Finite Group Databasebeta

← #11781266

Subgroups — #11781266

Order 1152.

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

normal subgroups only

This group has 384 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×#4834C211yesmaximal, characteristic, complemented
2#10590347C211yesmaximal, characteristic
3#10590273C211yesmaximal, characteristic, complemented
4#10590268C211yesmaximal, characteristic, complemented
5#10589347C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7#10589097C211yesmaximal, characteristic, complemented
8#70848—31nomaximal
9#68396—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×D3×C8—21no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C2×#3713—21no—
15C32×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×(C2×D3)⋊C8—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63573—21no—
21#63563—21no—
22#63563—21no—
23#63563—21no—
24#63562—21no—
25C3×C8×D4—31no—
26#5072—31no—
27#5070—31no—
28#5015—31no—
29#5008—31no—
30#4842—31no—
31#4834D311yescharacteristic, complemented
32#4694—31no—
33C3×#331—31no—
34#4485D311yescharacteristic, complemented
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×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×D3×C8—42no—
57#3713—42no—
58#1677—91noSylow
59C22×C3×C8—61no—
60C3×#127—31no—
61C3×C4×D4—31no—
62C2×#213—61no—
63C2×#213—61no—
64C2×D3×C8—21no—
65#874C2×D311yescharacteristic
66C4×D12C2×D311yescharacteristic
67#869—31no—
68#869—31no—
69#869—61no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4⋊C8C2×D311yescharacteristic
74C3×C22⋊C8—61no—
75C3×C4×C8—31no—
76#832—61no—
77#832—61no—
78#832—61no—
79#832—61no—
80#821—61no—
81#821—61no—
82#821—61no—
83(C2×D3)⋊C8—21no—
84#817—61no—
85#809—61no—
86#808—61no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C22×C3×D3—21no—
93C22×C3×D3—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—41no—
98#634—81no—
99C2×C3×Dic3—21no—
100C3×D12—21no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—81no—
106C3×D12SD1612yes—
107C3×C4×D3—41no—
108C3×C4×D3—41no—
109C32×C8—41no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114#486—91no—
115#476—91no—
116#459—91no—
117C8×D4—31no—
118#334—91no—
119#333—91no—
120#331—31no—
121C2×C3×D4—31no—
122C2×C3×D4—61no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C22×C3×C4—61no—
126C2×D12—21no—
127C2×D12—21no—
128C2×D12—21no—
129C2×D12D1211yescharacteristic
130C2×C4×D3—21no—
131C2×Dic6—62no—
132C2×Dic6—61no—
133C2×Dic6—61no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—31no—
137C2×C3×C8—31no—
138C2×C3×C8—41no—
139C2×C3×C8—61no—
140C2×C3×C8—122no—
141C3×C4⋊C4—31no—
142C3×C22⋊C4—61no—
143C3×C42—21no—
144C3×C42C22×D311yescharacteristic
145C3×C42C22×D311yescharacteristic
146#213—122no—
147#213—122no—
148(C2×D3)⋊C4—21no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—121no—
154C4⋊Dic3—121no—
155C4⋊Dic3D1211yescharacteristic
156C2×C3⋊C8—21no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—121no—
160C2×C3⋊C8#6711yescharacteristic
161C2×C3⋊C8#6711yescharacteristic
162D3×C8—42no—
163C22×C32#12111yescharacteristic
164C2×C3×D3—22no—
165C2×C3×D3—41no—
166C2×C3×D3—41no—
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C32×C4—21no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4AGL(1,ℤ/8)11yescharacteristic
175C3⋊Dic3—81no—
176C3×Dic3—41no—
177C2×D8—181no—
178C22×C8—61no—
179C4⋊Q8—91no—
180#127—31no—
181C4×D4—31no—
182#106—181no—
183C4⋊C8—31no—
184C4⋊C8—91no—
185C4⋊C8D3211yescharacteristic
186#102—181no—
187#102—181no—
188#102—181no—
189#102—181no—
190C22⋊C8—61no—
191C4×C8—31no—
192C23×C3—61no—
193C23×C3—121no—
194C22×D3—21no—
195C22×D3—41no—
196C3×D4—32no—
197C3×D4—61no—
198C3×D4—121no—
199C3×D4—121no—
