Finite Group Databasebeta

← C131×#10338 #45696222

Subgroups — C131×#10338 #45696222

Order 33536.

998 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 106 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#2483×C131C211yesmaximal, characteristic, complemented
2#2405×C131C212yesmaximal
3#1819×C131C212yesmaximal, complemented
4#1781×C131C211yesmaximal, characteristic
5#1304×C131C211yesmaximal, characteristic, complemented
6C23×D4×C131C2211yescharacteristic
7C2×#123×C131—22no—
8C22×C22⋊C4×C131C2212yes—
9C2×#99×C131—22no—
10#397×C131—22no—
11#394×C131—24no—
12#386×C131—22no—
13#385×C131—22no—
14#385×C131—22no—
15#381×C131—22no—
16#379×C131—22no—
17#379×C131C2211yescharacteristic
18#379×C131C2211yescharacteristic
19#379×C131C2212yes—
20#342×C131—24no—
21C25×C131D411yescharacteristic
22C25×C131C2311yescharacteristic
23C22×D4×C131—21no—
24C22×D4×C131—22no—
25C22×D4×C131—22no—
26C22×D4×C131—21no—
27C22×D4×C131—44no—
28C23×C4×C131D412yes—
29C23×C4×C131D412yes—
30C23×C4×C131D411yescharacteristic
31#123×C131—48no—
32C2×C4⋊C4×C131—24no—
33C2×C4⋊C4×C131—22no—
34C2×C22⋊C4×C131—24no—
35C2×C22⋊C4×C131—22no—
36C2×C22⋊C4×C131—22no—
37C2×C22⋊C4×C131—22no—
38C2×C22⋊C4×C131—22no—
39C2×C22⋊C4×C131—22no—
40C2×C22⋊C4×C131—22no—
41C2×C22⋊C4×C131—22no—
42C2×C22⋊C4×C131—22no—
43C2×C22⋊C4×C131—22no—
44C2×C22⋊C4×C131—21no—
45C2×C22⋊C4×C131—22no—
46C2×C22⋊C4×C131—24no—
47C2×C22⋊C4×C131D414yes—
48C2×C22⋊C4×C131D412yes—
49#99×C131—44no—
50#95×C131—24no—
51#95×C131—22no—
52#95×C131—24no—
53C24×C131—22no—
54C24×C131—21no—
55C24×C131—42no—
56C24×C131—42no—
57C24×C131—44no—
58C24×C131—44no—
59C24×C131C2×D411yescharacteristic
60C24×C131C2×D412yes—
61C24×C131C2×D411yescharacteristic
62C24×C131C2×D412yes—
63C24×C131#4111yescharacteristic
64C2×D4×C131—24no—
65C2×D4×C131—28no—
66C2×D4×C131—44no—
67C2×D4×C131—42no—
68C2×D4×C131—44no—
69C2×D4×C131—42no—
70C2×D4×C131—44no—
71C2×D4×C131—42no—
72C2×D4×C131—41no—
73C2×D4×C131—42no—
74C2×D4×C131—41no—
75C22×C4×C131—22no—
76C22×C4×C131—21no—
77C22×C4×C131—22no—
78C22×C4×C131—22no—
79C22×C4×C131—22no—
80C22×C4×C131—22no—
81C22×C4×C131—24no—
82C22×C4×C131—22no—
83C22×C4×C131—22no—
84C22×C4×C131—22no—
85C22×C4×C131—42no—
86C22×C4×C131—44no—
87C22×C4×C131—44no—
88C22×C4×C131—41no—
89C4⋊C4×C131—48no—
90C4⋊C4×C131—82no—
91C22⋊C4×C131—44no—
92C22⋊C4×C131—44no—
93C22⋊C4×C131—44no—
94C22⋊C4×C131—48no—
95C22⋊C4×C131—42no—
96C22⋊C4×C131—42no—
97C22⋊C4×C131—42no—
98C22⋊C4×C131—42no—
99C22⋊C4×C131—42no—
100C22⋊C4×C131—44no—
101C22⋊C4×C131—42no—
102C22⋊C4×C131—44no—
103C22⋊C4×C131—84no—
104C23×C131—24no—
105C23×C131—24no—
106C23×C131—24no—
107C23×C131—22no—
108C23×C131—24no—
109C23×C131—24no—
110C23×C131—22no—
111C23×C131—41no—
112C23×C131—42no—
113C23×C131—42no—
114C23×C131—41no—
115C23×C131—42no—
116C23×C131—42no—
117C23×C131—42no—
118C23×C131—42no—
119C23×C131—41no—
120C23×C131—44no—
121C23×C131—41no—
122C23×C131—44no—
123C23×C131—82no—
124C23×C131—88no—
125C23×C131—88no—
126C23×C131#12011yescharacteristic
127C23×C131#12012yes—
128C23×C131#12111yescharacteristic
129C23×C131#12112yes—
130C23×C131#12711yescharacteristic
131D4×C131—48no—
132D4×C131—44no—
133D4×C131—44no—
134C2×C4×C131—24no—
135C2×C4×C131—22no—
136C2×C4×C131—42no—
137C2×C4×C131—41no—
138C2×C4×C131—41no—
139C2×C4×C131—44no—
140C2×C4×C131—44no—
141C2×C4×C131—44no—
142C2×C4×C131—44no—
143C2×C4×C131—44no—
144C2×C4×C131—42no—
145C2×C4×C131—42no—
146C2×C4×C131—42no—
147C2×C4×C131—44no—
148C2×C4×C131—44no—
149C2×C4×C131—44no—
150C2×C4×C131—82no—
151C2×C4×C131—82no—
152C2×C4×C131—81no—
153C2×C4×C131—82no—
154C22×C131—22no—
155C22×C131—22no—
156C22×C131—22no—
157C22×C131—21no—
158C22×C131—22no—
159C22×C131—21no—
160C22×C131—22no—
161C22×C131—22no—
162C22×C131—22no—
163C22×C131—22no—
164C22×C131—48no—
165C22×C131—44no—
166C22×C131—48no—
167C22×C131—42no—
168C22×C131—84no—
169C22×C131—82no—
