Finite Group Databasebeta

← #11808858

Subgroups — #11808858

Order 1152.

1097 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 1097 conjugacy classes of subgroups — too many to draw. Only its 268 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×C4×#627C212yesmaximal
2#10592631C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C212yesmaximal
4#10591345C214yesmaximal
5#10591338C214yesmaximal
6C4×#3724C212yesmaximal
7#73669—32nomaximal
8C22×#627C2212yes—
9C2×C32×C42C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×C4⋊Dic3C2214yes—
13C2×C3×C4×Dic3C2214yes—
14C2×#3724C2214yes—
15C2×#3724C2212yes—
16C2×Dic3⋊Dic3C2214yes—
17C4×#627—28no—
18#63658C2214yes—
19C3×C3⋊#95C2212yes—
20C3×C3⋊#95C2212yes—
21#63579C2212yes—
22#63579C2212yes—
23C2×C4×Dic6—34no—
24C3×C4×C4⋊C4—32no—
25#4982—34no—
26#4979—34no—
27C4×C4⋊Dic3D312yes—
28#4932—32no—
29#4932—61no—
30C4×Dic3⋊C4—34no—
31#4657—34no—
32#4656—34no—
33C22×C32×C4C2312yes—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2312yes—
36C22×C3⋊Dic3C2312yes—
37C22×C3×Dic3C2314yes—
38C22×C3×Dic3C2314yes—
39C2×#627—24no—
40C2×#627—28no—
41C32×C42Q814yescomplemented
42C4×C3⋊Dic3D414yes—
43C4×C3⋊Dic3Q814yescomplemented
44C3×C4⋊Dic3—28no—
45C3×C4×Dic3—28no—
46#3724—24no—
47#3724—28no—
48Dic3⋊Dic3—28no—
49#2399—91noSylow
50C22×Dic6—34no—
51C2×C3×C4⋊C4—34no—
52C2×C3×C42—21no—
53C2×C3×C42—34no—
54C2×C3×C42C2×D312yes—
55C2×C4⋊Dic3—34no—
56C2×C4⋊Dic3C2×D314yes—
57C2×Dic3⋊C4—34no—
58C2×Dic3⋊C4—34no—
59C2×Dic3⋊C4—34no—
60C2×Dic3⋊C4—34no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—32no—
63C2×C4×Dic3—61no—
64C2×C4×Dic3—61no—
65C2×C4×Dic3C2×D314yes—
66C4×Dic6—616no—
67C3×#95—32no—
68C3×#95—32no—
69C3⋊#95—34no—
70C3⋊#95—34no—
71C3⋊#95—34no—
72C3⋊#95—34no—
73C3⋊#95—64no—
74C3⋊#95C2×D312yes—
75C3⋊#95C2×D312yes—
76C23×C32C2411yescharacteristic
77C2×C32×C4—24no—
78C2×C32×C4C2×D412yes—
79C2×C32×C4C2×Q814yes—
80C2×C32×C4C2×Q812yes—
81C2×C32×C4C2×Q812yes—
82C2×C3⋊Dic3—24no—
83C2×C3⋊Dic3—24no—
84C2×C3⋊Dic3C2×D414yes—
85C2×C3⋊Dic3C2×Q814yes—
86C2×C3×Dic3—24no—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—24no—
91C2×C3×Dic3#4118yes—
92#627—216no—
93C2×C4×Q8—92no—
94#398—94no—
95#395—94no—
96C4×C4⋊C4—32no—
97C4×C4⋊C4—92no—
98#376—91no—
99C22×C3×C4—22no—
100C22×C3×C4—21no—
101C22×C3×C4—34no—
102C22×C3×C4—34no—
103C22×C3×C4C22×D312yes—
104C22×C3×C4C22×D312yes—
105C22×C3×C4C22×D312yes—
106C22×Dic3—34no—
107C22×Dic3—34no—
108C22×Dic3—62no—
109C22×Dic3—62no—
110C22×Dic3C22×D314yes—
111C22×Dic3C22×D314yes—
112C2×Dic6—68no—
113C2×Dic6—68no—
114C2×Dic6—68no—
115C3×C4⋊C4—68no—
116C3×C42—24no—
117C3×C42—68no—
118C3×C42Dic618yescomplemented
119C4⋊Dic3—28no—
120C4⋊Dic3—68no—
121Dic3⋊C4—68no—
122Dic3⋊C4—68no—
123Dic3⋊C4—68no—
124Dic3⋊C4—68no—
125C4×Dic3—28no—
126C4×Dic3—38no—
127C4×Dic3—38no—
128C4×Dic3—64no—
129C4×Dic3—64no—
130C22×C32C22×D411yescharacteristic
131C22×C32C22×Q811yescharacteristic
132C22×C32C22×Q811yescharacteristic
133C22×C32C2×#4114yes—
134C32×C4—24no—
135C32×C4C4⋊Q814yes—
