Finite Group Databasebeta

← C131×#10384 #45696268

Subgroups — C131×#10384 #45696268

Order 33536.

438 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 90 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#2667×C131C211yesmaximal, characteristic, complemented
2#1964×C131C211yesmaximal, characteristic
3#1510×C131C211yesmaximal, characteristic
4#1507×C131C211yesmaximal, characteristic
5#1305×C131C211yesmaximal, characteristic, complemented
6#1297×C131C211yesmaximal, characteristic, complemented
7#1284×C131C211yesmaximal, characteristic, complemented
8C2×#121×C131C2211yescharacteristic
9C2×#99×C131—21no—
10C2×#99×C131—21no—
11#407×C131C2211yescharacteristic
12#407×C131C2211yescharacteristic
13#399×C131—21no—
14#398×C131—21no—
15#398×C131—21no—
16#396×C131—21no—
17#389×C131—21no—
18#387×C131—21no—
19#381×C131C2211yescharacteristic
20#380×C131C2211yescharacteristic
21C4×C22⋊C4×C131C2211yescharacteristic
22C4×C22⋊C4×C131C2211yescharacteristic
23#327×C131—21no—
24#327×C131—21no—
25#327×C131—21no—
26#327×C131—21no—
27C22×D4×C131—21no—
28C22×D4×C131Q811yescharacteristic
29C23×C4×C131C2311yescharacteristic
30C2×M16×C131—21no—
31C2×M16×C131—21no—
32#121×C131—21no—
33#121×C131—21no—
34#121×C131—21no—
35#121×C131—21no—
36C2×C4⋊C4×C131—21no—
37C2×C4⋊C4×C131—21no—
38C2×C4⋊C4×C131—21no—
39C2×C4⋊C4×C131—21no—
40C2×C4⋊C4×C131—21no—
41C2×C4⋊C4×C131—21no—
42C2×C4⋊C4×C131—21no—
43C2×C4⋊C4×C131Q811yescharacteristic
44C2×C22⋊C4×C131—21no—
45C2×C22⋊C4×C131—21no—
46C2×C22⋊C4×C131—21no—
47C2×C22⋊C4×C131—21no—
48C2×C22⋊C4×C131D411yescharacteristic
49C2×C22⋊C4×C131D411yescharacteristic
50C2×C42×C131—21no—
51C2×C42×C131—21no—
52#99×C131—42no—
53#99×C131—42no—
54C22⋊C8×C131—21no—
55C22⋊C8×C131—21no—
56C22⋊C8×C131—21no—
57C22⋊C8×C131—21no—
58#95×C131—21no—
59#95×C131—21no—
60#95×C131—21no—
61#95×C131—21no—
62#95×C131—21no—
63#95×C131D411yescharacteristic
64#95×C131D411yescharacteristic
65#95×C131D411yescharacteristic
66#95×C131D411yescharacteristic
67C24×C131—21no—
68C24×C131C2×D411yescharacteristic
69C2×D4×C131—21no—
70C2×D4×C131—21no—
71C2×D4×C131—41no—
72C2×D4×C131—41no—
73C2×D4×C131—41no—
74C2×D4×C131—41no—
75C2×D4×C131—41no—
76C2×D4×C131—41no—
77C2×D4×C131—81no—
78C22×C4×C131—21no—
79C22×C4×C131—21no—
80C22×C4×C131—21no—
81C22×C4×C131—21no—
82C22×C4×C131—21no—
83C22×C4×C131—21no—
84C22×C4×C131—21no—
85C22×C4×C131—41no—
86C22×C4×C131—81no—
87C22×C4×C131C2×D411yescharacteristic
88C22×C4×C131C2×D411yescharacteristic
89C22×C4×C131C2×Q811yescharacteristic
90C22×C4×C131#4111yescharacteristic
91C22×C4×C131#4111yescharacteristic
92C22×C4×C131#4111yescharacteristic
93M16×C131—81no—
94M16×C131—81no—
95C2×C8×C131—41no—
96C2×C8×C131—41no—
97C4⋊C4×C131—21no—
98C4⋊C4×C131—21no—
99C4⋊C4×C131—42no—
100C4⋊C4×C131—42no—
101C4⋊C4×C131—81no—
102C4⋊C4×C131—81no—
103C4⋊C4×C131—81no—
104C4⋊C4×C131—81no—
105C4⋊C4×C131—81no—
106C22⋊C4×C131—22no—
107C22⋊C4×C131—42no—
108C22⋊C4×C131—41no—
109C22⋊C4×C131—41no—
110C22⋊C4×C131—41no—
111C22⋊C4×C131—41no—
112C22⋊C4×C131—41no—
113C22⋊C4×C131—81no—
114C42×C131—81no—
115C42×C131—81no—
116C23×C131—21no—
117C23×C131—21no—
118C23×C131—41no—
119C23×C131—41no—
120C23×C131—41no—
121C23×C131—41no—
122C23×C131—41no—
123C23×C131—81no—
124C23×C131—81no—
125C23×C131#12011yescharacteristic
126C23×C131C22⋊Q811yescharacteristic
127C23×C131#12411yescharacteristic
128D4×C131—81no—
129D4×C131—81no—
130D4×C131—81no—
131D4×C131—81no—
132D4×C131—81no—
133D4×C131—81no—
134C2×C4×C131—22no—
135C2×C4×C131—41no—
136C2×C4×C131—41no—
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—42no—
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—41no—
157C2×C4×C131—41no—
158C2×C4×C131—41no—
159C2×C4×C131—41no—
160C2×C4×C131—41no—
161C2×C4×C131—41no—
162C2×C4×C131—81no—
163C2×C4×C131—81no—
164C2×C4×C131C22⋊Q811yescharacteristic
165C2×C4×C131C22⋊Q811yescharacteristic
166C2×C4×C131#12411yescharacteristic
167C2×C4×C131#12411yescharacteristic
168C8×C131—81no—
169C8×C131—81no—
170C22×C131—21no—
171C22×C131—21no—
172C22×C131—21no—
173C22×C131—21no—
174C22×C131—21no—
175C22×C131—21no—
176C22×C131—21no—
177C22×C131—21no—
178C22×C131—81no—
179C22×C131—81no—
180C22×C131—81no—
181C22×C131—81no—
182C22×C131—81no—
183C22×C131—161no—
