Finite Group Databasebeta

← #11800923

Subgroups — #11800923

Order 1152.

1725 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#626C213yesmaximal
2C3⋊D3×#95C211yesmaximal, characteristic, complemented
3C3×D3×#95C211yesmaximal, characteristic, complemented
4C3×#4648C211yesmaximal, characteristic, complemented
5#10591260C213yesmaximal, complemented
6#10591242C213yesmaximal, complemented
7#10591237C213yesmaximal, complemented
8#73412—31nomaximal
9#73322—31nomaximal
10C22×C4×C3⋊D3C2213yes—
11C22×C3×C4×D3C2213yes—
12C22×#626C2211yescharacteristic
13C2×C3×C4×Dic3C2213yes—
14C2×Dic3⋊Dic3C2213yes—
15C2×#3722C2213yes—
16C2×(C2×D3)⋊Dic3C2213yes—
17C2×Dic32C2216yes—
18C4×#626C4124yescomplemented
19C32×#95C2211yescharacteristic
20#63658C2213yes—
21C3×C3⋊#95C2213yes—
22C3×C3⋊#95C2213yes—
23C2×C4×#67—33no—
24C2×C4×D12—33no—
25C3×#376—31no—
26C2×C3×#95—31no—
27C4×#217—33no—
28C4×C4⋊Dic3—33no—
29#4666—33no—
30#4666—33no—
31#4666—33no—
32D3×#95—31no—
33D3×#95—31no—
34D3×#95—61no—
35D3×#95D311yescharacteristic, complemented
36#4649—33no—
37#4648D311yescharacteristic, complemented
38C23×C3⋊D3C2311yescharacteristic
39C23×C3×D3C2311yescharacteristic
40C22×C32×C4C2313yes—
41C22×C3⋊Dic3C2313yes—
42C2×C4×C3⋊D3—46no—
43C2×C4×C3⋊D3C2×C4112yescomplemented
44C22×C3×Dic3C2313yes—
45C22×C3×Dic3C2313yes—
46C22×C3×Dic3C2311yescharacteristic
47C2×C3×C4×D3—46no—
48C2×C3×C4×D3C2×C4112yescomplemented
49C2×#626C2×C4112yes—
50C3×C4×Dic3C2×C4112yescomplemented
51Dic3⋊Dic3C2×C4112yescomplemented
52#3722C2×C4112yescomplemented
53(C2×D3)⋊Dic3C2×C4112yescomplemented
54Dic32—46no—
55#2275—91noSylow
56C23×C3×C4—33no—
57C22×#67—31no—
58C22×D12—31no—
59C22×C4×D3—33no—
60C22×C4×D3—33no—
61C22×C4×D3—63no—
62C22×C4×D3C2×D313yes—
63C2×C3×C42—33no—
64C2×#217—33no—
65C4×#67—324no—
66C2×(C2×D3)⋊C4—33no—
67C2×(C2×D3)⋊C4—33no—
68C2×(C2×D3)⋊C4—33no—
69C2×C4⋊Dic3—33no—
70C2×Dic3⋊C4—33no—
71C2×C4×Dic3—36no—
72C2×C4×Dic3—36no—
73C2×C4×Dic3C2×D313yes—
74C4×D12—324no—
75C3×#95—21no—
76C3×#95—33no—
77C3×#95—33no—
78C3×#95C2×D311yescharacteristic
79C3×#95C2×D311yescharacteristic
80C3⋊#95—33no—
81C3⋊#95—33no—
82C3⋊#95—63no—
83C3⋊#95C2×D313yes—
84C3⋊#95C2×D313yes—
85C23×C32C2411yescharacteristic
86C22×C3⋊D3—23no—
87C22×C3⋊D3—21no—
88C22×C3⋊D3C22×C416yes—
89C22×C3×D3—23no—
90C22×C3×D3—21no—
91C22×C3×D3C22×C416yes—
92C2×C32×C4—26no—
93C2×C32×C4C22×C416yes—
94C2×C3⋊Dic3—26no—
95C2×C3⋊Dic3C22×C416yes—
96C4×C3⋊D3—412no—
97C2×C3×Dic3—23no—
98C2×C3×Dic3—26no—
99C2×C3×Dic3—23no—
100C2×C3×Dic3C22×C416yes—
101C2×C3×Dic3C22×C416yes—
102C2×C3×Dic3C22×C416yes—
103C3×C4×D3—412no—
104#626C42116yescomplemented
