Finite Group Databasebeta

← C31×#7829 #21464588

Subgroups — C31×#7829 #21464588

Order 7936.

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

normal subgroups only

This group has 394 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×#2100C212yesmaximal
3C31×#2095C211yesmaximal, characteristic
4C31×#1272C211yesmaximal, characteristic
5C31×#1271C212yesmaximal
6C2×C31×C4⋊Q8—21no—
7C2×C31×#107—21no—
8C2×C31×#103—21no—
9C31×#398—21no—
10C31×#395—22no—
11C31×#391C2211yescharacteristic
12C31×#389C2212yes—
13C31×#387—22no—
14C31×#384C2211yescharacteristic
15C31×#340—22no—
16C31×#340—22no—
17C31×#336C2211yescharacteristic
18C31×#336C2212yes—
19C22×Q8×C31—21no—
20C22×Q8×C31D411yescharacteristic
21C22×C8×C31—21no—
22C22×C8×C31—22no—
23C31×C4⋊Q8—42no—
24C31×C4⋊Q8—42no—
25C2×C4⋊C4×C31—22no—
26C2×C4⋊C4×C31—22no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31D412yes—
31C2×C4⋊C4×C31D412yes—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C42×C31—21no—
34C2×C42×C31C2311yescharacteristic
35C31×#107—42no—
36C31×#103—42no—
37C31×#95—22no—
38C31×#95—21no—
39C31×#95—22no—
40C31×#95—22no—
41C2×Q8×C31—21no—
42C2×Q8×C31—42no—
43C2×Q8×C31—41no—
44C2×Q8×C31—41no—
45C2×Q8×C31—81no—
46C2×Q8×C31—81no—
47C2×Q8×C31SD1612yes—
48C22×C4×C31—22no—
49C22×C4×C31—21no—
50C22×C4×C31—21no—
51C22×C4×C31—22no—
52C22×C4×C31—41no—
53C22×C4×C31C2×D411yescharacteristic
54C22×C4×C31C2×D412yes—
55C2×C8×C31—22no—
56C2×C8×C31—41no—
57C2×C8×C31—41no—
58C2×C8×C31—42no—
59C2×C8×C31—42no—
60C2×C8×C31—42no—
61C4⋊C4×C31—22no—
62C4⋊C4×C31—44no—
63C4⋊C4×C31—41no—
64C4⋊C4×C31—42no—
65C4⋊C4×C31—41no—
66C4⋊C4×C31—41no—
67C4⋊C4×C31—44no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—42no—
70C4⋊C4×C31—81no—
71C4⋊C4×C31Q1614yes—
72C42×C31—41no—
73C42×C31—42no—
74#7829C3111yesmaximal, characteristic, direct product factor, Sylow
75C23×C31#12011yescharacteristic
76Q8×C31—42no—
77Q8×C31—81no—
78Q8×C31—84no—
79C2×C4×C31—21no—
80C2×C4×C31—22no—
81C2×C4×C31—22no—
82C2×C4×C31—21no—
83C2×C4×C31—22no—
84C2×C4×C31—24no—
85C2×C4×C31—42no—
86C2×C4×C31—41no—
87C2×C4×C31—42no—
88C2×C4×C31—41no—
89C2×C4×C31—42no—
90C2×C4×C31—41no—
91C2×C4×C31—42no—
92C2×C4×C31—42no—
93C2×C4×C31—42no—
94C2×C4×C31—81no—
95C2×C4×C31—82no—
96C2×C4×C31C2×SD1611yescharacteristic
97C2×C4×C31C2×Q1612yes—
98C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C31#13712yes—
100C8×C31—42no—
101C8×C31—82no—
102#2734C2×C3111yescharacteristic
103#2100C2×C3112yes—
104#2095C2×C3111yescharacteristic
105#1272C2×C3111yescharacteristic
106#1271C2×C3112yes—
107C22×C31#45011yescharacteristic
108C22×C31#45112yes—
109C22×C31#45311yescharacteristic
110C22×C31#45412yes—
111C22×C31#45811yescharacteristic
112C4×C31—21no—
113C4×C31—21no—
114C4×C31—22no—
115C4×C31—22no—
116C4×C31—42no—
117C4×C31—44no—
118C4×C31—82no—
119C4×C31—81no—
120C4×C31—161no—
121C2×C4⋊Q8—21no—
122C2×#107—21no—
123C2×#103—21no—
124#398—21no—
125#395—22no—
126#391C22×C3111yescharacteristic
127#389C22×C3112yes—
128#387—22no—
129#384C22×C3111yescharacteristic
130#340—22no—
131#340—22no—
132#336C22×C3111yescharacteristic
133#336C22×C3112yes—
134C2×C31#161311yescharacteristic
135C2×C31#161712yes—
136C2×C31#163311yescharacteristic
137C2×C31#163712yes—
138C2×C31#165711yescharacteristic
139C22×Q8—21no—
140C22×Q8D4×C3111yescharacteristic
141C22×C8—21no—
142C22×C8—22no—
143C4⋊Q8—42no—
144C4⋊Q8—42no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4D4×C3112yes—
151C2×C4⋊C4D4×C3112yes—
152C2×C4⋊C4D4×C3111yescharacteristic
153C2×C42—21no—
154C2×C42C23×C3111yescharacteristic
155#107—42no—
156#103—42no—
157#95—21no—
158#95—22no—
159#95—22no—
160#95—22no—
161C31#782911yescharacteristic, direct product factor, Sylow
162C2×Q8—21no—
163C2×Q8—42no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—81no—
167C2×Q8—81no—
168C2×Q8SD16×C3112yes—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4C2×D4×C3111yescharacteristic
175C22×C4C2×D4×C3112yes—
176C2×C8—22no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C4⋊C4—22no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—44no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—44no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4Q16×C3114yes—
193C42—41no—
194C42—42no—
195C23C31×#12011yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—84no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4C2×SD16×C3111yescharacteristic
217C2×C4C2×Q16×C3112yes—
218C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
219C2×C4C31×#13712yes—
220C8—42no—
221C8—82no—
222C22C31×#45011yescharacteristic
223C22C31×#45112yes—
224C22C31×#45311yescharacteristic
225C22C31×#45412yes—
226C22C31×#45811yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—44no—
233C4—82no—
234C4—81no—
235C4—161no—
236C2C31×#161311yescharacteristic
237C2C31×#161712yes—
238C2C31×#163311yescharacteristic
239C2C31×#163712yes—
240C2C31×#165711yescharacteristic
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
74. #7829C31direct (N × H)
161. C31#7829direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#27342
C31×#21002
C31×#20952
C31×#12722
C31×#12712
#782931