Finite Group Databasebeta

← C31×#10345 #21467104

Subgroups — C31×#10345 #21467104

Order 7936.

640 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2646C211yesmaximal, characteristic
2C31×#1787C212yesmaximal
3C31×#1446C211yesmaximal, characteristic
4C31×#1294C212yesmaximal
5C31×#1280C211yesmaximal, characteristic
6C23×Q8×C31C2211yescharacteristic
7C2×C31×#103—22no—
8C2×C31×#103—22no—
9C2×C31×C22⋊C8C2212yes—
10C31×#400—22no—
11C31×#398—22no—
12C31×#385—22no—
13C31×#380C2212yes—
14C2×C31×#95—22no—
15C2×C31×#95C2211yescharacteristic
16C2×C31×#95C2211yescharacteristic
17C22×Q8×C31—21no—
18C22×Q8×C31—22no—
19C22×Q8×C31—22no—
20C22×Q8×C31—44no—
21C22×Q8×C31Q812yes—
22C23×C4×C31—21no—
23C23×C4×C31—21no—
24C23×C4×C31D412yes—
25C23×C4×C31C2311yescharacteristic
26C22×C8×C31—22no—
27C2×C4⋊C4×C31—22no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31D412yes—
30C2×C4⋊C4×C31D412yes—
31C2×C22⋊C4×C31—22no—
32C31×#103—44no—
33C31×#103—44no—
34C31×C22⋊C8—22no—
35C31×C22⋊C8—22no—
36C31×#95—22no—
37C31×#95—22no—
38C31×#95—22no—
39C31×#95—22no—
40C31×#95—22no—
41C31×#95—44no—
42C24×C31C2×D411yescharacteristic
43C2×Q8×C31—24no—
44C2×Q8×C31—24no—
45C2×Q8×C31—24no—
46C2×Q8×C31—44no—
47C2×Q8×C31—42no—
48C2×Q8×C31—42no—
49C2×Q8×C31—44no—
50C2×Q8×C31—48no—
51C2×Q8×C31—42no—
52C22×C4×C31—24no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—22no—
59C22×C4×C31—22no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—41no—
63C22×C4×C31—41no—
64C22×C4×C31—42no—
65C22×C4×C31—42no—
66C22×C4×C31—42no—
67C22×C4×C31—41no—
68C22×C4×C31—41no—
69C22×C4×C31—42no—
70C22×C4×C31C2×D412yes—
71C22×C4×C31C2×Q811yescharacteristic
72C22×C4×C31#4112yes—
73C22×C4×C31#4111yescharacteristic
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—82no—
80C4⋊C4×C31—82no—
81C22⋊C4×C31—42no—
82C22⋊C4×C31—42no—
83#10345C3111yesmaximal, characteristic, direct product factor, Sylow
84C23×C31—21no—
85C23×C31—21no—
86C23×C31—22no—
87C23×C31#12011yescharacteristic
88C23×C31C22⋊Q811yescharacteristic
89C23×C31#12411yescharacteristic
90C23×C31#13512yes—
91C23×C31#13712yes—
92Q8×C31—28no—
93Q8×C31—44no—
94Q8×C31—44no—
95Q8×C31—44no—
96C2×C4×C31—22no—
97C2×C4×C31—22no—
98C2×C4×C31—24no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—42no—
102C2×C4×C31—42no—
103C2×C4×C31—44no—
104C2×C4×C31—42no—
105C2×C4×C31—44no—
106C2×C4×C31—44no—
107C2×C4×C31—42no—
108C2×C4×C31—44no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—42no—
112C2×C4×C31—42no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—82no—
119C2×C4×C31—81no—
120C2×C4×C31—81no—
121C2×C4×C31—82no—
122C2×C4×C31C22⋊Q812yes—
123C2×C4×C31#12412yes—
124C8×C31—82no—
125#2646C2×C3111yescharacteristic
126#1787C2×C3112yes—
127#1446C2×C3111yescharacteristic
128#1294C2×C3112yes—
129#1280C2×C3111yescharacteristic
130C22×C31—22no—
131C22×C31—22no—
132C22×C31—22no—
133C22×C31—22no—
134C22×C31—21no—
135C22×C31—21no—
136C22×C31—21no—
137C22×C31—21no—
