Finite Group Databasebeta

← C131×#29685 #45715569

Subgroups — C131×#29685 #45715569

Order 33536.

1176 conjugacy classes of subgroups; only the 242 normal subgroups are shown.

normal subgroups only

This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 242 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#3459×C131C211yesmaximal, characteristic
2#2486×C131C213yesmaximal, complemented
3#2030×C131C212yesmaximal, complemented
4#2022×C131C216yesmaximal, complemented
5#1799×C131C213yesmaximal, complemented
6#543×C131C2211yescharacteristic
7#539×C131—23no—
8#538×C131—23no—
9#534×C131C2213yes—
10#529×C131—23no—
11#525×C131—23no—
12C2×#123×C131C2216yes—
13C2×C4×D4×C131C2213yes—
14C22×C4⋊C4×C131C2211yescharacteristic
15C2×#99×C131C2216yes—
16#398×C131—23no—
17#397×C131—23no—
18#389×C131—23no—
19#381×C131C2216yes—
20#380×C131—23no—
21#380×C131C2213yes—
22#342×C131C2216yes—
23C2×#41×C131—21no—
24C22×D4×C131C2313yes—
25C23×C4×C131D413yes—
26C23×C4×C131C2312yes—
27C23×C4×C131C2311yescharacteristic
28#126×C131—26no—
29#125×C131—23no—
30#124×C131—23no—
31#123×C131—26no—
32#123×C131—26no—
33#123×C131—412no—
34C22⋊Q8×C131—23no—
35C22⋊Q8×C131—23no—
36C22⋊Q8×C131—23no—
37#121×C131—23no—
38#121×C131—23no—
39#121×C131—23no—
40#120×C131—26no—
41C4×Q8×C131—21no—
42C4×D4×C131—23no—
43C4×D4×C131—26no—
44C4×D4×C131—26no—
45#117×C131—23no—
46C2×C4⋊C4×C131—26no—
47C2×C4⋊C4×C131—23no—
48C2×C4⋊C4×C131—23no—
49C2×C4⋊C4×C131—23no—
50C2×C4⋊C4×C131D413yes—
51C2×C22⋊C4×C131—26no—
52C2×C22⋊C4×C131D413yes—
53C2×C22⋊C4×C131C2316yes—
54C2×C22⋊C4×C131C2313yes—
55C2×C42×C131D413yes—
56#99×C131—46no—
57#95×C131—26no—
58#95×C131—23no—
59#95×C131—26no—
60C24×C131C2×D413yes—
61C24×C131C2411yescharacteristic
62#41×C131—82no—
63C2×Q8×C131—21no—
64C2×Q8×C131—21no—
65C2×D4×C131—26no—
66C2×D4×C131—23no—
67C2×D4×C131—26no—
68C2×D4×C131—23no—
69C2×D4×C131—23no—
70C2×D4×C131—23no—
71C22×C4×C131—23no—
72C22×C4×C131—23no—
73C22×C4×C131—26no—
74C22×C4×C131—26no—
75C22×C4×C131—26no—
76C22×C4×C131—22no—
77C22×C4×C131—42no—
78C22×C4×C131—46no—
79C22×C4×C131C2×D413yes—
80C22×C4×C131C2×D413yes—
81C22×C4×C131C2×D413yes—
82C22×C4×C131C2×D413yes—
83C22×C4×C131C2×D413yes—
84C4⋊C4×C131—23no—
85C4⋊C4×C131—23no—
86C4⋊C4×C131—23no—
87C4⋊C4×C131—23no—
88C4⋊C4×C131—26no—
89C4⋊C4×C131—46no—
90C4⋊C4×C131—412no—
91C4⋊C4×C131—43no—
92C4⋊C4×C131—41no—
93C22⋊C4×C131—26no—
94C22⋊C4×C131—26no—
95C22⋊C4×C131—26no—
96C22⋊C4×C131—26no—
97C22⋊C4×C131—212no—
98C22⋊C4×C131—412no—
99C42×C131—23no—
100C42×C131—23no—
101C23×C131—23no—
102C23×C131—23no—
103C23×C131—23no—
104C23×C131—41no—
105C23×C131—41no—
106C23×C131—43no—
107C23×C131—43no—
108C23×C131C22×D413yes—
109C23×C131H(5,𝔽2)13yes—
110C23×C1312−1+411yescharacteristic
111Q8×C131—81no—
112Q8×C131—81no—
113D4×C131—46no—
114D4×C131—46no—
115D4×C131—83no—
116D4×C131—83no—
117C2×C4×C131—26no—
118C2×C4×C131—23no—
119C2×C4×C131—23no—
120C2×C4×C131—23no—
121C2×C4×C131—23no—
122C2×C4×C131—23no—
123C2×C4×C131—43no—
124C2×C4×C131—46no—
125C2×C4×C131—43no—
126C2×C4×C131—43no—
127C2×C4×C131—46no—
128C2×C4×C131—46no—
129C2×C4×C131—42no—
130C2×C4×C131—46no—
131C2×C4×C131—46no—
132C2×C4×C131—46no—
133C2×C4×C131—83no—
134C2×C4×C131#12013yes—
135C2×C4×C131#12011yescharacteristic
136C22×C131—23no—
137C22×C131—23no—
138C22×C131—43no—
139C22×C131—41no—
140C22×C131—46no—
141C22×C131—43no—
142C22×C131—43no—
143C22×C131—43no—
144C22×C131—83no—
145C22×C131C2×#12011yescharacteristic
146C22×C131#53513yes—
147C22×C131#53713yes—
148C4×C131—23no—
149C4×C131—43no—
150C4×C131—43no—
151C4×C131—43no—
152C4×C131—86no—
153C4×C131—82no—
154C4×C131#45812yes—
155C2×C131—23no—
156C2×C131—23no—
157C2×C131—83no—
