Finite Group Databasebeta

← #11795368

Subgroups — #11795368

Order 1152.

539 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 539 conjugacy classes of subgroups — too many to draw. Only its 104 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#10592825C211yesmaximal, characteristic
2C3×#5124C212yesmaximal, complemented
3#10591143C211yesmaximal, characteristic, complemented
4#10591074C212yesmaximal
5#10589159C211yesmaximal, characteristic, complemented
6#70729—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×M16C2211yescharacteristic
9C2×#3748C2211yescharacteristic
10C2×C3×#208C2212yes—
11C2×C3×#208C2212yes—
12#63647—22no—
13C3×#822—24no—
14#63578—22no—
15#63557—24no—
16C3×#430—32no—
17#5126—32no—
18#5126—32no—
19#5126—32no—
20#5126—61no—
21#5124—32no—
22#5124D312yescomplemented
23C3⋊#338—32no—
24C23×C3⋊D3Q811yescharacteristic
25C22×C32×C4C2311yescharacteristic
26C22×C3⋊Dic3Q811yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—22no—
31C32×M16—22no—
32C2×C32×C8—21no—
33#3748—22no—
34C2×C3⋊(C3⋊C8)D412yes—
35C3×#208—22no—
36C3×#208—22no—
37C3×#208—22no—
38C3×#208—22no—
39C2×C3×C3⋊C8—22no—
40C2×C3×C3⋊C8D414yes—
41#2091—91noSylow
42C22×C4×D3—32no—
43C22×C4×D3—61no—
44C2×C3×M16—21no—
45C2×C3×M16—32no—
46C2×C3×M16—32no—
47C2×C3×M16C2×D312yes—
48C2×#208—32no—
49C2×#208—61no—
50C2×#208C2×D312yes—
51C2×#208C2×D312yes—
52C3×#108—64no—
53#822—24no—
54#822—64no—
55(C2×D3)⋊C8—64no—
56(C2×D3)⋊C8—64no—
57(C2×D3)⋊C8—64no—
58(C2×D3)⋊C8—64no—
59C23×C32C2×Q811yescharacteristic
60C22×C3⋊D3—21no—
61C22×C3⋊D3—22no—
62C22×C3⋊D3—42no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4C2×D412yes—
65C2×C32×C4#4111yescharacteristic
66C2×C32×C4#4112yes—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—22no—
69C4×C3⋊D3—41no—
70C4×C3⋊D3—42no—
71C4×C3⋊D3—41no—
72C32×C8—41no—
73C3⋊(C3⋊C8)—22no—
74C3×C3⋊C8—24no—
75C3×C3⋊C8—42no—
76#430—32no—
77#430—91no—
78#407—92no—
79#407—91no—
80#338—91no—
81C23×D3—32no—
82C23×D3—61no—
83C22×C3×C4—21no—
84C22×C3×C4C22×D312yes—
85C22×Dic3—32no—
86C22×Dic3—61no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—62no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—122no—
96C2×C4×D3—122no—
97C3×M16—22no—
98C3×M16—22no—
99C3×M16—42no—
100C3×M16—62no—
101C3×M16—62no—
102C3×M16—62no—
103C3×M16—62no—
104C2×C3×C8—22no—
105C2×C3×C8—22no—
106C2×C3×C8—34no—
107C2×C3×C8—62no—
108#208—22no—
109#208—22no—
110#208—22no—
111#208—22no—
112#208—62no—
113#208—62no—
114#208—122no—
115C2×C3⋊C8—22no—
116C2×C3⋊C8—34no—
117C2×C3⋊C8—62no—
118C2×C3⋊C8#6714yes—
119C22×C32—41no—
120C22×C32C22⋊Q811yescharacteristic
121C22×C32C22⋊Q812yes—
122C2×C3⋊D3—22no—
123C2×C3⋊D3—24no—
124C2×C3⋊D3—41no—
125C2×C3⋊D3—42no—
126C2×C3⋊D3—41no—
127C32×C4#12311yescharacteristic
128C32×C4#12312yes—
129C32×C4#12711yescharacteristic
130C3⋊Dic3—41no—
131C23×C4—91no—
132C2×M16—32no—
133C2×M16—32no—
134C2×M16—91no—
135C2×M16D3211yescharacteristic
