Finite Group Databasebeta

← C2×#23752400 #34078495

Subgroups — C2×#23752400 #34078495

Order 19328.

1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012784C211yesmaximal, characteristic, complemented
2C2×#18012709C212yesmaximal, complemented
3C2×#18012707C211yesmaximal, characteristic, complemented
4#23752400C218yesmaximal, direct product factor
5C2×#18012653C212yesmaximal, complemented
6C2×#99×C151C211yesmaximal, characteristic, complemented
7C24×D151C2211yescharacteristic, complemented
8#18012784—22no—
9#18012784—24no—
10#18012784C2214yescomplemented
11C2×#14559004—21no—
12C2×#14559003—22no—
13C22×D604—22no—
14C22×C22⋊D151—21no—
15C22×C22⋊D151—21no—
16C22×C22⋊D151C2212yes—
17C2×D4×D151—22no—
18#18012709—24no—
19#18012709C2218yescomplemented
20#18012707—22no—
21#18012707C2214yescomplemented
22C2×C22⋊Dic151C2211yescharacteristic, complemented
23C2×(C2×D151)⋊C4—21no—
24C2×(C2×D151)⋊C4—22no—
25#18012653C2218yescomplemented
26C22×D4×C151C2211yescharacteristic
27C2×C22⋊C4×C151C2212yescomplemented
28#99×C151C2214yescomplemented
29C23×D151—21no—
30C23×D151—21no—
31C23×D151—22no—
32C23×D151—21no—
33C23×D151—22no—
34C23×D151—44no—
35C23×D151D412yescomplemented
36C23×D151C2312yescomplemented
37#14559004—24no—
38#14559004—24no—
39#14559003—28no—
40#14559003—28no—
41C2×Dic302—21no—
42C2×D604—21no—
43C2×D604—28no—
44C2×D604—48no—
45C2×C22⋊D151—22no—
46C2×C22⋊D151—24no—
47C2×C22⋊D151—22no—
48C2×C22⋊D151—22no—
49C2×C22⋊D151—22no—
50C2×C22⋊D151—22no—
51C2×C22⋊D151—24no—
52C2×C22⋊D151—24no—
53C2×C22⋊D151—44no—
54C2×C22⋊D151D414yescomplemented
55C2×C22⋊D151C2314yes—
56D4×D151—28no—
57D4×D151—28no—
58C22×Dic151—21no—
59C22×Dic151—21no—
60C22×Dic151D412yescomplemented
61C2×C4×D151—22no—
62C22⋊Dic151—21no—
63C22⋊Dic151C2312yescomplemented
64(C2×D151)⋊C4—28no—
65(C2×D151)⋊C4—24no—
66C24×C151D411yescharacteristic, complemented
67C24×C151C2311yescharacteristic
68C2×D4×C151—22no—
69C2×D4×C151—22no—
70C2×D4×C151D412yescomplemented
71C2×D4×C151C2312yes—
72C22×C4×C151—22no—
73C22×C4×C151D411yescharacteristic, complemented
74C22⋊C4×C151—22no—
75C22⋊C4×C151C2314yescomplemented
76C22×D151—24no—
77C22×D151—28no—
78C22×D151—22no—
79C22×D151—22no—
80C22×D151—24no—
81C22×D151—24no—
82C22×D151—22no—
83C22×D151—44no—
84C22×D151—44no—
85C22×D151—48no—
86C22×D151—44no—
87C22×D151—42no—
88C22×D151—41no—
89C22×D151—42no—
90C22×D151—41no—
91C22×D151—44no—
92C22×D151—82no—
93C22×D151C2×D414yescomplemented
94Dic302—24no—
95D604—24no—
96D604—416no—
97C22⋊D151—28no—
98C22⋊D151—24no—
99C22⋊D151—24no—
100C22⋊D151—24no—
101C22⋊D151—24no—
102C22⋊D151—48no—
103C2×Dic151—24no—
104C2×Dic151—22no—
105C2×Dic151—22no—
106C2×Dic151—22no—
107C2×Dic151—42no—
108C2×Dic151C2×D414yescomplemented
109C4×D151—28no—
110C23×C151—21no—
111C23×C151—21no—
112C23×C151—42no—
113C23×C151—42no—
114C23×C151C2×D412yes—
