Finite Group Databasebeta

← C31×#11850 #21468609

Subgroups — C31×#11850 #21468609

Order 7936.

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

normal subgroups only

This group has 396 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×#2484C211yesmaximal, characteristic
2C31×#1821C211yesmaximal, characteristic
3C2×C31×#324C211yesmaximal, characteristic
4C31×#1353C212yesmaximal, complemented
5C31×#1346C212yesmaximal, complemented
6C2×C31×#117C411yescharacteristic
7C22×C4⋊C4×C31C2211yescharacteristic
8C31×#407—21no—
9C2×C31×C22⋊C8—21no—
10C31×#400C411yescharacteristic
11C31×#400C2211yescharacteristic
12C31×#398C411yescharacteristic
13C31×#398C2211yescharacteristic
14C31×#387—21no—
15C31×#387—21no—
16C31×#385—21no—
17C31×#381—21no—
18C31×#381C411yescharacteristic
19C31×#343—21no—
20C31×#343C2212yes—
21C31×#324—21no—
22C31×#324C2212yes—
23C23×C4×C31C2×C411yescharacteristic
24C23×C4×C31D411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C2×M16×C31—22no—
27C22×C8×C31—41no—
28C31×#117—41no—
29C31×#117—41no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—41no—
33C2×C4⋊C4×C31—41no—
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31D411yescharacteristic
38C2×C4⋊C4×C31D411yescharacteristic
39C2×C4⋊C4×C31C2311yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C42×C31—21no—
43C31×C22⋊C8—22no—
44C31×C22⋊C8—41no—
45C31×C22⋊C8—41no—
46C31×C22⋊C8—41no—
47C31×#95—21no—
48C31×#95—21no—
49C31×#95—21no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95C2×C411yescharacteristic
55C31×#95C2×C411yescharacteristic
56C24×C31C22⋊C411yescharacteristic
57C22×C4×C31—21no—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—21no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—22no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—41no—
69C22×C4×C31—42no—
70C22×C4×C31—42no—
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—42no—
78M16×C31—42no—
79C2×C8×C31—42no—
80C2×C8×C31—42no—
81C2×C8×C31—82no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—42no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—42no—
90C22⋊C4×C31—42no—
91C22⋊C4×C31—41no—
92C22⋊C4×C31—41no—
93C42×C31—42no—
94#11850C3111yesmaximal, characteristic, direct product factor, Sylow
95C23×C31—22no—
96C23×C31—21no—
97C23×C31—21no—
98C23×C31—41no—
99C23×C31#9911yescharacteristic
100C23×C31#9911yescharacteristic
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—42no—
112C2×C4×C31—42no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—42no—
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—81no—
132C2×C4×C31#13512yes—
133C8×C31—82no—
134C8×C31—82no—
135#2484C2×C3111yescharacteristic
136#1821C2×C3111yescharacteristic
137C2×#324C2×C3111yescharacteristic
138#1353C2×C3112yescomplemented
139#1346C2×C3112yescomplemented
140C22×C31—21no—
141C22×C31—21no—
142C22×C31—21no—
143C22×C31—21no—
144C22×C31—21no—
145C22×C31—21no—
146C22×C31—21no—
147C22×C31—42no—
148C22×C31—42no—
149C22×C31#35212yes—
150C22×C31C2×#9911yescharacteristic
151C22×C31#41611yescharacteristic
152C22×C31#42111yescharacteristic
153C4×C31—22no—
154C4×C31—41no—
155C4×C31—41no—
156C4×C31—41no—
157C4×C31—41no—
158C4×C31—41no—
159C4×C31—81no—
160C4×C31—81no—
161C4×C31—81no—
162C4×C31—81no—
163C2×#117C4×C3111yescharacteristic
164C22×C4⋊C4C22×C3111yescharacteristic
165#407—21no—
166C2×C22⋊C8—21no—
167#400C4×C3111yescharacteristic
168#400C22×C3111yescharacteristic
169#398C4×C3111yescharacteristic
170#398C22×C3111yescharacteristic
171#387—21no—
172#387—21no—
173#385—21no—
174#381—21no—
175#381C4×C3111yescharacteristic
176#343—21no—
177#343C22×C3112yes—
178#324—21no—
179#324C22×C3112yes—
180C2×C31—21no—
181C2×C31—21no—
182C2×C31—22no—
183C2×C31—41no—
184C2×C31#151611yescharacteristic
185C2×C31C2×#35211yescharacteristic
186C2×C31#213311yescharacteristic
187C23×C4C2×C4×C3111yescharacteristic
188C23×C4D4×C3111yescharacteristic
189C23×C4D4×C3111yescharacteristic
190C2×M16—22no—
191C22×C8—41no—
192#117—41no—
193#117—41no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4C2×C4×C3111yescharacteristic
199C2×C4⋊C4C2×C4×C3111yescharacteristic
200C2×C4⋊C4C2×C4×C3111yescharacteristic
201C2×C4⋊C4D4×C3111yescharacteristic
202C2×C4⋊C4D4×C3111yescharacteristic
203C2×C4⋊C4C23×C3111yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C42—21no—
207C22⋊C8—22no—
208C22⋊C8—41no—
209C22⋊C8—41no—
210C22⋊C8—41no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95C2×C4×C3111yescharacteristic
219#95C2×C4×C3111yescharacteristic
220C31#1185011yescharacteristic, direct product factor, Sylow
221C24C22⋊C4×C3111yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4C22⋊C4×C3111yescharacteristic
237C22×C4C22⋊C4×C3111yescharacteristic
238C22×C4C22⋊C4×C3111yescharacteristic
239C22×C4C22×C4×C3111yescharacteristic
240C22×C4C2×D4×C3111yescharacteristic
241C22×C4C2×D4×C3111yescharacteristic
242M16—42no—
243M16—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—82no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C42—42no—
259C23—21no—
260C23—21no—
261C23—22no—
262C23—41no—
263C23C31×#9911yescharacteristic
264C23C31×#9911yescharacteristic
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—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4C31×#13512yes—
297C8—82no—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22C31×#35212yes—
309C22C2×C31×#9911yescharacteristic
310C22C31×#41611yescharacteristic
311C22C31×#42111yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—41no—
326C2C31×#151611yescharacteristic
327C2C2×C31×#35211yescharacteristic
328C2C31×#213311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1353C2semidirect
5. C31×#1346C2semidirect
94. #11850C31direct (N × H)
138. #1353C2×C31semidirect
139. #1346C2×C31semidirect
220. C31#11850direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24842
C31×#18212
C2×C31×#3242
C31×#13532
C31×#13462
#1185031