Finite Group Databasebeta

← C31×#8613 #21465372

Subgroups — C31×#8613 #21465372

Order 7936.

460 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×#435C211yesmaximal, characteristic
2C31×#1810C212yesmaximal, complemented
3C31×#1465C212yesmaximal
4C31×#1293C212yesmaximal, complemented
5C22×M16×C31C411yescharacteristic
6C23×C8×C31C2211yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C31×#435—22no—
9C31×#435—22no—
10C2×C31×#108—22no—
11C2×C31×C4⋊C8C411yescharacteristic
12C31×#407C2214yes—
13C2×C31×C22⋊C8C411yescharacteristic
14C2×C31×C22⋊C8C2211yescharacteristic
15C2×C31×#97C411yescharacteristic
16C31×#341—22no—
17C31×#324—22no—
18C31×#323—22no—
19C22×D4×C31Q811yescharacteristic
20C23×C4×C31C2×C411yescharacteristic
21C23×C4×C31C2311yescharacteristic
22C2×M16×C31—21no—
23C2×M16×C31—21no—
24C2×M16×C31—24no—
25C2×M16×C31—42no—
26C22×C8×C31—42no—
27C22×C8×C31C2×C411yescharacteristic
28C22×C8×C31C2×C411yescharacteristic
29C22×C8×C31C2×C411yescharacteristic
30C22×C8×C31C2×C411yescharacteristic
31C22×C8×C31D412yes—
32C22×C8×C31D412yes—
33C4×D4×C31—22no—
34C4×D4×C31—22no—
35C2×C4⋊C4×C31D411yescharacteristic
36C2×C22⋊C4×C31D411yescharacteristic
37C2×C22⋊C4×C31Q811yescharacteristic
38C2×C42×C31C2×C411yescharacteristic
39C31×#108—44no—
40C31×C4⋊C8—22no—
41C31×C22⋊C8—22no—
42C31×C22⋊C8—22no—
43C31×C22⋊C8—24no—
44C31×C22⋊C8—24no—
45C31×#97—21no—
46C31×#97—21no—
47C24×C31C4⋊C411yescharacteristic
48C24×C31C2×Q811yescharacteristic
49C2×D4×C31—22no—
50C2×D4×C31—42no—
51C22×C4×C31—21no—
52C22×C4×C31—21no—
53C22×C4×C31—41no—
54C22×C4×C31—41no—
55C22×C4×C31—41no—
56C22×C4×C31—41no—
57C22×C4×C31C4⋊C411yescharacteristic
58C22×C4×C31C4⋊C411yescharacteristic
59C22×C4×C31C4⋊C411yescharacteristic
60C22×C4×C31C22×C411yescharacteristic
61C22×C4×C31C2×D412yes—
62C22×C4×C31C2×D411yescharacteristic
63C22×C4×C31#4112yes—
64M16×C31—42no—
65M16×C31—42no—
66M16×C31—44no—
67M16×C31—44no—
68C2×C8×C31—24no—
69C2×C8×C31—22no—
70C2×C8×C31—21no—
71C2×C8×C31—21no—
72C2×C8×C31—41no—
73C2×C8×C31—42no—
74C2×C8×C31—41no—
75C2×C8×C31—41no—
76C2×C8×C31—44no—
77C2×C8×C31C22⋊C411yescharacteristic
78C2×C8×C31C22⋊C412yes—
79C2×C8×C31C22⋊C411yescharacteristic
80C4⋊C4×C31—22no—
81C22⋊C4×C31—22no—
82C22⋊C4×C31—22no—
83C42×C31—21no—
84C42×C31—21no—
85#8613C3111yesmaximal, characteristic, direct product factor, Sylow
86C23×C31—22no—
87C23×C31—21no—
88C23×C31—22no—
89C23×C31—41no—
90C23×C31—41no—
91C23×C31—41no—
92C23×C31—41no—
93C23×C31C2×C4⋊C411yescharacteristic
94C23×C31C22⋊Q812yes—
95D4×C31—44no—
96C2×C4×C31—21no—
97C2×C4×C31—22no—
98C2×C4×C31—21no—
99C2×C4×C31—22no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—22no—
104C2×C4×C31—41no—
105C2×C4×C31—42no—
106C2×C4×C31—42no—
107C2×C4×C31—41no—
108C2×C4×C31—41no—
109C2×C4×C31—41no—
110C2×C4×C31—41no—
111C2×C4×C31C2×C22⋊C411yescharacteristic
112C2×C4×C31#11711yescharacteristic
113C2×C4×C31#12112yes—
114C8×C31—22no—
115C8×C31—21no—
116C8×C31—41no—
117C8×C31—41no—
118C8×C31—84no—
119C8×C31#9912yes—
120C2×#435C2×C3111yescharacteristic
121#1810C2×C3112yescomplemented
122#1465C2×C3112yes—
123#1293C2×C3112yescomplemented
124C22×C31—21no—
125C22×C31—21no—
126C22×C31—22no—
127C22×C31—22no—
128C22×C31—22no—
129C22×C31—44no—
130C22×C31—41no—
131C22×C31—41no—
132C22×C31—41no—
133C22×C31—82no—
134C22×C31#38011yescharacteristic
135C22×C31#43012yes—
136C4×C31—22no—
137C4×C31—21no—
138C4×C31—41no—
139C4×C31—41no—
