Finite Group Databasebeta

← #11808241

Subgroups — #11808241

Order 1152.

1989 conjugacy classes of subgroups; only the 258 normal subgroups are shown.

normal subgroups only

This group has 1989 conjugacy classes of subgroups — too many to draw. Only its 258 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
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C2×#63904C213yesmaximal, complemented
3#10592930C211yesmaximal, characteristic, complemented
4C3×#5230C211yesmaximal, characteristic, complemented
5#10591391C213yesmaximal, complemented
6#10591300C213yesmaximal, complemented
7#10591237C213yesmaximal, complemented
8#84095—31nomaximal
9#77169—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#239—212no—
12C22×C3×D12C2213yes—
13C22×C3×C4×D3C2213yes—
14C22×#626C2213yes—
15C22×#624C2211yescharacteristic
16C2×#3752C2213yes—
17C2×C3×Dic3⋊C4C2213yes—
18C2×(C2×D3)⋊Dic3C2216yes—
19C2×(C2×D3)⋊Dic3C2213yes—
20C2×Dic32C2213yes—
21#63904—212no—
22#63658C2213yes—
23C3×C3⋊#95C2213yes—
24C22×C3×#41—31no—
25C22×#239D311yescharacteristic, complemented
26C2×C4×#67—33no—
27C2×#893—33no—
28C3×#395—31no—
29#5231—31no—
30#5231—31no—
31#5231—61no—
32#5230D311yescharacteristic, complemented
33#5223—33no—
34#5222—33no—
35C4×#217—33no—
36#4991—33no—
37#4671—33no—
38#4666—33no—
39C23×C3⋊D3C2311yescharacteristic
40C23×C3×D3C2313yes—
41C2×C32×Q8—26no—
42C22×C32×C4C2313yes—
43C22×C3⋊Dic3C2313yes—
44C22×C3×Dic3C2311yescharacteristic
45C22×C3×Dic3C2313yes—
46C22×C3×Dic3C2311yescharacteristic
47C3×#239—232no—
48C2×C3×D12—212no—
49C2×C3×D12—26no—
50C2×C3×C4×D3—212no—
51C2×C3×C4×D3D4112yescomplemented
52C2×#626—26no—
53C2×#626—26no—
54C2×#626—26no—
55C2×#624—26no—
56#3752—26no—
57C3×Dic3⋊C4—26no—
58(C2×D3)⋊Dic3—26no—
59(C2×D3)⋊Dic3—212no—
60Dic32—26no—
61#2388—91noSylow
62C2×C3×#41—612no—
63C22×C3×Q8—21no—
64C22×C3×Q8C2×D311yescharacteristic
65C22×C3×Q8C2×D311yescharacteristic
66C22×C3×D4—33no—
67C23×C3×C4—33no—
68C22×#67—33no—
69C2×#239—212no—
70C22×D12—33no—
71C22×D12C2×D313yes—
72C22×C4×D3—31no—
73C22×C4×D3—31no—
74C22×C4×D3C2×D313yes—
75C2×C3×C4⋊C4—33no—
76C2×#217—36no—
77C2×#217—33no—
78C4×#67—612no—
79C2×(C2×D3)⋊C4—36no—
80C2×(C2×D3)⋊C4—33no—
81C2×(C2×D3)⋊C4—33no—
82C2×(C2×D3)⋊C4—33no—
83C2×(C2×D3)⋊C4—63no—
84C2×Dic3⋊C4C2×D313yes—
85C2×C4×Dic3—33no—
86C2×C4×Dic3—33no—
87#893—612no—
88C3×#95—33no—
89C3⋊#95—33no—
90C3⋊#95—33no—
91C3⋊#95—63no—
92C3⋊#95C2×D313yes—
93C23×C32C2411yescharacteristic
94C22×C3⋊D3—23no—
95C22×C3⋊D3—23no—
96C22×C3⋊D3#4112yescomplemented
97C22×C3×D3—26no—
98C22×C3×D3—26no—
99C22×C3×D3—23no—
100C22×C3×D3—23no—
101C22×C3×D3C2×D416yes—
102C32×Q8—28no—
103C2×C32×C4—26no—
104C2×C32×C4C2×D416yes—
105C2×C3⋊Dic3—23no—
106C2×C3⋊Dic3—26no—
107C2×C3×Dic3—23no—
108C2×C3×Dic3—23no—
109C2×C3×Dic3—23no—
110C2×C3×Dic3C2×D416yes—
