Finite Group Databasebeta

← #11808243

Subgroups — #11808243

Order 1152.

1979 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 1979 conjugacy classes of subgroups — too many to draw. Only its 254 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×#63879C213yesmaximal, complemented
3#10592929C211yesmaximal, characteristic, complemented
4C3×#5231C211yesmaximal, characteristic, complemented
5#10591389C213yesmaximal, complemented
6#10591302C213yesmaximal, complemented
7#10591237C213yesmaximal, complemented
8#84095—31nomaximal
9#76777—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#239—212no—
12C22×C3×D12C2213yes—
13C22×C3×C4×D3C2213yes—
14C22×#625C2213yes—
15C22×D3×Dic3C2211yescharacteristic
16C2×#3750C2213yes—
17C2×C3×(C2×D3)⋊C4C2213yes—
18C2×(C2×D3)⋊Dic3C2216yes—
19C2×(C2×D3)⋊Dic3C2213yes—
20C2×Dic32C2213yes—
21#63879—212no—
22#63658C2213yes—
23C3×C3⋊#95C2213yes—
24C22×C3×#41—31no—
25C22×#239D311yescharacteristic, complemented
26C2×C4×#67—33no—
27C2×#67⋊C4—33no—
28C3×#393—31no—
29#5231D311yescharacteristic, complemented
30#5230—31no—
31#5230—31no—
32#5230—61no—
33#5223—33no—
34#5222—33no—
35C4×#217—33no—
36#4960—33no—
37#4672—33no—
38#4666—33no—
39C23×C3×D3C2313yes—
40C23×C3×D3C2311yescharacteristic
41C2×C32×Q8—26no—
42C22×C32×C4C2313yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3⋊Dic3C2313yes—
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×#625—26no—
53C2×#625—26no—
54C2×#625—26no—
55C2×D3×Dic3—26no—
56#3750—26no—
57C3×(C2×D3)⋊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—
69C22×#67—33no—
70C23×Dic3—31no—
71C2×#239—212no—
72C22×D12C2×D313yes—
73C22×C4×D3—31no—
74C22×C4×D3C2×D313yes—
75C2×C3×C22⋊C4—33no—
76C2×#217—36no—
77C2×#217—33no—
78C4×#67—612no—
79C2×(C2×D3)⋊C4—36no—
80C2×(C2×D3)⋊C4—33no—
81C2×(C2×D3)⋊C4C2×D313yes—
82C2×Dic3⋊C4—33no—
83C2×Dic3⋊C4—33no—
84C2×Dic3⋊C4—63no—
85C2×C4×Dic3—33no—
86C2×C4×Dic3—33no—
87#67⋊C4—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—26no—
96C22×C3×D3—26no—
97C22×C3×D3—23no—
98C22×C3×D3—23no—
99C22×C3×D3—23no—
100C22×C3×D3C2×D416yes—
101C22×C3×D3#4112yescomplemented
102C32×Q8—28no—
103C2×C32×C4—26no—
104C2×C32×C4C2×D416yes—
105C2×C3⋊Dic3—23no—
106C2×C3⋊Dic3—23no—
107C2×C3⋊Dic3—23no—
108C2×C3⋊Dic3#4116yescomplemented
109C2×C3×Dic3—23no—
110C2×C3×Dic3—26no—
111C2×C3×Dic3C2×D416yes—
112C3×D12—224no—
113C3×C4×D3—224no—
114#625—224no—
115D3×Dic3—44no—
116C22×#41—31no—
117C2×C4×D4—93no—
118#395—91no—
119#394—93no—
120#393—31no—
121#392—93no—
122C4×C22⋊C4—93no—
123C24×C3—33no—
124C24×C3—31no—
125C23×D3C22×D311yescharacteristic
