Finite Group Databasebeta

← C131×#8864 #45694748

Subgroups — C131×#8864 #45694748

Order 33536.

418 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 126 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#2973×C131C211yesmaximal, characteristic
2#1955×C131C211yesmaximal, characteristic
3#1573×C131C212yesmaximal, complemented
4#1460×C131C211yesmaximal, characteristic
5#1302×C131C212yesmaximal, complemented
6C2×C4×D4×C131C2211yescharacteristic
7#435×C131—22no—
8#435×C131—22no—
9#432×C131C2212yes—
10#431×C131C2212yes—
11C2×C4⋊C8×C131C2211yescharacteristic
12#407×C131—21no—
13C2×C22⋊C8×C131—21no—
14C2×C22⋊C8×C131—21no—
15C2×C22⋊C8×C131—21no—
16C2×#97×C131C2211yescharacteristic
17#335×C131—22no—
18#334×C131—22no—
19#323×C131C412yes—
20#323×C131C412yes—
21C22×D4×C131Q811yescharacteristic
22C23×C4×C131D411yescharacteristic
23C23×C4×C131D411yescharacteristic
24C2×M16×C131—21no—
25C2×M16×C131—21no—
26C22×C8×C131—21no—
27C22×C8×C131—21no—
28C22×C8×C131—21no—
29C22×C8×C131—21no—
30C4×D4×C131—22no—
31C4×D4×C131—22no—
32C2×C4⋊C4×C131Q811yescharacteristic
33C2×C22⋊C4×C131C2×C411yescharacteristic
34C2×C22⋊C4×C131C2×C411yescharacteristic
35C2×C42×C131C2311yescharacteristic
36C4⋊C8×C131—22no—
37C4⋊C8×C131—22no—
38C4⋊C8×C131D412yes—
39C4⋊C8×C131D412yes—
40C22⋊C8×C131—22no—
41C22⋊C8×C131—22no—
42C22⋊C8×C131—22no—
43C22⋊C8×C131—42no—
44C22⋊C8×C131—42no—
45C22⋊C8×C131C2×C414yes—
46#97×C131—22no—
47#97×C131—22no—
48C4×C8×C131—22no—
49C24×C131C4⋊C411yescharacteristic
50C24×C131C4⋊C411yescharacteristic
51C2×D4×C131—22no—
52C2×D4×C131—22no—
53C2×D4×C131—41no—
54C22×C4×C131—21no—
55C22×C4×C131—21no—
56C22×C4×C131—21no—
57C22×C4×C131—21no—
58C22×C4×C131—41no—
59C22×C4×C131—41no—
60C22×C4×C131—41no—
61C22×C4×C131—41no—
62C22×C4×C131C4⋊C411yescharacteristic
63C22×C4×C131C4⋊C411yescharacteristic
64C22×C4×C131C22×C411yescharacteristic
65C22×C4×C131C2×D411yescharacteristic
66C22×C4×C131C2×Q811yescharacteristic
67M16×C131—81no—
68M16×C131—81no—
69C2×C8×C131—22no—
70C2×C8×C131—24no—
71C2×C8×C131—22no—
72C2×C8×C131—22no—
73C2×C8×C131—41no—
74C2×C8×C131—41no—
75C2×C8×C131—41no—
76C2×C8×C131—41no—
77C2×C8×C131—41no—
78C2×C8×C131—81no—
79C2×C8×C131—81no—
80C4⋊C4×C131—22no—
81C22⋊C4×C131—22no—
82C22⋊C4×C131—22no—
83C42×C131C2×D412yes—
84C42×C131#4112yes—
85C23×C131—21no—
86C23×C131—21no—
87C23×C131—21no—
88C23×C131—21no—
89C23×C131—21no—
90C23×C131—41no—
91C23×C131—41no—
92C23×C131—41no—
93C23×C131—41no—
94C23×C131#10812yes—
95C23×C131C2×C4⋊C411yescharacteristic
96D4×C131—44no—
97C2×C4×C131—21no—
98C2×C4×C131—21no—
99C2×C4×C131—21no—
100C2×C4×C131—21no—
101C2×C4×C131—21no—
102C2×C4×C131—21no—
103C2×C4×C131—41no—
104C2×C4×C131—41no—
105C2×C4×C131—41no—
106C2×C4×C131—41no—
107C2×C4×C131—41no—
108C2×C4×C131—41no—
109C2×C4×C131—41no—
110C2×C4×C131—81no—
111C2×C4×C131—81no—
112C2×C4×C131C4×D412yes—
113C2×C4×C131#12011yescharacteristic
114C2×C4×C131C22⋊Q812yes—
115C2×C4×C131#12311yescharacteristic
116C8×C131—44no—
117C8×C131—42no—
118C8×C131—42no—
119C8×C131—42no—
120C8×C131—81no—
121C22×C131—21no—
122C22×C131—21no—
123C22×C131—22no—
124C22×C131—42no—
125C22×C131—42no—
126C22×C131—41no—
127C22×C131—41no—
128C22×C131—41no—
129C22×C131—41no—
130C22×C131—41no—
131C22×C131—81no—
132C22×C131—81no—
133C22×C131#38511yescharacteristic
134C22×C131C2×#10811yescharacteristic
135C22×C131#43011yescharacteristic
136C4×C131—22no—
137C4×C131—21no—
138C4×C131—22no—
