Finite Group Databasebeta

← C131×#7716 #45693600

Subgroups — C131×#7716 #45693600

Order 33536.

414 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2861×C131C211yesmaximal, characteristic
2#1839×C131C211yesmaximal, characteristic, complemented
3#1831×C131C211yesmaximal, characteristic, complemented
4#1272×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal
6C2×#125×C131C411yescharacteristic
7C2×#124×C131C411yescharacteristic
8C2×C4⋊C8×C131—21no—
9#391×C131C411yescharacteristic
10#391×C131C2211yescharacteristic
11#390×C131C411yescharacteristic
12#390×C131C2211yescharacteristic
13#388×C131—21no—
14#388×C131—21no—
15#388×C131—21no—
16#388×C131—21no—
17C43×C131C2211yescharacteristic
18#336×C131—21no—
19#336×C131—21no—
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×Q8×C131C2×C411yescharacteristic
24C22×D4×C131C2×C411yescharacteristic
25C22×C8×C131—22no—
26C22×C8×C131—22no—
27#125×C131—42no—
28#124×C131—42no—
29C2×C4⋊C4×C131—21no—
30C2×C4⋊C4×C131—21no—
31C2×C4⋊C4×C131C2×C411yescharacteristic
32C2×C4⋊C4×C131C2×C411yescharacteristic
33C2×C22⋊C4×C131—21no—
34C2×C22⋊C4×C131—21no—
35C2×C22⋊C4×C131—21no—
36C2×C22⋊C4×C131—21no—
37C2×C22⋊C4×C131—21no—
38C2×C22⋊C4×C131—21no—
39C2×C42×C131C2×C411yescharacteristic
40C2×C42×C131C2×C411yescharacteristic
41C2×C42×C131D411yescharacteristic
42C2×C42×C131D411yescharacteristic
43C2×C42×C131D411yescharacteristic
44C2×C42×C131D411yescharacteristic
45C2×C42×C131C2311yescharacteristic
46C4⋊C8×C131—42no—
47#95×C131—21no—
48#95×C131—21no—
49#95×C131—21no—
50#95×C131—21no—
51C24×C131—21no—
52C2×Q8×C131—22no—
53C2×Q8×C131—41no—
54C2×Q8×C131—41no—
55C2×D4×C131—22no—
56C2×D4×C131—41no—
57C2×D4×C131—41no—
58C22×C4×C131—21no—
59C22×C4×C131—21no—
60C22×C4×C131—21no—
61C22×C4×C131C22⋊C411yescharacteristic
62C22×C4×C131C22⋊C411yescharacteristic
63C22×C4×C131C22⋊C411yescharacteristic
64C22×C4×C131C22⋊C411yescharacteristic
65C22×C4×C131C22×C411yescharacteristic
66C22×C4×C131C2×D411yescharacteristic
67C22×C4×C131C2×D411yescharacteristic
68C2×C8×C131—42no—
69C2×C8×C131—42no—
70C2×C8×C131—42no—
71C2×C8×C131—42no—
72C2×C8×C131—42no—
73C2×C8×C131—42no—
74C4⋊C4×C131—41no—
75C4⋊C4×C131—41no—
76C4⋊C4×C131—42no—
77C4⋊C4×C131—42no—
78C22⋊C4×C131—42no—
79C22⋊C4×C131—42no—
80C22⋊C4×C131—42no—
81C22⋊C4×C131—42no—
82C22⋊C4×C131—42no—
83C22⋊C4×C131—41no—
84C22⋊C4×C131—41no—
85C42×C131—22no—
86C42×C131—22no—
87C42×C131—22no—
88C42×C131—21no—
89C42×C131—21no—
90C42×C131—41no—
91C42×C131—41no—
92C42×C131—41no—
93C23×C131—41no—
94C23×C131—41no—
95C23×C131—41no—
96C23×C131—41no—
97C23×C131—41no—
98C23×C131—41no—
99C23×C131—41no—
100C23×C131C2×C22⋊C411yescharacteristic
101Q8×C131—82no—
102D4×C131—82no—
103C2×C4×C131—21no—
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—21no—
111C2×C4×C131—21no—
112C2×C4×C131—21no—
113C2×C4×C131—21no—
114C2×C4×C131—21no—
115C2×C4×C131—21no—
116C2×C4×C131—21no—
117C2×C4×C131—21no—
118C2×C4×C131—21no—
119C2×C4×C131—21no—
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—41no—
129C2×C4×C131#10012yes—
130C2×C4×C131#13112yes—
131C2×C4×C131#13512yes—
132C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C131#13711yescharacteristic
134C8×C131—82no—
135C8×C131—82no—
136C22×C131—81no—
137C22×C131—81no—
138C22×C131—81no—
139C22×C131—81no—
140C22×C131—81no—
141C22×C131—81no—
142C22×C131—81no—
143C22×C131#40811yescharacteristic
144C22×C131#41011yescharacteristic
145C22×C131C2×#10011yescharacteristic
146C22×C131#41611yescharacteristic
147C22×C131#41711yescharacteristic
148C22×C131#42111yescharacteristic
149C22×C131#42111yescharacteristic
150C4×C131—22no—
151C4×C131—22no—
152C4×C131—21no—
153C4×C131—21no—
154C4×C131—22no—
155C4×C131—41no—
