Finite Group Databasebeta

← C131×#13599 #45699483

Subgroups — C131×#13599 #45699483

Order 33536.

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

normal subgroups only

This group has 312 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
1#3139×C131C211yesmaximal, characteristic
2C2×#356×C131C212yesmaximal
3#1413×C131C214yesmaximal, complemented
4#533×C131C411yescharacteristic
5C2×C4⋊Q8×C131C2211yescharacteristic
6#491×C131C412yes—
7#491×C131C2212yes—
8#487×C131—22no—
9#419×C131—22no—
10C2×#101×C131—22no—
11C4×M16×C131C411yescharacteristic
12#356×C131—22no—
13#356×C131C2214yes—
14C22×Q8×C131D412yes—
15C2×M16×C131—21no—
16C2×M16×C131—42no—
17C4⋊Q8×C131—21no—
18C4⋊Q8×C131—41no—
19C4⋊Q8×C131C2×C411yescharacteristic
20C4⋊Q8×C131D412yes—
21C4⋊Q8×C131C2311yescharacteristic
22#125×C131C2×C412yes—
23C22⋊Q8×C131—41no—
24C4×Q8×C131—41no—
25#117×C131—21no—
26C2×C4⋊C4×C131—41no—
27C2×C42×C131C2×C411yescharacteristic
28#103×C131—24no—
29#103×C131—24no—
30#101×C131—24no—
31#101×C131—42no—
32#97×C131C2×C412yes—
33C4×C8×C131—21no—
34C2×Q8×C131—22no—
35C2×Q8×C131—41no—
36C2×Q8×C131—42no—
37C2×Q8×C131—42no—
38C2×Q8×C131C22⋊C412yes—
39C2×Q8×C131C2×D412yes—
40C22×C4×C131—21no—
41C22×C4×C131—22no—
42C22×C4×C131C22⋊C411yescharacteristic
43M16×C131—42no—
44M16×C131—44no—
45M16×C131—82no—
46C2×C8×C131—22no—
47C2×C8×C131—82no—
48C4⋊C4×C131—22no—
49C4⋊C4×C131—41no—
50C4⋊C4×C131—42no—
51C4⋊C4×C131—41no—
52C4⋊C4×C131—42no—
53C4⋊C4×C131—41no—
54C22⋊C4×C131—41no—
55C42×C131—21no—
56C42×C131—41no—
57C42×C131C22⋊C411yescharacteristic
58C42×C131C22×C411yescharacteristic
59C23×C131#9911yescharacteristic
60Q8×C131—42no—
61Q8×C131—42no—
62Q8×C131—82no—
63Q8×C131—82no—
64C2×C4×C131—22no—
65C2×C4×C131—21no—
66C2×C4×C131—21no—
67C2×C4×C131—22no—
68C2×C4×C131—22no—
69C2×C4×C131—42no—
70C2×C4×C131—42no—
71C2×C4×C131—42no—
72C2×C4×C131—42no—
73C2×C4×C131#9911yescharacteristic
74C2×C4×C131C2×C22⋊C411yescharacteristic
75C8×C131—42no—
76C8×C131—84no—
77C22×C131—41no—
78C22×C131#35412yes—
79C22×C131C2×#9911yescharacteristic
80C4×C131—22no—
81C4×C131—21no—
82C4×C131—21no—
83C4×C131—41no—
84C4×C131—42no—
85C4×C131—42no—
86C4×C131—82no—
87C2×C131—21no—
88C2×C131—22no—
89C2×C131C2×#35411yescharacteristic
90#13599C13111yesmaximal, characteristic, direct product factor, Sylow
91C131#1359911yescharacteristic, direct product factor, Sylow
92#3139C2×C13111yescharacteristic
93C2×#356C2×C13112yes—
94#1413C2×C13114yescomplemented
95#533C4×C13111yescharacteristic
96C2×C4⋊Q8C22×C13111yescharacteristic
97#491C4×C13112yes—
98#491C22×C13112yes—
99#487—22no—
100#419—22no—
101C2×#101—22no—
102C4×M16C4×C13111yescharacteristic
103#356—22no—
104#356C22×C13114yes—
105C22×Q8D4×C13112yes—
106C2×M16—21no—
107C2×M16—42no—
108C4⋊Q8—21no—
109C4⋊Q8—41no—
110C4⋊Q8C2×C4×C13111yescharacteristic
111C4⋊Q8D4×C13112yes—
112C4⋊Q8C23×C13111yescharacteristic
113#125C2×C4×C13112yes—
114C22⋊Q8—41no—
115C4×Q8—41no—
116#117—21no—
117C2×C4⋊C4—41no—
118C2×C42C2×C4×C13111yescharacteristic
119#103—24no—
120#103—24no—
121#101—24no—
122#101—42no—
123#97C2×C4×C13112yes—
124C4×C8—21no—
125C2×Q8—22no—
126C2×Q8—41no—
127C2×Q8—42no—
128C2×Q8—42no—
129C2×Q8C22⋊C4×C13112yes—
130C2×Q8C2×D4×C13112yes—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4C22⋊C4×C13111yescharacteristic
134M16—42no—
135M16—44no—
136M16—82no—
137C2×C8—22no—
138C2×C8—82no—
139C4⋊C4—22no—
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—41no—
143C4⋊C4—42no—
144C4⋊C4—41no—
145C22⋊C4—41no—
146C42—21no—
147C42—41no—
148C42C22⋊C4×C13111yescharacteristic
149C42C22×C4×C13111yescharacteristic
150C23#99×C13111yescharacteristic
151Q8—42no—
152Q8—42no—
153Q8—82no—
154Q8—82no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4#99×C13111yescharacteristic
165C2×C4C2×C22⋊C4×C13111yescharacteristic
166C8—42no—
167C8—84no—
168C22—41no—
169C22#354×C13112yes—
170C22C2×#99×C13111yescharacteristic
171C4—22no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—42no—
176C4—42no—
177C4—82no—
178C2—21no—
179C2—22no—
180C2C2×#354×C13111yescharacteristic
subgroupG/H
center, socleC2×C131C2×#354
commutatorC42C22×C4×C131
Frattini, cosocleC4⋊Q8C23×C131
prime radicalC23×C131#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C23×C131 ◁ C22×C4×C131 ◁ C2×C4⋊Q8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1413×C131C2semidirect
90. #13599C131direct (N × H)
91. C131#13599direct (N × H)
94. #1413C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3139×C1312
C2×#356×C1312
#1413×C1312
#13599131