105C2×C4×D4—93no—
106C4×C4⋊C4—93no—
107C4×C22⋊C4—93no—
108C4×C22⋊C4—93no—
109#376—31no—
110C2×#95—31no—
111C2×#95—91no—
112C24×C3—31no—
113C23×D3—31no—
114C23×D3—31no—
115C23×D3—61no—
116C23×D3C22×D311yescharacteristic
117C22×C3×C4—23no—
118C22×C3×C4—31no—
119C22×C3×C4—33no—
120C22×C3×C4—33no—
121C22×C3×C4—312no—
122C22×C3×C4—126no—
123C22×C3×C4C22×D313yes—
124C22×C3×C4C22×D313yes—
125C2×#67—312no—
126C22×Dic3—33no—
127C22×Dic3—33no—
128C22×Dic3—63no—
129C22×Dic3C22×D313yes—
130C22×Dic3C22×D313yes—
131C22×Dic3C22×D311yescharacteristic
132C2×D12—312no—
133C2×C4×D3—312no—
134C2×C4×D3—312no—
135C2×C4×D3—46no—
136C2×C4×D3—612no—
137C2×C4×D3—126no—
138C2×C4×D3—126no—
139C2×C4×D3—1212no—
140C2×C4×D3C4×D3112yescomplemented
141C3×C42—312no—
142#217—312no—
143(C2×D3)⋊C4—312no—
144(C2×D3)⋊C4—312no—
145(C2×D3)⋊C4—312no—
146C4⋊Dic3—312no—
147Dic3⋊C4—312no—
148C4×Dic3—126no—
149C4×Dic3—126no—
150C4×Dic3C4×D3112yescomplemented
151C22×C32C23×C413yes—
152C22×C32H(5,𝔽2)13yes—
153C22×C322−1+411yescharacteristic
154C2×C3⋊D3—26no—
155C2×C3⋊D3—26no—
156C2×C3⋊D3C2×C4214yes—
157C2×C3×D3—26no—
158C2×C3×D3—26no—
159C2×C3×D3C2×C4214yes—
160C32×C4—26no—
161C3⋊Dic3—26no—
162C3×Dic3—26no—
163C3×Dic3—26no—
164C3×Dic3C2×C4214yes—
165C22×D4—91no—
166C23×C4—33no—
167C23×C4—93no—
168C4×D4—924no—
169C2×C4⋊C4—93no—
170C2×C22⋊C4—93no—
171C2×C22⋊C4—93no—
172C2×C42—33no—
173C2×C42—96no—
174#95—33no—
175#95—33no—
176#95—93no—
177#95D3211yescharacteristic
178C23×C3—21no—
179C23×C3—36no—
180C23×C3—63no—
181C23×C3—61no—
182C23×C3C23×D311yescharacteristic
183C23×C3C23×D311yescharacteristic
184C22×D3—23no—
185C22×D3—21no—
186C22×D3—36no—
187C22×D3—36no—
188C22×D3—66no—
189C22×D3—66no—
190C22×D3—62no—
191C22×D3—63no—
192C22×D3—61no—
193C22×D3—63no—
194C22×D3—61no—
195C22×D3C2×C4×D316yes—
196C2×C3×C4—26no—
197C2×C3×C4—26no—
198C2×C3×C4—26no—
199C2×C3×C4—36no—
200C2×C3×C4—36no—
201C2×C3×C4—36no—
202C2×C3×C4—46no—
203C2×C3×C4—63no—
204C2×C3×C4—63no—
205C2×C3×C4—66no—
206C2×C3×C4—1212no—
207C2×C3×C4C2×C4×D316yes—
208C2×C3×C4C2×C4×D316yes—
209#67—316no—
210C2×Dic3—26no—
211C2×Dic3—23no—
212C2×Dic3—23no—
213C2×Dic3—36no—
214C2×Dic3—36no—
215C2×Dic3—66no—
216C2×Dic3—66no—
217C2×Dic3—66no—
218C2×Dic3—126no—
219C2×Dic3C2×C4×D316yes—
220C2×Dic3C2×C4×D316yes—
221C2×Dic3C2×C4×D316yes—
222D12—316no—
223C4×D3—412no—
224C4×D3—1212no—
225C4×D3—1212no—
226C4×D3—1224no—
227C2×C32C22×C4211yescharacteristic
228C2×C32#51813yes—
229C2×C32#52013yes—
230C3⋊D3—24no—
231C3×D3—24no—
232C24—31no—
233C24—91no—
234C2×D4—912no—
235C22×C4—31no—
236C22×C4—33no—
237C22×C4—33no—
238C22×C4—312no—
239C22×C4—93no—
240C22×C4—912no—
