—42no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—41no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—42no—
76C4⋊C4×C31—42no—
77C4⋊C4×C31—42no—
78C42×C31—21no—
79C42×C31—21no—
80C42×C31—21no—
81C42×C31—21no—
82C42×C31—21no—
83C42×C31—21no—
84C42×C31—42no—
85#13301C3111yesmaximal, characteristic, direct product factor, Sylow
86C23×C31C2×C22⋊C411yescharacteristic
87Q8×C31—42no—
88Q8×C31—42no—
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—22no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—41no—
102C2×C4×C31—41no—
103C2×C4×C31—41no—
104C2×C4×C31—42no—
105C2×C4×C31—42no—
106C2×C4×C31—44no—
107C2×C4×C31—42no—
108C2×C4×C31—42no—
109C2×C4×C31#9911yescharacteristic
110C2×C4×C31#9911yescharacteristic
111C2×C4×C31C4×Q812yes—
112C2×C4×C31C22⋊Q812yes—
113C2×C4×C31#12411yescharacteristic
114C2×C4×C31C4⋊Q811yescharacteristic
115C8×C31—44no—
116C8×C31—82no—
117#2568C2×C3111yescharacteristic
118#1801C2×C3111yescharacteristic
119C4×#101C2×C3111yescharacteristic
120#1394C2×C3114yes—
121C22×C31—21no—
122C22×C31—21no—
123C22×C31#39111yescharacteristic
124C22×C31C2×#9911yescharacteristic
125C22×C31#41011yescharacteristic
126C4×C31—21no—
127C4×C31—22no—
128C4×C31—21no—
129C4×C31—22no—
130C4×C31—21no—
131C4×C31—41no—
132C4×C31—41no—
133C4×C31—41no—
134C4×C31—82no—
135C4×C31—82no—
136C4×C31#35512yes—
137C2×C4⋊Q8C4×C3111yescharacteristic
138C2×C4×Q8C22×C3111yescharacteristic
139#423—21no—
140C2×#101C22×C3112yes—
141C2×#101C22×C3112yes—
142C4×M16—21no—
143#400—21no—
144#400—21no—
145#391—21no—
146#391—21no—
147#391C22×C3112yes—
148#382C4×C3112yes—
149C4×C4⋊C4C4×C3111yescharacteristic
150#343—21no—
151#343—21no—
152C2×C31—21no—
153C2×C31—21no—
154C2×C31#199611yescharacteristic
155C2×C31C2×#35511yescharacteristic
156C2×C31#213511yescharacteristic
157C22×Q8—21no—
158C22×Q8C23×C3111yescharacteristic
159C2×M16—22no—
160C2×M16—22no—
161C4⋊Q8—41no—
162C4⋊Q8—41no—
163C4×Q8—41no—
164C4×Q8—41no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4C2×C4×C3112yes—
168C2×C4⋊C4C2×C4×C3111yescharacteristic
169C2×C4⋊C4D4×C3111yescharacteristic
170C2×C4⋊C4D4×C3111yescharacteristic
171C2×C42C2×C4×C3111yescharacteristic
172C2×C42C2×C4×C3112yes—
173C2×C42D4×C3111yescharacteristic
174C2×C42D4×C3111yescharacteristic
175C4⋊C8—41no—
176C4⋊C8—41no—
177#101—22no—
178#101—24no—
179#101Q8×C3114yescomplemented
180#97—41no—
181C4×C8—41no—
182#95—21no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—22no—
187C31#1330111yescharacteristic, direct product factor, Sylow
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—44no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8C2×Q8×C3112yes—
194C2×Q8#41×C3112yes—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4C22⋊C4×C3111yescharacteristic
198C22×C4C22⋊C4×C3111yescharacteristic
199C22×C4C22⋊C4×C3111yescharacteristic
200C22×C4C22⋊C4×C3111yescharacteristic
201C22×C4C22×C4×C3111yescharacteristic
202C22×C4C2×D4×C3111yescharacteristic
203C22×C4C2×D4×C3111yescharacteristic
204M16—24no—
205M16—42no—
206M16—42no—
207M16—42no—
208C2×C8—42no—
209C2×C8—42no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—42no—
223C23C2×C22⋊C4×C3111yescharacteristic
224Q8—42no—
225Q8—42no—
226Q8—82no—
227Q8—82no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4C31×#9911yescharacteristic
247C2×C4C31×#9911yescharacteristic
248C2×C4C4×Q8×C3112yes—
249C2×C4C31×C22⋊Q812yes—
250C2×C4C31×#12411yescharacteristic
251C2×C4C31×C4⋊Q811yescharacteristic
252C8—44no—
253C8—82no—
254C22—21no—
255C22—21no—
256C22C31×#39111yescharacteristic
257C22C2×C31×#9911yescharacteristic
258C22C31×#41011yescharacteristic
259C4—21no—
260C4—22no—
261C4—21no—
262C4—22no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—82no—
268C4—82no—
269C4C31×#35512yes—
270C2—21no—
271C2—21no—
272C2C31×#199611yescharacteristic
273C2C2×C31×#35511yescharacteristic
274C2C31×#213511yescharacteristic
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
42. C31×#101Q8semidirect
85. #13301C31direct (N × H)
179. #101Q8×C31semidirect
187. C31#13301direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25682
C31×#18012
C4×C31×#1012
C31×#13942
#1330131