Finite Group Databasebeta

← C31×#12290 #21469049

Subgroups — C31×#12290 #21469049

Order 7936.

316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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×#3250C211yesmaximal, characteristic
2C31×#2235C211yesmaximal, characteristic, complemented
3C31×#2232C211yesmaximal, characteristic
4C31×#2086C211yesmaximal, characteristic, complemented
5C31×#1348C211yesmaximal, characteristic, complemented
6C31×#1347C211yesmaximal, characteristic
7C31×#1322C211yesmaximal, characteristic, complemented
8C31×#529—21no—
9C31×#479—21no—
10C31×#478—21no—
11C31×#467C2211yescharacteristic
12C31×#466C2211yescharacteristic
13C31×#465—21no—
14C31×#464—21no—
15C31×#463—21no—
16C2×C31×#107C2211yescharacteristic
17C2×C31×C4⋊C8C2211yescharacteristic
18C31×#389—21no—
19C31×#367—21no—
20C31×#366—21no—
21C31×#358—21no—
22C31×#357—21no—
23C31×C22⋊C16C2211yescharacteristic
24C31×C22⋊C16C2211yescharacteristic
25C31×#340—21no—
26C31×#340C2211yescharacteristic
27C2×Q16×C31D411yescharacteristic
28C2×SD16×C31—21no—
29C2×D8×C31D411yescharacteristic
30C22×C8×C31D411yescharacteristic
31C22×C8×C31C2311yescharacteristic
32C31×#126—41no—
33C31×#125—21no—
34C31×#124—21no—
35C31×#123—41no—
36C31×C22⋊Q8—21no—
37C31×#121—21no—
38C4×Q8×C31—21no—
39C4×D4×C31—21no—
40C4×D4×C31—41no—
41C31×#117—41no—
42C2×C4⋊C4×C31—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—41no—
45C2×C42×C31D411yescharacteristic
46C2×C16×C31—21no—
47C2×C16×C31—21no—
48C31×#107—21no—
49C31×#107—21no—
50C31×#107D411yescharacteristic
51C31×#107D411yescharacteristic
52C31×#106—21no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×#103—21no—
56C31×#103—21no—
57C31×#102—21no—
58C31×#102—21no—
59C31×#95—41no—
60C2×Q8×C31—21no—
61C2×D4×C31—21no—
62C2×D4×C31—41no—
63C22×C4×C31—41no—
64C22×C4×C31—41no—
65C22×C4×C31—41no—
66C22×C4×C31D811yescharacteristic
67C22×C4×C31D811yescharacteristic
68C22×C4×C31C2×D411yescharacteristic
69Q16×C31—41no—
70SD16×C31—81no—
71D8×C31—41no—
72C2×C8×C31—21no—
73C2×C8×C31—41no—
74C2×C8×C31—41no—
75C2×C8×C31C2×D411yescharacteristic
76C2×C8×C31C2×D411yescharacteristic
77C4⋊C4×C31—22no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—82no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—41no—
92C22⋊C4×C31—41no—
93C42×C31—21no—
94C42×C31—21no—
95C42×C31—41no—
96C16×C31—41no—
97C16×C31—41no—
98#12290C3111yesmaximal, characteristic, direct product factor, Sylow
99C23×C31—41no—
100C23×C31C2×D811yescharacteristic
101Q8×C31—41no—
102Q8×C31—41no—
103D4×C31—41no—
104D4×C31—41no—
105D4×C31—81no—
106D4×C31—81no—
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—41no—
114C2×C4×C31—42no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—41no—
118C2×C4×C31—82no—
119C2×C4×C31—81no—
120C2×C4×C31—81no—
121C2×C4×C31—81no—
122C2×C4×C31—81no—
123C2×C4×C31—81no—
124C2×C4×C31#12011yescharacteristic
125C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
126C8×C31—21no—
127C8×C31—21no—
128C8×C31—41no—
129#3250C2×C3111yescharacteristic
130#2235C2×C3111yescharacteristic, complemented
131#2232C2×C3111yescharacteristic
132#2086C2×C3111yescharacteristic, complemented
133#1348C2×C3111yescharacteristic, complemented
134#1347C2×C3111yescharacteristic
135#1322C2×C3111yescharacteristic, complemented
136C22×C31—21no—
137C22×C31—21no—
138C22×C31—81no—
139C22×C31—81no—
140C22×C31—81no—
141C22×C31#44711yescharacteristic
142C22×C31#50811yescharacteristic
143C22×C31#50911yescharacteristic
