Finite Group Databasebeta

← C2×#23752354 #34078308

Subgroups — C2×#23752354 #34078308

Order 19328.

812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14559003C211yesmaximal, characteristic, complemented
2C22×#14558992C211yesmaximal, characteristic, complemented
3C2×#18012710C211yesmaximal, characteristic, complemented
4#23752354C218yesmaximal, direct product factor
5C2×#18012664C211yesmaximal, characteristic, complemented
6C2×#18012660C211yesmaximal, characteristic, complemented
7C2×(C2×D151)⋊C8C211yesmaximal, characteristic, complemented
8C22×D8×C151C211yesmaximal, characteristic, complemented
9C2×#14559003—24no—
10C2×#14559003—24no—
11C2×#14559003—22no—
12C2×#14559003C2214yescomplemented
13C22×Dic302C2211yescharacteristic
14C22×C22⋊D151—21no—
15C22×C22⋊D151—21no—
16C23×Dic151—21no—
17C22×C4×D151C2211yescharacteristic
18C2×#14558992—24no—
19C2×#14558992C2214yescomplemented
20C22×C151⋊C8C2211yescharacteristic
21#18012710—22no—
22#18012710C2214yescomplemented
23C2×C4⋊Dic151C2211yescharacteristic
24C2×C22⋊Dic151—21no—
25#18012664C2214yescomplemented
26#18012660C2214yescomplemented
27(C2×D151)⋊C8C2214yescomplemented
28C22×D4×C151C2211yescharacteristic
29C22×D4×C151C2211yescharacteristic
30C2×D8×C151—24no—
31C2×D8×C151C2214yescomplemented
32C22×C8×C151C2211yescharacteristic
33C23×D151D411yescharacteristic
34#14559003—216no—
35#14559003—28no—
36#14559003—28no—
37C2×Dic302—21no—
38C2×Dic302—22no—
39C2×Dic302D414yescomplemented
40C2×Dic302C2312yes—
41C2×C22⋊D151—28no—
42C2×C22⋊D151—24no—
43C2×C22⋊D151—24no—
44C2×C22⋊D151—44no—
45C22×Dic151—28no—
46C22×Dic151—24no—
47C22×Dic151—21no—
48C22×Dic151—21no—
49C22×Dic151D411yescharacteristic
50C2×C4×D151—22no—
51C2×C4×D151—22no—
52C2×C4×D151D412yes—
53C2×C4×D151C2312yes—
54#14558992—28no—
55C2×C151⋊C8—22no—
56C2×C151⋊C8C2312yes—
57C4⋊Dic151—21no—
58C4⋊Dic151C2312yes—
59C22⋊Dic151—24no—
60C24×C151—21no—
61C24×C151—21no—
62C2×D4×C151—21no—
63C2×D4×C151—22no—
64C2×D4×C151—22no—
65C2×D4×C151—22no—
66C2×D4×C151—21no—
67C2×D4×C151D414yescomplemented
68C2×D4×C151C2312yes—
69C2×D4×C151C2312yes—
70C22×C4×C151C2311yescharacteristic
71D8×C151—28no—
72C2×C8×C151—22no—
73C2×C8×C151C2312yes—
74C22×D151—22no—
75C22×D151—22no—
76C22×D151—22no—
77C22×D151C2×D412yes—
78Dic302—24no—
79Dic302—22no—
80Dic302C2×D414yescomplemented
81C22⋊D151—216no—
82C22⋊D151—48no—
83C2×Dic151—216no—
84C2×Dic151—22no—
85C2×Dic151—24no—
86C2×Dic151—22no—
87C2×Dic151—22no—
88C2×Dic151—42no—
89C2×Dic151C2×D412yes—
90C4×D151—24no—
91C4×D151—22no—
92C4×D151—22no—
93C151⋊C8—22no—
94C23×C151—24no—
95C23×C151—22no—
96C23×C151—22no—
97C23×C151—42no—
98C23×C151—42no—
99C23×C151—42no—
100C23×C151—42no—
101C23×C151—42no—
102C23×C151C2×D411yescharacteristic
103D4×C151—24no—
104D4×C151—22no—
105D4×C151—22no—
106D4×C151—22no—
107D4×C151—42no—
108D4×C151C2×D414yescomplemented
109C2×C4×C151C2×D411yescharacteristic
110C2×C4×C151C2×D412yes—
111C2×C4×C151C2×D412yes—
112C2×C4×C151C2411yescharacteristic
113C8×C151—22no—
114C22×C151—24no—
115C22×C151—42no—
116C22×C151—42no—
117C22×C151—48no—
118C22×C151—42no—
119C22×C151—42no—
120C22×C151—42no—
121C22×C151—84no—
122C22×C151#12012yes—
123C22×C151#13512yes—
124C22×C151AGL(1,ℤ/8)12yes—
125C22×C151C22×D411yescharacteristic
126C2×D151—22no—
127C2×D151—22no—
128C2×D151—22no—
129C2×D151—44no—
130C4×C151#12012yes—
131C4×C151C22×D411yescharacteristic
132C4×C151C22×D411yescharacteristic
133Dic151—22no—
134Dic151—24no—
135Dic151—42no—
136C2×C151—44no—
137C2×C151—82no—
138C2×C151#44914yescomplemented
139C2×C151C2×#12011yescharacteristic
140C2×C151C2×#13511yescharacteristic
141C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
142D151—42no—
143C151C2×#44911yescharacteristic, complemented, Sylow
144C2×#449—1511nomaximal, Sylow
