Finite Group Databasebeta

← C131×#10174 #45696058

Subgroups — C131×#10174 #45696058

Order 33536.

578 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3226×C131C211yesmaximal, characteristic
2C2×#500×C131C211yesmaximal, characteristic, complemented
3#3152×C131C211yesmaximal, characteristic
4#1966×C131C211yesmaximal, characteristic, complemented
5#1546×C131C211yesmaximal, characteristic, complemented
6#1492×C131C211yesmaximal, characteristic
7#1278×C131C211yesmaximal, characteristic, complemented
8C2×#137×C131—22no—
9#532×C131C2211yescharacteristic
10C2×C4⋊Q8×C131C2211yescharacteristic
11C2×C4⋊Q8×C131C2211yescharacteristic
12#500×C131—22no—
13#500×C131—21no—
14#500×C131—22no—
15#497×C131—22no—
16#494×C131—21no—
17#492×C131—21no—
18#486×C131—21no—
19#480×C131—22no—
20#474×C131—22no—
21#431×C131C2211yescharacteristic
22C2×#107×C131—22no—
23#423×C131C2211yescharacteristic
24C2×#101×C131—22no—
25C4×M16×C131C2211yescharacteristic
26C2×C4×C8×C131C2211yescharacteristic
27#332×C131—22no—
28D4⋊C8×C131—22no—
29C2×#41×C131—21no—
30C22×Q8×C131—21no—
31C22×Q8×C131—21no—
32#137×C131—44no—
33#137×C131—44no—
34C2×Q16×C131—24no—
35C2×SD16×C131—24no—
36C2×M16×C131—21no—
37C2×M16×C131D412yes—
38C22×C8×C131—21no—
39C4⋊Q8×C131—21no—
40C4⋊Q8×C131—21no—
41C4⋊Q8×C131—21no—
42C4⋊Q8×C131—21no—
43C4⋊Q8×C131—21no—
44C4⋊Q8×C131—21no—
45C4⋊Q8×C131—21no—
46C4⋊Q8×C131D411yescharacteristic
47C4⋊Q8×C131D412yes—
48#127×C131D411yescharacteristic
49#124×C131—21no—
50#121×C131—21no—
51#121×C131—21no—
52C4×D4×C131—21no—
53C4×D4×C131—21no—
54C2×C4⋊C4×C131—21no—
55C2×C4⋊C4×C131—21no—
56C2×C4⋊C4×C131—21no—
57C2×C4⋊C4×C131D412yes—
58C2×C42×C131C2311yescharacteristic
59#107×C131—28no—
60#107×C131—24no—
61C4⋊C8×C131—21no—
62C4⋊C8×C131—21no—
63C4⋊C8×C131D412yes—
64#102×C131—24no—
65#101×C131—44no—
66C22⋊C8×C131—21no—
67#97×C131—21no—
68C4×C8×C131—21no—
69C4×C8×C131—21no—
70C4×C8×C131—21no—
71C4×C8×C131D412yes—
72#41×C131—42no—
73#41×C131—42no—
74C2×Q8×C131—21no—
75C2×Q8×C131—22no—
76C2×Q8×C131—41no—
77C2×Q8×C131—41no—
78C2×Q8×C131—41no—
79C2×Q8×C131—42no—
80C2×Q8×C131—42no—
81C2×Q8×C131—42no—
82C2×Q8×C131—42no—
83C2×D4×C131—21no—
84C2×D4×C131—21no—
85C2×D4×C131—21no—
86C2×D4×C131—41no—
87C22×C4×C131—22no—
88C22×C4×C131—41no—
89C22×C4×C131—41no—
90C22×C4×C131C2×D411yescharacteristic
91C22×C4×C131C2×D411yescharacteristic
92C22×C4×C131#4111yescharacteristic
93Q16×C131—48no—
94SD16×C131—48no—
95M16×C131—22no—
96M16×C131—42no—
97M16×C131D814yes—
98C2×C8×C131—24no—
99C2×C8×C131—22no—
100C2×C8×C131—22no—
101C2×C8×C131—22no—
102C2×C8×C131—41no—
103C4⋊C4×C131—22no—
104C4⋊C4×C131—22no—
105C4⋊C4×C131—22no—
106C4⋊C4×C131—21no—
107C4⋊C4×C131—22no—
108C4⋊C4×C131—21no—
109C4⋊C4×C131—41no—
110C4⋊C4×C131—41no—
111C4⋊C4×C131—41no—
112C4⋊C4×C131—41no—
113C22⋊C4×C131—41no—
114C22⋊C4×C131—41no—
115C42×C131C2×D411yescharacteristic
116C42×C131C2×D411yescharacteristic
117C42×C131C2×D411yescharacteristic
118C42×C131C2×D411yescharacteristic
119C23×C131—41no—
120C23×C131#12111yescharacteristic
121Q8×C131—44no—
122Q8×C131—42no—
123Q8×C131—82no—
124Q8×C131—81no—
125Q8×C131—81no—
126Q8×C131—81no—
127Q8×C131—81no—
128D4×C131—42no—
129D4×C131—42no—
130D4×C131—42no—
131D4×C131—82no—
132C2×C4×C131—22no—
133C2×C4×C131—22no—
134C2×C4×C131—41no—
135C2×C4×C131—42no—
136C2×C4×C131—42no—
137C2×C4×C131—44no—
138C2×C4×C131—82no—
139C2×C4×C131—81no—
140C2×C4×C131—81no—
141C2×C4×C131#12011yescharacteristic
142C2×C4×C131#12011yescharacteristic
143C2×C4×C131#12011yescharacteristic
144C2×C4×C131#12111yescharacteristic
145C2×C4×C131#12111yescharacteristic
146C2×C4×C131#12711yescharacteristic
147C2×C4×C131C2×D812yes—
148C2×C4×C131AGL(1,ℤ/8)12yes—
149C8×C131—24no—
150C8×C131—24no—
151C8×C131—42no—
152C8×C131—81no—
153C22×C131—21no—
154C22×C131—21no—
155C22×C131—81no—
156C22×C131—81no—
157C22×C131—81no—
158C22×C131#39211yescharacteristic
159C22×C131#45912yes—
160C4×C131—21no—
161C4×C131—21no—
162C4×C131—82no—
163C4×C131—81no—
164C4×C131—82no—
165C4×C131#44712yes—
