Finite Group Databasebeta

← C31×#8914 #21465673

Subgroups — C31×#8914 #21465673

Order 7936.

468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2379C211yesmaximal, characteristic
2C31×#1959C211yesmaximal, characteristic
3C31×#1836C212yesmaximal, complemented
4C2×C31×#329C211yesmaximal, characteristic
5C31×#1295C212yesmaximal, complemented
6C2×C31×#124C2211yescharacteristic
7C2×C31×#103—21no—
8C2×C31×#102—21no—
9C2×C31×#97C2211yescharacteristic
10C2×C31×#97C2212yes—
11C31×#391—21no—
12C31×#388—22no—
13C31×#386—21no—
14C31×#385—22no—
15C31×#384C2211yescharacteristic
16C31×#382C2212yes—
17C31×#340—22no—
18C31×#340—22no—
19C31×#329C414yescomplemented
20C22×Q8×C31D411yescharacteristic
21C22×D4×C31D411yescharacteristic
22C23×C4×C31—21no—
23C22×C8×C31—21no—
24C22×C8×C31—22no—
25C31×#124—22no—
26C31×#124C2×C412yes—
27C31×#124Q812yes—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31D412yes—
32C2×C4⋊C4×C31D412yes—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—21no—
36C2×C42×C31—21no—
37C2×C42×C31C2311yescharacteristic
38C31×#103—42no—
39C31×#102—42no—
40C31×#97—22no—
41C31×#97—22no—
42C31×#97C2×C414yescomplemented
43C31×#95—22no—
44C31×#95—22no—
45C31×#95—22no—
46C24×C31—21no—
47C2×Q8×C31—21no—
48C2×Q8×C31—41no—
49C2×Q8×C31—41no—
50C2×Q8×C31C4⋊C412yes—
51C2×D4×C31—21no—
52C2×D4×C31—41no—
53C2×D4×C31—41no—
54C2×D4×C31C4⋊C412yes—
55C22×C4×C31—21no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—41no—
59C22×C4×C31—81no—
60C22×C4×C31—82no—
61C22×C4×C31C2×D411yescharacteristic
62C22×C4×C31C2×D412yes—
63C2×C8×C31—22no—
64C2×C8×C31—24no—
65C2×C8×C31—42no—
66C2×C8×C31—42no—
67C2×C8×C31—41no—
68C2×C8×C31—41no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—42no—
71C4⋊C4×C31—41no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—44no—
74C4⋊C4×C31—81no—
75C22⋊C4×C31—24no—
76C22⋊C4×C31—24no—
77C22⋊C4×C31—81no—
78C22⋊C4×C31—82no—
79C42×C31—81no—
80C42×C31C22×C411yescharacteristic
81C42×C31C2×Q811yescharacteristic
82C42×C31#4112yes—
83#8914C3111yesmaximal, characteristic, direct product factor, Sylow
84C23×C31—22no—
85C23×C31—41no—
86C23×C31—42no—
87C23×C31—42no—
88C23×C31—41no—
89C23×C31#12011yescharacteristic
90Q8×C31—42no—
91Q8×C31—81no—
92D4×C31—42no—
93D4×C31—81no—
94C2×C4×C31—21no—
95C2×C4×C31—22no—
96C2×C4×C31—22no—
97C2×C4×C31—21no—
98C2×C4×C31—22no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—42no—
102C2×C4×C31—42no—
103C2×C4×C31—42no—
104C2×C4×C31—42no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—84no—
108C2×C4×C31—81no—
109C2×C4×C31—82no—
110C2×C4×C31C2×C4⋊C411yescharacteristic
111C2×C4×C31C4×D412yes—
112C2×C4×C31C22⋊Q812yes—
113C2×C4×C31#12311yescharacteristic
114C8×C31—42no—
115C8×C31—44no—
116#2379C2×C3111yescharacteristic
117#1959C2×C3111yescharacteristic
118#1836C2×C3112yescomplemented
119C2×#329C2×C3111yescharacteristic
120#1295C2×C3112yescomplemented
121C22×C31—42no—
122C22×C31—44no—
123C22×C31—81no—
124C22×C31—81no—
125C22×C31—82no—
126C22×C31#38511yescharacteristic
127C22×C31#45311yescharacteristic
128C22×C31#45412yes—
129C22×C31#45511yescharacteristic
130C22×C31#45512yes—
131C4×C31—21no—
