Finite Group Databasebeta

← #11776358

Subgroups — #11776358

Order 1152.

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

normal subgroups only

This group has 539 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#10592532C211yesmaximal, characteristic
3#10590340C211yesmaximal, characteristic
4C3×#4481C212yesmaximal, complemented
5#10589095C212yesmaximal, complemented
6#68483—32nomaximal
7C2×#3797C412yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×#869C2212yes—
10#63919—21no—
11#63919—21no—
12#63900—21no—
13#63900—21no—
14#63873C412yes—
15C2×#3712—21no—
16C32×C4⋊C8C2211yescharacteristic
17#63647—21no—
18C8×C3⋊Dic3—21no—
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2212yes—
21#63572—21no—
22D3×C4⋊Q8—32no—
23#4837—32no—
24#4833—32no—
25#4833—61no—
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—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3—22no—
45C2×C3×C3⋊C8—22no—
46#3724—22no—
47#3724—22no—
48#3712—42no—
49#1548—91noSylow
50C2×D3×Q8—34no—
51C3×C4⋊Q8—32no—
52#944—34no—
53C2×ΓL(1,𝔽25)—62no—
54D3×C4⋊C4—62no—
55D3×C4⋊C4—62no—
56#888—62no—
57#888—62no—
58C42×D3—32no—
59C42×D3—61no—
60#869C2×D312yes—
61C3×C4⋊C8—21no—
62C3×C4⋊C8—32no—
63C3×C4⋊C8C2×D312yes—
64(C2×D3)⋊C8—62no—
65(C2×D3)⋊C8—62no—
66Dic3⋊C8—62no—
67C8×Dic3—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—21no—
80C4×C3⋊D3—21no—
81C4×C3⋊D3—22no—
82C4×C3⋊D3SD1612yes—
83C4×C3⋊D3Q1612yes—
84C2×C3×Dic3—24no—
85C3×Dic6—44no—
86#627—44no—
87#624—44no—
88C32×C8—41no—
89C3⋊(C3⋊C8)—41no—
90C3×C3⋊C8—42no—
91C2×C4⋊Q8—91no—
92#431—91no—
93#423—91no—
94#333—32no—
95#333—92no—
96C2×C3×Q8—34no—
97D3×Q8—128no—
98C2×C4×D3—32no—
99C2×C4×D3—32no—
100C2×C4×D3—32no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—64no—
105C2×Dic6—64no—
106C2×Dic6C4×D314yes—
107C2×C3×C8—22no—
108C2×C3×C8—22no—
109C2×C3×C8—62no—
110C3×C4⋊C4—62no—
111C3×C4⋊C4—62no—
112C3×C42—21no—
113C3×C42C22×D312yes—
114C4⋊Dic3—22no—
115C4⋊Dic3—22no—
116Dic3⋊C4—64no—
117Dic3⋊C4—64no—
118C4×Dic3—32no—
119C4×Dic3—32no—
120C4×Dic3—32no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C2×C3⋊C8—22no—
125C2×C3⋊C8—62no—
126C2×C3⋊C8—62no—
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#13711yescharacteristic
136C32×C4#13711yescharacteristic
137C3⋊Dic3—21no—
138C3⋊Dic3#10012yes—
139C3⋊Dic3#10312yes—
140C3×Dic3—44no—
141C22×Q8—92no—
142C2×M16—181no—
143C4⋊Q8—32no—
144C4⋊Q8—92no—
145C4⋊Q8—181no—
146C4⋊Q8—181no—
147C2×C4⋊C4—181no—
148C2×C4⋊C4—181no—
149C2×C42—91no—
150C4⋊C8—32no—
151C4⋊C8—91no—
152C4⋊C8—181no—
153C4⋊C8D3211yescharacteristic
154C22⋊C8—181no—
155C4×C8—181no—
156C22×D3—32no—
157C22×D3—61no—
158C3×Q8—124no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—64no—
163C2×C3×C4C2×C4×D312yes—
164C2×C3×C4D3×D412yes—
165C2×C3×C4D3×D412yes—
166C2×Dic3—24no—
167C2×Dic3—32no—
168C2×Dic3—32no—
169C2×Dic3—32no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C4×D3—34no—
174C4×D3—34no—
175C4×D3—62no—
176C4×D3—62no—
177C4×D3—64no—
178C4×D3—62no—
179C4×D3—62no—
180C4×D3—122no—
181C4×D3—121no—
182C4×D3—121no—
183C4×D3—128no—
184Dic6—44no—
185Dic6—128no—
186C3×C8—42no—
187C3×C8—42no—
188C3×C8—122no—
189C3⋊C8—42no—
190C3⋊C8—122no—
191C3⋊C8—122no—
192C2×C32C2×#10011yescharacteristic
193C2×C32C2×#10311yescharacteristic
194C2×C32#41911yescharacteristic
195C3⋊D3—22no—
196C2×Q8—34no—
197C2×Q8—182no—
198C2×Q8—364no—
199C22×C4—91no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—182no—
203M16—362no—
204C2×C8—21no—
205C2×C8—62no—
206C2×C8—181no—
207C4⋊C4—62no—
208C4⋊C4—62no—
209C4⋊C4—182no—
210C4⋊C4—182no—
211C42—91no—
212C42—91no—
213C42—91no—
214C42C2×D3211yescharacteristic
215C22×C3—21no—
216C22×C3D3×C22⋊C412yes—
217C2×D3—34no—
218C2×D3—62no—
219C2×D3—62no—
220C2×D3—62no—
221C2×D3—121no—
222C2×D3—121no—
223C3×C4—22no—
224C3×C4—21no—
225C3×C4—21no—
226C3×C4—21no—
227C3×C4—21no—
228C3×C4—41no—
229C3×C4—124no—
230C3×C4D3×SD1612yes—
231C3×C4#91512yes—
232C3×C4D3×Q1612yes—
233C3×C4#91812yes—
234Dic3—34no—
235Dic3—34no—
236Dic3—44no—
237Dic3—62no—
238Dic3—62no—
239Dic3—62no—
240Dic3—121no—
241C32#154811yescharacteristic, complemented, Sylow
242C23—91no—
243Q8—124no—
244Q8—364no—
245C2×C4—64no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—92no—
249C2×C4—92no—
250C2×C4—91no—
251C2×C4—182no—
252C2×C4—181no—
253C2×C4—181no—
254C2×C4—364no—
255C2×C4C4×D3211yescharacteristic
256C2×C4#380211yescharacteristic
257C2×C4#381111yescharacteristic
258C8—41no—
259C8—122no—
260C8—361no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3D3×#10012yes—
265C2×C3D3×#10312yes—
266C2×C3#480212yes—
267D3—64no—
268D3—122no—
269C22—92no—
270C22—181no—
271C22—181no—
272C22#6392111yescharacteristic
273C4—21no—
274C4—92no—
275C4—92no—
276C4—124no—
277C4—181no—
278C4#6379611yescharacteristic
279C4#6380211yescharacteristic
280C4#6393111yescharacteristic
281C4#6394511yescharacteristic
282C3—21no—
283C3#6848312yescomplemented
284C2—182no—
285C2#1059060211yescharacteristic
286C2#1059067211yescharacteristic
287C2#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
241. C32#1548semidirect
283. C3#68483semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105925322
#105903402
C3×#44812
#105890952
#684833