111C2×C3×Dic3#4116yescomplemented
112C3×D12—224no—
113C3×C4×D3—224no—
114#626—224no—
115#624—44no—
116C22×#41—31no—
117C2×C4×D4—93no—
118#395—31no—
119#394—93no—
120#393—91no—
121#392—93no—
122C4×C22⋊C4—93no—
123C24×C3—33no—
124C23×D3—31no—
125C23×D3—31no—
126C23×D3—61no—
127C23×D3C22×D313yes—
128C3×#41—632no—
129C2×C3×Q8—26no—
130C2×C3×Q8—26no—
131C2×C3×Q8—46no—
132C2×C3×D4—612no—
133C2×C3×D4—66no—
134C22×C3×C4—23no—
135C22×C3×C4—31no—
136C22×C3×C4—33no—
137C22×C3×C4—312no—
138C22×C3×C4—31no—
139C22×C3×C4—612no—
140C22×C3×C4C22×D313yes—
141C22×C3×C4C22×D313yes—
142C2×#67—66no—
143C2×#67—66no—
144C2×#67—66no—
145C22×Dic3—33no—
146C22×Dic3—33no—
147C22×Dic3—63no—
148C22×Dic3C22×D311yescharacteristic
149C22×Dic3C22×D313yes—
150C22×Dic3C22×D311yescharacteristic
151#239—232no—
152C2×D12—212no—
153C2×D12—26no—
154C2×D12—66no—
155C2×D12—66no—
156C2×D12—66no—
157C2×C4×D3—212no—
158C2×C4×D3—66no—
159C2×C4×D3—66no—
160C2×C4×D3#67112yescomplemented
161C3×C4⋊C4—66no—
162#217—66no—
163#217—612no—
164(C2×D3)⋊C4—612no—
165(C2×D3)⋊C4—66no—
166(C2×D3)⋊C4—66no—
167(C2×D3)⋊C4—66no—
168(C2×D3)⋊C4—126no—
169Dic3⋊C4—26no—
170C4×Dic3—66no—
171C4×Dic3—66no—
172C22×C32C22×D413yes—
173C22×C32C2×#4113yes—
174C22×C32C2×#4111yescharacteristic
175C2×C3⋊D3—26no—
176C2×C3⋊D3—41no—
177C2×C3⋊D3—43no—
178C2×C3×D3—26no—
179C2×C3×D3—26no—
180C2×C3×D3—26no—
181C2×C3×D3—46no—
182C2×C3×D3—46no—
183C32×C4—26no—
184C3⋊Dic3—43no—
185C3×Dic3—26no—
186C3×Dic3—41no—
187C3×Dic3#12014yes—
188C2×#41—612no—
189C22×Q8D3211yescharacteristic
190C22×D4—33no—
191C22×D4—93no—
192C23×C4—33no—
193C23×C4—91no—
194C4×D4—1812no—
195C2×C4⋊C4—33no—
196C2×C22⋊C4—93no—
197C2×C22⋊C4—96no—
198C2×C22⋊C4—93no—
199C2×C42—93no—
200#95—33no—
201#95—93no—
202C23×C3—21no—
203C23×C3—36no—
204C23×C3—66no—
205C23×C3—66no—
206C23×C3—63no—
207C23×C3—63no—
208C23×C3C23×D311yescharacteristic
209C23×C3C23×D311yescharacteristic
210C22×D3—26no—
211C22×D3—23no—
212C22×D3—23no—
213C22×D3—26no—
214C22×D3—32no—
215C22×D3—32no—
216C22×D3—62no—
217C22×D3—63no—
218C22×D3—63no—
219C22×D3—63no—
220C22×D3—63no—
221C22×D3—123no—
222C22×D3—123no—
223C22×D3C2×#6716yes—
224C3×Q8—28no—
225C3×Q8—28no—
226C3×Q8—48no—
227C3×D4—624no—
228C2×C3×C4—26no—
229C2×C3×C4—26no—
230C2×C3×C4—26no—
231C2×C3×C4—36no—
232C2×C3×C4—36no—
233C2×C3×C4—46no—
234C2×C3×C4—624no—
235C2×C3×C4—63no—
236C2×C3×C4—63no—
237C2×C3×C4—63no—
238C2×C3×C4D3×D416yes—
239C2×C3×C4C2×#6716yes—
240#67—624no—
241C2×Dic3—23no—
242C2×Dic3—23no—
243C2×Dic3—23no—
244C2×Dic3—63no—
245C2×Dic3—66no—
246C2×Dic3—66no—
247C2×Dic3—63no—
248C2×Dic3—123no—
249C2×Dic3—126no—
250C2×Dic3#23916yescomplemented
251C2×Dic3C2×#6716yes—
252D12—224no—
253D12—624no—
254C4×D3—224no—
255C4×D3—124no—
256C4×D3—124no—
257C2×C32C2×#12011yescharacteristic
258C2×C32#52513yes—
