Finite Group Databasebeta

← C2×C31×#1409 #21470341

Subgroups — C2×C31×#1409 #21470341

Order 7936.

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

normal subgroups only

This group has 474 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×#353C212yesmaximal
3C31×#1409C214yesmaximal, direct product factor
4C22×SD16×C31—22no—
5C2×C31×C4⋊Q8C411yescharacteristic, complemented
6C2×C31×#127C2211yescharacteristic
7C31×#492—22no—
8C31×#492C412yescomplemented
9C31×#492C2212yes—
10C2×C31×#99—22no—
11C2×C4×C8×C31C411yescharacteristic, complemented
12C31×#353—22no—
13C31×#353C2214yes—
14C22×Q8×C31—21no—
15C22×D4×C31—41no—
16C22×D4×C31D412yes—
17C2×SD16×C31—24no—
18C2×SD16×C31—24no—
19C2×SD16×C31—44no—
20C2×SD16×C31—44no—
21C22×C8×C31—21no—
22C31×C4⋊Q8—21no—
23C31×C4⋊Q8—41no—
24C31×C4⋊Q8C2×C412yescomplemented
25C31×#127—41no—
26C31×#127C2×C411yescharacteristic
27C31×#127D412yes—
28C31×#127C2311yescharacteristic
29C2×C4⋊C4×C31—41no—
30C2×C22⋊C4×C31—42no—
31C2×C42×C31C2×C411yescharacteristic
32C31×#99—24no—
33C31×#99—42no—
34C4×C8×C31—21no—
35C4×C8×C31C2×C412yescomplemented
36C24×C31—22no—
37C2×Q8×C31—22no—
38C2×Q8×C31—42no—
39C2×Q8×C31—42no—
40C2×Q8×C31—41no—
41C2×D4×C31—22no—
42C2×D4×C31—42no—
43C2×D4×C31—42no—
44C2×D4×C31—41no—
45C2×D4×C31—42no—
46C2×D4×C31—41no—
47C2×D4×C31—84no—
48C2×D4×C31C22⋊C412yes—
49C2×D4×C31C2×D412yes—
50C22×C4×C31—21no—
51C22×C4×C31—41no—
52C22×C4×C31—82no—
53C22×C4×C31C22⋊C411yescharacteristic
54SD16×C31—48no—
55SD16×C31—48no—
56C2×C8×C31—22no—
57C2×C8×C31—22no—
58C2×C8×C31—22no—
59C4⋊C4×C31—42no—
60C4⋊C4×C31—42no—
61C22⋊C4×C31—44no—
62C22⋊C4×C31—82no—
63C42×C31—21no—
64C42×C31C22⋊C411yescharacteristic
65C42×C31C22×C411yescharacteristic
66C2×#1409C3111yesmaximal, characteristic, direct product factor, Sylow
67C23×C31—22no—
68C23×C31—22no—
69C23×C31—42no—
70C23×C31—42no—
71C23×C31—84no—
72C23×C31#9911yescharacteristic
73Q8×C31—44no—
74Q8×C31—82no—
75D4×C31—42no—
76D4×C31—42no—
77D4×C31—82no—
78D4×C31—82no—
79D4×C31—84no—
80D4×C31—82no—
81C2×C4×C31—24no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31—21no—
85C2×C4×C31—21no—
86C2×C4×C31—42no—
87C2×C4×C31—81no—
88C2×C4×C31—81no—
89C2×C4×C31—84no—
90C2×C4×C31—164no—
91C2×C4×C31#9911yescharacteristic
92C2×C4×C31C2×C22⋊C411yescharacteristic
93C8×C31—24no—
94C2×#492C2×C3111yescharacteristic
95C2×#353C2×C3112yes—
96#1409C2×C3114yesdirect product factor
97C22×C31—22no—
98C22×C31—42no—
99C22×C31—42no—
100C22×C31—82no—
101C22×C31—82no—
102C22×C31—84no—
103C22×C31—162no—
104C22×C31#35311yescharacteristic
105C22×C31#35311yescharacteristic
106C22×C31C2×#9911yescharacteristic
107C4×C31—22no—
108C4×C31—22no—
109C4×C31—21no—
110C4×C31—21no—
111C4×C31—82no—
112C4×C31—164no—
113C22×SD16—22no—
114C2×C4⋊Q8C4×C3111yescharacteristic, complemented
115C2×#127C22×C3111yescharacteristic
116#492—22no—
117#492C4×C3112yescomplemented
