Finite Group Databasebeta

← C131×#7628 #45693512

Subgroups — C131×#7628 #45693512

Order 33536.

510 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2293×C131C211yesmaximal, characteristic
2#1767×C131C211yesmaximal, characteristic, complemented
3#1745×C131C211yesmaximal, characteristic, complemented
4#1271×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal
6C2×C4×D4×C131C411yescharacteristic
7C2×#117×C131—21no—
8C2×C4⋊C8×C131—21no—
9C2×#97×C131—21no—
10C2×#97×C131—21no—
11#390×C131C411yescharacteristic
12#390×C131C2211yescharacteristic
13#389×C131C411yescharacteristic
14#389×C131C2211yescharacteristic
15#388×C131—21no—
16#388×C131—21no—
17C4×C4⋊C4×C131C411yescharacteristic
18C4×C22⋊C4×C131—21no—
19C43×C131C2211yescharacteristic
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×D4×C131C2×C411yescharacteristic
24C23×C4×C131—21no—
25C22×C8×C131—22no—
26C22×C8×C131—22no—
27C4×D4×C131—22no—
28C4×D4×C131—22no—
29#117×C131—44no—
30C2×C4⋊C4×C131—21no—
31C2×C4⋊C4×C131—21no—
32C2×C4⋊C4×C131C2×C411yescharacteristic
33C2×C4⋊C4×C131C2×C411yescharacteristic
34C2×C4⋊C4×C131C2×C411yescharacteristic
35C2×C22⋊C4×C131—21no—
36C2×C22⋊C4×C131—21no—
37C2×C22⋊C4×C131—21no—
38C2×C22⋊C4×C131—21no—
39C2×C22⋊C4×C131—21no—
40C2×C42×C131—21no—
41C2×C42×C131C2×C411yescharacteristic
42C2×C42×C131C2×C411yescharacteristic
43C2×C42×C131D411yescharacteristic
44C2×C42×C131D411yescharacteristic
45C2×C42×C131D411yescharacteristic
46C2×C42×C131D411yescharacteristic
47C2×C42×C131C2311yescharacteristic
48C4⋊C8×C131—24no—
49#97×C131—24no—
50#97×C131—42no—
51#95×C131—21no—
52#95×C131—21no—
53#95×C131—21no—
54C24×C131—21no—
55C2×D4×C131—21no—
56C2×D4×C131—41no—
57C2×D4×C131—41no—
58C2×D4×C131M1612yes—
59C22×C4×C131—24no—
60C22×C4×C131—21no—
61C22×C4×C131—21no—
62C22×C4×C131—21no—
63C22×C4×C131—42no—
64C22×C4×C131—42no—
65C22×C4×C131C22⋊C411yescharacteristic
66C22×C4×C131C22⋊C411yescharacteristic
67C22×C4×C131C22⋊C411yescharacteristic
68C22×C4×C131C22⋊C411yescharacteristic
69C22×C4×C131C22×C411yescharacteristic
70C22×C4×C131C2×D411yescharacteristic
71C22×C4×C131C2×D411yescharacteristic
72C2×C8×C131—24no—
73C2×C8×C131—24no—
74C2×C8×C131—42no—
75C2×C8×C131—42no—
76C2×C8×C131—42no—
77C2×C8×C131—42no—
78C4⋊C4×C131—21no—
79C4⋊C4×C131—41no—
80C4⋊C4×C131—41no—
81C4⋊C4×C131—42no—
82C4⋊C4×C131—42no—
83C4⋊C4×C131M1612yes—
84C22⋊C4×C131—24no—
85C22⋊C4×C131—42no—
86C22⋊C4×C131—42no—
87C22⋊C4×C131—41no—
88C22⋊C4×C131—42no—
89C22⋊C4×C131—41no—
90C42×C131—22no—
91C42×C131—22no—
92C42×C131—21no—
93C42×C131—21no—
94C42×C131—21no—
95C42×C131—22no—
96C42×C131—21no—
97C42×C131—41no—
98C42×C131—41no—
99C42×C131—42no—
100C23×C131—22no—
101C23×C131—41no—
102C23×C131—41no—
103C23×C131—41no—
104C23×C131—41no—
105C23×C131—41no—
106C23×C131—41no—
107C23×C131C2×C22⋊C411yescharacteristic
108D4×C131—42no—
109D4×C131—42no—
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—21no—
121C2×C4×C131—22no—
122C2×C4×C131—21no—
123C2×C4×C131—21no—
124C2×C4×C131—21no—
125C2×C4×C131—21no—
126C2×C4×C131—21no—
127C2×C4×C131—48no—
128C2×C4×C131—41no—
129C2×C4×C131—41no—
130C2×C4×C131—41no—
131C2×C4×C131—41no—
132C2×C4×C131—41no—
133C2×C4×C131—41no—
134C2×C4×C131—41no—
135C2×C4×C131—41no—
136C2×C4×C131#10412yes—
137C2×C4×C131#10412yes—
138C2×C4×C131C2×M1611yescharacteristic
139C2×C4×C131C2×M1611yescharacteristic
140C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C131AGL(1,ℤ/8)12yes—
142C2×C4×C131#13711yescharacteristic
143C8×C131—44no—
144C8×C131—44no—
145C22×C131—42no—
146C22×C131—42no—
147C22×C131—42no—
148C22×C131—81no—
149C22×C131—81no—
150C22×C131—81no—
151C22×C131—81no—
152C22×C131#40711yescharacteristic
153C22×C131#41011yescharacteristic
154C22×C131#41311yescharacteristic
155C22×C131#41711yescharacteristic
156C22×C131#41811yescharacteristic
157C22×C131C2×#10411yescharacteristic
158C22×C131C2×#10411yescharacteristic
159C4×C131—21no—
160C4×C131—21no—
161C4×C131—22no—
162C4×C131—22no—
163C4×C131—21no—
164C4×C131—21no—
165C4×C131—22no—
166C4×C131—41no—
167C4×C131—41no—
168C4×C131—42no—
