Finite Group Databasebeta

← #11796081

Subgroups — #11796081

Order 1152.

490 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C3⋊D3×#131C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic, complemented
3C2×#63764C211yesmaximal, characteristic, complemented
4#10590221C212yesmaximal, complemented
5#10590187C212yesmaximal, complemented
6#41×C3⋊D3C411yescharacteristic
7C32×#131C411yescharacteristic
8#64157C2211yescharacteristic
9#64116—21no—
10#64116C2211yescharacteristic
11M16×C3⋊D3—21no—
12M16×C3⋊D3C411yescharacteristic
13#64110—21no—
14#64110C411yescharacteristic
15C2×C8×C3⋊D3—21no—
16C2×C8×C3⋊D3C2211yescharacteristic
17#63773C2212yescomplemented
18C2×#3708C2212yescomplemented
19#63765—21no—
20#63764—21no—
21#63764—21no—
22#63764—21no—
23D3×#131—62no—
24C32×#41C2×C411yescharacteristic
25#3832C811yescharacteristic
26Q8×C3⋊D3C811yescharacteristic
27#3830—21no—
28#3830C811yescharacteristic
29D4×C3⋊D3—21no—
30D4×C3⋊D3C811yescharacteristic
31#3828—21no—
32#3828C2×C411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C32×M16—21no—
36C32×M16C2×C411yescharacteristic
37C2×C32×C8—21no—
38C2×C32×C8C2×C411yescharacteristic
39#3748—21no—
40#3748C2×C411yescharacteristic
41C2×C3⋊(C3⋊C8)—21no—
42C2×C3⋊(C3⋊C8)C2311yescharacteristic
43#3743—21no—
44#3743—21no—
45#3743—21no—
46C8×C3⋊D3—21no—
47C8×C3⋊D3—21no—
48C8×C3⋊D3—21no—
49C8×C3⋊D3D411yescharacteristic
50C8×C3⋊D3D411yescharacteristic
51C8×C3⋊D3D411yescharacteristic
52C8×C3⋊D3D411yescharacteristic
53#3708—22no—
54#3708—22no—
55C2×#350—91nomaximal, Sylow
56D3×#41—62no—
57C3×#131—22no—
58#948—62no—
59#907—62no—
60#907—64no—
61D3×M16—62no—
62D3×M16—64no—
63#901—62no—
64#901—64no—
65C2×D3×C8—62no—
66C2×D3×C8—64no—
67C22×C3⋊D3—21no—
68C22×C3⋊D3M1611yescharacteristic
69C32×Q8C2×C811yescharacteristic
70C32×D4—21no—
71C32×D4C2×C811yescharacteristic
72C2×C32×C4—21no—
73C2×C32×C4C22×C411yescharacteristic
74#638—21no—
75#638—21no—
76#638—21no—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3M1611yescharacteristic
79C4⋊(C3⋊D3)—21no—
80C4⋊(C3⋊D3)C2×C811yescharacteristic
81C4×C3⋊D3—21no—
82C4×C3⋊D3—21no—
83C4×C3⋊D3—21no—
84C4×C3⋊D3C22⋊C411yescharacteristic
85C4×C3⋊D3C22⋊C411yescharacteristic
86C4×C3⋊D3C2×C811yescharacteristic
87C4×C3⋊D3C2×C811yescharacteristic
88#634—21no—
89#634C2×C811yescharacteristic
90C32×C8—21no—
91C32×C8C22⋊C411yescharacteristic
92C32×C8C22⋊C411yescharacteristic
93C3⋊(C3⋊C8)—21no—
94C3⋊(C3⋊C8)C2×D411yescharacteristic
95C3⋊(C3⋊C8)C2×D411yescharacteristic
96C2×#131—91no—
97C2×M32—91no—
98C22×C16—91no—
99#350—92no—
100#350—92no—
101C3×#41—22no—
102#239—62no—
103D3×Q8—62no—
104#237—62no—
105#237—64no—
106D3×D4—62no—
107D3×D4—64no—
108#235—62no—
109#235—64no—
110C2×C4×D3—62no—
111C2×C4×D3—64no—
112C3×M16—24no—
113C3×M16—22no—
114C2×C3×C8—24no—
115C2×C3×C8—22no—
116#208—62no—
117#208—64no—
118C2×C3⋊C8—62no—
119C2×C3⋊C8—64no—
120ΓL(1,𝔽25)—64no—
121ΓL(1,𝔽25)—64no—
122ΓL(1,𝔽25)—64no—
123D3×C8—62no—
124D3×C8—62no—
125D3×C8—62no—
126D3×C8—62no—
127D3×C8—64no—
128D3×C8—64no—
129D3×C8—64no—
130C22×C32—21no—
131C22×C32C2×M1611yescharacteristic
132C2×C3⋊D3—21no—
133C2×C3⋊D3—22no—
134C2×C3⋊D3—42no—
135C2×C3⋊D3C22⋊C811yescharacteristic
136C2×C3⋊D3C22⋊C811yescharacteristic
137C32×C4—21no—
138C32×C4C2×C22⋊C411yescharacteristic
