Finite Group Databasebeta

← C31×#11765 #21468524

Subgroups — C31×#11765 #21468524

Order 7936.

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

normal subgroups only

This group has 470 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×#2610C211yesmaximal, characteristic
2C31×#1742C211yesmaximal, characteristic, complemented
3C31×#1464C211yesmaximal, characteristic, complemented
4C31×#1354C212yesmaximal, complemented
5C31×#1345C212yesmaximal, complemented
6C22×M16×C31—21no—
7C2×C31×#124C411yescharacteristic
8C2×C31×#117C2211yescharacteristic
9C31×#432—21no—
10C31×#395C2211yescharacteristic
11C31×#394C2211yescharacteristic
12C31×#393C411yescharacteristic
13C31×#392C411yescharacteristic
14C31×#390—21no—
15C31×#388—21no—
16C31×#388—21no—
17C31×#386—21no—
18C31×#376C411yescharacteristic
19C31×#343—21no—
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31—21no—
25C22×D4×C31C2×C411yescharacteristic
26C23×C4×C31D411yescharacteristic
27C2×M16×C31—24no—
28C2×M16×C31—22no—
29C2×M16×C31—41no—
30C2×M16×C31—42no—
31C22×C8×C31—41no—
32C31×#124—41no—
33C31×#124—41no—
34C31×#117—41no—
35C31×#117—41no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31D411yescharacteristic
38C2×C4⋊C4×C31C2311yescharacteristic
39C2×C22⋊C4×C31—21no—
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×C31—21no—
48C2×C42×C31C2×C411yescharacteristic
49C2×C42×C31D411yescharacteristic
50C31×C4⋊C8—41no—
51C31×C22⋊C8—22no—
52C31×#97—41no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31—21no—
59C24×C31C22⋊C411yescharacteristic
60C2×Q8×C31—41no—
61C2×Q8×C31—81no—
62C2×D4×C31—42no—
63C2×D4×C31—41no—
64C2×D4×C31—42no—
65C2×D4×C31—81no—
66C2×D4×C31—81no—
67C22×C4×C31—22no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22×C411yescharacteristic
79C22×C4×C31C2×D411yescharacteristic
80C22×C4×C31C2×D411yescharacteristic
81M16×C31—24no—
82M16×C31—44no—
83M16×C31—42no—
84C2×C8×C31—44no—
85C2×C8×C31—42no—
86C2×C8×C31—42no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—81no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—41no—
92C22⋊C4×C31—42no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—41no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—41no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—81no—
99C22⋊C4×C31—81no—
100C42×C31—21no—
101C42×C31—21no—
102C42×C31—21no—
103C42×C31—21no—
104C42×C31—42no—
105#11765C3111yesmaximal, characteristic, direct product factor, Sylow
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—41no—
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
119Q8×C31—82no—
120D4×C31—84no—
121D4×C31—82no—
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—22no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
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#9911yescharacteristic
148C2×C4×C31#9911yescharacteristic
149C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C31#13711yescharacteristic
151C8×C31—44no—
152C8×C31—82no—
153#2610C2×C3111yescharacteristic
154#1742C2×C3111yescharacteristic, complemented
155#1464C2×C3111yescharacteristic, complemented
156#1354C2×C3112yescomplemented
157#1345C2×C3112yescomplemented
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—22no—
161C22×C31—42no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—81no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31—81no—
171C22×C31—81no—
172C22×C31C2×#9911yescharacteristic
173C22×C31#41711yescharacteristic
174C22×C31C2×#10411yescharacteristic
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—42no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31—41no—
183C4×C31—41no—
184C4×C31—81no—
185C4×C31—81no—
186C22×M16—21no—
187C2×#124C4×C3111yescharacteristic
188C2×#117C22×C3111yescharacteristic
189#432—21no—
190#395C22×C3111yescharacteristic
191#394C22×C3111yescharacteristic
192#393C4×C3111yescharacteristic
193#392C4×C3111yescharacteristic
194#390—21no—
195#388—21no—
196#388—21no—
197#386—21no—
198#376C4×C3111yescharacteristic
199#343—21no—
200#343C22×C3112yes—
201#324C22×C3112yes—
202#323—21no—
203C2×C31—21no—
204C2×C31—21no—
205C2×C31—42no—
206C2×C31—161no—
207C2×C31#150411yescharacteristic
208C2×C31#212211yescharacteristic
209C2×C31#213211yescharacteristic
210C22×Q8C2×C4×C3111yescharacteristic
211C22×D4—21no—
212C22×D4C2×C4×C3111yescharacteristic
213C23×C4D4×C3111yescharacteristic
214C2×M16—24no—
215C2×M16—22no—
216C2×M16—41no—
217C2×M16—42no—
218C22×C8—41no—
219#124—41no—
220#124—41no—
221#117—41no—
222#117—41no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C3111yescharacteristic
225C2×C4⋊C4C23×C3111yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4C2×C4×C3111yescharacteristic
233C2×C22⋊C4D4×C3111yescharacteristic
234C2×C42—21no—
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#95C2×C4×C3111yescharacteristic
244#95C2×C4×C3111yescharacteristic
245C31#1176511yescharacteristic, direct product factor, Sylow
246C24—21no—
247C24C22⋊C4×C3111yescharacteristic
248C2×Q8—41no—
249C2×Q8—81no—
250C2×D4—41no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—81no—
254C2×D4—81no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4C22⋊C4×C3111yescharacteristic
264C22×C4C22⋊C4×C3111yescharacteristic
265C22×C4C22⋊C4×C3111yescharacteristic
266C22×C4C22×C4×C3111yescharacteristic
267C22×C4C2×D4×C3111yescharacteristic
268C22×C4C2×D4×C3111yescharacteristic
269M16—24no—
270M16—44no—
271M16—42no—
272C2×C8—44no—
273C2×C8—42no—
274C2×C8—42no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—81no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—81no—
287C22⋊C4—81no—
288C42—21no—
289C42—21no—
290C42—21no—
291C42—21no—
292C42—42no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23C31×#10412yes—
305C23C2×C22⋊C4×C3111yescharacteristic
306Q8—82no—
307D4—84no—
308D4—82no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
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×C4C31×#9911yescharacteristic
335C2×C4C31×#9911yescharacteristic
336C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
337C2×C4C31×#13711yescharacteristic
338C8—44no—
339C8—82no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22C2×C31×#9911yescharacteristic
355C22C31×#41711yescharacteristic
356C22C2×C31×#10411yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—81no—
368C2—21no—
369C2—21no—
370C2—42no—
371C2—161no—
372C2C31×#150411yescharacteristic
373C2C31×#212211yescharacteristic
374C2C31×#213211yescharacteristic
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×#1354C2semidirect
5. C31×#1345C2semidirect
105. #11765C31direct (N × H)
154. #1742C2×C31semidirect
155. #1464C2×C31semidirect
156. #1354C2×C31semidirect
157. #1345C2×C31semidirect
245. C31#11765direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26102
C31×#17422
C31×#14642
C31×#13542
C31×#13452
#1176531