Finite Group Databasebeta

← #11796090

Subgroups — #11796090

Order 1152.

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

normal subgroups only

This group has 493 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#10594669C211yesmaximal, characteristic
2C3⋊D3×M32C211yesmaximal, characteristic, complemented
3C2×#63542C211yesmaximal, characteristic, complemented
4C3×#4515C212yesmaximal, complemented
5#10589112C212yesmaximal, complemented
6D3×#350—32nomaximal
7#64306C411yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9C3×#901C2212yes—
10#63818C411yescharacteristic
11#63815C412yes—
12#63805—21no—
13#63803—21no—
14#63791—21no—
15D32×C8—21no—
16C32×M32C2211yescharacteristic, complemented
17#63639C2211yescharacteristic, complemented
18#63625—21no—
19C16×C3⋊D3—21no—
20C2×C3×C3⋊C16C2212yescomplemented
21#63542—21no—
22#63542—21no—
23D3×#131—32no—
24D3×M32—32no—
25D3×M32—61no—
26C2×D3×C16—32no—
27C3×#350—32no—
28#4561—32no—
29#4515D312yescomplemented
30#4508—32no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C3×#235C2×C412yes—
33#3811—21no—
34#3805—21no—
35#3802C811yescharacteristic
36C4×D32—21no—
37#3798—21no—
38#3797C811yescharacteristic
39#3796C812yes—
40C2×C32×C8C2311yescharacteristic
41C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
42C8×C3⋊D3D411yescharacteristic
43C8×C3⋊D3D411yescharacteristic
44C8×C3⋊D3D411yescharacteristic
45C8×C3⋊D3D411yescharacteristic
46C3×#208C2×C412yes—
47C3×ΓL(1,𝔽25)—22no—
48C3×D3×C8—22no—
49#3712—21no—
50#3711—22no—
51#3710—21no—
52D3×C3⋊C8—22no—
53C32×C16—21no—
54C3⋊(C3⋊C16)—21no—
55C3×C3⋊C16—22no—
56C2×#350—91noSylow
57D3×#41—32no—
58C3×#131—32no—
59#948—32no—
60#907—32no—
61#907—62no—
62D3×M16—32no—
63D3×M16—62no—
64#901—62no—
65#901C2×D312yes—
66C2×D3×C8—32no—
67C2×D3×C8—61no—
68C2×D3×C8—62no—
69C3×M32—21no—
70C3×M32C2×D312yescomplemented
71C2×C3×C16—32no—
72#812—32no—
73#812—61no—
74C2×C3⋊C16C2×D312yescomplemented
75#798—62no—
76#798—62no—
77D3×C16—62no—
78D3×C16—62no—
79D3×C16—62no—
80D3×C16—62no—
81C22×C3⋊D3M1611yescharacteristic
82C2×D32—21no—
83C2×C32×C4C22×C411yescharacteristic
84C2×C3⋊Dic3M1611yescharacteristic
85C4×C3⋊D3C22⋊C411yescharacteristic
86C4×C3⋊D3C22⋊C411yescharacteristic
87C4×C3⋊D3C2×C811yescharacteristic
88C4×C3⋊D3C2×C811yescharacteristic
89C3×#67—22no—
90C3×D12C2×C812yes—
91C3×C4×D3—22no—
92C3×Dic6C2×C812yes—
93#627—21no—
94#626—22no—
95#625—21no—
96#624—21no—
97D3×Dic3—22no—
98C32×C8C2×D411yescharacteristic
99C32×C8C2×D411yescharacteristic
100C3⋊(C3⋊C8)C22⋊C411yescharacteristic
101C3⋊(C3⋊C8)C22⋊C411yescharacteristic
102C3×C3⋊C8—22no—
103C2×#131—91no—
104C2×M32—91no—
105C22×C16—91no—
106#350—32no—
107#350—92no—
108C3×#41—32no—
109#239—32no—
110D3×Q8—32no—
111#237—32no—
112#237—62no—
113D3×D4—32no—
114D3×D4—62no—
115#235—62no—
116#235C4×D312yes—
117C2×C4×D3—32no—
118C2×C4×D3—61no—
119C2×C4×D3—62no—
120C3×M16—32no—
121C3×M16—62no—
122C2×C3×C8—21no—
123C2×C3×C8—62no—
124C2×C3×C8C22×D312yes—
125#208—62no—
126#208C4×D312yes—
127C2×C3⋊C8—32no—
128C2×C3⋊C8—61no—
129C2×C3⋊C8—62no—
130ΓL(1,𝔽25)—22no—
131ΓL(1,𝔽25)—62no—
132ΓL(1,𝔽25)—62no—
133D3×C8—22no—
134D3×C8—32no—
135D3×C8—32no—
136D3×C8—32no—
137D3×C8—32no—
138D3×C8—61no—
139D3×C8—61no—
140D3×C8—61no—
141D3×C8—61no—
142D3×C8—62no—
143D3×C8—62no—
144C3×C16—22no—
145C3×C16—22no—
146C3×C16—62no—
147C3⋊C16—22no—
148C3⋊C16—62no—
149C3⋊C16—62no—
150C22×C32C2×M1611yescharacteristic
151C2×C3⋊D3—22no—
152C2×C3⋊D3C22⋊C811yescharacteristic
153C2×C3⋊D3C22⋊C811yescharacteristic
154C2×C3×D3—22no—
155D32—42no—
