Finite Group Databasebeta

← C31×#11458 #21468217

Subgroups — C31×#11458 #21468217

Order 7936.

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2905C211yesmaximal, characteristic
2C2×C31×#349C212yesmaximal
3C31×#1328C214yesmaximal, complemented
4C22×M16×C31C411yescharacteristic
5C22×M16×C31C2211yescharacteristic
6C2×C31×#117C411yescharacteristic
7C2×C31×M32—22no—
8C31×#424—22no—
9C31×#424C412yes—
10C31×#424C2212yes—
11C31×#423—22no—
12C31×#349—22no—
13C31×#349C2214yes—
14C23×C4×C31C2×C411yescharacteristic
15C2×M16×C31—21no—
16C2×M16×C31—21no—
17C2×M16×C31—42no—
18C2×M16×C31—42no—
19C2×M16×C31C2×C411yescharacteristic
20C2×M16×C31D412yes—
21C2×M16×C31C2311yescharacteristic
22C22×C8×C31C2×C412yes—
23C22×C8×C31D412yes—
24C31×#117—21no—
25C31×#117—21no—
26C31×#117C812yes—
27C31×#117C2×C412yes—
28C2×C4⋊C4×C31—21no—
29C2×C22⋊C4×C31C812yes—
30C2×C42×C31—21no—
31C31×M32—24no—
32C31×M32—42no—
33C2×C16×C31—42no—
34C31×C4⋊C8—24no—
35C31×C4⋊C8—24no—
36C24×C31C2×C811yescharacteristic
37C22×C4×C31—22no—
38C22×C4×C31—22no—
39C22×C4×C31—22no—
40C22×C4×C31C22⋊C411yescharacteristic
41C22×C4×C31C22⋊C411yescharacteristic
42C22×C4×C31C2×C811yescharacteristic
43C22×C4×C31M1611yescharacteristic
44C22×C4×C31M1611yescharacteristic
45C22×C4×C31C22×C411yescharacteristic
46M16×C31—41no—
47M16×C31—42no—
48M16×C31—41no—
49M16×C31—42no—
50M16×C31—42no—
51C2×C8×C31—22no—
52C2×C8×C31—22no—
53C2×C8×C31—22no—
54C2×C8×C31—42no—
55C2×C8×C31C22⋊C412yes—
56C2×C8×C31C2×D412yes—
57C4⋊C4×C31—22no—
58C4⋊C4×C31—22no—
59C22⋊C4×C31—22no—
60C22⋊C4×C31C2×C814yes—
61C42×C31—22no—
62C42×C31—22no—
63C16×C31—44no—
64#11458C3111yesmaximal, characteristic, direct product factor, Sylow
65C23×C31—22no—
66C23×C31—81no—
67C23×C31C22⋊C811yescharacteristic
68C23×C31C22⋊C811yescharacteristic
69C23×C31C22×C811yescharacteristic
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—21no—
74C2×C4×C31—21no—
75C2×C4×C31—21no—
76C2×C4×C31—21no—
77C2×C4×C31—24no—
78C2×C4×C31—82no—
79C2×C4×C31C22⋊C811yescharacteristic
80C2×C4×C31C22⋊C811yescharacteristic
81C2×C4×C31#9912yes—
82C2×C4×C31#10112yes—
83C2×C4×C31C2×C22⋊C411yescharacteristic
84C2×C4×C31C2×M1611yescharacteristic
85C8×C31—22no—
86C8×C31—22no—
87C8×C31—42no—
88#2905C2×C3111yescharacteristic
89C2×#349C2×C3112yes—
90#1328C2×C3114yescomplemented
91C22×C31—21no—
92C22×C31—21no—
93C22×C31—41no—
94C22×C31—41no—
95C22×C31—41no—
96C22×C31—82no—
97C22×C31#32412yes—
98C22×C31C2×C22⋊C811yescharacteristic
99C4×C31—21no—
100C4×C31—21no—
101C4×C31—44no—
102C4×C31#32412yes—
103C4×C31C2×#9911yescharacteristic
104C4×C31C2×#10111yescharacteristic
105C22×M16C4×C3111yescharacteristic
106C22×M16C22×C3111yescharacteristic
107C2×#117C4×C3111yescharacteristic
108C2×M32—22no—
109#424—22no—
110#424C4×C3112yes—
111#424C22×C3112yes—
112#423—22no—
113#349—22no—
114#349C22×C3114yes—
115C2×C31—21no—
116C2×C31—22no—
117C2×C31—41no—
118C2×C31—41no—
119C2×C31C2×#32411yescharacteristic
120C23×C4C2×C4×C3111yescharacteristic
121C2×M16—21no—
122C2×M16—21no—
123C2×M16—42no—
124C2×M16—42no—
125C2×M16C2×C4×C3111yescharacteristic
126C2×M16D4×C3112yes—
127C2×M16C23×C3111yescharacteristic
128C22×C8C2×C4×C3112yes—
129C22×C8D4×C3112yes—
130#117—21no—
131#117—21no—
132#117C8×C3112yes—
133#117C2×C4×C3112yes—
134C2×C4⋊C4—21no—
135C2×C22⋊C4C8×C3112yes—
136C2×C42—21no—
137M32—24no—
138M32—42no—
139C2×C16—42no—
140C4⋊C8—24no—
141C4⋊C8—24no—
142C31#1145811yescharacteristic, direct product factor, Sylow
143C24C2×C8×C3111yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4C22⋊C4×C3111yescharacteristic
148C22×C4C22⋊C4×C3111yescharacteristic
149C22×C4C2×C8×C3111yescharacteristic
150C22×C4M16×C3111yescharacteristic
151C22×C4M16×C3111yescharacteristic
152C22×C4C22×C4×C3111yescharacteristic
153M16—41no—
154M16—42no—
155M16—41no—
156M16—42no—
157M16—42no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—22no—
161C2×C8—42no—
162C2×C8C22⋊C4×C3112yes—
163C2×C8C2×D4×C3112yes—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C22⋊C4—22no—
167C22⋊C4C2×C8×C3114yes—
168C42—22no—
169C42—22no—
170C16—44no—
171C23—22no—
172C23—81no—
173C23C31×C22⋊C811yescharacteristic
174C23C31×C22⋊C811yescharacteristic
175C23C22×C8×C3111yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—24no—
184C2×C4—82no—
185C2×C4C31×C22⋊C811yescharacteristic
186C2×C4C31×C22⋊C811yescharacteristic
187C2×C4C31×#9912yes—
188C2×C4C31×#10112yes—
189C2×C4C2×C22⋊C4×C3111yescharacteristic
190C2×C4C2×M16×C3111yescharacteristic
191C8—22no—
192C8—22no—
193C8—42no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—82no—
200C22C31×#32412yes—
201C22C2×C31×C22⋊C811yescharacteristic
202C4—21no—
203C4—21no—
204C4—44no—
205C4C31×#32412yes—
206C4C2×C31×#9911yescharacteristic
207C4C2×C31×#10111yescharacteristic
208C2—21no—
209C2—22no—
210C2—41no—
211C2—41no—
212C2C2×C31×#32411yescharacteristic
subgroupG/H
centerC4×C31C2×#99
commutatorC23C22×C8×C31
Frattini, cosocleC2×M16C23×C31
socleC2×C31C2×#324
prime radicalC24×C31C2×C8
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C22×C4×C31 ◁ C22×M16×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1328C2semidirect
64. #11458C31direct (N × H)
90. #1328C2×C31semidirect
142. C31#11458direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29052
C2×C31×#3492
C31×#13282
#1145831