Finite Group Databasebeta

← C2×#4948 #82102

Subgroups — C2×#4948 #82102

Order 384.

908 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊C4C211yesmaximal, characteristic
2C22×#217C211yesmaximal, characteristic
3C22×#217C211yesmaximal, characteristic
4C22×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C22×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C22×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C2×C3⋊#95C211yesmaximal, characteristic, complemented
8#4948C218yesmaximal, direct product factor
9C2×#396—31nomaximal, Sylow
10C25×C3C2211yescharacteristic
11C23×C3×C4C2211yescharacteristic
12C23×C3×C4C2211yescharacteristic
13C23×Dic3C2211yescharacteristic
14C23×Dic3C2211yescharacteristic
15C23×Dic3C2211yescharacteristic
16C23×Dic3C2211yescharacteristic
17C2×C3×C22⋊C4—24no—
18C2×C3×C22⋊C4C2214yes—
19C2×#217—24no—
20C2×#217—24no—
21C2×#217C2214yes—
22C2×#217C2214yes—
23C2×C4⋊Dic3—24no—
24C2×C4⋊Dic3C2214yescomplemented
25C2×Dic3⋊C4—24no—
26C2×Dic3⋊C4—24no—
27C2×Dic3⋊C4C2214yescomplemented
28C2×Dic3⋊C4C2214yescomplemented
29C3⋊#95C2214yescomplemented
30C22×C4⋊C4—31no—
31C22×C4⋊C4—31no—
32C22×C4⋊C4—31no—
33C22×C22⋊C4—31no—
34C22×C22⋊C4—31no—
35C22×C22⋊C4D311yescharacteristic
36#396—38no—
37C2×#95—31no—
38C24×C3—22no—
39C24×C3—22no—
40C24×C3—22no—
41C24×C3—22no—
42C24×C3—22no—
43C24×C3—22no—
44C24×C3Q814yes—
45C24×C3C2312yes—
46C24×C3C2311yescharacteristic
47C22×C3×C4—22no—
48C22×C3×C4—22no—
49C22×C3×C4—22no—
50C22×C3×C4—22no—
51C22×C3×C4—22no—
52C22×C3×C4D414yes—
53C22×C3×C4C2312yes—
54C22×C3×C4C2312yes—
55C22×Dic3—22no—
56C22×Dic3—22no—
57C22×Dic3—22no—
58C22×Dic3—22no—
59C22×Dic3—22no—
60C22×Dic3—22no—
61C22×Dic3—22no—
62C22×Dic3—22no—
63C22×Dic3—22no—
64C22×Dic3—22no—
65C22×Dic3D414yes—
66C22×Dic3D414yes—
67C22×Dic3C2312yes—
68C22×Dic3C2312yes—
69C22×Dic3C2312yes—
70C22×Dic3C2312yes—
71C3×C22⋊C4—28no—
72#217—28no—
73#217—28no—
74C4⋊Dic3—28no—
75Dic3⋊C4—28no—
76Dic3⋊C4—28no—
77C25C2×D311yescharacteristic
78C23×C4—31no—
79C23×C4—31no—
80C23×C4—31no—
81C23×C4—31no—
82C23×C4C2×D311yescharacteristic
83C23×C4C2×D311yescharacteristic
84C2×C4⋊C4—34no—
85C2×C4⋊C4—34no—
86C2×C4⋊C4—34no—
87C2×C4⋊C4—64no—
88C2×C4⋊C4—64no—
89C2×C4⋊C4—64no—
90C2×C22⋊C4—24no—
91C2×C22⋊C4—34no—
92C2×C22⋊C4—34no—
93C2×C22⋊C4—64no—
94C2×C22⋊C4—64no—
95C2×C22⋊C4C2×D314yes—
96#95—34no—
97C23×C3—28no—
98C23×C3—28no—
99C23×C3—28no—
100C23×C3—22no—
101C23×C3—22no—
102C23×C3—22no—
103C23×C3—22no—
104C23×C3—22no—
105C23×C3—22no—
106C23×C3—44no—
107C23×C3—44no—
108C23×C3—44no—
109C23×C3—44no—
110C23×C3C2×D412yes—
111C23×C3C2×D412yes—
112C23×C3C2×D412yes—
113C23×C3C2×Q814yes—
114C23×C3C2×Q812yes—
115C23×C3#4112yes—
116C23×C3#4112yes—
117C23×C3#4112yes—
118C23×C3C2411yescharacteristic
119C2×C3×C4—28no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—44no—
126C2×C3×C4C2×D414yes—
127C2×Dic3—28no—
128C2×Dic3—28no—
129C2×Dic3—22no—
130C2×Dic3—22no—
131C2×Dic3—22no—
132C2×Dic3—22no—
133C2×Dic3—22no—
134C2×Dic3—22no—
135C2×Dic3—22no—
136C2×Dic3—22no—
137C2×Dic3—22no—
138C2×Dic3—22no—
139C2×Dic3—44no—
140C2×Dic3—44no—
141C2×Dic3C2×D414yes—
142C2×Dic3C2×D414yes—
143C24—22no—
144C24—22no—
145C24—22no—
146C24—22no—
147C24—22no—
148C24—22no—
149C24Dic614yes—
150C24C22×D312yes—
151C24C22×D311yescharacteristic
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—34no—
158C22×C4—34no—
159C22×C4—32no—
160C22×C4—32no—
161C22×C4—32no—
162C22×C4—32no—
