Finite Group Databasebeta

← C31×#11895 #21468654

Subgroups — C31×#11895 #21468654

Order 7936.

442 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C2×C31×#466C211yesmaximal, characteristic
2C31×#2112C211yesmaximal, characteristic, complemented
3C31×#1810C211yesmaximal, characteristic, complemented
4C31×#1349C214yesmaximal, complemented
5C22×D8×C31C411yescharacteristic
6C23×C8×C31C2211yescharacteristic
7C2×C31×#121—21no—
8C2×C31×M32—21no—
9C31×#466—21no—
10C31×#466—21no—
11C31×#466C412yes—
12C31×#466C2212yes—
13C2×C31×#108—21no—
14C2×C31×#107C411yescharacteristic
15C2×C31×#102—21no—
16C31×#407—21no—
17C31×C22⋊C16—21no—
18C31×C22⋊C16C2212yescomplemented
19C31×#341C2212yescomplemented
20C22×D4×C31—21no—
21C22×D4×C31—41no—
22C23×C4×C31D411yescharacteristic
23C2×D8×C31—21no—
24C2×D8×C31—42no—
25C2×D8×C31C2×C412yes—
26C2×M16×C31—22no—
27C22×C8×C31—42no—
28C22×C8×C31C2×C411yescharacteristic
29C22×C8×C31C2×C411yescharacteristic
30C22×C8×C31D411yescharacteristic
31C22×C8×C31D411yescharacteristic
32C22×C8×C31D411yescharacteristic
33C22×C8×C31C2311yescharacteristic
34C31×#121—22no—
35C31×#121—22no—
36C31×#121—41no—
37C31×#121—41no—
38C2×C4⋊C4×C31—21no—
39C2×C22⋊C4×C31—41no—
40C31×M32—42no—
41C2×C16×C31—22no—
42C31×#108—42no—
43C31×#107—21no—
44C31×#107C2×C412yes—
45C31×#102—22no—
46C31×#102—22no—
47C31×C22⋊C8—41no—
48C31×C22⋊C8—41no—
49C24×C31—41no—
50C24×C31SD1611yescharacteristic
51C2×D4×C31—22no—
52C2×D4×C31—42no—
53C2×D4×C31—42no—
54C2×D4×C31—42no—
55C2×D4×C31—42no—
56C2×D4×C31—41no—
57C2×D4×C31—84no—
58C22×C4×C31—41no—
59C22×C4×C31—41no—
60C22×C4×C31—41no—
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31D811yescharacteristic
64C22×C4×C31D811yescharacteristic
65C22×C4×C31SD1611yescharacteristic
66C22×C4×C31C2×D411yescharacteristic
67D8×C31—42no—
68D8×C31—42no—
69M16×C31—42no—
70M16×C31—42no—
71C2×C8×C31—22no—
72C2×C8×C31—22no—
73C2×C8×C31—22no—
74C2×C8×C31—41no—
75C2×C8×C31—41no—
76C2×C8×C31—41no—
77C2×C8×C31—42no—
78C2×C8×C31C22⋊C411yescharacteristic
79C2×C8×C31C22⋊C411yescharacteristic
80C2×C8×C31C22×C411yescharacteristic
81C2×C8×C31C2×D411yescharacteristic
82C4⋊C4×C31—22no—
83C4⋊C4×C31—41no—
84C22⋊C4×C31—42no—
85C22⋊C4×C31—42no—
86C16×C31—42no—
87#11895C3111yesmaximal, characteristic, direct product factor, Sylow
88C23×C31—22no—
89C23×C31—41no—
90C23×C31—41no—
91C23×C31—42no—
92C23×C31—82no—
93C23×C31—82no—
94C23×C31—82no—
95C23×C31#10211yescharacteristic
96C23×C31#10211yescharacteristic
97C23×C31C2×SD1611yescharacteristic
98D4×C31—42no—
99D4×C31—42no—
100D4×C31—82no—
101D4×C31—84no—
102D4×C31—84no—
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—42no—
113C2×C4×C31—82no—
114C2×C4×C31#10211yescharacteristic
115C2×C4×C31#10211yescharacteristic
116C2×C4×C31C2×C22⋊C411yescharacteristic
117C2×C4×C31C2×D811yescharacteristic
118C8×C31—21no—
119C8×C31—21no—
120C8×C31—21no—
121C8×C31—82no—
122C8×C31#9912yes—
123C2×#466C2×C3111yescharacteristic
124#2112C2×C3111yescharacteristic, complemented
125#1810C2×C3111yescharacteristic, complemented
126#1349C2×C3114yescomplemented
127C22×C31—21no—
128C22×C31—21no—
129C22×C31—21no—
130C22×C31—21no—
131C22×C31—21no—
132C22×C31—21no—
133C22×C31—21no—
134C22×C31—21no—
135C22×C31—44no—
136C22×C31—82no—
137C22×C31—82no—
138C22×C31—82no—
139C22×C31—164no—
140C22×C31#36112yes—
141C22×C31C2×#10211yescharacteristic
142C4×C31—21no—
143C4×C31—21no—
144C4×C31—21no—
145C4×C31—82no—
146C4×C31C2×#9911yescharacteristic
147C4×C31#42111yescharacteristic
148C22×D8C4×C3111yescharacteristic
149C23×C8C22×C3111yescharacteristic
