Finite Group Databasebeta

← C2×C31×#1410 #21470346

Subgroups — C2×C31×#1410 #21470346

Order 7936.

450 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×C31×#492C211yesmaximal, characteristic
2C2×C31×#356C212yesmaximal, complemented
3C31×#1410C214yesmaximal, direct product factor
4C22×SD16×C31—22no—
5C2×C31×C4⋊Q8C2211yescharacteristic
6C2×C31×#127C411yescharacteristic
7C31×#492—22no—
8C31×#492C412yes—
9C31×#492C2212yes—
10C2×C31×#101—22no—
11C2×C4×C8×C31C411yescharacteristic
12C31×#356—22no—
13C31×#356C2214yescomplemented
14C22×Q8×C31D412yes—
15C22×D4×C31—21no—
16C22×D4×C31—41no—
17C2×SD16×C31—24no—
18C2×SD16×C31—24no—
19C2×SD16×C31—44no—
20C2×SD16×C31—44no—
21C2×M16×C31—42no—
22C22×C8×C31—21no—
23C31×C4⋊Q8—41no—
24C31×C4⋊Q8C2×C411yescharacteristic
25C31×C4⋊Q8D412yes—
26C31×C4⋊Q8C2311yescharacteristic
27C31×#127—21no—
28C31×#127—41no—
29C31×#127C2×C412yes—
30C2×C4⋊C4×C31—41no—
31C2×C42×C31C2×C411yescharacteristic
32C31×#101—24no—
33C31×#101—42no—
34C4×C8×C31—21no—
35C4×C8×C31C2×C412yes—
36C24×C31—41no—
37C2×Q8×C31—22no—
38C2×Q8×C31—42no—
39C2×Q8×C31—42no—
40C2×Q8×C31C22⋊C412yes—
41C2×Q8×C31C2×D412yes—
42C2×D4×C31—22no—
43C2×D4×C31—42no—
44C2×D4×C31—42no—
45C2×D4×C31—42no—
46C2×D4×C31—42no—
47C2×D4×C31—41no—
48C2×D4×C31—84no—
49C22×C4×C31—21no—
50C22×C4×C31—22no—
51C22×C4×C31C22⋊C411yescharacteristic
52SD16×C31—48no—
53SD16×C31—48no—
54M16×C31—44no—
55M16×C31—82no—
56C2×C8×C31—22no—
57C2×C8×C31—22no—
58C2×C8×C31—22no—
59C2×C8×C31—82no—
60C4⋊C4×C31—41no—
61C4⋊C4×C31—42no—
62C4⋊C4×C31—41no—
63C42×C31—21no—
64C42×C31C22⋊C411yescharacteristic
65C42×C31C22×C411yescharacteristic
66C2×#1410C3111yesmaximal, characteristic, direct product factor, Sylow
67C23×C31—42no—
68C23×C31—84no—
69C23×C31—81no—
70C23×C31—81no—
71C23×C31#9911yescharacteristic
72Q8×C31—42no—
73Q8×C31—42no—
74Q8×C31—82no—
75D4×C31—44no—
76D4×C31—82no—
77D4×C31—84no—
78D4×C31—84no—
79C2×C4×C31—24no—
80C2×C4×C31—21no—
81C2×C4×C31—21no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—22no—
85C2×C4×C31—22no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31#9911yescharacteristic
89C2×C4×C31C2×C22⋊C411yescharacteristic
90C8×C31—24no—
91C8×C31—84no—
92C2×#492C2×C3111yescharacteristic
93C2×#356C2×C3112yescomplemented
94#1410C2×C3114yesdirect product factor
95C22×C31—22no—
96C22×C31—84no—
97C22×C31—82no—
98C22×C31—162no—
99C22×C31—162no—
100C22×C31#35311yescharacteristic
101C22×C31#35311yescharacteristic
102C22×C31C2×#9911yescharacteristic
103C4×C31—22no—
104C4×C31—22no—
105C4×C31—21no—
106C4×C31—21no—
107C4×C31—42no—
108C4×C31—42no—
109C22×SD16—22no—
110C2×C4⋊Q8C22×C3111yescharacteristic