163C22×C4—62no—
164C22×C4—62no—
165C22×C4—62no—
166C22×C4—62no—
167C22×C4—62no—
168C22×C4—62no—
169C22×C4—62no—
170C22×C4—62no—
171C22×C4—62no—
172C22×C4—62no—
173C22×C4#6714yes—
174C22×C4C22×D312yes—
175C22×C4C22×D312yes—
176C4⋊C4—68no—
177C4⋊C4—68no—
178C4⋊C4—68no—
179C22⋊C4—28no—
180C22⋊C4—68no—
181C22⋊C4—68no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—24no—
185C22×C3—42no—
186C22×C3—42no—
187C22×C3—42no—
188C22×C3—42no—
189C22×C3—416no—
190C22×C3#12114yes—
191C22×C3#12114yes—
192C22×C3#12114yes—
193C22×C3C22⋊Q814yes—
194C22×C3C22⋊Q814yes—
195C22×C3C22⋊Q814yes—
196C22×C3#12614yes—
197C22×C3C22×D411yescharacteristic
198C22×C3C22×D411yescharacteristic
199C22×C3C22×D411yescharacteristic
200C22×C3C22×Q811yescharacteristic
201C22×C3C2×#4111yescharacteristic
202C22×C3C2×#4111yescharacteristic
203C22×C3C2×#4111yescharacteristic
204C3×C4—24no—
205C3×C4—42no—
206Dic3—24no—
207Dic3—24no—
208Dic3—42no—
209Dic3—42no—
210C23—28no—
211C23—28no—
212C23—28no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—44no—
220C23—44no—
221C23—44no—
222C23—44no—
223C23C2×Dic614yes—
224C23C2×Dic612yes—
225C23#23512yes—
226C23D3×D412yes—
227C23D3×D412yes—
228C23#23712yes—
229C23#23712yes—
230C23C2×#6712yes—
231C23C23×D311yescharacteristic
232C2×C4—28no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—34no—
239C2×C4—34no—
240C2×C4—44no—
241C2×C4—68no—
242C2×C4—68no—
243C2×C4—62no—
244C2×C4—62no—
245C2×C4—62no—
246C2×C4—62no—
247C2×C4—62no—
248C2×C4—62no—
249C2×C4—62no—
250C2×C4—62no—
251C2×C4—62no—
252C2×C4—62no—
253C2×C4—124no—
254C2×C4—124no—
255C2×C4C2×#6714yes—
256C2×C3—44no—
257C2×C3#39618yescomplemented
258C2×C3C2×#12111yescharacteristic
259C2×C3C2×#12111yescharacteristic
260C2×C3C2×#12111yescharacteristic
261C2×C3C2×C22⋊Q811yescharacteristic
262C2×C3C2×C22⋊Q811yescharacteristic
263C2×C3C2×C22⋊Q811yescharacteristic
264C2×C3C2×#12611yescharacteristic
265C22—24no—
266C22—24no—
267C22—24no—
268C22—416no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22#87814yes—
274C22#87814yes—
275C22#87914yes—
276C22#88414yes—
277C22#92414yes—
278C22#93814yes—
279C22#93914yes—
280C22C22×Dic611yescharacteristic
281C22C2×#23511yescharacteristic
282C22C2×D3×D411yescharacteristic
283C22C2×D3×D411yescharacteristic
284C22C2×#23711yescharacteristic
285C22C2×#23711yescharacteristic
286C22C22×#6711yescharacteristic
287C4—24no—
288C4—42no—
289C4—64no—
290C4—64no—
291C4—122no—
292C4—122no—
293C3C2×#39611yescharacteristic, complemented, Sylow
294C2—44no—
295C2#494818yesdirect product factor
296C2C2×#87811yescharacteristic
297C2C2×#87811yescharacteristic
298C2C2×#87911yescharacteristic
299C2C2×#88411yescharacteristic
300C2C2×#92411yescharacteristic
301C2C2×#93811yescharacteristic
302C2C2×#93911yescharacteristic
subgroupG/H
centerC24C22×D3
commutator, cosocleC23×C3C24
FrattiniC23C23×D3
FittingC22×C3×C22⋊C4C2
socleC24×C3C23
prime radicalC25×C3C22
hypercenterC22×C22⋊C4D3
hypocenterC3C2×#396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22×C4⋊Dic3C2semidirect
5. C22×Dic3⋊C4C2semidirect
6. C22×Dic3⋊C4C2semidirect
7. C2×C3⋊#95C2semidirect
8. #4948C2direct (N × H)
24. C2×C4⋊Dic3C22semidirect
27. C2×Dic3⋊C4C22semidirect
28. C2×Dic3⋊C4C22semidirect
29. C3⋊#95C22semidirect
257. C2×C3#396semidirect
293. C3C2×#396semidirect
295. C2#4948direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊C42
C22×#2172
C22×C4⋊Dic32
C22×Dic3⋊C42
C2×C3⋊#952
#49482
C2×#3963