Finite Group Databasebeta

← #11802912

Subgroups — #11802912

Order 1152.

1969 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3752C211yesmaximal, characteristic
2C2×#63974C212yesmaximal
3C3×#5212C212yesmaximal, complemented
4#10591720C212yesmaximal, complemented
5#10591378C218yesmaximal, complemented
6#74005—32nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C22×#624C2214yes—
11C2×#3752C418yescomplemented
12C2×#3752C2214yes—
13C2×C3×#217C2214yes—
14C2×C3×C4⋊Dic3C2214yescomplemented
15#63974—28no—
16C2×#3724C2214yescomplemented
17C2×#3722C2214yes—
18C3×C3⋊#95C2214yescomplemented
19#63579C2214yescomplemented
20C22×(C2×D3)⋊C4—32no—
21C22×(C2×D3)⋊C4—61no—
22C2×D3×C22⋊C4—34no—
23C3×#380—32no—
24#5212D312yescomplemented
25#4989—38no—
26#4942—34no—
27#4668—38no—
28C24×C32C2311yescharacteristic
29C23×C3⋊D3—42no—
30C23×C3⋊D3—42no—
31C23×C3⋊D3C2×C414yes—
32C23×C3⋊D3D414yes—
33C23×C3⋊D3Q814yes—
34C23×C3⋊D3C2312yes—
35C22×C32×C4—42no—
36C22×C32×C4C2×C414yescomplemented
37C22×C32×C4C2312yes—
38C22×C3⋊Dic3—42no—
39C22×C3⋊Dic3C2×C414yescomplemented
40C22×C3⋊Dic3C2312yes—
41C22×C3×Dic3C2318yes—
42C2×#624—28no—
43C2×#624—44no—
44C2×#624—44no—
45#3752C2×C4116yescomplemented
46C3×#217—28no—
47C3×C4⋊Dic3—44no—
48#3724—44no—
49#3722—28no—
50#2315—91noSylow
51C24×D3—32no—
52C24×D3—61no—
53C23×C3×C4—21no—
54C23×C3×C4C2×D312yes—
55C23×Dic3—32no—
56C23×Dic3—61no—
57C22×C4×D3—38no—
58C2×C3×C4⋊C4—34no—
59C2×C3×C22⋊C4—34no—
60C2×#217C2×D314yes—
61C2×(C2×D3)⋊C4—316no—
62C2×(C2×D3)⋊C4—34no—
63C2×(C2×D3)⋊C4—34no—
64C2×(C2×D3)⋊C4—38no—
65C2×(C2×D3)⋊C4—68no—
66C2×(C2×D3)⋊C4—64no—
67C2×C4⋊Dic3C2×D314yescomplemented
68C2×Dic3⋊C4—38no—
69D3×C22⋊C4—616no—
70C3×#95—34no—
71C3⋊#95—38no—
72C3⋊#95C2×D314yescomplemented
73C23×C32—22no—
74C23×C32—22no—
75C23×C32C22×C412yes—
76C23×C32C2×D412yes—
77C23×C32C2×Q812yes—
78C23×C32C2411yescharacteristic
79C22×C3⋊D3—24no—
80C22×C3⋊D3—24no—
81C22×C3⋊D3—44no—
82C22×C3⋊D3—44no—
83C22×C3⋊D3—48no—
84C22×C3⋊D3—48no—
85C22×C3⋊D3C4⋊C4116yescomplemented
86C22×C3⋊D3C22×C414yes—
87C22×C3⋊D3C2×D414yes—
88C22×C3⋊D3C2×Q814yes—
89C2×C32×C4—24no—
90C2×C32×C4—44no—
91C2×C32×C4C22×C414yes—
92C2×C3⋊Dic3—24no—
93C2×C3⋊Dic3—44no—
94C2×C3⋊Dic3C22×C414yes—
95C2×C3×Dic3—28no—
96C2×C3×Dic3—28no—
97C2×C3×Dic3—28no—
98#624—416no—
99C22×C22⋊C4—92no—
100C22×C22⋊C4—91no—
101#385—98no—
102#380—32no—
103#380—92no—
104C24×C3—21no—
105C24×C3C22×D312yes—
106C23×D3—34no—
107C23×D3—38no—
108C23×D3—38no—
109C23×D3—38no—
110C23×D3—64no—
111C23×D3—64no—
112C23×D3—64no—
113C23×D3—62no—
114C23×D3—124no—
115C23×D3—124no—
116C23×D3—124no—
117C23×D3—124no—
118C22×C3×C4—24no—
119C22×C3×C4—22no—
120C22×C3×C4—38no—
121C22×C3×C4—44no—