169C4×C131—81no—
170C4×C131—81no—
171C2×C131—82no—
172C2×C131#146411yescharacteristic
173C2×C131#148911yescharacteristic
174C2×C131#149011yescharacteristic
175C2×C131#150511yescharacteristic
176C2×C131#150911yescharacteristic
177C2×C131#152411yescharacteristic
178C2×C131#155711yescharacteristic
179#7628C13111yesmaximal, characteristic, direct product factor, Sylow
180C131#762811yescharacteristic, direct product factor, Sylow
181#2293C2×C13111yescharacteristic
182#1767C2×C13111yescharacteristic, complemented
183#1745C2×C13111yescharacteristic, complemented
184#1271C2×C13112yescomplemented
185#1270C2×C13112yes—
186C2×C4×D4C4×C13111yescharacteristic
187C2×#117—21no—
188C2×C4⋊C8—21no—
189C2×#97—21no—
190C2×#97—21no—
191#390C4×C13111yescharacteristic
192#390C22×C13111yescharacteristic
193#389C4×C13111yescharacteristic
194#389C22×C13111yescharacteristic
195#388—21no—
196#388—21no—
197C4×C4⋊C4C4×C13111yescharacteristic
198C4×C22⋊C4—21no—
199C43C22×C13111yescharacteristic
200#336—21no—
201#336C22×C13112yes—
202#336C22×C13112yes—
203C22×D4C2×C4×C13111yescharacteristic
204C23×C4—21no—
205C22×C8—22no—
206C22×C8—22no—
207C4×D4—22no—
208C4×D4—22no—
209#117—44no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C2×C4×C13111yescharacteristic
213C2×C4⋊C4C2×C4×C13111yescharacteristic
214C2×C4⋊C4C2×C4×C13111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C42—21no—
221C2×C42C2×C4×C13111yescharacteristic
222C2×C42C2×C4×C13111yescharacteristic
223C2×C42D4×C13111yescharacteristic
224C2×C42D4×C13111yescharacteristic
225C2×C42D4×C13111yescharacteristic
226C2×C42D4×C13111yescharacteristic
227C2×C42C23×C13111yescharacteristic
228C4⋊C8—24no—
229#97—24no—
230#97—42no—
231#95—21no—
232#95—21no—
233#95—21no—
234C24—21no—
235C2×D4—21no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4M16×C13112yes—
239C22×C4—24no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4C22⋊C4×C13111yescharacteristic
246C22×C4C22⋊C4×C13111yescharacteristic
247C22×C4C22⋊C4×C13111yescharacteristic
248C22×C4C22⋊C4×C13111yescharacteristic
249C22×C4C22×C4×C13111yescharacteristic
250C22×C4C2×D4×C13111yescharacteristic
251C22×C4C2×D4×C13111yescharacteristic
252C2×C8—24no—
253C2×C8—24no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4M16×C13112yes—
264C22⋊C4—24no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—41no—
270C42—22no—
271C42—22no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—22no—
276C42—21no—
277C42—41no—
278C42—41no—
279C42—42no—
280C23—22no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23C2×C22⋊C4×C13111yescharacteristic
288D4—42no—
289D4—42no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—48no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4#104×C13112yes—
317C2×C4#104×C13112yes—
318C2×C4C2×M16×C13111yescharacteristic
319C2×C4C2×M16×C13111yescharacteristic
320C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
321C2×C4AGL(1,ℤ/8)×C13112yes—
322C2×C4#137×C13111yescharacteristic
323C8—44no—
324C8—44no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22#407×C13111yescharacteristic
333C22#410×C13111yescharacteristic
334C22#413×C13111yescharacteristic
335C22#417×C13111yescharacteristic
336C22#418×C13111yescharacteristic
337C22C2×#104×C13111yescharacteristic
338C22C2×#104×C13111yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—22no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—41no—
347C4—42no—
348C4—41no—
349C4—81no—
350C4—81no—
351C2—82no—
352C2#1464×C13111yescharacteristic
353C2#1489×C13111yescharacteristic
354C2#1490×C13111yescharacteristic
355C2#1505×C13111yescharacteristic
356C2#1509×C13111yescharacteristic
357C2#1524×C13111yescharacteristic
358C2#1557×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. #1767×C131C2semidirect
3. #1745×C131C2semidirect
4. #1271×C131C2semidirect
179. #7628C131direct (N × H)
180. C131#7628direct (N × H)
182. #1767C2×C131semidirect
183. #1745C2×C131semidirect
184. #1271C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2293×C1312
#1767×C1312
#1745×C1312
#1271×C1312
#1270×C1312
#7628131