111C2×#127C4×C3111yescharacteristic
112#492—22no—
113#492C4×C3112yes—
114#492C22×C3112yes—
115C2×#101—22no—
116C2×C4×C8C4×C3111yescharacteristic
117#356—22no—
118#356C22×C3114yescomplemented
119C2×C31—21no—
120C2×C31—21no—
121C2×C31—162no—
122C2×C31#141012yesdirect product factor
123C2×C31C2×#35311yescharacteristic
124C22×Q8D4×C3112yes—
125C22×D4—21no—
126C22×D4—41no—
127C2×SD16—24no—
128C2×SD16—24no—
129C2×SD16—44no—
130C2×SD16—44no—
131C2×M16—42no—
132C22×C8—21no—
133C4⋊Q8—41no—
134C4⋊Q8C2×C4×C3111yescharacteristic
135C4⋊Q8D4×C3112yes—
136C4⋊Q8C23×C3111yescharacteristic
137#127—21no—
138#127—41no—
139#127C2×C4×C3112yes—
140C2×C4⋊C4—41no—
141C2×C42C2×C4×C3111yescharacteristic
142#101—24no—
143#101—42no—
144C4×C8—21no—
145C4×C8C2×C4×C3112yes—
146C31C2×#141011yescharacteristic, direct product factor, Sylow
147C24—41no—
148C2×Q8—22no—
149C2×Q8—42no—
150C2×Q8—42no—
151C2×Q8C22⋊C4×C3112yes—
152C2×Q8C2×D4×C3112yes—
153C2×D4—22no—
154C2×D4—42no—
155C2×D4—42no—
156C2×D4—42no—
157C2×D4—42no—
158C2×D4—41no—
159C2×D4—84no—
160C22×C4—21no—
161C22×C4—22no—
162C22×C4C22⋊C4×C3111yescharacteristic
163SD16—48no—
164SD16—48no—
165M16—44no—
166M16—82no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—82no—
171C4⋊C4—41no—
172C4⋊C4—42no—
173C4⋊C4—41no—
174C42—21no—
175C42C22⋊C4×C3111yescharacteristic
176C42C22×C4×C3111yescharacteristic
177C23—42no—
178C23—84no—
179C23—81no—
180C23—81no—
181C23C31×#9911yescharacteristic
182Q8—42no—
183Q8—42no—
184Q8—82no—
185D4—44no—
186D4—82no—
187D4—84no—
188D4—84no—
189C2×C4—24no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4C31×#9911yescharacteristic
199C2×C4C2×C22⋊C4×C3111yescharacteristic
200C8—24no—
201C8—84no—
202C22—22no—
203C22—84no—
204C22—82no—
205C22—162no—
206C22—162no—
207C22C31×#35311yescharacteristic
208C22C31×#35311yescharacteristic
209C22C2×C31×#9911yescharacteristic
210C4—22no—
211C4—22no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—42no—
216C2—21no—
217C2—21no—
218C2—162no—
219C2C31×#141012yesdirect product factor
220C2C2×C31×#35311yescharacteristic
subgroupG/H
center, socleC22×C31#353
commutatorC42C22×C4×C31
Frattini, cosocleC4⋊Q8C23×C31
prime radicalC2×C31×#127C4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C2×C31×C4⋊Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#356C2semidirect
3. C31×#1410C2direct (N × H)
13. C31×#356C22semidirect
66. C2×#1410C31direct (N × H)
93. C2×#356C2×C31semidirect
94. #1410C2×C31direct (N × H)
118. #356C22×C31semidirect
122. C2×C31#1410direct (N × H)
146. C31C2×#1410direct (N × H)
219. C2C31×#1410direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4922
C2×C31×#3562
C31×#14102
C2×#141031