Finite Group Databasebeta

← C31×#8338 #21465097

Subgroups — C31×#8338 #21465097

Order 7936.

814 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 174 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
1C2×C31×#533C211yesmaximal, characteristic
2C31×#1749C212yesmaximal
3C2×C31×#330C214yesmaximal, complemented
4C31×#533—28no—
5C2×C31×C4⋊Q8C412yes—
6C2×C31×#125C2212yes—
7C2×C31×C22⋊Q8—22no—
8C2×C4×Q8×C31—22no—
9C2×C31×#117C412yes—
10C22×C42×C31C2211yescharacteristic
11C2×C31×C22⋊C8—22no—
12C2×C31×#97C2214yes—
13C31×#336—22no—
14C31×#330—28no—
15C22×Q8×C31—22no—
16C23×C4×C31C2×C411yescharacteristic
17C23×C4×C31D412yes—
18C22×C8×C31—24no—
19C31×C4⋊Q8—28no—
20C31×#125—24no—
21C31×#125D418yes—
22C31×C22⋊Q8—216no—
23C4×Q8×C31—216no—
24C31×#117—28no—
25C2×C4⋊C4×C31—22no—
26C2×C4⋊C4×C31—24no—
27C2×C4⋊C4×C31C2×C414yes—
28C2×C22⋊C4×C31—22no—
29C2×C42×C31—22no—
30C2×C42×C31—24no—
31C2×C42×C31C2×C411yescharacteristic
32C2×C42×C31D412yes—
33C2×C42×C31C2311yescharacteristic
34C31×C22⋊C8—28no—
35C31×#97—28no—
36C24×C31C22⋊C411yescharacteristic
37C2×Q8×C31—28no—
38C2×Q8×C31—44no—
39C2×Q8×C31—44no—
40C22×C4×C31—22no—
41C22×C4×C31—22no—
42C22×C4×C31—22no—
43C22×C4×C31—24no—
44C22×C4×C31—24no—
45C22×C4×C31—24no—
46C22×C4×C31—42no—
47C22×C4×C31C22⋊C411yescharacteristic
48C22×C4×C31C22⋊C412yes—
49C22×C4×C31C22×C411yescharacteristic
50C22×C4×C31C2×D412yes—
51C2×C8×C31—28no—
52C2×C8×C31—44no—
53C2×C8×C31—44no—
54C4⋊C4×C31—28no—
55C4⋊C4×C31—24no—
56C4⋊C4×C31—216no—
57C4⋊C4×C31C22⋊C418yes—
58C22⋊C4×C31—28no—
59C42×C31—28no—
60C42×C31—22no—
61C42×C31—24no—
62C42×C31C2×D414yes—
63#8338C3111yesmaximal, characteristic, direct product factor, Sylow
64C23×C31—21no—
65C23×C31—21no—
66C23×C31—22no—
67C23×C31—22no—
68C23×C31#10112yes—
69C23×C31C2×C22⋊C411yescharacteristic
70Q8×C31—416no—
71C2×C4×C31—28no—
72C2×C4×C31—21no—
73C2×C4×C31—22no—
74C2×C4×C31—21no—
75C2×C4×C31—21no—
76C2×C4×C31—21no—
77C2×C4×C31—22no—
78C2×C4×C31—22no—
79C2×C4×C31—22no—
80C2×C4×C31—28no—
81C2×C4×C31—48no—
82C2×C4×C31—44no—
83C2×C4×C31—44no—
84C2×C4×C31#10112yes—
85C2×C4×C31#10414yes—
86C2×C4×C31C2×C22⋊C412yes—
87C2×C4×C31#12014yes—
88C8×C31—48no—
89C2×#533C2×C3111yescharacteristic
90#1749C2×C3112yes—
91C2×#330C2×C3114yescomplemented
92C22×C31—22no—
93C22×C31—24no—
94C22×C31—41no—
95C22×C31—41no—
96C22×C31—42no—
97C22×C31#37911yescharacteristic
98C22×C31C2×#10111yescharacteristic
99C22×C31C2×#10111yescharacteristic
100C22×C31C2×#10412yes—
101C22×C31#42112yes—
102C4×C31—22no—