166C4×C131#45612yes—
167C4×C131#47312yes—
168C4×C131#49311yescharacteristic
169C4×C131#49611yescharacteristic
170C2×C131—22no—
171C2×C131—161no—
172C2×C131#200511yescharacteristic
173C2×C131#201111yescharacteristic
174C2×C131#202011yescharacteristic
175#10174C13111yesmaximal, characteristic, direct product factor, Sylow
176C131#1017411yescharacteristic, direct product factor, Sylow
177#3226C2×C13111yescharacteristic
178C2×#500C2×C13111yescharacteristic, complemented
179#3152C2×C13111yescharacteristic
180#1966C2×C13111yescharacteristic, complemented
181#1546C2×C13111yescharacteristic, complemented
182#1492C2×C13111yescharacteristic
183#1278C2×C13111yescharacteristic, complemented
184C2×#137—22no—
185#532C22×C13111yescharacteristic
186C2×C4⋊Q8C22×C13111yescharacteristic
187C2×C4⋊Q8C22×C13111yescharacteristic
188#500—22no—
189#500—21no—
190#500—22no—
191#497—22no—
192#494—21no—
193#492—21no—
194#486—21no—
195#480—22no—
196#474—22no—
197#431C22×C13111yescharacteristic
198C2×#107—22no—
199#423C22×C13111yescharacteristic
200C2×#101—22no—
201C4×M16C22×C13111yescharacteristic
202C2×C4×C8C22×C13111yescharacteristic
203#332—22no—
204D4⋊C8—22no—
205C2×#41—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208#137—44no—
209#137—44no—
210C2×Q16—24no—
211C2×SD16—24no—
212C2×M16—21no—
213C2×M16D4×C13112yes—
214C22×C8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8D4×C13112yes—
223C4⋊Q8D4×C13111yescharacteristic
224#127D4×C13111yescharacteristic
225#124—21no—
226#121—21no—
227#121—21no—
228C4×D4—21no—
229C4×D4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4D4×C13112yes—
234C2×C42C23×C13111yescharacteristic
235#107—28no—
236#107—24no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8D4×C13112yes—
240#102—24no—
241#101—44no—
242C22⋊C8—21no—
243#97—21no—
244C4×C8—21no—
245C4×C8—21no—
246C4×C8—21no—
247C4×C8D4×C13112yes—
248#41—42no—
249#41—42no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C2×D4×C13111yescharacteristic
267C22×C4C2×D4×C13111yescharacteristic
268C22×C4#41×C13111yescharacteristic
269Q16—48no—
270SD16—48no—
271M16—22no—
272M16—42no—
273M16D8×C13114yes—
274C2×C8—24no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—41no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42C2×D4×C13111yescharacteristic
292C42C2×D4×C13111yescharacteristic
293C42C2×D4×C13111yescharacteristic
294C42C2×D4×C13111yescharacteristic
295C23—41no—
296C23#121×C13111yescharacteristic
297Q8—44no—
298Q8—42no—
299Q8—82no—
300Q8—81no—
301Q8—81no—
302Q8—81no—
303Q8—81no—
304D4—42no—
305D4—42no—
306D4—42no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—82no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4#120×C13111yescharacteristic
318C2×C4#120×C13111yescharacteristic
319C2×C4#120×C13111yescharacteristic
320C2×C4#121×C13111yescharacteristic
321C2×C4#121×C13111yescharacteristic
322C2×C4#127×C13111yescharacteristic
323C2×C4C2×D8×C13112yes—
324C2×C4AGL(1,ℤ/8)×C13112yes—
325C8—24no—
326C8—24no—
327C8—42no—
328C8—81no—
329C22—21no—
330C22—21no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22#392×C13111yescharacteristic
335C22#459×C13112yes—
336C4—21no—
337C4—21no—
338C4—82no—
339C4—81no—
340C4—82no—
341C4#447×C13112yes—
342C4#456×C13112yes—
343C4#473×C13112yes—
344C4#493×C13111yescharacteristic
345C4#496×C13111yescharacteristic
346C2—22no—
347C2—161no—
348C2#2005×C13111yescharacteristic
349C2#2011×C13111yescharacteristic
350C2#2020×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC2×C42C23×C131
prime radical#532×C131C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#500×C131C2semidirect
4. #1966×C131C2semidirect
5. #1546×C131C2semidirect
7. #1278×C131C2semidirect
175. #10174C131direct (N × H)
176. C131#10174direct (N × H)
178. C2×#500C2×C131semidirect
180. #1966C2×C131semidirect
181. #1546C2×C131semidirect
183. #1278C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3226×C1312
C2×#500×C1312
#3152×C1312
#1966×C1312
#1546×C1312
#1492×C1312
#1278×C1312
#10174131