Finite Group Databasebeta

← C31×#7396 #21464155

Subgroups — C31×#7396 #21464155

Order 7936.

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

normal subgroups only

This group has 296 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×#1297C211yesmaximal, characteristic, complemented
4C31×#575C411yescharacteristic, complemented
5C31×#525—21no—
6C31×#421—21no—
7C31×#407C2211yescharacteristic
8C4×C22⋊C4×C31—21no—
9C31×#349—21no—
10C31×H(3,ℤ/4)C411yescharacteristic, complemented
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
18C31×#123—41no—
19C31×C22⋊Q8—41no—
20C31×#121—41no—
21C31×#120—41no—
22C4×D4×C31—42no—
23C31×#117—21no—
24C2×C22⋊C4×C31—41no—
25C2×C42×C31—41no—
26C31×M32—41no—
27C31×#104—42no—
28C31×C22⋊C8—41no—
29C31×#95—22no—
30C24×C31D811yescharacteristic
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×C31—42no—
45C22×C4×C31C22⋊C411yescharacteristic
46C22×C4×C31SD1611yescharacteristic
47Q16×C31—41no—
48SD16×C31—42no—
49D8×C31—41no—
50M16×C31—41no—
51M16×C31—41no—
52C2×C8×C31—21no—
53C2×C8×C31—21no—
54C4⋊C4×C31—41no—
55C4⋊C4×C31—42no—
56C22⋊C4×C31—44no—
57C22⋊C4×C31—42no—
58C22⋊C4×C31—42no—
59C22⋊C4×C31—41no—
60C42×C31—22no—
61C42×C31—81no—
62C42×C31—81no—
63C16×C31—81no—
64#7396C3111yesmaximal, characteristic, direct product factor, Sylow
65C23×C31—21no—
66C23×C31—41no—
67C23×C31—42no—
68C23×C31—41no—
69C23×C31#10211yescharacteristic
70Q8×C31—41no—
71Q8×C31—41no—
72D4×C31—41no—
73D4×C31—41no—
74D4×C31—81no—
75D4×C31—84no—
76D4×C31—81no—
77C2×C4×C31—21no—
78C2×C4×C31—21no—
79C2×C4×C31—21no—
80C2×C4×C31—41no—
81C2×C4×C31—41no—
82C2×C4×C31—41no—
83C2×C4×C31—42no—
84C2×C4×C31—41no—
85C2×C4×C31—44no—
86C2×C4×C31—81no—
87C2×C4×C31—81no—
88C2×C4×C31—82no—
89C2×C4×C31—82no—
90C2×C4×C31—81no—
91C2×C4×C31#9911yescharacteristic
92C2×C4×C31#10411yescharacteristic
93C8×C31—41no—
94C8×C31—41no—
95#2010C2×C3111yescharacteristic
96#1320C2×C3111yescharacteristic, complemented
97#1297C2×C3111yescharacteristic, complemented
98C22×C31—22no—
99C22×C31—21no—
100C22×C31—41no—
101C22×C31—41no—
102C22×C31—42no—
103C22×C31—41no—
104C22×C31—81no—
105C22×C31—82no—
106C22×C31—81no—
107C22×C31#32711yescharacteristic
108C4×C31—21no—
109C4×C31—41no—
110C4×C31—84no—
111C4×C31—82no—
112C4×C31—81no—
113C4×C31AΣL(1,𝔽16)11yescharacteristic
114C4×C31#35311yescharacteristic
115#575C4×C3111yescharacteristic, complemented
116#525—21no—
117#421—21no—
118#407C22×C3111yescharacteristic
119C4×C22⋊C4—21no—
120#349—21no—
121H(3,ℤ/4)C4×C3111yescharacteristic, complemented
122C2×C31—21no—
123C2×C31—42no—
124C2×C31—41no—
125C2×C31—161no—
126C2×C31#134311yescharacteristic
127C2×#41—21no—
128C23×C4D4×C3111yescharacteristic
129#137—41no—
130AGL(1,ℤ/8)—41no—
131#135—41no—
132C2×M16C2×C4×C3111yescharacteristic
133C2×M16D4×C3111yescharacteristic
134#123—41no—
135C22⋊Q8—41no—
136#121—41no—
137#120—41no—
138C4×D4—42no—
139#117—21no—
140C2×C22⋊C4—41no—
141C2×C42—41no—
142M32—41no—
143#104—42no—
144C22⋊C8—41no—
145#95—22no—
146C31#739611yescharacteristic, direct product factor, Sylow
147C24D8×C3111yescharacteristic
148#41—41no—
149#41—41no—
150#41—41no—
151#41—41no—
152C2×Q8—21no—
153C2×D4—21no—
154C2×D4—42no—
155C2×D4—41no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—42no—
162C22×C4C22⋊C4×C3111yescharacteristic
163C22×C4SD16×C3111yescharacteristic
164Q16—41no—
165SD16—42no—
166D8—41no—
167M16—41no—
168M16—41no—
169C2×C8—21no—
170C2×C8—21no—
171C4⋊C4—41no—
172C4⋊C4—42no—
173C22⋊C4—44no—
174C22⋊C4—42no—
175C22⋊C4—42no—
176C22⋊C4—41no—
177C42—22no—
178C42—81no—
179C42—81no—
180C16—81no—
181C23—21no—
182C23—41no—
183C23—42no—
184C23—41no—
185C23C31×#10211yescharacteristic
186Q8—41no—
187Q8—41no—
188D4—41no—
189D4—41no—
190D4—81no—
191D4—84no—
192D4—81no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—44no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—82no—
205C2×C4—82no—
206C2×C4—81no—
207C2×C4C31×#9911yescharacteristic
208C2×C4C31×#10411yescharacteristic
209C8—41no—
210C8—41no—
211C22—22no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—42no—
216C22—41no—
217C22—81no—
218C22—82no—
219C22—81no—
220C22C31×#32711yescharacteristic
221C4—21no—
222C4—41no—
223C4—84no—
224C4—82no—
225C4—81no—
226C4C31×AΣL(1,𝔽16)11yescharacteristic
227C4C31×#35311yescharacteristic
228C2—21no—
229C2—41no—
230C2—42no—
231C2—161no—
232C2C31×#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×#1297C2semidirect
4. C31×#575C4semidirect
10. C31×H(3,ℤ/4)C4semidirect
64. #7396C31direct (N × H)
96. #1320C2×C31semidirect
97. #1297C2×C31semidirect
115. #575C4×C31semidirect
121. H(3,ℤ/4)C4×C31semidirect
146. C31#7396direct (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×#12972
#739631