Finite Group Databasebeta

← C131×#12302 #45698186

Subgroups — C131×#12302 #45698186

Order 33536.

310 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 70 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#3202×C131C211yesmaximal, characteristic
2#2239×C131C212yesmaximal, complemented
3#2098×C131C211yesmaximal, characteristic
4#1340×C131C212yesmaximal, complemented
5#1321×C131C211yesmaximal, characteristic
6#536×C131—21no—
7#485×C131—22no—
8#470×C131C2212yes—
9#467×C131—21no—
10#451×C131—22no—
11#430×C131C2211yescharacteristic
12#424×C131—21no—
13#421×C131—21no—
14#408×C131C2211yescharacteristic
15#365×C131—22no—
16#362×C131—22no—
17#349×C131C2212yes—
18H(3,ℤ/4)×C131C2211yescharacteristic
19C2×#41×C131D411yescharacteristic
20C22×Q8×C131—21no—
21C2×Q16×C131—21no—
22C2×Q16×C131D412yes—
23C2×M16×C131—21no—
24C2×M16×C131C2311yescharacteristic
25C22×C8×C131D411yescharacteristic
26C4⋊Q8×C131—41no—
27#124×C131—41no—
28#123×C131—41no—
29#123×C131—41no—
30C22⋊Q8×C131—22no—
31C22⋊Q8×C131—22no—
32#117×C131—21no—
33#117×C131—21no—
34M32×C131—22no—
35#108×C131—22no—
36#107×C131—21no—
37#106×C131D412yes—
38C4⋊C8×C131—42no—
39#104×C131—42no—
40#103×C131—22no—
41#103×C131—22no—
42C22⋊C8×C131—22no—
43#41×C131—41no—
44#41×C131—41no—
45C2×Q8×C131—22no—
46C2×Q8×C131—41no—
47C2×Q8×C131—81no—
48C2×Q8×C131—81no—
49C2×Q8×C131SD1611yescharacteristic
50C2×D4×C131—21no—
51C2×D4×C131SD1611yescharacteristic
52C22×C4×C131—21no—
53C22×C4×C131—41no—
54C22×C4×C131C2×D411yescharacteristic
55Q16×C131—42no—
56Q16×C131—81no—
57M16×C131—41no—
58M16×C131—41no—
59M16×C131—41no—
60C2×C8×C131—21no—
61C2×C8×C131—41no—
62C2×C8×C131—41no—
63C2×C8×C131C2×D412yes—
64C4⋊C4×C131—22no—
65C4⋊C4×C131—41no—
66C4⋊C4×C131—42no—
67C4⋊C4×C131—42no—
68C22⋊C4×C131—41no—
69C22⋊C4×C131—42no—
70C22⋊C4×C131—41no—
71C22⋊C4×C131—42no—
72C42×C131—22no—
73C42×C131—41no—
74C16×C131—42no—
75C23×C131—21no—
76C23×C131AGL(1,ℤ/8)11yescharacteristic
77Q8×C131—41no—
78Q8×C131—42no—
79Q8×C131—42no—
80Q8×C131—82no—
81D4×C131—41no—
82D4×C131—81no—
83C2×C4×C131—21no—
84C2×C4×C131—21no—
85C2×C4×C131—21no—
86C2×C4×C131—41no—
87C2×C4×C131—41no—
88C2×C4×C131—42no—
89C2×C4×C131—42no—
90C2×C4×C131—42no—
91C2×C4×C131—82no—
92C2×C4×C131#12011yescharacteristic
93C2×C4×C131C2×SD1611yescharacteristic
94C8×C131—22no—
95C8×C131—41no—
96C8×C131—81no—
97C22×C131—21no—
98C22×C131—41no—
99C22×C131—42no—
100C22×C131—41no—
101C22×C131#45011yescharacteristic
102C4×C131—21no—
103C4×C131—41no—
104C4×C131—82no—
105C4×C131—82no—
106C4×C131—82no—
107C4×C131#45311yescharacteristic
108C4×C131#45811yescharacteristic
109C2×C131—21no—
110C2×C131—41no—
111C2×C131—81no—
112C2×C131#161311yescharacteristic
113#12302C13111yesmaximal, characteristic, direct product factor, Sylow
114C131#1230211yescharacteristic, direct product factor, Sylow
115#3202C2×C13111yescharacteristic
116#2239C2×C13112yescomplemented
117#2098C2×C13111yescharacteristic
118#1340C2×C13112yescomplemented
119#1321C2×C13111yescharacteristic
120#536—21no—
121#485—22no—
122#470C22×C13112yes—
123#467—21no—
124#451—22no—
125#430C22×C13111yescharacteristic
126#424—21no—
127#421—21no—
128#408C22×C13111yescharacteristic
129#365—22no—
130#362—22no—
131#349C22×C13112yes—
132H(3,ℤ/4)C22×C13111yescharacteristic
133C2×#41D4×C13111yescharacteristic
134C22×Q8—21no—
135C2×Q16—21no—
136C2×Q16D4×C13112yes—
137C2×M16—21no—
138C2×M16C23×C13111yescharacteristic
139C22×C8D4×C13111yescharacteristic
140C4⋊Q8—41no—
141#124—41no—
142#123—41no—
143#123—41no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146#117—21no—
147#117—21no—
148M32—22no—
149#108—22no—
150#107—21no—
151#106D4×C13112yes—
152C4⋊C8—42no—
153#104—42no—
154#103—22no—
155#103—22no—
156C22⋊C8—22no—
157#41—41no—
158#41—41no—
159C2×Q8—22no—
160C2×Q8—41no—
161C2×Q8—81no—
162C2×Q8—81no—
163C2×Q8SD16×C13111yescharacteristic
164C2×D4—21no—
165C2×D4SD16×C13111yescharacteristic
166C22×C4—21no—
167C22×C4—41no—
168C22×C4C2×D4×C13111yescharacteristic
169Q16—42no—
170Q16—81no—
171M16—41no—
172M16—41no—
173M16—41no—
174C2×C8—21no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8C2×D4×C13112yes—
178C4⋊C4—22no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C22⋊C4—41no—
183C22⋊C4—42no—
184C22⋊C4—41no—
185C22⋊C4—42no—
186C42—22no—
187C42—41no—
188C16—42no—
189C23—21no—
190C23AGL(1,ℤ/8)×C13111yescharacteristic
191Q8—41no—
192Q8—42no—
193Q8—42no—
194Q8—82no—
195D4—41no—
196D4—81no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—82no—
206C2×C4#120×C13111yescharacteristic
207C2×C4C2×SD16×C13111yescharacteristic
208C8—22no—
209C8—41no—
210C8—81no—
211C22—21no—
212C22—41no—
213C22—42no—
214C22—41no—
215C22#450×C13111yescharacteristic
216C4—21no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4#453×C13111yescharacteristic
222C4#458×C13111yescharacteristic
223C2—21no—
224C2—41no—
225C2—81no—
226C2#1613×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1613
commutator, Frattini, cosocleC2×M16C23×C131
prime radicalC2×#41×C131D4
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C2×M16×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2239×C131C2semidirect
4. #1340×C131C2semidirect
113. #12302C131direct (N × H)
114. C131#12302direct (N × H)
116. #2239C2×C131semidirect
118. #1340C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3202×C1312
#2239×C1312
#2098×C1312
#1340×C1312
#1321×C1312
#12302131