Finite Group Databasebeta

← #11781750

Subgroups — #11781750

Order 1152.

410 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×#4848C211yesmaximal, characteristic, complemented
2#10590367C211yesmaximal, characteristic, complemented
3#10590350C211yesmaximal, characteristic
4#10590258C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71025—31nomaximal
9#68550—31nomaximal
10#64083C2211yescharacteristic
11C2×C3×#204—21no—
12C3×#874C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C2×#3717—21no—
15C2×#3714—21no—
16C2×#3714—21no—
17C32×C4⋊C8C2211yescharacteristic
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×#821—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22Dic3⋊(C3⋊C8)—21no—
23#63564—21no—
24#63554—21no—
25C3×#460—31no—
26#5073—31no—
27#5027—31no—
28#5024—31no—
29#4848—31no—
30#4848D311yescharacteristic, complemented
31#4695—31no—
32#4679—31no—
33C3×#334—31no—
34#4544—31no—
35#4485—31no—
36#4485—31no—
37#4485—31no—
38#4485—61no—
39#4480D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×#204—42no—
57#3717—42no—
58#3714—42no—
59#3714—42no—
60#1688—91noSylow
61C2×C3×SD16—61no—
62C3×#127—31no—
63C3×C4×Q8—31no—
64C2×#215—61no—
65C2×#213—61no—
66C2×#213—61no—
67C2×D24—61no—
68C2×D24—61no—
69C2×#204—21no—
70C2×#204—61no—
71#874—31no—
72#874—31no—
73#874—61no—
74#874C2×D311yescharacteristic
75C4×Dic6C2×D311yescharacteristic
76C3×C4⋊C8—21no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4⋊C8C2×D311yescharacteristic
80C3×#102—61no—
81C3×C4×C8—31no—
82#821—21no—
83#821—61no—
84#815—61no—
85Dic3⋊C8—61no—
86#809—61no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92#803—61no—
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊D3—41no—
95C22×C3×D3—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C4⋊(C3⋊D3)—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—81no—
104C2×C3×Dic3—21no—
105C2×C3×Dic3—21no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—81no—
111C3×Dic6—21no—
112C3×Dic6—21no—
113C32×C8—41no—
114C3⋊(C3⋊C8)—41no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8SD1612yescomplemented
118#493—91no—
119#460—31no—
120#460—91no—
121#446—91no—
122#334—31no—
123#331—91no—
124#331—91no—
125C2×C3×Q8—31no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—62no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—121no—
140C2×D12—121no—
141C2×Dic6#6711yescharacteristic
142C3×SD16—122no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—31no—
146C2×C3×C8—31no—
147C2×C3×C8—41no—
148C2×C3×C8—61no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—61no—
151C3×C42—21no—
152C3×C42—61no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
155#215—122no—
156#213—122no—
157#213—122no—
158C4⋊Dic3#6711yescharacteristic
159Dic3⋊C4—21no—
160C4×Dic3—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—121no—
165C2×C3⋊C8D1211yescharacteristic
166C2×C3⋊C8D1211yescharacteristic
167D24—122no—
168D24—122no—
169#204—42no—
170#204—122no—
171C22×C32#12111yescharacteristic
172C2×C3⋊D3—81no—
173C2×C3⋊D3—81no—
174C2×C3⋊D3—81no—
175C2×C3×D3—81no—
176C2×C3×D3—81no—
177C2×C3×D3—81no—
178C32×C4—21no—
179C32×C4C2×SD1611yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C32×C4AGL(1,ℤ/8)11yescharacteristic
182C32×C4AGL(1,ℤ/8)11yescharacteristic
183C3×Dic3—41no—
184C3×Dic3—41no—
185C2×SD16—61no—
186C2×SD16—181no—
187C2×D8—181no—
188C2×D8—181no—
189#127—31no—
190#127—91no—
191C4×Q8—31no—
192C4⋊C8—31no—
193C4⋊C8—91no—
194C4⋊C8—181no—
195C4⋊C8D3211yescharacteristic
196#102—61no—
197#102—181no—
198#97—181no—
199C4×C8—31no—
200C23×C3—121no—
201C22×D3—41no—
202C22×D3—122no—
203C22×D3—121no—
204C22×D3—121no—
205C3×Q8—61no—
206C3×Q8—61no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—121no—
210C3×D4—121no—
211C3×D4—241no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—61no—
