Finite Group Databasebeta

← C31×#10530 #21467289

Subgroups — C31×#10530 #21467289

Order 7936.

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

normal subgroups only

This group has 402 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×#1848C211yesmaximal, characteristic, complemented
3C31×#1560C212yesmaximal, complemented
4C31×#1492C212yesmaximal, complemented
5C31×#1309C211yesmaximal, characteristic, complemented
6C31×#532C2212yes—
7C31×#476—22no—
8C31×#469—22no—
9C31×#459—22no—
10C2×C31×#108—22no—
11C31×#423C2211yescharacteristic
12C31×#423C2212yes—
13C31×#423C2211yescharacteristic
14C2×C4×C8×C31C2211yescharacteristic
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×#108—44no—
33C31×#106—22no—
34C31×C4⋊C8—22no—
35C31×C4⋊C8—22no—
36C31×C4⋊C8—22no—
37C31×C4⋊C8—22no—
38C31×#102—24no—
39C4×C8×C31—21no—
40C4×C8×C31D412yes—
41#41×C31—82no—
42#41×C31—82no—
43C2×Q8×C31—22no—
44C2×D4×C31—22no—
45C2×D4×C31—22no—
46C2×D4×C31—22no—
47C2×D4×C31—42no—
48C22×C4×C31—42no—
49C22×C4×C31C2×D411yescharacteristic
50C22×C4×C31#4112yes—
51D8×C31—82no—
52M16×C31—42no—
53M16×C31—42no—
54M16×C31—82no—
55C2×C8×C31—22no—
56C2×C8×C31—22no—
57C2×C8×C31—22no—
58C2×C8×C31—22no—
59C2×C8×C31—41no—
60C2×C8×C31—42no—
61C4⋊C4×C31—22no—
62C4⋊C4×C31—22no—
63C22⋊C4×C31—42no—
64C22⋊C4×C31—42no—
65C42×C31C2×D412yes—
66C42×C31C2×D411yescharacteristic
67C42×C31#4111yescharacteristic
68#10530C3111yesmaximal, characteristic, direct product factor, Sylow
69C23×C31—42no—
70C23×C31#12411yescharacteristic
71Q8×C31—82no—
72D4×C31—42no—
73D4×C31—42no—
74D4×C31—42no—
75D4×C31—42no—
76D4×C31—82no—
77D4×C31—84no—
78C2×C4×C31—21no—
79C2×C4×C31—21no—
80C2×C4×C31—22no—
81C2×C4×C31—22no—
82C2×C4×C31—42no—
83C2×C4×C31—82no—
84C2×C4×C31—82no—
85C2×C4×C31#12011yescharacteristic
86C2×C4×C31#12111yescharacteristic
87C2×C4×C31#12112yes—
88C2×C4×C31#12312yes—
89C8×C31—24no—
90C8×C31—42no—
91C8×C31—81no—
92C8×C31—82no—
93#3253C2×C3111yescharacteristic
94#1848C2×C3111yescharacteristic, complemented
95#1560C2×C3112yescomplemented
96#1492C2×C3112yescomplemented
97#1309C2×C3111yescharacteristic, complemented
98C22×C31—22no—
99C22×C31—21no—
100C22×C31—82no—
101C22×C31—82no—
102C22×C31—82no—
103C22×C31#39411yescharacteristic
104C4×C31—22no—
105C4×C31—21no—
106C4×C31—82no—
107C4×C31#45311yescharacteristic
108C4×C31#45611yescharacteristic
109C4×C31#47112yes—
110C4×C31#47212yes—
111#532C22×C3112yes—
112#476—22no—
113#469—22no—
114#459—22no—
115C2×#108—22no—
116#423C22×C3111yescharacteristic
117#423C22×C3112yes—
118#423C22×C3111yescharacteristic
119C2×C4×C8C22×C3111yescharacteristic
120#333—22no—
121#331—22no—
122D4⋊C8—24no—
123C2×C31—41no—
124C2×C31—162no—
125C2×C31#203911yescharacteristic
126C2×C31#205112yes—
127C2×#41—22no—
128C2×D8—22no—
129C2×M16—21no—
130C2×M16—22no—
131C2×M16D4×C3112yes—
132C22×C8—21no—
133C4⋊Q8D4×C3112yes—
134#127D4×C3112yes—
135#124—22no—
136#121—22no—
137#121—22no—
138C4×D4—22no—
139C4×D4—22no—
140C2×C42C23×C3111yescharacteristic
141#108—44no—
142#106—22no—
143C4⋊C8—22no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8—22no—
147#102—24no—
148C4×C8—21no—
149C4×C8D4×C3112yes—
150C31#1053011yescharacteristic, direct product factor, Sylow
151#41—82no—
152#41—82no—
153C2×Q8—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—22no—
157C2×D4—42no—
158C22×C4—42no—
159C22×C4C2×D4×C3111yescharacteristic
160C22×C4#41×C3112yes—
161D8—82no—
162M16—42no—
163M16—42no—
164M16—82no—
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—42no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C22⋊C4—42no—
174C22⋊C4—42no—
175C42C2×D4×C3112yes—
176C42C2×D4×C3111yescharacteristic
177C42#41×C3111yescharacteristic
178C23—42no—
179C23C31×#12411yescharacteristic
180Q8—82no—
181D4—42no—
182D4—42no—
183D4—42no—
184D4—42no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—82no—
193C2×C4—82no—
194C2×C4C31×#12011yescharacteristic
195C2×C4C31×#12111yescharacteristic
196C2×C4C31×#12112yes—
197C2×C4C31×#12312yes—
198C8—24no—
199C8—42no—
200C8—81no—
201C8—82no—
202C22—22no—
203C22—21no—
204C22—82no—
205C22—82no—
206C22—82no—
207C22C31×#39411yescharacteristic
208C4—22no—
209C4—21no—
210C4—82no—
211C4C31×#45311yescharacteristic
212C4C31×#45611yescharacteristic
213C4C31×#47112yes—
214C4C31×#47212yes—
215C2—41no—
216C2—162no—
217C2C31×#203911yescharacteristic
218C2C31×#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×#1848C2semidirect
3. C31×#1560C2semidirect
4. C31×#1492C2semidirect
5. C31×#1309C2semidirect
68. #10530C31direct (N × H)
94. #1848C2×C31semidirect
95. #1560C2×C31semidirect
96. #1492C2×C31semidirect
97. #1309C2×C31semidirect
150. C31#10530direct (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×#18482
C31×#15602
C31×#14922
C31×#13092
#1053031