Finite Group Databasebeta

← C131×#7793 #45693677

Subgroups — C131×#7793 #45693677

Order 33536.

420 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 98 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#2727×C131C211yesmaximal, characteristic
2#2093×C131C211yesmaximal, characteristic
3#2084×C131C211yesmaximal, characteristic, complemented
4#2083×C131C211yesmaximal, characteristic, complemented
5#1271×C131C211yesmaximal, characteristic, complemented
6#1271×C131C211yesmaximal, characteristic, complemented
7#1270×C131C211yesmaximal, characteristic
8C2×#126×C131—21no—
9C2×#107×C131—21no—
10C2×#107×C131—21no—
11C2×#106×C131—21no—
12C2×#102×C131—21no—
13#399×C131—21no—
14#396×C131—21no—
15#394×C131—21no—
16#390×C131C2211yescharacteristic
17#389×C131—21no—
18#389×C131C2211yescharacteristic
19#389×C131C2211yescharacteristic
20#388×C131—21no—
21#384×C131C2211yescharacteristic
22#340×C131—21no—
23#340×C131—21no—
24#336×C131C2211yescharacteristic
25#336×C131C2211yescharacteristic
26#336×C131C2211yescharacteristic
27C22×D4×C131D411yescharacteristic
28C22×C8×C131—21no—
29C22×C8×C131—21no—
30C22×C8×C131—21no—
31#126×C131—42no—
32#126×C131—42no—
33C2×C4⋊C4×C131—21no—
34C2×C4⋊C4×C131—21no—
35C2×C4⋊C4×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×C131D411yescharacteristic
41C2×C4⋊C4×C131D411yescharacteristic
42C2×C4⋊C4×C131D411yescharacteristic
43C2×C4⋊C4×C131D411yescharacteristic
44C2×C4⋊C4×C131D411yescharacteristic
45C2×C22⋊C4×C131—21no—
46C2×C22⋊C4×C131—21no—
47C2×C22⋊C4×C131—21no—
48C2×C22⋊C4×C131—21no—
49C2×C22⋊C4×C131—21no—
50C2×C22⋊C4×C131—21no—
51C2×C42×C131—21no—
52C2×C42×C131C2311yescharacteristic
53#107×C131—42no—
54#107×C131—42no—
55#106×C131—42no—
56#102×C131—42no—
57#95×C131—21no—
58#95×C131—21no—
59#95×C131—21no—
60C24×C131—21no—
61C2×D4×C131—21no—
62C2×D4×C131—21no—
63C2×D4×C131—41no—
64C2×D4×C131—41no—
65C22×C4×C131—21no—
66C22×C4×C131—21no—
67C22×C4×C131—21no—
68C22×C4×C131—21no—
69C22×C4×C131—21no—
70C22×C4×C131—41no—
71C22×C4×C131C2×D411yescharacteristic
72C22×C4×C131C2×D411yescharacteristic
73C22×C4×C131C2×D411yescharacteristic
74C2×C8×C131—22no—
75C2×C8×C131—22no—
76C2×C8×C131—22no—
77C2×C8×C131—41no—
78C2×C8×C131—41no—
79C2×C8×C131—41no—
80C2×C8×C131—41no—
81C2×C8×C131—41no—
82C2×C8×C131—41no—
83C4⋊C4×C131—21no—
84C4⋊C4×C131—21no—
85C4⋊C4×C131—21no—
86C4⋊C4×C131—41no—
87C4⋊C4×C131—41no—
88C4⋊C4×C131—41no—
89C4⋊C4×C131—42no—
90C4⋊C4×C131—41no—
91C4⋊C4×C131—41no—
92C4⋊C4×C131—41no—
93C4⋊C4×C131—41no—
94C4⋊C4×C131—41no—
95C4⋊C4×C131—41no—
96C4⋊C4×C131—41no—
97C4⋊C4×C131—41no—
98C4⋊C4×C131—41no—
99C4⋊C4×C131—41no—
100C4⋊C4×C131—81no—
101C4⋊C4×C131D812yes—
102C22⋊C4×C131—42no—
103C22⋊C4×C131—42no—
104C22⋊C4×C131—41no—
105C22⋊C4×C131—41no—
106C22⋊C4×C131—41no—
107C22⋊C4×C131—41no—
108C22⋊C4×C131—81no—
109C22⋊C4×C131—81no—
110C42×C131—41no—
111C42×C131—42no—
112C23×C131—41no—
113C23×C131—41no—
114C23×C131—41no—
115C23×C131—41no—
116C23×C131—41no—
117C23×C131—41no—
118C23×C131—41no—
119C23×C131#12011yescharacteristic
120D4×C131—42no—
121D4×C131—81no—
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—22no—
129C2×C4×C131—41no—
130C2×C4×C131—41no—
131C2×C4×C131—41no—
132C2×C4×C131—41no—
133C2×C4×C131—41no—
134C2×C4×C131—41no—
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—81no—
144C2×C4×C131—81no—
145C2×C4×C131—81no—
146C2×C4×C131C2×D811yescharacteristic
147C2×C4×C131#13511yescharacteristic
148C2×C4×C131#13511yescharacteristic
149C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C131AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C131#13711yescharacteristic
152C8×C131—42no—
153C8×C131—42no—
154C8×C131—42no—
155C22×C131—81no—
156C22×C131—81no—
157C22×C131—81no—
158C22×C131—81no—
159C22×C131—81no—
160C22×C131—81no—
161C22×C131—81no—
162C22×C131#44711yescharacteristic
163C22×C131#44911yescharacteristic
164C22×C131#45211yescharacteristic
165C22×C131#45311yescharacteristic
