Finite Group Databasebeta

← C131×#7726 #45693610

Subgroups — C131×#7726 #45693610

Order 33536.

400 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2860×C131C211yesmaximal, characteristic
2#1839×C131C211yesmaximal, characteristic, complemented
3#1839×C131C211yesmaximal, characteristic, complemented
4#1271×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal
6C2×#126×C131—21no—
7#390×C131C411yescharacteristic
8#390×C131C411yescharacteristic
9#390×C131C2211yescharacteristic
10#389×C131C411yescharacteristic
11#389×C131C411yescharacteristic
12#389×C131C2211yescharacteristic
13#388×C131—21no—
14#388×C131—21no—
15#388×C131—21no—
16C43×C131C2211yescharacteristic
17#336×C131—21no—
18#336×C131—21no—
19#336×C131—21no—
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×D4×C131C2×C411yescharacteristic
24C22×C8×C131—22no—
25C22×C8×C131—22no—
26#126×C131—44no—
27C2×C4⋊C4×C131—21no—
28C2×C4⋊C4×C131—21no—
29C2×C4⋊C4×C131—21no—
30C2×C4⋊C4×C131C2×C411yescharacteristic
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
46#95×C131—21no—
47#95×C131—21no—
48#95×C131—21no—
49C24×C131—21no—
50C2×D4×C131—22no—
51C2×D4×C131—41no—
52C2×D4×C131—41no—
53C22×C4×C131—21no—
54C22×C4×C131—21no—
55C22×C4×C131—21no—
56C22×C4×C131C22⋊C411yescharacteristic
57C22×C4×C131C22⋊C411yescharacteristic
58C22×C4×C131C22⋊C411yescharacteristic
59C22×C4×C131C22⋊C411yescharacteristic
60C22×C4×C131C22×C411yescharacteristic
61C22×C4×C131C2×D411yescharacteristic
62C22×C4×C131C2×D411yescharacteristic
63C2×C8×C131—42no—
64C2×C8×C131—42no—
65C2×C8×C131—42no—
66C2×C8×C131—42no—
67C2×C8×C131—42no—
68C2×C8×C131—42no—
69C4⋊C4×C131—22no—
70C4⋊C4×C131—41no—
71C4⋊C4×C131—41no—
72C4⋊C4×C131—42no—
73C4⋊C4×C131—42no—
74C4⋊C4×C131—42no—
75C22⋊C4×C131—42no—
76C22⋊C4×C131—42no—
77C22⋊C4×C131—42no—
78C22⋊C4×C131—42no—
79C22⋊C4×C131—42no—
80C22⋊C4×C131—42no—
81C42×C131—22no—
82C42×C131—22no—
83C42×C131—22no—
84C42×C131—41no—
85C42×C131—41no—
86C42×C131—41no—
87C42×C131—41no—
88C23×C131—41no—
89C23×C131—41no—
90C23×C131—41no—
91C23×C131—41no—
92C23×C131—41no—
93C23×C131—41no—
94C23×C131—41no—
95C23×C131C2×C22⋊C411yescharacteristic
96D4×C131—82no—
97C2×C4×C131—21no—
98C2×C4×C131—21no—
99C2×C4×C131—21no—
100C2×C4×C131—21no—
101C2×C4×C131—21no—
102C2×C4×C131—21no—
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—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#13112yes—
125C2×C4×C131#13512yes—
126C2×C4×C131AGL(1,ℤ/8)12yes—
127C8×C131—82no—
128C8×C131—82no—
129C22×C131—81no—
130C22×C131—81no—
131C22×C131—81no—
132C22×C131—81no—
133C22×C131—81no—
134C22×C131—81no—
135C22×C131—81no—
136C22×C131#40811yescharacteristic
137C22×C131#41011yescharacteristic
138C22×C131#41311yescharacteristic
139C22×C131#41611yescharacteristic
140C22×C131#41811yescharacteristic
141C22×C131#42111yescharacteristic
142C22×C131#42111yescharacteristic
143C4×C131—22no—
144C4×C131—22no—
145C4×C131—22no—
146C4×C131—41no—
147C4×C131—41no—
148C4×C131—41no—
149C4×C131—41no—
150C4×C131—81no—
151C4×C131—81no—
152C4×C131—81no—
153C2×C131—161no—
154C2×C131#147311yescharacteristic
155C2×C131#148211yescharacteristic
156C2×C131#149611yescharacteristic
157C2×C131#151411yescharacteristic
