Finite Group Databasebeta

← C31×#11899 #21468658

Subgroups — C31×#11899 #21468658

Order 7936.

452 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2487C211yesmaximal, characteristic
2C31×#1799C211yesmaximal, characteristic
3C31×#1460C211yesmaximal, characteristic
4C31×#1352C214yesmaximal, complemented
5C2×C4×D4×C31C2211yescharacteristic
6C22×C4⋊C4×C31C411yescharacteristic, complemented
7C31×#431—21no—
8C2×C31×#99—21no—
9C31×#400C412yescomplemented
10C31×#399C2212yes—
11C31×#389—21no—
12C31×#386—21no—
13C31×#385—21no—
14C31×#380—21no—
15C31×#380—21no—
16C31×#380C411yescharacteristic, complemented
17C31×#342C2212yes—
18C31×#323—21no—
19C31×#323C2212yes—
20C22×D4×C31D411yescharacteristic
21C23×C4×C31—21no—
22C23×C4×C31C2×C411yescharacteristic
23C23×C4×C31D411yescharacteristic
24C4×D4×C31—41no—
25C4×D4×C31—41no—
26C2×C4⋊C4×C31—21no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—41no—
30C2×C4⋊C4×C31—41no—
31C2×C4⋊C4×C31—41no—
32C2×C4⋊C4×C31C2×C412yes—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31D411yescharacteristic
38C2×C22⋊C4×C31C2311yescharacteristic
39C2×C42×C31D411yescharacteristic
40C31×C4⋊C8—41no—
41C31×#99—42no—
42C31×C22⋊C8—22no—
43C4×C8×C31—41no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95—41no—
47C31×#95C2×C412yes—
48C24×C31C22⋊C411yescharacteristic
49C24×C31C2×D411yescharacteristic
50C2×D4×C31—41no—
51C2×D4×C31—41no—
52C2×D4×C31SD1612yes—
53C2×D4×C31Q1612yes—
54C22×C4×C31—21no—
55C22×C4×C31—21no—
56C22×C4×C31—21no—
57C22×C4×C31—21no—
58C22×C4×C31—22no—
59C22×C4×C31—22no—
60C22×C4×C31—42no—
61C22×C4×C31—42no—
62C22×C4×C31—42no—
63C22×C4×C31—42no—
64C22×C4×C31—82no—
65C22×C4×C31C22⋊C411yescharacteristic
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22×C411yescharacteristic
69C22×C4×C31C2×D411yescharacteristic
70C2×C8×C31—42no—
71C4⋊C4×C31—41no—
72C4⋊C4×C31—42no—
73C4⋊C4×C31—42no—
74C4⋊C4×C31—41no—
75C4⋊C4×C31—41no—
76C4⋊C4×C31—82no—
77C4⋊C4×C31—82no—
78C22⋊C4×C31—41no—
79C22⋊C4×C31—41no—
80C22⋊C4×C31—42no—
81C22⋊C4×C31—42no—
82C22⋊C4×C31—42no—
83C22⋊C4×C31—82no—
84C42×C31—21no—
85C42×C31—21no—
86#11899C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—21no—
88C23×C31—21no—
89C23×C31—21no—
90C23×C31—21no—
91C23×C31—41no—
92C23×C31—41no—
93C23×C31—41no—
94C23×C31—41no—
95C23×C31#10312yes—
96C23×C31C2×C22⋊C411yescharacteristic
97C23×C31C2×SD1611yescharacteristic
98C23×C31C2×Q1611yescharacteristic
99D4×C31—42no—
100D4×C31—42no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—22no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—42no—
108C2×C4×C31—42no—
109C2×C4×C31—42no—
110C2×C4×C31—41no—
111C2×C4×C31—41no—
112C2×C4×C31—41no—
113C2×C4×C31—42no—
114C2×C4×C31—42no—
115C2×C4×C31—42no—
116C2×C4×C31—42no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—81no—
120C2×C4×C31—84no—
121C2×C4×C31—82no—
122C2×C4×C31—82no—
123C2×C4×C31—82no—
124C2×C4×C31#9911yescharacteristic
125C2×C4×C31#9911yescharacteristic
126C2×C4×C31#10312yes—
127C8×C31—82no—
128#2487C2×C3111yescharacteristic
129#1799C2×C3111yescharacteristic
130#1460C2×C3111yescharacteristic
131#1352C2×C3114yescomplemented
132C22×C31—21no—
133C22×C31—21no—
134C22×C31—21no—
135C22×C31—22no—
136C22×C31—21no—
137C22×C31—42no—
138C22×C31—41no—
139C22×C31—41no—
140C22×C31—42no—
141C22×C31—41no—
