Finite Group Databasebeta

← C31×#7757 #21464516

Subgroups — C31×#7757 #21464516

Order 7936.

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

normal subgroups only

This group has 468 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×#2734C211yesmaximal, characteristic
2C31×#2057C212yesmaximal
3C31×#2016C211yesmaximal, characteristic
4C31×#1272C211yesmaximal, characteristic
5C31×#1271C212yesmaximal
6C22×Q16×C31—21no—
7C2×C31×C4⋊Q8—21no—
8C2×C31×C4⋊Q8C2211yescharacteristic
9C2×C31×#107—22no—
10C2×C31×#103—21no—
11C31×#398—21no—
12C31×#395—22no—
13C31×#391C2211yescharacteristic
14C31×#389C2212yes—
15C31×#387—22no—
16C31×#340—22no—
17C31×#336C2212yes—
18C31×#336C2211yescharacteristic
19C22×Q8×C31—21no—
20C22×Q8×C31—21no—
21C22×Q8×C31D411yescharacteristic
22C2×Q16×C31—42no—
23C2×Q16×C31—42no—
24C2×Q16×C31—42no—
25C22×C8×C31—21no—
26C22×C8×C31—22no—
27C31×C4⋊Q8—42no—
28C31×C4⋊Q8—42no—
29C31×C4⋊Q8—42no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—22no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31D412yes—
35C2×C4⋊C4×C31D412yes—
36C2×C4⋊C4×C31D411yescharacteristic
37C2×C42×C31—21no—
38C2×C42×C31C2311yescharacteristic
39C31×#107—44no—
40C31×#103—42no—
41C31×#95—22no—
42C31×#95—21no—
43C31×#95—22no—
44C31×#95—22no—
45C2×Q8×C31—21no—
46C2×Q8×C31—22no—
47C2×Q8×C31—41no—
48C2×Q8×C31—42no—
49C2×Q8×C31—41no—
50C2×Q8×C31—41no—
51C2×Q8×C31—41no—
52C2×Q8×C31—41no—
53C2×Q8×C31—41no—
54C2×Q8×C31—41no—
55C2×Q8×C31—81no—
56C2×Q8×C31—81no—
57C2×Q8×C31D812yes—
58C22×C4×C31—22no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—22no—
62C22×C4×C31—41no—
63C22×C4×C31C2×D411yescharacteristic
64C22×C4×C31C2×D412yes—
65Q16×C31—48no—
66C2×C8×C31—22no—
67C2×C8×C31—24no—
68C2×C8×C31—42no—
69C2×C8×C31—41no—
70C2×C8×C31—41no—
71C2×C8×C31—42no—
72C4⋊C4×C31—22no—
73C4⋊C4×C31—24no—
74C4⋊C4×C31—42no—
75C4⋊C4×C31—44no—
76C4⋊C4×C31—41no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—42no—
80C4⋊C4×C31—81no—
81C4⋊C4×C31Q1614yescomplemented
82C42×C31—41no—
83C42×C31—42no—
84#7757C3111yesmaximal, characteristic, direct product factor, Sylow
85C23×C31#12011yescharacteristic
86Q8×C31—42no—
87Q8×C31—42no—
88Q8×C31—42no—
89Q8×C31—81no—
90Q8×C31—81no—
91Q8×C31—81no—
92Q8×C31—84no—
93C2×C4×C31—21no—
94C2×C4×C31—22no—
95C2×C4×C31—22no—
96C2×C4×C31—21no—
97C2×C4×C31—22no—
98C2×C4×C31—24no—
99C2×C4×C31—42no—
100C2×C4×C31—41no—
101C2×C4×C31—42no—
102C2×C4×C31—41no—
103C2×C4×C31—42no—
104C2×C4×C31—41no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—42no—
109C2×C4×C31—81no—
110C2×C4×C31—81no—
111C2×C4×C31C2×D811yescharacteristic
112C2×C4×C31C2×Q1612yes—
113C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C31#13712yes—
115C8×C31—44no—
116C8×C31—42no—
117#2734C2×C3111yescharacteristic
118#2057C2×C3112yes—
119#2016C2×C3111yescharacteristic
120#1272C2×C3111yescharacteristic
