Finite Group Databasebeta

← #11776587

Subgroups — #11776587

Order 1152.

636 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 61 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
2#10593806C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4#10590037C214yesmaximal, complemented
5C22×C3×D12—21no—
6C22×#625—21no—
7C22×#625C412yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9#63914—21no—
10#63914—21no—
11#63914C412yes—
12#63914C2212yes—
13C22⋊#622—21no—
14#63777—21no—
15C4⋊#622C2212yescomplemented
16C3×#830—21no—
17#63572C2212yescomplemented
18#63555—21no—
19C2×#940—61no—
20#4719—61no—
21C23×C3×D3—22no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C3×D12—22no—
26C2×C3×D12—22no—
27C2×C3×D12—44no—
28C2×#625—22no—
29C2×#625—22no—
30C2×#625—22no—
31C2×#625—44no—
32C2×#625—44no—
33C2×#625C2×C414yes—
34C2×#622—22no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C2×C3×C3⋊C8—22no—
40#1555—91nomaximal, Sylow
41C22×C3×D4—61no—
42C22×#67—62no—
43C22×#67—62no—
44C22×D12—21no—
45#940—62no—
46#940—62no—
47#940—62no—
48#940—62no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51C3×C22⋊C8—61no—
52#830—21no—
53#815—62no—
54Dic3⋊C8—62no—
55C23×C32C22⋊C411yescharacteristic
56C22×C3×D3—24no—
57C22×C3×D3—44no—
58C22×C3×D3—44no—
59C22×C3×D3—44no—
60C2×C32×C4—22no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C3×D12—44no—
70C3×D12—44no—
71#625—44no—
72#625—44no—
73#625—44no—
74#625—44no—
75#622—42no—
76C3×C3⋊C8—42no—
77C2×#127—91no—
78#432—91no—
79#432—91no—
80#331—94no—
81C24×C3—62no—
82C23×D3—22no—
83C2×C3×D4—62no—
84C2×C3×D4—62no—
85C2×C3×D4—124no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C2×#67—64no—
89C2×#67—64no—
90C2×#67—64no—
91C2×#67—64no—
92C2×#67—128no—
93C2×#67—128no—
94C22×Dic3—61no—
95C22×Dic3—61no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C2×D12—22no—
99C2×D12—22no—
100C2×D12—44no—
101C2×C3×C8—62no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C2×C3⋊C8—22no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32#10012yes—
114C22×C32C2×C22⋊C411yescharacteristic
115C2×C3×D3—44no—
116C2×C3×D3—44no—
117C2×C3×D3—44no—
118C2×C3×D3—88no—
119C32×C4—21no—
120C32×C4AGL(1,ℤ/8)12yes—
121C3⋊Dic3—21no—
122C3⋊Dic3—21no—
123C3⋊Dic3—21no—
124C3⋊Dic3AGL(1,ℤ/8)12yes—
125C22×D4—61no—
126C22×D4—92no—
127C22×D4—181no—
128#127—92no—
129#127—92no—
130#127—181no—
131#127—181no—
132C2×C42—91no—
133C4⋊C8—92no—
134C4⋊C8—92no—
135C22⋊C8—61no—
136C22⋊C8—181no—
137#97—181no—
138#97—181no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—64no—
142C23×C3—124no—
143C23×C3—124no—
144C23×C3—124no—
145C22×D3—24no—
146C22×D3—44no—
147C22×D3—44no—
148C22×D3—44no—
149C3×D4—124no—
150C3×D4—124no—
151C2×C3×C4—24no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—42no—
157#67—128no—
158#67—128no—
159#67—128no—
160#67—128no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—64no—
170C2×Dic3—64no—
171C2×Dic3—122no—
172C2×Dic3—122no—
173D12—44no—
174D12—44no—
175C3×C8—122no—
176C3⋊C8—42no—
177C2×C32—22no—
178C2×C32C2×#10011yescharacteristic
179C2×C32#41811yescharacteristic
180C2×C32#41811yescharacteristic
181C3×D3—84no—
182C24—62no—
183C2×D4—62no—
184C2×D4—62no—
185C2×D4—94no—
186C2×D4—124no—
187C2×D4—182no—
188C2×D4—182no—
189C2×D4—182no—
190C2×D4—364no—
191C2×D4—364no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4GO+(4,𝔽2)11yescharacteristic
195C2×C8—62no—
196C2×C8—182no—
197C42—91no—
198C42—91no—
199C42—91no—
200C42—91no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—22no—
206C22×C3—22no—
207C22×C3—41no—
208C22×C3—41no—
209C22×C3—124no—
210C22×C3—124no—
211C22×C3—124no—
212C22×C3—248no—
213C2×D3—44no—
214C2×D3—44no—
215C2×D3—44no—
216C2×D3—88no—
217C3×C4—22no—
218C3×C4—22no—
219C3×C4—22no—
220C3×C4—41no—
221Dic3—62no—
222Dic3—62no—
223Dic3—62no—
224Dic3—62no—
225Dic3—62no—
226Dic3—121no—
227Dic3—121no—
228Dic3—121no—
229C32#155511yescharacteristic, complemented, Sylow
230C23—64no—
231C23—124no—
232C23—124no—
233C23—124no—
234C23D32⋊C411yescharacteristic
235D4—124no—
236D4—124no—
237D4—364no—
238D4—364no—
239D4—364no—
240D4—364no—
241C2×C4—22no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—182no—
247C2×C4—182no—
248C2×C4D32⋊C411yescharacteristic
249C2×C4C2×GO+(4,𝔽2)11yescharacteristic
250C8—122no—
251C8—362no—
252C2×C3—24no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—42no—
260C2×C3—244no—
261D3—84no—
262C22—21no—
263C22—21no—
264C22—124no—
265C22—124no—
266C22—124no—
267C22—248no—
268C22#6372712yes—
269C22C2×D32⋊C411yescharacteristic
270C4—21no—
271C4—92no—
272C4—181no—
273C4—181no—
274C4—181no—
275C4#6423612yes—
276C3—21no—
277C3—21no—
278C2—22no—
279C2—244no—
280C2C2×#6372711yescharacteristic
281C2#1059331811yescharacteristic
282C2#1059349311yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#63914C2
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1555
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593806C2semidirect
3. #10591066C2semidirect
4. #10590037C2semidirect
15. C4⋊#622C22semidirect
17. #63572C22semidirect
229. C32#1555semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
#105938062
#105910662
#105900372
#15559