Finite Group Databasebeta

← C31×#12291 #21469050

Subgroups — C31×#12291 #21469050

Order 7936.

354 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3245C211yesmaximal, characteristic
2C31×#2233C212yesmaximal, complemented
3C31×#2087C211yesmaximal, characteristic, complemented
4C31×#1347C212yesmaximal, complemented
5C31×#1322C211yesmaximal, characteristic, complemented
6C31×#532—21no—
7C31×#474—22no—
8C31×#466—21no—
9C31×#466C2212yes—
10C31×#459—22no—
11C2×C31×#107C2211yescharacteristic
12C2×C31×C4⋊C8C2211yescharacteristic
13C31×#389—21no—
14C31×#367—22no—
15C31×#357—22no—
16C31×C22⋊C16C2212yes—
17C31×#340—21no—
18C31×#340C2211yescharacteristic
19C2×#41×C31—41no—
20C2×D8×C31—21no—
21C2×D8×C31D412yes—
22C22×C8×C31D411yescharacteristic
23C22×C8×C31C2311yescharacteristic
24C31×C4⋊Q8—21no—
25C31×#127—21no—
26C31×#124—41no—
27C31×#121—22no—
28C31×#121—41no—
29C4×D4×C31—22no—
30C4×D4×C31—41no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—41no—
34C2×C42×C31D411yescharacteristic
35C2×C16×C31—22no—
36C31×#107—21no—
37C31×#107—22no—
38C31×#107D412yes—
39C31×C4⋊C8—22no—
40C31×#102—22no—
41C31×#102—22no—
42C31×#95—41no—
43#41×C31—82no—
44#41×C31—82no—
45C2×Q8×C31—41no—
46C2×D4×C31—22no—
47C2×D4×C31—41no—
48C2×D4×C31—41no—
49C2×D4×C31—42no—
50C22×C4×C31—42no—
51C22×C4×C31—41no—
52C22×C4×C31—41no—
53C22×C4×C31D811yescharacteristic
54C22×C4×C31D811yescharacteristic
55C22×C4×C31C2×D411yescharacteristic
56D8×C31—42no—
57D8×C31—81no—
58C2×C8×C31—21no—
59C2×C8×C31—41no—
60C2×C8×C31—41no—
61C2×C8×C31C2×D412yes—
62C4⋊C4×C31—22no—
63C4⋊C4×C31—22no—
64C4⋊C4×C31—41no—
65C4⋊C4×C31—41no—
66C4⋊C4×C31—41no—
67C4⋊C4×C31—41no—
68C4⋊C4×C31—82no—
69C22⋊C4×C31—42no—
70C22⋊C4×C31—42no—
71C42×C31—21no—
72C42×C31—21no—
73C16×C31—42no—
74#12291C3111yesmaximal, characteristic, direct product factor, Sylow
75C23×C31—42no—
76C23×C31C2×D811yescharacteristic
77Q8×C31—82no—
78D4×C31—42no—
79D4×C31—42no—
80D4×C31—82no—
81D4×C31—82no—
82D4×C31—82no—
83D4×C31—82no—
84C2×C4×C31—21no—
85C2×C4×C31—21no—
86C2×C4×C31—21no—
87C2×C4×C31—21no—
88C2×C4×C31—21no—
89C2×C4×C31—41no—
90C2×C4×C31—42no—
91C2×C4×C31—42no—
92C2×C4×C31—84no—
93C2×C4×C31—81no—
94C2×C4×C31—81no—
95C2×C4×C31—81no—
96C2×C4×C31—81no—
97C2×C4×C31—81no—
98C2×C4×C31SD3212yes—
99C2×C4×C31#12011yescharacteristic
100C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
101C8×C31—22no—
102C8×C31—41no—
103#3245C2×C3111yescharacteristic
104#2233C2×C3112yescomplemented
105#2087C2×C3111yescharacteristic, complemented
106#1347C2×C3112yescomplemented
107#1322C2×C3111yescharacteristic, complemented
108C22×C31—21no—
109C22×C31—21no—
110C22×C31—82no—
111C22×C31—82no—
112C22×C31—82no—
113C22×C31#44711yescharacteristic
114C22×C31C2×SD3211yescharacteristic
115C22×C31#50911yescharacteristic
116C4×C31—21no—
117C4×C31—22no—
118C4×C31—41no—
119C4×C31—82no—
120C4×C31—82no—
121C4×C31—161no—
122C4×C31#45611yescharacteristic
123C4×C31#45811yescharacteristic
124#532—21no—
125#474—22no—
126#466—21no—
127#466C22×C3112yes—
128#459—22no—
129C2×#107C22×C3111yescharacteristic
130C2×C4⋊C8C22×C3111yescharacteristic
131#389—21no—
132#367—22no—
133#357—22no—
134C22⋊C16C22×C3112yes—
135#340—21no—
136#340C22×C3111yescharacteristic
137C2×C31—21no—
138C2×C31—21no—
139C2×C31—162no—
140C2×C31#161011yescharacteristic
141C2×C31#218711yescharacteristic
142C2×C31#219011yescharacteristic
143C2×#41—41no—
144C2×D8—21no—
145C2×D8D4×C3112yes—
146C22×C8D4×C3111yescharacteristic
147C22×C8C23×C3111yescharacteristic
148C4⋊Q8—21no—
149#127—21no—
150#124—41no—
151#121—22no—
152#121—41no—
153C4×D4—22no—
154C4×D4—41no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—41no—
158C2×C42D4×C3111yescharacteristic
159C2×C16—22no—
160#107—21no—
161#107—22no—
162#107D4×C3112yes—
163C4⋊C8—22no—
164#102—22no—
165#102—22no—
166#95—41no—
167C31#1229111yescharacteristic, direct product factor, Sylow
168#41—82no—
169#41—82no—
170C2×Q8—41no—
171C2×D4—22no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4—42no—
175C22×C4—42no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4D8×C3111yescharacteristic
179C22×C4D8×C3111yescharacteristic
180C22×C4C2×D4×C3111yescharacteristic
181D8—42no—
182D8—81no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8C2×D4×C3112yes—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—82no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C42—21no—
197C42—21no—
198C16—42no—
199C23—42no—
200C23C2×D8×C3111yescharacteristic
201Q8—82no—
202D4—42no—
203D4—42no—
204D4—82no—
205D4—82no—
206D4—82no—
207D4—82no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—84no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4C31×SD3212yes—
223C2×C4C31×#12011yescharacteristic
224C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—82no—
230C22—82no—
231C22—82no—
232C22C31×#44711yescharacteristic
233C22C2×C31×SD3211yescharacteristic
234C22C31×#50911yescharacteristic
235C4—21no—
236C4—22no—
237C4—41no—
238C4—82no—
239C4—82no—
240C4—161no—
241C4C31×#45611yescharacteristic
242C4C31×#45811yescharacteristic
243C2—21no—
244C2—21no—
245C2—162no—
246C2C31×#161011yescharacteristic
247C2C31×#218711yescharacteristic
248C2C31×#219011yescharacteristic
subgroupG/H
center, socleC22×C31#447
commutator, Frattini, cosocleC22×C8C23×C31
prime radicalC31×#3245C2
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×#2233C2semidirect
3. C31×#2087C2semidirect
4. C31×#1347C2semidirect
5. C31×#1322C2semidirect
74. #12291C31direct (N × H)
104. #2233C2×C31semidirect
105. #2087C2×C31semidirect
106. #1347C2×C31semidirect
107. #1322C2×C31semidirect
167. C31#12291direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32452
C31×#22332
C31×#20872
C31×#13472
C31×#13222
#1229131