Finite Group Databasebeta

← C31×#11792 #21468551

Subgroups — C31×#11792 #21468551

Order 7936.

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

normal subgroups only

This group has 378 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×#2581C211yesmaximal, characteristic
2C4×C31×#101C211yesmaximal, characteristic
3C31×#1467C211yesmaximal, characteristic
4C31×#1354C212yesmaximal
5C31×#1353C212yesmaximal
6C2×C4×Q8×C31C411yescharacteristic
7C2×C4×Q8×C31C2211yescharacteristic
8C31×#432—21no—
9C2×C31×#101—21no—
10C4×M16×C31—21no—
11C31×#400C411yescharacteristic
12C31×#400C2211yescharacteristic
13C31×#395C411yescharacteristic
14C31×#395C2211yescharacteristic
15C31×#391—21no—
16C31×#389—21no—
17C31×#387—21no—
18C31×#387—21no—
19C31×#382C411yescharacteristic
20C31×#343C2212yes—
21C31×#324—21no—
22C31×#324C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C22×Q8×C31D411yescharacteristic
25C2×M16×C31—22no—
26C4×Q8×C31—41no—
27C4×Q8×C31—41no—
28C4×Q8×C31—41no—
29C4×Q8×C31—41no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31D411yescharacteristic
37C2×C4⋊C4×C31C2311yescharacteristic
38C2×C42×C31—21no—
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C31×C4⋊C8—41no—
43C31×#101—24no—
44C31×C22⋊C8—22no—
45C31×#97—41no—
46C31×#97—41no—
47C4×C8×C31—41no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C2×Q8×C31—22no—
58C2×Q8×C31—22no—
59C2×Q8×C31—41no—
60C2×Q8×C31—42no—
61C2×Q8×C31—41no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22×C411yescharacteristic
71C22×C4×C31C2×D411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73M16×C31—24no—
74M16×C31—42no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C4⋊C4×C31—41no—
78C4⋊C4×C31—41no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—42no—
81C4⋊C4×C31—42no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—42no—
86C42×C31—21no—
87C42×C31—21no—
88C42×C31—21no—
89C42×C31—21no—
90C42×C31—21no—
91C42×C31—21no—
92C42×C31—42no—
93#11792C3111yesmaximal, characteristic, direct product factor, Sylow
94C23×C31C2×C22⋊C411yescharacteristic
95Q8×C31—44no—
96Q8×C31—42no—
97Q8×C31—42no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—22no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—41no—
110C2×C4×C31—41no—
111C2×C4×C31—41no—
112C2×C4×C31—41no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—42no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31#9911yescharacteristic
124C2×C4×C31#9911yescharacteristic
125C2×C4×C31#10412yes—
126C2×C4×C31#13712yes—
127C8×C31—44no—
128C8×C31—82no—
129#2581C2×C3111yescharacteristic
130C4×#101C2×C3111yescharacteristic
131#1467C2×C3111yescharacteristic
132#1354C2×C3112yes—
133#1353C2×C3112yes—
134C22×C31—21no—
135C22×C31—21no—
136C22×C31C2×#9911yescharacteristic
137C22×C31#41911yescharacteristic
138C22×C31C2×#10411yescharacteristic
139C4×C31—21no—
140C4×C31—21no—
141C4×C31—22no—
142C4×C31—22no—
143C4×C31—41no—
144C4×C31—41no—
145C4×C31—42no—
146C4×C31—41no—
147C4×C31—41no—
148C4×C31—81no—
149C4×C31—81no—
150C4×C31—81no—
151C2×C4×Q8C4×C3111yescharacteristic
152C2×C4×Q8C22×C3111yescharacteristic
153#432—21no—
154C2×#101—21no—
155C4×M16—21no—
156#400C4×C3111yescharacteristic
157#400C22×C3111yescharacteristic
158#395C4×C3111yescharacteristic
159#395C22×C3111yescharacteristic
160#391—21no—
161#389—21no—
162#387—21no—
163#387—21no—
164#382C4×C3111yescharacteristic
165#343C22×C3112yes—
166#324—21no—
167#324C22×C3112yes—
168C2×C31—21no—
169C2×C31—21no—
170C2×C31#150811yescharacteristic
171C2×C31#212011yescharacteristic
172C2×C31#213311yescharacteristic
173C22×Q8C2×C4×C3111yescharacteristic
174C22×Q8D4×C3111yescharacteristic
175C2×M16—22no—
176C4×Q8—41no—
177C4×Q8—41no—
178C4×Q8—41no—
179C4×Q8—41no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4C2×C4×C3111yescharacteristic
185C2×C4⋊C4C2×C4×C3111yescharacteristic
186C2×C4⋊C4D4×C3111yescharacteristic
187C2×C4⋊C4C23×C3111yescharacteristic
188C2×C42—21no—
189C2×C42C2×C4×C3111yescharacteristic
190C2×C42D4×C3111yescharacteristic
191C2×C42D4×C3111yescharacteristic
192C4⋊C8—41no—
193#101—24no—
194C22⋊C8—22no—
195#97—41no—
196#97—41no—
197C4×C8—41no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95C2×C4×C3111yescharacteristic
206#95C2×C4×C3111yescharacteristic
207C31#1179211yescharacteristic, direct product factor, Sylow
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—42no—
212C2×Q8—41no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4C22⋊C4×C3111yescharacteristic
218C22×C4C22⋊C4×C3111yescharacteristic
219C22×C4C22⋊C4×C3111yescharacteristic
220C22×C4C22⋊C4×C3111yescharacteristic
221C22×C4C22×C4×C3111yescharacteristic
222C22×C4C2×D4×C3111yescharacteristic
223C22×C4C2×D4×C3111yescharacteristic
224M16—24no—
225M16—42no—
226C2×C8—42no—
227C2×C8—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—42no—
244C23C2×C22⋊C4×C3111yescharacteristic
245Q8—44no—
246Q8—42no—
247Q8—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4C31×#9911yescharacteristic
274C2×C4C31×#9911yescharacteristic
275C2×C4C31×#10412yes—
276C2×C4C31×#13712yes—
277C8—44no—
278C8—82no—
279C22—21no—
280C22—21no—
281C22C2×C31×#9911yescharacteristic
282C22C31×#41911yescharacteristic
283C22C2×C31×#10411yescharacteristic
284C4—21no—
285C4—21no—
286C4—22no—
287C4—22no—
288C4—41no—
289C4—42no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—81no—
294C4—81no—
295C4—81no—
296C2—21no—
297C2—21no—
298C2C31×#150811yescharacteristic
299C2C31×#212011yescharacteristic
300C2C31×#213311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
93. #11792C31direct (N × H)
207. C31#11792direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25812
C4×C31×#1012
C31×#14672
C31×#13542
C31×#13532
#1179231