Finite Group Databasebeta

← #11796034

Subgroups — #11796034

Order 1152.

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

normal subgroups only

This group has 517 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
1C2×#63791C211yesmaximal, characteristic
2C3⋊D3×M32C211yesmaximal, characteristic, complemented
3#10590625C211yesmaximal, characteristic, complemented
4C3×#4514C212yesmaximal, complemented
5#10589109C212yesmaximal, complemented
6D3×#349—32nomaximal
7C2×C4×D32C411yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×ΓL(1,𝔽25)C2212yes—
10C2×#3711C412yes—
11C2×#3710C411yescharacteristic
12#63791—21no—
13#63791—21no—
14#63791—21no—
15#63791—21no—
16C32×M32C2211yescharacteristic, complemented
17#63639C2211yescharacteristic, complemented
18#63625—21no—
19C16×C3⋊D3—21no—
20C3×#812C2212yescomplemented
21#63544—21no—
22#63542—21no—
23C2×D3×M16—32no—
24D3×M32—32no—
25D3×M32—32no—
26D3×M32—61no—
27C3×#349—32no—
28#4553—32no—
29#4514—32no—
30#4514D312yescomplemented
31C22×D32C811yescharacteristic
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C3×C4×D3C2×C412yes—
34C2×#624C811yescharacteristic
35C2×D3×Dic3C812yes—
36C4×D32—21no—
37C4×D32—21no—
38C4×D32—21no—
39C4×D32—21no—
40C2×C32×C8C2311yescharacteristic
41C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
42C8×C3⋊D3D411yescharacteristic
43C8×C3⋊D3D411yescharacteristic
44C8×C3⋊D3D411yescharacteristic
45C8×C3⋊D3D411yescharacteristic
46C2×C3×C3⋊C8C2×C412yes—
47C3×ΓL(1,𝔽25)—22no—
48C3×ΓL(1,𝔽25)—22no—
49#3711—22no—
50#3711—22no—
51#3710—21no—
52#3710—21no—
53C32×C16—21no—
54C3⋊(C3⋊C16)—21no—
55C3×C3⋊C16—22no—
56C2×#349—91noSylow
57C22×C4×D3—32no—
58C2×C3×M16—32no—
59C2×#208—32no—
60D3×M16—62no—
61D3×M16—62no—
62D3×M16—62no—
63D3×M16—62no—
64C2×ΓL(1,𝔽25)—32no—
65C2×ΓL(1,𝔽25)C2×D312yes—
66C2×D3×C8—32no—
67C2×D3×C8—32no—
68C2×D3×C8—61no—
69C3×M32—21no—
70C3×M32—32no—
71C3×M32C2×D312yescomplemented
72#812—32no—
73#812—61no—
74#812C2×D312yescomplemented
75#798—62no—
76#798—62no—
77#798—62no—
78D3×C16—62no—
79D3×C16—62no—
80D3×C16—62no—
81C22×C3⋊D3C2×C811yescharacteristic
82C22×C3×D3C2×C812yes—
83C2×D32—21no—
84C2×D32—21no—
85C2×D32—42no—
86C2×C32×C4C22×C411yescharacteristic
87C2×C3⋊Dic3C2×C811yescharacteristic
88C4×C3⋊D3C22⋊C411yescharacteristic
89C4×C3⋊D3C22⋊C411yescharacteristic
90C4×C3⋊D3M1611yescharacteristic
91C4×C3⋊D3M1611yescharacteristic
92C2×C3×Dic3C2×C812yes—
93C3×C4×D3—22no—
94C3×C4×D3—22no—
95#624—21no—
96#624—21no—
97D3×Dic3—22no—
98D3×Dic3—22no—
99C32×C8C2×D411yescharacteristic
100C32×C8C2×D411yescharacteristic
101C3⋊(C3⋊C8)C22⋊C411yescharacteristic
102C3⋊(C3⋊C8)C22⋊C411yescharacteristic
103C3×C3⋊C8—22no—
104C22×M16—91no—
105C2×M32—91no—
106C2×M32—91no—
107#349—32no—
108#349—92no—
109C23×D3—32no—
110C22×C3×C4—32no—
111C22×Dic3—32no—
112C2×C4×D3—32no—
113C2×C4×D3—32no—
114C2×C4×D3—32no—
115C2×C4×D3—61no—
116C2×C4×D3—62no—
117C2×C4×D3—62no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3C4×D312yes—
121C3×M16—62no—
122C3×M16—62no—
123C2×C3×C8—21no—
124C2×C3×C8—32no—
125C2×C3×C8C22×D312yes—
126#208—62no—
127#208—62no—
128C2×C3⋊C8—32no—
129C2×C3⋊C8—61no—
130C2×C3⋊C8C4×D312yes—
131ΓL(1,𝔽25)—22no—
132ΓL(1,𝔽25)—22no—
133ΓL(1,𝔽25)—62no—
134ΓL(1,𝔽25)—62no—
135D3×C8—32no—
136D3×C8—32no—
137D3×C8—32no—
138D3×C8—32no—
139D3×C8—61no—
140D3×C8—61no—
141D3×C8—61no—
142D3×C8—61no—
143D3×C8—62no—
144D3×C8—62no—
145C3×C16—22no—
146C3×C16—22no—
147C3×C16—62no—
148C3⋊C16—22no—
149C3⋊C16—62no—
150C3⋊C16—62no—
151C22×C32C22×C811yescharacteristic
152C2×C3⋊D3—22no—
153C2×C3⋊D3C22⋊C811yescharacteristic
154C2×C3⋊D3C22⋊C811yescharacteristic
155C2×C3×D3—22no—
156C2×C3×D3—42no—
157D32—42no—
158D32—42no—
159C32×C4C2×C22⋊C411yescharacteristic