121#1271C2×C3112yes—
122C22×C31#44711yescharacteristic
123C22×C31#45112yes—
124C22×C31#45311yescharacteristic
125C22×C31#45612yes—
126C22×C31B(4,𝔽2)11yescharacteristic
127C4×C31—21no—
128C4×C31—21no—
129C4×C31—22no—
130C4×C31—22no—
131C4×C31—42no—
132C4×C31—44no—
133C4×C31—82no—
134C4×C31—82no—
135C4×C31—81no—
136C22×Q16—21no—
137C2×C4⋊Q8—21no—
138C2×C4⋊Q8C22×C3111yescharacteristic
139C2×#107—22no—
140C2×#103—21no—
141#398—21no—
142#395—22no—
143#391C22×C3111yescharacteristic
144#389C22×C3112yes—
145#387—22no—
146#340—22no—
147#336C22×C3112yes—
148#336C22×C3111yescharacteristic
149C2×C31#159511yescharacteristic
150C2×C31#160512yes—
151C2×C31#163311yescharacteristic
152C2×C31#164912yes—
153C2×C31#166011yescharacteristic
154C22×Q8—21no—
155C22×Q8—21no—
156C22×Q8D4×C3111yescharacteristic
157C2×Q16—42no—
158C2×Q16—42no—
159C2×Q16—42no—
160C22×C8—21no—
161C22×C8—22no—
162C4⋊Q8—42no—
163C4⋊Q8—42no—
164C4⋊Q8—42no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4D4×C3112yes—
170C2×C4⋊C4D4×C3112yes—
171C2×C4⋊C4D4×C3111yescharacteristic
172C2×C42—21no—
173C2×C42C23×C3111yescharacteristic
174#107—44no—
175#103—42no—
176#95—21no—
177#95—22no—
178#95—22no—
179#95—22no—
180C31#775711yescharacteristic, direct product factor, Sylow
181C2×Q8—21no—
182C2×Q8—22no—
183C2×Q8—41no—
184C2×Q8—42no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—81no—
192C2×Q8—81no—
193C2×Q8D8×C3112yes—
194C22×C4—22no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—41no—
199C22×C4C2×D4×C3111yescharacteristic
200C22×C4C2×D4×C3112yes—
201Q16—48no—
202C2×C8—22no—
203C2×C8—24no—
204C2×C8—42no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—42no—
208C4⋊C4—22no—
209C4⋊C4—24no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—44no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—81no—
217C4⋊C4Q16×C3114yescomplemented
218C42—41no—
219C42—42no—
220C23C31×#12011yescharacteristic
221Q8—42no—
222Q8—42no—
223Q8—42no—
224Q8—81no—
225Q8—81no—
226Q8—81no—
227Q8—84no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C2×D8×C3111yescharacteristic
247C2×C4C2×Q16×C3112yes—
248C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
249C2×C4C31×#13712yes—
250C8—44no—
251C8—42no—
252C22C31×#44711yescharacteristic
253C22C31×#45112yes—
254C22C31×#45311yescharacteristic
255C22C31×#45612yes—
256C22C31×B(4,𝔽2)11yescharacteristic
257C4—21no—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—44no—
263C4—82no—
264C4—82no—
265C4—81no—
266C2C31×#159511yescharacteristic
267C2C31×#160512yes—
268C2C31×#163311yescharacteristic
269C2C31×#164912yes—
270C2C31×#166011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
81. C4⋊C4×C31Q16semidirect
84. #7757C31direct (N × H)
180. C31#7757direct (N × H)
217. C4⋊C4Q16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#27342
C31×#20572
C31×#20162
C31×#12722
C31×#12712
#775731