158C2×C131#261511yescharacteristic
159C2×C131C2×#45811yescharacteristic
160C2×C131#302811yescharacteristic
161#29685C13111yesmaximal, characteristic, direct product factor, Sylow
162C131#2968511yescharacteristic, direct product factor, Sylow
163#3459C2×C13111yescharacteristic
164#2486C2×C13113yescomplemented
165#2030C2×C13112yescomplemented
166#2022C2×C13116yescomplemented
167#1799C2×C13113yescomplemented
168#543C22×C13111yescharacteristic
169#539—23no—
170#538—23no—
171#534C22×C13113yes—
172#529—23no—
173#525—23no—
174C2×#123C22×C13116yes—
175C2×C4×D4C22×C13113yes—
176C22×C4⋊C4C22×C13111yescharacteristic
177C2×#99C22×C13116yes—
178#398—23no—
179#397—23no—
180#389—23no—
181#381C22×C13116yes—
182#380—23no—
183#380C22×C13113yes—
184#342C22×C13116yes—
185C2×#41—21no—
186C22×D4C23×C13113yes—
187C23×C4D4×C13113yes—
188C23×C4C23×C13112yes—
189C23×C4C23×C13111yescharacteristic
190#126—26no—
191#125—23no—
192#124—23no—
193#123—26no—
194#123—26no—
195#123—412no—
196C22⋊Q8—23no—
197C22⋊Q8—23no—
198C22⋊Q8—23no—
199#121—23no—
200#121—23no—
201#121—23no—
202#120—26no—
203C4×Q8—21no—
204C4×D4—23no—
205C4×D4—26no—
206C4×D4—26no—
207#117—23no—
208C2×C4⋊C4—23no—
209C2×C4⋊C4—23no—
210C2×C4⋊C4—26no—
211C2×C4⋊C4—23no—
212C2×C4⋊C4D4×C13113yes—
213C2×C22⋊C4—26no—
214C2×C22⋊C4D4×C13113yes—
215C2×C22⋊C4C23×C13116yes—
216C2×C22⋊C4C23×C13113yes—
217C2×C42D4×C13113yes—
218#99—46no—
219#95—26no—
220#95—23no—
221#95—26no—
222C24C2×D4×C13113yes—
223C24C24×C13111yescharacteristic
224#41—82no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×D4—26no—
228C2×D4—23no—
229C2×D4—26no—
230C2×D4—23no—
231C2×D4—23no—
232C2×D4—23no—
233C22×C4—23no—
234C22×C4—23no—
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—22no—
239C22×C4—42no—
240C22×C4—46no—
241C22×C4C2×D4×C13113yes—
242C22×C4C2×D4×C13113yes—
243C22×C4C2×D4×C13113yes—
244C22×C4C2×D4×C13113yes—
245C22×C4C2×D4×C13113yes—
246C4⋊C4—23no—
247C4⋊C4—23no—
248C4⋊C4—23no—
249C4⋊C4—23no—
250C4⋊C4—26no—
251C4⋊C4—46no—
252C4⋊C4—412no—
253C4⋊C4—43no—
254C4⋊C4—41no—
255C22⋊C4—26no—
256C22⋊C4—26no—
257C22⋊C4—26no—
258C22⋊C4—26no—
259C22⋊C4—212no—
260C22⋊C4—412no—
261C42—23no—
262C42—23no—
263C23—23no—
264C23—23no—
265C23—23no—
266C23—41no—
267C23—41no—
268C23—43no—
269C23—43no—
270C23C22×D4×C13113yes—
271C23H(5,𝔽2)×C13113yes—
272C232−1+4×C13111yescharacteristic
273Q8—81no—
274Q8—81no—
275D4—46no—
276D4—46no—
277D4—83no—
278D4—83no—
279C2×C4—26no—
280C2×C4—23no—
281C2×C4—23no—
282C2×C4—23no—
283C2×C4—23no—
284C2×C4—23no—
285C2×C4—43no—
286C2×C4—46no—
287C2×C4—43no—
288C2×C4—43no—
289C2×C4—46no—
290C2×C4—46no—
291C2×C4—42no—
292C2×C4—46no—
293C2×C4—46no—
294C2×C4—46no—
295C2×C4—83no—
296C2×C4#120×C13113yes—
297C2×C4#120×C13111yescharacteristic
298C22—23no—
299C22—23no—
300C22—43no—
301C22—41no—
302C22—46no—
303C22—43no—
304C22—43no—
305C22—43no—
306C22—83no—
307C22C2×#120×C13111yescharacteristic
308C22#535×C13113yes—
309C22#537×C13113yes—
310C4—23no—
311C4—43no—
312C4—43no—
313C4—43no—
314C4—86no—
315C4—82no—
316C4#458×C13112yes—
317C2—23no—
318C2—23no—
319C2—83no—
320C2#2615×C13111yescharacteristic
321C2C2×#458×C13111yescharacteristic
322C2#3028×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC24C24×C131
prime radical#3459×C131C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2486×C131C2semidirect
3. #2030×C131C2semidirect
4. #2022×C131C2semidirect
5. #1799×C131C2semidirect
161. #29685C131direct (N × H)
162. C131#29685direct (N × H)
164. #2486C2×C131semidirect
165. #2030C2×C131semidirect
166. #2022C2×C131semidirect
167. #1799C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3459×C1312
#2486×C1312
#2030×C1312
#2022×C1312
#1799×C1312
#29685131