Finite Group Databasebeta

← C131×#12268 #45698152

Subgroups — C131×#12268 #45698152

Order 33536.

458 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 70 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#2735×C131C211yesmaximal, characteristic
2#2029×C131C211yesmaximal, characteristic
3#1614×C131C211yesmaximal, characteristic, complemented
4#1608×C131C211yesmaximal, characteristic, complemented
5#1352×C131C211yesmaximal, characteristic, complemented
6#1344×C131C211yesmaximal, characteristic, complemented
7#1316×C131C211yesmaximal, characteristic
8#543×C131C2211yescharacteristic
9#484×C131—21no—
10#483×C131—21no—
11#399×C131C2211yescharacteristic
12#397×C131—21no—
13#397×C131C2211yescharacteristic
14#396×C131—21no—
15#388×C131—21no—
16#388×C131—21no—
17#388×C131—21no—
18#379×C131—21no—
19#379×C131—21no—
20#379×C131C2211yescharacteristic
21#342×C131—21no—
22#342×C131C2211yescharacteristic
23#328×C131—21no—
24#328×C131—21no—
25#323×C131C2211yescharacteristic
26#323×C131C2211yescharacteristic
27C25×C131D411yescharacteristic
28C22⋊Q8×C131—21no—
29C22⋊Q8×C131—21no—
30C22⋊Q8×C131—41no—
31C22⋊Q8×C131—41no—
32C2×C4⋊C4×C131—21no—
33C2×C4⋊C4×C131—21no—
34C2×C4⋊C4×C131D411yescharacteristic
35C2×C4⋊C4×C131D411yescharacteristic
36C2×C22⋊C4×C131—21no—
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×C22⋊C4×C131—21no—
44C2×C22⋊C4×C131—21no—
45C2×C22⋊C4×C131—21no—
46C2×C22⋊C4×C131—41no—
47C2×C22⋊C4×C131—41no—
48C2×C22⋊C4×C131D411yescharacteristic
49C2×C22⋊C4×C131C2311yescharacteristic
50C2×C42×C131—21no—
51#107×C131—41no—
52#106×C131—41no—
53#103×C131—41no—
54#103×C131—41no—
55C22⋊C8×C131—21no—
56C22⋊C8×C131—21no—
57#95×C131—21no—
58#95×C131—21no—
59#95×C131—21no—
60#95×C131D411yescharacteristic
61#95×C131D411yescharacteristic
62C24×C131—21no—
63C24×C131—21no—
64C24×C131—21no—
65C24×C131—41no—
66C24×C131—41no—
67C24×C131—42no—
68C24×C131—81no—
69C24×C131C2×D411yescharacteristic
70C2×Q8×C131—21no—
71C2×Q8×C131—21no—
72C22×C4×C131—21no—
73C22×C4×C131—21no—
74C22×C4×C131—21no—
75C22×C4×C131—21no—
76C22×C4×C131—21no—
77C22×C4×C131—21no—
78C22×C4×C131—21no—
79C22×C4×C131—41no—
80C22×C4×C131C2×D411yescharacteristic
81C22×C4×C131C2×D411yescharacteristic
82C2×C8×C131—41no—
83C2×C8×C131—41no—
84C4⋊C4×C131—21no—
85C4⋊C4×C131—21no—
86C4⋊C4×C131—41no—
87C4⋊C4×C131—41no—
88C4⋊C4×C131—41no—
89C4⋊C4×C131—41no—
90C4⋊C4×C131—81no—
91C4⋊C4×C131—81no—
92C22⋊C4×C131—41no—
93C22⋊C4×C131—42no—
94C22⋊C4×C131—42no—
95C22⋊C4×C131—41no—
96C22⋊C4×C131—41no—
97C22⋊C4×C131—41no—
98C22⋊C4×C131—41no—
99C22⋊C4×C131—41no—
100C22⋊C4×C131—41no—
101C22⋊C4×C131—41no—
102C22⋊C4×C131—81no—
103C22⋊C4×C131—81no—
104C22⋊C4×C131—81no—
105C22⋊C4×C131—81no—
106C22⋊C4×C131—81no—
107C22⋊C4×C131—82no—
108C22⋊C4×C131—82no—
109C42×C131—81no—
110C23×C131—21no—
111C23×C131—21no—
112C23×C131—22no—
113C23×C131—41no—
114C23×C131—41no—
115C23×C131—41no—
116C23×C131—41no—
117C23×C131—41no—
118C23×C131—42no—
119C23×C131—42no—
120C23×C131—42no—
121C23×C131—41no—
122C23×C131—41no—
123C23×C131—41no—
124C23×C131—81no—
125C23×C131—82no—
126C23×C131—81no—
127C23×C131—82no—
128C23×C131—84no—
129C23×C131—81no—
130C23×C131#12011yescharacteristic
131C23×C131#13511yescharacteristic
132C23×C131#13711yescharacteristic
133Q8×C131—81no—
134Q8×C131—81no—
135C2×C4×C131—21no—
136C2×C4×C131—21no—
137C2×C4×C131—41no—
138C2×C4×C131—41no—
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—41no—
149C2×C4×C131—41no—
150C2×C4×C131—41no—
151C2×C4×C131—41no—
152C2×C4×C131—41no—
153C2×C4×C131—41no—
154C2×C4×C131—41no—
155C2×C4×C131—41no—
156C2×C4×C131—81no—
157C2×C4×C131—81no—
158C2×C4×C131—81no—
159C2×C4×C131—81no—
160C2×C4×C131—81no—
161C8×C131—81no—
162C8×C131—81no—
163C22×C131—21no—
164C22×C131—21no—
165C22×C131—21no—
166C22×C131—21no—
167C22×C131—41no—
168C22×C131—41no—
169C22×C131—42no—
170C22×C131—42no—
171C22×C131—41no—
172C22×C131—41no—
173C22×C131—44no—
174C22×C131—42no—
175C22×C131—81no—
176C22×C131—81no—
177C22×C131—81no—
178C22×C131—82no—
