Finite Group Databasebeta

← #11791467

Subgroups — #11791467

Order 1152.

774 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 91 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×#63914C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic, complemented
3C2×#63739C214yesmaximal, complemented
4#10591257C211yesmaximal, characteristic, complemented
5C22×C3×D12—21no—
6C22×#625—21no—
7C22×#625C2212yes—
8C22×#622C2212yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×#3724C2212yes—
11C2×Dic32—21no—
12#63914—22no—
13#63914C414yescomplemented
14#63779—22no—
15#63739—28no—
16C3×C3⋊#95—21no—
17C2×#940—61no—
18#4649—61no—
19C23×C3×D3—22no—
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3D411yescharacteristic
22C22×C3⋊Dic3C2311yescharacteristic
23C22×C3×Dic3—22no—
24C2×C3×D12—24no—
25C2×C3×D12—44no—
26C2×#625—24no—
27C2×#625—24no—
28C2×#625—24no—
29C2×#625—22no—
30C2×#625—42no—
31C2×#625—42no—
32C2×#625C2×C414yes—
33C2×#622—22no—
34C2×#622—24no—
35C4×C3⋊Dic3C2×C412yes—
36C4×C3⋊Dic3D412yes—
37#3724—22no—
38#3724D414yescomplemented
39Dic32—42no—
40#1982—91nomaximal, Sylow
41C22×C3×D4—61no—
42C22×#67—62no—
43C22×#67—62no—
44C22×D12—21no—
45#940—64no—
46#940—64no—
47C2×Dic3⋊C4—62no—
48C2×C4×Dic3—61no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—62no—
51C3×#95—61no—
52C3⋊#95—21no—
53C23×C32C2×D411yescharacteristic
54C22×C3×D3—24no—
55C22×C3×D3—44no—
56C22×C3×D3—42no—
57C22×C3×D3—42no—
58C22×C3×D3—44no—
59C2×C32×C4—22no—
60C2×C32×C4C22⋊C412yes—
61C2×C3⋊Dic3C22⋊C412yes—
62C2×C3⋊Dic3D812yes—
63C2×C3⋊Dic3SD1612yes—
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C2×D412yes—
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3#4112yes—
68C2×C3×Dic3—24no—
69C2×C3×Dic3—42no—
70C2×C3×Dic3—42no—
71C3×D12—48no—
72#625—28no—
73#625—48no—
74#625—42no—
75#625—42no—
76#622—42no—
77C2×#127—91no—
78C2×C4⋊C8—91no—
79C2×#102—94no—
80C4×C4⋊C4—91no—
81C24×C3—62no—
82C23×D3—22no—
83C2×C3×D4—64no—
84C2×C3×D4—124no—
85C22×C3×C4—21no—
86C22×C3×C4—21no—
87C22×C3×C4—62no—
88C2×#67—64no—
89C2×#67—68no—
90C2×#67—64no—
91C2×#67—124no—
92C2×#67—124no—
93C2×#67—124no—
94C2×#67—124no—
95C22×Dic3—22no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C2×D12—24no—
101C2×D12—44no—
102Dic3⋊C4—64no—
103Dic3⋊C4—64no—
104C4×Dic3—62no—
105C4×Dic3—62no—
106C4×Dic3—62no—
107C4×Dic3—62no—
108C4×Dic3—124no—
109C22×C32C2×C22⋊C411yescharacteristic
110C22×C32#12112yes—
111C22×C32C2×D811yescharacteristic
112C22×C32C2×SD1611yescharacteristic
113C22×C32AGL(1,ℤ/8)12yes—
114C2×C3×D3—44no—
115C2×C3×D3—44no—
116C2×C3×D3—44no—
117C2×C3×D3—84no—
118C2×C3×D3—84no—
119C32×C4—22no—
120C3⋊Dic3#10214yescomplemented
121C3⋊Dic3C4×D412yes—
122C3⋊Dic3#12411yescharacteristic
123C3⋊Dic3#12711yescharacteristic
124C3×Dic3—44no—
125C22×D4—61no—
126C22×D4—92no—
127C22×D4—181no—
128C22×C8—92no—
129#127—94no—
130#127—182no—
131C2×C4⋊C4—92no—
132C2×C42—91no—
133C2×C42—181no—
134C4⋊C8—182no—
135#102—188no—
136#95—61no—
137C23×C3—21no—