138C22×C31#39311yescharacteristic
139C22×C31#45212yes—
140C22×C31#45511yescharacteristic
141C22×C31#45611yescharacteristic
142C22×C31B(4,𝔽2)12yes—
143C22×C31#47912yes—
144C22×C31#48811yescharacteristic
145C22×C31#49111yescharacteristic
146C4×C31—22no—
147C4×C31—22no—
148C4×C31—44no—
149C4×C31—82no—
150C4×C31—82no—
151C4×C31—82no—
152C4×C31—82no—
153C23×Q8C22×C3111yescharacteristic
154C2×#103—22no—
155C2×#103—22no—
156C2×C22⋊C8C22×C3112yes—
157#400—22no—
158#398—22no—
159#385—22no—
160#380C22×C3112yes—
161C2×#95—22no—
162C2×#95C22×C3111yescharacteristic
163C2×#95C22×C3111yescharacteristic
164C2×C31—21no—
165C2×C31—22no—
166C2×C31—21no—
167C2×C31#160312yes—
168C2×C31#160612yes—
169C2×C31#202611yescharacteristic
170C2×C31#202811yescharacteristic
171C2×C31#202911yescharacteristic
172C22×Q8—21no—
173C22×Q8—22no—
174C22×Q8—22no—
175C22×Q8—44no—
176C22×Q8Q8×C3112yes—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4D4×C3112yes—
180C23×C4C23×C3111yescharacteristic
181C22×C8—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4D4×C3112yes—
185C2×C4⋊C4D4×C3112yes—
186C2×C22⋊C4—22no—
187#103—44no—
188#103—44no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191#95—22no—
192#95—22no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—44no—
197C31#1034511yescharacteristic, direct product factor, Sylow
198C24C2×D4×C3111yescharacteristic
199C2×Q8—24no—
200C2×Q8—24no—
201C2×Q8—24no—
202C2×Q8—44no—
203C2×Q8—42no—
204C2×Q8—42no—
205C2×Q8—44no—
206C2×Q8—48no—
207C2×Q8—42no—
208C22×C4—24no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4C2×D4×C3112yes—
227C22×C4C2×Q8×C3111yescharacteristic
228C22×C4#41×C3112yes—
229C22×C4#41×C3111yescharacteristic
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—82no—
236C4⋊C4—82no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23C31×#12011yescharacteristic
243C23C31×C22⋊Q811yescharacteristic
244C23C31×#12411yescharacteristic
245C23C31×#13512yes—
246C23C31×#13712yes—
247Q8—28no—
248Q8—44no—
249Q8—44no—
250Q8—44no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—82no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—82no—
277C2×C4C31×C22⋊Q812yes—
278C2×C4C31×#12412yes—
279C8—82no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22C31×#39311yescharacteristic
289C22C31×#45212yes—
290C22C31×#45511yescharacteristic
291C22C31×#45611yescharacteristic
292C22C31×B(4,𝔽2)12yes—
293C22C31×#47912yes—
294C22C31×#48811yescharacteristic
295C22C31×#49111yescharacteristic
296C4—22no—
297C4—22no—
298C4—44no—
299C4—82no—
300C4—82no—
301C4—82no—
302C4—82no—
303C2—21no—
304C2—22no—
305C2—21no—
306C2C31×#160312yes—
307C2C31×#160612yes—
308C2C31×#202611yescharacteristic
309C2C31×#202811yescharacteristic
310C2C31×#202911yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
83. #10345C31direct (N × H)
197. C31#10345direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26462
C31×#17872
C31×#14462
C31×#12942
C31×#12802
#1034531