Finite Group Databasebeta

← C131×#7792 #45693676

Subgroups — C131×#7792 #45693676

Order 33536.

374 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 102 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#2726×C131C211yesmaximal, characteristic
2#2099×C131C211yesmaximal, characteristic
3#2083×C131C211yesmaximal, characteristic
4#2083×C131C211yesmaximal, characteristic
5#1271×C131C211yesmaximal, characteristic
6#1271×C131C211yesmaximal, characteristic
7#1271×C131C211yesmaximal, characteristic
8C2×#125×C131—21no—
9C2×#107×C131—21no—
10C2×#107×C131—21no—
11#398×C131—21no—
12#398×C131—21no—
13#398×C131—21no—
14#389×C131—21no—
15#389×C131C2211yescharacteristic
16#389×C131C2211yescharacteristic
17#389×C131C2211yescharacteristic
18#387×C131—21no—
19#384×C131C2211yescharacteristic
20#340×C131—21no—
21#340×C131—21no—
22#340×C131—21no—
23#340×C131—21no—
24#336×C131C2211yescharacteristic
25#336×C131C2211yescharacteristic
26#336×C131C2211yescharacteristic
27C22×C8×C131—21no—
28C22×C8×C131—21no—
29C22×C8×C131—21no—
30#125×C131—42no—
31#125×C131—42no—
32C2×C4⋊C4×C131—21no—
33C2×C4⋊C4×C131—21no—
34C2×C4⋊C4×C131—21no—
35C2×C4⋊C4×C131—21no—
36C2×C4⋊C4×C131—21no—
37C2×C4⋊C4×C131—21no—
38C2×C4⋊C4×C131—21no—
39C2×C4⋊C4×C131—21no—
40C2×C4⋊C4×C131—21no—
41C2×C4⋊C4×C131—21no—
42C2×C4⋊C4×C131D411yescharacteristic
43C2×C4⋊C4×C131D411yescharacteristic
44C2×C4⋊C4×C131D411yescharacteristic
45C2×C4⋊C4×C131D411yescharacteristic
46C2×C4⋊C4×C131D411yescharacteristic
47C2×C4⋊C4×C131D411yescharacteristic
48C2×C42×C131—21no—
49C2×C42×C131C2311yescharacteristic
50#107×C131—42no—
51#107×C131—42no—
52#95×C131—21no—
53#95×C131—21no—
54#95×C131—21no—
55#95×C131—21no—
56#95×C131—21no—
57#95×C131—21no—
58C22×C4×C131—21no—
59C22×C4×C131—21no—
60C22×C4×C131—21no—
61C22×C4×C131—21no—
62C22×C4×C131—21no—
63C22×C4×C131—21no—
64C22×C4×C131—41no—
65C22×C4×C131C2×D411yescharacteristic
66C22×C4×C131C2×D411yescharacteristic
67C22×C4×C131C2×D411yescharacteristic
68C2×C8×C131—22no—
69C2×C8×C131—22no—
70C2×C8×C131—41no—
71C2×C8×C131—41no—
72C2×C8×C131—41no—
73C2×C8×C131—41no—
74C2×C8×C131—41no—
75C2×C8×C131—41no—
76C2×C8×C131—41no—
77C4⋊C4×C131—21no—
78C4⋊C4×C131—21no—
79C4⋊C4×C131—21no—
80C4⋊C4×C131—21no—
81C4⋊C4×C131—41no—
82C4⋊C4×C131—41no—
83C4⋊C4×C131—41no—
84C4⋊C4×C131—42no—
85C4⋊C4×C131—42no—
86C4⋊C4×C131—42no—
87C4⋊C4×C131—42no—
88C4⋊C4×C131—41no—
89C4⋊C4×C131—41no—
90C4⋊C4×C131—41no—
91C4⋊C4×C131—41no—
92C4⋊C4×C131—41no—
93C4⋊C4×C131—41no—
94C4⋊C4×C131—41no—
95C4⋊C4×C131—41no—
96C4⋊C4×C131—41no—
97C4⋊C4×C131—41no—
98C4⋊C4×C131—81no—
99C4⋊C4×C131D812yes—
100C4⋊C4×C131Q1612yes—
101C42×C131—41no—
102C42×C131—42no—
103C23×C131#12011yescharacteristic
104C2×C4×C131—21no—
105C2×C4×C131—21no—
106C2×C4×C131—21no—
107C2×C4×C131—21no—
108C2×C4×C131—21no—
109C2×C4×C131—21no—
110C2×C4×C131—22no—
111C2×C4×C131—22no—
112C2×C4×C131—41no—
113C2×C4×C131—41no—
114C2×C4×C131—41no—
115C2×C4×C131—41no—
116C2×C4×C131—41no—
117C2×C4×C131—41no—
118C2×C4×C131—41no—
119C2×C4×C131—41no—
120C2×C4×C131—41no—
121C2×C4×C131—41no—
122C2×C4×C131—41no—
123C2×C4×C131—41no—
124C2×C4×C131—41no—
125C2×C4×C131—41no—
126C2×C4×C131—41no—
127C2×C4×C131—41no—
128C2×C4×C131—81no—
129C2×C4×C131—81no—
130C2×C4×C131—81no—
131C2×C4×C131C2×D811yescharacteristic
132C2×C4×C131C2×Q1611yescharacteristic
133C2×C4×C131#13511yescharacteristic
134C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C131#13711yescharacteristic
137C8×C131—42no—
138C8×C131—42no—
139C8×C131—81no—
140C22×C131#44711yescharacteristic
