Finite Group Databasebeta

← C31×#11829 #21468588

Subgroups — C31×#11829 #21468588

Order 7936.

416 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2398C211yesmaximal, characteristic
2C31×#1801C211yesmaximal, characteristic, complemented
3C31×#1467C211yesmaximal, characteristic, complemented
4C31×#1353C212yesmaximal, complemented
5C31×#1345C212yesmaximal
6C2×C4×Q8×C31C2211yescharacteristic
7C2×C4×D4×C31C411yescharacteristic
8C31×#432—21no—
9C31×#423—21no—
10C2×C31×#101—21no—
11C31×#400C411yescharacteristic
12C31×#400C2211yescharacteristic
13C31×#397—21no—
14C31×#394C411yescharacteristic
15C31×#394C2211yescharacteristic
16C31×#393—21no—
17C4×C22⋊C4×C31—21no—
18C4×C22⋊C4×C31—21no—
19C31×#376C411yescharacteristic
20C31×#343C2212yes—
21C31×#324—21no—
22C31×#324C2212yes—
23C22×Q8×C31D411yescharacteristic
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31—21no—
26C2×M16×C31—22no—
27C4×Q8×C31—41no—
28C4×Q8×C31—41no—
29C4×D4×C31—41no—
30C4×D4×C31—41no—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C4⋊C4×C31D411yescharacteristic
34C2×C4⋊C4×C31C2311yescharacteristic
35C2×C22⋊C4×C31—21no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C42×C31—21no—
41C2×C42×C31C2×C411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C31×C4⋊C8—41no—
45C31×C4⋊C8—41no—
46C31×C4⋊C8—41no—
47C31×#101—42no—
48C31×C22⋊C8—22no—
49C31×#97—41no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C24×C31—21no—
58C2×Q8×C31—21no—
59C2×Q8×C31—21no—
60C2×Q8×C31—41no—
61C2×Q8×C31—41no—
62C2×D4×C31—41no—
63C2×D4×C31—42no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31—41no—
70C22×C4×C31—41no—
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22×C411yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77C22×C4×C31C2×D411yescharacteristic
78M16×C31—42no—
79M16×C31—42no—
80C2×C8×C31—42no—
81C2×C8×C31—42no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—42no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—41no—
92C42×C31—21no—
93C42×C31—21no—
94C42×C31—21no—
95C42×C31—21no—
96C42×C31—21no—
97C42×C31—21no—
98C42×C31—42no—
99#11829C3111yesmaximal, characteristic, direct product factor, Sylow
100C23×C31—22no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31—41no—
105C23×C31—41no—
106C23×C31—41no—
107C23×C31C2×C22⋊C411yescharacteristic
108Q8×C31—42no—
109Q8×C31—42no—
110D4×C31—42no—
111D4×C31—42no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—22no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—82no—
137C2×C4×C31—82no—
138C2×C4×C31#9911yescharacteristic
139C2×C4×C31#9911yescharacteristic
140C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C31#13711yescharacteristic
142C8×C31—82no—
143C8×C31—82no—
144#2398C2×C3111yescharacteristic
145#1801C2×C3111yescharacteristic, complemented
146#1467C2×C3111yescharacteristic, complemented
147#1353C2×C3112yescomplemented
148#1345C2×C3112yes—
149C22×C31—21no—
150C22×C31—21no—
151C22×C31—42no—
152C22×C31—42no—
153C22×C31—42no—
154C22×C31—81no—
155C22×C31—81no—
156C22×C31—81no—
157C22×C31—81no—
158C22×C31C2×#9911yescharacteristic
159C22×C31#41711yescharacteristic
160C22×C31#42111yescharacteristic
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—41no—
168C4×C31—41no—
169C4×C31—81no—
170C4×C31—81no—
171C4×C31—81no—
172C4×C31#35512yes—
173C2×C4×Q8C22×C3111yescharacteristic
174C2×C4×D4C4×C3111yescharacteristic
175#432—21no—
176#423—21no—
177C2×#101—21no—
178#400C4×C3111yescharacteristic
179#400C22×C3111yescharacteristic
180#397—21no—
181#394C4×C3111yescharacteristic
182#394C22×C3111yescharacteristic
183#393—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4—21no—
186#376C4×C3111yescharacteristic
187#343C22×C3112yes—
188#324—21no—
189#324C22×C3112yes—
190C2×C31—21no—
191C2×C31—21no—
192C2×C31—82no—
193C2×C31#151311yescharacteristic
194C2×C31#212011yescharacteristic
195C2×C31C2×#35511yescharacteristic
196C22×Q8D4×C3111yescharacteristic
197C22×D4C2×C4×C3111yescharacteristic
198C23×C4—21no—
199C2×M16—22no—
200C4×Q8—41no—
201C4×Q8—41no—
202C4×D4—41no—
203C4×D4—41no—
204C2×C4⋊C4C2×C4×C3111yescharacteristic
205C2×C4⋊C4C2×C4×C3111yescharacteristic
206C2×C4⋊C4D4×C3111yescharacteristic
207C2×C4⋊C4C23×C3111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42—21no—
214C2×C42C2×C4×C3111yescharacteristic
215C2×C42D4×C3111yescharacteristic
216C2×C42D4×C3111yescharacteristic
217C4⋊C8—41no—
218C4⋊C8—41no—
219C4⋊C8—41no—
220#101—42no—
221C22⋊C8—22no—
222#97—41no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95C2×C4×C3111yescharacteristic
229#95C2×C4×C3111yescharacteristic
230C31#1182911yescharacteristic, direct product factor, Sylow
231C24—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×D4—41no—
237C2×D4—42no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4C22⋊C4×C3111yescharacteristic
246C22×C4C22⋊C4×C3111yescharacteristic
247C22×C4C22⋊C4×C3111yescharacteristic
248C22×C4C22⋊C4×C3111yescharacteristic
249C22×C4C22×C4×C3111yescharacteristic
250C22×C4C2×D4×C3111yescharacteristic
251C22×C4C2×D4×C3111yescharacteristic
252M16—42no—
253M16—42no—
254C2×C8—42no—
255C2×C8—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—42no—
273C23—22no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×C22⋊C4×C3111yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—42no—
284D4—42no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4C31×#9911yescharacteristic
312C2×C4C31×#9911yescharacteristic
313C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
314C2×C4C31×#13711yescharacteristic
315C8—82no—
316C8—82no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22C2×C31×#9911yescharacteristic
327C22C31×#41711yescharacteristic
328C22C31×#42111yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4C31×#35512yes—
341C2—21no—
342C2—21no—
343C2—82no—
344C2C31×#151311yescharacteristic
345C2C31×#212011yescharacteristic
346C2C2×C31×#35511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1801C2semidirect
3. C31×#1467C2semidirect
4. C31×#1353C2semidirect
99. #11829C31direct (N × H)
145. #1801C2×C31semidirect
146. #1467C2×C31semidirect
147. #1353C2×C31semidirect
230. C31#11829direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23982
C31×#18012
C31×#14672
C31×#13532
C31×#13452
#1182931