Finite Group Databasebeta

← C131×#7698 #45693582

Subgroups — C131×#7698 #45693582

Order 33536.

532 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854×C131C211yesmaximal, characteristic
2#1797×C131C211yesmaximal, characteristic, complemented
3#1749×C131C211yesmaximal, characteristic, complemented
4#1271×C131C212yesmaximal, complemented
5#1270×C131C212yesmaximal, complemented
6C2×#123×C131—21no—
7C2×#121×C131C411yescharacteristic
8C22×C42×C131C2211yescharacteristic
9C2×C4⋊C8×C131—21no—
10C2×C22⋊C8×C131—21no—
11C2×C22⋊C8×C131—21no—
12C2×#97×C131—21no—
13#390×C131C411yescharacteristic
14#390×C131C2211yescharacteristic
15#389×C131C411yescharacteristic
16#389×C131C2211yescharacteristic
17#388×C131—21no—
18#388×C131—21no—
19#386×C131—21no—
20#380×C131C411yescharacteristic
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×D4×C131—21no—
24C22×D4×C131C2×C411yescharacteristic
25C23×C4×C131C2×C411yescharacteristic
26C23×C4×C131D411yescharacteristic
27C23×C4×C131D411yescharacteristic
28C22×C8×C131—22no—
29C22×C8×C131—22no—
30#123×C131—44no—
31#121×C131—42no—
32C2×C4⋊C4×C131—21no—
33C2×C4⋊C4×C131—21no—
34C2×C4⋊C4×C131C2×C411yescharacteristic
35C2×C4⋊C4×C131C2×C411yescharacteristic
36C2×C4⋊C4×C131C2×C411yescharacteristic
37C2×C22⋊C4×C131—21no—
38C2×C22⋊C4×C131—21no—
39C2×C22⋊C4×C131—21no—
40C2×C22⋊C4×C131—21no—
41C2×C22⋊C4×C131—21no—
42C2×C22⋊C4×C131—21no—
43C2×C42×C131—42no—
44C2×C42×C131C2×C411yescharacteristic
45C2×C42×C131D411yescharacteristic
46C2×C42×C131D411yescharacteristic
47C2×C42×C131C2311yescharacteristic
48C4⋊C8×C131—42no—
49C22⋊C8×C131—24no—
50C22⋊C8×C131—42no—
51#97×C131—42no—
52#95×C131—21no—
53#95×C131—21no—
54#95×C131—21no—
55C24×C131—21no—
56C24×C131C22⋊C411yescharacteristic
57C2×D4×C131—22no—
58C2×D4×C131—41no—
59C2×D4×C131—41no—
60C2×D4×C131—42no—
61C2×D4×C131—42no—
62C2×D4×C131—42no—
63C22×C4×C131—22no—
64C22×C4×C131—22no—
65C22×C4×C131—22no—
66C22×C4×C131—21no—
67C22×C4×C131—22no—
68C22×C4×C131—21no—
69C22×C4×C131—21no—
70C22×C4×C131—21no—
71C22×C4×C131—21no—
72C22×C4×C131—41no—
73C22×C4×C131—41no—
74C22×C4×C131—41no—
75C22×C4×C131—41no—
76C22×C4×C131C22⋊C411yescharacteristic
77C22×C4×C131C22⋊C411yescharacteristic
78C22×C4×C131C22⋊C411yescharacteristic
79C22×C4×C131C22×C411yescharacteristic
80C22×C4×C131C2×D411yescharacteristic
81C22×C4×C131C2×D411yescharacteristic
82C2×C8×C131—24no—
83C2×C8×C131—42no—
84C2×C8×C131—42no—
85C2×C8×C131—42no—
86C2×C8×C131—42no—
87C2×C8×C131—42no—
88C4⋊C4×C131—22no—
89C4⋊C4×C131—41no—
90C4⋊C4×C131—41no—
91C4⋊C4×C131—42no—
92C4⋊C4×C131—42no—
93C22⋊C4×C131—42no—
94C22⋊C4×C131—42no—
95C22⋊C4×C131—42no—
96C22⋊C4×C131—42no—
97C22⋊C4×C131—41no—
98C22⋊C4×C131—42no—
99C22⋊C4×C131—41no—
100C42×C131—22no—
101C42×C131—22no—
102C42×C131—41no—
103C42×C131—41no—
104C23×C131—21no—
105C23×C131—21no—
106C23×C131—21no—
107C23×C131—21no—
108C23×C131—21no—
109C23×C131—21no—
110C23×C131—41no—
111C23×C131—41no—
112C23×C131—41no—
113C23×C131—41no—
114C23×C131—41no—
115C23×C131—41no—
116C23×C131—41no—
117C23×C131#10412yes—
118C23×C131C2×C22⋊C411yescharacteristic
119D4×C131—82no—
120D4×C131—84no—
121C2×C4×C131—21no—
122C2×C4×C131—21no—
123C2×C4×C131—21no—
124C2×C4×C131—21no—
125C2×C4×C131—21no—
126C2×C4×C131—21no—
127C2×C4×C131—21no—
128C2×C4×C131—21no—
129C2×C4×C131—21no—
130C2×C4×C131—21no—
131C2×C4×C131—21no—
132C2×C4×C131—21no—
133C2×C4×C131—21no—
134C2×C4×C131—21no—
135C2×C4×C131—44no—
136C2×C4×C131—44no—
137C2×C4×C131—42no—
138C2×C4×C131—42no—
139C2×C4×C131—41no—
140C2×C4×C131—41no—
141C2×C4×C131—41no—
142C2×C4×C131—41no—
143C2×C4×C131—41no—
144C2×C4×C131—41no—
145C2×C4×C131—41no—
146C2×C4×C131—41no—
147C2×C4×C131—41no—
148C2×C4×C131#9912yes—
149C2×C4×C131#13112yes—
150C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C131AGL(1,ℤ/8)12yes—
152C2×C4×C131#13711yescharacteristic
153C8×C131—44no—
154C8×C131—82no—
155C22×C131—22no—
156C22×C131—22no—
157C22×C131—22no—
158C22×C131—41no—
159C22×C131—41no—
160C22×C131—41no—
161C22×C131—41no—
162C22×C131—81no—
163C22×C131—81no—
164C22×C131—81no—
165C22×C131—81no—
166C22×C131—81no—
167C22×C131—81no—
168C22×C131—81no—
169C22×C131#40811yescharacteristic
