Finite Group Databasebeta

← C31×#13592 #21470351

Subgroups — C31×#13592 #21470351

Order 7936.

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

normal subgroups only

This group has 398 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×#3152C211yesmaximal, characteristic
2C31×#2132C212yesmaximal
3C31×#1411C214yesmaximal, complemented
4C2×C31×#137—22no—
5C31×#532C2211yescharacteristic
6C2×C31×C4⋊Q8C411yescharacteristic
7C31×#497—22no—
8C31×#494C2212yes—
9C31×#492C412yes—
10C31×#413—22no—
11C4×M16×C31C411yescharacteristic
12C31×#356C2214yes—
13C31×#355—22no—
14C2×#41×C31D412yes—
15C22×Q8×C31—21no—
16C31×#137—44no—
17C31×#137—44no—
18C2×Q16×C31—24no—
19C2×SD16×C31—24no—
20C2×M16×C31—21no—
21C2×M16×C31—42no—
22C31×C4⋊Q8—21no—
23C31×C4⋊Q8—41no—
24C31×C4⋊Q8C2×C412yes—
25C31×C4⋊Q8C2311yescharacteristic
26C31×#127C2×C411yescharacteristic
27C31×#124D412yes—
28C31×#121—41no—
29C4×D4×C31—41no—
30C2×C4⋊C4×C31—41no—
31C2×C42×C31C2×C411yescharacteristic
32C31×#101—24no—
33C31×#100—42no—
34C31×#97—21no—
35C4×C8×C31C2×C412yes—
36#41×C31—42no—
37#41×C31—42no—
38C2×Q8×C31—22no—
39C2×Q8×C31—42no—
40C2×Q8×C31—42no—
41C2×Q8×C31—41no—
42C2×Q8×C31C2×D412yes—
43C2×D4×C31—22no—
44C2×D4×C31—41no—
45C2×D4×C31C22⋊C412yes—
46C22×C4×C31—21no—
47C22×C4×C31—22no—
48C22×C4×C31—41no—
49C22×C4×C31C22⋊C411yescharacteristic
50Q16×C31—48no—
51SD16×C31—48no—
52M16×C31—24no—
53M16×C31—44no—
54M16×C31—82no—
55C2×C8×C31—22no—
56C2×C8×C31—82no—
57C4⋊C4×C31—41no—
58C4⋊C4×C31—42no—
59C4⋊C4×C31—42no—
60C22⋊C4×C31—42no—
61C42×C31—21no—
62C42×C31C22⋊C411yescharacteristic
63C42×C31C22×C411yescharacteristic
64#13592C3111yesmaximal, characteristic, direct product factor, Sylow
65C23×C31—22no—
66C23×C31#9911yescharacteristic
67Q8×C31—42no—
68Q8×C31—44no—
69Q8×C31—82no—
70D4×C31—42no—
71D4×C31—82no—
72D4×C31—82no—
73C2×C4×C31—21no—
74C2×C4×C31—22no—
75C2×C4×C31—21no—
76C2×C4×C31—22no—
77C2×C4×C31—42no—
78C2×C4×C31—42no—
79C2×C4×C31—42no—
80C2×C4×C31—42no—
81C2×C4×C31—81no—
82C2×C4×C31—81no—
83C2×C4×C31#9911yescharacteristic
84C2×C4×C31C2×C22⋊C411yescharacteristic
85C8×C31—24no—
86C8×C31—84no—
87#3152C2×C3111yescharacteristic
88#2132C2×C3112yes—
89#1411C2×C3114yescomplemented
90C22×C31—21no—
91C22×C31—41no—
92C22×C31—42no—
93C22×C31—82no—
94C22×C31C2×#9911yescharacteristic
95C4×C31—22no—
96C4×C31—21no—
97C4×C31—41no—
98C4×C31—42no—
99C4×C31—82no—
100C4×C31#35312yes—
101C2×#137—22no—
102#532C22×C3111yescharacteristic
103C2×C4⋊Q8C4×C3111yescharacteristic
104#497—22no—
105#494C22×C3112yes—
106#492C4×C3112yes—
107#413—22no—
108C4×M16C4×C3111yescharacteristic
109#356C22×C3114yes—
110#355—22no—
111C2×C31—21no—
112C2×C31—41no—
113C2×C31—82no—
114C2×C31C2×#35311yescharacteristic
115C2×#41D4×C3112yes—
116C22×Q8—21no—
117#137—44no—
118#137—44no—
119C2×Q16—24no—
120C2×SD16—24no—
121C2×M16—21no—
122C2×M16—42no—
123C4⋊Q8—21no—
124C4⋊Q8—41no—
125C4⋊Q8C2×C4×C3112yes—
126C4⋊Q8C23×C3111yescharacteristic
127#127C2×C4×C3111yescharacteristic
128#124D4×C3112yes—
129#121—41no—
130C4×D4—41no—
131C2×C4⋊C4—41no—
132C2×C42C2×C4×C3111yescharacteristic
133#101—24no—
134#100—42no—
135#97—21no—
136C4×C8C2×C4×C3112yes—
137C31#1359211yescharacteristic, direct product factor, Sylow
138#41—42no—
139#41—42no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—41no—
144C2×Q8C2×D4×C3112yes—
145C2×D4—22no—
146C2×D4—41no—
147C2×D4C22⋊C4×C3112yes—
148C22×C4—21no—
149C22×C4—22no—
150C22×C4—41no—
151C22×C4C22⋊C4×C3111yescharacteristic
152Q16—48no—
153SD16—48no—
154M16—24no—
155M16—44no—
156M16—82no—
157C2×C8—22no—
158C2×C8—82no—
159C4⋊C4—41no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C22⋊C4—42no—
163C42—21no—
164C42C22⋊C4×C3111yescharacteristic
165C42C22×C4×C3111yescharacteristic
166C23—22no—
167C23C31×#9911yescharacteristic
168Q8—42no—
169Q8—44no—
170Q8—82no—
171D4—42no—
172D4—82no—
173D4—82no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—81no—
183C2×C4—81no—
184C2×C4C31×#9911yescharacteristic
185C2×C4C2×C22⋊C4×C3111yescharacteristic
186C8—24no—
187C8—84no—
188C22—21no—
189C22—41no—
190C22—42no—
191C22—82no—
192C22C2×C31×#9911yescharacteristic
193C4—22no—
194C4—21no—
195C4—41no—
196C4—42no—
197C4—82no—
198C4C31×#35312yes—
199C2—21no—
200C2—41no—
201C2—82no—
202C2C2×C31×#35311yescharacteristic
subgroupG/H
center, socleC2×C31C2×#353
commutatorC42C22×C4×C31
Frattini, cosocleC4⋊Q8C23×C31
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#532 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1411C2semidirect
64. #13592C31direct (N × H)
89. #1411C2×C31semidirect
137. C31#13592direct (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×#21322
C31×#14112
#1359231