Finite Group Databasebeta

← C31×#10531 #21467290

Subgroups — C31×#10531 #21467290

Order 7936.

386 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3253C211yesmaximal, characteristic
2C31×#1837C211yesmaximal, characteristic, complemented
3C31×#1560C212yesmaximal, complemented
4C31×#1492C212yesmaximal, complemented
5C31×#1309C211yesmaximal, characteristic, complemented
6C31×#532C2212yes—
7C31×#476—22no—
8C31×#469—22no—
9C31×#459—22no—
10C31×#423C2211yescharacteristic
11C31×#423C2212yes—
12C31×#423C2211yescharacteristic
13C2×C4×C8×C31C2211yescharacteristic
14C31×#341—22no—
15C31×#333—22no—
16C31×#331—22no—
17C31×D4⋊C8—24no—
18C2×#41×C31—22no—
19C2×D8×C31—22no—
20C2×M16×C31—21no—
21C2×M16×C31—22no—
22C2×M16×C31D412yes—
23C22×C8×C31—21no—
24C31×C4⋊Q8D412yes—
25C31×#127D412yes—
26C31×#124—22no—
27C31×#121—22no—
28C31×#121—22no—
29C4×D4×C31—22no—
30C4×D4×C31—22no—
31C2×C42×C31C2311yescharacteristic
32C31×#106—22no—
33C31×C4⋊C8—22no—
34C31×C4⋊C8—22no—
35C31×C4⋊C8—22no—
36C31×C4⋊C8—22no—
37C31×#102—24no—
38C4×C8×C31—21no—
39C4×C8×C31D412yes—
40#41×C31—82no—
41#41×C31—82no—
42C2×Q8×C31—22no—
43C2×D4×C31—22no—
44C2×D4×C31—22no—
45C2×D4×C31—22no—
46C2×D4×C31—42no—
47C22×C4×C31—42no—
48C22×C4×C31C2×D411yescharacteristic
49C22×C4×C31#4112yes—
50D8×C31—82no—
51M16×C31—42no—
52M16×C31—42no—
53M16×C31—82no—
54C2×C8×C31—22no—
55C2×C8×C31—22no—
56C2×C8×C31—41no—
57C2×C8×C31—41no—
58C2×C8×C31—41no—
59C2×C8×C31—42no—
60C4⋊C4×C31—22no—
61C4⋊C4×C31—22no—
62C22⋊C4×C31—42no—
63C22⋊C4×C31—42no—
64C42×C31C2×D412yes—
65C42×C31C2×D411yescharacteristic
66C42×C31#4111yescharacteristic
67#10531C3111yesmaximal, characteristic, direct product factor, Sylow
68C23×C31—42no—
69C23×C31#12411yescharacteristic
70Q8×C31—82no—
71D4×C31—42no—
72D4×C31—42no—
73D4×C31—42no—
74D4×C31—42no—
75D4×C31—82no—
76D4×C31—84no—
77C2×C4×C31—21no—
78C2×C4×C31—21no—
79C2×C4×C31—22no—
80C2×C4×C31—22no—
81C2×C4×C31—42no—
82C2×C4×C31—82no—
83C2×C4×C31—82no—
84C2×C4×C31#12011yescharacteristic
85C2×C4×C31#12111yescharacteristic
86C2×C4×C31#12112yes—
87C2×C4×C31#12312yes—
88C8×C31—42no—
89C8×C31—42no—
90C8×C31—81no—
91C8×C31—82no—
92#3253C2×C3111yescharacteristic
93#1837C2×C3111yescharacteristic, complemented
94#1560C2×C3112yescomplemented
95#1492C2×C3112yescomplemented
96#1309C2×C3111yescharacteristic, complemented
97C22×C31—22no—
98C22×C31—21no—
99C22×C31—82no—
100C22×C31—82no—
101C22×C31—82no—
102C22×C31#39411yescharacteristic
103C4×C31—22no—
104C4×C31—21no—
105C4×C31—82no—
106C4×C31#45411yescharacteristic
107C4×C31#45511yescharacteristic
108C4×C31#47112yes—
109C4×C31#47212yes—
110#532C22×C3112yes—
111#476—22no—
112#469—22no—
113#459—22no—
114#423C22×C3111yescharacteristic
115#423C22×C3112yes—
116#423C22×C3111yescharacteristic
117C2×C4×C8C22×C3111yescharacteristic
118#341—22no—
119#333—22no—
120#331—22no—
121D4⋊C8—24no—
122C2×C31—41no—
123C2×C31—162no—
124C2×C31#204011yescharacteristic
125C2×C31#205112yes—
126C2×#41—22no—
127C2×D8—22no—
128C2×M16—21no—
129C2×M16—22no—
130C2×M16D4×C3112yes—
131C22×C8—21no—
132C4⋊Q8D4×C3112yes—
133#127D4×C3112yes—
134#124—22no—
135#121—22no—
136#121—22no—
137C4×D4—22no—
138C4×D4—22no—
139C2×C42C23×C3111yescharacteristic
140#106—22no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—22no—
145#102—24no—
146C4×C8—21no—
147C4×C8D4×C3112yes—
148C31#1053111yescharacteristic, direct product factor, Sylow
149#41—82no—
150#41—82no—
151C2×Q8—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—42no—
156C22×C4—42no—
157C22×C4C2×D4×C3111yescharacteristic
158C22×C4#41×C3112yes—
159D8—82no—
160M16—42no—
161M16—42no—
162M16—82no—
163C2×C8—22no—
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—42no—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C42C2×D4×C3112yes—
174C42C2×D4×C3111yescharacteristic
175C42#41×C3111yescharacteristic
176C23—42no—
177C23C31×#12411yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—42no—
182D4—42no—
183D4—82no—
184D4—84no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—82no—
191C2×C4—82no—
192C2×C4C31×#12011yescharacteristic
193C2×C4C31×#12111yescharacteristic
194C2×C4C31×#12112yes—
195C2×C4C31×#12312yes—
196C8—42no—
197C8—42no—
198C8—81no—
199C8—82no—
200C22—22no—
201C22—21no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22C31×#39411yescharacteristic
206C4—22no—
207C4—21no—
208C4—82no—
209C4C31×#45411yescharacteristic
210C4C31×#45511yescharacteristic
211C4C31×#47112yes—
212C4C31×#47212yes—
213C2—41no—
214C2—162no—
215C2C31×#204011yescharacteristic
216C2C31×#205112yes—
subgroupG/H
center, socleC22×C31#394
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3253C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1837C2semidirect
3. C31×#1560C2semidirect
4. C31×#1492C2semidirect
5. C31×#1309C2semidirect
67. #10531C31direct (N × H)
93. #1837C2×C31semidirect
94. #1560C2×C31semidirect
95. #1492C2×C31semidirect
96. #1309C2×C31semidirect
148. C31#10531direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32532
C31×#18372
C31×#15602
C31×#14922
C31×#13092
#1053131