138C23×C3—21no—
139C23×C3—64no—
140C23×C3—122no—
141C23×C3—122no—
142C23×C3—124no—
143C23×C3—124no—
144C22×D3—24no—
145C22×D3—44no—
146C22×D3—42no—
147C22×D3—42no—
148C22×D3—44no—
149C3×D4—128no—
150C2×C3×C4—24no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—42no—
154C2×C3×C4—64no—
155C2×C3×C4—122no—
156C2×C3×C4—122no—
157#67—128no—
158#67—124no—
159#67—124no—
160#67—1216no—
161C2×Dic3—24no—
162C2×Dic3—42no—
163C2×Dic3—42no—
164C2×Dic3—62no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178D12—48no—
179C2×C32#39011yescharacteristic
180C2×C32C2×#10211yescharacteristic
181C2×C32#41811yescharacteristic
182C2×C32#45912yes—
183C2×C32#46012yes—
184C3×D3—84no—
185C24—62no—
186C2×D4—64no—
187C2×D4—94no—
188C2×D4—124no—
189C2×D4—184no—
190C2×D4—184no—
191C2×D4—184no—
192C2×D4—182no—
193C2×D4—362no—
194C2×D4—362no—
195C22×C4—62no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4GO+(4,𝔽2)11yescharacteristic
199C2×C8—184no—
200C2×C8—182no—
201C4⋊C4—94no—
202C4⋊C4—182no—
203C42—92no—
204C42—92no—
205C42—362no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—22no—
215C22×C3—22no—
216C22×C3—124no—
217C22×C3—124no—
218C22×C3—124no—
219C22×C3—244no—
220C22×C3—244no—
221C2×D3—44no—
222C2×D3—44no—
223C2×D3—44no—
224C2×D3—84no—
225C2×D3—84no—
226C3×C4—24no—
227C3×C4—42no—
228C3×C4—124no—
229Dic3—44no—
230Dic3—64no—
231Dic3—62no—
232Dic3—61no—
233Dic3—61no—
234Dic3—64no—
235Dic3—62no—
236Dic3—61no—
237Dic3—61no—
238C32#198211yescharacteristic, complemented, Sylow
239C23—64no—
240C23—122no—
241C23—122no—
242C23—124no—
243C23—124no—
244C23C2×GO+(4,𝔽2)11yescharacteristic
245D4—128no—
246D4—188no—
247D4—362no—
248D4—362no—
249D4—368no—
250C2×C4—22no—
251C2×C4—64no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—92no—
255C2×C4—92no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—92no—
259C2×C4—122no—
260C2×C4—122no—
261C2×C4D32⋊C412yes—
262C8—362no—
263C2×C3—22no—
264C2×C3—22no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—22no—
270C2×C3—22no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—244no—
274D3—84no—
275C22—124no—
276C22—124no—
277C22—124no—
278C22—244no—
279C22—244no—
280C22#6422511yescharacteristic
281C22#6422711yescharacteristic
282C22#6423012yes—
283C22C2×D32⋊C411yescharacteristic
284C22#6423612yes—
285C4—22no—
286C4—94no—
287C4—91no—
288C4—92no—
289C4—91no—
290C4—124no—
291C3—21no—
292C3—21no—
293C2—244no—
294C2#1059335512yes—
295C2#1059336511yescharacteristic
296C2#1059340511yescharacteristic
297C2#1059342612yes—
298C2#1059349311yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC2×#63914C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1982
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63779C2semidirect
3. C2×#63739C2semidirect
4. #10591257C2semidirect
13. #63914C4semidirect
38. #3724D4semidirect
120. C3⋊Dic3#102semidirect
238. C32#1982semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
C2×#637792
C2×#637392
#105912572
#19829