Finite Group Databasebeta

← C31×#9442 #21466201

Subgroups — C31×#9442 #21466201

Order 7936.

456 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3142C211yesmaximal, characteristic
2C31×#2371C211yesmaximal, characteristic, complemented
3C31×#1534C211yesmaximal, characteristic, complemented
4C31×#1505C212yesmaximal
5C31×#1300C212yesmaximal, complemented
6C31×#532C2211yescharacteristic
7C2×C31×#125C2211yescharacteristic
8C31×#491C412yescomplemented
9C31×#490C412yescomplemented
10C31×#488—22no—
11C31×#432C2212yes—
12C31×#417—22no—
13C4×M16×C31C2211yescharacteristic
14C31×#387—22no—
15C31×#387—22no—
16C4×C4⋊C4×C31—22no—
17C31×#376C2212yes—
18C31×#330—22no—
19C31×#327—22no—
20C31×#327—22no—
21C2×#41×C31—21no—
22C2×M16×C31—21no—
23C31×C4⋊Q8C2×C411yescharacteristic
24C31×#127C2×C411yescharacteristic
25C31×#125—22no—
26C31×#125C2×C412yes—
27C31×#125D412yes—
28C31×#124—21no—
29C31×#121—22no—
30C4×D4×C31—22no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—22no—
33C2×C4⋊C4×C31D412yes—
34C2×C42×C31—22no—
35C2×C42×C31—22no—
36C2×C42×C31C2311yescharacteristic
37C31×C4⋊C8—22no—
38C31×#103—24no—
39C31×#102—24no—
40C31×C22⋊C8—22no—
41C31×#97—22no—
42C31×#97C2×C412yes—
43C4×C8×C31—21no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95D412yes—
48C31×#95D412yes—
49#41×C31—44no—
50C2×Q8×C31—21no—
51C2×D4×C31—21no—
52C2×D4×C31—22no—
53C2×D4×C31—41no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—41no—
58C22×C4×C31C2×D411yescharacteristic
59C22×C4×C31C2×D412yes—
60M16×C31—42no—
61C2×C8×C31—22no—
62C2×C8×C31—42no—
63C4⋊C4×C31—24no—
64C4⋊C4×C31—24no—
65C4⋊C4×C31—22no—
66C4⋊C4×C31—22no—
67C4⋊C4×C31—44no—
68C4⋊C4×C31C22⋊C414yes—
69C22⋊C4×C31—42no—
70C42×C31—44no—
71C42×C31—44no—
72C42×C31C22×C411yescharacteristic
73C42×C31C2×D411yescharacteristic
74C42×C31#4112yes—
75#9442C3111yesmaximal, characteristic, direct product factor, Sylow
76C23×C31—41no—
77C23×C31#12011yescharacteristic
78Q8×C31—42no—
79D4×C31—42no—
80D4×C31—82no—
81D4×C31—82no—
82C2×C4×C31—22no—
83C2×C4×C31—24no—
84C2×C4×C31—24no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—42no—
91C2×C4×C31—42no—
92C2×C4×C31—41no—
93C2×C4×C31—42no—
94C2×C4×C31—82no—
95C2×C4×C31C2×C22⋊C411yescharacteristic
96C2×C4×C31C4×D412yes—
97C2×C4×C31#12112yes—
98C2×C4×C31#12311yescharacteristic
99C8×C31—42no—
100C8×C31—82no—
101#3142C2×C3111yescharacteristic
102#2371C2×C3111yescharacteristic, complemented
103#1534C2×C3111yescharacteristic, complemented
104#1505C2×C3112yes—
105#1300C2×C3112yescomplemented
106C22×C31—22no—
107C22×C31—81no—
108C22×C31—82no—
109C22×C31#38611yescharacteristic
110C22×C31#45412yes—
111C4×C31—21no—
112C4×C31—21no—
113C4×C31—22no—
114C4×C31—22no—
115C4×C31—44no—
116C4×C31—44no—
117C4×C31—82no—
118C4×C31—81no—
119#532C22×C3111yescharacteristic
120C2×#125C22×C3111yescharacteristic
121#491C4×C3112yescomplemented
122#490C4×C3112yescomplemented
123#488—22no—
124#432C22×C3112yes—
125#417—22no—
126C4×M16C22×C3111yescharacteristic
127#387—22no—
128#387—22no—
129C4×C4⋊C4—22no—
130#376C22×C3112yes—
131#330—22no—
132#327—22no—
133#327—22no—
134C2×C31—22no—
135C2×C31—161no—
136C2×C31#188811yescharacteristic
137C2×C31#190612yes—
138C2×#41—21no—
139C2×M16—21no—
140C4⋊Q8C2×C4×C3111yescharacteristic
141#127C2×C4×C3111yescharacteristic
142#125—22no—
143#125C2×C4×C3112yes—
144#125D4×C3112yes—
145#124—21no—
146#121—22no—
147C4×D4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4D4×C3112yes—
151C2×C42—22no—
152C2×C42—22no—
153C2×C42C23×C3111yescharacteristic
154C4⋊C8—22no—
155#103—24no—
156#102—24no—
157C22⋊C8—22no—
158#97—22no—
159#97C2×C4×C3112yes—
160C4×C8—21no—
161#95—22no—
162#95—22no—
163#95—22no—
164#95D4×C3112yes—
165#95D4×C3112yes—
166C31#944211yescharacteristic, direct product factor, Sylow
167#41—44no—
168C2×Q8—21no—
169C2×D4—21no—
170C2×D4—22no—
171C2×D4—41no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—41no—
176C22×C4C2×D4×C3111yescharacteristic
177C22×C4C2×D4×C3112yes—
178M16—42no—
179C2×C8—22no—
180C2×C8—42no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—44no—
186C4⋊C4C22⋊C4×C3114yes—
187C22⋊C4—42no—
188C42—44no—
189C42—44no—
190C42C22×C4×C3111yescharacteristic
191C42C2×D4×C3111yescharacteristic
192C42#41×C3112yes—
193C23—41no—
194C23C31×#12011yescharacteristic
195Q8—42no—
196D4—42no—
197D4—82no—
198D4—82no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—24no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—82no—
212C2×C4C2×C22⋊C4×C3111yescharacteristic
213C2×C4C4×D4×C3112yes—
214C2×C4C31×#12112yes—
215C2×C4C31×#12311yescharacteristic
216C8—42no—
217C8—82no—
218C22—22no—
219C22—81no—
220C22—82no—
221C22C31×#38611yescharacteristic
222C22C31×#45412yes—
223C4—21no—
224C4—21no—
225C4—22no—
226C4—22no—
227C4—44no—
228C4—44no—
229C4—82no—
230C4—81no—
231C2—22no—
232C2—161no—
233C2C31×#188811yescharacteristic
234C2C31×#190612yes—
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2371C2semidirect
3. C31×#1534C2semidirect
5. C31×#1300C2semidirect
8. C31×#491C4semidirect
9. C31×#490C4semidirect
75. #9442C31direct (N × H)
102. #2371C2×C31semidirect
103. #1534C2×C31semidirect
105. #1300C2×C31semidirect
121. #491C4×C31semidirect
122. #490C4×C31semidirect
166. C31#9442direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31422
C31×#23712
C31×#15342
C31×#15052
C31×#13002
#944231