Finite Group Databasebeta

← C2×#23752456 #34078696

Subgroups — C2×#23752456 #34078696

Order 19328.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×#14558992C211yesmaximal, characteristic, complemented
2C22×#14558988C211yesmaximal, characteristic, complemented
3C2×#18012718C211yesmaximal, characteristic, complemented
4#23752456C218yesmaximal, direct product factor
5C2×#18012672C211yesmaximal, characteristic, complemented
6C2×#18012662C211yesmaximal, characteristic, complemented
7C2×#18012660C211yesmaximal, characteristic, complemented
8C2×#121×C151C211yesmaximal, characteristic
9C22×Dic302C2211yescharacteristic
10C2×#14558992—24no—
11C2×#14558992C2214yescomplemented
12C2×#14558988—24no—
13C2×#14558988C2214yescomplemented
14C22×C151⋊C8C2211yescharacteristic
15C22×C151⋊C8C2211yescharacteristic
16#18012718—22no—
17#18012718C2214yescomplemented
18C2×C4⋊Dic151C2211yescharacteristic
19C2×Dic151⋊C4—21no—
20C2×C22⋊Dic151—21no—
21#18012672C2214yescomplemented
22#18012662C2214yescomplemented
23#18012660C2214yescomplemented
24C22×D4×C151—21no—
25C22×D4×C151C2211yescharacteristic
26C23×C4×C151C2211yescharacteristic
27#121×C151—22no—
28#121×C151C2214yes—
29C2×C4⋊C4×C151C2211yescharacteristic
30C2×C22⋊C4×C151—21no—
31C2×Dic302—21no—
32C2×Dic302—22no—
33C2×Dic302—22no—
34C2×Dic302C2312yes—
35C22×Dic151—21no—
36C22×Dic151—21no—
37#14558992—28no—
38#14558988—28no—
39C2×C151⋊C8—22no—
40C2×C151⋊C8D414yescomplemented
41C2×C151⋊C8C2312yes—
42C2×C151⋊C8C2312yes—
43C4⋊Dic151—21no—
44C4⋊Dic151C2312yes—
45Dic151⋊C4—24no—
46C22⋊Dic151—24no—
47C24×C151—21no—
48C24×C151D411yescharacteristic
49C2×D4×C151—24no—
50C2×D4×C151—22no—
51C2×D4×C151—21no—
52C2×D4×C151—22no—
53C2×D4×C151—44no—
54C2×D4×C151C2312yes—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—21no—
58C22×C4×C151D411yescharacteristic
59C22×C4×C151D412yes—
60C22×C4×C151C2312yes—
61C22×C4×C151C2311yescharacteristic
62C4⋊C4×C151—21no—
63C4⋊C4×C151C2312yes—
64C22⋊C4×C151—24no—
65Dic302—22no—
66Dic302—22no—
67Dic302—42no—
68C2×Dic151—22no—
69C2×Dic151—22no—
70C2×Dic151—42no—
71C2×Dic151—42no—
72C151⋊C8—22no—
73C151⋊C8C2×D414yescomplemented
74C23×C151—22no—
75C23×C151—22no—
76C23×C151—22no—
77C23×C151—22no—
78C23×C151—42no—
79C23×C151—42no—
80C23×C151—42no—
81C23×C151C2×D412yes—
82C23×C151C2×D411yescharacteristic
83D4×C151—22no—
84D4×C151—22no—
85D4×C151—48no—
86D4×C151—42no—
87C2×C4×C151—22no—
88C2×C4×C151—24no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—42no—
93C2×C4×C151C2×D412yes—
94C2×C4×C151C2×D412yes—
95C2×C4×C151C2×D411yescharacteristic
96C2×C4×C151#4112yes—
97C2×C4×C151C2411yescharacteristic
98C22×C151—22no—
99C22×C151—22no—
100C22×C151—22no—
101C22×C151—44no—
102C22×C151—42no—
103C22×C151—42no—
104C22×C151—42no—
105C22×C151—84no—
106C22×C151#12112yes—
107C22×C151AGL(1,ℤ/8)12yes—
108C22×C151#13712yes—
109C22×C151C22×D411yescharacteristic
110C4×C151—22no—
111C4×C151—42no—
112C4×C151#12112yes—
113C4×C151C22×D411yescharacteristic
114C4×C151C2×#4111yescharacteristic
115Dic151—42no—
116Dic151—42no—
117C2×C151—42no—
118C2×C151—82no—
119C2×C151#46814yescomplemented
120C2×C151C2×#12111yescharacteristic
121C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
122C2×C151C2×#13711yescharacteristic
