Finite Group Databasebeta

← C31×#8582 #21465341

Subgroups — C31×#8582 #21465341

Order 7936.

456 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#125C211yesmaximal, characteristic
2C31×#1767C211yesmaximal, characteristic
3C31×#1767C211yesmaximal, characteristic
4C2×C31×#330C212yesmaximal
5C31×#1295C212yesmaximal
6C2×C31×#125C2211yescharacteristic
7C2×C31×C4⋊C8—21no—
8C2×C31×C4⋊C8—21no—
9C2×C31×#97C2212yes—
10C2×C31×#97C2212yes—
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×#330—24no—
24C22×C8×C31—22no—
25C22×C8×C31—22no—
26C31×#125—21no—
27C31×#125—21no—
28C31×#125D412yes—
29C31×#125Q812yes—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C42×C31—21no—
39C2×C42×C31—21no—
40C2×C42×C31C2×C411yescharacteristic
41C2×C42×C31C2×C411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31C2311yescharacteristic
47C31×C4⋊C8—24no—
48C31×C4⋊C8—24no—
49C31×#97—22no—
50C31×#97—22no—
51C31×#97—22no—
52C31×#97—22no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31C22⋊C411yescharacteristic
64C22×C4×C31C22⋊C411yescharacteristic
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22×C411yescharacteristic
68C22×C4×C31C2×D411yescharacteristic
69C22×C4×C31C2×D411yescharacteristic
70C2×C8×C31—24no—
71C2×C8×C31—24no—
72C2×C8×C31—42no—
73C2×C8×C31—42no—
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C4⋊C4×C31—21no—
77C4⋊C4×C31—21no—
78C4⋊C4×C31—22no—
79C4⋊C4×C31—22no—
80C4⋊C4×C31—22no—
81C4⋊C4×C31—22no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31C4⋊C412yes—
87C4⋊C4×C31C4⋊C412yes—
88C42×C31—22no—
89C42×C31—22no—
90C42×C31—22no—
91C42×C31—41no—
92C42×C31—41no—
93C42×C31—41no—
94C42×C31—42no—
95C42×C31—42no—
96C42×C31C2×D411yescharacteristic
97C42×C31C2×Q811yescharacteristic
98C42×C31#4111yescharacteristic
99C42×C31#4111yescharacteristic
100#8582C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31C2×C22⋊C411yescharacteristic
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—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—22no—
115C2×C4×C31—22no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31#10112yes—
130C2×C4×C31#10412yes—
131C2×C4×C31#10412yes—
132C2×C4×C31C2×C4⋊C411yescharacteristic
133C2×C4×C31#11711yescharacteristic
134C2×C4×C31#12111yescharacteristic
135C2×C4×C31#12111yescharacteristic
136C2×C4×C31C22⋊Q811yescharacteristic
137C2×C4×C31C22⋊Q811yescharacteristic
138C8×C31—44no—
139C8×C31—44no—
140C4×#125C2×C3111yescharacteristic
141#1767C2×C3111yescharacteristic
142#1767C2×C3111yescharacteristic
143C2×#330C2×C3112yes—
144#1295C2×C3112yes—
145C22×C31#38011yescharacteristic
146C22×C31C2×#10111yescharacteristic
147C22×C31#41311yescharacteristic
148C22×C31C2×#10411yescharacteristic
149C22×C31C2×#10411yescharacteristic
150C22×C31#42111yescharacteristic
151C22×C31#42111yescharacteristic
152C4×C31—21no—
153C4×C31—21no—
154C4×C31—21no—
155C4×C31—21no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—22no—
159C4×C31—22no—
160C4×C31—22no—
161C4×C31—42no—
162C4×C31—42no—
163C4×C31—41no—
164C4×C31—81no—
165C4×C31—81no—
166C2×#125C22×C3111yescharacteristic
167C2×C4⋊C8—21no—
168C2×C4⋊C8—21no—
169C2×#97C22×C3112yes—
170C2×#97C22×C3112yes—
