Finite Group Databasebeta

← C131×#8477 #45694361

Subgroups — C131×#8477 #45694361

Order 33536.

682 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 142 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#3510×C131C211yesmaximal, characteristic
2#1544×C131C211yesmaximal, characteristic, complemented
3#1537×C131C211yesmaximal, characteristic, complemented
4#1488×C131C212yesmaximal, complemented
5#1469×C131C212yesmaximal, complemented
6#559×C131—22no—
7#556×C131—22no—
8#551×C131—24no—
9#542×C131—22no—
10#536×C131C411yescharacteristic
11#535×C131C411yescharacteristic
12#533×C131C2211yescharacteristic
13#529×C131—22no—
14C2×#124×C131C2211yescharacteristic
15#519×C131C411yescharacteristic
16#518×C131C411yescharacteristic
17C4×#41×C131C2211yescharacteristic
18#432×C131C2212yes—
19#431×C131C2212yes—
20#332×C131—22no—
21#330×C131—22no—
22Q8⋊C8×C131—22no—
23D4⋊C8×C131—22no—
24#323×C131—24no—
25C2×#41×C131C2×C411yescharacteristic
26C22×Q8×C131C2×C411yescharacteristic
27C22×D4×C131C2×C411yescharacteristic
28C4⋊Q8×C131—21no—
29C4⋊Q8×C131D412yes—
30#127×C131—21no—
31#126×C131—24no—
32#126×C131—24no—
33#125×C131D412yes—
34#124×C131—24no—
35#124×C131—21no—
36#124×C131—21no—
37#124×C131—21no—
38#124×C131—21no—
39#124×C131—22no—
40#123×C131—24no—
41#123×C131—24no—
42#123×C131—22no—
43C22⋊Q8×C131—24no—
44C22⋊Q8×C131—22no—
45C22⋊Q8×C131—22no—
46#121×C131—22no—
47#120×C131—22no—
48C4×Q8×C131—22no—
49C4×Q8×C131—22no—
50C4×Q8×C131—22no—
51C4×Q8×C131D412yes—
52C4×D4×C131—24no—
53C4×D4×C131—22no—
54C4×D4×C131—22no—
55C4×D4×C131—22no—
56C4×D4×C131D412yes—
57#117×C131—24no—
58#117×C131—22no—
59#117×C131—21no—
60#117×C131C2×C411yescharacteristic
61#117×C131C2×C411yescharacteristic
62#117×C131C2×C411yescharacteristic
63C2×C22⋊C4×C131—22no—
64C2×C22⋊C4×C131D414yes—
65C2×C42×C131—21no—
66C2×C42×C131C2311yescharacteristic
67C4⋊C8×C131—22no—
68C4⋊C8×C131—22no—
69C22⋊C8×C131—22no—
70C22⋊C8×C131—22no—
71#97×C131—22no—
72C4×C8×C131—22no—
73C24×C131C22⋊C412yes—
74#41×C131—42no—
75C2×Q8×C131—21no—
76C2×Q8×C131—21no—
77C2×Q8×C131—22no—
78C2×Q8×C131—42no—
79C2×Q8×C131C22⋊C411yescharacteristic
80C2×D4×C131—21no—
81C2×D4×C131—24no—
82C2×D4×C131—21no—
83C2×D4×C131—21no—
84C2×D4×C131—42no—
85C2×D4×C131C22⋊C411yescharacteristic
86C22×C4×C131—24no—
87C22×C4×C131—21no—
88C22×C4×C131—22no—
89C22×C4×C131C22⋊C412yes—
90C22×C4×C131C22×C411yescharacteristic
91C22×C4×C131C2×D412yes—
92C2×C8×C131—42no—
93C2×C8×C131—42no—
94C4⋊C4×C131—24no—
95C4⋊C4×C131—24no—
96C4⋊C4×C131—22no—
97C4⋊C4×C131—22no—
98C4⋊C4×C131—22no—
99C4⋊C4×C131—22no—
100C4⋊C4×C131C22⋊C412yes—
101C4⋊C4×C131C22⋊C412yes—
102C4⋊C4×C131C22⋊C412yes—
103C22⋊C4×C131—24no—
104C22⋊C4×C131—24no—
105C22⋊C4×C131—24no—
106C22⋊C4×C131—21no—
107C22⋊C4×C131—21no—
108C22⋊C4×C131—21no—
109C22⋊C4×C131—24no—
110C22⋊C4×C131—24no—
111C22⋊C4×C131—22no—
112C42×C131—24no—
113C42×C131—21no—
114C42×C131—21no—
115C42×C131—21no—
116C42×C131—22no—
117C42×C131C2×D412yes—
118C42×C131C2×D411yescharacteristic
119C42×C131C2×D411yescharacteristic
120C23×C131—22no—
121C23×C131—21no—
122C23×C131—42no—
123C23×C131—44no—
124C23×C131C2×C22⋊C411yescharacteristic
125Q8×C131—22no—
126Q8×C131—42no—
127Q8×C131—42no—
128Q8×C131—82no—
129D4×C131—22no—
130D4×C131—42no—
131D4×C131—42no—
132D4×C131—42no—
133D4×C131—84no—
134C2×C4×C131—22no—
135C2×C4×C131—22no—
136C2×C4×C131—22no—
137C2×C4×C131—22no—
138C2×C4×C131—21no—
139C2×C4×C131—22no—
140C2×C4×C131—42no—
141C2×C4×C131—42no—
142C2×C4×C131—42no—
143C2×C4×C131—82no—
144C2×C4×C131—84no—
145C2×C4×C131C2×C22⋊C411yescharacteristic
146C2×C4×C131C2×C22⋊C411yescharacteristic
147C2×C4×C131#12012yes—
148C2×C4×C131#12012yes—
149C8×C131—82no—
150C8×C131—82no—
151C22×C131—22no—
152C22×C131—21no—
153C22×C131—42no—
154C22×C131—44no—
155C22×C131—41no—
156C22×C131—42no—
157C22×C131—162no—
158C22×C131#37911yescharacteristic
159C4×C131—22no—
160C4×C131—22no—
161C4×C131—21no—
162C4×C131—42no—
163C4×C131—42no—
164C4×C131—42no—
165C4×C131—41no—
166C4×C131—42no—
167C4×C131#41312yes—
168C2×C131—41no—
