Finite Group Databasebeta

← #11783625

Subgroups — #11783625

Order 1152.

582 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 95 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#10593992C211yesmaximal, characteristic
2#10593723C211yesmaximal, characteristic, complemented
3C2×D32⋊C8C212yesmaximal
4C4×#3710C211yesmaximal, characteristic, complemented
5#10590043C212yesmaximal, complemented
6C2×C4×D32C2211yescharacteristic
7C2×#3787C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×#872—21no—
10#63921C412yes—
11#63883C412yes—
12C4×#624C2211yescharacteristic
13#63878—22no—
14#63855—21no—
15C2×#3710C2212yes—
16#63777—22no—
17D32⋊C8C418yescomplemented
18C3×C4×C3⋊C8—21no—
19#63553—21no—
20D3×#117—61no—
21C4×D3×C8—61no—
22C22×D32C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C412yes—
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×C3×C4×D3—21no—
26C2×#624C2×C412yes—
27C2×#624C2×C411yescharacteristic
28C2×D3×Dic3—21no—
29C4×D32—22no—
30C4×D32C2×C414yes—
31C2×#622—22no—
32#3787—22no—
33#3787C2×C414yes—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3D412yes—
37C3×(C2×D3)⋊C4—22no—
38C3×Dic3⋊C4—22no—
39C3×C4×Dic3—21no—
40C2×C3×C3⋊C8—22no—
41Dic3⋊Dic3—22no—
42(C2×D3)⋊Dic3—22no—
43Dic32—21no—
44#3710—22no—
45#3710C2×C414yes—
46#1750—91nomaximal, Sylow
47C22×C4×D3—61no—
48C3×#117—61no—
49#926—61no—
50C2×D3×C8—62no—
51#892—62no—
52D3×C4⋊C4—62no—
53D3×C22⋊C4—62no—
54#877—62no—
55#872—21no—
56#872—61no—
57C42×D3—61no—
58C42×D3—61no—
59C42×D3—61no—
60C3×C4×C8—61no—
61C8×Dic3—62no—
62C4×C3⋊C8—21no—
63C22×C3⋊D3C22×C411yescharacteristic
64C22×C3×D3—21no—
65C2×D32—21no—
66C2×D32—24no—
67C2×D32C4212yes—
68C2×C32×C4C22⋊C412yes—
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3C22⋊C412yes—
71C2×C3⋊Dic3C2×D411yescharacteristic
72C4×C3⋊D3—24no—
73C4×C3⋊D3C22×C412yes—
74C4×C3⋊D3#4112yes—
75C2×C3×Dic3—21no—
76C2×C3×Dic3—22no—
77C3×C4×D3—24no—
78#624—21no—
79#624—24no—
80#624C4212yes—
81D3×Dic3—24no—
82#622—24no—
83C3×C3⋊C8—24no—
84C2×#117—91no—
85C2×C22⋊C8—92no—
86C2×#97—91no—
87C2×C4×C8—91no—
88#336—92no—
89C23×D3—61no—
90C22×C3×C4—61no—
91C22×Dic3—61no—
92C2×C4×D3—21no—
93C2×C4×D3—64no—
94C2×C4×D3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—62no—
98C2×C4×D3—62no—
99C2×C4×D3—62no—
100C2×C4×D3—64no—
101C2×C4×D3—61no—
102C2×C3×C8—62no—
103C3×C4⋊C4—62no—
104C3×C22⋊C4—62no—
105C3×C42—21no—
106C3×C42—21no—
107C3×C42—61no—
108#217—62no—
109(C2×D3)⋊C4—22no—
110(C2×D3)⋊C4—62no—
111C4⋊Dic3—62no—
112Dic3⋊C4—22no—
113Dic3⋊C4—62no—
114C4×Dic3—21no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—62no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C2×C3⋊C8—22no—
121D3×C8—64no—
122D3×C8—64no—
123C22×C32C2×C22⋊C411yescharacteristic
124C2×C3⋊D3C2×C4211yescharacteristic
125C2×C3⋊D3#11711yescharacteristic
126C2×C3⋊D3#13114yes—
127C2×C3×D3—22no—
128C2×C3×D3—42no—
129D32—24no—
130D32—42no—
131C32×C4—22no—
132C32×C4C4×D412yes—
133C3⋊Dic3—22no—
134C3⋊Dic3C4×D412yes—
135C3×Dic3—22no—
136C3×Dic3—42no—
137C23×C4—91no—
138C22×C8—92no—