184C22×C131—161no—
185C22×C131#39311yescharacteristic
186C22×C131#45311yescharacteristic
187C22×C131#45411yescharacteristic
188C4×C131—21no—
189C4×C131—21no—
190C4×C131—21no—
191C4×C131—21no—
192C4×C131—42no—
193C4×C131—81no—
194C4×C131—81no—
195C4×C131—81no—
196C4×C131—81no—
197C4×C131—81no—
198C4×C131—82no—
199C4×C131—81no—
200C2×C131—21no—
201C2×C131—21no—
202C2×C131—41no—
203C2×C131—41no—
204C2×C131—161no—
205C2×C131#202711yescharacteristic
206C2×C131#203111yescharacteristic
207C2×C131#203211yescharacteristic
208#10384C13111yesmaximal, characteristic, direct product factor, Sylow
209C131#1038411yescharacteristic, direct product factor, Sylow
210#2667C2×C13111yescharacteristic, complemented
211#1964C2×C13111yescharacteristic
212#1510C2×C13111yescharacteristic
213#1507C2×C13111yescharacteristic
214#1305C2×C13111yescharacteristic, complemented
215#1297C2×C13111yescharacteristic, complemented
216#1284C2×C13111yescharacteristic, complemented
217C2×#121C22×C13111yescharacteristic
218C2×#99—21no—
219C2×#99—21no—
220#407C22×C13111yescharacteristic
221#407C22×C13111yescharacteristic
222#399—21no—
223#398—21no—
224#398—21no—
225#396—21no—
226#389—21no—
227#387—21no—
228#381C22×C13111yescharacteristic
229#380C22×C13111yescharacteristic
230C4×C22⋊C4C22×C13111yescharacteristic
231C4×C22⋊C4C22×C13111yescharacteristic
232#327—21no—
233#327—21no—
234#327—21no—
235#327—21no—
236C22×D4—21no—
237C22×D4Q8×C13111yescharacteristic
238C23×C4C23×C13111yescharacteristic
239C2×M16—21no—
240C2×M16—21no—
241#121—21no—
242#121—21no—
243#121—21no—
244#121—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4Q8×C13111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4D4×C13111yescharacteristic
258C2×C22⋊C4D4×C13111yescharacteristic
259C2×C42—21no—
260C2×C42—21no—
261#99—42no—
262#99—42no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95D4×C13111yescharacteristic
273#95D4×C13111yescharacteristic
274#95D4×C13111yescharacteristic
275#95D4×C13111yescharacteristic
276C24—21no—
277C24C2×D4×C13111yescharacteristic
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—81no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4—81no—
296C22×C4C2×D4×C13111yescharacteristic
297C22×C4C2×D4×C13111yescharacteristic
298C22×C4C2×Q8×C13111yescharacteristic
299C22×C4#41×C13111yescharacteristic
300C22×C4#41×C13111yescharacteristic
301C22×C4#41×C13111yescharacteristic
302M16—81no—
303M16—81no—
304C2×C8—41no—
305C2×C8—41no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—81no—
311C4⋊C4—81no—
312C4⋊C4—81no—
313C4⋊C4—81no—
314C4⋊C4—81no—
315C22⋊C4—22no—
316C22⋊C4—42no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—81no—
323C42—81no—
324C42—81no—
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—81no—
333C23—81no—
334C23#120×C13111yescharacteristic
335C23C22⋊Q8×C13111yescharacteristic
336C23#124×C13111yescharacteristic
337D4—81no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—81no—
343C2×C4—22no—
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—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4C22⋊Q8×C13111yescharacteristic
374C2×C4C22⋊Q8×C13111yescharacteristic
375C2×C4#124×C13111yescharacteristic
376C2×C4#124×C13111yescharacteristic
377C8—81no—
378C8—81no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—161no—
393C22—161no—
394C22#393×C13111yescharacteristic
395C22#453×C13111yescharacteristic
396C22#454×C13111yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4—82no—
408C4—81no—
409C2—21no—
410C2—21no—
411C2—41no—
412C2—41no—
413C2—161no—
414C2#2027×C13111yescharacteristic
415C2#2031×C13111yescharacteristic
416C2#2032×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#393
commutator, Frattini, cosocleC23×C4C23×C131
prime radicalC2×#121×C131C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2667×C131C2semidirect
5. #1305×C131C2semidirect
6. #1297×C131C2semidirect
7. #1284×C131C2semidirect
208. #10384C131direct (N × H)
209. C131#10384direct (N × H)
210. #2667C2×C131semidirect
214. #1305C2×C131semidirect
215. #1297C2×C131semidirect
216. #1284C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2667×C1312
#1964×C1312
#1510×C1312
#1507×C1312
#1305×C1312
#1297×C1312
#1284×C1312
#10384131