Finite Group Databasebeta

← #11781361

Subgroups — #11781361

Order 1152.

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

normal subgroups only

This group has 359 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×#4841C211yesmaximal, characteristic
2#10590329C211yesmaximal, characteristic
3#10590290C211yesmaximal, characteristic, complemented
4#10590269C211yesmaximal, characteristic
5#10589346C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71038—31nomaximal
9#68444—31nomaximal
10C2×C3×#204—21no—
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×D3×C3⋊C8—21no—
15C32×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#816—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20#63576—21no—
21#63565—21no—
22#63565—21no—
23#63562—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#461—31no—
26#5093—31no—
27#5087—31no—
28#5079—31no—
29D4×C3⋊C8—31no—
30#5007—31no—
31#4841D311yescharacteristic
32#4834—31no—
33C3×#332—31no—
34#4547—31no—
35#4486—31no—
36#4486D311yescharacteristic, complemented
37#4480—31no—
38#4480—31no—
39#4480—61no—
40C2×C3×D12D411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C3×#204—42no—
57D3×C3⋊C8—42no—
58#1679—91noSylow
59C2×C3×SD16—61no—
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8—31no—
62C3×C4×D4—31no—
63C22×C3⋊C8—61no—
64C2×#204—21no—
65C2×D3×C8—61no—
66C4×D12C2×D311yescharacteristic
67#869C2×D311yescharacteristic
68#869C2×D311yescharacteristic
69C3×C4⋊C8—21no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4⋊C8C2×D311yescharacteristic
73C3×#103—61no—
74#835—61no—
75#835—61no—
76#832—61no—
77#830—61no—
78(C2×D3)⋊C8—61no—
79#816—21no—
80#810—61no—
81#810—61no—
82#809—61no—
83#807—61no—
84#807—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—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3×Dic3—21no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99C3×D12—21no—
100C3×D12SD1612yes—
101C3×C4×D3—41no—
102C3×C4×D3—41no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—21no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—41no—
112#487—91no—
113#474—91no—
114#461—31no—
115C8×D4—91no—
116#334—91no—
117#332—31no—
118#332—91no—
119C2×C3×Q8—61no—
120C2×C3×Q8—61no—
121C2×C3×D4—31no—
122C22×C3×C4—61no—
123C2×D12#6711yescharacteristic
124C2×C4×D3—21no—
125C2×Dic6—21no—
126C2×Dic6—21no—
127C3×SD16—122no—
128C2×C3×C8—21no—
129C2×C3×C8—21no—
130C2×C3×C8—41no—
131C2×C3×C8—61no—
132C3×C4⋊C4—31no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C22⋊C4—61no—
138C3×C42—21no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141(C2×D3)⋊C4—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3#6711yescharacteristic
147C2×C3⋊C8—21no—
148C2×C3⋊C8—31no—
149C2×C3⋊C8—31no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—121no—
157C2×C3⋊C8—122no—
158#204—42no—
159D3×C8—122no—
160C22×C32#12111yescharacteristic
161C2×C3×D3—22no—
162C2×C3×D3—41no—
163C2×C3×D3—41no—
164C32×C4—21no—
165C32×C4C2×SD1611yescharacteristic
166C32×C4#13511yescharacteristic
167C32×C4#13511yescharacteristic
168C32×C4AGL(1,ℤ/8)11yescharacteristic
169C3×Dic3—41no—
170C3×Dic3—81no—
171C3×Dic3—81no—
172C2×SD16—61no—
173C22×C8—181no—
174C4⋊Q8—31no—
175C4⋊Q8—31no—
176C4×D4—31no—
177#107—181no—
178C4⋊C8—31no—
179C4⋊C8—91no—
180C4⋊C8D3211yescharacteristic
181#103—61no—
182#103—181no—
183#103—181no—
184#102—181no—
185C22⋊C8—181no—
186C4×C8—91no—
187C23×C3—61no—
