Finite Group Databasebeta

← C31×#11575 #21468334

Subgroups — C31×#11575 #21468334

Order 7936.

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

normal subgroups only

This group has 554 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
1C31×#2409C211yesmaximal, characteristic
2C31×#1466C211yesmaximal, characteristic
3C31×#1459C211yesmaximal, characteristic
4C31×#1326C214yesmaximal, complemented
5C23×Q8×C31C411yescharacteristic
6C2×C31×C22⋊Q8—21no—
7C2×C4×D4×C31C2211yescharacteristic
8C31×#432—21no—
9C2×C31×C22⋊C8—21no—
10C31×#395—21no—
11C31×#393—21no—
12C31×#391—21no—
13C31×#386C412yes—
14C31×#385C2212yes—
15C31×#380C411yescharacteristic
16C31×#324—21no—
17C31×#323—21no—
18C31×#323C2212yes—
19C31×#323C2212yes—
20C22×Q8×C31—21no—
21C22×Q8×C31—21no—
22C22×Q8×C31—41no—
23C22×Q8×C31—41no—
24C22×Q8×C31—44no—
25C22×D4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2×C412yes—
28C23×C4×C31D411yescharacteristic
29C22×C8×C31—41no—
30C31×C22⋊Q8—44no—
31C4×D4×C31—41no—
32C4×D4×C31—41no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31D411yescharacteristic
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31C2×C412yes—
38C2×C22⋊C4×C31D411yescharacteristic
39C2×C22⋊C4×C31C2311yescharacteristic
40C2×C42×C31D411yescharacteristic
41C31×C4⋊C8—41no—
42C31×C22⋊C8—22no—
43C31×C22⋊C8—22no—
44C31×C22⋊C8—41no—
45C31×#97—41no—
46C31×#95—21no—
47C31×#95—22no—
48C31×#95—22no—
49C24×C31C22⋊C411yescharacteristic
50C24×C31C22×C411yescharacteristic
51C2×Q8×C31—24no—
52C2×Q8×C31—42no—
53C2×Q8×C31—44no—
54C2×Q8×C31—42no—
55C2×Q8×C31—48no—
56C2×Q8×C31—44no—
57C2×Q8×C31—44no—
58C2×Q8×C31—41no—
59C2×Q8×C31—41no—
60C2×D4×C31—22no—
61C2×D4×C31—22no—
62C2×D4×C31—41no—
63C22×C4×C31—22no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—22no—
69C22×C4×C31—42no—
70C22×C4×C31—44no—
71C22×C4×C31—42no—
72C22×C4×C31—42no—
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77C22×C4×C31C2×D411yescharacteristic
78C2×C8×C31—42no—
79C2×C8×C31—42no—
80C2×C8×C31—82no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—44no—
84C22⋊C4×C31—24no—
85C22⋊C4×C31—41no—
86C22⋊C4×C31—41no—
87C22⋊C4×C31—44no—
88C42×C31—21no—
89C42×C31—21no—
90#11575C3111yesmaximal, characteristic, direct product factor, Sylow
91C23×C31—21no—
92C23×C31—21no—
93C23×C31—21no—
94C23×C31—21no—
95C23×C31—41no—
96C23×C31—41no—
97C23×C31—41no—
98C23×C31—41no—
99C23×C31#10112yes—
100C23×C31C2×C22⋊C411yescharacteristic
101C23×C31#13112yes—
102Q8×C31—44no—
103Q8×C31—48no—
104Q8×C31—44no—
105D4×C31—44no—
106C2×C4×C31—22no—
107C2×C4×C31—24no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—44no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—44no—
124C2×C4×C31—42no—
125C2×C4×C31—42no—
126C2×C4×C31—42no—
127C2×C4×C31—81no—
128C2×C4×C31#9911yescharacteristic
129C2×C4×C31#9911yescharacteristic
130C8×C31—82no—
131C8×C31—82no—
132#2409C2×C3111yescharacteristic
133#1466C2×C3111yescharacteristic
134#1459C2×C3111yescharacteristic
135#1326C2×C3114yescomplemented
136C22×C31—21no—
137C22×C31—21no—
138C22×C31—22no—
139C22×C31—22no—
140C22×C31—42no—
141C22×C31—42no—
142C22×C31—42no—
143C22×C31—41no—
144C22×C31—41no—
145C22×C31—41no—
146C22×C31—41no—
147C22×C31—81no—
148C22×C31#40811yescharacteristic
149C22×C31C2×#9911yescharacteristic