169C2×C131—81no—
170C2×C131—82no—
171C2×C131#178511yescharacteristic
172C2×C131#179412yes—
173#8477C13111yesmaximal, characteristic, direct product factor, Sylow
174C131#847711yescharacteristic, direct product factor, Sylow
175#3510C2×C13111yescharacteristic
176#1544C2×C13111yescharacteristic, complemented
177#1537C2×C13111yescharacteristic, complemented
178#1488C2×C13112yescomplemented
179#1469C2×C13112yescomplemented
180#559—22no—
181#556—22no—
182#551—24no—
183#542—22no—
184#536C4×C13111yescharacteristic
185#535C4×C13111yescharacteristic
186#533C22×C13111yescharacteristic
187#529—22no—
188C2×#124C22×C13111yescharacteristic
189#519C4×C13111yescharacteristic
190#518C4×C13111yescharacteristic
191C4×#41C22×C13111yescharacteristic
192#432C22×C13112yes—
193#431C22×C13112yes—
194#332—22no—
195#330—22no—
196Q8⋊C8—22no—
197D4⋊C8—22no—
198#323—24no—
199C2×#41C2×C4×C13111yescharacteristic
200C22×Q8C2×C4×C13111yescharacteristic
201C22×D4C2×C4×C13111yescharacteristic
202C4⋊Q8—21no—
203C4⋊Q8D4×C13112yes—
204#127—21no—
205#126—24no—
206#126—24no—
207#125D4×C13112yes—
208#124—24no—
209#124—21no—
210#124—21no—
211#124—21no—
212#124—21no—
213#124—22no—
214#123—24no—
215#123—24no—
216#123—22no—
217C22⋊Q8—24no—
218C22⋊Q8—22no—
219C22⋊Q8—22no—
220#121—22no—
221#120—22no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8—22no—
225C4×Q8D4×C13112yes—
226C4×D4—24no—
227C4×D4—22no—
228C4×D4—22no—
229C4×D4—22no—
230C4×D4D4×C13112yes—
231#117—24no—
232#117—22no—
233#117—21no—
234#117C2×C4×C13111yescharacteristic
235#117C2×C4×C13111yescharacteristic
236#117C2×C4×C13111yescharacteristic
237C2×C22⋊C4—22no—
238C2×C22⋊C4D4×C13114yes—
239C2×C42—21no—
240C2×C42C23×C13111yescharacteristic
241C4⋊C8—22no—
242C4⋊C8—22no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245#97—22no—
246C4×C8—22no—
247C24C22⋊C4×C13112yes—
248#41—42no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—42no—
253C2×Q8C22⋊C4×C13111yescharacteristic
254C2×D4—21no—
255C2×D4—24no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—42no—
259C2×D4C22⋊C4×C13111yescharacteristic
260C22×C4—24no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4C22⋊C4×C13112yes—
264C22×C4C22×C4×C13111yescharacteristic
265C22×C4C2×D4×C13112yes—
266C2×C8—42no—
267C2×C8—42no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4C22⋊C4×C13112yes—
275C4⋊C4C22⋊C4×C13112yes—
276C4⋊C4C22⋊C4×C13112yes—
277C22⋊C4—24no—
278C22⋊C4—24no—
279C22⋊C4—24no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—24no—
284C22⋊C4—24no—
285C22⋊C4—22no—
286C42—24no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—22no—
291C42C2×D4×C13112yes—
292C42C2×D4×C13111yescharacteristic
293C42C2×D4×C13111yescharacteristic
294C23—22no—
295C23—21no—
296C23—42no—
297C23—44no—
298C23C2×C22⋊C4×C13111yescharacteristic
299Q8—22no—
300Q8—42no—
301Q8—42no—
302Q8—82no—
303D4—22no—
304D4—42no—
305D4—42no—
306D4—42no—
307D4—84no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—82no—
318C2×C4—84no—
319C2×C4C2×C22⋊C4×C13111yescharacteristic
320C2×C4C2×C22⋊C4×C13111yescharacteristic
321C2×C4#120×C13112yes—
322C2×C4#120×C13112yes—
323C8—82no—
324C8—82no—
325C22—21no—
326C22—22no—
327C22—41no—
328C22—42no—
329C22—42no—
330C22—44no—
331C22—162no—
332C22#379×C13111yescharacteristic
333C4—21no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—42no—
338C4—42no—
339C4—42no—
340C4—42no—
341C4#413×C13112yes—
342C2—41no—
343C2—82no—
344C2—81no—
345C2#1785×C13111yescharacteristic
346C2#1794×C13112yes—
subgroupG/H
center, socleC22×C131#379
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radical#535×C131C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1544×C131C2semidirect
3. #1537×C131C2semidirect
4. #1488×C131C2semidirect
5. #1469×C131C2semidirect
173. #8477C131direct (N × H)
174. C131#8477direct (N × H)
176. #1544C2×C131semidirect
177. #1537C2×C131semidirect
178. #1488C2×C131semidirect
179. #1469C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3510×C1312
#1544×C1312
#1537×C1312
#1488×C1312
#1469×C1312
#8477131