Finite Group Databasebeta

← #11794305

Subgroups — #11794305

Order 1152.

942 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 191 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#10595954C211yesmaximal, characteristic
2#10592649C212yesmaximal
3#10592645C211yesmaximal, characteristic
4C32×#342C211yesmaximal, characteristic
5#10589393C212yesmaximal
6#68958—34nomaximal
7C23×C3⋊Dic3C2211yescharacteristic
8C2×C32×C22⋊C4C2211yescharacteristic
9C2×C32×C22⋊C4C2212yes—
10C2×#3757C2212yes—
11C2×#3757C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)—22no—
13#64133—21no—
14#64133—21no—
15C2×#3750—21no—
16#64087—22no—
17#64087—22no—
18#63658—21no—
19#63658—22no—
20#5483—34no—
21#4950—38no—
22#4946—34no—
23C3×#342D314yes—
24#4527—38no—
25C24×C32C2311yescharacteristic
26C22×C32×C4—22no—
27C22×C32×C4D411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—22no—
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3—42no—
33C22×C3⋊Dic3D412yes—
34C22×C3⋊Dic3D412yes—
35C2×#634—21no—
36C2×#634—21no—
37C32×C22⋊C4—22no—
38C32×C22⋊C4—22no—
39C32×C22⋊C4Q814yescomplemented
40#3757—22no—
41#3757—22no—
42#3757—21no—
43#3757Q812yescomplemented
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—44no—
47#3750—22no—
48#3750—22no—
49#3750—42no—
50#2062—91noSylow
51C23×Dic3—34no—
52C2×C3×C22⋊C4C2×D314yes—
53C2×C3×C22⋊C4C2×D318yes—
54C2×#217—34no—
55C2×#217—38no—
56C2×C4⋊Dic3—68no—
57#924—64no—
58#924—64no—
59C2×Dic3⋊C4—64no—
60#878—68no—
61#878—68no—
62C3⋊#95—68no—
63C3⋊#95—64no—
64C23×C32—41no—
65C23×C32—41no—
66C23×C32C2×D411yescharacteristic
67C23×C32C2×D412yes—
68C23×C32C2×Q812yes—
69C23×C32C2×Q811yescharacteristic
70C23×C32#4111yescharacteristic
71C2×C32×C4—21no—
72C2×C32×C4—21no—
73C2×C32×C4—24no—
74C2×C32×C4—42no—
75C2×C32×C4—42no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—24no—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—42no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—42no—
89C2×C3⋊Dic3—42no—
90#634—81no—
91#634—81no—
92#543—91no—
93#385—91no—
94#385—92no—
95#342—92no—
96#342C3⋊D311yescharacteristic
97C24×C3C22×D314yes—
98C22×C3×C4—28no—
99C22×C3×C4D1214yes—
100C22×C3×C4D1214yes—
101C22×Dic3—38no—
102C22×Dic3—38no—
103C22×Dic3—64no—
104C22×Dic3—64no—
105C22×Dic3—68no—
106C22×Dic3—128no—
107C2×Dic6—64no—
108C2×Dic6—64no—
109C3×C22⋊C4—28no—
110C3×C22⋊C4—28no—
111C3×C22⋊C4Dic6116yescomplemented
112#217—38no—
113#217—68no—
114#217—68no—
115#217—64no—
116C4⋊Dic3—64no—
117C4⋊Dic3—64no—
118C4⋊Dic3—1216no—
119Dic3⋊C4—68no—
120Dic3⋊C4—68no—
121Dic3⋊C4—128no—
122C22×C32—21no—
123C22×C32—22no—
124C22×C32—21no—
125C22×C32—22no—
126C22×C32—42no—
127C22×C32—41no—
128C22×C32—41no—
129C22×C32#12011yescharacteristic
130C22×C32C22⋊Q812yes—
131C22×C32C22⋊Q811yescharacteristic
132C22×C32C4⋊Q811yescharacteristic
133C22×C32C4⋊Q812yes—
134C32×C4—44no—
135C32×C4—41no—
136C32×C4—41no—
137C3⋊Dic3—42no—
138C3⋊Dic3—42no—
139C3⋊Dic3—42no—
140C3⋊Dic3—42no—
141C23×C4—91no—
142C22⋊Q8—182no—
143C22⋊Q8—182no—
144C22⋊Q8—181no—
145C22⋊Q8—181no—
146C2×C4⋊C4—182no—
147C2×C4⋊C4—181no—
148C2×C22⋊C4—91no—
149C2×C22⋊C4—92no—
150C2×C22⋊C4C2×C3⋊D311yescharacteristic
151C2×C22⋊C4C2×C3⋊D312yes—
152#95—182no—