150C22×C31C2×#10111yescharacteristic
151C4×C31—21no—
152C4×C31—41no—
153C4×C31—44no—
154C4×C31—41no—
155C4×C31—41no—
156C4×C31—41no—
157C4×C31—82no—
158C4×C31AΣL(1,𝔽16)12yes—
159C23×Q8C4×C3111yescharacteristic
160C2×C22⋊Q8—21no—
161C2×C4×D4C22×C3111yescharacteristic
162#432—21no—
163C2×C22⋊C8—21no—
164#395—21no—
165#393—21no—
166#391—21no—
167#386C4×C3112yes—
168#385C22×C3112yes—
169#380C4×C3111yescharacteristic
170#324—21no—
171#323—21no—
172#323C22×C3112yes—
173#323C22×C3112yes—
174C2×C31—21no—
175C2×C31—21no—
176C2×C31—42no—
177C2×C31—42no—
178C2×C31#147211yescharacteristic
179C2×C31C2×AΣL(1,𝔽16)11yescharacteristic
180C2×C31#212311yescharacteristic
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—41no—
184C22×Q8—41no—
185C22×Q8—44no—
186C22×D4C2×C4×C3111yescharacteristic
187C23×C4C2×C4×C3111yescharacteristic
188C23×C4C2×C4×C3112yes—
189C23×C4D4×C3111yescharacteristic
190C22×C8—41no—
191C22⋊Q8—44no—
192C4×D4—41no—
193C4×D4—41no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4D4×C3111yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4C2×C4×C3112yes—
199C2×C22⋊C4D4×C3111yescharacteristic
200C2×C22⋊C4C23×C3111yescharacteristic
201C2×C42D4×C3111yescharacteristic
202C4⋊C8—41no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205C22⋊C8—41no—
206#97—41no—
207#95—21no—
208#95—22no—
209#95—22no—
210C31#1157511yescharacteristic, direct product factor, Sylow
211C24C22⋊C4×C3111yescharacteristic
212C24C22×C4×C3111yescharacteristic
213C2×Q8—24no—
214C2×Q8—42no—
215C2×Q8—44no—
216C2×Q8—42no—
217C2×Q8—44no—
218C2×Q8—48no—
219C2×Q8—44no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—41no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—42no—
232C22×C4—44no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C22⋊C4×C3111yescharacteristic
236C22×C4C22⋊C4×C3111yescharacteristic
237C22×C4C22⋊C4×C3111yescharacteristic
238C22×C4C2×D4×C3111yescharacteristic
239C22×C4C2×D4×C3111yescharacteristic
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—82no—
243C4⋊C4—41no—
244C4⋊C4—42no—
245C4⋊C4—44no—
246C22⋊C4—24no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—44no—
250C42—21no—
251C42—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23C31×#10112yes—
261C23C2×C22⋊C4×C3111yescharacteristic
262C23C31×#13112yes—
263Q8—44no—
264Q8—48no—
265Q8—44no—
266D4—44no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—44no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4C31×#9911yescharacteristic
290C2×C4C31×#9911yescharacteristic
291C8—82no—
292C8—82no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22C31×#40811yescharacteristic
306C22C2×C31×#9911yescharacteristic
307C22C2×C31×#10111yescharacteristic
308C4—21no—
309C4—41no—
310C4—44no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—82no—
315C4C31×AΣL(1,𝔽16)12yes—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—42no—
320C2C31×#147211yescharacteristic
321C2C2×C31×AΣL(1,𝔽16)11yescharacteristic
322C2C31×#212311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC24C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1326C2semidirect
90. #11575C31direct (N × H)
135. #1326C2×C31semidirect
210. C31#11575direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24092
C31×#14662
C31×#14592
C31×#13262
#1157531