Finite Group Databasebeta

← C31×#11712 #21468471

Subgroups — C31×#11712 #21468471

Order 7936.

440 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#467C211yesmaximal, characteristic
2C31×#2112C211yesmaximal, characteristic
3C2×C31×#341C211yesmaximal, characteristic
4C31×#1350C214yesmaximal, complemented
5C22×Q16×C31C411yescharacteristic
6C22×M16×C31—21no—
7C23×C8×C31C2211yescharacteristic
8C2×C31×C22⋊Q8—21no—
9C2×C31×M32—21no—
10C31×#467—21no—
11C31×#467—21no—
12C31×#467C412yes—
13C31×#467C2212yes—
14C2×C31×#107C411yescharacteristic
15C2×C31×#103—21no—
16C31×C22⋊C16—21no—
17C31×C22⋊C16C2212yes—
18C31×#341—21no—
19C31×#341C2212yes—
20C22×Q8×C31—21no—
21C23×C4×C31D411yescharacteristic
22C2×Q16×C31—21no—
23C2×Q16×C31—42no—
24C2×Q16×C31C2×C412yes—
25C2×M16×C31—24no—
26C2×M16×C31—22no—
27C2×M16×C31—42no—
28C2×M16×C31—41no—
29C22×C8×C31—42no—
30C22×C8×C31—41no—
31C22×C8×C31C2×C411yescharacteristic
32C22×C8×C31C2×C411yescharacteristic
33C22×C8×C31D411yescharacteristic
34C22×C8×C31D411yescharacteristic
35C22×C8×C31D411yescharacteristic
36C22×C8×C31C2311yescharacteristic
37C31×C22⋊Q8—22no—
38C31×C22⋊Q8—22no—
39C31×C22⋊Q8—41no—
40C31×C22⋊Q8—41no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31—41no—
43C2×C22⋊C4×C31—41no—
44C31×M32—42no—
45C2×C16×C31—22no—
46C31×#107—21no—
47C31×#107C2×C412yes—
48C31×#103—22no—
49C31×#103—22no—
50C24×C31SD1611yescharacteristic
51C2×Q8×C31—22no—
52C2×Q8×C31—41no—
53C2×Q8×C31—42no—
54C2×Q8×C31—42no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—41no—
58C22×C4×C31—41no—
59C22×C4×C31C22⋊C411yescharacteristic
60C22×C4×C31C22⋊C411yescharacteristic
61C22×C4×C31D811yescharacteristic
62C22×C4×C31D811yescharacteristic
63C22×C4×C31SD1611yescharacteristic
64C22×C4×C31C2×D411yescharacteristic
65Q16×C31—42no—
66Q16×C31—42no—
67M16×C31—24no—
68M16×C31—44no—
69M16×C31—42no—
70C2×C8×C31—22no—
71C2×C8×C31—22no—
72C2×C8×C31—41no—
73C2×C8×C31—41no—
74C2×C8×C31—41no—
75C2×C8×C31—41no—
76C2×C8×C31—44no—
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—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—42no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C16×C31—42no—
89#11712C3111yesmaximal, characteristic, direct product factor, Sylow
90C23×C31—22no—
91C23×C31—22no—
92C23×C31—41no—
93C23×C31#10211yescharacteristic
94C23×C31#10211yescharacteristic
95C23×C31C2×SD1611yescharacteristic
96Q8×C31—42no—
97Q8×C31—42no—
98Q8×C31—82no—
99C2×C4×C31—22no—
100C2×C4×C31—22no—
101C2×C4×C31—22no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—42no—
107C2×C4×C31—42no—
108C2×C4×C31—82no—
109C2×C4×C31—82no—
110C2×C4×C31#9912yes—
111C2×C4×C31#10211yescharacteristic
112C2×C4×C31#10211yescharacteristic
113C2×C4×C31#10412yes—
114C2×C4×C31C2×C22⋊C411yescharacteristic
115C2×C4×C31C2×D811yescharacteristic
116C8×C31—21no—
117C8×C31—21no—
118C8×C31—21no—
119C8×C31—21no—
120C8×C31—44no—
121C2×#467C2×C3111yescharacteristic
122#2112C2×C3111yescharacteristic
123C2×#341C2×C3111yescharacteristic
124#1350C2×C3114yescomplemented
125C22×C31—21no—
126C22×C31—21no—
127C22×C31—21no—
128C22×C31—21no—
129C22×C31—21no—
130C22×C31—21no—
131C22×C31—21no—
132C22×C31—44no—
133C22×C31#32712yes—
134C22×C31#36212yes—
135C22×C31C2×#10211yescharacteristic
136C4×C31—21no—
137C4×C31—21no—
138C4×C31—82no—
139C4×C31—82no—
140C4×C31#32712yes—