136C3⋊Dic3—24no—
137C3⋊Dic3—24no—
138C3×Dic3—28no—
139C3×Dic3—44no—
140C22×Q8—92no—
141C4×Q8—188no—
142C2×C4⋊C4—34no—
143C2×C4⋊C4—94no—
144C2×C4⋊C4—92no—
145C2×C4⋊C4—94no—
146C2×C42—34no—
147C2×C42—91no—
148C2×C42—91no—
149C2×C42D3211yescharacteristic
150#95—32no—
151#95—32no—
152#95—92no—
153#95—92no—
154#95—94no—
155C23×C3—21no—
156C23×C3C23×D312yes—
157C2×C3×C4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—24no—
163C2×C3×C4—38no—
164C2×C3×C4—44no—
165C2×C3×C4—64no—
166C2×C3×C4—64no—
167C2×C3×C4—64no—
168C2×C3×C4—64no—
169C2×C3×C4—64no—
170C2×C3×C4C2×Dic614yes—
171C2×C3×C4C2×Dic614yes—
172C2×C3×C4C2×Dic614yes—
173C2×C3×C4D3×D414yes—
174C2×C3×C4D3×Q814yes—
175C2×Dic3—24no—
176C2×Dic3—24no—
177C2×Dic3—24no—
178C2×Dic3—24no—
179C2×Dic3—24no—
180C2×Dic3—38no—
181C2×Dic3—38no—
182C2×Dic3—64no—
183C2×Dic3—64no—
184C2×Dic3—64no—
185C2×Dic3—64no—
186C2×Dic3—64no—
187C2×Dic3—64no—
188C2×Dic3—124no—
189C2×Dic3—124no—
190C2×Dic3#23518yes—
191Dic6—632no—
192C2×C32#52512yes—
193C2×C32C2×C4⋊Q811yescharacteristic
194C2×C32#53312yes—
195C2×C32#53312yes—
196C2×Q8—188no—
197C2×Q8—184no—
198C22×C4—34no—
199C22×C4—34no—
200C22×C4—92no—
201C22×C4—92no—
202C22×C4C2×D3212yes—
203C22×C4C2×D3211yescharacteristic
204C4⋊C4—68no—
205C4⋊C4—188no—
206C4⋊C4—184no—
207C4⋊C4—188no—
208C42—68no—
209C42—94no—
210C42—94no—
211C42#62714yescomplemented
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—24no—
215C22×C3—21no—
216C22×C3C22×Dic612yes—
217C22×C3C2×#23514yes—
218C22×C3C2×D3×D412yes—
219C22×C3C2×D3×Q812yes—
220C22×C3D3×#4114yes—
221C3×C4—24no—
222C3×C4—24no—
223C3×C4—24no—
224C3×C4—44no—
225C3×C4—68no—
226C3×C4—124no—
227C3×C4#88818yes—
228Dic3—28no—
229Dic3—44no—
230Dic3—68no—
231Dic3—68no—
232Dic3—124no—
233Dic3—124no—
234C32#239911yescharacteristic, complemented, Sylow
235C23C22×D3211yescharacteristic
236Q8—1816no—
237C2×C4—24no—
238C2×C4—38no—
239C2×C4—64no—
240C2×C4—64no—
241C2×C4—64no—
242C2×C4—64no—
243C2×C4—64no—
244C2×C4—94no—
245C2×C4—94no—
246C2×C4—184no—
247C2×C4—184no—
248C2×C4#379712yes—
249C2×C4#380212yes—
250C2×C4C2×#62714yes—
251C2×C4C2×#62712yes—
252C2×C3—22no—
253C2×C3—22no—
254C2×C3—21no—
255C2×C3—22no—
256C2×C3#547012yes—
257C2×C3C2×#88812yes—
258C2×C3#551712yes—
259C2×C3#554714yes—
260C2×C3#557814yes—
261C22C2×#379711yescharacteristic
262C22C2×#380211yescharacteristic
263C22D3×#23514yes—
264C22C22×#62711yescharacteristic
265C4—24no—
266C4—68no—
267C4—124no—
268C4—184no—
269C4—184no—
270C4#6391914yes—
271C3—21no—
272C3#7366912yescomplemented
273C2#1059393512yes—
274C2#1059400612yes—
275C2C2×#6391911yescharacteristic
276C2#1059504912yes—
subgroupG/H
centerC22×C4C2×D32
commutator, socle, prime radical, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
41. C32×C42Q8semidirect
43. C4×C3⋊Dic3Q8semidirect
118. C3×C42Dic6semidirect
211. C42#627semidirect
234. C32#2399semidirect
272. C3#73669semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
#105926312
C3×C4×C4⋊Dic32
#105913452
#105913382
C4×#37242
#736693