158C2×C131#152111yescharacteristic
159C2×C131#153511yescharacteristic
160C2×C131#155311yescharacteristic
161#7726C13111yesmaximal, characteristic, direct product factor, Sylow
162C131#772611yescharacteristic, direct product factor, Sylow
163#2860C2×C13111yescharacteristic
164#1839C2×C13111yescharacteristic, complemented
165#1839C2×C13111yescharacteristic, complemented
166#1271C2×C13112yescomplemented
167#1270C2×C13112yes—
168C2×#126—21no—
169#390C4×C13111yescharacteristic
170#390C4×C13111yescharacteristic
171#390C22×C13111yescharacteristic
172#389C4×C13111yescharacteristic
173#389C4×C13111yescharacteristic
174#389C22×C13111yescharacteristic
175#388—21no—
176#388—21no—
177#388—21no—
178C43C22×C13111yescharacteristic
179#336—21no—
180#336—21no—
181#336—21no—
182#336—21no—
183#336C22×C13112yes—
184#336C22×C13112yes—
185C22×D4C2×C4×C13111yescharacteristic
186C22×C8—22no—
187C22×C8—22no—
188#126—44no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×C4×C13111yescharacteristic
193C2×C4⋊C4C2×C4×C13111yescharacteristic
194C2×C4⋊C4C2×C4×C13111yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C42C2×C4×C13111yescharacteristic
202C2×C42C2×C4×C13111yescharacteristic
203C2×C42D4×C13111yescharacteristic
204C2×C42D4×C13111yescharacteristic
205C2×C42D4×C13111yescharacteristic
206C2×C42D4×C13111yescharacteristic
207C2×C42C23×C13111yescharacteristic
208#95—21no—
209#95—21no—
210#95—21no—
211C24—21no—
212C2×D4—22no—
213C2×D4—41no—
214C2×D4—41no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4C22⋊C4×C13111yescharacteristic
219C22×C4C22⋊C4×C13111yescharacteristic
220C22×C4C22⋊C4×C13111yescharacteristic
221C22×C4C22⋊C4×C13111yescharacteristic
222C22×C4C22×C4×C13111yescharacteristic
223C22×C4C2×D4×C13111yescharacteristic
224C22×C4C2×D4×C13111yescharacteristic
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C4⋊C4—22no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C42—22no—
244C42—22no—
245C42—22no—
246C42—41no—
247C42—41no—
248C42—41no—
249C42—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23C2×C22⋊C4×C13111yescharacteristic
258D4—82no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4#131×C13112yes—
287C2×C4#135×C13112yes—
288C2×C4AGL(1,ℤ/8)×C13112yes—
289C8—82no—
290C8—82no—
291C22—81no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22#408×C13111yescharacteristic
299C22#410×C13111yescharacteristic
300C22#413×C13111yescharacteristic
301C22#416×C13111yescharacteristic
302C22#418×C13111yescharacteristic
303C22#421×C13111yescharacteristic
304C22#421×C13111yescharacteristic
305C4—22no—
306C4—22no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4—81no—
315C2—161no—
316C2#1473×C13111yescharacteristic
317C2#1482×C13111yescharacteristic
318C2#1496×C13111yescharacteristic
319C2#1514×C13111yescharacteristic
320C2#1521×C13111yescharacteristic
321C2#1535×C13111yescharacteristic
322C2#1553×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. #1839×C131C2semidirect
4. #1271×C131C2semidirect
161. #7726C131direct (N × H)
162. C131#7726direct (N × H)
164. #1839C2×C131semidirect
165. #1839C2×C131semidirect
166. #1271C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2860×C1312
#1839×C1312
#1271×C1312
#1270×C1312
#7726131