Finite Group Databasebeta

← C31×#7797 #21464556

Subgroups — C31×#7797 #21464556

Order 7936.

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

normal subgroups only

This group has 478 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×#2683C211yesmaximal, characteristic
2C31×#2093C211yesmaximal, characteristic
3C31×#2083C212yesmaximal, complemented
4C31×#1271C212yesmaximal, complemented
5C31×#1270C211yesmaximal, characteristic
6C2×C31×C22⋊Q8—22no—
7C2×C31×#107—22no—
8C2×C31×#107—21no—
9C2×C31×#102—21no—
10C31×#396—22no—
11C31×#395—21no—
12C31×#390C2211yescharacteristic
13C31×#389C2212yes—
14C31×#386—21no—
15C31×#384C2211yescharacteristic
16C31×#340—22no—
17C31×#336C2212yes—
18C31×#336C2211yescharacteristic
19C22×Q8×C31—21no—
20C22×D4×C31D411yescharacteristic
21C23×C4×C31—21no—
22C22×C8×C31—21no—
23C22×C8×C31—22no—
24C31×C22⋊Q8—44no—
25C31×C22⋊Q8—44no—
26C2×C4⋊C4×C31—22no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31D412yes—
31C2×C4⋊C4×C31D411yescharacteristic
32C2×C4⋊C4×C31D412yes—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31—22no—
35C2×C22⋊C4×C31—21no—
36C2×C42×C31C2311yescharacteristic
37C31×#107—42no—
38C31×#107—44no—
39C31×#102—42no—
40C31×#95—21no—
41C31×#95—22no—
42C24×C31—21no—
43C2×Q8×C31—44no—
44C2×Q8×C31—81no—
45C2×D4×C31—21no—
46C2×D4×C31—41no—
47C2×D4×C31—41no—
48C2×D4×C31Q1612yes—
49C22×C4×C31—22no—
50C22×C4×C31—22no—
51C22×C4×C31—21no—
52C22×C4×C31—44no—
53C22×C4×C31—41no—
54C22×C4×C31—81no—
55C22×C4×C31C2×D412yes—
56C22×C4×C31C2×D411yescharacteristic
57C2×C8×C31—22no—
58C2×C8×C31—24no—
59C2×C8×C31—42no—
60C2×C8×C31—41no—
61C2×C8×C31—42no—
62C2×C8×C31—41no—
63C4⋊C4×C31—22no—
64C4⋊C4×C31—44no—
65C4⋊C4×C31—41no—
66C4⋊C4×C31—42no—
67C4⋊C4×C31—41no—
68C4⋊C4×C31—41no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—42no—
71C4⋊C4×C31—42no—
72C4⋊C4×C31—42no—
73C4⋊C4×C31D814yes—
74C22⋊C4×C31—44no—
75C22⋊C4×C31—42no—
76C22⋊C4×C31—42no—
77C22⋊C4×C31—81no—
78C42×C31—41no—
79#7797C3111yesmaximal, characteristic, direct product factor, Sylow
80C23×C31—22no—
81C23×C31—42no—
82C23×C31—41no—
83C23×C31—42no—
84C23×C31—41no—
85C23×C31#12011yescharacteristic
86Q8×C31—84no—
87D4×C31—42no—
88D4×C31—81no—
89C2×C4×C31—21no—
90C2×C4×C31—22no—
91C2×C4×C31—22no—
92C2×C4×C31—21no—
93C2×C4×C31—24no—
94C2×C4×C31—42no—
95C2×C4×C31—42no—
96C2×C4×C31—42no—
97C2×C4×C31—42no—
98C2×C4×C31—41no—
99C2×C4×C31—42no—
100C2×C4×C31—42no—
101C2×C4×C31—84no—
102C2×C4×C31—82no—
103C2×C4×C31—81no—
104C2×C4×C31C2×D812yes—
105C2×C4×C31C2×Q1611yescharacteristic
106C2×C4×C31AGL(1,ℤ/8)12yes—
107C2×C4×C31#13711yescharacteristic
108C8×C31—44no—
109C8×C31—42no—
110#2683C2×C3111yescharacteristic
111#2093C2×C3111yescharacteristic
112#2083C2×C3112yescomplemented
113#1271C2×C3112yescomplemented
114#1270C2×C3111yescharacteristic
115C22×C31—42no—
116C22×C31—44no—
117C22×C31—82no—
118C22×C31—81no—
119C22×C31—81no—
120C22×C31#44712yes—
