Finite Group Databasebeta

← C2×#23752344 #34078284

Subgroups — C2×#23752344 #34078284

Order 19328.

1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×D151C211yesmaximal, characteristic, complemented
2C22×#14558989C211yesmaximal, characteristic, complemented
3C2×#18012710C211yesmaximal, characteristic, complemented
4#23752344C218yesmaximal, direct product factor
5C2×#18012661C211yesmaximal, characteristic, complemented
6C2×#18012660C211yesmaximal, characteristic, complemented
7C2×(C2×D151)⋊C8C211yesmaximal, characteristic, complemented
8C22×D8×C151C211yesmaximal, characteristic, complemented
9C24×D151—21no—
10C22×D604C2211yescharacteristic
11C22×C22⋊D151—21no—
12C22×C22⋊D151—21no—
13C2×D4×D151—24no—
14C2×D4×D151—24no—
15C2×D4×D151—22no—
16C2×D4×D151C2214yescomplemented
17C22×C4×D151C2211yescharacteristic
18C2×#14558989—24no—
19C2×#14558989C2214yescomplemented
20C22×C151⋊C8C2211yescharacteristic, complemented
21#18012710—22no—
22#18012710C2214yescomplemented
23C2×C4⋊Dic151C2211yescharacteristic, complemented
24C2×C22⋊Dic151—21no—
25#18012661C2214yescomplemented
26#18012660C2214yescomplemented
27(C2×D151)⋊C8C2214yescomplemented
28C22×D4×C151C2211yescharacteristic
29C22×D4×C151C2211yescharacteristic, complemented
30C2×D8×C151—24no—
31C2×D8×C151C2214yescomplemented
32C22×C8×C151C2211yescharacteristic, complemented
33C23×D151—28no—
34C23×D151—24no—
35C23×D151—21no—
36C23×D151—44no—
37C23×D151—44no—
38C23×D151D411yescharacteristic
39C2×D604—21no—
40C2×D604—22no—
41C2×D604D414yescomplemented
42C2×D604C2312yes—
43C2×C22⋊D151—28no—
44C2×C22⋊D151—24no—
45C2×C22⋊D151—24no—
46C2×C22⋊D151—44no—
47D4×D151—216no—
48D4×D151—28no—
49D4×D151—28no—
50C22×Dic151—21no—
51C22×Dic151D411yescharacteristic
52C2×C4×D151—22no—
53C2×C4×D151—22no—
54C2×C4×D151D412yes—
55C2×C4×D151C2312yes—
56#14558989—28no—
57C2×C151⋊C8—22no—
58C2×C151⋊C8C2312yescomplemented
59C4⋊Dic151—21no—
60C4⋊Dic151C2312yescomplemented
61C22⋊Dic151—24no—
62C24×C151—21no—
63C24×C151—21no—
64C2×D4×C151—21no—
65C2×D4×C151—22no—
66C2×D4×C151—22no—
67C2×D4×C151—22no—
68C2×D4×C151—21no—
69C2×D4×C151D414yescomplemented
70C2×D4×C151C2312yes—
71C2×D4×C151C2312yescomplemented
72C22×C4×C151C2311yescharacteristic
73D8×C151—28no—
74C2×C8×C151—22no—
75C2×C8×C151C2312yescomplemented
76C22×D151—22no—
77C22×D151—22no—
78C22×D151—216no—
79C22×D151—24no—
80C22×D151—22no—
81C22×D151—48no—
82C22×D151—432no—
83C22×D151—42no—
84C22×D151—42no—
85C22×D151—48no—
86C22×D151D814yescomplemented
87C22×D151C2×D412yes—
88D604—24no—
89D604—22no—
90D604C2×D414yescomplemented
91C22⋊D151—216no—
92C22⋊D151—48no—
93C2×Dic151—22no—
94C2×Dic151—22no—
95C2×Dic151—42no—
96C2×Dic151C2×D412yes—
97C4×D151—24no—
98C4×D151—22no—
99C4×D151—22no—
100C151⋊C8—22no—
101C23×C151—24no—
102C23×C151—22no—