200C3×D4—121no—
201C3×D4—121no—
202C3×D4—241no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—61no—
207C2×C3×C4—121no—
208C2×C3×C4—121no—
209C2×C3×C4C2×D1211yescharacteristic
210C2×C3×C4#23511yescharacteristic
211C2×C3×C4#23511yescharacteristic
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4C2×#6711yescharacteristic
215C2×Dic3—21no—
216C2×Dic3—122no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219D12—21no—
220D12—41no—
221D12—41no—
222D12—41no—
223D12—41no—
224D12—81no—
225D12#20412yes—
226C4×D3—41no—
227C4×D3—41no—
228Dic6—241no—
229Dic6—241no—
230Dic6—242no—
231C3×C8—41no—
232C3×C8—41no—
233C3×C8—61no—
234C3×C8—61no—
235C3×C8—81no—
236C3×C8—121no—
237C3⋊C8—21no—
238C3⋊C8—21no—
239C3⋊C8—41no—
240C3⋊C8—121no—
241C3⋊C8—121no—
242C3⋊C8—241no—
243C2×C32#46311yescharacteristic
244C2×C32#46511yescharacteristic
245C2×C32#47211yescharacteristic
246C3×D3—42no—
247C3×D3—161no—
248C2×Q8—181no—
249C2×D4—31no—
250C2×D4—61no—
251C2×D4—61no—
252C2×D4—61no—
253C22×C4—61no—
254D8—362no—
255C2×C8—21no—
256C2×C8—31no—
257C2×C8—31no—
258C2×C8—61no—
259C2×C8—122no—
260C2×C8—181no—
261C4⋊C4—31no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C22⋊C4—61no—
265C42C2×D3211yescharacteristic
266C22×C3—21no—
267C22×C3—62no—
268C22×C3—121no—
269C22×C3—121no—
270C22×C3—241no—
271C22×C3—241no—
272C22×C3—241no—
273C22×C3#88411yescharacteristic
274C22×C3#93011yescharacteristic
275C2×D3—22no—
276C2×D3—41no—
277C2×D3—41no—
278C2×D3—81no—
279C2×D3—81no—
280C2×D3—81no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—41no—
288C3×C4—121no—
289C3×C4C2×#20411yescharacteristic
290C3×C4#90411yescharacteristic
291C3×C4#91111yescharacteristic
292C3×C4#91211yescharacteristic
293C3×C4D3×SD1611yescharacteristic
294C3×C4#91611yescharacteristic
295C3×C4#93211yescharacteristic
296C3×C4#95011yescharacteristic
297Dic3—41no—
298Dic3—242no—
299Dic3—241no—
300Dic3—241no—
301C32#167711yescharacteristic, complemented, Sylow
302C23—61no—
303C23—121no—
304Q8—721no—
305D4—32no—
306D4—61no—
307D4—121no—
308D4—121no—
309D4—121no—
310D4—121no—
311D4—241no—
312C2×C4—61no—
313C2×C4—121no—
314C2×C4—121no—
315C2×C4—361no—
316C2×C4#379811yescharacteristic
317C2×C4D3×D1211yescharacteristic
318C2×C4D3×#6711yescharacteristic
319C8—41no—
320C8—61no—
321C8—61no—
322C8—121no—
323C8—361no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—122no—
328C2×C3—481no—
329C2×C3#474911yescharacteristic
330C2×C3#477811yescharacteristic
331C2×C3#478711yescharacteristic
332C2×C3#501611yescharacteristic
333C2×C3#511411yescharacteristic
334C2×C3#514211yescharacteristic
335D3—42no—
336D3—161no—
337C22—62no—
338C22—121no—
339C22—121no—
340C22—241no—
341C22—241no—
342C22—241no—
343C22#6390611yescharacteristic
344C4—21no—
345C4—121no—
346C4—721no—
347C4D3×#20411yescharacteristic
348C4#6380711yescharacteristic
349C4#6393211yescharacteristic
350C4#6394711yescharacteristic
351C3—21no—
352C3#6839611yescharacteristic, complemented
353C3#7084811yescharacteristic, complemented
354C2—122no—
355C2—481no—
356C2#1059053011yescharacteristic
357C2#1059082511yescharacteristic
358C2#1059099711yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10590347C2
hypercenterC4⋊C8D32
hypocenterC32#1677
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×#4834C2semidirect
3. #10590273C2semidirect
4. #10590268C2semidirect
5. #10589347C2semidirect
6. C3×#4485C2semidirect
7. #10589097C2semidirect
31. #4834D3semidirect
34. #4485D3semidirect
301. C32#1677semidirect
352. C3#68396semidirect
353. C3#70848semidirect

Maximal subgroups

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

subgroupindex
C3×#48342
#105903472
#105902732
#105902682
#105893472
C3×#44852
#105890972
#708483
#683963