118#492C22×C3112yes—
119C2×#99—22no—
120C2×C4×C8C4×C3111yescharacteristic, complemented
121#353—22no—
122#353C22×C3114yes—
123C2×C31—21no—
124C2×C31—21no—
125C2×C31—82no—
126C2×C31—82no—
127C2×C31#140912yesdirect product factor
128C2×C31C2×#35311yescharacteristic
129C22×Q8—21no—
130C22×D4—41no—
131C22×D4D4×C3112yes—
132C2×SD16—24no—
133C2×SD16—24no—
134C2×SD16—44no—
135C2×SD16—44no—
136C22×C8—21no—
137C4⋊Q8—21no—
138C4⋊Q8—41no—
139C4⋊Q8C2×C4×C3112yescomplemented
140#127—41no—
141#127C2×C4×C3111yescharacteristic
142#127D4×C3112yes—
143#127C23×C3111yescharacteristic
144C2×C4⋊C4—41no—
145C2×C22⋊C4—42no—
146C2×C42C2×C4×C3111yescharacteristic
147#99—24no—
148#99—42no—
149C4×C8—21no—
150C4×C8C2×C4×C3112yescomplemented
151C31C2×#140911yescharacteristic, direct product factor, Sylow
152C24—22no—
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—41no—
157C2×D4—22no—
158C2×D4—42no—
159C2×D4—42no—
160C2×D4—41no—
161C2×D4—42no—
162C2×D4—41no—
163C2×D4—84no—
164C2×D4C22⋊C4×C3112yes—
165C2×D4C2×D4×C3112yes—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—82no—
169C22×C4C22⋊C4×C3111yescharacteristic
170SD16—48no—
171SD16—48no—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—22no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C22⋊C4—44no—
178C22⋊C4—82no—
179C42—21no—
180C42C22⋊C4×C3111yescharacteristic
181C42C22×C4×C3111yescharacteristic
182C23—22no—
183C23—22no—
184C23—42no—
185C23—42no—
186C23—84no—
187C23C31×#9911yescharacteristic
188Q8—44no—
189Q8—82no—
190D4—42no—
191D4—42no—
192D4—82no—
193D4—82no—
194D4—84no—
195D4—82no—
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—84no—
205C2×C4—164no—
206C2×C4C31×#9911yescharacteristic
207C2×C4C2×C22⋊C4×C3111yescharacteristic
208C8—24no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—82no—
213C22—82no—
214C22—84no—
215C22—162no—
216C22C31×#35311yescharacteristic
217C22C31×#35311yescharacteristic
218C22C2×C31×#9911yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—164no—
225C2—21no—
226C2—21no—
227C2—82no—
228C2—82no—
229C2C31×#140912yesdirect product factor
230C2C2×C31×#35311yescharacteristic
subgroupG/H
center, socleC22×C31#353
commutatorC42C22×C4×C31
Frattini, cosocle#127C23×C31
prime radicalC2×C31×#127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C2×C31×#127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1409C2direct (N × H)
5. C2×C31×C4⋊Q8C4semidirect
8. C31×#492C4semidirect
11. C2×C4×C8×C31C4semidirect
24. C31×C4⋊Q8C2×C4semidirect
35. C4×C8×C31C2×C4semidirect
66. C2×#1409C31direct (N × H)
96. #1409C2×C31direct (N × H)
114. C2×C4⋊Q8C4×C31semidirect
117. #492C4×C31semidirect
120. C2×C4×C8C4×C31semidirect
127. C2×C31#1409direct (N × H)
139. C4⋊Q8C2×C4×C31semidirect
150. C4×C8C2×C4×C31semidirect
151. C31C2×#1409direct (N × H)
229. C2C31×#1409direct (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×#3532
C31×#14092
C2×#140931