Finite Group Databasebeta

← C131×#9205 #45695089

Subgroups — C131×#9205 #45695089

Order 33536.

690 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 134 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#2617×C131C211yesmaximal, characteristic
2#2312×C131C211yesmaximal, characteristic, complemented
3#1519×C131C212yesmaximal, complemented
4C2×#323×C131C211yesmaximal, characteristic, complemented
5#1289×C131C212yesmaximal, complemented
6C2×#121×C131C2211yescharacteristic
7C2×#120×C131—21no—
8C22×C22⋊C4×C131C2211yescharacteristic
9C2×C22⋊C8×C131C2212yes—
10#397×C131C412yescomplemented
11#394×C131—22no—
12#392×C131C412yescomplemented
13#388×C131—24no—
14#386×C131—21no—
15#380×C131C2211yescharacteristic
16#380×C131C2212yes—
17#379×C131—21no—
18C4×C22⋊C4×C131—21no—
19#327×C131—24no—
20#323×C131—22no—
21C25×C131D411yescharacteristic
22C22×D4×C131—21no—
23C22×D4×C131—22no—
24C22×D4×C131C2×C411yescharacteristic
25C23×C4×C131D411yescharacteristic
26C23×C4×C131C2311yescharacteristic
27C22×C8×C131—22no—
28#121×C131—22no—
29#121×C131—22no—
30#120×C131—44no—
31C2×C4⋊C4×C131—22no—
32C2×C4⋊C4×C131—21no—
33C2×C4⋊C4×C131C2×C411yescharacteristic
34C2×C22⋊C4×C131—22no—
35C2×C22⋊C4×C131—22no—
36C2×C22⋊C4×C131—22no—
37C2×C22⋊C4×C131—21no—
38C2×C22⋊C4×C131—22no—
39C2×C22⋊C4×C131—21no—
40C2×C22⋊C4×C131—22no—
41C2×C22⋊C4×C131—22no—
42C2×C22⋊C4×C131—22no—
43C2×C22⋊C4×C131C2×C412yes—
44C2×C22⋊C4×C131D412yes—
45C2×C42×C131—22no—
46C22⋊C8×C131—22no—
47C22⋊C8×C131—22no—
48#95×C131—22no—
49#95×C131—22no—
50#95×C131C2×C412yes—
51#95×C131D414yescomplemented
52C24×C131—21no—
53C24×C131—21no—
54C24×C131—22no—
55C24×C131—22no—
56C24×C131—21no—
57C24×C131—81no—
58C24×C131—81no—
59C24×C131C22⋊C412yes—
60C24×C131C2×D411yescharacteristic
61C2×D4×C131—22no—
62C2×D4×C131—44no—
63C2×D4×C131—41no—
64C2×D4×C131—41no—
65C2×D4×C131—42no—
66C2×D4×C131—42no—
67C2×D4×C131—82no—
68C2×D4×C131—82no—
69C2×D4×C131—81no—
70C22×C4×C131—21no—
71C22×C4×C131—21no—
72C22×C4×C131—21no—
73C22×C4×C131—22no—
74C22×C4×C131—24no—
75C22×C4×C131—81no—
76C22×C4×C131—81no—
77C22×C4×C131C22⋊C412yes—
78C22×C4×C131C22×C411yescharacteristic
79C22×C4×C131C2×D412yes—
80C22×C4×C131C2×D411yescharacteristic
81C22×C4×C131#4112yes—
82C2×C8×C131—42no—
83C2×C8×C131—82no—
84C4⋊C4×C131—22no—
85C4⋊C4×C131—82no—
86C4⋊C4×C131—81no—
87C22⋊C4×C131—24no—
88C22⋊C4×C131—24no—
89C22⋊C4×C131—44no—
90C22⋊C4×C131—42no—
91C22⋊C4×C131—42no—
92C22⋊C4×C131—42no—
93C22⋊C4×C131—42no—
94C22⋊C4×C131—82no—
95C22⋊C4×C131—82no—
96C22⋊C4×C131—82no—
97C42×C131—82no—
98C23×C131—22no—
99C23×C131—22no—
100C23×C131—22no—
101C23×C131—41no—
102C23×C131—41no—
103C23×C131—42no—
104C23×C131—42no—
105C23×C131—42no—
106C23×C131—42no—
107C23×C131—42no—
108C23×C131—42no—
109C23×C131—42no—
110C23×C131—42no—
111C23×C131—41no—
112C23×C131—41no—
113C23×C131—41no—
114C23×C131—81no—
115C23×C131—81no—
116C23×C131—84no—
117C23×C131—84no—
118C23×C131C2×C22⋊C411yescharacteristic
119C23×C131#12011yescharacteristic
120C23×C131#12311yescharacteristic
121C23×C131#13512yes—
122C23×C131AGL(1,ℤ/8)12yes—
123D4×C131—82no—
124D4×C131—88no—
125D4×C131—82no—
126D4×C131—82no—
127C2×C4×C131—22no—
128C2×C4×C131—41no—
129C2×C4×C131—42no—
130C2×C4×C131—42no—
131C2×C4×C131—41no—
132C2×C4×C131—42no—
133C2×C4×C131—42no—
134C2×C4×C131—44no—
135C2×C4×C131—44no—
136C2×C4×C131—42no—
137C2×C4×C131—42no—
138C2×C4×C131—41no—
139C2×C4×C131—41no—
140C2×C4×C131—42no—
141C2×C4×C131—41no—
142C2×C4×C131—44no—
143C2×C4×C131—81no—
144C2×C4×C131C4×D412yes—
145C2×C4×C131#12112yes—
146C8×C131—82no—
147C22×C131—21no—
148C22×C131—21no—
149C22×C131—21no—
150C22×C131—21no—
151C22×C131—21no—
152C22×C131—21no—
153C22×C131—42no—
154C22×C131—42no—
155C22×C131—44no—
156C22×C131—42no—
157C22×C131—42no—
158C22×C131—42no—
159C22×C131—82no—
160C22×C131—84no—
161C22×C131—84no—
162C22×C131—82no—
163C22×C131—82no—
164C22×C131—81no—
165C22×C131—81no—
166C22×C131—81no—
167C22×C131#38611yescharacteristic
168C22×C131#41611yescharacteristic
169C22×C131#41811yescharacteristic
170C22×C131#44912yes—
171C22×C131#48212yes—
172C4×C131—22no—
173C4×C131—22no—
174C4×C131—42no—
