Finite Group Databasebeta

← C31×#7593 #21464352

Subgroups — C31×#7593 #21464352

Order 7936.

566 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C31×#1817C211yesmaximal, characteristic
3C31×#1817C211yesmaximal, characteristic
4C31×#1271C214yesmaximal, complemented
5C22×C4⋊C4×C31—21no—
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C4⋊C4×C31C411yescharacteristic
8C22×C42×C31C2211yescharacteristic
9C2×C31×C22⋊C8—21no—
10C2×C31×C22⋊C8—21no—
11C31×#389—21no—
12C31×#389—21no—
13C31×#389C412yes—
14C31×#389C2212yes—
15C2×C31×#95—21no—
16C31×#336—21no—
17C31×#336—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×C22⋊C8—42no—
43C31×C22⋊C8—42no—
44C31×#95—22no—
45C31×#95—22no—
46C24×C31C22⋊C411yescharacteristic
47C22×C4×C31—22no—
48C22×C4×C31—22no—
49C22×C4×C31—24no—
50C22×C4×C31—22no—
51C22×C4×C31—22no—
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—42no—
59C22×C4×C31—42no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31C22⋊C411yescharacteristic
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C2×C812yes—
67C22×C4×C31M1612yes—
68C22×C4×C31C22×C411yescharacteristic
69C22×C4×C31C2×D411yescharacteristic
70C22×C4×C31C2×D411yescharacteristic
71C2×C8×C31—42no—
72C2×C8×C31—42no—
73C2×C8×C31—42no—
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C4⋊C4×C31—24no—
78C4⋊C4×C31—22no—
79C4⋊C4×C31—42no—
80C4⋊C4×C31—44no—
81C4⋊C4×C31—42no—
82C4⋊C4×C31—44no—
83C4⋊C4×C31C2×C814yes—
84C42×C31—41no—
85C42×C31—41no—
86C42×C31—41no—
87C42×C31—41no—
88#7593C3111yesmaximal, characteristic, direct product factor, Sylow
89C23×C31—21no—
90C23×C31—21no—
91C23×C31—21no—
92C23×C31—21no—
93C23×C31C22⋊C812yes—
94C23×C31#9912yes—
95C23×C31#10112yes—
96C23×C31C2×C22⋊C411yescharacteristic
97C2×C4×C31—24no—
98C2×C4×C31—24no—
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—24no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—44no—
115C2×C4×C31—44no—
116C2×C4×C31—48no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—42no—
120C2×C4×C31—42no—
121C2×C4×C31—42no—
122C2×C4×C31—84no—
123C2×C4×C31C22⋊C812yes—
124C2×C4×C31C22×C811yescharacteristic
125C2×C4×C31C2×M1611yescharacteristic
126C2×C4×C31AGL(1,ℤ/8)12yes—
127C2×C4×C31#13712yes—
128C8×C31—82no—
129C8×C31—82no—
130C2×#389C2×C3111yescharacteristic
131#1817C2×C3111yescharacteristic
132#1817C2×C3111yescharacteristic
133#1271C2×C3114yescomplemented
134C22×C31—22no—
135C22×C31—22no—
136C22×C31—22no—
137C22×C31—22no—
138C22×C31—22no—
139C22×C31—22no—
140C22×C31#32414yes—
141C22×C31C2×C22⋊C811yescharacteristic
142C22×C31C2×#9911yescharacteristic
143C22×C31C2×#10111yescharacteristic
144C22×C31#41811yescharacteristic
145C22×C31#41911yescharacteristic
146C22×C31#42111yescharacteristic
147C22×C31#42111yescharacteristic
148C4×C31—22no—
149C4×C31—21no—
150C4×C31—21no—
151C4×C31—22no—
152C4×C31—22no—
153C4×C31—44no—
154C4×C31—41no—
155C4×C31—41no—
156C4×C31—82no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4C4×C3111yescharacteristic
159C22×C4⋊C4C4×C3111yescharacteristic
160C22×C42C22×C3111yescharacteristic
161C2×C22⋊C8—21no—
162C2×C22⋊C8—21no—
163#389—21no—
164#389—21no—
165#389C4×C3112yes—
166#389C22×C3112yes—
167C2×#95—21no—
168#336—21no—
169#336—21no—
170#336C22×C3112yes—
171#336C22×C3112yes—
172C2×C31—24no—
173C2×C31C2×#32411yescharacteristic
174C2×C31#147811yescharacteristic
175C2×C31#147911yescharacteristic
176C2×C31#151011yescharacteristic
177C2×C31#151111yescharacteristic
178C2×C31#153411yescharacteristic
179C2×C31#155611yescharacteristic
180C23×C4—21no—
181C23×C4—21no—
182C23×C4C2×C4×C3111yescharacteristic
183C23×C4D4×C3111yescharacteristic
184C23×C4D4×C3111yescharacteristic
185C22×C8—22no—
186C22×C8—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4C8×C3114yescomplemented
195C2×C4⋊C4C2×C4×C3112yes—
196C2×C4⋊C4C2×C4×C3112yes—
197C2×C42—42no—
198C2×C42C2×C4×C3111yescharacteristic
199C2×C42D4×C3111yescharacteristic
200C2×C42D4×C3111yescharacteristic
201C2×C42C23×C3111yescharacteristic
202C22⋊C8—42no—
203C22⋊C8—42no—
204#95—22no—
205#95—22no—
206C31#759311yescharacteristic, direct product factor, Sylow
207C24C22⋊C4×C3111yescharacteristic
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4C22⋊C4×C3111yescharacteristic
225C22×C4C22⋊C4×C3111yescharacteristic
226C22×C4C22⋊C4×C3111yescharacteristic
227C22×C4C2×C8×C3112yes—
228C22×C4M16×C3112yes—
229C22×C4C22×C4×C3111yescharacteristic
230C22×C4C2×D4×C3111yescharacteristic
231C22×C4C2×D4×C3111yescharacteristic
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—44no—
243C4⋊C4—44no—
244C4⋊C4C2×C8×C3114yes—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—41no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23C31×C22⋊C812yes—
254C23C31×#9912yes—
255C23C31×#10112yes—
256C23C2×C22⋊C4×C3111yescharacteristic
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—24no—
266C2×C4—24no—
267C2×C4—24no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—48no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—84no—
283C2×C4C31×C22⋊C812yes—
284C2×C4C22×C8×C3111yescharacteristic
285C2×C4C2×M16×C3111yescharacteristic
286C2×C4C31×AGL(1,ℤ/8)12yes—
287C2×C4C31×#13712yes—
288C8—82no—
289C8—82no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22C31×#32414yes—
297C22C2×C31×C22⋊C811yescharacteristic
298C22C2×C31×#9911yescharacteristic
299C22C2×C31×#10111yescharacteristic
300C22C31×#41811yescharacteristic
301C22C31×#41911yescharacteristic
302C22C31×#42111yescharacteristic
303C22C31×#42111yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—22no—
308C4—22no—
309C4—44no—
310C4—41no—
311C4—41no—
312C4—82no—
313C2—24no—
314C2C2×C31×#32411yescharacteristic
315C2C31×#147811yescharacteristic
316C2C31×#147911yescharacteristic
317C2C31×#151011yescharacteristic
318C2C31×#151111yescharacteristic
319C2C31×#153411yescharacteristic
320C2C31×#155611yescharacteristic
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
88. #7593C31direct (N × H)
133. #1271C2×C31semidirect
194. C2×C4⋊C4C8×C31semidirect
206. C31#7593direct (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×#18172
C31×#12712
#759331