Finite Group Databasebeta

← #11781313

Subgroups — #11781313

Order 1152.

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

normal subgroups only

This group has 352 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×#4830C211yesmaximal, characteristic, complemented
2#10590364C211yesmaximal, characteristic
3#10590283C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic
5#10589347C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7#10589097C211yesmaximal, characteristic, complemented
8#70940—31nomaximal
9#68410—31nomaximal
10#64078C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3715—21no—
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×Dic3⋊C8—21no—
17C3×C8×Dic3—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63575—21no—
21#63566—21no—
22#63563—21no—
23#63563—21no—
24#63562—21no—
25C3×C8×Q8—31no—
26#5075—31no—
27#5070—31no—
28#5027—31no—
29#5021—31no—
30#4850—31no—
31#4830D311yescharacteristic, complemented
32#4694—31no—
33C3×#331—31no—
34#4485D311yescharacteristic
35#4481—31no—
36#4481—31no—
37#4481—61no—
38#4480—31no—
39#4457—31no—
40C2×#634—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
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
56#3715—42no—
57#1678—91noSylow
58C3×#127—31no—
59C3×C4×Q8—31no—
60C2×#215—61no—
61C2×#214—61no—
62#874C2×D311yescharacteristic
63#869—31no—
64#869—31no—
65#869—61no—
66C4×Dic6C2×D311yescharacteristic
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—61no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4×C8—31no—
73C3×C4×C8—61no—
74#835—61no—
75#832—61no—
76#832—61no—
77#832—61no—
78#821—61no—
79#821—61no—
80#818—61no—
81#816—61no—
82Dic3⋊C8—21no—
83C8×Dic3—21no—
84#809—61no—
85#807—61no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8C2×D311yescharacteristic
91C22×C3×D3—41no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3⋊Dic3—41no—
96#634—81no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C3×D12—41no—
100C3×D12—41no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—81no—
104C3×Dic6—21no—
105C3×Dic6SD1612yes—
106C32×C8—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111#486—91no—
112#477—91no—
113#460—91no—
114C8×Q8—31no—
115#334—91no—
116#333—91no—
117#331—31no—
118C2×C3×Q8—31no—
119C2×C3×D4—61no—
120C2×C3×D4—61no—
121C2×C3×D4—61no—
122C2×D12—21no—
123C2×D12—21no—
124C2×D12—21no—
125C2×Dic6—62no—
126C2×Dic6—61no—
127C2×Dic6—61no—
128C2×Dic6D1211yescharacteristic
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—31no—
132C2×C3×C8—31no—
133C2×C3×C8—41no—
134C2×C3×C8—61no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—61no—
137C3×C42—21no—
138C3×C42—61no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#215—122no—
142#214—122no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—121no—
148C4⋊Dic3—121no—
149C4⋊Dic3D1211yescharacteristic
150Dic3⋊C4—21no—
151C4×Dic3—21no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—121no—
156C2×C3⋊C8#6711yescharacteristic
157C2×C3⋊C8#6711yescharacteristic
158C22×C32#12111yescharacteristic
159C2×C3×D3—81no—
160C2×C3×D3—81no—
161C2×C3×D3—81no—
162C32×C4—21no—
163C32×C4C2×SD1611yescharacteristic
164C32×C4#13511yescharacteristic
165C32×C4#13511yescharacteristic
166C32×C4#13711yescharacteristic
167C3⋊Dic3—81no—
168C3×Dic3—22no—
169C3×Dic3—41no—
170C2×SD16—181no—
171C4⋊Q8—91no—
172#127—31no—
173C4×Q8—31no—
174#107—181no—
175C4⋊C8—31no—
176C4⋊C8—61no—
177C4⋊C8—91no—
178C4⋊C8D3211yescharacteristic
179#103—181no—
180#102—181no—
