Finite Group Databasebeta

← C31×#7576 #21464335

Subgroups — C31×#7576 #21464335

Order 7936.

604 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C4×C31×C22⋊C8C211yesmaximal, characteristic
4C31×#1271C214yesmaximal, complemented
5C22×C4⋊C4×C31—21no—
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C4⋊C4×C31C411yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C2×C31×C4⋊C8—21no—
10C2×C31×C22⋊C8—21no—
11C2×C31×C22⋊C8—21no—
12C2×C4×C8×C31—21no—
13C31×#389—21no—
14C31×#389—21no—
15C31×#389C412yes—
16C31×#389C2212yes—
17C2×C31×#95—21no—
18C31×#336C2212yes—
19C31×#336C2212yes—
20C23×C4×C31—21no—
21C23×C4×C31—21no—
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C22×C8×C31—22no—
26C22×C8×C31—22no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—44no—
33C2×C4⋊C4×C31—42no—
34C2×C4⋊C4×C31C814yescomplemented
35C2×C4⋊C4×C31C2×C412yes—
36C2×C4⋊C4×C31C2×C412yes—
37C2×C42×C31—42no—
38C2×C42×C31C2×C411yescharacteristic
39C2×C42×C31D411yescharacteristic
40C2×C42×C31D411yescharacteristic
41C2×C42×C31C2311yescharacteristic
42C31×C4⋊C8—42no—
43C31×C22⋊C8—24no—
44C31×C22⋊C8—42no—
45C4×C8×C31—42no—
46C31×#95—22no—
47C31×#95—22no—
48C24×C31C22⋊C411yescharacteristic
49C22×C4×C31—22no—
50C22×C4×C31—22no—
51C22×C4×C31—24no—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—41no—
57C22×C4×C31—41no—
58C22×C4×C31—41no—
59C22×C4×C31—42no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31—42no—
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C2×C812yes—
68C22×C4×C31M1612yes—
69C22×C4×C31SD1612yes—
70C22×C4×C31Q1612yes—
71C22×C4×C31C22×C411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74C2×C8×C31—24no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C2×C8×C31—42no—
78C2×C8×C31—42no—
79C2×C8×C31—42no—
80C4⋊C4×C31—24no—
81C4⋊C4×C31—22no—
82C4⋊C4×C31—44no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—44no—
86C4⋊C4×C31C2×C814yes—
87C42×C31—22no—
88C42×C31—22no—
89C42×C31—41no—
90C42×C31—41no—
91#7576C3111yesmaximal, characteristic, direct product factor, Sylow
92C23×C31—21no—
93C23×C31—21no—
94C23×C31—21no—
95C23×C31—21no—
96C23×C31C22⋊C812yes—
97C23×C31#10312yes—
98C23×C31#10412yes—
99C23×C31C2×C22⋊C411yescharacteristic
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—24no—
109C2×C4×C31—24no—
110C2×C4×C31—24no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—44no—
117C2×C4×C31—48no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—42no—
123C2×C4×C31—84no—
124C2×C4×C31C22⋊C812yes—
125C2×C4×C31#9912yes—
126C2×C4×C31#10112yes—
127C2×C4×C31#10312yes—
128C2×C4×C31C22×C811yescharacteristic
129C2×C4×C31C2×M1611yescharacteristic
130C2×C4×C31C2×SD1611yescharacteristic
131C2×C4×C31C2×Q1611yescharacteristic
132C2×C4×C31AGL(1,ℤ/8)12yes—
133C8×C31—44no—
134C8×C31—82no—
135C2×#389C2×C3111yescharacteristic
136#1797C2×C3111yescharacteristic
137C4×C22⋊C8C2×C3111yescharacteristic
138#1271C2×C3114yescomplemented
139C22×C31—22no—
140C22×C31—22no—
141C22×C31—22no—
142C22×C31—22no—
143C22×C31—22no—
144C22×C31—22no—
145C22×C31Q8⋊C814yes—
146C22×C31C2×C22⋊C811yescharacteristic
147C22×C31C2×#9911yescharacteristic
148C22×C31C2×#10111yescharacteristic
149C22×C31C2×#10311yescharacteristic
150C22×C31#41811yescharacteristic
151C22×C31C2×#10411yescharacteristic
152C22×C31#42111yescharacteristic
153C4×C31—21no—
154C4×C31—21no—
155C4×C31—22no—
156C4×C31—21no—
157C4×C31—22no—
158C4×C31—21no—
159C4×C31—44no—
160C4×C31—41no—
161C4×C31—82no—
162C4×C31#32414yes—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C4×C3111yescharacteristic
