Finite Group Databasebeta

← C31×#11734 #21468493

Subgroups — C31×#11734 #21468493

Order 7936.

434 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 106 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
2C4×C31×#101C211yesmaximal, characteristic, complemented
3C31×#1461C211yesmaximal, characteristic, complemented
4C31×#1353C212yesmaximal, complemented
5C31×#1345C212yesmaximal
6C2×C4×Q8×C31C2211yescharacteristic
7C2×C4×D4×C31C411yescharacteristic
8C31×#431—21no—
9C2×C31×#101—21no—
10C4×M16×C31—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×#101—24no—
46C31×C22⋊C8—22no—
47C31×#97—41no—
48C4×C8×C31—41no—
49C4×C8×C31—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—22no—
59C2×Q8×C31—22no—
60C2×Q8×C31—41no—
61C2×D4×C31—41no—
62C2×D4×C31—42no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—42no—
67C22×C4×C31—42no—
68C22×C4×C31—41no—
69C22×C4×C31—41no—
70C22×C4×C31C22⋊C411yescharacteristic
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22×C411yescharacteristic
75C22×C4×C31C2×D411yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77M16×C31—24no—
78M16×C31—42no—
79C2×C8×C31—42no—
80C2×C8×C31—42no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C22⋊C4×C31—42no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—42no—
90C42×C31—21no—
91C42×C31—21no—
92C42×C31—21no—
93C42×C31—21no—
94C42×C31—21no—
95C42×C31—21no—
96C42×C31—42no—
97#11734C3111yesmaximal, characteristic, direct product factor, Sylow
98C23×C31—22no—
99C23×C31—41no—
100C23×C31—41no—
101C23×C31—41no—
102C23×C31—41no—
103C23×C31—41no—
104C23×C31—41no—
105C23×C31C2×C22⋊C411yescharacteristic
106Q8×C31—44no—
107D4×C31—42no—
108D4×C31—42no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—22no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
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—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—82no—
133C2×C4×C31—82no—
134C2×C4×C31#9911yescharacteristic
135C2×C4×C31#9911yescharacteristic
136C2×C4×C31#10412yes—
137C2×C4×C31#13512yes—
138C8×C31—44no—
139C8×C31—82no—
140#2398C2×C3111yescharacteristic
141C4×#101C2×C3111yescharacteristic, complemented
142#1461C2×C3111yescharacteristic, complemented
143#1353C2×C3112yescomplemented
144#1345C2×C3112yes—
145C22×C31—21no—
146C22×C31—21no—
147C22×C31—42no—
148C22×C31—42no—
149C22×C31—42no—
150C22×C31—81no—
151C22×C31—81no—
152C22×C31—81no—
153C22×C31—81no—
154C22×C31C2×#9911yescharacteristic
155C22×C31#41611yescharacteristic
156C22×C31C2×#10411yescharacteristic
157C4×C31—21no—
158C4×C31—22no—
159C4×C31—22no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31—81no—
165C4×C31—81no—
166C4×C31—81no—
167C4×C31#35512yes—
168C2×C4×Q8C22×C3111yescharacteristic
169C2×C4×D4C4×C3111yescharacteristic
170#431—21no—
171C2×#101—21no—
172C4×M16—21no—
173#400C4×C3111yescharacteristic
174#400C22×C3111yescharacteristic
175#397—21no—
176#394C4×C3111yescharacteristic
177#394C22×C3111yescharacteristic
178#393—21no—
179C4×C22⋊C4—21no—
180C4×C22⋊C4—21no—
181#376C4×C3111yescharacteristic
182#343C22×C3112yes—
183#324—21no—
184#324C22×C3112yes—
185C2×C31—21no—
186C2×C31—21no—
187C2×C31—82no—
188C2×C31#150111yescharacteristic
189C2×C31#212011yescharacteristic
190C2×C31C2×#35511yescharacteristic
191C22×Q8D4×C3111yescharacteristic
192C22×D4C2×C4×C3111yescharacteristic
193C23×C4—21no—
194C2×M16—22no—
195C4×Q8—41no—
196C4×Q8—41no—
197C4×D4—41no—
198C4×D4—41no—
199C2×C4⋊C4C2×C4×C3111yescharacteristic
200C2×C4⋊C4C2×C4×C3111yescharacteristic
201C2×C4⋊C4D4×C3111yescharacteristic
202C2×C4⋊C4C23×C3111yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42—21no—
209C2×C42C2×C4×C3111yescharacteristic
210C2×C42D4×C3111yescharacteristic
211C2×C42D4×C3111yescharacteristic
212C4⋊C8—41no—
213#101—24no—
214C22⋊C8—22no—
215#97—41no—
216C4×C8—41no—
217C4×C8—41no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95C2×C4×C3111yescharacteristic
224#95C2×C4×C3111yescharacteristic
225C31#1173411yescharacteristic, direct product factor, Sylow
226C24—21no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—41no—
230C2×D4—41no—
231C2×D4—42no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4C22⋊C4×C3111yescharacteristic
240C22×C4C22⋊C4×C3111yescharacteristic
241C22×C4C22⋊C4×C3111yescharacteristic
242C22×C4C22⋊C4×C3111yescharacteristic
243C22×C4C22×C4×C3111yescharacteristic
244C22×C4C2×D4×C3111yescharacteristic
245C22×C4C2×D4×C3111yescharacteristic
246M16—24no—
247M16—42no—
248C2×C8—42no—
249C2×C8—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—42no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23C2×C22⋊C4×C3111yescharacteristic
274Q8—44no—
275D4—42no—
276D4—42no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
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×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4C31×#9911yescharacteristic
303C2×C4C31×#9911yescharacteristic
304C2×C4C31×#10412yes—
305C2×C4C31×#13512yes—
306C8—44no—
307C8—82no—
308C22—21no—
309C22—21no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22C2×C31×#9911yescharacteristic
318C22C31×#41611yescharacteristic
319C22C2×C31×#10411yescharacteristic
320C4—21no—
321C4—22no—
322C4—22no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4C31×#35512yes—
331C2—21no—
332C2—21no—
333C2—82no—
334C2C31×#150111yescharacteristic
335C2C31×#212011yescharacteristic
336C2C2×C31×#35511yescharacteristic
subgroupG/H
centerC2×C4×C31#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
socleC22×C31C2×#99
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C31×#101C2semidirect
3. C31×#1461C2semidirect
4. C31×#1353C2semidirect
97. #11734C31direct (N × H)
141. C4×#101C2×C31semidirect
142. #1461C2×C31semidirect
143. #1353C2×C31semidirect
225. C31#11734direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23982
C4×C31×#1012
C31×#14612
C31×#13532
C31×#13452
#1173431