Finite Group Databasebeta

← C131×#8463 #45694347

Subgroups — C131×#8463 #45694347

Order 33536.

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

normal subgroups only

This group has 718 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#3493×C131C211yesmaximal, characteristic
2#1820×C131C211yesmaximal, characteristic, complemented
3#1818×C131C211yesmaximal, characteristic, complemented
4#1516×C131C212yesmaximal, complemented
5#1516×C131C212yesmaximal, complemented
6#556×C131—22no—
7#555×C131—22no—
8#553×C131—22no—
9#552×C131—22no—
10#544×C131C411yescharacteristic, complemented
11#538×C131—22no—
12#537×C131C411yescharacteristic, complemented
13#529×C131—22no—
14#525×C131C2212yes—
15#520×C131C412yescomplemented
16C2×#117×C131C2211yescharacteristic
17C2×C22⋊C8×C131C2211yescharacteristic
18C2×C22⋊C8×C131C2211yescharacteristic
19#381×C131C2212yes—
20#342×C131—22no—
21#336×C131—22no—
22#328×C131—22no—
23#328×C131—22no—
24#327×C131—22no—
25#327×C131—22no—
26C2×#41×C131C2×C412yes—
27C23×C4×C131C2311yescharacteristic
28C22×C8×C131—21no—
29C22×C8×C131—21no—
30C4⋊Q8×C131—22no—
31#126×C131—24no—
32#126×C131—24no—
33#125×C131—22no—
34#125×C131—22no—
35#124×C131—22no—
36#124×C131—24no—
37#123×C131—24no—
38#123×C131—22no—
39C22⋊Q8×C131—22no—
40C22⋊Q8×C131—22no—
41C22⋊Q8×C131D412yes—
42C22⋊Q8×C131D412yes—
43#121×C131—24no—
44#121×C131—22no—
45#121×C131—22no—
46#121×C131D412yes—
47#121×C131D412yes—
48#120×C131—22no—
49C4×Q8×C131—22no—
50C4×Q8×C131—22no—
51C4×D4×C131—22no—
52C4×D4×C131—22no—
53C4×D4×C131—24no—
54C4×D4×C131—22no—
55C4×D4×C131—22no—
56#117×C131—24no—
57#117×C131—22no—
58#117×C131—22no—
59#117×C131—22no—
60#117×C131C2×C412yes—
61C2×C4⋊C4×C131—22no—
62C2×C4⋊C4×C131C2×C411yescharacteristic
63C2×C4⋊C4×C131C2×C411yescharacteristic
64C2×C22⋊C4×C131—22no—
65C2×C22⋊C4×C131D412yes—
66C2×C42×C131D412yes—
67C22⋊C8×C131—22no—
68C22⋊C8×C131—22no—
69#95×C131—22no—
70#95×C131—22no—
71C24×C131C2×D411yescharacteristic
72#41×C131—44no—
73C2×Q8×C131—22no—
74C2×Q8×C131C22⋊C412yes—
75C2×D4×C131—22no—
76C2×D4×C131—22no—
77C2×D4×C131—22no—
78C2×D4×C131—22no—
79C2×D4×C131C22⋊C412yes—
80C22×C4×C131—24no—
81C22×C4×C131—22no—
82C22×C4×C131—42no—
83C22×C4×C131—42no—
84C22×C4×C131C22⋊C412yes—
85C22×C4×C131C22⋊C412yes—
86C22×C4×C131C22×C411yescharacteristic
87C22×C4×C131C2×D411yescharacteristic
88C22×C4×C131C2×D412yes—
89C22×C4×C131C2×D412yes—
90C2×C8×C131—42no—
91C2×C8×C131—42no—
92C2×C8×C131—41no—
93C2×C8×C131—41no—
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×C131—22no—
101C4⋊C4×C131—22no—
102C4⋊C4×C131C22⋊C412yes—
103C4⋊C4×C131C22⋊C412yes—
104C22⋊C4×C131—24no—
105C22⋊C4×C131—24no—
106C22⋊C4×C131—22no—
107C22⋊C4×C131—24no—
108C22⋊C4×C131—22no—
109C22⋊C4×C131—22no—
110C22⋊C4×C131—22no—
111C22⋊C4×C131—22no—
112C22⋊C4×C131—44no—
113C42×C131—24no—
114C42×C131—22no—
115C42×C131—22no—
116C42×C131—22no—
117C23×C131—22no—
118C23×C131—22no—
119C23×C131—41no—
120C23×C131—41no—
121C23×C131C2×C22⋊C411yescharacteristic
122C23×C131#12012yes—
123Q8×C131—42no—
124Q8×C131—82no—
125D4×C131—42no—
126D4×C131—44no—
127D4×C131—82no—
128D4×C131—82no—
129D4×C131—82no—
130C2×C4×C131—22no—
131C2×C4×C131—22no—
132C2×C4×C131—22no—
133C2×C4×C131—22no—
134C2×C4×C131—22no—
135C2×C4×C131—22no—
136C2×C4×C131—22no—
137C2×C4×C131—42no—
138C2×C4×C131—42no—
139C2×C4×C131—44no—
140C2×C4×C131—42no—
141C2×C4×C131—42no—
142C2×C4×C131—84no—
143C2×C4×C131—82no—
144C2×C4×C131—82no—
145C2×C4×C131—82no—
146C2×C4×C131C2×C22⋊C412yes—
147C2×C4×C131#12011yescharacteristic
148C2×C4×C131#12011yescharacteristic
149C8×C131—81no—
150C8×C131—81no—
151C22×C131—21no—
152C22×C131—21no—
153C22×C131—22no—
154C22×C131—22no—
155C22×C131—22no—
156C22×C131—42no—
157C22×C131—42no—
158C22×C131—42no—
159C22×C131—82no—
160C22×C131#37911yescharacteristic
161C22×C131#41012yes—
162C4×C131—21no—
163C4×C131—21no—
164C4×C131—22no—
165C4×C131—42no—
166C4×C131—42no—
167C4×C131—42no—
168C4×C131—42no—
169C4×C131—42no—
170C4×C131—162no—
171C2×C131—22no—
172C2×C131—42no—
173C2×C131—82no—
