Finite Group Databasebeta

← C2×#4773 #78743

Subgroups — C2×#4773 #78743

Order 384.

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×D3×D4C211yesmaximal, characteristic, complemented
2C22×#213C211yesmaximal, characteristic, complemented
3C22×D24C211yesmaximal, characteristic, complemented
4C2×#895C211yesmaximal, characteristic, complemented
5C2×C3×#102C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#809C211yesmaximal, characteristic, complemented
8#4773C218yesmaximal, direct product factor
9C2×#447—31nomaximal, Sylow
10C24×D3—21no—
11C22×C3×D4C2211yescharacteristic
12C22×#67—21no—
13C2×D3×D4—24no—
14C2×D3×D4—24no—
15C2×D3×D4—22no—
16C2×D3×D4C2214yescomplemented
17C22×D12—21no—
18C22×D12C2211yescharacteristic
19C22×D12C2211yescharacteristic, complemented
20C22×C4×D3C2211yescharacteristic
21C22×C3×C8C2211yescharacteristic, complemented
22C2×C3×C4⋊C4C2211yescharacteristic, complemented
23C2×#213—24no—
24C2×#213C2214yescomplemented
25C2×(C2×D3)⋊C4—21no—
26C22×C3⋊C8C2211yescharacteristic, complemented
27C2×D24—24no—
28C2×D24C2214yescomplemented
29#895—22no—
30#895C2214yescomplemented
31C3×#102C2214yescomplemented
32(C2×D3)⋊C8C2214yescomplemented
33#809C2214yescomplemented
34C23×D4—31no—
35C22×D8—31no—
36C22×D8—31no—
37C2×#121—31no—
38#447—38no—
39C2×#102—31no—
40C2×#102D311yescharacteristic, complemented
41C2×C22⋊C8—31no—
42C24×C3—21no—
43C23×D3—28no—
44C23×D3—21no—
45C23×D3—24no—
46C23×D3—21no—
47C23×D3—44no—
48C23×D3—44no—
49C23×D3D411yescharacteristic
50C2×C3×D4—21no—
51C2×C3×D4—22no—
52C2×C3×D4D414yescomplemented
53C2×C3×D4C2312yes—
54C22×C3×C4—21no—
55C22×C3×C4C2311yescharacteristic
56C2×#67—28no—
57C2×#67—24no—
58C22×Dic3D411yescharacteristic
59D3×D4—216no—
60D3×D4—28no—
61D3×D4—28no—
62C2×D12—22no—
63C2×D12—21no—
64C2×D12—22no—
65C2×D12—22no—
66C2×D12—24no—
67C2×D12—21no—
68C2×D12—44no—
69C2×D12D414yescomplemented
70C2×D12C2312yes—
71C2×D12C2312yescomplemented
72C2×C4×D3—22no—
73C2×C4×D3—22no—
74C2×C4×D3D412yes—
75C2×C4×D3C2312yes—
76C2×C3×C8—22no—
77C2×C3×C8C2312yescomplemented
78C3×C4⋊C4—21no—
79C3×C4⋊C4C2312yescomplemented
80#213—28no—
81(C2×D3)⋊C4—24no—
82C2×C3⋊C8—22no—
83C2×C3⋊C8C2312yescomplemented
84D24—28no—
85C25—61no—
86C22×D4—34no—
87C22×D4—31no—
88C22×D4—31no—
89C22×D4—61no—
90C22×D4—62no—
91C22×D4—61no—
92C22×D4—64no—
93C22×D4—64no—
94C22×D4C2×D311yescharacteristic
95C23×C4—31no—
96C2×D8—34no—
97C2×D8—34no—
98C2×D8—64no—
99C2×D8—64no—
100C22×C8—31no—
101C22×C8C2×D311yescharacteristic, complemented
102#121—34no—
103#121—62no—
104C2×C4⋊C4C2×D311yescharacteristic, complemented
105C2×C22⋊C4—61no—
106#102—34no—
107#102C2×D314yescomplemented
108C22⋊C8—34no—
109C23×C3—24no—
110C23×C3—22no—
111C23×C3—42no—
112C23×C3—42no—
113C23×C3C2×D411yescharacteristic
114C22×D3—22no—
115C22×D3—22no—
116C22×D3—216no—
117C22×D3—24no—
118C22×D3—22no—
119C22×D3—22no—
120C22×D3—48no—
121C22×D3—432no—
122C22×D3—42no—
123C22×D3—42no—
124C22×D3—48no—
125C22×D3—42no—
126C22×D3—42no—
127C22×D3—42no—
128C22×D3D814yescomplemented
129C22×D3C2×D412yes—
130C3×D4—24no—
131C3×D4—22no—
132C3×D4C2×D414yescomplemented
133C2×C3×C4—22no—
134C2×C3×C4—42no—
135C2×C3×C4C2×D412yes—
136C2×C3×C4C2×D411yescharacteristic
137C2×C3×C4C2×D412yes—
138C2×C3×C4C2411yescharacteristic
139#67—216no—
140C2×Dic3—22no—
141C2×Dic3C2×D412yes—
142D12—24no—
143D12—22no—
144D12—22no—
145D12—22no—
146D12—48no—
147D12—42no—
148D12C2×D414yescomplemented
149C4×D3—24no—
150C4×D3—22no—
151C4×D3—22no—
152C3×C8—22no—
153C3⋊C8—22no—
154C24—21no—
155C24—31no—
156C24—64no—
157C24—68no—
158C24—61no—
159C24—61no—
160C24—124no—
161C24—124no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—34no—
165C2×D4—32no—
166C2×D4—32no—
167C2×D4—64no—
168C2×D4—64no—
169C2×D4—68no—
170C2×D4—616no—
171C2×D4—68no—
172C2×D4—68no—
173C2×D4—62no—
174C2×D4—62no—
175C2×D4—61no—