141C4×C31C2×#9911yescharacteristic
142C4×C31C2×#10411yescharacteristic
143C22×Q16C4×C3111yescharacteristic
144C22×M16—21no—
145C23×C8C22×C3111yescharacteristic
146C2×C22⋊Q8—21no—
147C2×M32—21no—
148#467—21no—
149#467—21no—
150#467C4×C3112yes—
151#467C22×C3112yes—
152C2×#107C4×C3111yescharacteristic
153C2×#103—21no—
154C22⋊C16—21no—
155C22⋊C16C22×C3112yes—
156#341—21no—
157#341C22×C3112yes—
158C2×C31—22no—
159C2×C31—22no—
160C2×C31—41no—
161C2×C31C2×#32711yescharacteristic
162C2×C31#214311yescharacteristic
163C2×C31C2×#36211yescharacteristic
164C22×Q8—21no—
165C23×C4D4×C3111yescharacteristic
166C2×Q16—21no—
167C2×Q16—42no—
168C2×Q16C2×C4×C3112yes—
169C2×M16—24no—
170C2×M16—22no—
171C2×M16—42no—
172C2×M16—41no—
173C22×C8—42no—
174C22×C8—41no—
175C22×C8C2×C4×C3111yescharacteristic
176C22×C8C2×C4×C3111yescharacteristic
177C22×C8D4×C3111yescharacteristic
178C22×C8D4×C3111yescharacteristic
179C22×C8D4×C3111yescharacteristic
180C22×C8C23×C3111yescharacteristic
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—41no—
184C22⋊Q8—41no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—41no—
187C2×C22⋊C4—41no—
188M32—42no—
189C2×C16—22no—
190#107—21no—
191#107C2×C4×C3112yes—
192#103—22no—
193#103—22no—
194C31#1171211yescharacteristic, direct product factor, Sylow
195C24SD16×C3111yescharacteristic
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—42no—
199C2×Q8—42no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4C22⋊C4×C3111yescharacteristic
205C22×C4C22⋊C4×C3111yescharacteristic
206C22×C4D8×C3111yescharacteristic
207C22×C4D8×C3111yescharacteristic
208C22×C4SD16×C3111yescharacteristic
209C22×C4C2×D4×C3111yescharacteristic
210Q16—42no—
211Q16—42no—
212M16—24no—
213M16—44no—
214M16—42no—
215C2×C8—22no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—44no—
222C2×C8—42no—
223C2×C8C22⋊C4×C3111yescharacteristic
224C2×C8C22⋊C4×C3111yescharacteristic
225C2×C8C22×C4×C3111yescharacteristic
226C2×C8C2×D4×C3111yescharacteristic
227C4⋊C4—22no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C16—42no—
234C23—22no—
235C23—22no—
236C23—41no—
237C23C31×#10211yescharacteristic
238C23C31×#10211yescharacteristic
239C23C2×SD16×C3111yescharacteristic
240Q8—42no—
241Q8—42no—
242Q8—82no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4C31×#9912yes—
255C2×C4C31×#10211yescharacteristic
256C2×C4C31×#10211yescharacteristic
257C2×C4C31×#10412yes—
258C2×C4C2×C22⋊C4×C3111yescharacteristic
259C2×C4C2×D8×C3111yescharacteristic
260C8—21no—
261C8—21no—
262C8—21no—
263C8—21no—
264C8—44no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—44no—
273C22C31×#32712yes—
274C22C31×#36212yes—
275C22C2×C31×#10211yescharacteristic
276C4—21no—
277C4—21no—
278C4—82no—
279C4—82no—
280C4C31×#32712yes—
281C4C2×C31×#9911yescharacteristic
282C4C2×C31×#10411yescharacteristic
283C2—22no—
284C2—22no—
285C2—41no—
286C2C2×C31×#32711yescharacteristic
287C2C31×#214311yescharacteristic
288C2C2×C31×#36211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#102
commutatorC2×C8C22×C4×C31
Frattini, cosocleC22×C8C23×C31
prime radicalC24×C31SD16
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
4. C31×#1350C2semidirect
89. #11712C31direct (N × H)
124. #1350C2×C31semidirect
194. C31#11712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4672
C31×#21122
C2×C31×#3412
C31×#13502
#1171231