141C22×C131#44911yescharacteristic
142C22×C131#45111yescharacteristic
143C22×C131#45411yescharacteristic
144C22×C131#45611yescharacteristic
145C22×C131#45611yescharacteristic
146C22×C131#45811yescharacteristic
147C4×C131—21no—
148C4×C131—21no—
149C4×C131—21no—
150C4×C131—21no—
151C4×C131—21no—
152C4×C131—21no—
153C4×C131—42no—
154C4×C131—42no—
155C4×C131—81no—
156C4×C131—81no—
157C4×C131—81no—
158C4×C131—81no—
159C4×C131—161no—
160C2×C131#160911yescharacteristic
161C2×C131#161011yescharacteristic
162C2×C131#161711yescharacteristic
163C2×C131#162511yescharacteristic
164C2×C131#164811yescharacteristic
165C2×C131#164911yescharacteristic
166C2×C131#166311yescharacteristic
167#7792C13111yesmaximal, characteristic, direct product factor, Sylow
168C131#779211yescharacteristic, direct product factor, Sylow
169#2726C2×C13111yescharacteristic
170#2099C2×C13111yescharacteristic
171#2083C2×C13111yescharacteristic
172#2083C2×C13111yescharacteristic
173#1271C2×C13111yescharacteristic
174#1271C2×C13111yescharacteristic
175#1271C2×C13111yescharacteristic
176C2×#125—21no—
177C2×#107—21no—
178C2×#107—21no—
179#398—21no—
180#398—21no—
181#398—21no—
182#389—21no—
183#389C22×C13111yescharacteristic
184#389C22×C13111yescharacteristic
185#389C22×C13111yescharacteristic
186#387—21no—
187#384C22×C13111yescharacteristic
188#340—21no—
189#340—21no—
190#340—21no—
191#340—21no—
192#336C22×C13111yescharacteristic
193#336C22×C13111yescharacteristic
194#336C22×C13111yescharacteristic
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198#125—42no—
199#125—42no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4D4×C13111yescharacteristic
211C2×C4⋊C4D4×C13111yescharacteristic
212C2×C4⋊C4D4×C13111yescharacteristic
213C2×C4⋊C4D4×C13111yescharacteristic
214C2×C4⋊C4D4×C13111yescharacteristic
215C2×C4⋊C4D4×C13111yescharacteristic
216C2×C42—21no—
217C2×C42C23×C13111yescharacteristic
218#107—42no—
219#107—42no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4C2×D4×C13111yescharacteristic
234C22×C4C2×D4×C13111yescharacteristic
235C22×C4C2×D4×C13111yescharacteristic
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—81no—
267C4⋊C4D8×C13112yes—
268C4⋊C4Q16×C13112yes—
269C42—41no—
270C42—42no—
271C23#120×C13111yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4C2×D8×C13111yescharacteristic
300C2×C4C2×Q16×C13111yescharacteristic
301C2×C4#135×C13111yescharacteristic
302C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
303C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
304C2×C4#137×C13111yescharacteristic
305C8—42no—
306C8—42no—
307C8—81no—
308C22#447×C13111yescharacteristic
309C22#449×C13111yescharacteristic
310C22#451×C13111yescharacteristic
311C22#454×C13111yescharacteristic
312C22#456×C13111yescharacteristic
313C22#456×C13111yescharacteristic
314C22#458×C13111yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—42no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—161no—
328C2#1609×C13111yescharacteristic
329C2#1610×C13111yescharacteristic
330C2#1617×C13111yescharacteristic
331C2#1625×C13111yescharacteristic
332C2#1648×C13111yescharacteristic
333C2#1649×C13111yescharacteristic
334C2#1663×C13111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C131#120
commutator, Frattini, cosocleC2×C42C23×C131
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
167. #7792C131direct (N × H)
168. C131#7792direct (N × H)

Maximal subgroups

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

subgroupindex
#2726×C1312
#2099×C1312
#2083×C1312
#1271×C1312
#7792131