175C4×C131—84no—
176C4×C131—82no—
177C4×C131—81no—
178C2×C131—21no—
179C2×C131—22no—
180C2×C131—21no—
181C2×C131—22no—
182C2×C131—82no—
183C2×C131—161no—
184C2×C131#187511yescharacteristic
185C2×C131#191111yescharacteristic
186C2×C131#191311yescharacteristic
187#9205C13111yesmaximal, characteristic, direct product factor, Sylow
188C131#920511yescharacteristic, direct product factor, Sylow
189#2617C2×C13111yescharacteristic
190#2312C2×C13111yescharacteristic, complemented
191#1519C2×C13112yescomplemented
192C2×#323C2×C13111yescharacteristic, complemented
193#1289C2×C13112yescomplemented
194C2×#121C22×C13111yescharacteristic
195C2×#120—21no—
196C22×C22⋊C4C22×C13111yescharacteristic
197C2×C22⋊C8C22×C13112yes—
198#397C4×C13112yescomplemented
199#394—22no—
200#392C4×C13112yescomplemented
201#388—24no—
202#386—21no—
203#380C22×C13111yescharacteristic
204#380C22×C13112yes—
205#379—21no—
206C4×C22⋊C4—21no—
207#327—24no—
208#323—22no—
209C25D4×C13111yescharacteristic
210C22×D4—21no—
211C22×D4—22no—
212C22×D4C2×C4×C13111yescharacteristic
213C23×C4D4×C13111yescharacteristic
214C23×C4C23×C13111yescharacteristic
215C22×C8—22no—
216#121—22no—
217#121—22no—
218#120—44no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×C4×C13111yescharacteristic
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4C2×C4×C13112yes—
232C2×C22⋊C4D4×C13112yes—
233C2×C42—22no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236#95—22no—
237#95—22no—
238#95C2×C4×C13112yes—
239#95D4×C13114yescomplemented
240C24—21no—
241C24—21no—
242C24—22no—
243C24—22no—
244C24—21no—
245C24—81no—
246C24—81no—
247C24C22⋊C4×C13112yes—
248C24C2×D4×C13111yescharacteristic
249C2×D4—22no—
250C2×D4—44no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—82no—
256C2×D4—82no—
257C2×D4—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4C22⋊C4×C13112yes—
266C22×C4C22×C4×C13111yescharacteristic
267C22×C4C2×D4×C13112yes—
268C22×C4C2×D4×C13111yescharacteristic
269C22×C4#41×C13112yes—
270C2×C8—42no—
271C2×C8—82no—
272C4⋊C4—22no—
273C4⋊C4—82no—
274C4⋊C4—81no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—44no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—82no—
283C22⋊C4—82no—
284C22⋊C4—82no—
285C42—82no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—42no—
297C23—42no—
298C23—42no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—81no—
303C23—81no—
304C23—84no—
305C23—84no—
306C23C2×C22⋊C4×C13111yescharacteristic
307C23#120×C13111yescharacteristic
308C23#123×C13111yescharacteristic
309C23#135×C13112yes—
310C23AGL(1,ℤ/8)×C13112yes—
311D4—82no—
312D4—88no—
313D4—82no—
314D4—82no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—44no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4C4×D4×C13112yes—
333C2×C4#121×C13112yes—
334C8—82no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—42no—
342C22—42no—
343C22—44no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—82no—
348C22—84no—
349C22—84no—
350C22—82no—
351C22—82no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22#386×C13111yescharacteristic
356C22#416×C13111yescharacteristic
357C22#418×C13111yescharacteristic
358C22#449×C13112yes—
359C22#482×C13112yes—
360C4—22no—
361C4—22no—
362C4—42no—
363C4—82no—
364C4—84no—
365C4—81no—
366C2—21no—
367C2—22no—
368C2—21no—
369C2—22no—
370C2—82no—
371C2—161no—
372C2#1875×C13111yescharacteristic
373C2#1911×C13111yescharacteristic
374C2#1913×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radical#2617×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. #2312×C131C2semidirect
3. #1519×C131C2semidirect
4. C2×#323×C131C2semidirect
5. #1289×C131C2semidirect
10. #397×C131C4semidirect
12. #392×C131C4semidirect
51. #95×C131D4semidirect
187. #9205C131direct (N × H)
188. C131#9205direct (N × H)
190. #2312C2×C131semidirect
191. #1519C2×C131semidirect
192. C2×#323C2×C131semidirect
193. #1289C2×C131semidirect
198. #397C4×C131semidirect
200. #392C4×C131semidirect
239. #95D4×C131semidirect

Maximal subgroups

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

subgroupindex
#2617×C1312
#2312×C1312
#1519×C1312
C2×#323×C1312
#1289×C1312
#9205131