103C23×C151—22no—
104C23×C151—42no—
105C23×C151—42no—
106C23×C151—42no—
107C23×C151—42no—
108C23×C151—42no—
109C23×C151C2×D411yescharacteristic
110D4×C151—24no—
111D4×C151—22no—
112D4×C151—22no—
113D4×C151—22no—
114D4×C151—42no—
115D4×C151C2×D414yescomplemented
116C2×C4×C151C2×D411yescharacteristic
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2×D412yes—
119C2×C4×C151C2411yescharacteristic
120C8×C151—22no—
121C22×C151—24no—
122C22×C151—42no—
123C22×C151—42no—
124C22×C151—48no—
125C22×C151—42no—
126C22×C151—42no—
127C22×C151—42no—
128C22×C151—84no—
129C22×C151#12012yes—
130C22×C151C2×D812yes—
131C22×C151AGL(1,ℤ/8)12yes—
132C22×C151C22×D411yescharacteristic
133C2×D151—22no—
134C2×D151—22no—
135C2×D151—28no—
136C2×D151—24no—
137C2×D151—432no—
138C2×D151—42no—
139C2×D151—42no—
140C2×D151—48no—
141C2×D151C2×D814yescomplemented
142C4×C151#12012yes—
143C4×C151C22×D411yescharacteristic
144C4×C151C22×D411yescharacteristic
145Dic151—22no—
146Dic151—42no—
147C2×C151—44no—
148C2×C151—82no—
149C2×C151#44714yescomplemented
150C2×C151C2×#12011yescharacteristic
151C2×C151C22×D811yescharacteristic
152C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
153D151—24no—
154D151—44no—
155C151C2×#44711yescharacteristic, complemented, Sylow
156C2×#447—1511nomaximal, Sylow
157C23×D4—1511no—
158C22×D8—1511no—
159C22×D8D15111yescharacteristic, complemented
160C2×#121—1511no—
161#447—1518no—
162C2×#102—1511no—
163C2×#102—1511no—
164C2×C22⋊C8—1511no—
165C25—3021no—
166C22×D4—3024no—
167C22×D4—3024no—
168C22×D4—3021no—
169C22×D4—3022no—
170C22×D4—3021no—
171C22×D4—1514no—
172C22×D4—1511no—
173C22×D4C2×D15111yescharacteristic
174C22×D4C2×D15111yescharacteristic, complemented
175C23×C4—1511no—
176C2×D8—24no—
177C2×D8—3024no—
178C2×D8—1514no—
179C2×D8C2×D15114yescomplemented
180C22×C8—1511no—
181C22×C8C2×D15111yescharacteristic, complemented
182#121—3022no—
183#121—1514no—
184C2×C4⋊C4—1511no—
185C2×C22⋊C4—3021no—
186#102—1514no—
187#102—1514no—
188C22⋊C8—1514no—
189C24—21no—
190C24—21no—
191C24—3028no—
192C24—3024no—
193C24—3021no—
194C24—6044no—
195C24—6044no—
196C24—1511no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—22no—
202C2×D4—30216no—
203C2×D4—3028no—
204C2×D4—3028no—
205C2×D4—3028no—
206C2×D4—3024no—
207C2×D4—3024no—
208C2×D4—3021no—
209C2×D4—3022no—
210C2×D4—6044no—
211C2×D4—1514no—
212C2×D4—1512no—
213C2×D4C22⋊D15114yescomplemented
214C2×D4C22×D15112yes—
215C2×D4C22×D15112yescomplemented
216C22×C4—3022no—
217C22×C4—3022no—
218C22×C4—3021no—
219C22×C4—1511no—
220C22×C4—1512no—
221C22×C4—1512no—
222C22×C4C22×D15111yescharacteristic
223D8—28no—
224D8—3028no—
225C2×C8—22no—
226C2×C8—3022no—
227C2×C8—1512no—
228C2×C8C22×D15112yescomplemented
229C4⋊C4—3021no—
230C4⋊C4—1512no—
231C22⋊C4—3024no—
232C23—24no—
