Finite Group Databasebeta

← #11775261

Subgroups — #11775261

Order 1152.

726 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 181 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
3C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4#10589336C212yesmaximal
5#10589333C212yesmaximal, complemented
6#70833—34nomaximal
7C2×C32×C42C2211yescharacteristic
8#64139C2211yescharacteristic
9#64138—21no—
10C4×#638—21no—
11C2×C4⋊(C3⋊Dic3)—21no—
12#64133C2211yescharacteristic
13C2×C4×C3⋊Dic3—21no—
14#64085—21no—
15#64084C411yescharacteristic, complemented
16C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
17#64081—21no—
18#64079C411yescharacteristic, complemented
19C4×#634C411yescharacteristic, complemented
20C32×C4⋊C8—21no—
21C32×C22⋊C8C2212yes—
22C32×#97—21no—
23#63658C2212yes—
24#5479—34no—
25C3×#432D314yescomplemented
26C4×C4⋊Dic3—34no—
27#4470—38no—
28#4467—38no—
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C2×#638—21no—
33C22×C3⋊Dic3—22no—
34C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
35C2×C4×C3⋊D3—21no—
36C2×#634C2×C411yescharacteristic
37C2×C32×C8—22no—
38C32×C42C2×C411yescharacteristic
39C32×C42C2×C411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42#3757—21no—
43#3752—21no—
44#3752—21no—
45#3752—21no—
46#3752—21no—
47C4⋊(C3⋊Dic3)—24no—
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
49C4⋊(C3⋊Dic3)C2×C411yescharacteristic
50#3750—21no—
51#3750—21no—
52#3750—21no—
53#3750—21no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—42no—
56#1509—91noSylow
57C2×C3×C42C2×D314yes—
58#930—34no—
59#929—64no—
60C4×#67—64no—
61C2×C4⋊Dic3—64no—
62#924—34no—
63C2×C4×Dic3—64no—
64#876—64no—
65#875—34no—
66C4×D12—34no—
67#872—64no—
68#870—34no—
69C4×Dic6—34no—
70C3×C4⋊C8—24no—
71C3×C22⋊C8C2×D318yes—
72C3×#97—24no—
73C3⋊#95—38no—
74C23×C32C2×D411yescharacteristic
75C22×C3⋊D3—21no—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—22no—
79C2×C32×C4—41no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C22⋊C411yescharacteristic
84C2×C32×C4C22×C411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86#638—41no—
87#638—41no—
88C2×C3⋊Dic3—24no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—42no—
93C2×C3⋊Dic3—42no—
94C4⋊(C3⋊D3)—41no—
95C4×C3⋊D3—42no—
96#634—41no—
97C32×C8—42no—
98#529—91no—
99#432C3⋊D311yescharacteristic, complemented
100C4×C4⋊C4—91no—
101#328—92no—
102#327—92no—
103C22×C3×C4D1214yes—
104C22×C3×C4D1214yes—
105C22×C3×C4C22×D314yes—
106C2×#67—64no—
107C22×Dic3—68no—
108C2×D12—34no—
109C2×C4×D3—64no—
110C2×Dic6—34no—
111C2×C3×C8—28no—
112C3×C42C4×D314yes—
113C3×C42C4×D314yes—
114C3×C42#6714yes—
115C3×C42#6714yes—
116#217—64no—
117(C2×D3)⋊C4—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120(C2×D3)⋊C4—64no—
121C4⋊Dic3—34no—
122C4⋊Dic3—34no—
123C4⋊Dic3—616no—
124Dic3⋊C4—64no—
125Dic3⋊C4—64no—
126Dic3⋊C4—64no—
127Dic3⋊C4—64no—
128C4×Dic3—64no—
129C4×Dic3—128no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32C2×C22⋊C411yescharacteristic
133C22×C32AGL(1,ℤ/8)11yescharacteristic
134C22×C32#13711yescharacteristic
135C2×C3⋊D3—41no—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—41no—
138C32×C4—21no—
139C32×C4—21no—
140C32×C4—21no—
141C32×C4—21no—
142C32×C4—21no—
143C32×C4#10412yes—
144C3⋊Dic3—44no—
145C3⋊Dic3—41no—
146C3⋊Dic3—41no—
147C3⋊Dic3—41no—
148#126—181no—
149#125—91no—
150#124—91no—
151#123—181no—
152C22⋊Q8—91no—
153#121—91no—
154C4×Q8—91no—
155C4×D4—91no—
156C4×D4—181no—
157#117—181no—