115C23×C151C2×D412yes—
116C23×C151C2×D411yescharacteristic
117C23×C151C2×D411yescharacteristic
118C23×C151C2×D412yescomplemented
119C23×C151C2411yescharacteristic
120D4×C151—24no—
121D4×C151—24no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—24no—
125C2×C4×C151—44no—
126C2×C4×C151C2×D412yescomplemented
127C22×C151—24no—
128C22×C151—22no—
129C22×C151—22no—
130C22×C151—42no—
131C22×C151—41no—
132C22×C151—41no—
133C22×C151—42no—
134C22×C151—42no—
135C22×C151—81no—
136C22×C151#12011yescharacteristic
137C22×C151#12012yes—
138C22×C151#12011yescharacteristic
139C22×C151C22×D412yes—
140C22×C151C22×D411yescharacteristic
141C2×D151—24no—
142C2×D151—28no—
143C2×D151—24no—
144C2×D151—42no—
145C2×D151—44no—
146C2×D151—48no—
147C2×D151—44no—
148C2×D151—42no—
149C2×D151—44no—
150C2×D151—44no—
151C2×D151—44no—
152C2×D151—82no—
153C2×D151—84no—
154C4×C151—22no—
155C4×C151—44no—
156Dic151—24no—
157Dic151—42no—
158C2×C151—21no—
159C2×C151—22no—
160C2×C151—22no—
161C2×C151—21no—
162C2×C151—42no—
163C2×C151B(4,𝔽2)12yescomplemented
164C2×C151C2×#12011yescharacteristic
165D151—44no—
166D151—44no—
167C151C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
168C2×B(4,𝔽2)—1511nomaximal, Sylow
169C2×H(5,𝔽2)—1511no—
170C2×#120—1511no—
171C2×#120—1512no—
172B(4,𝔽2)—1518no—
173C2×#99—1512no—
174C2×#99D15111yescharacteristic, complemented
175C25—1511no—
176H(5,𝔽2)—3024no—
177H(5,𝔽2)—3022no—
178H(5,𝔽2)—1514no—
179C2×#41—3022no—
180C2×#41—3021no—
181C22×D4—3022no—
182C22×D4—3022no—
183C22×D4—3021no—
184C22×D4—3021no—
185C22×D4—1512no—
186C22×D4C2×D15111yescharacteristic
187#120—3024no—
188#120—3022no—
189#120—1514no—
190#120—1518no—
191C2×C22⋊C4—3022no—
192C2×C22⋊C4—3021no—
193C2×C22⋊C4—1511no—
194C2×C22⋊C4C2×D15112yescomplemented
195#99—1518no—
196#99C2×D15114yescomplemented
197C24—3021no—
198C24—3022no—
199C24—3021no—
200C24—3022no—
201C24—3021no—
202C24—6044no—
203C24—1512no—
204C24—1512no—
205C24D60411yescharacteristic, complemented
206C24C22×D15111yescharacteristic
207#41—3024no—
208#41—3028no—
209#41—3028no—
210#41—3024no—
211C2×Q8—3021no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—3021no—
215C2×D4—3028no—
216C2×D4—3028no—
217C2×D4—3028no—
218C2×D4—3022no—
219C2×D4—3024no—
220C2×D4—3022no—
221C2×D4—3022no—
222C2×D4—3022no—
223C2×D4—3022no—
224C2×D4—3024no—
225C2×D4—3024no—
226C2×D4—6048no—
227C2×D4—6044no—
228C2×D4—1514no—
229C2×D4—1514no—
230C2×D4D60412yescomplemented
231C2×D4C22×D15112yes—
232C22×C4—22no—
233C22×C4—3022no—
234C22×C4—3021no—
235C22×C4—3021no—
236C22×C4—1512no—
237C22×C4D60411yescharacteristic, complemented
238C22⋊C4—22no—
239C22⋊C4—3028no—
240C22⋊C4—3021no—
241C22⋊C4—3024no—
242C22⋊C4—1512no—
243C22⋊C4C22×D15114yescomplemented
244C23—21no—
245C23—21no—
246C23—42no—
247C23—42no—
248C23—3028no—
249C23—3024no—
250C23—3024no—
251C23—3022no—
252C23—3024no—
