Finite Group Databasebeta

← C31×#13463 #21470222

Subgroups — C31×#13463 #21470222

Order 7936.

484 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2804C211yesmaximal, characteristic
2C31×#1867C212yesmaximal
3C31×#1856C211yesmaximal, characteristic
4C31×#1393C211yesmaximal, characteristic
5C31×#1390C212yesmaximal
6C31×#518C2211yescharacteristic
7C31×#428—21no—
8C2×C31×#100C2211yescharacteristic
9C2×C31×#99C2212yes—
10C31×#400—21no—
11C31×#393—22no—
12C31×#391—21no—
13C31×#390C2211yescharacteristic
14C31×#386C2212yes—
15C31×#385—22no—
16C31×#385—22no—
17C31×#342—22no—
18C31×#339—21no—
19C22×Q8×C31—21no—
20C22×D4×C31C2311yescharacteristic
21C23×C4×C31D412yes—
22C2×M16×C31—21no—
23C4×D4×C31—41no—
24C4×D4×C31—41no—
25C31×#117—21no—
26C2×C4⋊C4×C31—21no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—42no—
29C2×C4⋊C4×C31D411yescharacteristic
30C2×C22⋊C4×C31—22no—
31C2×C22⋊C4×C31—22no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—22no—
34C2×C22⋊C4×C31D412yes—
35C2×C42×C31D411yescharacteristic
36C31×#107—41no—
37C31×#106—41no—
38C31×#100—21no—
39C31×#100Q812yescomplemented
40C31×#99—22no—
41C31×#99Q814yescomplemented
42C31×#95—22no—
43C31×#95—21no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95—42no—
47C24×C31C2×D412yes—
48C2×Q8×C31—42no—
49C2×Q8×C31—81no—
50C2×Q8×C31—81no—
51C2×D4×C31—41no—
52C2×D4×C31—41no—
53C2×D4×C31C2×Q811yescharacteristic
54C2×D4×C31C2×Q812yes—
55C2×D4×C31#4111yescharacteristic
56C22×C4×C31—21no—
57C22×C4×C31—22no—
58C22×C4×C31—21no—
59C22×C4×C31—22no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31—42no—
63C22×C4×C31—42no—
64C22×C4×C31—82no—
65C22×C4×C31C2×D411yescharacteristic
66M16×C31—22no—
67M16×C31—41no—
68C2×C8×C31—41no—
69C4⋊C4×C31—21no—
70C4⋊C4×C31—21no—
71C4⋊C4×C31—41no—
72C4⋊C4×C31—81no—
73C4⋊C4×C31—81no—
74C4⋊C4×C31—84no—
75C22⋊C4×C31—24no—
76C22⋊C4×C31—44no—
77C22⋊C4×C31—42no—
78C22⋊C4×C31—42no—
79C22⋊C4×C31—41no—
80C22⋊C4×C31—42no—
81C22⋊C4×C31—82no—
82C42×C31—41no—
83C42×C31—41no—
84#13463C3111yesmaximal, characteristic, direct product factor, Sylow
85C23×C31—22no—
86C23×C31—22no—
87C23×C31—42no—
88C23×C31—42no—
89C23×C31#12011yescharacteristic
90C23×C31C22⋊Q812yes—
91C23×C31C4⋊Q812yes—
92Q8×C31—84no—
93D4×C31—41no—
94D4×C31—42no—
95D4×C31—41no—
96C2×C4×C31—21no—
97C2×C4×C31—21no—
98C2×C4×C31—22no—
99C2×C4×C31—41no—
100C2×C4×C31—41no—
101C2×C4×C31—44no—
102C2×C4×C31—42no—
103C2×C4×C31—42no—
104C2×C4×C31—42no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—44no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
110C2×C4×C31—41no—
111C2×C4×C31—42no—
112C2×C4×C31—42no—
113C2×C4×C31—82no—
114C2×C4×C31—82no—
115C2×C4×C31—82no—
116C2×C4×C31—82no—
117C2×C4×C31—82no—
118C2×C4×C31C22⋊Q811yescharacteristic
119C2×C4×C31C4⋊Q811yescharacteristic
120C8×C31—42no—
121#2804C2×C3111yescharacteristic
122#1867C2×C3112yes—
123#1856C2×C3111yescharacteristic
124#1393C2×C3111yescharacteristic
125#1390C2×C3112yes—
126C22×C31—21no—
127C22×C31—21no—
128C22×C31—22no—
129C22×C31—22no—
130C22×C31—42no—
131C22×C31—42no—