122C22×C3×C4—44no—
123C22×C3×C4C4×D318yescomplemented
124C22×C3×C4C22×D312yes—
125C22×C3×C4C22×D312yes—
126C22×Dic3—34no—
127C22×Dic3—38no—
128C22×Dic3—64no—
129C22×Dic3—62no—
130C22×Dic3—124no—
131C22×Dic3—124no—
132C22×Dic3C22×D318yes—
133C2×C4×D3—616no—
134C2×C4×D3—128no—
135C2×C4×D3—128no—
136C3×C4⋊C4—124no—
137C3×C22⋊C4—68no—
138#217—28no—
139(C2×D3)⋊C4—316no—
140(C2×D3)⋊C4—316no—
141(C2×D3)⋊C4—616no—
142(C2×D3)⋊C4—616no—
143C4⋊Dic3—44no—
144Dic3⋊C4—128no—
145C22×C32—22no—
146C22×C32—22no—
147C22×C32—24no—
148C22×C32—24no—
149C22×C32C2×C4⋊C414yes—
150C22×C32C23×C411yescharacteristic
151C22×C32C22×D411yescharacteristic
152C22×C32C22×Q811yescharacteristic
153C22×C32H(5,𝔽2)12yes—
154C22×C32H(5,𝔽2)12yes—
155C2×C3⋊D3—24no—
156C2×C3⋊D3—24no—
157C2×C3⋊D3—28no—
158C2×C3⋊D3—28no—
159C2×C3⋊D3—416no—
160C2×C3⋊D3C2×C4⋊C418yes—
161C32×C4—24no—
162C3⋊Dic3—24no—
163C3×Dic3—48no—
164C25—91no—
165C23×C4—94no—
166C23×C4—91no—
167C23×C4D3211yescharacteristic
168C2×C4⋊C4—34no—
169C2×C4⋊C4—94no—
170C2×C22⋊C4—34no—
171C2×C22⋊C4—98no—
172C2×C22⋊C4—94no—
173C2×C22⋊C4—94no—
174C2×C22⋊C4—188no—
175#95—34no—
176#95—94no—
177C23×C3—24no—
178C23×C3—24no—
179C23×C3—24no—
180C23×C3—24no—
181C23×C3—21no—
182C23×C3—22no—
183C23×C3—22no—
184C23×C3—22no—
185C23×C3C2×C4×D314yes—
186C23×C3D3×D414yes—
187C23×C3D3×Q814yes—
188C23×C3C23×D312yes—
189C22×D3—38no—
190C22×D3—38no—
191C22×D3—38no—
192C22×D3—332no—
193C22×D3—616no—
194C22×D3—64no—
195C22×D3—64no—
196C22×D3—64no—
197C22×D3—68no—
198C22×D3—68no—
199C22×D3—124no—
200C22×D3—124no—
201C22×D3—1216no—
202C22×D3—128no—
203C22×D3—128no—
204C22×D3—1216no—
205C22×D3—128no—
206C22×D3—128no—
207C22×D3—1216no—
208C22×D3—1216no—
209C2×C3×C4—24no—
210C2×C3×C4—24no—
211C2×C3×C4—24no—
212C2×C3×C4—44no—
213C2×C3×C4—48no—
214C2×C3×C4—48no—
215C2×C3×C4—68no—
216C2×C3×C4—68no—
217C2×C3×C4—68no—
218C2×C3×C4C2×C4×D314yes—
219C2×C3×C4C2×C4×D314yes—
220C2×Dic3—28no—
221C2×Dic3—28no—
222C2×Dic3—28no—
223C2×Dic3—38no—
224C2×Dic3—64no—
225C2×Dic3—68no—
226C2×Dic3—124no—
227C2×Dic3—128no—
228C2×Dic3—128no—
229C4×D3—1232no—
230C2×C32—24no—
231C2×C32C22×C4⋊C411yescharacteristic
232C2×C32#51811yescharacteristic
233C2×C32#51811yescharacteristic
234C2×C32#53412yes—
235C2×C32#54312yes—
236C3⋊D3—28no—
237C24—92no—
238C24—94no—
239C24—94no—
240C24—94no—
241C24—362no—
242C24—362no—
243C24C2×D3211yescharacteristic
244C22×C4—38no—
245C22×C4—42no—
246C22×C4—92no—
247C22×C4—94no—
248C22×C4—188no—
249C22×C4—364no—
250C22×C4—364no—
251C22×C4—362no—
252C22×C4#62414yescomplemented
253C22×C4C2×D3212yes—
254C4⋊C4—124no—
255C4⋊C4—364no—
256C22⋊C4—68no—
257C22⋊C4—916no—
258C22⋊C4—188no—
259C22×C3—24no—
260C22×C3—24no—