253C23—3022no—
254C23—3022no—
255C23—6044no—
256C23—6042no—
257C23—6044no—
258C23—6044no—
259C23—6048no—
260C23—6044no—
261C23—6041no—
262C23—6042no—
263C23—6041no—
264C23—1514no—
265C23—12082no—
266C23D4×D15112yes—
267C23D4×D15112yes—
268C23C2×D60411yescharacteristic
269C23C2×D60411yescharacteristic
270C23C2×D60412yescomplemented
271C23C23×D15111yescharacteristic
272Q8—3024no—
273D4—24no—
274D4—24no—
275D4—3024no—
276D4—3028no—
277D4—3024no—
278D4—3024no—
279D4—3024no—
280D4—3024no—
281D4—60416no—
282D4—6048no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—44no—
287C2×C4—3028no—
288C2×C4—3024no—
289C2×C4—3022no—
290C2×C4—3022no—
291C2×C4—3022no—
292C2×C4—6042no—
293C2×C4—1514no—
294C2×C4C2×D60412yescomplemented
295C22—24no—
296C22—22no—
297C22—22no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—3028no—
305C22—3024no—
306C22—3024no—
307C22—6044no—
308C22—6044no—
309C22—6042no—
310C22—6044no—
311C22—6048no—
312C22—6044no—
313C22—6044no—
314C22—6042no—
315C22—12082no—
316C22—12084no—
317C22#1801270911yescharacteristic
318C22#1801270912yes—
319C22#1801270911yescharacteristic
320C22C2×D4×D15112yes—
321C22C22×D60411yescharacteristic
322C4—22no—
323C4—44no—
324C4—3024no—
325C4—6042no—
326C2—22no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2—42no—
331C2—6044no—
332C2—6044no—
333C2#2375240012yesdirect product factor
334C2C2×#1801270911yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC23×C151C24
FrattiniC23C23×D151
FittingC2×#99×C151C2
socleC22×C151#120
hypercenterC2×#99D151
hypocenterC151C2×B(4,𝔽2)
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#18012784C2semidirect
2. C2×#18012709C2semidirect
3. C2×#18012707C2semidirect
4. #23752400C2direct (N × H)
5. C2×#18012653C2semidirect
6. C2×#99×C151C2semidirect
7. C24×D151C22semidirect
10. #18012784C22semidirect
19. #18012709C22semidirect
21. #18012707C22semidirect
22. C2×C22⋊Dic151C22semidirect
25. #18012653C22semidirect
27. C2×C22⋊C4×C151C22semidirect
28. #99×C151C22semidirect
35. C23×D151D4semidirect
36. C23×D151C23semidirect
54. C2×C22⋊D151D4semidirect
60. C22×Dic151D4semidirect
63. C22⋊Dic151C23semidirect
66. C24×C151D4semidirect
70. C2×D4×C151D4semidirect
73. C22×C4×C151D4semidirect
75. C22⋊C4×C151C23semidirect
93. C22×D151C2×D4semidirect
108. C2×Dic151C2×D4semidirect
118. C23×C151C2×D4semidirect
126. C2×C4×C151C2×D4semidirect
163. C2×C151B(4,𝔽2)semidirect
167. C151C2×B(4,𝔽2)semidirect
174. C2×#99D151semidirect
194. C2×C22⋊C4C2×D151semidirect
196. #99C2×D151semidirect
205. C24D604semidirect
230. C2×D4D604semidirect
237. C22×C4D604semidirect
243. C22⋊C4C22×D151semidirect
270. C23C2×D604semidirect
294. C2×C4C2×D604semidirect
333. C2#23752400direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180127842
C2×#180127092
C2×#180127072
#237524002
C2×#180126532
C2×#99×C1512
C2×B(4,𝔽2)151