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—30216no—
241C23—3022no—
242C23—3022no—
243C23—3024no—
244C23—3022no—
245C23—6048no—
246C23—60432no—
247C23—6048no—
248C23—6042no—
249C23—6042no—
250C23—1514no—
251C23—1512no—
252C23D4×D15111yescharacteristic
253D4—24no—
254D4—22no—
255D4—22no—
256D4—22no—
257D4—42no—
258D4—30216no—
259D4—3024no—
260D4—3022no—
261D4—6048no—
262D4—1514no—
263D4C2×C22⋊D15114yescomplemented
264C2×C4—3022no—
265C2×C4—3024no—
266C2×C4—3022no—
267C2×C4—3022no—
268C2×C4—3022no—
269C2×C4—6042no—
270C2×C4—1512no—
271C2×C4D4×D15111yescharacteristic
272C2×C4D4×D15112yes—
273C2×C4C2×C22⋊D15112yes—
274C2×C4C23×D15111yescharacteristic
275C8—22no—
276C8—3022no—
277C22—24no—
278C22—42no—
279C22—42no—
280C22—48no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—3022no—
286C22—3028no—
287C22—3022no—
288C22—3024no—
289C22—60432no—
290C22—6042no—
291C22—6042no—
292C22—6048no—
293C22—1514no—
294C22#1801270712yes—
295C22D8×D15112yes—
296C22#1801276312yes—
297C22C2×D4×D15111yescharacteristic
298C4—3022no—
299C4—6042no—
300C4#1801270712yes—
301C4C2×D4×D15111yescharacteristic
302C4C22×C22⋊D15111yescharacteristic
303C2—44no—
304C2—82no—
305C2—3024no—
306C2—6044no—
307C2#2375234414yesdirect product factor
308C2C2×#1801270711yescharacteristic
309C2C2×D8×D15111yescharacteristic
310C2C2×#1801276311yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×D8×C151C2
socleC23×C151C2×D4
hypercenterC22×D8D151
hypocenterC151C2×#447
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×D4×D151C2semidirect
2. C22×#14558989C2semidirect
3. C2×#18012710C2semidirect
4. #23752344C2direct (N × H)
5. C2×#18012661C2semidirect
6. C2×#18012660C2semidirect
7. C2×(C2×D151)⋊C8C2semidirect
8. C22×D8×C151C2semidirect
16. C2×D4×D151C22semidirect
19. C2×#14558989C22semidirect
20. C22×C151⋊C8C22semidirect
22. #18012710C22semidirect
23. C2×C4⋊Dic151C22semidirect
25. #18012661C22semidirect
26. #18012660C22semidirect
27. (C2×D151)⋊C8C22semidirect
29. C22×D4×C151C22semidirect
31. C2×D8×C151C22semidirect
32. C22×C8×C151C22semidirect
41. C2×D604D4semidirect
58. C2×C151⋊C8C23semidirect
60. C4⋊Dic151C23semidirect
69. C2×D4×C151D4semidirect
71. C2×D4×C151C23semidirect
75. C2×C8×C151C23semidirect
86. C22×D151D8semidirect
90. D604C2×D4semidirect
115. D4×C151C2×D4semidirect
141. C2×D151C2×D8semidirect
149. C2×C151#447semidirect
155. C151C2×#447semidirect
159. C22×D8D151semidirect
174. C22×D4C2×D151semidirect
179. C2×D8C2×D151semidirect
181. C22×C8C2×D151semidirect
213. C2×D4C22⋊D151semidirect
215. C2×D4C22×D151semidirect
228. C2×C8C22×D151semidirect
263. D4C2×C22⋊D151semidirect
307. C2#23752344direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1512
C22×#145589892
C2×#180127102
#237523442
C2×#180126612
C2×#180126602
C2×(C2×D151)⋊C82
C22×D8×C1512
C2×#447151