126C23×D3C22×D313yes—
127C3×#41—632no—
128C2×C3×Q8—26no—
129C2×C3×Q8—26no—
130C2×C3×Q8—46no—
131C2×C3×D4—612no—
132C2×C3×D4—66no—
133C22×C3×C4—23no—
134C22×C3×C4—31no—
135C22×C3×C4—312no—
136C22×C3×C4—33no—
137C22×C3×C4—612no—
138C22×C3×C4C22×D313yes—
139C22×C3×C4C22×D313yes—
140C2×#67—66no—
141C2×#67—66no—
142C2×#67—66no—
143C2×#67—66no—
144C2×#67—66no—
145C2×#67—66no—
146C22×Dic3—33no—
147C22×Dic3—33no—
148C22×Dic3—31no—
149C22×Dic3—31no—
150C22×Dic3—63no—
151C22×Dic3—61no—
152C22×Dic3—66no—
153C22×Dic3C22×D313yes—
154C22×Dic3C22×D311yescharacteristic
155#239—232no—
156C2×D12—212no—
157C2×D12—26no—
158C2×C4×D3—212no—
159C2×C4×D3—66no—
160C2×C4×D3#67112yescomplemented
161C3×C22⋊C4—66no—
162#217—612no—
163#217—66no—
164(C2×D3)⋊C4—26no—
165(C2×D3)⋊C4—612no—
166(C2×D3)⋊C4—66no—
167Dic3⋊C4—66no—
168Dic3⋊C4—66no—
169Dic3⋊C4—126no—
170C4×Dic3—66no—
171C4×Dic3—66no—
172C22×C32C22×D413yes—
173C22×C32C2×#4111yescharacteristic
174C22×C32C2×#4113yes—
175C2×C3×D3—26no—
176C2×C3×D3—26no—
177C2×C3×D3—26no—
178C2×C3×D3—26no—
179C2×C3×D3—41no—
180C2×C3×D3—46no—
181C2×C3×D3—43no—
182C2×C3×D3—46no—
183C32×C4—26no—
184C3⋊Dic3—26no—
185C3⋊Dic3—41no—
186C3×Dic3—43no—
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—93no—
196C2×C22⋊C4—33no—
197C2×C22⋊C4—93no—
198C2×C22⋊C4—96no—
199C2×C42—93no—
200#95—33no—
201#95—93no—
202C23×C3—21no—
203C23×C3—36no—
204C23×C3—32no—
205C23×C3—66no—
206C23×C3—63no—
207C23×C3—66no—
208C23×C3—63no—
209C23×C3—63no—
210C23×C3—63no—
211C23×C3C23×D311yescharacteristic
212C23×C3C23×D311yescharacteristic
213C22×D3—23no—
214C22×D3—26no—
215C22×D3—23no—
216C22×D3—23no—
217C22×D3—23no—
218C22×D3—26no—
219C22×D3#23912yescomplemented
220C22×D3C2×#6716yes—
221C3×Q8—28no—
222C3×Q8—28no—
223C3×Q8—48no—
224C3×D4—624no—
225C2×C3×C4—26no—
226C2×C3×C4—26no—
227C2×C3×C4—26no—
228C2×C3×C4—36no—
229C2×C3×C4—46no—
230C2×C3×C4—624no—
231C2×C3×C4—66no—
232C2×C3×C4—63no—
233C2×C3×C4D3×D416yes—
234C2×C3×C4C2×#6716yes—
235#67—624no—
236#67—624no—
237C2×Dic3—23no—
238C2×Dic3—26no—
239C2×Dic3—36no—
240C2×Dic3—36no—
241C2×Dic3—66no—
242C2×Dic3—63no—
243C2×Dic3—63no—
244C2×Dic3—63no—
245C2×Dic3—63no—
246C2×Dic3—63no—
247C2×Dic3—63no—
248C2×Dic3—123no—
249C2×Dic3—123no—
250C2×Dic3—123no—
251C2×Dic3—124no—
252C2×Dic3C2×#6716yes—
253D12—224no—
254C4×D3—224no—
255C4×D3—124no—
256C2×C32C2×#12011yescharacteristic
257C2×C32#52513yes—
258C2×C32#53213yes—
259C3×D3—46no—
260C3×D3—42no—
261C24—31no—
262C24—33no—
263#41—632no—
264C2×Q8—26no—
265C2×D4—612no—
266C2×D4—66no—
267C2×D4—186no—
268C2×D4—186no—