121C22×C31#45111yescharacteristic
122C22×C31#45311yescharacteristic
123C22×C31#45612yes—
124C22×C31#45811yescharacteristic
125C4×C31—22no—
126C4×C31—22no—
127C4×C31—21no—
128C4×C31—21no—
129C4×C31—44no—
130C4×C31—82no—
131C4×C31—81no—
132C4×C31—161no—
133C2×C22⋊Q8—22no—
134C2×#107—22no—
135C2×#107—21no—
136C2×#102—21no—
137#396—22no—
138#395—21no—
139#390C22×C3111yescharacteristic
140#389C22×C3112yes—
141#386—21no—
142#384C22×C3111yescharacteristic
143#340—22no—
144#336C22×C3112yes—
145#336C22×C3111yescharacteristic
146C2×C31—82no—
147C2×C31#161012yes—
148C2×C31#161411yescharacteristic
149C2×C31#161911yescharacteristic
150C2×C31#164912yes—
151C2×C31#166011yescharacteristic
152C22×Q8—21no—
153C22×D4D4×C3111yescharacteristic
154C23×C4—21no—
155C22×C8—22no—
156C22×C8—21no—
157C22⋊Q8—44no—
158C22⋊Q8—44no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4D4×C3112yes—
164C2×C4⋊C4D4×C3112yes—
165C2×C4⋊C4D4×C3111yescharacteristic
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—21no—
169C2×C42C23×C3111yescharacteristic
170#107—42no—
171#107—44no—
172#102—42no—
173#95—21no—
174#95—22no—
175C31#779711yescharacteristic, direct product factor, Sylow
176C24—21no—
177C2×Q8—44no—
178C2×Q8—81no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4Q16×C3112yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—44no—
187C22×C4—41no—
188C22×C4—81no—
189C22×C4C2×D4×C3112yes—
190C22×C4C2×D4×C3111yescharacteristic
191C2×C8—22no—
192C2×C8—24no—
193C2×C8—42no—
194C2×C8—41no—
195C2×C8—42no—
196C2×C8—41no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—44no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4D8×C3114yes—
208C22⋊C4—44no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C22⋊C4—81no—
212C42—41no—
213C23—22no—
214C23—42no—
215C23—41no—
216C23—42no—
217C23—41no—
218C23C31×#12011yescharacteristic
219Q8—84no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—82no—
236C2×C4—81no—
237C2×C4C2×D8×C3112yes—
238C2×C4C2×Q16×C3111yescharacteristic
239C2×C4C31×AGL(1,ℤ/8)12yes—
240C2×C4C31×#13711yescharacteristic
241C8—44no—
242C8—42no—
243C22—42no—
244C22—44no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22C31×#44712yes—
249C22C31×#45111yescharacteristic
250C22C31×#45311yescharacteristic
251C22C31×#45612yes—
252C22C31×#45811yescharacteristic
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—44no—
258C4—82no—
259C4—81no—
260C4—161no—
261C2—82no—
262C2C31×#161012yes—
263C2C31×#161411yescharacteristic
264C2C31×#161911yescharacteristic
265C2C31×#164912yes—
266C2C31×#166011yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
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
3. C31×#2083C2semidirect
4. C31×#1271C2semidirect
79. #7797C31direct (N × H)
112. #2083C2×C31semidirect
113. #1271C2×C31semidirect
175. C31#7797direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26832
C31×#20932
C31×#20832
C31×#12712
C31×#12702
#779731