123C151C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—1511nomaximal, Sylow
125C22×SD16—1511no—
126C22×M16—1511no—
127C2×C22⋊Q8—1511no—
128C2×#121D15111yescharacteristic
129#468—1518no—
130C2×#107—1511no—
131C2×#103—1511no—
132C2×#102—1511no—
133C22×Q8—1511no—
134C22×D4—21no—
135C22×D4C2×D15111yescharacteristic
136C23×C4C2×D15111yescharacteristic
137C2×SD16—3024no—
138C2×SD16—1514no—
139C2×M16—3024no—
140C2×M16—1514no—
141C22×C8—1511no—
142C22×C8—1511no—
143C22⋊Q8—3022no—
144C22⋊Q8—1514no—
145#121—22no—
146#121C2×D15114yes—
147C2×C4⋊C4—3021no—
148C2×C4⋊C4—1511no—
149C2×C4⋊C4C2×D15111yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—3021no—
152#107—1514no—
153#103—1514no—
154#102—1514no—
155C24—21no—
156C24C22⋊D15111yescharacteristic
157C2×Q8—3021no—
158C2×Q8—3022no—
159C2×Q8—3022no—
160C2×Q8—1512no—
161C2×D4—24no—
162C2×D4—22no—
163C2×D4—21no—
164C2×D4—22no—
165C2×D4—44no—
166C2×D4C22×D15112yes—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—3021no—
171C22×C4—3021no—
172C22×C4C22⋊D15112yes—
173C22×C4C22⋊D15111yescharacteristic
174C22×C4C22×D15112yes—
175C22×C4C22×D15111yescharacteristic
176SD16—3028no—
177M16—3028no—
178C2×C8—3022no—
179C2×C8—1512no—
180C2×C8—1514no—
181C2×C8—1512no—
182C4⋊C4—21no—
183C4⋊C4—3024no—
184C4⋊C4—3021no—
185C4⋊C4—1512no—
186C4⋊C4C22×D15112yes—
187C22⋊C4—24no—
188C22⋊C4—3024no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23C2×C22⋊D15112yes—
197C23C2×C22⋊D15111yescharacteristic
198Q8—3022no—
199Q8—3022no—
200Q8—6042no—
201D4—22no—
202D4—22no—
203D4—48no—
204D4—42no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—3022no—
212C2×C4—3022no—
213C2×C4—6042no—
214C2×C4—6042no—
215C2×C4D4×D15112yes—
216C2×C4C2×C22⋊D15112yes—
217C2×C4C2×C22⋊D15111yescharacteristic
218C2×C4#1455900312yes—
219C2×C4C23×D15111yescharacteristic
220C8—3022no—
221C8—1514no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22—44no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—84no—
230C22#1801271112yes—
231C22#1801276512yes—
232C22#1801276912yes—
233C22C22×C22⋊D15111yescharacteristic
234C4—22no—
235C4—42no—
236C4—6042no—
237C4—6042no—
238C4#1801271112yes—
239C4C2×D4×D15111yescharacteristic
240C4C2×#1455900311yescharacteristic
241C2—42no—
242C2—82no—
243C2#2375245614yesdirect product factor
244C2C2×#1801271111yescharacteristic
245C2C2×#1801276511yescharacteristic
246C2C2×#1801276911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting, prime radicalC2×#121×C151C2
socleC23×C151C2×D4
hypercenterC2×#121D151
hypocenterC151C2×#468
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#14558992C2semidirect
2. C22×#14558988C2semidirect
3. C2×#18012718C2semidirect
4. #23752456C2direct (N × H)
5. C2×#18012672C2semidirect
6. C2×#18012662C2semidirect
7. C2×#18012660C2semidirect
11. C2×#14558992C22semidirect
13. C2×#14558988C22semidirect
17. #18012718C22semidirect
21. #18012672C22semidirect
22. #18012662C22semidirect
23. #18012660C22semidirect
40. C2×C151⋊C8D4semidirect
73. C151⋊C8C2×D4semidirect
119. C2×C151#468semidirect
123. C151C2×#468semidirect
243. C2#23752456direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145589922
C22×#145589882
C2×#180127182
#237524562
C2×#180126722
C2×#180126622
C2×#180126602
C2×#121×C1512
C2×#468151