241C22×C4—126no—
242C22×C4—366no—
243C22×C4C2×D3213yes—
244C4⋊C4—912no—
245C22⋊C4—912no—
246C22⋊C4—912no—
247C42—312no—
248C42—366no—
249C22×C3—23no—
250C22×C3—23no—
251C22×C3—21no—
252C22×C3—34no—
253C22×C3—66no—
254C22×C3—66no—
255C22×C3C22×C4×D313yes—
256C22×C3C22×C4×D313yes—
257C22×C3#100413yes—
258C22×C3#100711yescharacteristic
259C22×C3#100913yes—
260C22×C3#101011yescharacteristic
261C2×D3—26no—
262C2×D3—26no—
263C2×D3—34no—
264C2×D3—34no—
265C2×D3—64no—
266C2×D3—612no—
267C2×D3—612no—
268C2×D3—66no—
269C2×D3—66no—
270C2×D3—66no—
271C2×D3—66no—
272C2×D3C42×D314yes—
273C3×C4—26no—
274C3×C4—26no—
275C3×C4—34no—
276C3×C4—46no—
277C3×C4—66no—
278C3×C4—66no—
279Dic3—26no—
280Dic3—26no—
281Dic3—66no—
282Dic3—66no—
283Dic3—126no—
284Dic3C42×D314yes—
285C32#227511yescharacteristic, complemented, Sylow
286C23—36no—
287C23—63no—
288C23—61no—
289C23—96no—
290C23—183no—
291C23—181no—
292C23C22×D3211yescharacteristic
293D4—916no—
294C2×C4—26no—
295C2×C4—36no—
296C2×C4—36no—
297C2×C4—36no—
298C2×C4—63no—
299C2×C4—66no—
300C2×C4—63no—
301C2×C4—96no—
302C2×C4—1212no—
303C2×C4—186no—
304C2×C4—3612no—
305C2×C4C4×D3216yes—
306C2×C3—23no—
307C2×C3—21no—
308C2×C3—23no—
309C2×C3—64no—
310C2×C3C2×C42×D311yescharacteristic
311C2×C3C2×C42×D311yescharacteristic
312C2×C3#548613yes—
313C2×C3#550413yes—
314C2×C3#552113yes—
315C2×C3#552313yes—
316D3—24no—
317D3—68no—
318D3—64no—
319D3—64no—
320C22—34no—
321C22—66no—
322C22—66no—
323C22—94no—
324C22—186no—
325C22—186no—
326C22C2×C4×D3213yes—
327C22#6431413yes—
328C22#6431511yescharacteristic
329C4—26no—
330C4—34no—
331C4—66no—
332C4—66no—
333C4—186no—
334C3—21no—
335C3#7332211yescharacteristic, complemented
336C3#7341211yescharacteristic, complemented
337C2—64no—
338C2—184no—
339C2C42×D3211yescharacteristic
340C2#1059418213yes—
341C2#1059451013yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2275
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#95C2semidirect
3. C3×D3×#95C2semidirect
4. C3×#4648C2semidirect
5. #10591260C2semidirect
6. #10591242C2semidirect
7. #10591237C2semidirect
18. C4×#626C4semidirect
35. D3×#95D3semidirect
37. #4648D3semidirect
43. C2×C4×C3⋊D3C2×C4semidirect
48. C2×C3×C4×D3C2×C4semidirect
50. C3×C4×Dic3C2×C4semidirect
51. Dic3⋊Dic3C2×C4semidirect
52. #3722C2×C4semidirect
53. (C2×D3)⋊Dic3C2×C4semidirect
104. #626C42semidirect
140. C2×C4×D3C4×D3semidirect
150. C4×Dic3C4×D3semidirect
285. C32#2275semidirect
335. C3#73322semidirect
336. C3#73412semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6262
C3⋊D3×#952
C3×D3×#952
C3×#46482
#105912602
#105912422
#105912372
#734123
#733223