Finite Group Databasebeta

← C31×#7397 #21464156

Subgroups — C31×#7397 #21464156

Order 7936.

268 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 42 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×#2010C211yesmaximal, characteristic
2C31×#1320C211yesmaximal, characteristic, complemented
3C31×#1298C211yesmaximal, characteristic, complemented
4C31×#575C411yescharacteristic
5C31×#525—21no—
6C31×#421—21no—
7C31×#407C2211yescharacteristic
8C2×C31×C22⋊C8—21no—
9C31×#349—21no—
10C31×H(3,ℤ/4)C411yescharacteristic
11C2×#41×C31—21no—
12C23×C4×C31D411yescharacteristic
13C31×#137—41no—
14C31×AGL(1,ℤ/8)—41no—
15C31×#135—41no—
16C2×M16×C31C2×C411yescharacteristic
17C2×M16×C31D411yescharacteristic
18C22×C8×C31—41no—
19C31×#123—41no—
20C31×C22⋊Q8—41no—
21C31×#121—41no—
22C31×#120—41no—
23C4×D4×C31—42no—
24C31×#117—21no—
25C31×M32—41no—
26C31×#104—42no—
27C31×C22⋊C8—22no—
28C31×C22⋊C8—41no—
29C31×C22⋊C8—41no—
30C24×C31SD1611yescharacteristic
31#41×C31—41no—
32#41×C31—41no—
33#41×C31—41no—
34#41×C31—41no—
35C2×Q8×C31—21no—
36C2×D4×C31—21no—
37C2×D4×C31—42no—
38C2×D4×C31—41no—
39C22×C4×C31—21no—
40C22×C4×C31—21no—
41C22×C4×C31—41no—
42C22×C4×C31—41no—
43C22×C4×C31—41no—
44C22×C4×C31C22⋊C411yescharacteristic
45C22×C4×C31D811yescharacteristic
46Q16×C31—41no—
47SD16×C31—42no—
48D8×C31—41no—
49M16×C31—41no—
50M16×C31—41no—
51C2×C8×C31—21no—
52C2×C8×C31—21no—
53C2×C8×C31—42no—
54C2×C8×C31—81no—
55C2×C8×C31—81no—
56C4⋊C4×C31—41no—
57C4⋊C4×C31—42no—
58C22⋊C4×C31—42no—
59C22⋊C4×C31—42no—
60C22⋊C4×C31—41no—
61C42×C31—22no—
62C16×C31—81no—
63#7397C3111yesmaximal, characteristic, direct product factor, Sylow
64C23×C31—21no—
65C23×C31—41no—
66C23×C31—42no—
67C23×C31—41no—
68C23×C31#10211yescharacteristic
69Q8×C31—41no—
70Q8×C31—41no—
71D4×C31—41no—
72D4×C31—41no—
73D4×C31—81no—
74D4×C31—84no—
75D4×C31—81no—
76C2×C4×C31—21no—
77C2×C4×C31—21no—
78C2×C4×C31—21no—
79C2×C4×C31—41no—
80C2×C4×C31—41no—
81C2×C4×C31—41no—
82C2×C4×C31—42no—
83C2×C4×C31—41no—
84C2×C4×C31—81no—
85C2×C4×C31—81no—
86C2×C4×C31—81no—
87C2×C4×C31#9911yescharacteristic
88C2×C4×C31#10411yescharacteristic
89C8×C31—41no—
90C8×C31—41no—
91C8×C31—82no—
92#2010C2×C3111yescharacteristic
93#1320C2×C3111yescharacteristic, complemented
94#1298C2×C3111yescharacteristic, complemented
95C22×C31—22no—
96C22×C31—21no—
97C22×C31—41no—
98C22×C31—41no—
99C22×C31—42no—
100C22×C31—41no—
101C22×C31—81no—
102C22×C31—82no—
103C22×C31—81no—
104C22×C31#32711yescharacteristic
105C4×C31—21no—
106C4×C31—41no—
107C4×C31—82no—
108C4×C31—81no—
109C4×C31AΣL(1,𝔽16)11yescharacteristic
110C4×C31#35311yescharacteristic
111#575C4×C3111yescharacteristic
112#525—21no—
113#421—21no—
114#407C22×C3111yescharacteristic
115C2×C22⋊C8—21no—
116#349—21no—
117H(3,ℤ/4)C4×C3111yescharacteristic
118C2×C31—21no—
119C2×C31—41no—
120C2×C31—42no—
121C2×C31—161no—
122C2×C31#134311yescharacteristic
123C2×#41—21no—
124C23×C4D4×C3111yescharacteristic
125#137—41no—
126AGL(1,ℤ/8)—41no—
127#135—41no—
128C2×M16C2×C4×C3111yescharacteristic
129C2×M16D4×C3111yescharacteristic
130C22×C8—41no—
131#123—41no—
132C22⋊Q8—41no—
133#121—41no—
134#120—41no—
135C4×D4—42no—
136#117—21no—
137M32—41no—
138#104—42no—
139C22⋊C8—22no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C31#739711yescharacteristic, direct product factor, Sylow
143C24SD16×C3111yescharacteristic
144#41—41no—
145#41—41no—
146#41—41no—
147#41—41no—
148C2×Q8—21no—
149C2×D4—21no—
150C2×D4—42no—
151C2×D4—41no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4C22⋊C4×C3111yescharacteristic
158C22×C4D8×C3111yescharacteristic
159Q16—41no—
160SD16—42no—
161D8—41no—
162M16—41no—
163M16—41no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—42no—
167C2×C8—81no—
168C2×C8—81no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C22⋊C4—41no—
174C42—22no—
175C16—81no—
176C23—21no—
177C23—41no—
178C23—42no—
179C23—41no—
180C23C31×#10211yescharacteristic
181Q8—41no—
182Q8—41no—
183D4—41no—
184D4—41no—
185D4—81no—
186D4—84no—
187D4—81no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4C31×#9911yescharacteristic
200C2×C4C31×#10411yescharacteristic
201C8—41no—
202C8—41no—
203C8—82no—
204C22—22no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—41no—
210C22—81no—
211C22—82no—
212C22—81no—
213C22C31×#32711yescharacteristic
214C4—21no—
215C4—41no—
216C4—82no—
217C4—81no—
218C4C31×AΣL(1,𝔽16)11yescharacteristic
219C4C31×#35311yescharacteristic
220C2—21no—
221C2—41no—
222C2—42no—
223C2—161no—
224C2C31×#134311yescharacteristic
subgroupG/H
centerC4×C31#353
commutatorC2×M16C2×C4×C31
Frattini, cosocle#407C22×C31
socleC2×C31#1343
prime radicalC31×#2010C2
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#407 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1320C2semidirect
3. C31×#1298C2semidirect
63. #7397C31direct (N × H)
93. #1320C2×C31semidirect
94. #1298C2×C31semidirect
142. C31#7397direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#20102
C31×#13202
C31×#12982
#739731