170C22×C131C2×#9911yescharacteristic
171C22×C131#41311yescharacteristic
172C22×C131#41711yescharacteristic
173C22×C131#41811yescharacteristic
174C22×C131C2×#10411yescharacteristic
175C22×C131#42111yescharacteristic
176C4×C131—22no—
177C4×C131—22no—
178C4×C131—22no—
179C4×C131—21no—
180C4×C131—21no—
181C4×C131—41no—
182C4×C131—41no—
183C4×C131—81no—
184C4×C131—81no—
185C4×C131—81no—
186C2×C131—42no—
187C2×C131—161no—
188C2×C131#146811yescharacteristic
189C2×C131#148311yescharacteristic
190C2×C131#149611yescharacteristic
191C2×C131#150711yescharacteristic
192C2×C131#151311yescharacteristic
193C2×C131#153211yescharacteristic
194C2×C131#155711yescharacteristic
195#7698C13111yesmaximal, characteristic, direct product factor, Sylow
196C131#769811yescharacteristic, direct product factor, Sylow
197#2854C2×C13111yescharacteristic
198#1797C2×C13111yescharacteristic, complemented
199#1749C2×C13111yescharacteristic, complemented
200#1271C2×C13112yescomplemented
201#1270C2×C13112yescomplemented
202C2×#123—21no—
203C2×#121C4×C13111yescharacteristic
204C22×C42C22×C13111yescharacteristic
205C2×C4⋊C8—21no—
206C2×C22⋊C8—21no—
207C2×C22⋊C8—21no—
208C2×#97—21no—
209#390C4×C13111yescharacteristic
210#390C22×C13111yescharacteristic
211#389C4×C13111yescharacteristic
212#389C22×C13111yescharacteristic
213#388—21no—
214#388—21no—
215#386—21no—
216#380C4×C13111yescharacteristic
217#336C22×C13112yes—
218#336C22×C13112yes—
219C22×D4—21no—
220C22×D4C2×C4×C13111yescharacteristic
221C23×C4C2×C4×C13111yescharacteristic
222C23×C4D4×C13111yescharacteristic
223C23×C4D4×C13111yescharacteristic
224C22×C8—22no—
225C22×C8—22no—
226#123—44no—
227#121—42no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C2×C4×C13111yescharacteristic
231C2×C4⋊C4C2×C4×C13111yescharacteristic
232C2×C4⋊C4C2×C4×C13111yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C42—42no—
240C2×C42C2×C4×C13111yescharacteristic
241C2×C42D4×C13111yescharacteristic
242C2×C42D4×C13111yescharacteristic
243C2×C42C23×C13111yescharacteristic
244C4⋊C8—42no—
245C22⋊C8—24no—
246C22⋊C8—42no—
247#97—42no—
248#95—21no—
249#95—21no—
250#95—21no—
251C24—21no—
252C24C22⋊C4×C13111yescharacteristic
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—42no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C22⋊C4×C13111yescharacteristic
273C22×C4C22⋊C4×C13111yescharacteristic
274C22×C4C22⋊C4×C13111yescharacteristic
275C22×C4C22×C4×C13111yescharacteristic
276C22×C4C2×D4×C13111yescharacteristic
277C22×C4C2×D4×C13111yescharacteristic
278C2×C8—24no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—42no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—41no—
296C42—22no—
297C42—22no—
298C42—41no—
299C42—41no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#104×C13112yes—
314C23C2×C22⋊C4×C13111yescharacteristic
315D4—82no—
316D4—84no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4#99×C13112yes—
345C2×C4#131×C13112yes—
346C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
347C2×C4AGL(1,ℤ/8)×C13112yes—
348C2×C4#137×C13111yescharacteristic
349C8—44no—
350C8—82no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22#408×C13111yescharacteristic
366C22C2×#99×C13111yescharacteristic
367C22#413×C13111yescharacteristic
368C22#417×C13111yescharacteristic
369C22#418×C13111yescharacteristic
370C22C2×#104×C13111yescharacteristic
371C22#421×C13111yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C2—42no—
383C2—161no—
384C2#1468×C13111yescharacteristic
385C2#1483×C13111yescharacteristic
386C2#1496×C13111yescharacteristic
387C2#1507×C13111yescharacteristic
388C2#1513×C13111yescharacteristic
389C2#1532×C13111yescharacteristic
390C2#1557×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC2×#121×C131C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1797×C131C2semidirect
3. #1749×C131C2semidirect
4. #1271×C131C2semidirect
5. #1270×C131C2semidirect
195. #7698C131direct (N × H)
196. C131#7698direct (N × H)
198. #1797C2×C131semidirect
199. #1749C2×C131semidirect
200. #1271C2×C131semidirect
201. #1270C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2854×C1312
#1797×C1312
#1749×C1312
#1271×C1312
#1270×C1312
#7698131