160C32×C4C2×M1611yescharacteristic
161C3⋊Dic3C22⋊C811yescharacteristic
162C3⋊Dic3C22⋊C811yescharacteristic
163C3×Dic3—22no—
164C23×C4—91no—
165C2×M16—32no—
166C2×M16—92no—
167C2×M16—181no—
168C2×M16—181no—
169C2×M16—181no—
170C2×M16—181no—
171C22×C8—91no—
172C22×C8—91no—
173M32—32no—
174M32—91no—
175M32—181no—
176M32—181no—
177M32D3211yescharacteristic, complemented
178C2×C16—181no—
179C2×C16—181no—
180C23×C3—32no—
181C22×D3—32no—
182C22×D3—61no—
183C22×D3—62no—
184C22×D3—62no—
185C22×D3—124no—
186C22×D3D3×C812yes—
187C2×C3×C4—21no—
188C2×C3×C4—32no—
189C2×C3×C4—62no—
190C2×C3×C4—62no—
191C2×C3×C4C2×C4×D312yes—
192C2×Dic3—32no—
193C2×Dic3—61no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3D3×C812yes—
197C4×D3—22no—
198C4×D3—22no—
199C4×D3—32no—
200C4×D3—32no—
201C4×D3—32no—
202C4×D3—32no—
203C4×D3—61no—
204C4×D3—61no—
205C4×D3—61no—
206C4×D3—61no—
207C4×D3—62no—
208C4×D3—62no—
209C4×D3—62no—
210C4×D3—62no—
211C3×C8—21no—
212C3×C8—21no—
213C3×C8—62no—
214C3×C8D3×D412yes—
215C3×C8D3×D412yes—
216C3⋊C8—22no—
217C3⋊C8—32no—
218C3⋊C8—32no—
219C3⋊C8—61no—
220C3⋊C8—61no—
221C2×C32—21no—
222C2×C32C2×C22⋊C811yescharacteristic
223C3⋊D3—21no—
224C3⋊D3#34912yescomplemented
225C3×D3—42no—
226C24—91no—
227C22×C4—32no—
228C22×C4—91no—
229C22×C4—92no—
230C22×C4—91no—
231C22×C4—181no—
232C22×C4—181no—
233C22×C4—181no—
234C22×C4—181no—
235M16—62no—
236M16—62no—
237M16—182no—
238M16—182no—
239C2×C8—32no—
240C2×C8—91no—
241C2×C8—91no—
242C2×C8—91no—
243C2×C8—91no—
244C2×C8—91no—
245C2×C8—181no—
246C2×C8—181no—
247C2×C8C2×D3211yescharacteristic
248C16—21no—
249C16—62no—
250C16—181no—
251C22×C3—21no—
252C22×C3—62no—
253C22×C3—122no—
254C22×C3C2×D3×C812yes—
255C2×D3—22no—
256C2×D3—32no—
257C2×D3—32no—
258C2×D3—42no—
259C2×D3—61no—
260C2×D3—61no—
261C2×D3—64no—
262C2×D3—122no—
263C2×D3—124no—
264C2×D3—124no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—62no—
268C3×C4D3×C22⋊C412yes—
269C3×C4D3×M1612yes—
270Dic3—22no—
271Dic3—32no—
272Dic3—32no—
273Dic3—61no—
274Dic3—61no—
275C32C2×#34911yescharacteristic, complemented, Sylow
276C23—32no—
277C23—91no—
278C23—181no—
279C23—181no—
280C23—362no—
281C2×C4—32no—
282C2×C4—62no—
283C2×C4—62no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—91no—
288C2×C4—91no—
289C2×C4—181no—
290C2×C4—181no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4C4×D3211yescharacteristic
294C8—62no—
295C8—91no—
296C8—91no—
297C8#380211yescharacteristic
298C8#381111yescharacteristic
299C2×C3—22no—
300C2×C3—21no—
301C2×C3—41no—
302C2×C3—122no—
303C2×C3D3×C22⋊C812yes—
304D3—34no—
305D3—42no—
306D3—62no—
307D3—62no—
308D3—121no—
309C22—62no—
310C22—91no—
311C22—91no—
312C22—122no—
313C22—182no—
314C22—362no—
315C22—362no—
316C22D32×C811yescharacteristic
317C4—62no—
318C4—91no—
319C4—91no—
320C4#6379111yescharacteristic
321C4#6392111yescharacteristic
322C3—21no—
323C3D3×#34912yescomplemented
324C2—21no—
325C2—92no—
326C2—122no—
327C2—181no—
328C2#1059093511yescharacteristic
subgroupG/H
centerC4#63921
commutatorC22×C32C22×C8
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32C2×C22⋊C8
prime radicalC22×D32C8
cosocleC2×C32×C8C23
hypercenterM32D32
hypocenterC32C2×#349
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×M32C2semidirect
3. #10590625C2semidirect
4. C3×#4514C2semidirect
5. #10589109C2semidirect
16. C32×M32C22semidirect
17. #63639C22semidirect
20. C3×#812C22semidirect
30. #4514D3semidirect
71. C3×M32C2×D3semidirect
74. #812C2×D3semidirect
177. M32D32semidirect
224. C3⋊D3#349semidirect
275. C32C2×#349semidirect
323. C3D3×#349semidirect

Maximal subgroups

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

subgroupindex
C2×#637912
C3⋊D3×M322
#105906252
C3×#45142
#105891092
D3×#3493