179C22×C131—82no—
180C22×C131—82no—
181C22×C131—81no—
182C22×C131—81no—
183C22×C131#45211yescharacteristic
184C22×C131#45511yescharacteristic
185C22×C131B(4,𝔽2)11yescharacteristic
186C4×C131—41no—
187C4×C131—41no—
188C4×C131—81no—
189C4×C131—81no—
190C4×C131—81no—
191C4×C131—81no—
192C4×C131—81no—
193C4×C131—81no—
194C4×C131—81no—
195C4×C131—161no—
196C2×C131—21no—
197C2×C131—21no—
198C2×C131—41no—
199C2×C131—41no—
200C2×C131—82no—
201C2×C131#160611yescharacteristic
202C2×C131#219711yescharacteristic
203C2×C131#220011yescharacteristic
204#12268C13111yesmaximal, characteristic, direct product factor, Sylow
205C131#1226811yescharacteristic, direct product factor, Sylow
206#2735C2×C13111yescharacteristic
207#2029C2×C13111yescharacteristic
208#1614C2×C13111yescharacteristic, complemented
209#1608C2×C13111yescharacteristic, complemented
210#1352C2×C13111yescharacteristic, complemented
211#1344C2×C13111yescharacteristic, complemented
212#1316C2×C13111yescharacteristic
213#543C22×C13111yescharacteristic
214#484—21no—
215#483—21no—
216#399C22×C13111yescharacteristic
217#397—21no—
218#397C22×C13111yescharacteristic
219#396—21no—
220#388—21no—
221#388—21no—
222#388—21no—
223#379—21no—
224#379—21no—
225#379C22×C13111yescharacteristic
226#342—21no—
227#342C22×C13111yescharacteristic
228#328—21no—
229#328—21no—
230#323C22×C13111yescharacteristic
231#323C22×C13111yescharacteristic
232C25D4×C13111yescharacteristic
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—41no—
236C22⋊Q8—41no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C13111yescharacteristic
240C2×C4⋊C4D4×C13111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—41no—
252C2×C22⋊C4—41no—
253C2×C22⋊C4D4×C13111yescharacteristic
254C2×C22⋊C4C23×C13111yescharacteristic
255C2×C42—21no—
256#107—41no—
257#106—41no—
258#103—41no—
259#103—41no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95D4×C13111yescharacteristic
266#95D4×C13111yescharacteristic
267C24—21no—
268C24—21no—
269C24—21no—
270C24—41no—
271C24—41no—
272C24—42no—
273C24—81no—
274C24C2×D4×C13111yescharacteristic
275C2×Q8—21no—
276C2×Q8—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4C2×D4×C13111yescharacteristic
286C22×C4C2×D4×C13111yescharacteristic
287C2×C8—41no—
288C2×C8—41no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—81no—
296C4⋊C4—81no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C22⋊C4—82no—
313C22⋊C4—82no—
314C42—81no—
315C23—21no—
316C23—21no—
317C23—22no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—81no—
330C23—82no—
331C23—81no—
332C23—82no—
333C23—84no—
334C23—81no—
335C23#120×C13111yescharacteristic
336C23#135×C13111yescharacteristic
337C23#137×C13111yescharacteristic
338Q8—81no—
339Q8—81no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C8—81no—
367C8—81no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—42no—
376C22—41no—
377C22—41no—
378C22—44no—
379C22—42no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22#452×C13111yescharacteristic
389C22#455×C13111yescharacteristic
390C22B(4,𝔽2)×C13111yescharacteristic
391C4—41no—
392C4—41no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—81no—
399C4—81no—
400C4—161no—
401C2—21no—
402C2—21no—
403C2—41no—
404C2—41no—
405C2—82no—
406C2#1606×C13111yescharacteristic
407C2#2197×C13111yescharacteristic
408C2#2200×C13111yescharacteristic
subgroupG/H
center, socleC22×C131B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C131
prime radicalC25×C131D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C2×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1614×C131C2semidirect
4. #1608×C131C2semidirect
5. #1352×C131C2semidirect
6. #1344×C131C2semidirect
204. #12268C131direct (N × H)
205. C131#12268direct (N × H)
208. #1614C2×C131semidirect
209. #1608C2×C131semidirect
210. #1352C2×C131semidirect
211. #1344C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2735×C1312
#2029×C1312
#1614×C1312
#1608×C1312
#1352×C1312
#1344×C1312
#1316×C1312
#12268131