Finite Group Databasebeta

← #11808756

Subgroups — #11808756

Order 1152.

1769 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 1769 conjugacy classes of subgroups — too many to draw. Only its 232 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×#63902C213yesmaximal, complemented
2C2×#63898C213yesmaximal, complemented
3#10592347C211yesmaximal, characteristic, complemented
4C3×#4677C211yesmaximal, characteristic, complemented
5C3×#4671C211yesmaximal, characteristic, complemented
6#10591389C213yesmaximal, complemented
7#10591324C213yesmaximal, complemented
8#78019—31nomaximal
9#76667—31nomaximal
10C22×C3×D12C2213yes—
11C22×#625C2213yes—
12C22×D3×Dic3C2213yes—
13C22×D3×Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2213yes—
15C2×C3×(C2×D3)⋊C4C2213yes—
16C2×C3×(C2×D3)⋊C4C2213yes—
17C2×C3×C4⋊Dic3C2213yes—
18C2×#3724C2213yes—
19C2×(C2×D3)⋊Dic3C2216yes—
20#63902—212no—
21#63898—212no—
22C32×#95C2211yescharacteristic
23#63658C2213yes—
24C2×D4×Dic3—33no—
25C2×#893—33no—
26C2×#67⋊C4—33no—
27C2×#67⋊C4—33no—
28C3×#399—31no—
29C3×#392—31no—
30#5223—33no—
31#4993—33no—
32#4960—33no—
33#4949—33no—
34#4677D311yescharacteristic, complemented
35#4671D311yescharacteristic, complemented
36#4648—31no—
37#4648—31no—
38#4648—61no—
39C23×C3×D3C2311yescharacteristic
40C23×C3×D3C2313yes—
41C22×C32×C4C2313yes—
42C22×C3⋊Dic3C2313yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3×Dic3C2313yes—
45C22×C3×Dic3C2311yescharacteristic
46C2×C3×D12—212no—
47C2×C3×D12—26no—
48C2×#625—26no—
49C2×#625—26no—
50C2×#625—26no—
51C2×D3×Dic3—212no—
52C2×D3×Dic3—26no—
53C2×D3×Dic3—26no—
54C4×C3⋊Dic3D4112yescomplemented
55C3×(C2×D3)⋊C4—26no—
56C3×(C2×D3)⋊C4—26no—
57C3×C4⋊Dic3—26no—
58#3724—26no—
59(C2×D3)⋊Dic3—212no—
60#2397—91noSylow
61C22×C3×D4—33no—
62C22×#67—33no—
63C22×#67—33no—
64C23×Dic3—31no—
65C23×Dic3—33no—
66C22×D12C2×D313yes—
67C22×C4×D3—31no—
68C22×C4×D3—33no—
69C2×C3×C4⋊C4—33no—
70C2×C3×C22⋊C4—33no—
71C2×C3×C22⋊C4—33no—
72C2×#217—36no—
73D4×Dic3—612no—
74C2×(C2×D3)⋊C4—36no—
75C2×(C2×D3)⋊C4C2×D313yes—
76C2×(C2×D3)⋊C4C2×D313yes—
77C2×C4⋊Dic3C2×D313yes—
78C2×Dic3⋊C4—33no—
79C2×Dic3⋊C4—33no—
80C2×C4×Dic3—33no—
81C2×C4×Dic3—33no—
82C2×C4×Dic3—63no—
83#893—612no—
84#67⋊C4—612no—
85#67⋊C4—612no—
86C3×#95—21no—
87C3×#95C2×D311yescharacteristic
88C3×#95C2×D311yescharacteristic
89C3⋊#95—33no—
90C3⋊#95—33no—
91C3⋊#95—63no—
92C23×C32C2411yescharacteristic
93C22×C3×D3—26no—
94C22×C3×D3—23no—
95C22×C3×D3—23no—
96C22×C3×D3—23no—
97C22×C3×D3—23no—
98C22×C3×D3—26no—
99C22×C3×D3#4116yes—
100C22×C3×D3#4112yes—
101C2×C32×C4—26no—
102C2×C32×C4C2×D416yes—
103C2×C3⋊Dic3—23no—
104C2×C3⋊Dic3—23no—
105C2×C3⋊Dic3C2×D416yes—
106C2×C3⋊Dic3C2×D416yes—
107C2×C3×Dic3—26no—
