Finite Group Databasebeta

← #11776365

Subgroups — #11776365

Order 1152.

543 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 543 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#10593909C211yesmaximal, characteristic
2#10592536C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4481C212yesmaximal, complemented
5#10589095C212yesmaximal, complemented
6#68483—32nomaximal
7C2×#3797C412yes—
8C2×#3743—21no—
9C42×C3⋊D3C2211yescharacteristic
10C3×#869C2212yes—
11#63919—21no—
12#63919—21no—
13#63900—21no—
14#63900—21no—
15#63873C412yes—
16C32×C4⋊C8C2211yescharacteristic
17#63641—21no—
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2212yes—
20#63557—21no—
21#63553—21no—
22D3×C4⋊Q8—32no—
23#4837—32no—
24#4837—61no—
25#4833—32no—
26C3×#333—32no—
27#4546—32no—
28#4481—32no—
29#4481D312yescomplemented
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C3×Dic6C2×C414yes—
34C2×#627—22no—
35C2×#624—22no—
36#3797—44no—
37C2×C32×C8—21no—
38C32×C42C2311yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C2×C3⋊(C3⋊C8)—21no—
43#3743—42no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3—22no—
46C2×C3×C3⋊C8—22no—
47#3724—22no—
48#3724—22no—
49#1548—91noSylow
50C2×D3×Q8—34no—
51C3×C4⋊Q8—32no—
52#944—34no—
53C2×ΓL(1,𝔽25)—62no—
54C2×ΓL(1,𝔽25)—62no—
55D3×C4⋊C4—62no—
56D3×C4⋊C4—62no—
57#888—62no—
58#888—62no—
59C42×D3—32no—
60C42×D3—61no—
61#869C2×D312yes—
62C3×C4⋊C8—21no—
63C3×C4⋊C8—32no—
64C3×C4⋊C8C2×D312yes—
65(C2×D3)⋊C8—62no—
66Dic3⋊C8—62no—
67Dic3⋊C8—62no—
68C8×Dic3—62no—
69C4⋊(C3⋊C8)—32no—
70C4⋊(C3⋊C8)—61no—
71C4⋊(C3⋊C8)C2×D312yes—
72C22×C3⋊D3C22⋊C411yescharacteristic
73C2×C32×C4C22×C411yescharacteristic
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C4×C3⋊D3—22no—
80C4×C3⋊D3—22no—
81C4×C3⋊D3SD1612yes—
82C4×C3⋊D3Q1612yes—
83C2×C3×Dic3—24no—
84C3×Dic6—44no—
85#627—44no—
86#624—44no—
87C32×C8—41no—
88C3⋊(C3⋊C8)—41no—
89C3×C3⋊C8—42no—
90C2×C4⋊Q8—91no—
91#431—91no—
92#423—91no—
93#333—32no—
94#333—92no—
95C2×C3×Q8—34no—
96D3×Q8—128no—
97C2×C4×D3—32no—
98C2×C4×D3—32no—
99C2×C4×D3—32no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—64no—
104C2×Dic6—64no—
105C2×Dic6C4×D314yes—
106C2×C3×C8—22no—
107C2×C3×C8—22no—
108C2×C3×C8—62no—
109C3×C4⋊C4—62no—
110C3×C4⋊C4—62no—
111C3×C42—21no—
112C3×C42C22×D312yes—
113C4⋊Dic3—22no—
114C4⋊Dic3—22no—
115Dic3⋊C4—64no—
116Dic3⋊C4—64no—
117C4×Dic3—32no—
118C4×Dic3—32no—
119C4×Dic3—32no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C2×C3⋊C8—22no—
124C2×C3⋊C8—62no—
125C2×C3⋊C8—62no—
126ΓL(1,𝔽25)—124no—
127ΓL(1,𝔽25)—124no—
128C22×C32C2×C22⋊C411yescharacteristic
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3#10312yes—
132C32×C4—21no—
133C32×C4C2×SD1611yescharacteristic
134C32×C4C2×Q1611yescharacteristic
135C32×C4#13712yes—
136C3⋊Dic3—21no—
137C3⋊Dic3#10012yes—
138C3⋊Dic3#10312yes—
139C3×Dic3—44no—
140C22×Q8—92no—
141C2×M16—181no—
