Finite Group Databasebeta

← C31×#8227 #21464986

Subgroups — C31×#8227 #21464986

Order 7936.

488 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#125C211yesmaximal, characteristic
2C31×#1745C211yesmaximal, characteristic
3C4×C31×#97C211yesmaximal, characteristic
4C2×C31×#330C212yesmaximal
5C31×#1295C212yesmaximal
6C2×C31×#125C2211yescharacteristic
7C2×C31×#97—21no—
8C2×C31×#97C2212yes—
9C2×C31×#97C2212yes—
10C2×C4×C8×C31—21no—
11C31×#389C411yescharacteristic
12C31×#389C411yescharacteristic
13C31×#387—21no—
14C31×#387—21no—
15C31×#382C2211yescharacteristic
16C4×C4⋊C4×C31—21no—
17C4×C4⋊C4×C31—21no—
18C4×C4⋊C4×C31C411yescharacteristic
19C4×C4⋊C4×C31C411yescharacteristic
20C43×C31C2211yescharacteristic
21C31×#336—21no—
22C31×#336—21no—
23C31×#330C418yescomplemented
24C22×C8×C31—22no—
25C22×C8×C31—22no—
26C31×#125—22no—
27C31×#125C2×C414yes—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C42×C31—21no—
37C2×C42×C31—21no—
38C2×C42×C31C2×C411yescharacteristic
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C2×C42×C31C2311yescharacteristic
45C31×#97—24no—
46C31×#97—22no—
47C31×#97—22no—
48C31×#97C2×C414yes—
49C31×#97C2×C414yes—
50C4×C8×C31—24no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31C22⋊C411yescharacteristic
62C22×C4×C31C22⋊C411yescharacteristic
63C22×C4×C31C22⋊C411yescharacteristic
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22×C411yescharacteristic
66C22×C4×C31C2×D411yescharacteristic
67C22×C4×C31C2×D411yescharacteristic
68C2×C8×C31—24no—
69C2×C8×C31—24no—
70C2×C8×C31—24no—
71C2×C8×C31—24no—
72C2×C8×C31—42no—
73C2×C8×C31—42no—
74C4⋊C4×C31—21no—
75C4⋊C4×C31—21no—
76C4⋊C4×C31—24no—
77C4⋊C4×C31—24no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—41no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—42no—
82C4⋊C4×C31C4212yes—
83C4⋊C4×C31C4212yes—
84C42×C31—22no—
85C42×C31—22no—
86C42×C31—22no—
87C42×C31—41no—
88C42×C31—41no—
89C42×C31—41no—
90C42×C31—42no—
91C42×C31—42no—
92C42×C31C22×C412yes—
93C42×C31#4112yes—
94#8227C3111yesmaximal, characteristic, direct product factor, Sylow
95C23×C31C2×C22⋊C411yescharacteristic
96C2×C4×C31—21no—
97C2×C4×C31—21no—
98C2×C4×C31—21no—
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—22no—
109C2×C4×C31—22no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—41no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31#10112yes—
124C2×C4×C31#10412yes—
125C2×C4×C31#10412yes—
126C2×C4×C31C2×C4211yescharacteristic
127C2×C4×C31#11711yescharacteristic
128C2×C4×C31C4×D412yes—
129C2×C4×C31C4×D412yes—
130C8×C31—28no—
131C8×C31—44no—
132C4×#125C2×C3111yescharacteristic
133#1745C2×C3111yescharacteristic
134C4×#97C2×C3111yescharacteristic
135C2×#330C2×C3112yes—
136#1295C2×C3112yes—
137C22×C31C4×C22⋊C411yescharacteristic
138C22×C31C2×#10111yescharacteristic
139C22×C31#41311yescharacteristic
140C22×C31C2×#10411yescharacteristic
141C22×C31C2×#10411yescharacteristic
142C22×C31#42111yescharacteristic
143C22×C31#42111yescharacteristic
144C4×C31—21no—
145C4×C31—21no—
146C4×C31—22no—
147C4×C31—22no—
148C4×C31—22no—
149C4×C31—22no—
150C4×C31—22no—
151C4×C31—42no—
152C4×C31—42no—
153C4×C31—41no—
154C4×C31—81no—
155C4×C31—81no—
156C2×#125C22×C3111yescharacteristic
157C2×#97—21no—
158C2×#97C22×C3112yes—
159C2×#97C22×C3112yes—
