Finite Group Databasebeta

← C31×#11782 #21468541

Subgroups — C31×#11782 #21468541

Order 7936.

414 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2546C211yesmaximal, characteristic
2C4×C31×#101C211yesmaximal, characteristic
3C31×#1467C211yesmaximal, characteristic
4C31×#1346C214yesmaximal
5C2×C31×C4⋊Q8—21no—
6C2×C31×C4⋊Q8C411yescharacteristic
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#432—21no—
9C2×C31×#101—21no—
10C4×M16×C31—21no—
11C31×#398C412yes—
12C31×#398C2212yes—
13C31×#391—21no—
14C31×#389—21no—
15C31×#389—21no—
16C4×C4⋊C4×C31C411yescharacteristic
17C31×#343C2212yes—
18C31×#324—21no—
19C31×#324C2212yes—
20C22×Q8×C31—21no—
21C22×Q8×C31D411yescharacteristic
22C2×M16×C31—22no—
23C31×C4⋊Q8—41no—
24C31×C4⋊Q8—41no—
25C31×C4⋊Q8—44no—
26C4×Q8×C31—41no—
27C4×Q8×C31—41no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31C2×C412yes—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31D411yescharacteristic
35C2×C4⋊C4×C31C2311yescharacteristic
36C2×C42×C31—21no—
37C2×C42×C31C2×C411yescharacteristic
38C2×C42×C31D411yescharacteristic
39C2×C42×C31D411yescharacteristic
40C31×C4⋊C8—41no—
41C31×#101—24no—
42C31×C22⋊C8—22no—
43C31×#97—41no—
44C31×#97—41no—
45C4×C8×C31—41no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95C2×C412yes—
49C2×Q8×C31—22no—
50C2×Q8×C31—22no—
51C2×Q8×C31—41no—
52C2×Q8×C31—42no—
53C2×Q8×C31—42no—
54C2×Q8×C31—42no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31C22⋊C411yescharacteristic
58C22×C4×C31C22⋊C411yescharacteristic
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31C22×C411yescharacteristic
62C22×C4×C31C2×D411yescharacteristic
63C22×C4×C31C2×D411yescharacteristic
64M16×C31—24no—
65M16×C31—42no—
66C2×C8×C31—42no—
67C2×C8×C31—42no—
68C4⋊C4×C31—24no—
69C4⋊C4×C31—41no—
70C4⋊C4×C31—41no—
71C4⋊C4×C31—41no—
72C4⋊C4×C31—44no—
73C4⋊C4×C31—42no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—44no—
77C42×C31—21no—
78C42×C31—21no—
79C42×C31—21no—
80C42×C31—21no—
81C42×C31—21no—
82C42×C31—21no—
83C42×C31—42no—
84#11782C3111yesmaximal, characteristic, direct product factor, Sylow
85C23×C31C2×C22⋊C411yescharacteristic
86Q8×C31—44no—
87Q8×C31—84no—
88C2×C4×C31—21no—
89C2×C4×C31—21no—
90C2×C4×C31—21no—
91C2×C4×C31—21no—
92C2×C4×C31—22no—
93C2×C4×C31—24no—
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—42no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31#9911yescharacteristic
109C2×C4×C31#9911yescharacteristic
110C2×C4×C31#10412yes—
111C2×C4×C31AGL(1,ℤ/8)12yes—
112C8×C31—44no—
113C8×C31—82no—
114#2546C2×C3111yescharacteristic
115C4×#101C2×C3111yescharacteristic
116#1467C2×C3111yescharacteristic
117#1346C2×C3114yes—
118C22×C31—21no—
119C22×C31—21no—
120C22×C31C2×#9911yescharacteristic
121C22×C31#41811yescharacteristic
122C22×C31C2×#10411yescharacteristic
123C4×C31—21no—
124C4×C31—22no—
125C4×C31—22no—
126C4×C31—44no—
127C4×C31—41no—
128C4×C31—41no—
129C4×C31—41no—
130C4×C31—41no—
131C4×C31—82no—
132C4×C31#35612yes—
133C2×C4⋊Q8—21no—
134C2×C4⋊Q8C4×C3111yescharacteristic
135C2×C4×Q8C22×C3111yescharacteristic
136#432—21no—
137C2×#101—21no—
138C4×M16—21no—
139#398C4×C3112yes—
140#398C22×C3112yes—
141#391—21no—
142#389—21no—
143#389—21no—
144C4×C4⋊C4C4×C3111yescharacteristic
145#343C22×C3112yes—
146#324—21no—
147#324C22×C3112yes—
148C2×C31—21no—
149C2×C31—21no—
150C2×C31#150711yescharacteristic
151C2×C31#212311yescharacteristic
152C2×C31C2×#35611yescharacteristic
153C22×Q8—21no—
154C22×Q8D4×C3111yescharacteristic
155C2×M16—22no—
156C4⋊Q8—41no—
157C4⋊Q8—41no—
158C4⋊Q8—44no—
159C4×Q8—41no—
160C4×Q8—41no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4C2×C4×C3112yes—
166C2×C4⋊C4C2×C4×C3111yescharacteristic
167C2×C4⋊C4D4×C3111yescharacteristic
168C2×C4⋊C4C23×C3111yescharacteristic
169C2×C42—21no—
170C2×C42C2×C4×C3111yescharacteristic
171C2×C42D4×C3111yescharacteristic
172C2×C42D4×C3111yescharacteristic
173C4⋊C8—41no—
174#101—24no—
175C22⋊C8—22no—
176#97—41no—
177#97—41no—
178C4×C8—41no—
179#95—22no—
180#95—22no—
181#95C2×C4×C3112yes—
182C31#1178211yescharacteristic, direct product factor, Sylow
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—42no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4C22⋊C4×C3111yescharacteristic
192C22×C4C22⋊C4×C3111yescharacteristic
193C22×C4C22⋊C4×C3111yescharacteristic
194C22×C4C22⋊C4×C3111yescharacteristic
195C22×C4C22×C4×C3111yescharacteristic
196C22×C4C2×D4×C3111yescharacteristic
197C22×C4C2×D4×C3111yescharacteristic
198M16—24no—
199M16—42no—
200C2×C8—42no—
201C2×C8—42no—
202C4⋊C4—24no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—44no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—44no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—42no—
218C23C2×C22⋊C4×C3111yescharacteristic
219Q8—44no—
220Q8—84no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4C31×#9911yescharacteristic
242C2×C4C31×#9911yescharacteristic
243C2×C4C31×#10412yes—
244C2×C4C31×AGL(1,ℤ/8)12yes—
245C8—44no—
246C8—82no—
247C22—21no—
248C22—21no—
249C22C2×C31×#9911yescharacteristic
250C22C31×#41811yescharacteristic
251C22C2×C31×#10411yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—44no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4C31×#35612yes—
262C2—21no—
263C2—21no—
264C2C31×#150711yescharacteristic
265C2C31×#212311yescharacteristic
266C2C2×C31×#35611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
84. #11782C31direct (N × H)
182. C31#11782direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25462
C4×C31×#1012
C31×#14672
C31×#13462
#1178231