139C22×C8—92no—
140#117—61no—
141#117—181no—
142#117—182no—
143C2×C4⋊C4—92no—
144C2×C22⋊C4—92no—
145C2×C42—91no—
146C2×C42—91no—
147C22⋊C8—98no—
148#97—182no—
149C4×C8—61no—
150C4×C8—181no—
151C23×C3—61no—
152C22×D3—21no—
153C22×D3—62no—
154C22×D3—61no—
155C22×D3—61no—
156C22×D3—62no—
157C22×D3—124no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—64no—
163C2×C3×C4—61no—
164C2×C3×C4—62no—
165C2×Dic3—21no—
166C2×Dic3—22no—
167C2×Dic3—62no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—62no—
171C2×Dic3—64no—
172C4×D3—24no—
173C4×D3—62no—
174C4×D3—62no—
175C4×D3—62no—
176C4×D3—62no—
177C4×D3—62no—
178C4×D3—62no—
179C4×D3—68no—
180C4×D3—64no—
181C4×D3—124no—
182C4×D3—124no—
183C3×C8—64no—
184C3⋊C8—24no—
185C2×C32C4×C22⋊C411yescharacteristic
186C2×C32#40812yes—
187C3⋊D3#40512yes—
188C3⋊D3#43312yes—
189C3×D3—42no—
190C24—91no—
191C22×C4—61no—
192C22×C4—94no—
193C22×C4—91no—
194C22×C4—92no—
195C22×C4—91no—
196C22×C4—92no—
197C22×C4—182no—
198C22×C4—181no—
199C2×C8—62no—
200C2×C8—94no—
201C2×C8—94no—
202C2×C8—182no—
203C2×C8—182no—
204C2×C8—182no—
205C4⋊C4—62no—
206C4⋊C4—182no—
207C22⋊C4—62no—
208C22⋊C4—182no—
209C42—61no—
210C42—91no—
211C42—92no—
212C42—181no—
213C42GO+(4,𝔽2)11yescharacteristic
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—62no—
217C22×C3—122no—
218C2×D3—22no—
219C2×D3—42no—
220C2×D3—61no—
221C2×D3—61no—
222C2×D3—61no—
223C2×D3—61no—
224C2×D3—64no—
225C2×D3—64no—
226C2×D3—124no—
227C2×D3—124no—
228C3×C4—24no—
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—42no—
232C3×C4—62no—
233C3×C4—122no—
234Dic3—22no—
235Dic3—42no—
236Dic3—62no—
237Dic3—62no—
238Dic3—64no—
239Dic3—122no—
240C32#175011yescharacteristic, complemented, Sylow
241C23—61no—
242C23—92no—
243C23—91no—
244C23—181no—
245C23—184no—
246C2×C4—61no—
247C2×C4—64no—
248C2×C4—62no—
249C2×C4—92no—
250C2×C4—91no—
251C2×C4—92no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—184no—
255C2×C4—181no—
256C2×C4—184no—
257C2×C4—184no—
258C2×C4D32⋊C412yes—
259C2×C4C2×GO+(4,𝔽2)11yescharacteristic
260C8—64no—
261C8—184no—
262C2×C3—22no—
263C2×C3—22no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—122no—
267D3—42no—
268D3—62no—
269D3—62no—
270D3—62no—
271D3—62no—
272C22—62no—
273C22—94no—
274C22—91no—
275C22—91no—
276C22—122no—
277C22—184no—
278C22—362no—
279C22C2×D32⋊C411yescharacteristic
280C4—22no—
281C4—62no—
282C4—92no—
283C4—122no—
284C4—182no—
285C4C4×GO+(4,𝔽2)12yes—
286C3—21no—
287C3—21no—
288C2—92no—
289C2—92no—
290C2—122no—
291C2#1059330812yes—
292C2C4×D32⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C2×C42
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×D32C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1750
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593723C2semidirect
4. C4×#3710C2semidirect
5. #10590043C2semidirect
17. D32⋊C8C4semidirect
240. C32#1750semidirect

Maximal subgroups

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

subgroupindex
#105939922
#105937232
C2×D32⋊C82
C4×#37102
#105900432
#17509