160C2×C4×C8—21no—
161#389C4×C3111yescharacteristic
162#389C4×C3111yescharacteristic
163#387—21no—
164#387—21no—
165#382C22×C3111yescharacteristic
166C4×C4⋊C4—21no—
167C4×C4⋊C4—21no—
168C4×C4⋊C4C4×C3111yescharacteristic
169C4×C4⋊C4C4×C3111yescharacteristic
170C43C22×C3111yescharacteristic
171#336—21no—
172#336—21no—
173#330C4×C3118yescomplemented
174C2×C31#152811yescharacteristic
175C2×C31#152911yescharacteristic
176C2×C31#153111yescharacteristic
177C2×C31#153211yescharacteristic
178C2×C31C4×#10111yescharacteristic
179C2×C31C4×#10411yescharacteristic
180C2×C31#175911yescharacteristic
181C22×C8—22no—
182C22×C8—22no—
183#125—22no—
184#125C2×C4×C3114yes—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×C4×C3111yescharacteristic
190C2×C4⋊C4C2×C4×C3111yescharacteristic
191C2×C4⋊C4C2×C4×C3111yescharacteristic
192C2×C4⋊C4C2×C4×C3111yescharacteristic
193C2×C42—21no—
194C2×C42—21no—
195C2×C42C2×C4×C3111yescharacteristic
196C2×C42C2×C4×C3111yescharacteristic
197C2×C42D4×C3111yescharacteristic
198C2×C42D4×C3111yescharacteristic
199C2×C42D4×C3111yescharacteristic
200C2×C42D4×C3111yescharacteristic
201C2×C42C23×C3111yescharacteristic
202#97—24no—
203#97—22no—
204#97—22no—
205#97C2×C4×C3114yes—
206#97C2×C4×C3114yes—
207C4×C8—24no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214C31#822711yescharacteristic, direct product factor, Sylow
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4C22⋊C4×C3111yescharacteristic
220C22×C4C22⋊C4×C3111yescharacteristic
221C22×C4C22⋊C4×C3111yescharacteristic
222C22×C4C22⋊C4×C3111yescharacteristic
223C22×C4C22×C4×C3111yescharacteristic
224C22×C4C2×D4×C3111yescharacteristic
225C22×C4C2×D4×C3111yescharacteristic
226C2×C8—24no—
227C2×C8—24no—
228C2×C8—24no—
229C2×C8—24no—
230C2×C8—42no—
231C2×C8—42no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4C42×C3112yes—
241C4⋊C4C42×C3112yes—
242C42—22no—
243C42—22no—
244C42—22no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—42no—
249C42—42no—
250C42C22×C4×C3112yes—
251C42#41×C3112yes—
252C23C2×C22⋊C4×C3111yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4C31×#10112yes—
281C2×C4C31×#10412yes—
282C2×C4C31×#10412yes—
283C2×C4C2×C42×C3111yescharacteristic
284C2×C4C31×#11711yescharacteristic
285C2×C4C4×D4×C3112yes—
286C2×C4C4×D4×C3112yes—
287C8—28no—
288C8—44no—
289C22C4×C22⋊C4×C3111yescharacteristic
290C22C2×C31×#10111yescharacteristic
291C22C31×#41311yescharacteristic
292C22C2×C31×#10411yescharacteristic
293C22C2×C31×#10411yescharacteristic
294C22C31×#42111yescharacteristic
295C22C31×#42111yescharacteristic
296C4—21no—
297C4—21no—
298C4—22no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—42no—
304C4—42no—
305C4—41no—
306C4—81no—
307C4—81no—
308C2C31×#152811yescharacteristic
309C2C31×#152911yescharacteristic
310C2C31×#153111yescharacteristic
311C2C31×#153211yescharacteristic
312C2C4×C31×#10111yescharacteristic
313C2C4×C31×#10411yescharacteristic
314C2C31×#175911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31C2×C22⋊C4
commutatorC2×C4C2×C42×C31
Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
23. C31×#330C4semidirect
94. #8227C31direct (N × H)
173. #330C4×C31semidirect
214. C31#8227direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1252
C31×#17452
C4×C31×#972
C2×C31×#3302
C31×#12952
#822731