Finite Group Databasebeta

← C31×#9421 #21466180

Subgroups — C31×#9421 #21466180

Order 7936.

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

normal subgroups only

This group has 488 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×#3152C211yesmaximal, characteristic
2C31×#2980C211yesmaximal, characteristic
3C31×#1556C212yesmaximal, complemented
4C31×#1536C211yesmaximal, characteristic
5C31×#1291C212yesmaximal, complemented
6C2×C31×#137—22no—
7C31×#532C2211yescharacteristic
8C2×C31×C4⋊Q8C2211yescharacteristic
9C31×#497—22no—
10C31×#494C412yes—
11C31×#492C412yes—
12C31×#435—24no—
13C31×#432C2212yes—
14C31×#432C2212yes—
15C31×#408—22no—
16C4×M16×C31C2211yescharacteristic
17C31×#332—24no—
18C31×#329—22no—
19C2×#41×C31D412yes—
20C22×Q8×C31—21no—
21C31×#137—44no—
22C31×#137—44no—
23C2×Q16×C31—24no—
24C2×SD16×C31—24no—
25C2×M16×C31—21no—
26C2×M16×C31—22no—
27C22×C8×C31—22no—
28C31×C4⋊Q8—22no—
29C31×C4⋊Q8—21no—
30C31×C4⋊Q8C2×C412yes—
31C31×C4⋊Q8C2×C411yescharacteristic
32C31×#127C2×C411yescharacteristic
33C31×#124D412yes—
34C31×#121—22no—
35C4×D4×C31—22no—
36C2×C4⋊C4×C31—22no—
37C2×C42×C31C2311yescharacteristic
38C31×C4⋊C8—22no—
39C31×C4⋊C8D414yes—
40C31×C22⋊C8—24no—
41C31×C22⋊C8—22no—
42C31×C22⋊C8—22no—
43C31×#97—21no—
44C31×#97—22no—
45C31×#97—22no—
46C4×C8×C31C2×C412yes—
47#41×C31—42no—
48#41×C31—42no—
49C2×Q8×C31—22no—
50C2×Q8×C31—42no—
51C2×Q8×C31—42no—
52C2×Q8×C31—41no—
53C2×Q8×C31C22⋊C412yes—
54C2×D4×C31—22no—
55C2×D4×C31—22no—
56C2×D4×C31C22⋊C412yes—
57C22×C4×C31—22no—
58C22×C4×C31—41no—
59C22×C4×C31C2×D411yescharacteristic
60C22×C4×C31#4112yes—
61Q16×C31—48no—
62SD16×C31—48no—
63M16×C31—24no—
64M16×C31—82no—
65C2×C8×C31—22no—
66C2×C8×C31—24no—
67C2×C8×C31—42no—
68C2×C8×C31—82no—
69C4⋊C4×C31—22no—
70C4⋊C4×C31—24no—
71C4⋊C4×C31—42no—
72C22⋊C4×C31—24no—
73C42×C31C22×C411yescharacteristic
74C42×C31C2×D411yescharacteristic
75C42×C31C2×D412yes—
76#9421C3111yesmaximal, characteristic, direct product factor, Sylow
77C23×C31—22no—
78C23×C31#12311yescharacteristic
79Q8×C31—42no—
80Q8×C31—44no—
81Q8×C31—82no—
82D4×C31—42no—
83D4×C31—82no—
84D4×C31—82no—
85C2×C4×C31—22no—
86C2×C4×C31—22no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—42no—
91C2×C4×C31—81no—
92C2×C4×C31—81no—
93C2×C4×C31C2×C22⋊C411yescharacteristic
94C2×C4×C31C4×D412yes—
95C2×C4×C31#12011yescharacteristic
96C2×C4×C31#12112yes—
97C8×C31—24no—
98C8×C31—44no—
99C8×C31—82no—
100#3152C2×C3111yescharacteristic
101#2980C2×C3111yescharacteristic
102#1556C2×C3112yescomplemented
103#1536C2×C3111yescharacteristic
104#1291C2×C3112yescomplemented