132C4×C31—21no—
133C4×C31—22no—
134C4×C31—22no—
135C4×C31—42no—
136C4×C31—82no—
137C4×C31—82no—
138C4×C31—161no—
139C2×#124C22×C3111yescharacteristic
140C2×#103—21no—
141C2×#102—21no—
142C2×#97C22×C3111yescharacteristic
143C2×#97C22×C3112yes—
144#391—21no—
145#388—22no—
146#386—21no—
147#385—22no—
148#384C22×C3111yescharacteristic
149#382C22×C3112yes—
150#340—22no—
151#340—22no—
152#329C4×C3114yescomplemented
153C2×C31—82no—
154C2×C31#165711yescharacteristic
155C2×C31#165911yescharacteristic
156C2×C31#166212yes—
157C2×C31#185611yescharacteristic
158C2×C31#186012yes—
159C22×Q8D4×C3111yescharacteristic
160C22×D4D4×C3111yescharacteristic
161C23×C4—21no—
162C22×C8—22no—
163C22×C8—21no—
164#124—22no—
165#124C2×C4×C3112yes—
166#124Q8×C3112yes—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4D4×C3112yes—
171C2×C4⋊C4D4×C3112yes—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—21no—
175C2×C42—21no—
176C2×C42C23×C3111yescharacteristic
177#103—42no—
178#102—42no—
179#97—22no—
180#97—22no—
181#97C2×C4×C3114yescomplemented
182#95—22no—
183#95—22no—
184#95—22no—
185C31#891411yescharacteristic, direct product factor, Sylow
186C24—21no—
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8C4⋊C4×C3112yes—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C4⋊C4×C3112yes—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—41no—
199C22×C4—81no—
200C22×C4—82no—
201C22×C4C2×D4×C3111yescharacteristic
202C22×C4C2×D4×C3112yes—
203C2×C8—22no—
204C2×C8—24no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—41no—
208C2×C8—41no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—44no—
214C4⋊C4—81no—
215C22⋊C4—24no—
216C22⋊C4—24no—
217C22⋊C4—81no—
218C22⋊C4—82no—
219C42—81no—
220C42C22×C4×C3111yescharacteristic
221C42C2×Q8×C3111yescharacteristic
222C42#41×C3112yes—
223C23—22no—
224C23—41no—
225C23—42no—
226C23—42no—
227C23—41no—
228C23C31×#12011yescharacteristic
229Q8—42no—
230Q8—81no—
231D4—42no—
232D4—81no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—84no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4C2×C4⋊C4×C3111yescharacteristic
250C2×C4C4×D4×C3112yes—
251C2×C4C31×C22⋊Q812yes—
252C2×C4C31×#12311yescharacteristic
253C8—42no—
254C8—44no—
255C22—42no—
256C22—44no—
257C22—81no—
258C22—81no—
259C22—82no—
260C22C31×#38511yescharacteristic
261C22C31×#45311yescharacteristic
262C22C31×#45412yes—
263C22C31×#45511yescharacteristic
264C22C31×#45512yes—
265C4—21no—
266C4—21no—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—82no—
271C4—82no—
272C4—161no—
273C2—82no—
274C2C31×#165711yescharacteristic
275C2C31×#165911yescharacteristic
276C2C31×#166212yes—
277C2C31×#185611yescharacteristic
278C2C31×#186012yes—
subgroupG/H
center, socleC23×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1836C2semidirect
5. C31×#1295C2semidirect
19. C31×#329C4semidirect
42. C31×#97C2×C4semidirect
83. #8914C31direct (N × H)
118. #1836C2×C31semidirect
120. #1295C2×C31semidirect
152. #329C4×C31semidirect
181. #97C2×C4×C31semidirect
185. C31#8914direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23792
C31×#19592
C31×#18362
C2×C31×#3292
C31×#12952
#891431