Finite Group Databasebeta

← #11790769

Subgroups — #11790769

Order 1152.

738 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 83 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×#63777C211yesmaximal, characteristic, complemented
3C2×#63739C214yesmaximal, complemented
4#10591360C211yesmaximal, characteristic, complemented
5C22×C3×D12—21no—
6C22×#625—21no—
7C22×#625C2212yes—
8C22×#622C2212yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×#3724C2212yes—
11#63914—22no—
12#63914C414yescomplemented
13#63777—22no—
14#63739—28no—
15C3×C3⋊#95—21no—
16#63579—21no—
17C2×#940—61no—
18#4650—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—44no—
31C2×#625C2×C414yes—
32C2×#622—22no—
33C2×#622—22no—
34C2×#622D414yescomplemented
35C4×C3⋊Dic3C2×C412yes—
36C4×C3⋊Dic3D412yes—
37#3724—24no—
38#1961—91nomaximal, Sylow
39C22×C3×D4—61no—
40C22×#67—62no—
41C22×#67—62no—
42C22×D12—21no—
43#940—64no—
44#940—64no—
45C2×Dic3⋊C4—62no—
46C2×C4×Dic3—61no—
47C2×C4×Dic3—61no—
48C3×#95—61no—
49C3⋊#95—21no—
50C3⋊#95—62no—
51C23×C32C2×D411yescharacteristic
52C22×C3×D3—24no—
53C22×C3×D3—42no—
54C22×C3×D3—42no—
55C22×C3×D3—44no—
56C22×C3×D3—44no—
57C2×C32×C4—22no—
58C2×C32×C4C22⋊C412yes—
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3C22⋊C412yes—
61C2×C3⋊Dic3C22×C411yescharacteristic
62C2×C3⋊Dic3C2×D412yes—
63C2×C3⋊Dic3C2×D411yescharacteristic
64C2×C3⋊Dic3#4112yes—
65C2×C3×Dic3—42no—
66C2×C3×Dic3—42no—
67C2×C3×Dic3—42no—
68C3×D12—48no—
69#625—28no—
70#625—48no—
71#625—44no—
72#622—24no—
73C2×#127—91no—
74C2×#102—94no—
75C2×#97—91no—
76#382—91no—
77C24×C3—62no—
78C23×D3—22no—
79C2×C3×D4—64no—
80C2×C3×D4—124no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×C3×C4—62no—
84C2×#67—64no—
85C2×#67—68no—
86C2×#67—64no—
87C2×#67—124no—
88C2×#67—124no—
89C2×#67—128no—
90C22×Dic3—22no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C2×D12—24no—
96C2×D12—44no—
97Dic3⋊C4—124no—
98C4×Dic3—62no—
99C4×Dic3—62no—
100C4×Dic3—62no—
101C4×Dic3—62no—
102C22×C32C2×C22⋊C411yescharacteristic
103C22×C32#12411yescharacteristic
104C22×C32#12711yescharacteristic
105C22×C32AGL(1,ℤ/8)12yes—
106C22×C32AGL(1,ℤ/8)12yes—
107C2×C3×D3—44no—
108C2×C3×D3—44no—
109C2×C3×D3—44no—
110C2×C3×D3—84no—
111C2×C3×D3—84no—
112C32×C4—22no—
113C3⋊Dic3—22no—
114C3⋊Dic3C4×D412yes—
115C3⋊Dic3#12112yes—
116C3×Dic3—82no—
117C22×D4—61no—
118C22×D4—92no—
119C22×D4—181no—
120C22×C8—92no—
121#127—94no—
122#127—182no—
123C2×C4⋊C4—92no—
124C2×C42—91no—
125#102—188no—
126#97—182no—
127#95—61no—
128#95—181no—
129C23×C3—21no—
130C23×C3—21no—
131C23×C3—64no—
132C23×C3—122no—
133C23×C3—124no—
134C23×C3—122no—
135C23×C3—124no—
136C22×D3—24no—
137C22×D3—44no—
138C22×D3—42no—
139C22×D3—44no—
140C22×D3—42no—
141C3×D4—128no—
142C2×C3×C4—24no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—42no—
146C2×C3×C4—122no—
147C2×C3×C4—122no—
148C2×C3×C4—122no—
149#67—128no—
150#67—128no—
151#67—1216no—
152C2×Dic3—42no—
153C2×Dic3—42no—
154C2×Dic3—42no—
155C2×Dic3—62no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—62no—
165C2×Dic3—64no—
166C2×Dic3—122no—
167D12—48no—
168C2×C32#39011yescharacteristic
169C2×C32#41811yescharacteristic
170C2×C32#41811yescharacteristic
171C2×C32#49012yes—
172C2×C32#49612yes—
173C3×D3—84no—
174C24—62no—
175C2×D4—64no—
176C2×D4—94no—
177C2×D4—124no—
178C2×D4—184no—
179C2×D4—184no—
180C2×D4—184no—
181C2×D4—182no—
182C2×D4—364no—
183C22×C4—62no—
184C22×C4—91no—
185C22×C4—91no—
186C22×C4GO+(4,𝔽2)11yescharacteristic
187C2×C8—94no—
188C2×C8—182no—
189C2×C8—182no—
190C4⋊C4—184no—
191C42—92no—
192C42—92no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3—22no—
196C22×C3—22no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—21no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—124no—
204C22×C3—124no—
205C22×C3—124no—
206C22×C3—244no—
207C22×C3—244no—
208C2×D3—44no—
209C2×D3—44no—
210C2×D3—44no—
211C2×D3—84no—
212C2×D3—84no—
213C3×C4—24no—
214C3×C4—42no—
215C3×C4—242no—
216Dic3—62no—
217Dic3—62no—
218Dic3—62no—
219Dic3—62no—
220Dic3—64no—
221Dic3—82no—
222Dic3—122no—
223C32#196111yescharacteristic, complemented, Sylow
224C23—64no—
225C23—122no—
226C23—124no—
227C23—122no—
228C23—124no—
229C23C2×GO+(4,𝔽2)11yescharacteristic
230D4—128no—
231D4—188no—
232D4—364no—
233D4—368no—
234C2×C4—22no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—92no—
240C2×C4—122no—
241C2×C4—122no—
242C2×C4—122no—
243C2×C4—182no—
244C2×C4D32⋊C412yes—
245C8—184no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—22no—
253C2×C3—22no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—244no—
257D3—84no—
258C22—124no—
259C22—124no—
260C22—124no—
261C22—244no—
262C22—244no—
263C22#6422111yescharacteristic
264C22#6422412yes—
265C22#6423111yescharacteristic
266C22C2×D32⋊C411yescharacteristic
267C22#6423612yes—
268C4—22no—
269C4—92no—
270C4—92no—
271C4—182no—
272C4—242no—
273C3—21no—
274C3—21no—
275C2—244no—
276C2#1059335612yes—
277C2#1059336311yescharacteristic
278C2#1059340711yescharacteristic
279C2#1059342712yes—
280C2#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#1961
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×#63777C2semidirect
3. C2×#63739C2semidirect
4. #10591360C2semidirect
12. #63914C4semidirect
34. C2×#622D4semidirect
223. C32#1961semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
C2×#637772
C2×#637392
#105913602
#19619