188C22×D3—21no—
189C3×Q8—121no—
190C3×Q8—121no—
191C3×Q8—121no—
192C3×Q8—121no—
193C3×D4—32no—
194C3×D4—61no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—61no—
199C2×C3×C4—121no—
200C2×C3×C4—121no—
201C2×C3×C4—121no—
202C2×C3×C4—121no—
203C2×C3×C4#23511yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4#23711yescharacteristic
208C2×C3×C4C2×#6711yescharacteristic
209C2×Dic3—21no—
210C2×Dic3—41no—
211C2×Dic3—41no—
212D12—21no—
213D12#21412yes—
214C4×D3—41no—
215C4×D3—41no—
216Dic6—41no—
217Dic6—41no—
218Dic6—41no—
219Dic6—41no—
220C3×C8—41no—
221C3×C8—41no—
222C3×C8—81no—
223C3×C8—121no—
224C3⋊C8—41no—
225C3⋊C8—62no—
226C3⋊C8—61no—
227C3⋊C8—61no—
228C3⋊C8—61no—
229C3⋊C8—61no—
230C3⋊C8—121no—
231C3⋊C8—121no—
232C3⋊C8—121no—
233C3⋊C8—241no—
234C2×C32#46311yescharacteristic
235C2×C32#46511yescharacteristic
236C2×C32#47311yescharacteristic
237C3×D3—42no—
238C2×Q8—61no—
239C2×Q8—61no—
240C2×D4—31no—
241C22×C4—61no—
242SD16—122no—
243C2×C8—21no—
244C2×C8—61no—
245C2×C8—91no—
246C2×C8—91no—
247C2×C8—181no—
248C2×C8—362no—
249C4⋊C4—31no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4—61no—
253C4⋊C4—61no—
254C22⋊C4—61no—
255C42C2×D3211yescharacteristic
256C22×C3—21no—
257C22×C3—62no—
258C22×C3—121no—
259C22×C3—121no—
260C22×C3#88411yescharacteristic
261C22×C3#93911yescharacteristic
262C2×D3—22no—
263C2×D3—41no—
264C2×D3—41no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—41no—
272C3×C4—121no—
273C3×C4—241no—
274C3×C4—241no—
275C3×C4#91111yescharacteristic
276C3×C4D3×SD1611yescharacteristic
277C3×C4#91411yescharacteristic
278C3×C4#91611yescharacteristic
279C3×C4#91611yescharacteristic
280C3×C4#91911yescharacteristic
281C3×C4C2×#21411yescharacteristic
282C3×C4#95011yescharacteristic
283Dic3—41no—
284Dic3—81no—
285Dic3—81no—
286C32#167911yescharacteristic, complemented, Sylow
287C23—61no—
288Q8—121no—
289Q8—121no—
290Q8—121no—
291Q8—121no—
292D4—32no—
293D4—61no—
294C2×C4—61no—
295C2×C4—121no—
296C2×C4—121no—
297C2×C4—121no—
298C2×C4—121no—
299C2×C4#379511yescharacteristic
300C2×C4#380211yescharacteristic
301C2×C4D3×#6711yescharacteristic
302C8—41no—
303C8—121no—
304C8—181no—
305C8—181no—
306C8—361no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—122no—
311C2×C3#475511yescharacteristic
312C2×C3#478711yescharacteristic
313C2×C3#480711yescharacteristic
314C2×C3#504111yescharacteristic
315C2×C3#516511yescharacteristic
316C2×C3#520411yescharacteristic
317D3—42no—
318C22—62no—
319C22—121no—
320C22—121no—
321C22#6388511yescharacteristic
322C4—21no—
323C4—121no—
324C4—241no—
325C4—241no—
326C4#6379811yescharacteristic
327C4#6380911yescharacteristic
328C4D3×#21411yescharacteristic
329C4#6394911yescharacteristic
330C3—21no—
331C3#6844411yescharacteristic, complemented
332C3#7103811yescharacteristic, complemented
333C2—122no—
334C2#1059051411yescharacteristic
335C2#1059075011yescharacteristic
336C2#1059098111yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1679
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
3. #10590290C2semidirect
5. #10589346C2semidirect
6. C3×#4486C2semidirect
7. #10589092C2semidirect
36. #4486D3semidirect
286. C32#1679semidirect
331. C3#68444semidirect
332. C3#71038semidirect

Maximal subgroups

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

subgroupindex
C3×#48412
#105903292
#105902902
#105902692
#105893462
C3×#44862
#105890922
#710383
#684443