Finite Group Databasebeta

← C31×#1618 #16841551

Subgroups — C31×#1618 #16841551

Order 3968.

240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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×#538C211yesmaximal, characteristic
2C31×#484C211yesmaximal, characteristic, complemented
3C31×#481C211yesmaximal, characteristic, complemented
4C31×#399C211yesmaximal, characteristic, complemented
5C31×#328C211yesmaximal, characteristic, complemented
6C31×#327C211yesmaximal, characteristic, complemented
7C31×#323C211yesmaximal, characteristic, complemented
8C31×#126—21no—
9C31×#124—21no—
10C31×#123—21no—
11C31×C22⋊Q8C2211yescharacteristic
12C31×#121—21no—
13C31×#121C2211yescharacteristic
14C31×#120—21no—
15C4×D4×C31—21no—
16C2×C4⋊C4×C31—21no—
17C2×C4⋊C4×C31C2211yescharacteristic
18C2×C22⋊C4×C31—21no—
19C2×C22⋊C4×C31C2211yescharacteristic
20C31×#107—21no—
21C31×#106—21no—
22C31×#103—21no—
23C31×#102—21no—
24C31×C22⋊C8C2211yescharacteristic
25C31×C22⋊C8C2211yescharacteristic
26C31×#95C2211yescharacteristic
27C24×C31D411yescharacteristic
28C2×Q8×C31D411yescharacteristic
29C2×D4×C31—21no—
30C2×D4×C31—21no—
31C2×D4×C31—21no—
32C2×D4×C31D411yescharacteristic
33C22×C4×C31—21no—
34C22×C4×C31—21no—
35C22×C4×C31—21no—
36C22×C4×C31D411yescharacteristic
37C22×C4×C31C2311yescharacteristic
38C2×C8×C31—21no—
39C2×C8×C31—21no—
40C4⋊C4×C31—21no—
41C4⋊C4×C31—21no—
42C4⋊C4×C31—21no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31—42no—
45C4⋊C4×C31D411yescharacteristic
46C4⋊C4×C31D411yescharacteristic
47C22⋊C4×C31—21no—
48C22⋊C4×C31—21no—
49C22⋊C4×C31—21no—
50C22⋊C4×C31—21no—
51C22⋊C4×C31—21no—
52C22⋊C4×C31—21no—
53C22⋊C4×C31—21no—
54C22⋊C4×C31—42no—
55C42×C31—21no—
56C23×C31—21no—
57C23×C31—21no—
58C23×C31—21no—
59C23×C31—21no—
60C23×C31—41no—
61C23×C31—41no—
62C23×C31C2×D411yescharacteristic
63Q8×C31—41no—
64D4×C31—41no—
65D4×C31—41no—
66D4×C31—41no—
67D4×C31—81no—
68D4×C31—81no—
69C2×C4×C31—22no—
70C2×C4×C31—21no—
71C2×C4×C31—21no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31—41no—
78C2×C4×C31—41no—
79C2×C4×C31—41no—
80C2×C4×C31—41no—
81C2×C4×C31—81no—
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31C2×D411yescharacteristic
84C8×C31—41no—
85C8×C31—41no—
86#1618C3111yesmaximal, characteristic, direct product factor, Sylow
87C22×C31—21no—
88C22×C31—21no—
89C22×C31—42no—
90C22×C31—41no—
91C22×C31—41no—
92C22×C31—41no—
93C22×C31—41no—
94C22×C31—41no—
95C22×C31—41no—
96C22×C31—81no—
97C22×C31#12011yescharacteristic
98C22×C31#13511yescharacteristic
99C22×C31#13711yescharacteristic
100C4×C31—21no—
101C4×C31—21no—
102C4×C31—42no—
103C4×C31—41no—
104C4×C31—41no—
105C4×C31—41no—
106C4×C31—41no—
107C4×C31—81no—
108#538C2×C3111yescharacteristic
109#484C2×C3111yescharacteristic, complemented
110#481C2×C3111yescharacteristic, complemented
111#399C2×C3111yescharacteristic, complemented
112#328C2×C3111yescharacteristic, complemented
113#327C2×C3111yescharacteristic, complemented
114#323C2×C3111yescharacteristic, complemented
115C2×C31—21no—
116C2×C31—21no—
117C2×C31—81no—
118C2×C31—81no—
119C2×C31#45211yescharacteristic
120C2×C31#45311yescharacteristic
121C2×C31#45811yescharacteristic
122#126—21no—
123#124—21no—
124#123—21no—
125C22⋊Q8C22×C3111yescharacteristic
126#121—21no—
127#121C22×C3111yescharacteristic
128#120—21no—
129C4×D4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4C22×C3111yescharacteristic
132C2×C22⋊C4—21no—
133C2×C22⋊C4C22×C3111yescharacteristic
134#107—21no—
135#106—21no—
136#103—21no—
137#102—21no—
138C22⋊C8C22×C3111yescharacteristic
139C22⋊C8C22×C3111yescharacteristic
140#95C22×C3111yescharacteristic
141C31#161811yescharacteristic, direct product factor, Sylow
142C24D4×C3111yescharacteristic
143C2×Q8D4×C3111yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4D4×C3111yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4D4×C3111yescharacteristic
152C22×C4C23×C3111yescharacteristic
153C2×C8—21no—
154C2×C8—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—42no—
160C4⋊C4D4×C3111yescharacteristic
161C4⋊C4D4×C3111yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—42no—
170C42—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—21no—
175C23—41no—
176C23—41no—
177C23C2×D4×C3111yescharacteristic
178Q8—41no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—81no—
183D4—81no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—81no—
197C2×C4C2×D4×C3111yescharacteristic
198C2×C4C2×D4×C3111yescharacteristic
199C8—41no—
200C8—41no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—81no—
211C22C31×#12011yescharacteristic
212C22C31×#13511yescharacteristic
213C22C31×#13711yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—41no—
221C4—81no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—81no—
226C2C31×#45211yescharacteristic
227C2C31×#45311yescharacteristic
228C2C31×#45811yescharacteristic
subgroupG/H
center, socleC22×C31#120
commutator, Frattini, cosocleC22×C4C23×C31
prime radicalC31×#538C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#484C2semidirect
3. C31×#481C2semidirect
4. C31×#399C2semidirect
5. C31×#328C2semidirect
6. C31×#327C2semidirect
7. C31×#323C2semidirect
86. #1618C31direct (N × H)
109. #484C2×C31semidirect
110. #481C2×C31semidirect
111. #399C2×C31semidirect
112. #328C2×C31semidirect
113. #327C2×C31semidirect
114. #323C2×C31semidirect
141. C31#1618direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#5382
C31×#4842
C31×#4812
C31×#3992
C31×#3282
C31×#3272
C31×#3232
#161831