Finite Group Databasebeta

← #11781267

Subgroups — #11781267

Order 1152.

379 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 379 conjugacy classes of subgroups — too many to draw. Only its 86 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×#4842C211yesmaximal, characteristic, complemented
2#10590347C211yesmaximal, characteristic
3#10590329C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic, complemented
5#10589346C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7#10589095C211yesmaximal, characteristic, complemented
8#71134—31nomaximal
9#68396—31nomaximal
10C3×#874C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3713—21no—
14C2×D3×C3⋊C8—21no—
15C32×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#821—21no—
19C3×#817—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63562—21no—
22#63562—21no—
23#63562—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#476—31no—
26#5088—31no—
27#5072—31no—
28#5070—31no—
29#5015—31no—
30D4×C3⋊C8—31no—
31#4842D311yescharacteristic, complemented
32#4834—31no—
33C3×#331—31no—
34#4546—31no—
35#4485D311yescharacteristic, complemented
36#4481—31no—
37#4480—31no—
38#4480—31no—
39#4480—61no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56#3713—42no—
57D3×C3⋊C8—42no—
58#1677—91noSylow
59C3×C4⋊Q8—31no—
60C3×#127—31no—
61C3×C4×D4—31no—
62C2×#213—61no—
63C2×#213—61no—
64C22×C3⋊C8—61no—
65C2×D3×C8—61no—
66#874C2×D311yescharacteristic
67C4×D12C2×D311yescharacteristic
68#869C2×D311yescharacteristic
69C3×#106—61no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4⋊C8C2×D311yescharacteristic
74C3×#102—61no—
75#832—61no—
76#832—61no—
77#832—61no—
78#830—61no—
79#821—21no—
80(C2×D3)⋊C8—61no—
81#817—21no—
82#809—61no—
83#809—61no—
84#809—61no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4×C3⋊C8—31no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—61no—
92C22×C3×D3—21no—
93C22×C3×D3—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—21no—
98C2×C3×Dic3—41no—
99C3×D12—21no—
100C3×D12—41no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—81no—
105C3×D12SD1612yes—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C3×Dic6—81no—
109C32×C8—41no—
110C3⋊(C3⋊C8)—21no—
111C3⋊(C3⋊C8)—21no—
112C3⋊(C3⋊C8)—41no—
113C3×C3⋊C8—41no—
114#486—91no—
115#476—31no—
116#459—91no—
117C8×D4—91no—
118#334—91no—
119#333—91no—
120#331—31no—
121C2×C3×Q8—61no—
122C2×C3×D4—31no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C22×C3×C4—61no—
127C2×D12—21no—
128C2×D12—21no—
129C2×D12—21no—
130C2×D12#6711yescharacteristic
131C2×C4×D3—21no—
132C2×Dic6—21no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C2×C3×C8—41no—
136C2×C3×C8—61no—
137C3×C4⋊C4—31no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—61no—
140C3×C22⋊C4—61no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#213—122no—
145#213—122no—
146(C2×D3)⋊C4—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3#6711yescharacteristic
150C2×C3⋊C8—21no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—121no—
160C2×C3⋊C8—122no—
161D3×C8—122no—
162C22×C32#12111yescharacteristic
163C2×C3×D3—22no—
164C2×C3×D3—41no—
165C2×C3×D3—41no—
166C2×C3×D3—81no—
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C32×C4—21no—
170C32×C4C2×SD1611yescharacteristic
171C32×C4#13511yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4AGL(1,ℤ/8)11yescharacteristic
174C3×Dic3—41no—
175C3×Dic3—81no—
176C2×D8—181no—
177C22×C8—181no—
178C4⋊Q8—31no—
179#127—31no—
180C4×D4—31no—
181#106—61no—
182C4⋊C8—31no—
183C4⋊C8—91no—
184C4⋊C8D3211yescharacteristic
185#102—61no—
186#102—181no—