174C2×C131#178211yescharacteristic
175C2×C131#179411yescharacteristic
176C2×C131#179411yescharacteristic
177#8463C13111yesmaximal, characteristic, direct product factor, Sylow
178C131#846311yescharacteristic, direct product factor, Sylow
179#3493C2×C13111yescharacteristic
180#1820C2×C13111yescharacteristic, complemented
181#1818C2×C13111yescharacteristic, complemented
182#1516C2×C13112yescomplemented
183#1516C2×C13112yescomplemented
184#556—22no—
185#555—22no—
186#553—22no—
187#552—22no—
188#544C4×C13111yescharacteristic, complemented
189#538—22no—
190#537C4×C13111yescharacteristic, complemented
191#529—22no—
192#525C22×C13112yes—
193#520C4×C13112yescomplemented
194C2×#117C22×C13111yescharacteristic
195C2×C22⋊C8C22×C13111yescharacteristic
196C2×C22⋊C8C22×C13111yescharacteristic
197#381C22×C13112yes—
198#342—22no—
199#336—22no—
200#328—22no—
201#328—22no—
202#327—22no—
203#327—22no—
204C2×#41C2×C4×C13112yes—
205C23×C4C23×C13111yescharacteristic
206C22×C8—21no—
207C22×C8—21no—
208C4⋊Q8—22no—
209#126—24no—
210#126—24no—
211#125—22no—
212#125—22no—
213#124—22no—
214#124—24no—
215#123—24no—
216#123—22no—
217C22⋊Q8—22no—
218C22⋊Q8—22no—
219C22⋊Q8D4×C13112yes—
220C22⋊Q8D4×C13112yes—
221#121—24no—
222#121—22no—
223#121—22no—
224#121D4×C13112yes—
225#121D4×C13112yes—
226#120—22no—
227C4×Q8—22no—
228C4×Q8—22no—
229C4×D4—22no—
230C4×D4—22no—
231C4×D4—24no—
232C4×D4—22no—
233C4×D4—22no—
234#117—24no—
235#117—22no—
236#117—22no—
237#117—22no—
238#117C2×C4×C13112yes—
239C2×C4⋊C4—22no—
240C2×C4⋊C4C2×C4×C13111yescharacteristic
241C2×C4⋊C4C2×C4×C13111yescharacteristic
242C2×C22⋊C4—22no—
243C2×C22⋊C4D4×C13112yes—
244C2×C42D4×C13112yes—
245C22⋊C8—22no—
246C22⋊C8—22no—
247#95—22no—
248#95—22no—
249C24C2×D4×C13111yescharacteristic
250#41—44no—
251C2×Q8—22no—
252C2×Q8C22⋊C4×C13112yes—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4C22⋊C4×C13112yes—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4C22⋊C4×C13112yes—
263C22×C4C22⋊C4×C13112yes—
264C22×C4C22×C4×C13111yescharacteristic
265C22×C4C2×D4×C13111yescharacteristic
266C22×C4C2×D4×C13112yes—
267C22×C4C2×D4×C13112yes—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—41no—
271C2×C8—41no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4C22⋊C4×C13112yes—
281C4⋊C4C22⋊C4×C13112yes—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—22no—
285C22⋊C4—24no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—44no—
291C42—24no—
292C42—22no—
293C42—22no—
294C42—22no—
295C23—22no—
296C23—22no—
297C23—41no—
298C23—41no—
299C23C2×C22⋊C4×C13111yescharacteristic
300C23#120×C13112yes—
301Q8—42no—
302Q8—82no—
303D4—42no—
304D4—44no—
305D4—82no—
306D4—82no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—84no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4C2×C22⋊C4×C13112yes—
325C2×C4#120×C13111yescharacteristic
326C2×C4#120×C13111yescharacteristic
327C8—81no—
328C8—81no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—82no—
338C22#379×C13111yescharacteristic
339C22#410×C13112yes—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—42no—
344C4—42no—
345C4—42no—
346C4—42no—
347C4—42no—
348C4—162no—
349C2—22no—
350C2—42no—
351C2—82no—
352C2#1782×C13111yescharacteristic
353C2#1794×C13111yescharacteristic
354C2#1794×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#379
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radical#3493×C131C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1820×C131C2semidirect
3. #1818×C131C2semidirect
4. #1516×C131C2semidirect
5. #1516×C131C2semidirect
10. #544×C131C4semidirect
12. #537×C131C4semidirect
15. #520×C131C4semidirect
177. #8463C131direct (N × H)
178. C131#8463direct (N × H)
180. #1820C2×C131semidirect
181. #1818C2×C131semidirect
182. #1516C2×C131semidirect
183. #1516C2×C131semidirect
188. #544C4×C131semidirect
190. #537C4×C131semidirect
193. #520C4×C131semidirect

Maximal subgroups

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

subgroupindex
#3493×C1312
#1820×C1312
#1818×C1312
#1516×C1312
#8463131