166C22×C131#45611yescharacteristic
167C22×C131#45611yescharacteristic
168C22×C131#45811yescharacteristic
169C4×C131—21no—
170C4×C131—21no—
171C4×C131—21no—
172C4×C131—21no—
173C4×C131—21no—
174C4×C131—21no—
175C4×C131—42no—
176C4×C131—81no—
177C4×C131—81no—
178C4×C131—81no—
179C4×C131—81no—
180C4×C131—161no—
181C2×C131—161no—
182C2×C131#160911yescharacteristic
183C2×C131#161011yescharacteristic
184C2×C131#161811yescharacteristic
185C2×C131#162111yescharacteristic
186C2×C131#164711yescharacteristic
187C2×C131#165211yescharacteristic
188C2×C131#166011yescharacteristic
189#7793C13111yesmaximal, characteristic, direct product factor, Sylow
190C131#779311yescharacteristic, direct product factor, Sylow
191#2727C2×C13111yescharacteristic
192#2093C2×C13111yescharacteristic
193#2084C2×C13111yescharacteristic, complemented
194#2083C2×C13111yescharacteristic, complemented
195#1271C2×C13111yescharacteristic, complemented
196#1271C2×C13111yescharacteristic, complemented
197#1270C2×C13111yescharacteristic
198C2×#126—21no—
199C2×#107—21no—
200C2×#107—21no—
201C2×#106—21no—
202C2×#102—21no—
203#399—21no—
204#396—21no—
205#394—21no—
206#390C22×C13111yescharacteristic
207#389—21no—
208#389C22×C13111yescharacteristic
209#389C22×C13111yescharacteristic
210#388—21no—
211#384C22×C13111yescharacteristic
212#340—21no—
213#340—21no—
214#336C22×C13111yescharacteristic
215#336C22×C13111yescharacteristic
216#336C22×C13111yescharacteristic
217C22×D4D4×C13111yescharacteristic
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221#126—42no—
222#126—42no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4D4×C13111yescharacteristic
231C2×C4⋊C4D4×C13111yescharacteristic
232C2×C4⋊C4D4×C13111yescharacteristic
233C2×C4⋊C4D4×C13111yescharacteristic
234C2×C4⋊C4D4×C13111yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C42—21no—
242C2×C42C23×C13111yescharacteristic
243#107—42no—
244#107—42no—
245#106—42no—
246#102—42no—
247#95—21no—
248#95—21no—
249#95—21no—
250C24—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4C2×D4×C13111yescharacteristic
262C22×C4C2×D4×C13111yescharacteristic
263C22×C4C2×D4×C13111yescharacteristic
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—81no—
291C4⋊C4D8×C13112yes—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C42—41no—
301C42—42no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#120×C13111yescharacteristic
310D4—42no—
311D4—81no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4C2×D8×C13111yescharacteristic
337C2×C4#135×C13111yescharacteristic
338C2×C4#135×C13111yescharacteristic
339C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
340C2×C4AGL(1,ℤ/8)×C13111yescharacteristic
341C2×C4#137×C13111yescharacteristic
342C8—42no—
343C8—42no—
344C8—42no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#447×C13111yescharacteristic
353C22#449×C13111yescharacteristic
354C22#452×C13111yescharacteristic
355C22#453×C13111yescharacteristic
356C22#456×C13111yescharacteristic
357C22#456×C13111yescharacteristic
358C22#458×C13111yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4—161no—
371C2—161no—
372C2#1609×C13111yescharacteristic
373C2#1610×C13111yescharacteristic
374C2#1618×C13111yescharacteristic
375C2#1621×C13111yescharacteristic
376C2#1647×C13111yescharacteristic
377C2#1652×C13111yescharacteristic
378C2#1660×C13111yescharacteristic
subgroupG/H
center, socleC23×C131#120
commutator, Frattini, cosocleC2×C42C23×C131
prime radicalC22×D4×C131D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2084×C131C2semidirect
4. #2083×C131C2semidirect
5. #1271×C131C2semidirect
6. #1271×C131C2semidirect
189. #7793C131direct (N × H)
190. C131#7793direct (N × H)
193. #2084C2×C131semidirect
194. #2083C2×C131semidirect
195. #1271C2×C131semidirect
196. #1271C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2727×C1312
#2093×C1312
#2084×C1312
#2083×C1312
#1271×C1312
#1270×C1312
#7793131