105C22×C31—21no—
106C22×C31—22no—
107C22×C31—42no—
108C22×C31—44no—
109C22×C31#38611yescharacteristic
110C4×C31—21no—
111C4×C31—22no—
112C4×C31—22no—
113C4×C31—42no—
114C4×C31—82no—
115C4×C31#45312yes—
116C2×#137—22no—
117#532C22×C3111yescharacteristic
118C2×C4⋊Q8C22×C3111yescharacteristic
119#497—22no—
120#494C4×C3112yes—
121#492C4×C3112yes—
122#435—24no—
123#432C22×C3112yes—
124#432C22×C3112yes—
125#408—22no—
126C4×M16C22×C3111yescharacteristic
127#332—24no—
128#329—22no—
129C2×C31—41no—
130C2×C31—82no—
131C2×C31#188711yescharacteristic
132C2×C31#190212yes—
133C2×#41D4×C3112yes—
134C22×Q8—21no—
135#137—44no—
136#137—44no—
137C2×Q16—24no—
138C2×SD16—24no—
139C2×M16—21no—
140C2×M16—22no—
141C22×C8—22no—
142C4⋊Q8—22no—
143C4⋊Q8—21no—
144C4⋊Q8C2×C4×C3112yes—
145C4⋊Q8C2×C4×C3111yescharacteristic
146#127C2×C4×C3111yescharacteristic
147#124D4×C3112yes—
148#121—22no—
149C4×D4—22no—
150C2×C4⋊C4—22no—
151C2×C42C23×C3111yescharacteristic
152C4⋊C8—22no—
153C4⋊C8D4×C3114yes—
154C22⋊C8—24no—
155C22⋊C8—22no—
156C22⋊C8—22no—
157#97—21no—
158#97—22no—
159#97—22no—
160C4×C8C2×C4×C3112yes—
161C31#942111yescharacteristic, direct product factor, Sylow
162#41—42no—
163#41—42no—
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—41no—
168C2×Q8C22⋊C4×C3112yes—
169C2×D4—22no—
170C2×D4—22no—
171C2×D4C22⋊C4×C3112yes—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4C2×D4×C3111yescharacteristic
175C22×C4#41×C3112yes—
176Q16—48no—
177SD16—48no—
178M16—24no—
179M16—82no—
180C2×C8—22no—
181C2×C8—24no—
182C2×C8—42no—
183C2×C8—82no—
184C4⋊C4—22no—
185C4⋊C4—24no—
186C4⋊C4—42no—
187C22⋊C4—24no—
188C42C22×C4×C3111yescharacteristic
189C42C2×D4×C3111yescharacteristic
190C42C2×D4×C3112yes—
191C23—22no—
192C23C31×#12311yescharacteristic
193Q8—42no—
194Q8—44no—
195Q8—82no—
196D4—42no—
197D4—82no—
198D4—82no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4C2×C22⋊C4×C3111yescharacteristic
208C2×C4C4×D4×C3112yes—
209C2×C4C31×#12011yescharacteristic
210C2×C4C31×#12112yes—
211C8—24no—
212C8—44no—
213C8—82no—
214C22—21no—
215C22—22no—
216C22—42no—
217C22—44no—
218C22C31×#38611yescharacteristic
219C4—21no—
220C4—22no—
221C4—22no—
222C4—42no—
223C4—82no—
224C4C31×#45312yes—
225C2—41no—
226C2—82no—
227C2C31×#188711yescharacteristic
228C2C31×#190212yes—
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
3. C31×#1556C2semidirect
5. C31×#1291C2semidirect
76. #9421C31direct (N × H)
102. #1556C2×C31semidirect
104. #1291C2×C31semidirect
161. C31#9421direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31522
C31×#29802
C31×#15562
C31×#15362
C31×#12912
#942131