153#95—181no—
154C23×C3—44no—
155C23×C3—44no—
156C23×C3C2×Dic618yes—
157C23×C3C2×D1214yes—
158C23×C3D3×D418yes—
159C23×C3#23714yes—
160C23×C3D3×Q814yes—
161C2×C3×C4—216no—
162C2×C3×C4—24no—
163C2×C3×C4—24no—
164C2×C3×C4—48no—
165C2×C3×C4—48no—
166C2×C3×C4—44no—
167C2×C3×C4—44no—
168C2×Dic3—68no—
169C2×Dic3—616no—
170C2×Dic3—68no—
171C2×Dic3—68no—
172C2×Dic3—68no—
173C2×Dic3—124no—
174C2×Dic3—124no—
175C2×Dic3—124no—
176C2×Dic3—128no—
177C2×Dic3—124no—
178C2×Dic3—128no—
179C2×Dic3—128no—
180Dic6—244no—
181Dic6—244no—
182C2×C32—21no—
183C2×C32—22no—
184C2×C32—21no—
185C2×C32—22no—
186C2×C32#39511yescharacteristic
187C2×C32B(4,𝔽2)11yescharacteristic
188C2×C32#45811yescharacteristic
189C24C22×C3⋊D311yescharacteristic
190C2×Q8—181no—
191C2×Q8—181no—
192C22×C4—22no—
193C22×C4—92no—
194C22×C4—92no—
195C22×C4—181no—
196C22×C4—181no—
197C22×C4—182no—
198C22×C4—362no—
199C22×C4C4⋊(C3⋊D3)11yescharacteristic
200C22×C4C4⋊(C3⋊D3)11yescharacteristic
201C4⋊C4—182no—
202C4⋊C4—182no—
203C4⋊C4—181no—
204C4⋊C4—181no—
205C4⋊C4—362no—
206C4⋊C4—364no—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—92no—
210C22⋊C4—182no—
211C22⋊C4—182no—
212C22⋊C4—181no—
213C22⋊C4#63414yescomplemented
214C22×C3—24no—
215C22×C3—28no—
216C22×C3—24no—
217C22×C3—28no—
218C22×C3—48no—
219C22×C3—44no—
220C22×C3—44no—
221C22×C3#86914yes—
222C22×C3#87818yes—
223C22×C3#88214yes—
224C22×C3#88818yes—
225C22×C3#89714yes—
226C3×C4—416no—
227C3×C4—44no—
228C3×C4—44no—
229Dic3—128no—
230Dic3—128no—
231Dic3—128no—
232Dic3—128no—
233C32#206211yescharacteristic, complemented, Sylow
234C23—41no—
235C23—41no—
236C23C2×#63412yes—
237C23C2×C4⋊(C3⋊D3)11yescharacteristic
238C23D4×C3⋊D312yes—
239C23#383011yescharacteristic
240C23Q8×C3⋊D311yescharacteristic
241Q8—721no—
242Q8—721no—
243C2×C4—24no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—182no—
251C2×C4—184no—
252C2×C4—182no—
253C2×C4—182no—
254C2×C4—182no—
255C2×C4—361no—
256C2×C4—361no—
257C2×C4—362no—
258C2×C4—361no—
259C2×C4—361no—
260C2×C4—362no—
261C2×C4—362no—
262C2×C3—24no—
263C2×C3—28no—
264C2×C3—24no—
265C2×C3—28no—
266C2×C3#465614yes—
267C2×C3#474114yes—
268C2×C3#474214yes—
269C22—21no—
270C22—22no—
271C22—21no—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22#6407811yescharacteristic
277C22#6408712yes—
278C22#6409111yescharacteristic
279C22#6409712yes—
280C22#6410611yescharacteristic
281C4—44no—
282C4—41no—
283C4—41no—
284C4—362no—
285C4—362no—
286C4—362no—
287C4—362no—
288C3#6895814yescomplemented
289C2—22no—
290C2—21no—
291C2—21no—
292C2—22no—
293C2#1059235511yescharacteristic
294C2#1059244011yescharacteristic
295C2#1059244111yescharacteristic
subgroupG/H
centerC22#64091
commutator, prime radical, cosocleC24×C32C23
FrattiniC24C22×C3⋊D3
FittingC32×#342C2
socleC22×C32#120
hypercenter#342C3⋊D3
hypocenterC32#2062
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
39. C32×C22⋊C4Q8semidirect
43. #3757Q8semidirect
111. C3×C22⋊C4Dic6semidirect
213. C22⋊C4#634semidirect
233. C32#2062semidirect
288. C3#68958semidirect

Maximal subgroups

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

subgroupindex
#105959542
#105926492
#105926452
C32×#3422
#105893932
#689583