156C32×C4C2×C22⋊C411yescharacteristic
157C32×C4C22×C811yescharacteristic
158C3⋊Dic3C22⋊C811yescharacteristic
159C3⋊Dic3C22⋊C811yescharacteristic
160C3×Dic3—22no—
161C2×#41—91no—
162#131—32no—
163#131—92no—
164#131—181no—
165#131—181no—
166C2×M16—91no—
167C2×M16—181no—
168C22×C8—91no—
169C22×C8—181no—
170M32—91no—
171M32—181no—
172M32D3211yescharacteristic, complemented
173C2×C16—32no—
174C2×C16—181no—
175C2×C16—181no—
176C2×C16—181no—
177C22×D3—32no—
178C22×D3—61no—
179C22×D3—62no—
180C3×Q8—32no—
181C3×D4—32no—
182C3×D4—62no—
183C2×C3×C4—21no—
184C2×C3×C4—62no—
185C2×C3×C4C2×C4×D312yes—
186#67—22no—
187#67—62no—
188#67—62no—
189C2×Dic3—32no—
190C2×Dic3—61no—
191C2×Dic3—62no—
192D12—62no—
193D12D3×C812yes—
194C4×D3—22no—
195C4×D3—32no—
196C4×D3—32no—
197C4×D3—32no—
198C4×D3—32no—
199C4×D3—61no—
200C4×D3—61no—
201C4×D3—61no—
202C4×D3—61no—
203C4×D3—62no—
204C4×D3—62no—
205Dic6—62no—
206Dic6D3×C812yes—
207C3×C8—21no—
208C3×C8—21no—
209C3×C8—62no—
210C3×C8D3×D412yes—
211C3×C8D3×D412yes—
212C3⋊C8—22no—
213C3⋊C8—32no—
214C3⋊C8—32no—
215C3⋊C8—61no—
216C3⋊C8—61no—
217C2×C32—21no—
218C2×C32C2×C22⋊C811yescharacteristic
219C3⋊D3—21no—
220C3⋊D3#35012yescomplemented
221C3×D3—42no—
222#41—32no—
223#41—92no—
224#41—181no—
225#41—181no—
226C2×Q8—91no—
227C2×D4—91no—
228C2×D4—181no—
229C22×C4—91no—
230C22×C4—181no—
231M16—32no—
232M16—62no—
233M16—181no—
234M16—182no—
235C2×C8—62no—
236C2×C8—91no—
237C2×C8—91no—
238C2×C8—91no—
239C2×C8—91no—
240C2×C8—91no—
241C2×C8—181no—
242C2×C8—182no—
243C2×C8C2×D3211yescharacteristic
244C16—21no—
245C16—62no—
246C16—181no—
247C22×C3—21no—
248C22×C3—62no—
249C22×C3D3×M1612yes—
250C2×D3—22no—
251C2×D3—32no—
252C2×D3—32no—
253C2×D3—61no—
254C2×D3—61no—
255C2×D3—64no—
256C2×D3—122no—
257C2×D3—124no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—62no—
261C3×C4D3×C22⋊C412yes—
262C3×C4C2×D3×C812yes—
263Dic3—22no—
264Dic3—32no—
265Dic3—32no—
266Dic3—61no—
267Dic3—61no—
268C32C2×#35011yescharacteristic, complemented, Sylow
269C23—91no—
270C23—181no—
271Q8—32no—
272Q8—181no—
273D4—32no—
274D4—62no—
275D4—182no—
276D4—181no—
277C2×C4—62no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—181no—
284C2×C4—182no—
285C2×C4C4×D3211yescharacteristic
286C8—62no—
287C8—91no—
288C8—91no—
289C8#380211yescharacteristic
290C8#381111yescharacteristic
291C2×C3—22no—
292C2×C3—21no—
293C2×C3—41no—
294C2×C3—122no—
295C2×C3D3×C22⋊C812yes—
296D3—34no—
297D3—42no—
298D3—62no—
299D3—62no—
300D3—121no—
301C22—62no—
302C22—91no—
303C22—91no—
304C22—182no—
305C22—362no—
306C22#6379111yescharacteristic
307C4—62no—
308C4—91no—
309C4—91no—
310C4D32×C811yescharacteristic
311C4#6392111yescharacteristic
312C3—21no—
313C3D3×#35012yescomplemented
314C2—21no—
315C2—92no—
316C2—122no—
317C2—181no—
318C2#1059093511yescharacteristic
subgroupG/H
centerC8#3811
commutatorC32×C4C22×C8
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32C2×C22⋊C8
prime radical#64306C4
cosocleC2×C32×C8C23
hypercenterM32D32
hypocenterC32C2×#350
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×M32C2semidirect
3. C2×#63542C2semidirect
4. C3×#4515C2semidirect
5. #10589112C2semidirect
16. C32×M32C22semidirect
17. #63639C22semidirect
20. C2×C3×C3⋊C16C22semidirect
29. #4515D3semidirect
70. C3×M32C2×D3semidirect
74. C2×C3⋊C16C2×D3semidirect
172. M32D32semidirect
220. C3⋊D3#350semidirect
268. C32C2×#350semidirect
313. C3D3×#350semidirect

Maximal subgroups

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

subgroupindex
#105946692
C3⋊D3×M322
C2×#635422
C3×#45152
#105891122
D3×#3503