261C22×C3—28no—
262C22×C3—28no—
263C22×C3—28no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—28no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—22no—
270C22×C3—21no—
271C22×C3—22no—
272C22×C3—24no—
273C22×C3D3×C4⋊C418yes—
274C22×C3C22×C4×D312yes—
275C22×C3C2×D3×D412yes—
276C22×C3#100414yes—
277C22×C3C2×D3×Q812yes—
278C22×C3#100914yes—
279C2×D3—316no—
280C2×D3—68no—
281C2×D3—616no—
282C2×D3—68no—
283C2×D3—68no—
284C2×D3—616no—
285C2×D3—128no—
286C2×D3—128no—
287C2×D3—124no—
288C2×D3—124no—
289C2×D3—1232no—
290C2×D3—1232no—
291C3×C4—24no—
292C3×C4—24no—
293C3×C4—44no—
294C3×C4—128no—
295Dic3—48no—
296Dic3—68no—
297Dic3—124no—
298C32#231511yescharacteristic, complemented, Sylow
299C23—22no—
300C23—22no—
301C23—94no—
302C23—94no—
303C23—94no—
304C23—916no—
305C23—184no—
306C23—184no—
307C23—368no—
308C23—368no—
309C23—364no—
310C23—364no—
311C23#379712yes—
312C23#380212yes—
313C23C2×#62412yes—
314C23C22×D3211yescharacteristic
315C2×C4—24no—
316C2×C4—44no—
317C2×C4—68no—
318C2×C4—68no—
319C2×C4—68no—
320C2×C4—94no—
321C2×C4—184no—
322C2×C4—3616no—
323C2×C4—364no—
324C2×C4C2×#62414yes—
325C2×C3—28no—
326C2×C3—28no—
327C2×C3—22no—
328C2×C3—21no—
329C2×C3—22no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3#548612yes—
333C2×C3C2×D3×C4⋊C412yes—
334C2×C3#552112yes—
335C2×C3#560514yes—
336C2×C3#563414yes—
337D3—616no—
338D3—128no—
339C22—24no—
340C22—24no—
341C22—22no—
342C22—22no—
343C22—98no—
344C22—188no—
345C22—188no—
346C22—184no—
347C22—184no—
348C22—3616no—
349C22#6390014yes—
350C22C2×#379711yescharacteristic
351C22C2×#380211yescharacteristic
352C22#6430812yes—
353C22C22×#62411yescharacteristic
354C22#6433012yes—
355C4—24no—
356C4—128no—
357C4—184no—
358C3—21no—
359C3#7400512yescomplemented
360C2—24no—
361C2—188no—
362C2C2×#6390011yescharacteristic
363C2#1059498112yes—
364C2#1059499611yescharacteristic
365C2#1059508412yes—
366C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32#2315
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C3×#5212C2semidirect
4. #10591720C2semidirect
5. #10591378C2semidirect
11. C2×#3752C4semidirect
14. C2×C3×C4⋊Dic3C22semidirect
16. C2×#3724C22semidirect
18. C3×C3⋊#95C22semidirect
19. #63579C22semidirect
24. #5212D3semidirect
36. C22×C32×C4C2×C4semidirect
39. C22×C3⋊Dic3C2×C4semidirect
45. #3752C2×C4semidirect
67. C2×C4⋊Dic3C2×D3semidirect
72. C3⋊#95C2×D3semidirect
85. C22×C3⋊D3C4⋊C4semidirect
123. C22×C3×C4C4×D3semidirect
252. C22×C4#624semidirect
298. C32#2315semidirect
359. C3#74005semidirect

Maximal subgroups

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

subgroupindex
C22×#37522
C2×#639742
C3×#52122
#105917202
#105913782
#740053