150C2×#121—21no—
151C2×M32—21no—
152#466—21no—
153#466—21no—
154#466C4×C3112yes—
155#466C22×C3112yes—
156C2×#108—21no—
157C2×#107C4×C3111yescharacteristic
158C2×#102—21no—
159#407—21no—
160C22⋊C16—21no—
161C22⋊C16C22×C3112yescomplemented
162#341C22×C3112yescomplemented
163C2×C31—22no—
164C2×C31—41no—
165C2×C31—41no—
166C2×C31—162no—
167C2×C31#151911yescharacteristic
168C2×C31#214311yescharacteristic
169C2×C31C2×#36111yescharacteristic
170C22×D4—21no—
171C22×D4—41no—
172C23×C4D4×C3111yescharacteristic
173C2×D8—21no—
174C2×D8—42no—
175C2×D8C2×C4×C3112yes—
176C2×M16—22no—
177C22×C8—42no—
178C22×C8C2×C4×C3111yescharacteristic
179C22×C8C2×C4×C3111yescharacteristic
180C22×C8D4×C3111yescharacteristic
181C22×C8D4×C3111yescharacteristic
182C22×C8D4×C3111yescharacteristic
183C22×C8C23×C3111yescharacteristic
184#121—22no—
185#121—22no—
186#121—41no—
187#121—41no—
188C2×C4⋊C4—21no—
189C2×C22⋊C4—41no—
190M32—42no—
191C2×C16—22no—
192#108—42no—
193#107—21no—
194#107C2×C4×C3112yes—
195#102—22no—
196#102—22no—
197C22⋊C8—41no—
198C22⋊C8—41no—
199C31#1189511yescharacteristic, direct product factor, Sylow
200C24—41no—
201C24SD16×C3111yescharacteristic
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—41no—
208C2×D4—84no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4C22⋊C4×C3111yescharacteristic
213C22×C4C22⋊C4×C3111yescharacteristic
214C22×C4D8×C3111yescharacteristic
215C22×C4D8×C3111yescharacteristic
216C22×C4SD16×C3111yescharacteristic
217C22×C4C2×D4×C3111yescharacteristic
218D8—42no—
219D8—42no—
220M16—42no—
221M16—42no—
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—22no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—42no—
229C2×C8C22⋊C4×C3111yescharacteristic
230C2×C8C22⋊C4×C3111yescharacteristic
231C2×C8C22×C4×C3111yescharacteristic
232C2×C8C2×D4×C3111yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—41no—
235C22⋊C4—42no—
236C22⋊C4—42no—
237C16—42no—
238C23—22no—
239C23—41no—
240C23—41no—
241C23—42no—
242C23—82no—
243C23—82no—
244C23—82no—
245C23C31×#10211yescharacteristic
246C23C31×#10211yescharacteristic
247C23C2×SD16×C3111yescharacteristic
248D4—42no—
249D4—42no—
250D4—82no—
251D4—84no—
252D4—84no—
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—42no—
263C2×C4—82no—
264C2×C4C31×#10211yescharacteristic
265C2×C4C31×#10211yescharacteristic
266C2×C4C2×C22⋊C4×C3111yescharacteristic
267C2×C4C2×D8×C3111yescharacteristic
268C8—21no—
269C8—21no—
270C8—21no—
271C8—82no—
272C8C31×#9912yes—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—44no—
282C22—82no—
283C22—82no—
284C22—82no—
285C22—164no—
286C22C31×#36112yes—
287C22C2×C31×#10211yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—82no—
292C4C2×C31×#9911yescharacteristic
293C4C31×#42111yescharacteristic
294C2—22no—
295C2—41no—
296C2—41no—
297C2—162no—
298C2C31×#151911yescharacteristic
299C2C31×#214311yescharacteristic
300C2C2×C31×#36111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#102
commutatorC2×C8C22×C4×C31
Frattini, cosocleC22×C8C23×C31
prime radicalC2×C31×#466C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ C23×C8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2112C2semidirect
3. C31×#1810C2semidirect
4. C31×#1349C2semidirect
18. C31×C22⋊C16C22semidirect
19. C31×#341C22semidirect
87. #11895C31direct (N × H)
124. #2112C2×C31semidirect
125. #1810C2×C31semidirect
126. #1349C2×C31semidirect
161. C22⋊C16C22×C31semidirect
162. #341C22×C31semidirect
199. C31#11895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4662
C31×#21122
C31×#18102
C31×#13492
#1189531