Finite Group Databasebeta

← #11774788

Subgroups — #11774788

Order 1152.

690 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 193 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#10595950C211yesmaximal, characteristic
2C32×#432C211yesmaximal, characteristic, complemented
3C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10589350C212yesmaximal, complemented
5#10589349C212yesmaximal, complemented
6#70800—34nomaximal
7C2×C32×C42C2211yescharacteristic
8#64139C411yescharacteristic
9#64138—21no—
10C4×#638—21no—
11#64133C411yescharacteristic
12C22×C3⋊(C3⋊C8)—21no—
13#64085—21no—
14#64084C411yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64081—21no—
17#64079C411yescharacteristic
18C4×#634C2211yescharacteristic
19C32×C4⋊C8C2212yes—
20C32×C22⋊C8—21no—
21C32×#97—21no—
22C4×C3⋊(C3⋊C8)—21no—
23C4×C3⋊(C3⋊C8)C2212yes—
24#5479—34no—
25C3×#432D314yescomplemented
26C2×C4×C3⋊C8—34no—
27#4484—38no—
28#4483—38no—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C2×#638—21no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×#634C2×C411yescharacteristic
36C2×C32×C8—22no—
37C32×C42C2×C411yescharacteristic
38C32×C42D411yescharacteristic
39C32×C42D411yescharacteristic
40C32×C42C2311yescharacteristic
41#3757—21no—
42#3752—21no—
43#3752—21no—
44#3752—21no—
45#3752—21no—
46C4⋊(C3⋊Dic3)C2×C411yescharacteristic
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49#3750—21no—
50#3750—21no—
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—24no—
54C2×C3⋊(C3⋊C8)—22no—
55#1494—91noSylow
56C2×C3×C42C2×D314yes—
57#930—34no—
58#929—64no—
59C4×#67—64no—
60#924—34no—
61C22×C3⋊C8—64no—
62#876—64no—
63#875—34no—
64C4×D12—34no—
65#872—64no—
66#870—34no—
67C4×Dic6—34no—
68C3×C4⋊C8C2×D318yes—
69C3×C22⋊C8—24no—
70C3×#97—24no—
71C4×C3⋊C8—38no—
72C4×C3⋊C8—64no—
73C23×C32C22⋊C411yescharacteristic
74C22×C3⋊D3—21no—
75C2×C32×C4—22no—
76C2×C32×C4—22no—
77C2×C32×C4—22no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84#638—42no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C4⋊(C3⋊D3)—22no—
89C4×C3⋊D3—42no—
90#634—22no—
91C32×C8—42no—
92C3⋊(C3⋊C8)—24no—
93#529—91no—
94#432C3⋊D311yescharacteristic, complemented
95C2×C4×C8—91no—
96Q8⋊C8—92no—
97D4⋊C8—92no—
98C22×C3×C4C4×D314yes—
99C22×C3×C4D1214yes—
100C22×C3×C4#6714yes—
101C2×#67—64no—
102C2×D12—34no—
103C2×C4×D3—64no—
104C2×Dic6—34no—
105C2×C3×C8—28no—
106C3×C42C4×D314yes—
107C3×C42D1214yes—
108C3×C42#6714yes—
109C3×C42C22×D314yes—
110#217—64no—
111(C2×D3)⋊C4—64no—
112(C2×D3)⋊C4—64no—
113(C2×D3)⋊C4—64no—
114(C2×D3)⋊C4—64no—
115C4⋊Dic3—34no—
116C4⋊Dic3—34no—
117Dic3⋊C4—64no—
118Dic3⋊C4—64no—
119Dic3⋊C4—64no—
120Dic3⋊C4—64no—
121C4×Dic3—64no—
122C2×C3⋊C8—616no—
123C2×C3⋊C8—68no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32#10412yes—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3⋊D3—41no—
129C2×C3⋊D3—41no—
130C2×C3⋊D3—41no—
131C32×C4—21no—
132C32×C4—21no—
133C32×C4—21no—
134C32×C4—21no—
135C32×C4#13112yes—
136C32×C4#13512yes—
137C3⋊Dic3—41no—
138C3⋊Dic3—41no—
139C3⋊Dic3—41no—
140C22×C8—181no—
141#126—181no—
142#125—91no—
143#124—91no—
144#123—181no—
145C22⋊Q8—91no—
146#121—91no—