142C22×C31—41no—
143C22×C31—41no—
144C22×C31—41no—
145C22×C31—81no—
146C22×C31C2×#9911yescharacteristic
147C22×C31C2×#10311yescharacteristic
148C22×C31#42111yescharacteristic
149C4×C31—21no—
150C4×C31—22no—
151C4×C31—41no—
152C4×C31—41no—
153C4×C31—41no—
154C4×C31—82no—
155C4×C31—82no—
156C4×C31—162no—
157C4×C31#35212yes—
158C2×C4×D4C22×C3111yescharacteristic
159C22×C4⋊C4C4×C3111yescharacteristic, complemented
160#431—21no—
161C2×#99—21no—
162#400C4×C3112yescomplemented
163#399C22×C3112yes—
164#389—21no—
165#386—21no—
166#385—21no—
167#380—21no—
168#380—21no—
169#380C4×C3111yescharacteristic, complemented
170#342C22×C3112yes—
171#323—21no—
172#323C22×C3112yes—
173C2×C31—21no—
174C2×C31—21no—
175C2×C31—41no—
176C2×C31—42no—
177C2×C31—41no—
178C2×C31#152011yescharacteristic
179C2×C31C2×#35211yescharacteristic
180C2×C31#212811yescharacteristic
181C22×D4D4×C3111yescharacteristic
182C23×C4—21no—
183C23×C4C2×C4×C3111yescharacteristic
184C23×C4D4×C3111yescharacteristic
185C4×D4—41no—
186C4×D4—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4C2×C4×C3112yes—
194C2×C4⋊C4C2×C4×C3111yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4D4×C3111yescharacteristic
199C2×C22⋊C4C23×C3111yescharacteristic
200C2×C42D4×C3111yescharacteristic
201C4⋊C8—41no—
202#99—42no—
203C22⋊C8—22no—
204C4×C8—41no—
205#95—22no—
206#95—22no—
207#95—41no—
208#95C2×C4×C3112yes—
209C31#1189911yescharacteristic, direct product factor, Sylow
210C24C22⋊C4×C3111yescharacteristic
211C24C2×D4×C3111yescharacteristic
212C2×D4—41no—
213C2×D4—41no—
214C2×D4SD16×C3112yes—
215C2×D4Q16×C3112yes—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—82no—
227C22×C4C22⋊C4×C3111yescharacteristic
228C22×C4C22⋊C4×C3111yescharacteristic
229C22×C4C22⋊C4×C3111yescharacteristic
230C22×C4C22×C4×C3111yescharacteristic
231C22×C4C2×D4×C3111yescharacteristic
232C2×C8—42no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—82no—
239C4⋊C4—82no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—82no—
246C42—21no—
247C42—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23C31×#10312yes—
257C23C2×C22⋊C4×C3111yescharacteristic
258C23C2×SD16×C3111yescharacteristic
259C23C2×Q16×C3111yescharacteristic
260D4—42no—
261D4—42no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—84no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4C31×#9911yescharacteristic
286C2×C4C31×#9911yescharacteristic
287C2×C4C31×#10312yes—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—22no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×C31×#9911yescharacteristic
304C22C2×C31×#10311yescharacteristic
305C22C31×#42111yescharacteristic
306C4—21no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4—162no—
314C4C31×#35212yes—
315C2—21no—
316C2—21no—
317C2—41no—
318C2—42no—
319C2—41no—
320C2C31×#152011yescharacteristic
321C2C2×C31×#35211yescharacteristic
322C2C31×#212811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1352C2semidirect
6. C22×C4⋊C4×C31C4semidirect
9. C31×#400C4semidirect
16. C31×#380C4semidirect
86. #11899C31direct (N × H)
131. #1352C2×C31semidirect
159. C22×C4⋊C4C4×C31semidirect
162. #400C4×C31semidirect
169. #380C4×C31semidirect
209. C31#11899direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24872
C31×#17992
C31×#14602
C31×#13522
#1189931