Finite Group Databasebeta

← C31×#10217 #21466976

Subgroups — C31×#10217 #21466976

Order 7936.

430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3255C211yesmaximal, characteristic
2C31×#3237C212yesmaximal
3C31×#1995C211yesmaximal, characteristic
4C31×#1506C212yesmaximal
5C31×#1307C211yesmaximal, characteristic
6C31×#533C2211yescharacteristic
7C31×#533C2212yes—
8C31×#501—22no—
9C31×#491—22no—
10C31×#485—24no—
11C31×#477—22no—
12C31×#475—22no—
13C31×#475—22no—
14C31×#470—22no—
15C31×#462—22no—
16C31×#432C2212yes—
17C31×#423C2211yescharacteristic
18C31×#376C2211yescharacteristic
19C31×#339—22no—
20C31×#328—24no—
21C2×Q16×C31—22no—
22C2×M16×C31D412yes—
23C31×C4⋊Q8D412yes—
24C31×C4⋊Q8D412yes—
25C31×C4⋊Q8D412yes—
26C31×#125—22no—
27C31×#125—21no—
28C31×C22⋊Q8—22no—
29C31×C22⋊Q8—22no—
30C31×C22⋊Q8—22no—
31C4×Q8×C31—22no—
32C4×Q8×C31—22no—
33C4×Q8×C31—22no—
34C31×#117—22no—
35C31×#117—21no—
36C2×C42×C31—21no—
37C2×C42×C31C2311yescharacteristic
38C31×#107—24no—
39C31×#106—22no—
40C31×#106—24no—
41C31×C4⋊C8—22no—
42C31×C4⋊C8—22no—
43C31×#103—24no—
44C31×#103—24no—
45C31×#103—24no—
46C31×C22⋊C8D414yes—
47C31×#97—22no—
48C31×#95—22no—
49C2×Q8×C31—22no—
50C2×Q8×C31—22no—
51C2×Q8×C31—22no—
52C22×C4×C31—41no—
53C22×C4×C31C2×D411yescharacteristic
54C22×C4×C31C2×D412yes—
55Q16×C31—82no—
56M16×C31—42no—
57C2×C8×C31—24no—
58C2×C8×C31—22no—
59C4⋊C4×C31—22no—
60C4⋊C4×C31—22no—
61C4⋊C4×C31—22no—
62C4⋊C4×C31—22no—
63C4⋊C4×C31—22no—
64C4⋊C4×C31—22no—
65C4⋊C4×C31—42no—
66C4⋊C4×C31—42no—
67C4⋊C4×C31—42no—
68C22⋊C4×C31—42no—
69C22⋊C4×C31—41no—
70C42×C31—22no—
71C42×C31—41no—
72C42×C31—41no—
73C42×C31—42no—
74C42×C31C2×D411yescharacteristic
75C42×C31C2×D412yes—
76C42×C31#4111yescharacteristic
77#10217C3111yesmaximal, characteristic, direct product factor, Sylow
78C23×C31#12711yescharacteristic
79Q8×C31—44no—
80Q8×C31—42no—
81Q8×C31—42no—
82Q8×C31—82no—
83C2×C4×C31—21no—
84C2×C4×C31—21no—
85C2×C4×C31—42no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—82no—
91C2×C4×C31#12012yes—
92C2×C4×C31#12011yescharacteristic
93C2×C4×C31#12112yes—
94C2×C4×C31#12111yescharacteristic
95C8×C31—44no—
96C8×C31—42no—
97#3255C2×C3111yescharacteristic
98#3237C2×C3112yes—
99#1995C2×C3111yescharacteristic
100#1506C2×C3112yes—
101#1307C2×C3111yescharacteristic
102C22×C31—21no—
103C22×C31—22no—
104C22×C31#39211yescharacteristic
105C4×C31—21no—
106C4×C31—22no—
107C4×C31—22no—
108C4×C31—82no—
109C4×C31—82no—
110C4×C31—82no—
111C4×C31—82no—
112C4×C31#45511yescharacteristic
113C4×C31#45611yescharacteristic
114#533C22×C3111yescharacteristic
115#533C22×C3112yes—
116#501—22no—
117#491—22no—
118#485—24no—
119#477—22no—
120#475—22no—
121#475—22no—
122#470—22no—
123#462—22no—
124#432C22×C3112yes—
125#423C22×C3111yescharacteristic
126#376C22×C3111yescharacteristic
127#339—22no—
128#328—24no—
129C2×C31—41no—
130C2×C31#200711yescharacteristic
131C2×C31#200912yes—
132C2×Q16—22no—
133C2×M16D4×C3112yes—
134C4⋊Q8D4×C3112yes—
135C4⋊Q8D4×C3112yes—
136C4⋊Q8D4×C3112yes—
137#125—22no—
138#125—21no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145#117—21no—
146#117—22no—
147C2×C42—21no—
148C2×C42C23×C3111yescharacteristic
149#107—24no—
150#106—22no—
151#106—24no—
152C4⋊C8—22no—
153C4⋊C8—22no—
154#103—24no—
155#103—24no—
156#103—24no—
157C22⋊C8D4×C3114yes—
158#97—22no—
159#95—22no—
160C31#1021711yescharacteristic, direct product factor, Sylow
161C2×Q8—22no—
162C2×Q8—22no—
163C2×Q8—22no—
164C22×C4—41no—
165C22×C4C2×D4×C3111yescharacteristic
166C22×C4C2×D4×C3112yes—
167Q16—82no—
168M16—42no—
169C2×C8—24no—
170C2×C8—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—42no—
182C42—22no—
183C42—41no—
184C42—41no—
185C42—42no—
186C42C2×D4×C3111yescharacteristic
187C42C2×D4×C3112yes—
188C42#41×C3111yescharacteristic
189C23C31×#12711yescharacteristic
190Q8—44no—
191Q8—42no—
192Q8—42no—
193Q8—82no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—82no—
202C2×C4C31×#12012yes—
203C2×C4C31×#12011yescharacteristic
204C2×C4C31×#12112yes—
205C2×C4C31×#12111yescharacteristic
206C8—44no—
207C8—42no—
208C22—21no—
209C22—22no—
210C22C31×#39211yescharacteristic
211C4—21no—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—82no—
216C4—82no—
217C4—82no—
218C4C31×#45511yescharacteristic
219C4C31×#45611yescharacteristic
220C2—41no—
221C2C31×#200711yescharacteristic
222C2C31×#200912yes—
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
77. #10217C31direct (N × H)
160. C31#10217direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32552
C31×#32372
C31×#19952
C31×#15062
C31×#13072
#1021731