187#102—181no—
188#102—181no—
189C22⋊C8—181no—
190C4×C8—91no—
191C23×C3—61no—
192C23×C3—121no—
193C22×D3—21no—
194C22×D3—41no—
195C3×Q8—241no—
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×C4—121no—
210C2×C3×C4#23511yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4#23711yescharacteristic
215C2×C3×C4C2×#6711yescharacteristic
216C2×Dic3—21no—
217C2×Dic3—41no—
218D12—21no—
219D12—41no—
220D12—41no—
221D12—41no—
222D12—41no—
223D12—81no—
224D12#21512yes—
225C4×D3—41no—
226C4×D3—41no—
227Dic6—81no—
228C3×C8—41no—
229C3×C8—41no—
230C3×C8—81no—
231C3×C8—121no—
232C3⋊C8—41no—
233C3⋊C8—62no—
234C3⋊C8—61no—
235C3⋊C8—61no—
236C3⋊C8—61no—
237C3⋊C8—61no—
238C3⋊C8—121no—
239C3⋊C8—121no—
240C3⋊C8—121no—
241C3⋊C8—241no—
242C2×C32#46311yescharacteristic
243C2×C32#46511yescharacteristic
244C2×C32#47211yescharacteristic
245C3×D3—42no—
246C3×D3—161no—
247C2×Q8—61no—
248C2×D4—31no—
249C2×D4—61no—
250C2×D4—61no—
251C2×D4—61no—
252C22×C4—61no—
253D8—362no—
254C2×C8—21no—
255C2×C8—61no—
256C2×C8—91no—
257C2×C8—91no—
258C2×C8—181no—
259C2×C8—362no—
260C4⋊C4—31no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C22⋊C4—61no—
264C42C2×D3211yescharacteristic
265C22×C3—21no—
266C22×C3—62no—
267C22×C3—121no—
268C22×C3—121no—
269C22×C3—241no—
270C22×C3—241no—
271C22×C3—241no—
272C22×C3#88411yescharacteristic
273C22×C3#93911yescharacteristic
274C2×D3—22no—
275C2×D3—41no—
276C2×D3—41no—
277C2×D3—81no—
278C2×D3—81no—
279C2×D3—81no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—121no—
288C3×C4—241no—
289C3×C4#91111yescharacteristic
290C3×C4#91211yescharacteristic
291C3×C4D3×SD1611yescharacteristic
292C3×C4#91411yescharacteristic
293C3×C4#91611yescharacteristic
294C3×C4#91611yescharacteristic
295C3×C4C2×#21511yescharacteristic
296C3×C4#95011yescharacteristic
297Dic3—41no—
298Dic3—81no—
299C32#167711yescharacteristic, complemented, Sylow
300C23—61no—
301C23—121no—
302Q8—241no—
303D4—32no—
304D4—61no—
305D4—121no—
306D4—121no—
307D4—121no—
308D4—121no—
309D4—241no—
310C2×C4—61no—
311C2×C4—121no—
312C2×C4—121no—
313C2×C4—121no—
314C2×C4#379511yescharacteristic
315C2×C4#380211yescharacteristic
316C2×C4D3×#6711yescharacteristic
317C8—41no—
318C8—121no—
319C8—181no—
320C8—181no—
321C8—361no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—122no—
326C2×C3—481no—
327C2×C3#474911yescharacteristic
328C2×C3#477811yescharacteristic
329C2×C3#478711yescharacteristic
330C2×C3#504811yescharacteristic
331C2×C3#516511yescharacteristic
332C2×C3#519911yescharacteristic
333D3—42no—
334D3—161no—
335C22—62no—
336C22—121no—
337C22—121no—
338C22—241no—
339C22—241no—
340C22—241no—
341C22#6388511yescharacteristic
342C4—21no—
343C4—121no—
344C4—241no—
345C4#6379811yescharacteristic
346C4#6380911yescharacteristic
347C4#6393311yescharacteristic
348C4D3×#21511yescharacteristic
349C3—21no—
350C3#6839611yescharacteristic, complemented
351C3#7113411yescharacteristic, complemented
352C2—122no—
353C2—481no—
354C2#1059050111yescharacteristic
355C2#1059075011yescharacteristic
356C2#1059098211yescharacteristic
subgroupG/H
centerC22#63885
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×#4842C2semidirect
3. #10590329C2semidirect
4. #10590277C2semidirect
5. #10589346C2semidirect
6. C3×#4485C2semidirect
7. #10589095C2semidirect
31. #4842D3semidirect
35. #4485D3semidirect
299. C32#1677semidirect
350. C3#68396semidirect
351. C3#71134semidirect

Maximal subgroups

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

subgroupindex
C3×#48422
#105903472
#105903292
#105902772
#105893462
C3×#44852
#105890952
#711343
#683963