269C2×D4—186no—
270C22×C4—31no—
271C22×C4—312no—
272C22×C4—33no—
273C22×C4—612no—
274C22×C4—93no—
275C22×C4—91no—
276C22×C4—186no—
277C22×C4C2×D3213yes—
278C4⋊C4—186no—
279C22⋊C4—66no—
280C22⋊C4—1812no—
281C22⋊C4—186no—
282C42—186no—
283C22×C3—21no—
284C22×C3—23no—
285C22×C3—23no—
286C22×C3—66no—
287C22×C3—66no—
288C22×C3—66no—
289C22×C3—66no—
290C22×C3—126no—
291C22×C3—123no—
292C22×C3—121no—
293C22×C3—126no—
294C22×C3C2×D3×D413yes—
295C22×C3C2×#23911yescharacteristic
296C22×C3D3×#4111yescharacteristic
297C22×C3D3×#4113yes—
298C22×C3D3×#4113yes—
299C22×C3C22×#6713yes—
300C2×D3—26no—
301C2×D3—26no—
302C2×D3—26no—
303C2×D3—26no—
304C2×D3—43no—
305C2×D3—46no—
306C2×D3—46no—
307C2×D3—41no—
308C3×C4—26no—
309C3×C4—26no—
310C3×C4—34no—
311C3×C4—46no—
312C3×C4—123no—
313Dic3—43no—
314Dic3—66no—
315Dic3—66no—
316Dic3—126no—
317Dic3—121no—
318Dic3—121no—
319Dic3—241no—
320Dic3#95314yes—
321C32#238811yescharacteristic, complemented, Sylow
322C23—32no—
323C23—36no—
324C23—63no—
325C23—66no—
326C23—63no—
327C23—63no—
328C23—63no—
329C23—66no—
330C23C22×D3211yescharacteristic
331Q8—28no—
332D4—624no—
333D4—1824no—
334C2×C4—26no—
335C2×C4—36no—
336C2×C4—624no—
337C2×C4—66no—
338C2×C4—63no—
339C2×C4—96no—
340C2×C4—183no—
341C2×C4—183no—
342C2×C4—183no—
343C2×C4—364no—
344C2×C4D3×#6716yes—
345C2×C3—23no—
346C2×C3—23no—
347C2×C3—21no—
348C2×C3—122no—
349C2×C3—126no—
350C2×C3D3×#12011yescharacteristic
351C2×C3#562713yes—
352C2×C3#566813yes—
353C2×C3#582813yes—
354C2×C3#583213yes—
355C2×C3C2×#95311yescharacteristic
356D3—46no—
357D3—42no—
358C22—66no—
359C22—66no—
360C22—66no—
361C22—66no—
362C22—126no—
363C22—123no—
364C22—126no—
365C22—121no—
366C22D3×#23911yescharacteristic
367C22#6431913yes—
368C22C2×D3×#6713yes—
369C4—26no—
370C4—34no—
371C4—123no—
372C4—186no—
373C4—361no—
374C3—21no—
375C3#7677711yescharacteristic, complemented
376C3#8409511yescharacteristic, complemented
377C2—126no—
378C2—122no—
379C2#1059535913yes—
380C2#1059542413yes—
381C2D3×#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×#63879C2semidirect
3. #10592929C2semidirect
4. C3×#5231C2semidirect
5. #10591389C2semidirect
6. #10591302C2semidirect
7. #10591237C2semidirect
25. C22×#239D3semidirect
29. #5231D3semidirect
51. C2×C3×C4×D3D4semidirect
101. C22×C3×D3#41semidirect
108. C2×C3⋊Dic3#41semidirect
160. C2×C4×D3#67semidirect
219. C22×D3#239semidirect
321. C32#2388semidirect
375. C3#76777semidirect
376. 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×#638792
#105929292
C3×#52312
#105913892
#105913022
#105912372
#840953
#767773