156C4×C131—41no—
157C4×C131—41no—
158C4×C131—81no—
159C4×C131—81no—
160C4×C131—81no—
161C2×C131—161no—
162C2×C131#146911yescharacteristic
163C2×C131#148211yescharacteristic
164C2×C131#149511yescharacteristic
165C2×C131#151211yescharacteristic
166C2×C131#152111yescharacteristic
167C2×C131#153611yescharacteristic
168C2×C131#155111yescharacteristic
169#7716C13111yesmaximal, characteristic, direct product factor, Sylow
170C131#771611yescharacteristic, direct product factor, Sylow
171#2861C2×C13111yescharacteristic
172#1839C2×C13111yescharacteristic, complemented
173#1831C2×C13111yescharacteristic, complemented
174#1272C2×C13112yescomplemented
175#1270C2×C13112yes—
176C2×#125C4×C13111yescharacteristic
177C2×#124C4×C13111yescharacteristic
178C2×C4⋊C8—21no—
179#391C4×C13111yescharacteristic
180#391C22×C13111yescharacteristic
181#390C4×C13111yescharacteristic
182#390C22×C13111yescharacteristic
183#388—21no—
184#388—21no—
185#388—21no—
186#388—21no—
187C43C22×C13111yescharacteristic
188#336—21no—
189#336—21no—
190#336—21no—
191#336C22×C13112yes—
192#336C22×C13112yes—
193C22×Q8C2×C4×C13111yescharacteristic
194C22×D4C2×C4×C13111yescharacteristic
195C22×C8—22no—
196C22×C8—22no—
197#125—42no—
198#124—42no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×C4×C13111yescharacteristic
202C2×C4⋊C4C2×C4×C13111yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C42C2×C4×C13111yescharacteristic
210C2×C42C2×C4×C13111yescharacteristic
211C2×C42D4×C13111yescharacteristic
212C2×C42D4×C13111yescharacteristic
213C2×C42D4×C13111yescharacteristic
214C2×C42D4×C13111yescharacteristic
215C2×C42C23×C13111yescharacteristic
216C4⋊C8—42no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221C24—21no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×D4—22no—
226C2×D4—41no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4C22⋊C4×C13111yescharacteristic
232C22×C4C22⋊C4×C13111yescharacteristic
233C22×C4C22⋊C4×C13111yescharacteristic
234C22×C4C22⋊C4×C13111yescharacteristic
235C22×C4C22×C4×C13111yescharacteristic
236C22×C4C2×D4×C13111yescharacteristic
237C22×C4C2×D4×C13111yescharacteristic
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C42—22no—
256C42—22no—
257C42—22no—
258C42—21no—
259C42—21no—
260C42—41no—
261C42—41no—
262C42—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23C2×C22⋊C4×C13111yescharacteristic
271Q8—82no—
272D4—82no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4#100×C13112yes—
300C2×C4#131×C13112yes—
301C2×C4#135×C13112yes—
302C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
303C2×C4#137×C13111yescharacteristic
304C8—82no—
305C8—82no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22#408×C13111yescharacteristic
314C22#410×C13111yescharacteristic
315C22C2×#100×C13111yescharacteristic
316C22#416×C13111yescharacteristic
317C22#417×C13111yescharacteristic
318C22#421×C13111yescharacteristic
319C22#421×C13111yescharacteristic
320C4—22no—
321C4—21no—
322C4—21no—
323C4—22no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2#1469×C13111yescharacteristic
333C2#1482×C13111yescharacteristic
334C2#1495×C13111yescharacteristic
335C2#1512×C13111yescharacteristic
336C2#1521×C13111yescharacteristic
337C2#1536×C13111yescharacteristic
338C2#1551×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C43×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1839×C131C2semidirect
3. #1831×C131C2semidirect
4. #1272×C131C2semidirect
169. #7716C131direct (N × H)
170. C131#7716direct (N × H)
172. #1839C2×C131semidirect
173. #1831C2×C131semidirect
174. #1272C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2861×C1312
#1839×C1312
#1831×C1312
#1272×C1312
#1270×C1312
#7716131