Finite Group Databasebeta

← C31×#13599 #21470358

Subgroups — C31×#13599 #21470358

Order 7936.

312 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3139C211yesmaximal, characteristic
2C2×C31×#356C212yesmaximal
3C31×#1413C214yesmaximal, complemented
4C31×#533C411yescharacteristic
5C2×C31×C4⋊Q8C2211yescharacteristic
6C31×#491C412yes—
7C31×#491C2212yes—
8C31×#487—22no—
9C31×#419—22no—
10C2×C31×#101—22no—
11C4×M16×C31C411yescharacteristic
12C31×#356—22no—
13C31×#356C2214yes—
14C22×Q8×C31D412yes—
15C2×M16×C31—21no—
16C2×M16×C31—42no—
17C31×C4⋊Q8—21no—
18C31×C4⋊Q8—41no—
19C31×C4⋊Q8C2×C411yescharacteristic
20C31×C4⋊Q8D412yes—
21C31×C4⋊Q8C2311yescharacteristic
22C31×#125C2×C412yes—
23C31×C22⋊Q8—41no—
24C4×Q8×C31—41no—
25C31×#117—21no—
26C2×C4⋊C4×C31—41no—
27C2×C42×C31C2×C411yescharacteristic
28C31×#103—24no—
29C31×#103—24no—
30C31×#101—24no—
31C31×#101—42no—
32C31×#97C2×C412yes—
33C4×C8×C31—21no—
34C2×Q8×C31—22no—
35C2×Q8×C31—41no—
36C2×Q8×C31—42no—
37C2×Q8×C31—42no—
38C2×Q8×C31C22⋊C412yes—
39C2×Q8×C31C2×D412yes—
40C22×C4×C31—21no—
41C22×C4×C31—22no—
42C22×C4×C31C22⋊C411yescharacteristic
43M16×C31—42no—
44M16×C31—44no—
45M16×C31—82no—
46C2×C8×C31—22no—
47C2×C8×C31—82no—
48C4⋊C4×C31—22no—
49C4⋊C4×C31—41no—
50C4⋊C4×C31—42no—
51C4⋊C4×C31—41no—
52C4⋊C4×C31—41no—
53C4⋊C4×C31—42no—
54C22⋊C4×C31—41no—
55C42×C31—21no—
56C42×C31—41no—
57C42×C31C22⋊C411yescharacteristic
58C42×C31C22×C411yescharacteristic
59#13599C3111yesmaximal, characteristic, direct product factor, Sylow
60C23×C31#9911yescharacteristic
61Q8×C31—42no—
62Q8×C31—42no—
63Q8×C31—82no—
64Q8×C31—82no—
65C2×C4×C31—22no—
66C2×C4×C31—21no—
67C2×C4×C31—21no—
68C2×C4×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31—42no—
71C2×C4×C31—42no—
72C2×C4×C31—42no—
73C2×C4×C31—42no—
74C2×C4×C31#9911yescharacteristic
75C2×C4×C31C2×C22⋊C411yescharacteristic
76C8×C31—42no—
77C8×C31—84no—
78#3139C2×C3111yescharacteristic
79C2×#356C2×C3112yes—
80#1413C2×C3114yescomplemented
81C22×C31—41no—
82C22×C31#35412yes—
83C22×C31C2×#9911yescharacteristic
84C4×C31—22no—
85C4×C31—21no—
86C4×C31—21no—
87C4×C31—41no—
88C4×C31—42no—
89C4×C31—42no—
90C4×C31—82no—
91#533C4×C3111yescharacteristic
92C2×C4⋊Q8C22×C3111yescharacteristic
93#491C4×C3112yes—
94#491C22×C3112yes—
95#487—22no—
96#419—22no—
97C2×#101—22no—
98C4×M16C4×C3111yescharacteristic
99#356—22no—
100#356C22×C3114yes—
101C2×C31—21no—
102C2×C31—22no—
103C2×C31C2×#35411yescharacteristic
104C22×Q8D4×C3112yes—
105C2×M16—21no—
106C2×M16—42no—
107C4⋊Q8—21no—
108C4⋊Q8—41no—
109C4⋊Q8C2×C4×C3111yescharacteristic
110C4⋊Q8D4×C3112yes—
111C4⋊Q8C23×C3111yescharacteristic
112#125C2×C4×C3112yes—
113C22⋊Q8—41no—
114C4×Q8—41no—
115#117—21no—
116C2×C4⋊C4—41no—
117C2×C42C2×C4×C3111yescharacteristic
118#103—24no—
119#103—24no—
120#101—24no—
121#101—42no—
122#97C2×C4×C3112yes—
123C4×C8—21no—
124C31#1359911yescharacteristic, direct product factor, Sylow
125C2×Q8—22no—
126C2×Q8—41no—
127C2×Q8—42no—
128C2×Q8—42no—
129C2×Q8C22⋊C4×C3112yes—
130C2×Q8C2×D4×C3112yes—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4C22⋊C4×C3111yescharacteristic
134M16—42no—
135M16—44no—
136M16—82no—
137C2×C8—22no—
138C2×C8—82no—
139C4⋊C4—22no—
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—41no—
143C4⋊C4—42no—
144C4⋊C4—41no—
145C22⋊C4—41no—
146C42—21no—
147C42—41no—
148C42C22⋊C4×C3111yescharacteristic
149C42C22×C4×C3111yescharacteristic
150C23C31×#9911yescharacteristic
151Q8—42no—
152Q8—42no—
153Q8—82no—
154Q8—82no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4C31×#9911yescharacteristic
165C2×C4C2×C22⋊C4×C3111yescharacteristic
166C8—42no—
167C8—84no—
168C22—41no—
169C22C31×#35412yes—
170C22C2×C31×#9911yescharacteristic
171C4—22no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—42no—
176C4—42no—
177C4—82no—
178C2—21no—
179C2—22no—
180C2C2×C31×#35411yescharacteristic
subgroupG/H
center, socleC2×C31C2×#354
commutatorC42C22×C4×C31
Frattini, cosocleC4⋊Q8C23×C31
prime radicalC23×C31#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C2×C31×C4⋊Q8 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1413C2semidirect
59. #13599C31direct (N × H)
80. #1413C2×C31semidirect
124. C31#13599direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31392
C2×C31×#3562
C31×#14132
#1359931