145C22×#41—1511no—
146C22×SD16—1511no—
147C22×D8D15111yescharacteristic, complemented
148C2×#121—1511no—
149#449—1518no—
150C2×#103—1511no—
151C2×#102—1511no—
152C2×C22⋊C8—1511no—
153C2×#41—3024no—
154C2×#41—3024no—
155C2×#41—3022no—
156C2×#41—1514no—
157C22×Q8—1511no—
158C22×D4—3021no—
159C22×D4—3021no—
160C22×D4C2×D15111yescharacteristic
161C22×D4C2×D15111yescharacteristic
162C23×C4—3021no—
163C23×C4—1511no—
164C2×SD16—3024no—
165C2×SD16—1514no—
166C2×D8—24no—
167C2×D8C2×D15114yescomplemented
168C22×C8—1511no—
169C22×C8C2×D15111yescharacteristic
170#121—3022no—
171#121—1514no—
172C2×C4⋊C4—1511no—
173C2×C22⋊C4—3021no—
174#103—1514no—
175#102—1514no—
176C22⋊C8—1514no—
177C24—21no—
178C24—21no—
179C24—1511no—
180#41—30216no—
181#41—3028no—
182#41—3028no—
183C2×Q8—3021no—
184C2×Q8—3022no—
185C2×Q8—1514no—
186C2×Q8—1512no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—22no—
192C2×D4—3028no—
193C2×D4—3024no—
194C2×D4—3024no—
195C2×D4—6044no—
196C2×D4C22⋊D15114yescomplemented
197C2×D4C22×D15112yes—
198C2×D4C22×D15112yes—
199C22×C4—3028no—
200C22×C4—3021no—
201C22×C4—3024no—
202C22×C4—3022no—
203C22×C4—3022no—
204C22×C4—3021no—
205C22×C4—1511no—
206C22×C4—1512no—
207C22×C4—1512no—
208C22×C4C22×D15111yescharacteristic
209SD16—3028no—
210D8—28no—
211C2×C8—22no—
212C2×C8—3022no—
213C2×C8—1512no—
214C2×C8C22×D15112yes—
215C4⋊C4—3021no—
216C4⋊C4—1512no—
217C22⋊C4—3024no—
218C23—24no—
219C23—22no—
220C23—22no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23—42no—
225C23—42no—
226C23—3022no—
227C23—3022no—
228C23—3022no—
229C23—1512no—
230C23D4×D15111yescharacteristic
231Q8—3024no—
232Q8—3022no—
233Q8—1514no—
234D4—24no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—42no—
239D4—30216no—
240D4—6048no—
241D4C2×C22⋊D15114yescomplemented
242C2×C4—30216no—
243C2×C4—3022no—
244C2×C4—3024no—
245C2×C4—3022no—
246C2×C4—3024no—
247C2×C4—3022no—
248C2×C4—3022no—
249C2×C4—3022no—
250C2×C4—6042no—
251C2×C4—1512no—
252C2×C4D4×D15111yescharacteristic
253C2×C4D4×D15112yes—
254C2×C4C2×C22⋊D15112yes—
255C2×C4C23×D15111yescharacteristic
256C8—22no—
257C8—3022no—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—48no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—3022no—
267C22—3022no—
268C22—3022no—
269C22—6044no—
270C22#1801270712yes—
271C22#1801275812yes—
272C22#1801276312yes—
273C22C2×D4×D15111yescharacteristic
274C4—3022no—
275C4—3024no—
276C4—6042no—
277C4#1801270712yes—
278C4C2×D4×D15111yescharacteristic
279C4C22×C22⋊D15111yescharacteristic
280C2—44no—
281C2—82no—
282C2—6042no—
283C2#2375235414yesdirect product factor
284C2C2×#1801270711yescharacteristic
285C2C2×#1801275811yescharacteristic
286C2C2×#1801276311yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×D8×C151C2
socleC23×C151C2×D4
hypercenterC22×D8D151
hypocenterC151C2×#449
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#14559003C2semidirect
2. C22×#14558992C2semidirect
3. C2×#18012710C2semidirect
4. #23752354C2direct (N × H)
5. C2×#18012664C2semidirect
6. C2×#18012660C2semidirect
7. C2×(C2×D151)⋊C8C2semidirect
8. C22×D8×C151C2semidirect
12. C2×#14559003C22semidirect
19. C2×#14558992C22semidirect
22. #18012710C22semidirect
25. #18012664C22semidirect
26. #18012660C22semidirect
27. (C2×D151)⋊C8C22semidirect
31. C2×D8×C151C22semidirect
39. C2×Dic302D4semidirect
67. C2×D4×C151D4semidirect
80. Dic302C2×D4semidirect
108. D4×C151C2×D4semidirect
138. C2×C151#449semidirect
143. C151C2×#449semidirect
147. C22×D8D151semidirect
167. C2×D8C2×D151semidirect
196. C2×D4C22⋊D151semidirect
241. D4C2×C22⋊D151semidirect
283. C2#23752354direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145590032
C22×#145589922
C2×#180127102
#237523542
C2×#180126642
C2×#180126602
C2×(C2×D151)⋊C82
C22×D8×C1512
C2×#449151