170C22×C131—84no—
171C22×C131—82no—
172C22×C131—82no—
173C22×C131—82no—
174C22×C131—82no—
175C22×C131#39211yescharacteristic
176C22×C131B(4,𝔽2)12yes—
177C22×C131#45814yes—
178C4×C131—42no—
179C4×C131—84no—
180C4×C131—82no—
181C4×C131—82no—
182C4×C131—82no—
183C4×C131—161no—
184C2×C131—24no—
185C2×C131—22no—
186C2×C131—41no—
187C2×C131—42no—
188C2×C131—41no—
189C2×C131—82no—
190C2×C131#202111yescharacteristic
191C2×C131#202212yes—
192#10338C13111yesmaximal, characteristic, direct product factor, Sylow
193C131#1033811yescharacteristic, direct product factor, Sylow
194#2483C2×C13111yescharacteristic, complemented
195#2405C2×C13112yes—
196#1819C2×C13112yescomplemented
197#1781C2×C13111yescharacteristic
198#1304C2×C13111yescharacteristic, complemented
199C23×D4C22×C13111yescharacteristic
200C2×#123—22no—
201C22×C22⋊C4C22×C13112yes—
202C2×#99—22no—
203#397—22no—
204#394—24no—
205#386—22no—
206#385—22no—
207#385—22no—
208#381—22no—
209#379—22no—
210#379C22×C13111yescharacteristic
211#379C22×C13112yes—
212#379C22×C13111yescharacteristic
213#342—24no—
214C25D4×C13111yescharacteristic
215C25C23×C13111yescharacteristic
216C22×D4—22no—
217C22×D4—21no—
218C22×D4—22no—
219C22×D4—21no—
220C22×D4—44no—
221C23×C4D4×C13112yes—
222C23×C4D4×C13112yes—
223C23×C4D4×C13111yescharacteristic
224#123—48no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—22no—
227C2×C22⋊C4—24no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4D4×C13114yes—
241C2×C22⋊C4D4×C13112yes—
242#99—44no—
243#95—22no—
244#95—24no—
245#95—24no—
246C24—22no—
247C24—21no—
248C24—42no—
249C24—42no—
250C24—44no—
251C24—44no—
252C24C2×D4×C13111yescharacteristic
253C24C2×D4×C13112yes—
254C24C2×D4×C13111yescharacteristic
255C24C2×D4×C13112yes—
256C24#41×C13111yescharacteristic
257C2×D4—24no—
258C2×D4—28no—
259C2×D4—44no—
260C2×D4—42no—
261C2×D4—44no—
262C2×D4—42no—
263C2×D4—44no—
264C2×D4—42no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—41no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4—44no—
281C22×C4—41no—
282C4⋊C4—48no—
283C4⋊C4—82no—
284C22⋊C4—44no—
285C22⋊C4—44no—
286C22⋊C4—44no—
287C22⋊C4—48no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—44no—
294C22⋊C4—42no—
295C22⋊C4—44no—
296C22⋊C4—84no—
297C23—24no—
298C23—24no—
299C23—24no—
300C23—22no—
301C23—24no—
302C23—24no—
303C23—22no—
304C23—41no—
305C23—42no—
306C23—42no—
307C23—41no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—44no—
314C23—41no—
315C23—44no—
316C23—82no—
317C23—88no—
318C23—88no—
319C23#120×C13111yescharacteristic
320C23#120×C13112yes—
321C23#121×C13111yescharacteristic
322C23#121×C13112yes—
323C23#127×C13111yescharacteristic
324D4—48no—
325D4—44no—
326D4—44no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—81no—
346C2×C4—82no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—21no—
351C22—22no—
352C22—21no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—44no—
358C22—48no—
359C22—48no—
360C22—42no—
361C22—84no—
362C22—82no—
363C22—84no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22#392×C13111yescharacteristic
369C22B(4,𝔽2)×C13112yes—
370C22#458×C13114yes—
371C4—42no—
372C4—84no—
373C4—82no—
374C4—82no—
375C4—82no—
376C4—161no—
377C2—24no—
378C2—22no—
379C2—41no—
380C2—41no—
381C2—42no—
382C2—82no—
383C2#2021×C13111yescharacteristic
384C2#2022×C13112yes—
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC25C23×C131
prime radicalC23×D4×C131C22
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C25×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2483×C131C2semidirect
3. #1819×C131C2semidirect
5. #1304×C131C2semidirect
192. #10338C131direct (N × H)
193. C131#10338direct (N × H)
194. #2483C2×C131semidirect
196. #1819C2×C131semidirect
198. #1304C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2483×C1312
#2405×C1312
#1819×C1312
#1781×C1312
#1304×C1312
#10338131