140C4×C31—41no—
141C4×C31C2×#9911yescharacteristic
142C4×C31#41011yescharacteristic
143C22×M16C4×C3111yescharacteristic
144C23×C8C22×C3111yescharacteristic
145C2×C4×D4C22×C3111yescharacteristic
146#435—22no—
147#435—22no—
148C2×#108—22no—
149C2×C4⋊C8C4×C3111yescharacteristic
150#407C22×C3114yes—
151C2×C22⋊C8C4×C3111yescharacteristic
152C2×C22⋊C8C22×C3111yescharacteristic
153C2×#97C4×C3111yescharacteristic
154#341—22no—
155#324—22no—
156#323—22no—
157C2×C31—22no—
158C2×C31—42no—
159C2×C31—81no—
160C2×C31#179911yescharacteristic
161C2×C31#181111yescharacteristic
162C2×C31#181311yescharacteristic
163C22×D4Q8×C3111yescharacteristic
164C23×C4C2×C4×C3111yescharacteristic
165C23×C4C23×C3111yescharacteristic
166C2×M16—21no—
167C2×M16—21no—
168C2×M16—24no—
169C2×M16—42no—
170C22×C8—42no—
171C22×C8C2×C4×C3111yescharacteristic
172C22×C8C2×C4×C3111yescharacteristic
173C22×C8C2×C4×C3111yescharacteristic
174C22×C8C2×C4×C3111yescharacteristic
175C22×C8D4×C3112yes—
176C22×C8D4×C3112yes—
177C4×D4—22no—
178C4×D4—22no—
179C2×C4⋊C4D4×C3111yescharacteristic
180C2×C22⋊C4D4×C3111yescharacteristic
181C2×C22⋊C4Q8×C3111yescharacteristic
182C2×C42C2×C4×C3111yescharacteristic
183#108—44no—
184C4⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—24no—
188C22⋊C8—24no—
189#97—21no—
190#97—21no—
191C31#861311yescharacteristic, direct product factor, Sylow
192C24C4⋊C4×C3111yescharacteristic
193C24C2×Q8×C3111yescharacteristic
194C2×D4—22no—
195C2×D4—42no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4C4⋊C4×C3111yescharacteristic
203C22×C4C4⋊C4×C3111yescharacteristic
204C22×C4C4⋊C4×C3111yescharacteristic
205C22×C4C22×C4×C3111yescharacteristic
206C22×C4C2×D4×C3112yes—
207C22×C4C2×D4×C3111yescharacteristic
208C22×C4#41×C3112yes—
209M16—42no—
210M16—42no—
211M16—44no—
212M16—44no—
213C2×C8—24no—
214C2×C8—22no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—41no—
218C2×C8—42no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—44no—
222C2×C8C22⋊C4×C3111yescharacteristic
223C2×C8C22⋊C4×C3112yes—
224C2×C8C22⋊C4×C3111yescharacteristic
225C4⋊C4—22no—
226C22⋊C4—22no—
227C22⋊C4—22no—
228C42—21no—
229C42—21no—
230C23—22no—
231C23—21no—
232C23—22no—
233C23—41no—
234C23—41no—
235C23—41no—
236C23—41no—
237C23C2×C4⋊C4×C3111yescharacteristic
238C23C31×C22⋊Q812yes—
239D4—44no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4C2×C22⋊C4×C3111yescharacteristic
256C2×C4C31×#11711yescharacteristic
257C2×C4C31×#12112yes—
258C8—22no—
259C8—21no—
260C8—41no—
261C8—41no—
262C8—84no—
263C8C31×#9912yes—
264C22—21no—
265C22—21no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—44no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—82no—
274C22C31×#38011yescharacteristic
275C22C31×#43012yes—
276C4—22no—
277C4—21no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4C2×C31×#9911yescharacteristic
282C4C31×#41011yescharacteristic
283C2—22no—
284C2—42no—
285C2—81no—
286C2C31×#179911yescharacteristic
287C2C31×#181111yescharacteristic
288C2C31×#181311yescharacteristic
subgroupG/H
center, socleC22×C31#380
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×D4×C31Q8
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1810C2semidirect
4. C31×#1293C2semidirect
85. #8613C31direct (N × H)
121. #1810C2×C31semidirect
123. #1293C2×C31semidirect
191. C31#8613direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4352
C31×#18102
C31×#14652
C31×#12932
#861331