181#102—181no—
182#102—181no—
183C4×C8—31no—
184C4×C8—61no—
185C23×C3—121no—
186C22×D3—41no—
187C3×Q8—32no—
188C3×Q8—61no—
189C3×D4—121no—
190C3×D4—121no—
191C3×D4—121no—
192C3×D4—121no—
193C3×D4—241no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—61no—
198C2×C3×C4—61no—
199C2×C3×C4C2×D1211yescharacteristic
200C2×C3×C4#23511yescharacteristic
201C2×C3×C4#23511yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4C2×#6711yescharacteristic
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—122no—
208C2×Dic3—121no—
209C2×Dic3—121no—
210D12—41no—
211D12—41no—
212D12—41no—
213D12—41no—
214D12—81no—
215Dic6—21no—
216Dic6—241no—
217Dic6—241no—
218Dic6—242no—
219Dic6#20412yes—
220C3×C8—41no—
221C3×C8—41no—
222C3×C8—61no—
223C3×C8—61no—
224C3×C8—81no—
225C3×C8—121no—
226C3⋊C8—21no—
227C3⋊C8—21no—
228C3⋊C8—41no—
229C3⋊C8—121no—
230C3⋊C8—121no—
231C3⋊C8—241no—
232C2×C32#46411yescharacteristic
233C2×C32#46511yescharacteristic
234C2×C32#47211yescharacteristic
235C3×D3—161no—
236C2×Q8—31no—
237C2×Q8—181no—
238C2×D4—61no—
239C2×D4—61no—
240C2×D4—61no—
241SD16—362no—
242C2×C8—21no—
243C2×C8—31no—
244C2×C8—31no—
245C2×C8—61no—
246C2×C8—181no—
247C4⋊C4—31no—
248C4⋊C4—61no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C42—61no—
252C42C2×D3211yescharacteristic
253C22×C3—21no—
254C22×C3—241no—
255C22×C3—241no—
256C22×C3—241no—
257C22×C3#88411yescharacteristic
258C22×C3#93011yescharacteristic
259C2×D3—81no—
260C2×D3—81no—
261C2×D3—81no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—41no—
269C3×C4—62no—
270C3×C4—121no—
271C3×C4C2×#20411yescharacteristic
272C3×C4#90411yescharacteristic
273C3×C4#91211yescharacteristic
274C3×C4#91211yescharacteristic
275C3×C4D3×SD1611yescharacteristic
276C3×C4#91511yescharacteristic
277C3×C4#94211yescharacteristic
278C3×C4#95011yescharacteristic
279Dic3—22no—
280Dic3—41no—
281Dic3—242no—
282Dic3—241no—
283Dic3—241no—
284C32#167811yescharacteristic, complemented, Sylow
285C23—121no—
286Q8—32no—
287Q8—61no—
288Q8—721no—
289D4—121no—
290D4—121no—
291D4—121no—
292D4—121no—
293D4—241no—
294C2×C4—61no—
295C2×C4—61no—
296C2×C4—361no—
297C2×C4#379811yescharacteristic
298C2×C4D3×D1211yescharacteristic
299C2×C4D3×#6711yescharacteristic
300C8—41no—
301C8—61no—
302C8—61no—
303C8—121no—
304C8—361no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—481no—
309C2×C3#474911yescharacteristic
310C2×C3#476711yescharacteristic
311C2×C3#477811yescharacteristic
312C2×C3#502811yescharacteristic
313C2×C3#511411yescharacteristic
314C2×C3#514211yescharacteristic
315D3—161no—
316C22—241no—
317C22—241no—
318C22—241no—
319C22#6390611yescharacteristic
320C4—21no—
321C4—62no—
322C4—121no—
323C4—721no—
324C4D3×#20411yescharacteristic
325C4#6380711yescharacteristic
326C4#6393311yescharacteristic
327C4#6394611yescharacteristic
328C3—21no—
329C3#6841011yescharacteristic, complemented
330C3#7094011yescharacteristic, complemented
331C2—481no—
332C2#1059053211yescharacteristic
333C2#1059082511yescharacteristic
334C2#1059099711yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#1678
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×#4830C2semidirect
3. #10590283C2semidirect
5. #10589347C2semidirect
7. #10589097C2semidirect
31. #4830D3semidirect
284. C32#1678semidirect
329. C3#68410semidirect
330. C3#70940semidirect

Maximal subgroups

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

subgroupindex
C3×#48302
#105903642
#105902832
#105902732
#105893472
C3×#44852
#105890972
#709403
#684103