108C2×C3×Dic3—23no—
109C2×C3×Dic3—23no—
110C3×D12—224no—
111#625—224no—
112D3×Dic3—412no—
113D3×Dic3—44no—
114C2×C4×D4—93no—
115C2×C4×D4—93no—
116#399—31no—
117#399—93no—
118#392—31no—
119#392—93no—
120#376—91no—
121C24×C3—33no—
122C24×C3—31no—
123C23×D3C22×D313yes—
124C23×D3C22×D311yescharacteristic
125C2×C3×D4—612no—
126C2×C3×D4—66no—
127C22×C3×C4—23no—
128C22×C3×C4—31no—
129C22×C3×C4—33no—
130C22×C3×C4C22×D313yes—
131C22×C3×C4C22×D313yes—
132C2×#67—66no—
133C2×#67—66no—
134C2×#67—66no—
135C2×#67—66no—
136C2×#67—66no—
137C2×#67—66no—
138C22×Dic3—31no—
139C22×Dic3—31no—
140C22×Dic3—33no—
141C22×Dic3—33no—
142C22×Dic3—61no—
143C22×Dic3—63no—
144C22×Dic3—66no—
145C22×Dic3—66no—
146C22×Dic3—612no—
147C22×Dic3C22×D311yescharacteristic
148C22×Dic3C22×D313yes—
149C2×D12—212no—
150C2×D12—26no—
151C2×C4×D3—66no—
152C2×C4×D3—66no—
153C2×C4×D3—612no—
154C3×C4⋊C4—66no—
155C3×C22⋊C4—66no—
156C3×C22⋊C4—66no—
157#217—612no—
158(C2×D3)⋊C4—26no—
159(C2×D3)⋊C4—26no—
160(C2×D3)⋊C4—612no—
161C4⋊Dic3—26no—
162Dic3⋊C4—66no—
163Dic3⋊C4—66no—
164C4×Dic3—312no—
165C4×Dic3—312no—
166C4×Dic3—612no—
167C22×C32C22×D413yes—
168C22×C32C2×#4113yes—
169C22×C32C2×#4111yescharacteristic
170C2×C3×D3—26no—
171C2×C3×D3—26no—
172C2×C3×D3—212no—
173C2×C3×D3—43no—
174C2×C3×D3—43no—
175C2×C3×D3—46no—
176C2×C3×D3—43no—
177C2×C3×D3—41no—
178C32×C4—26no—
179C3⋊Dic3—26no—
180C3⋊Dic3#12714yes—
181C3×Dic3—43no—
182C3×Dic3—41no—
183C22×D4—33no—
184C22×D4—93no—
185C23×C4—91no—
186C23×C4—93no—
187C4×D4—1812no—
188C4×D4—1812no—
189C2×C4⋊C4—33no—
190C2×C4⋊C4—93no—
191C2×C22⋊C4—33no—
192C2×C22⋊C4—33no—
193C2×C22⋊C4—96no—
194C2×C42—93no—
195#95—93no—
196#95D3211yescharacteristic
197C23×C3—21no—
198C23×C3—32no—
199C23×C3—36no—
200C23×C3—66no—
201C23×C3—63no—
202C23×C3—63no—
203C23×C3—63no—
204C23×C3—63no—
205C23×C3—66no—
206C23×C3C23×D311yescharacteristic
207C23×C3C23×D311yescharacteristic
208C22×D3—23no—
209C22×D3—23no—
210C22×D3—26no—
211C22×D3—26no—
212C22×D3—23no—
213C22×D3—23no—
214C22×D3#23716yes—
215C22×D3#23912yes—
216C3×D4—624no—
217C2×C3×C4—26no—
218C2×C3×C4—26no—
219C2×C3×C4—26no—
220C2×C3×C4—46no—
221C2×C3×C4—63no—
222C2×C3×C4—63no—
223C2×C3×C4—66no—
224C2×C3×C4D3×D416yes—
225C2×C3×C4D3×D416yes—
226#67—624no—
227#67—624no—
228C2×Dic3—23no—
229C2×Dic3—23no—
230C2×Dic3—26no—
231C2×Dic3—36no—
232C2×Dic3—36no—
233C2×Dic3—36no—
234C2×Dic3—36no—
235C2×Dic3—66no—
236C2×Dic3—66no—
237C2×Dic3—63no—
238C2×Dic3—63no—
239C2×Dic3—63no—
240C2×Dic3—63no—
241C2×Dic3—123no—
242C2×Dic3—123no—
243C2×Dic3—124no—
244C2×Dic3—1212no—
245D12—224no—
246C4×D3—1212no—
247C4×D3—124no—
248C2×C32#52513yes—
249C2×C32#52513yes—
250C2×C32C2×#12711yescharacteristic
251C3×D3—46no—