216C2×C3×C4—61no—
217C2×C3×C4C2×D1211yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4#23711yescharacteristic
221C2×C3×C4#23911yescharacteristic
222C2×C3×C4C2×#6711yescharacteristic
223C2×Dic3—21no—
224C2×Dic3—21no—
225D12—41no—
226D12—41no—
227D12—41no—
228D12—41no—
229D12—81no—
230D12—121no—
231D12—121no—
232D12—121no—
233D12—121no—
234D12—121no—
235D12—121no—
236D12—121no—
237D12—121no—
238D12—241no—
239D12—241no—
240D12—241no—
241D12—241no—
242D12—241no—
243D12—241no—
244D12—242no—
245Dic6—21no—
246Dic6—21no—
247C3×C8—32no—
248C3×C8—41no—
249C3×C8—41no—
250C3×C8—61no—
251C3×C8—81no—
252C3×C8—121no—
253C3⋊C8—21no—
254C3⋊C8—41no—
255C3⋊C8—121no—
256C3⋊C8—121no—
257C3⋊C8—241no—
258C3⋊C8#20412yescomplemented
259C2×C32#46011yescharacteristic
260C2×C32#46911yescharacteristic
261C2×C32#47211yescharacteristic
262C3⋊D3—161no—
263C3×D3—161no—
264C2×Q8—31no—
265C2×D4—61no—
266C2×D4—61no—
267C2×D4—61no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—181no—
271SD16—122no—
272SD16—362no—
273D8—362no—
274D8—362no—
275C2×C8—21no—
276C2×C8—31no—
277C2×C8—31no—
278C2×C8—61no—
279C2×C8—181no—
280C4⋊C4—31no—
281C4⋊C4—61no—
282C42—61no—
283C42C2×D3211yescharacteristic
284C22×C3—21no—
285C22×C3—241no—
286C22×C3—241no—
287C22×C3—241no—
288C22×C3#89511yescharacteristic
289C22×C3#93911yescharacteristic
290C2×D3—81no—
291C2×D3—81no—
292C2×D3—81no—
293C2×D3—242no—
294C2×D3—242no—
295C2×D3—242no—
296C2×D3—241no—
297C2×D3—241no—
298C2×D3—241no—
299C2×D3—241no—
300C2×D3—241no—
301C2×D3—241no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—121no—
310C3×C4—121no—
311C3×C4C2×#20411yescharacteristic
312C3×C4#90811yescharacteristic
313C3×C4D3×SD1611yescharacteristic
314C3×C4#91411yescharacteristic
315C3×C4#91411yescharacteristic
316C3×C4#91411yescharacteristic
317C3×C4#93211yescharacteristic
318C3×C4#94911yescharacteristic
319Dic3—41no—
320Dic3—41no—
321C32#168811yescharacteristic, complemented, Sylow
322C23—121no—
323C23—361no—
324Q8—61no—
325Q8—61no—
326D4—121no—
327D4—121no—
328D4—121no—
329D4—121no—
330D4—241no—
331D4—361no—
332D4—361no—
333D4—361no—
334D4—361no—
335D4—721no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4#379611yescharacteristic
339C2×C4D3×D1211yescharacteristic
340C2×C4D3×#6711yescharacteristic
341C8—32no—
342C8—41no—
343C8—61no—
344C8—121no—
345C8—361no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—481no—
350C2×C3#484811yescharacteristic
351C2×C3#486511yescharacteristic
352C2×C3#489711yescharacteristic
353C2×C3#503911yescharacteristic
354C2×C3#516311yescharacteristic
355C2×C3#519911yescharacteristic
356D3—161no—
357D3—482no—
358D3—481no—
359D3—481no—
360C22—241no—
361C22—241no—
362C22—241no—
363C22—721no—
364C22—721no—
365C22—721no—
366C22#6388611yescharacteristic
367C4—21no—
368C4—121no—
369C4—121no—
370C4D3×#20411yescharacteristic
371C4#6379411yescharacteristic
372C4#6393411yescharacteristic
373C4#6393911yescharacteristic
374C3—21no—
375C3#6855011yescharacteristic, complemented
376C3#7102511yescharacteristic, complemented
377C2—481no—
378C2—1441no—
379C2#1059058611yescharacteristic
380C2#1059079911yescharacteristic
381C2#1059098411yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10590350C2
hypercenterC4⋊C8D32
hypocenterC32#1688
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×#4848C2semidirect
2. #10590367C2semidirect
4. #10590258C2semidirect
5. #10589351C2semidirect
6. C3×#4480C2semidirect
7. #10589090C2semidirect
30. #4848D3semidirect
39. #4480D3semidirect
117. C3×C3⋊C8SD16semidirect
258. C3⋊C8#204semidirect
321. C32#1688semidirect
375. C3#68550semidirect
376. C3#71025semidirect

Maximal subgroups

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

subgroupindex
C3×#48482
#105903672
#105903502
#105902582
#105893512
C3×#44802
#105890902
#710253
#685503