Finite Group Databasebeta

← #11781264

Subgroups — #11781264

Order 1152.

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

normal subgroups only

This group has 394 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#10590349C211yesmaximal, characteristic
3#10590281C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589097C211yesmaximal, characteristic, complemented
8#70848—31nomaximal
9#68498—31nomaximal
10#64083C2211yescharacteristic
11C2×C3×D3×C8—21no—
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3714—21no—
15C32×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×(C2×D3)⋊C8—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63574—21no—
21#63564—21no—
22#63564—21no—
23#63564—21no—
24#63562—21no—
25C3×C8×D4—31no—
26#5088—31no—
27#5084—31no—
28#5015—31no—
29#5008—31no—
30#4843—31no—
31#4834D311yescharacteristic, complemented
32#4694—31no—
33C3×#333—31no—
34#4485—31no—
35#4485—31no—
36#4485—61no—
37#4481D311yescharacteristic, complemented
38#4480—31no—
39#4457—31no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C2×C3⋊(C3⋊C8)—21no—
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×D3×C8—42no—
57#3714—42no—
58#1677—91noSylow
59C22×C3×C8—61no—
60C3×C4⋊Q8—31no—
61C3×C4×D4—31no—
62C2×#213—61no—
63C2×D24—61no—
64C2×D3×C8—21no—
65#874—31no—
66#874—31no—
67#874—61no—
68C4×D12C2×D311yescharacteristic
69#869C2×D311yescharacteristic
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#821—61no—
78#821—61no—
79#821—61no—
80(C2×D3)⋊C8—21no—
81#809—61no—
82#809—61no—
83#809—61no—
84#809—61no—
85#808—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—41no—
93C22×C3×D3—21no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C4⋊(C3⋊D3)—41no—
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—81no—
102C2×C3×Dic3—21no—
103C2×C3×Dic3—41no—
104C3×D12—21no—
105C3×D12SD1612yes—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C3×Dic6—81no—
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—31no—
120#331—91no—
121C2×C3×Q8—61no—
122C2×C3×D4—31no—
123C22×C3×C4—61no—
124C2×D12—61no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—62no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—121no—
132C2×D12—121no—
133C2×D12D1211yescharacteristic
134C2×C4×D3—21no—
135C2×Dic6—21no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—31no—
139C2×C3×C8—31no—
140C2×C3×C8—41no—
141C2×C3×C8—61no—
142C2×C3×C8—122no—
143C3×C4⋊C4—31no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C22⋊C4—61no—
147C3×C42—21no—
148C3×C42C22×D311yescharacteristic
149C3×C42C22×D311yescharacteristic
150#213—122no—
151(C2×D3)⋊C4—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—21no—
154C4⋊Dic3D1211yescharacteristic
155C2×C3⋊C8—21no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—121no—
159C2×C3⋊C8#6711yescharacteristic
160C2×C3⋊C8#6711yescharacteristic
161D24—122no—
162D3×C8—42no—
163C22×C32#12111yescharacteristic
164C2×C3⋊D3—81no—
165C2×C3⋊D3—81no—
166C2×C3⋊D3—81no—
167C2×C3×D3—22no—
168C2×C3×D3—41no—
169C2×C3×D3—41no—
170C32×C4—21no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4AGL(1,ℤ/8)11yescharacteristic
175C3×Dic3—41no—
176C3×Dic3—81no—
177C2×D8—181no—
178C22×C8—61no—
179C4⋊Q8—31no—
180#127—91no—
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—
193C22×D3—21no—
194C22×D3—122no—
195C22×D3—121no—
196C22×D3—121no—
197C3×Q8—241no—
198C3×D4—32no—
199C3×D4—61no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—61no—
204C2×C3×C4—121no—
205C2×C3×C4—121no—
206C2×C3×C4—121no—
207C2×C3×C4C2×D1211yescharacteristic
208C2×C3×C4#23511yescharacteristic