139C32×C4C22×C811yescharacteristic
140C3⋊Dic3—21no—
141C3⋊Dic3C22⋊C811yescharacteristic
142C3⋊Dic3C22⋊C811yescharacteristic
143C2×#41—91no—
144#131—91no—
145#131—91no—
146#131—91no—
147#131—181no—
148#131—181no—
149#131#15711yescharacteristic
150C2×M16—91no—
151C2×M16—181no—
152C22×C8—91no—
153C22×C8—181no—
154M32—92no—
155M32—181no—
156C2×C16—92no—
157C2×C16—181no—
158C2×C16—181no—
159C2×C16—181no—
160C22×D3—62no—
161C22×D3—64no—
162C3×Q8—22no—
163C3×D4—24no—
164C3×D4—22no—
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167#67—64no—
168#67—64no—
169#67—64no—
170C2×Dic3—62no—
171C2×Dic3—64no—
172D12—62no—
173D12—64no—
174C4×D3—62no—
175C4×D3—62no—
176C4×D3—62no—
177C4×D3—62no—
178C4×D3—64no—
179C4×D3—64no—
180C4×D3—64no—
181Dic6—62no—
182Dic6—64no—
183C3×C8—24no—
184C3×C8—22no—
185C3×C8—22no—
186C3⋊C8—62no—
187C3⋊C8—62no—
188C3⋊C8—64no—
189C2×C32—21no—
190C2×C32—41no—
191C2×C32C2×C22⋊C811yescharacteristic
192C3⋊D3—21no—
193C3⋊D3—41no—
194C3⋊D3#35012yescomplemented
195#41—91no—
196#41—91no—
197#41—91no—
198#41—181no—
199#41—181no—
200#41C2×#15711yescharacteristic
201C2×Q8—91no—
202C2×D4—91no—
203C2×D4—181no—
204C22×C4—91no—
205C22×C4—181no—
206M16—21no—
207M16—91no—
208M16—181no—
209M16—181no—
210M16—181no—
211M16—181no—
212M16C2×#15711yescharacteristic
213C2×C8—21no—
214C2×C8—91no—
215C2×C8—91no—
216C2×C8—91no—
217C2×C8—91no—
218C2×C8—91no—
219C2×C8—181no—
220C2×C8—181no—
221C2×C8—181no—
222C2×C8—181no—
223C2×C8C2×#15711yescharacteristic
224C16—182no—
225C16—182no—
226C22×C3—24no—
227C22×C3—22no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—64no—
231C2×D3—124no—
232C2×D3—128no—
233C3×C4—24no—
234C3×C4—22no—
235C3×C4—22no—
236Dic3—62no—
237Dic3—62no—
238Dic3—64no—
239C32C2×#35011yescharacteristic, complemented, Sylow
240C23—91no—
241C23—181no—
242Q8—91no—
243Q8—181no—
244Q8#378711yescharacteristic
245D4—21no—
246D4—91no—
247D4—181no—
248D4—181no—
249D4—181no—
250D4—181no—
251D4#378711yescharacteristic
252C2×C4—21no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—181no—
259C2×C4—181no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4C22×#15711yescharacteristic
263C8—21no—
264C8—91no—
265C8—91no—
266C8—181no—
267C8C22⋊#15711yescharacteristic
268C8C22⋊#15711yescharacteristic
269C2×C3—22no—
270C2×C3—42no—
271C2×C3—44no—
272D3—64no—
273D3—122no—
274D3—124no—
275C22—21no—
276C22—91no—
277C22—91no—
278C22—182no—
279C22—181no—
280C22—362no—
281C22#6428311yescharacteristic
282C4—21no—
283C4—91no—
284C4—91no—
285C4—181no—
286C4C2×#378711yescharacteristic
287C4C2×C22⋊#15711yescharacteristic
288C3—22no—
289C2—21no—
290C2—41no—
291C2—92no—
292C2—181no—
293C2—361no—
294C2#1059380011yescharacteristic
subgroupG/H
centerC8C22⋊#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×#131C4
socleC2×C32C2×C22⋊C8
prime radical#41×C3⋊D3C4
cosocleC2×C3⋊(C3⋊C8)C23
hypercenter#131#157
hypocenterC32C2×#350
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
2. #10593762C2semidirect
3. C2×#63764C2semidirect
4. #10590221C2semidirect
5. #10590187C2semidirect
17. #63773C22semidirect
18. C2×#3708C22semidirect
194. C3⋊D3#350semidirect
239. C32C2×#350semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1312
#105937622
C2×#637642
#105902212
#105901872
C2×#3509