252C3×D3—42no—
253C24—31no—
254C24—33no—
255C2×D4—612no—
256C2×D4—66no—
257C2×D4—186no—
258C2×D4—186no—
259C2×D4—186no—
260C22×C4—31no—
261C22×C4—33no—
262C22×C4—91no—
263C22×C4—93no—
264C22×C4—186no—
265C22×C4—186no—
266C22×C4—1812no—
267C22×C4C2×D3213yes—
268C4⋊C4—66no—
269C4⋊C4—186no—
270C22⋊C4—66no—
271C22⋊C4—66no—
272C22⋊C4—1812no—
273C42—912no—
274C22×C3—23no—
275C22×C3—23no—
276C22×C3—21no—
277C22×C3—612no—
278C22×C3—66no—
279C22×C3—66no—
280C22×C3—123no—
281C22×C3—121no—
282C22×C3—123no—
283C22×C3—123no—
284C22×C3—126no—
285C22×C3C2×D3×D413yes—
286C22×C3C2×D3×D413yes—
287C22×C3C2×#23713yes—
288C22×C3C2×#23911yescharacteristic
289C22×C3D3×#4113yes—
290C22×C3D3×#4111yescharacteristic
291C2×D3—212no—
292C2×D3—26no—
293C2×D3—26no—
294C2×D3—43no—
295C2×D3—43no—
296C2×D3—41no—
297C2×D3—43no—
298C2×D3—46no—
299C3×C4—26no—
300C3×C4—26no—
301C3×C4—46no—
302C3×C4—123no—
303C3×C4—121no—
304Dic3—34no—
305Dic3—34no—
306Dic3—41no—
307Dic3—43no—
308Dic3—64no—
309Dic3—66no—
310Dic3—66no—
311Dic3—126no—
312C32#239711yescharacteristic, complemented, Sylow
313C23—36no—
314C23—32no—
315C23—63no—
316C23—63no—
317C23—66no—
318C23—66no—
319C23—63no—
320C23—63no—
321C23C22×D3211yescharacteristic
322D4—624no—
323D4—1824no—
324C2×C4—26no—
325C2×C4—63no—
326C2×C4—63no—
327C2×C4—66no—
328C2×C4—96no—
329C2×C4—96no—
330C2×C4—183no—
331C2×C4—183no—
332C2×C4—364no—
333C2×C4—3612no—
334C2×C4#380216yes—
335C2×C3—23no—
336C2×C3—23no—
337C2×C3—21no—
338C2×C3—122no—
339C2×C3—126no—
340C2×C3#558613yes—
341C2×C3#560613yes—
342C2×C3#562713yes—
343C2×C3#565613yes—
344C2×C3D3×#12711yescharacteristic
345C2×C3D3×#12711yescharacteristic
346D3—46no—
347D3—42no—
348C22—612no—
349C22—66no—
350C22—66no—
351C22—123no—
352C22—123no—
353C22—126no—
354C22—121no—
355C22—123no—
356C22C2×#380213yes—
357C22D3×#23713yes—
358C22D3×#23911yescharacteristic
359C4—26no—
360C4—94no—
361C4—121no—
362C4—123no—
363C4—186no—
364C3—21no—
365C3#7666711yescharacteristic, complemented
366C3#7801911yescharacteristic, complemented
367C2—126no—
368C2—122no—
369C2#1059400811yescharacteristic
370C2#1059408213yes—
371C2#1059463213yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
hypercenter#95D32
hypocenterC32#2397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63902C2semidirect
2. C2×#63898C2semidirect
3. #10592347C2semidirect
4. C3×#4677C2semidirect
5. C3×#4671C2semidirect
6. #10591389C2semidirect
7. #10591324C2semidirect
34. #4677D3semidirect
35. #4671D3semidirect
54. C4×C3⋊Dic3D4semidirect
312. C32#2397semidirect
365. C3#76667semidirect
366. C3#78019semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
C2×#638982
#105923472
C3×#46772
C3×#46712
#105913892
#105913242
#780193
#766673