142C4⋊Q8—32no—
143C4⋊Q8—92no—
144C4⋊Q8—181no—
145C4⋊Q8—181no—
146C2×C4⋊C4—181no—
147C2×C4⋊C4—181no—
148C2×C42—91no—
149C4⋊C8—32no—
150C4⋊C8—91no—
151C4⋊C8—181no—
152C4⋊C8D3211yescharacteristic
153C22⋊C8—181no—
154C4×C8—181no—
155C22×D3—32no—
156C22×D3—61no—
157C3×Q8—124no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—64no—
162C2×C3×C4C2×C4×D312yes—
163C2×C3×C4D3×D412yes—
164C2×C3×C4D3×D412yes—
165C2×Dic3—24no—
166C2×Dic3—32no—
167C2×Dic3—32no—
168C2×Dic3—32no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C4×D3—34no—
173C4×D3—34no—
174C4×D3—62no—
175C4×D3—62no—
176C4×D3—64no—
177C4×D3—62no—
178C4×D3—62no—
179C4×D3—122no—
180C4×D3—122no—
181C4×D3—128no—
182Dic6—44no—
183Dic6—128no—
184C3×C8—42no—
185C3×C8—42no—
186C3×C8—122no—
187C3⋊C8—42no—
188C3⋊C8—122no—
189C3⋊C8—122no—
190C2×C32C2×#10011yescharacteristic
191C2×C32C2×#10311yescharacteristic
192C2×C32#41911yescharacteristic
193C3⋊D3—22no—
194C2×Q8—34no—
195C2×Q8—182no—
196C2×Q8—364no—
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—91no—
200C22×C4—182no—
201M16—362no—
202C2×C8—21no—
203C2×C8—62no—
204C2×C8—181no—
205C4⋊C4—62no—
206C4⋊C4—62no—
207C4⋊C4—182no—
208C4⋊C4—182no—
209C42—91no—
210C42—91no—
211C42—91no—
212C42C2×D3211yescharacteristic
213C22×C3—21no—
214C22×C3D3×C22⋊C412yes—
215C2×D3—34no—
216C2×D3—62no—
217C2×D3—62no—
218C2×D3—62no—
219C2×D3—121no—
220C2×D3—121no—
221C3×C4—22no—
222C3×C4—22no—
223C3×C4—21no—
224C3×C4—21no—
225C3×C4—41no—
226C3×C4—124no—
227C3×C4D3×SD1612yes—
228C3×C4#91512yes—
229C3×C4D3×Q1612yes—
230C3×C4#91812yes—
231Dic3—34no—
232Dic3—34no—
233Dic3—44no—
234Dic3—62no—
235Dic3—62no—
236Dic3—62no—
237Dic3—121no—
238C32#154811yescharacteristic, complemented, Sylow
239C23—91no—
240Q8—124no—
241Q8—364no—
242C2×C4—64no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4—92no—
246C2×C4—92no—
247C2×C4—91no—
248C2×C4—182no—
249C2×C4—182no—
250C2×C4—364no—
251C2×C4C4×D3211yescharacteristic
252C2×C4#380211yescharacteristic
253C2×C4#381111yescharacteristic
254C8—41no—
255C8—122no—
256C8—361no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3D3×#10012yes—
261C2×C3D3×#10312yes—
262C2×C3#480212yes—
263D3—64no—
264D3—122no—
265C22—92no—
266C22—181no—
267C22—181no—
268C22#6392111yescharacteristic
269C4—21no—
270C4—92no—
271C4—92no—
272C4—124no—
273C4—181no—
274C4#6381112yes—
275C4#6393011yescharacteristic
276C4#6394411yescharacteristic
277C3—21no—
278C3#6848312yescomplemented
279C2—182no—
280C2#1059060111yescharacteristic
281C2#1059069111yescharacteristic
282C2#1059100111yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1548
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4481C2semidirect
5. #10589095C2semidirect
29. #4481D3semidirect
238. C32#1548semidirect
278. C3#68483semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105925362
#105902562
C3×#44812
#105890952
#684833