132C22×C31—42no—
133C22×C31—42no—
134C22×C31—82no—
135C22×C31#39511yescharacteristic
136C22×C31B(4,𝔽2)11yescharacteristic
137C22×C31#45811yescharacteristic
138C4×C31—21no—
139C4×C31—21no—
140C4×C31—42no—
141C4×C31—82no—
142C4×C31—84no—
143C4×C31—81no—
144C4×C31—81no—
145C4×C31—82no—
146C4×C31—81no—
147#518C22×C3111yescharacteristic
148#428—21no—
149C2×#100C22×C3111yescharacteristic
150C2×#99C22×C3112yes—
151#400—21no—
152#393—22no—
153#391—21no—
154#390C22×C3111yescharacteristic
155#386C22×C3112yes—
156#385—22no—
157#385—22no—
158#342—22no—
159#339—21no—
160C2×C31—21no—
161C2×C31—21no—
162C2×C31—42no—
163C2×C31—42no—
164C2×C31#206211yescharacteristic
165C2×C31#219811yescharacteristic
166C2×C31#219911yescharacteristic
167C22×Q8—21no—
168C22×D4C23×C3111yescharacteristic
169C23×C4D4×C3112yes—
170C2×M16—21no—
171C4×D4—41no—
172C4×D4—41no—
173#117—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4D4×C3111yescharacteristic
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4D4×C3112yes—
183C2×C42D4×C3111yescharacteristic
184#107—41no—
185#106—41no—
186#100—21no—
187#100Q8×C3112yescomplemented
188#99—22no—
189#99Q8×C3114yescomplemented
190#95—22no—
191#95—22no—
192#95—21no—
193#95—22no—
194#95—42no—
195C31#1346311yescharacteristic, direct product factor, Sylow
196C24C2×D4×C3112yes—
197C2×Q8—42no—
198C2×Q8—81no—
199C2×Q8—81no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4C2×Q8×C3111yescharacteristic
203C2×D4C2×Q8×C3112yes—
204C2×D4#41×C3111yescharacteristic
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—82no—
214C22×C4C2×D4×C3111yescharacteristic
215M16—22no—
216M16—41no—
217C2×C8—41no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—41no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C4⋊C4—84no—
224C22⋊C4—24no—
225C22⋊C4—44no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—41no—
229C22⋊C4—42no—
230C22⋊C4—82no—
231C42—41no—
232C42—41no—
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23C31×#12011yescharacteristic
238C23C31×C22⋊Q812yes—
239C23C31×C4⋊Q812yes—
240Q8—84no—
241D4—41no—
242D4—42no—
243D4—41no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4C31×C22⋊Q811yescharacteristic
267C2×C4C31×C4⋊Q811yescharacteristic
268C8—42no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22C31×#39511yescharacteristic
279C22C31×B(4,𝔽2)11yescharacteristic
280C22C31×#45811yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—82no—
285C4—84no—
286C4—81no—
287C4—81no—
288C4—82no—
289C4—81no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2C31×#206211yescharacteristic
295C2C31×#219811yescharacteristic
296C2C31×#219911yescharacteristic
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C31
prime radicalC22×D4×C31C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
39. C31×#100Q8semidirect
41. C31×#99Q8semidirect
84. #13463C31direct (N × H)
187. #100Q8×C31semidirect
189. #99Q8×C31semidirect
195. C31#13463direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28042
C31×#18672
C31×#18562
C31×#13932
C31×#13902
#1346331