144C4×C31—21no—
145C4×C31—41no—
146C4×C31—41no—
147C4×C31—82no—
148C4×C31—81no—
149C4×C31—81no—
150C4×C31—81no—
151C4×C31—161no—
152C4×C31#45611yescharacteristic
153C4×C31#45811yescharacteristic
154#529—21no—
155#479—21no—
156#478—21no—
157#467C22×C3111yescharacteristic
158#466C22×C3111yescharacteristic
159#465—21no—
160#464—21no—
161#463—21no—
162C2×#107C22×C3111yescharacteristic
163C2×C4⋊C8C22×C3111yescharacteristic
164#389—21no—
165#367—21no—
166#366—21no—
167#358—21no—
168#357—21no—
169C22⋊C16C22×C3111yescharacteristic
170C22⋊C16C22×C3111yescharacteristic
171#340—21no—
172#340C22×C3111yescharacteristic
173C2×C31—21no—
174C2×C31—21no—
175C2×C31—161no—
176C2×C31#161011yescharacteristic
177C2×C31#218611yescharacteristic
178C2×C31#219111yescharacteristic
179C2×Q16D4×C3111yescharacteristic
180C2×SD16—21no—
181C2×D8D4×C3111yescharacteristic
182C22×C8D4×C3111yescharacteristic
183C22×C8C23×C3111yescharacteristic
184#126—41no—
185#125—21no—
186#124—21no—
187#123—41no—
188C22⋊Q8—21no—
189#121—21no—
190C4×Q8—21no—
191C4×D4—21no—
192C4×D4—41no—
193#117—41no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—41no—
197C2×C42D4×C3111yescharacteristic
198C2×C16—21no—
199C2×C16—21no—
200#107—21no—
201#107—21no—
202#107D4×C3111yescharacteristic
203#107D4×C3111yescharacteristic
204#106—21no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207#103—21no—
208#103—21no—
209#102—21no—
210#102—21no—
211#95—41no—
212C31#1229011yescharacteristic, direct product factor, Sylow
213C2×Q8—21no—
214C2×D4—21no—
215C2×D4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4D8×C3111yescharacteristic
220C22×C4D8×C3111yescharacteristic
221C22×C4C2×D4×C3111yescharacteristic
222Q16—41no—
223SD16—81no—
224D8—41no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8C2×D4×C3111yescharacteristic
229C2×C8C2×D4×C3111yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—82no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C42—21no—
247C42—21no—
248C42—41no—
249C16—41no—
250C16—41no—
251C23—41no—
252C23C2×D8×C3111yescharacteristic
253Q8—41no—
254Q8—41no—
255D4—41no—
256D4—41no—
257D4—81no—
258D4—81no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—82no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4C31×#12011yescharacteristic
277C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
278C8—21no—
279C8—21no—
280C8—41no—
281C22—21no—
282C22—21no—
283C22—81no—
284C22—81no—
285C22—81no—
286C22C31×#44711yescharacteristic
287C22C31×#50811yescharacteristic
288C22C31×#50911yescharacteristic
289C4—21no—
290C4—41no—
291C4—41no—
292C4—82no—
293C4—81no—
294C4—81no—
295C4—81no—
296C4—161no—
297C4C31×#45611yescharacteristic
298C4C31×#45811yescharacteristic
299C2—21no—
300C2—21no—
301C2—161no—
302C2C31×#161011yescharacteristic
303C2C31×#218611yescharacteristic
304C2C31×#219111yescharacteristic
subgroupG/H
center, socleC22×C31#447
commutator, Frattini, cosocleC22×C8C23×C31
prime radicalC31×#466C22
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×C4⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2235C2semidirect
4. C31×#2086C2semidirect
5. C31×#1348C2semidirect
7. C31×#1322C2semidirect
98. #12290C31direct (N × H)
130. #2235C2×C31semidirect
132. #2086C2×C31semidirect
133. #1348C2×C31semidirect
135. #1322C2×C31semidirect
212. C31#12290direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32502
C31×#22352
C31×#22322
C31×#20862
C31×#13482
C31×#13472
C31×#13222
#1229031