139C4×C131—41no—
140C4×C131—41no—
141C4×C131#45311yescharacteristic
142C4×C131#45511yescharacteristic
143C2×C131—21no—
144C2×C131—21no—
145C2×C131—42no—
146C2×C131—81no—
147C2×C131#185511yescharacteristic
148C2×C131#185611yescharacteristic
149C2×C131#186811yescharacteristic
150#8864C13111yesmaximal, characteristic, direct product factor, Sylow
151C131#886411yescharacteristic, direct product factor, Sylow
152#2973C2×C13111yescharacteristic
153#1955C2×C13111yescharacteristic
154#1573C2×C13112yescomplemented
155#1460C2×C13111yescharacteristic
156#1302C2×C13112yescomplemented
157C2×C4×D4C22×C13111yescharacteristic
158#435—22no—
159#435—22no—
160#432C22×C13112yes—
161#431C22×C13112yes—
162C2×C4⋊C8C22×C13111yescharacteristic
163#407—21no—
164C2×C22⋊C8—21no—
165C2×C22⋊C8—21no—
166C2×C22⋊C8—21no—
167C2×#97C22×C13111yescharacteristic
168#335—22no—
169#334—22no—
170#323C4×C13112yes—
171#323C4×C13112yes—
172C22×D4Q8×C13111yescharacteristic
173C23×C4D4×C13111yescharacteristic
174C23×C4D4×C13111yescharacteristic
175C2×M16—21no—
176C2×M16—21no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8—21no—
180C22×C8—21no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4Q8×C13111yescharacteristic
184C2×C22⋊C4C2×C4×C13111yescharacteristic
185C2×C22⋊C4C2×C4×C13111yescharacteristic
186C2×C42C23×C13111yescharacteristic
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8D4×C13112yes—
190C4⋊C8D4×C13112yes—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—42no—
195C22⋊C8—42no—
196C22⋊C8C2×C4×C13114yes—
197#97—22no—
198#97—22no—
199C4×C8—22no—
200C24C4⋊C4×C13111yescharacteristic
201C24C4⋊C4×C13111yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4C4⋊C4×C13111yescharacteristic
214C22×C4C4⋊C4×C13111yescharacteristic
215C22×C4C22×C4×C13111yescharacteristic
216C22×C4C2×D4×C13111yescharacteristic
217C22×C4C2×Q8×C13111yescharacteristic
218M16—81no—
219M16—81no—
220C2×C8—22no—
221C2×C8—24no—
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—81no—
230C2×C8—81no—
231C4⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C42C2×D4×C13112yes—
235C42#41×C13112yes—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23#108×C13112yes—
246C23C2×C4⋊C4×C13111yescharacteristic
247D4—44no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4C4×D4×C13112yes—
264C2×C4#120×C13111yescharacteristic
265C2×C4C22⋊Q8×C13112yes—
266C2×C4#123×C13111yescharacteristic
267C8—42no—
268C8—44no—
269C8—42no—
270C8—42no—
271C8—81no—
272C22—21no—
273C22—21no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22—81no—
284C22#385×C13111yescharacteristic
285C22C2×#108×C13111yescharacteristic
286C22#430×C13111yescharacteristic
287C4—22no—
288C4—21no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4#453×C13111yescharacteristic
293C4#455×C13111yescharacteristic
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2#1855×C13111yescharacteristic
299C2#1856×C13111yescharacteristic
300C2#1868×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#120
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
socleC22×C131#385
prime radicalC22×D4×C131Q8
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1573×C131C2semidirect
5. #1302×C131C2semidirect
150. #8864C131direct (N × H)
151. C131#8864direct (N × H)
154. #1573C2×C131semidirect
156. #1302C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2973×C1312
#1955×C1312
#1573×C1312
#1460×C1312
#1302×C1312
#8864131