171#389C4×C3111yescharacteristic
172#389C4×C3111yescharacteristic
173#387—21no—
174#387—21no—
175#382C22×C3111yescharacteristic
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4C4×C3111yescharacteristic
179C4×C4⋊C4C4×C3111yescharacteristic
180C43C22×C3111yescharacteristic
181#336—21no—
182#336—21no—
183#330—24no—
184C2×C31#152411yescharacteristic
185C2×C31#152811yescharacteristic
186C2×C31#153111yescharacteristic
187C2×C31#153511yescharacteristic
188C2×C31#180111yescharacteristic
189C2×C31#180611yescharacteristic
190C2×C31#180611yescharacteristic
191C22×C8—22no—
192C22×C8—22no—
193#125—21no—
194#125—21no—
195#125D4×C3112yes—
196#125Q8×C3112yes—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×C4×C3111yescharacteristic
202C2×C4⋊C4C2×C4×C3111yescharacteristic
203C2×C4⋊C4C2×C4×C3111yescharacteristic
204C2×C4⋊C4C2×C4×C3111yescharacteristic
205C2×C42—21no—
206C2×C42—21no—
207C2×C42C2×C4×C3111yescharacteristic
208C2×C42C2×C4×C3111yescharacteristic
209C2×C42D4×C3111yescharacteristic
210C2×C42D4×C3111yescharacteristic
211C2×C42D4×C3111yescharacteristic
212C2×C42D4×C3111yescharacteristic
213C2×C42C23×C3111yescharacteristic
214C4⋊C8—24no—
215C4⋊C8—24no—
216#97—22no—
217#97—22no—
218#97—22no—
219#97—22no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226C31#858211yescharacteristic, direct product factor, Sylow
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4C22⋊C4×C3111yescharacteristic
232C22×C4C22⋊C4×C3111yescharacteristic
233C22×C4C22⋊C4×C3111yescharacteristic
234C22×C4C22⋊C4×C3111yescharacteristic
235C22×C4C22×C4×C3111yescharacteristic
236C22×C4C2×D4×C3111yescharacteristic
237C22×C4C2×D4×C3111yescharacteristic
238C2×C8—24no—
239C2×C8—24no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4C4⋊C4×C3112yes—
255C4⋊C4C4⋊C4×C3112yes—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—42no—
263C42—42no—
264C42C2×D4×C3111yescharacteristic
265C42C2×Q8×C3111yescharacteristic
266C42#41×C3111yescharacteristic
267C42#41×C3111yescharacteristic
268C23C2×C22⋊C4×C3111yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4C31×#10112yes—
297C2×C4C31×#10412yes—
298C2×C4C31×#10412yes—
299C2×C4C2×C4⋊C4×C3111yescharacteristic
300C2×C4C31×#11711yescharacteristic
301C2×C4C31×#12111yescharacteristic
302C2×C4C31×#12111yescharacteristic
303C2×C4C31×C22⋊Q811yescharacteristic
304C2×C4C31×C22⋊Q811yescharacteristic
305C8—44no—
306C8—44no—
307C22C31×#38011yescharacteristic
308C22C2×C31×#10111yescharacteristic
309C22C31×#41311yescharacteristic
310C22C2×C31×#10411yescharacteristic
311C22C2×C31×#10411yescharacteristic
312C22C31×#42111yescharacteristic
313C22C31×#42111yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—22no—
321C4—22no—
322C4—22no—
323C4—42no—
324C4—42no—
325C4—41no—
326C4—81no—
327C4—81no—
328C2C31×#152411yescharacteristic
329C2C31×#152811yescharacteristic
330C2C31×#153111yescharacteristic
331C2C31×#153511yescharacteristic
332C2C31×#180111yescharacteristic
333C2C31×#180611yescharacteristic
334C2C31×#180611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
100. #8582C31direct (N × H)
226. C31#8582direct (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×#17672
C2×C31×#3302
C31×#12952
#858231