Finite Group Databasebeta

← C31×#11761 #21468520

Subgroups — C31×#11761 #21468520

Order 7936.

484 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C31×#2598C211yesmaximal, characteristic
2C31×#1742C211yesmaximal, characteristic, complemented
3C31×#1464C211yesmaximal, characteristic, complemented
4C31×#1353C212yesmaximal, complemented
5C31×#1345C212yesmaximal, complemented
6C22×M16×C31—21no—
7C2×C4×D4×C31C411yescharacteristic
8C2×C31×#117C2211yescharacteristic
9C31×#432—21no—
10C31×#400C2211yescharacteristic
11C31×#399C411yescharacteristic
12C31×#394C2211yescharacteristic
13C31×#392C411yescharacteristic
14C31×#388—21no—
15C31×#386—21no—
16C31×#386—21no—
17C31×#385—21no—
18C31×#383C411yescharacteristic
19C31×#343—21no—
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C22×D4×C31—21no—
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31—21no—
26C23×C4×C31D411yescharacteristic
27C2×M16×C31—24no—
28C2×M16×C31—22no—
29C2×M16×C31—41no—
30C2×M16×C31—42no—
31C22×C8×C31—41no—
32C4×D4×C31—41no—
33C4×D4×C31—41no—
34C31×#117—41no—
35C31×#117—41no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31C2311yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31C2×C411yescharacteristic
46C2×C22⋊C4×C31D411yescharacteristic
47C2×C42×C31C2×C411yescharacteristic
48C2×C42×C31D411yescharacteristic
49C31×C4⋊C8—41no—
50C31×C22⋊C8—22no—
51C31×#97—41no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31—21no—
59C24×C31C22⋊C411yescharacteristic
60C2×D4×C31—41no—
61C2×D4×C31—42no—
62C2×D4×C31—42no—
63C2×D4×C31—42no—
64C2×D4×C31—81no—
65C22×C4×C31—22no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—42no—
74C22×C4×C31—81no—
75C22×C4×C31—81no—
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22×C411yescharacteristic
80C22×C4×C31C2×D411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82M16×C31—24no—
83M16×C31—44no—
84M16×C31—42no—
85C2×C8×C31—44no—
86C2×C8×C31—42no—
87C2×C8×C31—42no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—81no—
92C22⋊C4×C31—41no—
93C22⋊C4×C31—41no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—41no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—41no—
99C22⋊C4×C31—81no—
100C22⋊C4×C31—81no—
101C42×C31—21no—
102C42×C31—21no—
103C42×C31—21no—
104C42×C31—21no—
105#11761C3111yesmaximal, characteristic, direct product factor, Sylow
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—22no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31#10412yes—
118C23×C31C2×C22⋊C411yescharacteristic
119D4×C31—42no—
120D4×C31—42no—
121D4×C31—84no—
122C2×C4×C31—22no—
123C2×C4×C31—22no—
124C2×C4×C31—22no—
125C2×C4×C31—22no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—84no—
148C2×C4×C31#9911yescharacteristic
149C2×C4×C31#9911yescharacteristic
150C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C31#13711yescharacteristic
152C8×C31—44no—
153C8×C31—82no—
154#2598C2×C3111yescharacteristic
155#1742C2×C3111yescharacteristic, complemented
156#1464C2×C3111yescharacteristic, complemented
157#1353C2×C3112yescomplemented
158#1345C2×C3112yescomplemented
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—22no—
162C22×C31—42no—
163C22×C31—42no—
164C22×C31—42no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—42no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31—81no—
171C22×C31—81no—
172C22×C31—81no—
173C22×C31C2×#9911yescharacteristic
174C22×C31#41711yescharacteristic
175C22×C31C2×#10411yescharacteristic
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—21no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31—41no—
183C4×C31—41no—
184C4×C31—81no—
185C4×C31—81no—
186C4×C31—81no—
187C22×M16—21no—
188C2×C4×D4C4×C3111yescharacteristic
189C2×#117C22×C3111yescharacteristic
190#432—21no—
191#400C22×C3111yescharacteristic
192#399C4×C3111yescharacteristic
193#394C22×C3111yescharacteristic
194#392C4×C3111yescharacteristic
195#388—21no—
196#386—21no—
197#386—21no—
198#385—21no—
199#383C4×C3111yescharacteristic
200#343—21no—
201#343C22×C3112yes—
202#324C22×C3112yes—
203#323—21no—
204C2×C31—21no—
205C2×C31—21no—
206C2×C31—42no—
207C2×C31—82no—
208C2×C31#150411yescharacteristic
209C2×C31#212011yescharacteristic
210C2×C31#213411yescharacteristic
211C22×D4—21no—
212C22×D4C2×C4×C3111yescharacteristic
213C23×C4—21no—
214C23×C4D4×C3111yescharacteristic
215C2×M16—24no—
216C2×M16—22no—
217C2×M16—41no—
218C2×M16—42no—
219C22×C8—41no—
220C4×D4—41no—
221C4×D4—41no—
222#117—41no—
223#117—41no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C2×C4×C3111yescharacteristic
226C2×C4⋊C4D4×C3111yescharacteristic
227C2×C4⋊C4C23×C3111yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4C2×C4×C3111yescharacteristic
234C2×C22⋊C4D4×C3111yescharacteristic
235C2×C42C2×C4×C3111yescharacteristic
236C2×C42D4×C3111yescharacteristic
237C4⋊C8—41no—
238C22⋊C8—22no—
239#97—41no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95C2×C4×C3111yescharacteristic
245#95C2×C4×C3111yescharacteristic
246C31#1176111yescharacteristic, direct product factor, Sylow
247C24—21no—
248C24C22⋊C4×C3111yescharacteristic
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—81no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4C22⋊C4×C3111yescharacteristic
266C22×C4C22⋊C4×C3111yescharacteristic
267C22×C4C22⋊C4×C3111yescharacteristic
268C22×C4C22×C4×C3111yescharacteristic
269C22×C4C2×D4×C3111yescharacteristic
270C22×C4C2×D4×C3111yescharacteristic
271M16—24no—
272M16—44no—
273M16—42no—
274C2×C8—44no—
275C2×C8—42no—
276C2×C8—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—81no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—42no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—81no—
289C22⋊C4—81no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C23—21no—
295C23—21no—
296C23—22no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23C31×#10412yes—
306C23C2×C22⋊C4×C3111yescharacteristic
307D4—42no—
308D4—42no—
309D4—84no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
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—41no—
334C2×C4—41no—
335C2×C4—84no—
336C2×C4C31×#9911yescharacteristic
337C2×C4C31×#9911yescharacteristic
338C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
339C2×C4C31×#13711yescharacteristic
340C8—44no—
341C8—82no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—41no—
349C22—41no—
350C22—42no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22C2×C31×#9911yescharacteristic
357C22C31×#41711yescharacteristic
358C22C2×C31×#10411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—81no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—82no—
374C2C31×#150411yescharacteristic
375C2C31×#212011yescharacteristic
376C2C31×#213411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC31×#392C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1742C2semidirect
3. C31×#1464C2semidirect
4. C31×#1353C2semidirect
5. C31×#1345C2semidirect
105. #11761C31direct (N × H)
155. #1742C2×C31semidirect
156. #1464C2×C31semidirect
157. #1353C2×C31semidirect
158. #1345C2×C31semidirect
246. C31#11761direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25982
C31×#17422
C31×#14642
C31×#13532
C31×#13452
#1176131