147C4×Q8—91no—
148C4×D4—91no—
149C4×D4—181no—
150#117—181no—
151C2×C42C2×C3⋊D311yescharacteristic
152C4⋊C8C2×C3⋊D312yes—
153C22⋊C8—21no—
154#97—21no—
155C4×C8—92no—
156C4×C8—181no—
157C23×C3(C2×D3)⋊C414yes—
158C22×D3—64no—
159C2×C3×C4—28no—
160C2×C3×C4—28no—
161C2×C3×C4—28no—
162C2×C3×C4(C2×D3)⋊C414yes—
163C2×C3×C4(C2×D3)⋊C414yes—
164C2×C3×C4(C2×D3)⋊C414yes—
165C2×C3×C4C2×C4×D314yes—
166C2×C3×C4C2×D1214yes—
167C2×C3×C4C2×#6714yes—
168#67—128no—
169C2×Dic3—64no—
170C2×Dic3—64no—
171C2×Dic3—64no—
172D12—68no—
173C4×D3—128no—
174Dic6—68no—
175C3×C8—48no—
176C3⋊C8—616no—
177C2×C32—22no—
178C2×C32#40811yescharacteristic
179C2×C32#41611yescharacteristic
180C2×C32C2×#10411yescharacteristic
181C3⋊D3—81no—
182C2×Q8—91no—
183C2×D4—91no—
184C2×D4—181no—
185C22×C4—181no—
186C22×C4C4×C3⋊D311yescharacteristic
187C22×C4C4⋊(C3⋊D3)11yescharacteristic
188C22×C4#63811yescharacteristic
189C2×C8—22no—
190C2×C8—184no—
191C2×C8—182no—
192C4⋊C4—91no—
193C4⋊C4—91no—
194C4⋊C4—181no—
195C4⋊C4—181no—
196C4⋊C4—181no—
197C4⋊C4—181no—
198C22⋊C4—181no—
199C22⋊C4—181no—
200C22⋊C4—181no—
201C22⋊C4—181no—
202C22⋊C4—181no—
203C42—181no—
204C42C4×C3⋊D311yescharacteristic
205C42C4⋊(C3⋊D3)11yescharacteristic
206C42#63811yescharacteristic
207C42C22×C3⋊D311yescharacteristic
208C22×C3—24no—
209C22×C3—24no—
210C22×C3#82518yes—
211C22×C3C2×(C2×D3)⋊C414yes—
212C2×D3—124no—
213C2×D3—124no—
214C2×D3—124no—
215C3×C4—24no—
216C3×C4—24no—
217C3×C4—24no—
218C3×C4—24no—
219C3×C4#90718yes—
220C3×C4#95018yes—
221Dic3—124no—
222Dic3—124no—
223Dic3—124no—
224C32#149411yescharacteristic, complemented, Sylow
225C23—181no—
226C23#375211yescharacteristic
227Q8—182no—
228D4—182no—
229D4—362no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—181no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4—362no—
237C2×C4#375211yescharacteristic
238C2×C4#375211yescharacteristic
239C2×C4#375211yescharacteristic
240C2×C4C2×C4×C3⋊D311yescharacteristic
241C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
242C2×C4C2×#63811yescharacteristic
243C8—42no—
244C8—184no—
245C2×C3—28no—
246C2×C3#500214yes—
247C2×C3#512914yes—
248C2×C3C2×#82514yes—
249D3—244no—
250C22—21no—
251C22—21no—
252C22—361no—
253C22—361no—
254C22—361no—
255C22#6365212yes—
256C22C2×#375211yescharacteristic
257C4—21no—
258C4—21no—
259C4—21no—
260C4—21no—
261C4—361no—
262C4—361no—
263C4—361no—
264C4#6411612yes—
265C4#6415912yes—
266C3#7080014yescomplemented
267C2—22no—
268C2—721no—
269C2#1059270111yescharacteristic
270C2#1059282811yescharacteristic
271C2C2×#6365211yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#432C2
socleC22×C32C2×C22⋊C4
prime radical#64139C4
cosocleC32×C42C23
hypercenter#432C3⋊D3
hypocenterC32#1494
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C32×#432C2semidirect
3. C2×C4×C3⋊(C3⋊C8)C2semidirect
4. #10589350C2semidirect
5. #10589349C2semidirect
25. C3×#432D3semidirect
94. #432C3⋊D3semidirect
224. C32#1494semidirect
266. C3#70800semidirect

Maximal subgroups

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

subgroupindex
#105959502
C32×#4322
C2×C4×C3⋊(C3⋊C8)2
#105893502
#105893492
#708003