259C2×C32#53213yes—
260C3⋊D3—42no—
261C3×D3—46no—
262C24—33no—
263C24—91no—
264#41—632no—
265C2×Q8—26no—
266C2×D4—612no—
267C2×D4—66no—
268C2×D4—186no—
269C2×D4—186no—
270C2×D4—186no—
271C22×C4—31no—
272C22×C4—33no—
273C22×C4—312no—
274C22×C4—31no—
275C22×C4—612no—
276C22×C4—93no—
277C22×C4—186no—
278C22×C4C2×D3213yes—
279C4⋊C4—66no—
280C22⋊C4—1812no—
281C22⋊C4—186no—
282C22⋊C4—186no—
283C42—186no—
284C22×C3—23no—
285C22×C3—21no—
286C22×C3—23no—
287C22×C3—66no—
288C22×C3—66no—
289C22×C3—66no—
290C22×C3—126no—
291C22×C3—126no—
292C22×C3C2×D3×D413yes—
293C22×C3C2×#23913yes—
294C22×C3D3×#4113yes—
295C22×C3D3×#4111yescharacteristic
296C22×C3D3×#4111yescharacteristic
297C22×C3C22×#6713yes—
298C2×D3—26no—
299C2×D3—26no—
300C2×D3—26no—
301C2×D3—46no—
302C2×D3—46no—
303C2×D3—66no—
304C2×D3—66no—
305C2×D3—126no—
306C2×D3—123no—
307C2×D3—123no—
308C2×D3—121no—
309C2×D3—121no—
310C2×D3—243no—
311C2×D3—241no—
312C3×C4—26no—
313C3×C4—26no—
314C3×C4—34no—
315C3×C4—46no—
316C3×C4—66no—
317C3×C4—121no—
318Dic3—26no—
319Dic3—41no—
320Dic3—123no—
321Dic3—123no—
322Dic3—243no—
323Dic3#95314yes—
324C32#238811yescharacteristic, complemented, Sylow
325C23—36no—
326C23—66no—
327C23—63no—
328C23—63no—
329C23—66no—
330C23—92no—
331C23—183no—
332C23—183no—
333C23C22×D3211yescharacteristic
334Q8—28no—
335D4—624no—
336D4—1824no—
337C2×C4—26no—
338C2×C4—36no—
339C2×C4—36no—
340C2×C4—624no—
341C2×C4—63no—
342C2×C4—63no—
343C2×C4—63no—
344C2×C4—186no—
345C2×C4—183no—
346C2×C4—364no—
347C2×C4D3×#6716yes—
348C2×C3—23no—
349C2×C3—23no—
350C2×C3—21no—
351C2×C3—126no—
352C2×C3D3×#12011yescharacteristic
353C2×C3#562713yes—
354C2×C3#572513yes—
355C2×C3#582813yes—
356C2×C3#583213yes—
357C2×C3C2×#95311yescharacteristic
358D3—46no—
359D3—122no—
360D3—122no—
361D3—242no—
362C22—66no—
363C22—66no—
364C22—66no—
365C22—126no—
366C22—126no—
367C22—186no—
368C22—363no—
369C22—361no—
370C22D3×#23913yes—
371C22#6431911yescharacteristic
372C22C2×D3×#6713yes—
373C4—26no—
374C4—34no—
375C4—66no—
376C4—121no—
377C4—363no—
378C3—21no—
379C3#7716911yescharacteristic, complemented
380C3#8409511yescharacteristic, complemented
381C2—126no—
382C2—362no—
383C2#1059536013yes—
384C2#1059542413yes—
385C2D3×#95311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C2×#63904C2semidirect
3. #10592930C2semidirect
4. C3×#5230C2semidirect
5. #10591391C2semidirect
6. #10591300C2semidirect
7. #10591237C2semidirect
25. C22×#239D3semidirect
32. #5230D3semidirect
51. C2×C3×C4×D3D4semidirect
96. C22×C3⋊D3#41semidirect
111. C2×C3×Dic3#41semidirect
160. C2×C4×D3#67semidirect
250. C2×Dic3#239semidirect
324. C32#2388semidirect
379. C3#77169semidirect
380. C3#84095semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×#639042
#105929302
C3×#52302
#105913912
#105913002
#105912372
#840953
#771693