209C2×C3×C4#23511yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4C2×#6711yescharacteristic
213C2×Dic3—21no—
214C2×Dic3—41no—
215D12—21no—
216D12—121no—
217D12—121no—
218D12—121no—
219D12—121no—
220D12—121no—
221D12—121no—
222D12—121no—
223D12—121no—
224D12—241no—
225D12—241no—
226D12—241no—
227D12—241no—
228D12—241no—
229D12—241no—
230D12—242no—
231D12#20412yes—
232C4×D3—41no—
233C4×D3—41no—
234Dic6—81no—
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—61no—
238C3×C8—61no—
239C3×C8—81no—
240C3×C8—121no—
241C3⋊C8—21no—
242C3⋊C8—21no—
243C3⋊C8—41no—
244C3⋊C8—121no—
245C3⋊C8—121no—
246C3⋊C8—241no—
247C2×C32#46311yescharacteristic
248C2×C32#46511yescharacteristic
249C2×C32#47211yescharacteristic
250C3⋊D3—161no—
251C3×D3—42no—
252C2×Q8—61no—
253C2×D4—31no—
254C2×D4—181no—
255C2×D4—181no—
256C2×D4—181no—
257C22×C4—61no—
258D8—362no—
259C2×C8—21no—
260C2×C8—31no—
261C2×C8—31no—
262C2×C8—61no—
263C2×C8—122no—
264C2×C8—181no—
265C4⋊C4—31no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C22⋊C4—61no—
269C42C2×D3211yescharacteristic
270C22×C3—21no—
271C22×C3—62no—
272C22×C3—121no—
273C22×C3—121no—
274C22×C3#88411yescharacteristic
275C22×C3#93011yescharacteristic
276C2×D3—22no—
277C2×D3—41no—
278C2×D3—41no—
279C2×D3—242no—
280C2×D3—242no—
281C2×D3—242no—
282C2×D3—241no—
283C2×D3—241no—
284C2×D3—241no—
285C2×D3—241no—
286C2×D3—241no—
287C2×D3—241no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—41no—
295C3×C4—121no—
296C3×C4—241no—
297C3×C4C2×#20411yescharacteristic
298C3×C4#90411yescharacteristic
299C3×C4D3×SD1611yescharacteristic
300C3×C4#91411yescharacteristic
301C3×C4#91911yescharacteristic
302C3×C4#91911yescharacteristic
303C3×C4#93211yescharacteristic
304C3×C4#95011yescharacteristic
305Dic3—41no—
306Dic3—81no—
307C32#167711yescharacteristic, complemented, Sylow
308C23—61no—
309C23—361no—
310Q8—241no—
311D4—32no—
312D4—61no—
313D4—361no—
314D4—361no—
315D4—361no—
316D4—361no—
317D4—721no—
318C2×C4—61no—
319C2×C4—121no—
320C2×C4—121no—
321C2×C4—121no—
322C2×C4#379811yescharacteristic
323C2×C4D3×D1211yescharacteristic
324C2×C4D3×#6711yescharacteristic
325C8—41no—
326C8—61no—
327C8—61no—
328C8—121no—
329C8—361no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—122no—
334C2×C3#474911yescharacteristic
335C2×C3#480711yescharacteristic
336C2×C3#481911yescharacteristic
337C2×C3#501611yescharacteristic
338C2×C3#511411yescharacteristic
339C2×C3#514211yescharacteristic
340D3—42no—
341D3—482no—
342D3—481no—
343D3—481no—
344C22—62no—
345C22—121no—
346C22—121no—
347C22—721no—
348C22—721no—
349C22—721no—
350C22#6390611yescharacteristic
351C4—21no—
352C4—121no—
353C4—241no—
354C4D3×#20411yescharacteristic
355C4#6380811yescharacteristic
356C4#6393411yescharacteristic
357C4#6394911yescharacteristic
358C3—21no—
359C3#6849811yescharacteristic, complemented
360C3#7084811yescharacteristic, complemented
361C2—122no—
362C2—1441no—
363C2#1059053411yescharacteristic
364C2#1059084711yescharacteristic
365C2#1059099711yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10590349C2
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. #10590281C2semidirect
4. #10590266C2semidirect
5. #10589351C2semidirect
6. C3×#4481C2semidirect
7. #10589097C2semidirect
31. #4834D3semidirect
37. #4481D3semidirect
307. C32#1677semidirect
359. C3#68498semidirect
360. C3#70848semidirect

Maximal subgroups

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

subgroupindex
C3×#48342
#105903492
#105902812
#105902662
#105893512
C3×#44812
#105890972
#708483
#684983