176C2×D4—62no—
177C2×D4—61no—
178C2×D4—124no—
179C2×D4D1214yescomplemented
180C2×D4C22×D312yes—
181C22×C4—21no—
182C22×C4—31no—
183C22×C4—32no—
184C22×C4—32no—
185C22×C4—62no—
186C22×C4—62no—
187C22×C4C22×D311yescharacteristic
188D8—68no—
189D8—68no—
190C2×C8—22no—
191C2×C8—32no—
192C2×C8—62no—
193C2×C8C22×D312yescomplemented
194C4⋊C4—21no—
195C4⋊C4C22×D312yescomplemented
196C22⋊C4—64no—
197C22×C3—24no—
198C22×C3—42no—
199C22×C3—42no—
200C22×C3—48no—
201C22×C3#12012yes—
202C22×C3C2×D812yes—
203C22×C3AGL(1,ℤ/8)12yes—
204C22×C3C22×D411yescharacteristic
205C2×D3—22no—
206C2×D3—22no—
207C2×D3—28no—
208C2×D3—24no—
209C2×D3—432no—
210C2×D3—42no—
211C2×D3—42no—
212C2×D3—48no—
213C2×D3—42no—
214C2×D3—42no—
215C2×D3—42no—
216C2×D3—84no—
217C2×D3C2×D814yescomplemented
218C3×C4—42no—
219C3×C4#12012yes—
220C3×C4C22×D411yescharacteristic
221C3×C4C22×D411yescharacteristic
222Dic3—22no—
223C23—24no—
224C23—22no—
225C23—34no—
226C23—32no—
227C23—42no—
228C23—42no—
229C23—616no—
230C23—62no—
231C23—62no—
232C23—64no—
233C23—62no—
234C23—62no—
235C23—128no—
236C23—128no—
237C23—1232no—
238C23—122no—
239C23—122no—
240C23—122no—
241C23—122no—
242C23—122no—
243C23D3×D411yescharacteristic
244D4—24no—
245D4—22no—
246D4—34no—
247D4—616no—
248D4—64no—
249D4—62no—
250D4—62no—
251D4—62no—
252D4—128no—
253D4—122no—
254D4C2×D1214yescomplemented
255C2×C4—22no—
256C2×C4—32no—
257C2×C4—42no—
258C2×C4—62no—
259C2×C4—64no—
260C2×C4—62no—
261C2×C4—62no—
262C2×C4C2×D1212yes—
263C2×C4D3×D411yescharacteristic
264C2×C4D3×D412yes—
265C2×C4C23×D311yescharacteristic
266C8—22no—
267C8—62no—
268C2×C3—44no—
269C2×C3#44714yescomplemented
270C2×C3C2×#12011yescharacteristic
271C2×C3C22×D811yescharacteristic
272C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
273D3—24no—
274D3—44no—
275D3—82no—
276C22—24no—
277C22—34no—
278C22—42no—
279C22—42no—
280C22—48no—
281C22—62no—
282C22—62no—
283C22—68no—
284C22—64no—
285C22—1232no—
286C22—122no—
287C22—122no—
288C22—128no—
289C22—122no—
290C22—122no—
291C22—122no—
292C22—244no—
293C22#88212yes—
294C22D3×D812yes—
295C22#91412yes—
296C22C2×D3×D411yescharacteristic
297C4—42no—
298C4—62no—
299C4#88212yes—
300C4C22×D1211yescharacteristic
301C4C2×D3×D411yescharacteristic
302C3C2×#44711yescharacteristic, complemented, Sylow
303C2—44no—
304C2—64no—
305C2—124no—
306C2—242no—
307C2#477314yesdirect product factor
308C2C2×#88211yescharacteristic
309C2C2×D3×D811yescharacteristic
310C2C2×#91411yescharacteristic
subgroupG/H
centerC23D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC2×C3×#102C2
socleC23×C3C2×D4
hypercenterC2×#102D3
hypocenterC3C2×#447
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×D3×D4C2semidirect
2. C22×#213C2semidirect
3. C22×D24C2semidirect
4. C2×#895C2semidirect
5. C2×C3×#102C2semidirect
6. C2×(C2×D3)⋊C8C2semidirect
7. C2×#809C2semidirect
8. #4773C2direct (N × H)
16. C2×D3×D4C22semidirect
19. C22×D12C22semidirect
21. C22×C3×C8C22semidirect
22. C2×C3×C4⋊C4C22semidirect
24. C2×#213C22semidirect
26. C22×C3⋊C8C22semidirect
28. C2×D24C22semidirect
30. #895C22semidirect
31. C3×#102C22semidirect
32. (C2×D3)⋊C8C22semidirect
33. #809C22semidirect
40. C2×#102D3semidirect
52. C2×C3×D4D4semidirect
69. C2×D12D4semidirect
71. C2×D12C23semidirect
77. C2×C3×C8C23semidirect
79. C3×C4⋊C4C23semidirect
83. C2×C3⋊C8C23semidirect
101. C22×C8C2×D3semidirect
104. C2×C4⋊C4C2×D3semidirect
107. #102C2×D3semidirect
128. C22×D3D8semidirect
132. C3×D4C2×D4semidirect
148. D12C2×D4semidirect
179. C2×D4D12semidirect
193. C2×C8C22×D3semidirect
195. C4⋊C4C22×D3semidirect
217. C2×D3C2×D8semidirect
254. D4C2×D12semidirect
269. C2×C3#447semidirect
302. C3C2×#447semidirect
307. C2#4773direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D42
C22×#2132
C22×D242
C2×#8952
C2×C3×#1022
C2×(C2×D3)⋊C82
C2×#8092
#47732
C2×#4473