103C4×C31—22no—
104C4×C31—24no—
105C4×C31—24no—
106C4×C31—48no—
107#533—28no—
108C2×C4⋊Q8C4×C3112yes—
109C2×#125C22×C3112yes—
110C2×C22⋊Q8—22no—
111C2×C4×Q8—22no—
112C2×#117C4×C3112yes—
113C22×C42C22×C3111yescharacteristic
114C2×C22⋊C8—22no—
115C2×#97C22×C3114yes—
116#336—22no—
117#330—28no—
118C2×C31—42no—
119C2×C31#152611yescharacteristic
120C2×C31#153112yes—
121C2×C31#153711yescharacteristic
122C2×C31#178411yescharacteristic
123C2×C31#178912yes—
124C22×Q8—22no—
125C23×C4C2×C4×C3111yescharacteristic
126C23×C4D4×C3112yes—
127C22×C8—24no—
128C4⋊Q8—28no—
129#125—24no—
130#125D4×C3118yes—
131C22⋊Q8—216no—
132C4×Q8—216no—
133#117—28no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4C2×C4×C3114yes—
137C2×C22⋊C4—22no—
138C2×C42—22no—
139C2×C42—24no—
140C2×C42C2×C4×C3111yescharacteristic
141C2×C42D4×C3112yes—
142C2×C42C23×C3111yescharacteristic
143C22⋊C8—28no—
144#97—28no—
145C31#833811yescharacteristic, direct product factor, Sylow
146C24C22⋊C4×C3111yescharacteristic
147C2×Q8—28no—
148C2×Q8—44no—
149C2×Q8—44no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—24no—
154C22×C4—24no—
155C22×C4—24no—
156C22×C4—42no—
157C22×C4C22⋊C4×C3111yescharacteristic
158C22×C4C22⋊C4×C3112yes—
159C22×C4C22×C4×C3111yescharacteristic
160C22×C4C2×D4×C3112yes—
161C2×C8—28no—
162C2×C8—44no—
163C2×C8—44no—
164C4⋊C4—28no—
165C4⋊C4—24no—
166C4⋊C4—216no—
167C4⋊C4C22⋊C4×C3118yes—
168C22⋊C4—28no—
169C42—28no—
170C42—22no—
171C42—24no—
172C42C2×D4×C3114yes—
173C23—21no—
174C23—22no—
175C23—22no—
176C23—21no—
177C23C31×#10112yes—
178C23C2×C22⋊C4×C3111yescharacteristic
179Q8—416no—
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—28no—
190C2×C4—48no—
191C2×C4—44no—
192C2×C4—44no—
193C2×C4C31×#10112yes—
194C2×C4C31×#10414yes—
195C2×C4C2×C22⋊C4×C3112yes—
196C2×C4C31×#12014yes—
197C8—48no—
198C22—22no—
199C22—24no—
200C22—41no—
201C22—42no—
202C22—41no—
203C22C31×#37911yescharacteristic
204C22C2×C31×#10111yescharacteristic
205C22C2×C31×#10111yescharacteristic
206C22C2×C31×#10412yes—
207C22C31×#42112yes—
208C4—22no—
209C4—22no—
210C4—24no—
211C4—24no—
212C4—48no—
213C2—42no—
214C2C31×#152611yescharacteristic
215C2C31×#153112yes—
216C2C31×#153711yescharacteristic
217C2C31×#178411yescharacteristic
218C2C31×#178912yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#330C2semidirect
63. #8338C31direct (N × H)
91. C2×#330C2×C31semidirect
145. C31#8338direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5332
C31×#17492
C2×C31×#3302
#833831