158C2×C4⋊C4—181no—
159C2×C42—181no—
160C2×C42C2×C3⋊D311yescharacteristic
161C4⋊C8—21no—
162C22⋊C8C2×C3⋊D312yes—
163#97—21no—
164#95—92no—
165C23×C3C2×D1214yes—
166C22×D3—64no—
167C2×C3×C4—24no—
168C2×C3×C4—24no—
169C2×C3×C4—28no—
170C2×C3×C4—44no—
171C2×C3×C4(C2×D3)⋊C414yes—
172C2×C3×C4(C2×D3)⋊C414yes—
173C2×C3×C4(C2×D3)⋊C414yes—
174C2×C3×C4(C2×D3)⋊C414yes—
175C2×C3×C4C2×C4×D314yes—
176C2×C3×C4C2×#6714yes—
177#67—124no—
178#67—124no—
179C2×Dic3—616no—
180C2×Dic3—64no—
181C2×Dic3—64no—
182C2×Dic3—64no—
183C2×Dic3—128no—
184C2×Dic3—128no—
185D12—124no—
186C4×D3—128no—
187Dic6—124no—
188C3×C8—48no—
189C2×C32—21no—
190C2×C32—21no—
191C2×C32#41011yescharacteristic
192C2×C32#41711yescharacteristic
193C2×C32C2×#10411yescharacteristic
194C3⋊D3—81no—
195C2×Q8—91no—
196C2×D4—91no—
197C2×D4—181no—
198C22×C4—182no—
199C22×C4—181no—
200C22×C4C4⋊(C3⋊D3)11yescharacteristic
201C22×C4C4⋊(C3⋊D3)11yescharacteristic
202C22×C4C22×C3⋊D311yescharacteristic
203C2×C8—22no—
204C4⋊C4—91no—
205C4⋊C4—91no—
206C4⋊C4—184no—
207C4⋊C4—181no—
208C4⋊C4—181no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C22⋊C4—181no—
212C22⋊C4—181no—
213C22⋊C4—181no—
214C22⋊C4—181no—
215C22⋊C4—181no—
216C42—181no—
217C42—362no—
218C42C4×C3⋊D311yescharacteristic
219C42C4×C3⋊D311yescharacteristic
220C42#63811yescharacteristic
221C42#63811yescharacteristic
222C22×C3—24no—
223C22×C3—24no—
224C22×C3#90814yes—
225C22×C3#90914yes—
226C22×C3C2×(C2×D3)⋊C414yes—
227C2×D3—124no—
228C2×D3—124no—
229C2×D3—124no—
230C3×C4—24no—
231C3×C4—24no—
232C3×C4—24no—
233C3×C4—24no—
234C3×C4—24no—
235C3×C4#82518yes—
236Dic3—1216no—
237Dic3—124no—
238Dic3—124no—
239Dic3—124no—
240C32#150911yescharacteristic, complemented, Sylow
241C23—181no—
242C23C2×C4⋊(C3⋊D3)11yescharacteristic
243Q8—361no—
244D4—361no—
245D4—361no—
246D4—361no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—41no—
251C2×C4—184no—
252C2×C4—181no—
253C2×C4—181no—
254C2×C4—181no—
255C2×C4—362no—
256C2×C4—362no—
257C2×C4—362no—
258C2×C4#375211yescharacteristic
259C2×C4#375211yescharacteristic
260C2×C4#375211yescharacteristic
261C2×C4#375211yescharacteristic
262C2×C4C2×C4×C3⋊D311yescharacteristic
263C2×C4C2×#63811yescharacteristic
264C8—42no—
265C2×C3—24no—
266C2×C3—24no—
267C2×C3#500614yes—
268C2×C3#513314yes—
269C2×C3C2×#82514yes—
270D3—244no—
271C22—21no—
272C22—21no—
273C22—361no—
274C22—361no—
275C22—361no—
276C22#6411711yescharacteristic
277C22#6411811yescharacteristic
278C22C2×#375211yescharacteristic
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—364no—
285C4—361no—
286C4—361no—
287C4—361no—
288C4#6365212yes—
289C3#7083314yescomplemented
290C2—21no—
291C2—21no—
292C2—721no—
293C2#1059270511yescharacteristic
294C2#1059283211yescharacteristic
295C2C2×#6365211yescharacteristic
subgroupG/H
centerC22C2×#3752
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#432C2
socleC22×C32C2×C22⋊C4
prime radical#64139C22
cosocleC22×C32×C4C23
hypercenter#432C3⋊D3
hypocenterC32#1509
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C32×#432C2semidirect
3. C4×C4⋊(C3⋊Dic3)C2semidirect
5. #10589333C2semidirect
15. #64084C4semidirect
16. C4×C4⋊(C3⋊D3)C4semidirect
18. #64079C4semidirect
19. C4×#634C4semidirect
25. C3×#432D3semidirect
99. #432C3⋊D3semidirect
240. C32#1509semidirect
289. C3#70833semidirect

Maximal subgroups

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

subgroupindex
#105959502
C32×#4322
C4×C4⋊(C3⋊Dic3)2
#105893362
#105893332
#708333