165C22×C4⋊C4C4×C3111yescharacteristic
166C22×C42C22×C3111yescharacteristic
167C2×C4⋊C8—21no—
168C2×C22⋊C8—21no—
169C2×C22⋊C8—21no—
170C2×C4×C8—21no—
171#389—21no—
172#389—21no—
173#389C4×C3112yes—
174#389C22×C3112yes—
175C2×#95—21no—
176#336C22×C3112yes—
177#336C22×C3112yes—
178C2×C31—24no—
179C2×C31C2×#32411yescharacteristic
180C2×C31C2×Q8⋊C811yescharacteristic
181C2×C31#147811yescharacteristic
182C2×C31#150711yescharacteristic
183C2×C31#152011yescharacteristic
184C2×C31#152811yescharacteristic
185C2×C31#154911yescharacteristic
186C23×C4—21no—
187C23×C4—21no—
188C23×C4C2×C4×C3111yescharacteristic
189C23×C4D4×C3111yescharacteristic
190C23×C4D4×C3111yescharacteristic
191C22×C8—22no—
192C22×C8—22no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—44no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4C8×C3114yescomplemented
201C2×C4⋊C4C2×C4×C3112yes—
202C2×C4⋊C4C2×C4×C3112yes—
203C2×C42—42no—
204C2×C42C2×C4×C3111yescharacteristic
205C2×C42D4×C3111yescharacteristic
206C2×C42D4×C3111yescharacteristic
207C2×C42C23×C3111yescharacteristic
208C4⋊C8—42no—
209C22⋊C8—24no—
210C22⋊C8—42no—
211C4×C8—42no—
212#95—22no—
213#95—22no—
214C31#757611yescharacteristic, direct product factor, Sylow
215C24C22⋊C4×C3111yescharacteristic
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—24no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4C22⋊C4×C3111yescharacteristic
232C22×C4C22⋊C4×C3111yescharacteristic
233C22×C4C22⋊C4×C3111yescharacteristic
234C22×C4C2×C8×C3112yes—
235C22×C4M16×C3112yes—
236C22×C4SD16×C3112yes—
237C22×C4Q16×C3112yes—
238C22×C4C22×C4×C3111yescharacteristic
239C22×C4C2×D4×C3111yescharacteristic
240C22×C4C2×D4×C3111yescharacteristic
241C2×C8—24no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C4⋊C4—24no—
248C4⋊C4—22no—
249C4⋊C4—42no—
250C4⋊C4—44no—
251C4⋊C4—42no—
252C4⋊C4—44no—
253C4⋊C4C2×C8×C3114yes—
254C42—22no—
255C42—22no—
256C42—41no—
257C42—41no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23C31×C22⋊C812yes—
263C23C31×#10312yes—
264C23C31×#10412yes—
265C23C2×C22⋊C4×C3111yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—48no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—84no—
290C2×C4C31×C22⋊C812yes—
291C2×C4C31×#9912yes—
292C2×C4C31×#10112yes—
293C2×C4C31×#10312yes—
294C2×C4C22×C8×C3111yescharacteristic
295C2×C4C2×M16×C3111yescharacteristic
296C2×C4C2×SD16×C3111yescharacteristic
297C2×C4C2×Q16×C3111yescharacteristic
298C2×C4C31×AGL(1,ℤ/8)12yes—
299C8—44no—
300C8—82no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22C31×Q8⋊C814yes—
308C22C2×C31×C22⋊C811yescharacteristic
309C22C2×C31×#9911yescharacteristic
310C22C2×C31×#10111yescharacteristic
311C22C2×C31×#10311yescharacteristic
312C22C31×#41811yescharacteristic
313C22C2×C31×#10411yescharacteristic
314C22C31×#42111yescharacteristic
315C4—21no—
316C4—21no—
317C4—22no—
318C4—21no—
319C4—22no—
320C4—21no—
321C4—44no—
322C4—41no—
323C4—82no—
324C4C31×#32414yes—
325C2—24no—
326C2C2×C31×#32411yescharacteristic
327C2C2×C31×Q8⋊C811yescharacteristic
328C2C31×#147811yescharacteristic
329C2C31×#150711yescharacteristic
330C2C31×#152011yescharacteristic
331C2C31×#152811yescharacteristic
332C2C31×#154911yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC2×C4C22×C8×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1271C2semidirect
34. C2×C4⋊C4×C31C8semidirect
91. #7576C31direct (N × H)
138. #1271C2×C31semidirect
200. C2×C4⋊C4C8×C31semidirect
214. C31#7576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C31×#17972
C4×C31×C22⋊C82
C31×#12712
#757631