136#108—64no—
137#108—182no—
138C22⋊C8—182no—
139C22⋊C8—184no—
140C23×C3—21no—
141C23×C3D3×Q812yes—
142C22×D3—62no—
143C22×D3—62no—
144C22×D3—62no—
145C22×D3—62no—
146C22×D3—122no—
147C22×D3—124no—
148C22×D3—124no—
149C2×C3×C4—21no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—21no—
153C2×C3×C4#23512yes—
154C2×C3×C4#23512yes—
155C2×C3×C4D3×D412yes—
156C2×C3×C4D3×D412yes—
157C2×C3×C4#23912yes—
158C2×C3×C4C2×#6712yes—
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—122no—
164C4×D3—124no—
165C4×D3—122no—
166C4×D3—122no—
167C4×D3—122no—
168C4×D3—122no—
169C4×D3—122no—
170C4×D3—122no—
171C3×C8—42no—
172C3×C8—42no—
173C3×C8—64no—
174C3×C8—122no—
175C3⋊C8—24no—
176C3⋊C8—42no—
177C3⋊C8—64no—
178C3⋊C8—122no—
179C2×C32—21no—
180C2×C32—22no—
181C2×C32#39911yescharacteristic
182C3⋊D3—42no—
183C24—91no—
184C22×C4—91no—
185C22×C4—181no—
186C22×C4—182no—
187C22×C4—182no—
188C22×C4—181no—
189C22×C4C2×D3211yescharacteristic
190M16—22no—
191M16—62no—
192M16—62no—
193M16—62no—
194M16—62no—
195M16—182no—
196C2×C8—21no—
197C2×C8—34no—
198C2×C8—62no—
199C2×C8—92no—
200C22×C3—21no—
201C22×C3—22no—
202C22×C3—42no—
203C22×C3—42no—
204C22×C3#89612yes—
205C22×C3#89612yes—
206C22×C3#94612yes—
207C2×D3—64no—
208C2×D3—64no—
209C2×D3—64no—
210C2×D3—64no—
211C2×D3—124no—
212C2×D3—122no—
213C2×D3—122no—
214C2×D3—122no—
215C2×D3—122no—
216C2×D3—122no—
217C2×D3—124no—
218C2×D3—122no—
219C3×C4—22no—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4#89412yes—
223C3×C4#89412yes—
224C3×C4#92912yes—
225C3×C4#94012yes—
226Dic3—122no—
227Dic3—122no—
228C32#209111yescharacteristic, complemented, Sylow
229C23—181no—
230C23—182no—
231C23—362no—
232C23#379711yescharacteristic
233C2×C4—181no—
234C2×C4—182no—
235C2×C4—362no—
236C2×C4—361no—
237C2×C4—361no—
238C2×C4#379811yescharacteristic
239C2×C4#379912yes—
240C2×C4D3×#6712yes—
241C2×C4#381111yescharacteristic
242C8—41no—
243C8—64no—
244C8—122no—
245C8—182no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—21no—
251C2×C3—42no—
252C2×C3#499312yes—
253D3—124no—
254D3—124no—
255C22—41no—
256C22—182no—
257C22—184no—
258C22—361no—
259C22—362no—
260C22—361no—
261C22#6386511yescharacteristic
262C22#6388812yes—
263C4—361no—
264C4#6385012yes—
265C4#6389711yescharacteristic
266C4#6397911yescharacteristic
267C3—21no—
268C3#7072912yescomplemented
269C2—21no—
270C2—22no—
271C2—362no—
272C2#1059120311yescharacteristic
subgroupG/H
centerC4#63979
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#399
prime radicalC23×C3⋊D3Q8
hypercenterC2×M16D32
hypocenterC32#2091
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#5124C2semidirect
3. #10591143C2semidirect
5. #10589159C2semidirect
22. #5124D3semidirect
228. C32#2091semidirect
268. C3#70729semidirect

Maximal subgroups

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

subgroupindex
#105928252
C3×#51242
#105911432
#105910742
#105891592
#707293