Finite Group Databasebeta

← #11876996

Subgroups — #11876996

Order 1152.

963 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 963 conjugacy classes of subgroups — too many to draw. Only its 192 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×#5477C212yesmaximal, complemented
2C4×#3748C211yesmaximal, characteristic, complemented
3#10591167C214yesmaximal, complemented
4#10590352C211yesmaximal, characteristic, complemented
5#10590344C214yesmaximal, complemented
6#10590309C211yesmaximal, characteristic, complemented
7#10590277C212yesmaximal, complemented
8#83295—32nomaximal
9C2×C3×#235—22no—
10C2×C32×C42C2211yescharacteristic
11C2×#3748C2212yes—
12C3×#930—22no—
13C3×#930C2214yes—
14C3×#875—22no—
15C3×#874C2212yes—
16C3×C4×D12—22no—
17C3×C4×D12C2214yes—
18C3×#869C2212yes—
19C2×#3713C2214yes—
20#63630C2212yes—
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23#63574C2214yes—
24#63562C2218yes—
25C3×#532—32no—
26#5477D312yescomplemented
27#5088—32no—
28#5080—32no—
29#5073—32no—
30#5070—32no—
31#5039—38no—
32#5014—38no—
33C4×#208—32no—
34C4×#208—61no—
35C22×C32×C4D412yes—
36C22×C32×C4C2311yescharacteristic
37C2×C3×#67—24no—
38C3×#235—48no—
39C2×C3×D12—22no—
40C2×C3×D12—22no—
41C2×C3×D12C2314yes—
42C2×C3×C4×D3—24no—
43C2×C3×Dic6—22no—
44C32×C42D412yes—
45C32×C42C2311yescharacteristic
46C32×C42C2311yescharacteristic
47#3748—24no—
48C2×C3⋊(C3⋊C8)C2312yes—
49C2×C3⋊(C3⋊C8)C2312yes—
50C3×(C2×D3)⋊C4—24no—
51C3×(C2×D3)⋊C4—24no—
52C3×C4⋊Dic3—22no—
53C3×C4⋊Dic3C2314yes—
54#3713—28no—
55#3184—91noSylow
56C2×C3×#41—62no—
57C2×#235—22no—
58C3×C4⋊Q8—32no—
59C3×#127—32no—
60C3×#124—62no—
61C3×#121—34no—
62C3×#121—62no—
63C3×C4×D4—34no—
64C3×C4×D4—62no—
65C2×C3×C42—21no—
66C2×C3×C42C2×D312yes—
67C2×#213—38no—
68#930—22no—
69#930C2×D314yes—
70C2×#208—34no—
71C2×#208—62no—
72#875—22no—
73#874C2×D312yes—
74C4×D12—22no—
75C4×D12C2×D314yes—
76#869C2×D312yes—
77#832—38no—
78#809—38no—
79#808—38no—
80#803—34no—
81#803—62no—
82C4×C3⋊C8—32no—
83C4×C3⋊C8—32no—
84C4×C3⋊C8—61no—
85C4×C3⋊C8—61no—
86C23×C32C2×D411yescharacteristic
87C22×C3×D3—24no—
88C2×C32×C4—22no—
89C2×C32×C4—24no—
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D412yes—
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2411yescharacteristic
94C3×#67—48no—
95C2×C3×Dic3—24no—
96C3×D12—28no—
97C3×D12—44no—
98C3×D12—44no—
99C3×C4×D3—48no—
100C3×Dic6—44no—
101C3⋊(C3⋊C8)—22no—
102C3⋊(C3⋊C8)#4114yescomplemented
103#532—32no—
104#498—91no—
105#493—91no—
106#486—92no—
107#469—94no—
108#442—94no—
109C4×M16—91no—
110C3×#41—128no—
111C2×C3×Q8—62no—
112C2×C3×D4—34no—
113C2×C3×D4—64no—
114C2×C3×D4—62no—
115C2×C3×D4—62no—
116C22×C3×C4—22no—
117C22×C3×C4—21no—
118C22×C3×C4—64no—
119C22×C3×C4#6712yes—
120C22×C3×C4#6712yes—
121C22×C3×C4C22×D312yes—
122C2×#67—24no—
123#235—48no—
124C2×D12—22no—
125C2×D12—22no—
126C2×D12C22×D314yes—
127C2×C4×D3—24no—
128C2×Dic6—22no—
129C3×C4⋊C4—34no—
130C3×C4⋊C4—62no—
131C3×C22⋊C4—64no—
132C3×C22⋊C4—64no—
133C3×C42—22no—
134C3×C42—21no—
135C3×C42—21no—
136C3×C42#6712yes—
137C3×C42#6712yes—
138C3×C42C22×D312yes—
139C3×C42C22×D312yes—
140#213—616no—
141(C2×D3)⋊C4—24no—
142(C2×D3)⋊C4—24no—
143C4⋊Dic3—22no—
144C4⋊Dic3C22×D314yes—
145#208—68no—
146#208—68no—
147C2×C3⋊C8—34no—
148C2×C3⋊C8—34no—
149C2×C3⋊C8—62no—
150C2×C3⋊C8—62no—
151C22×C32—21no—
152C22×C32—22no—
153C22×C32C22×D411yescharacteristic
154C2×C3×D3—44no—
155C2×C3×D3—44no—
156C2×C3×D3—44no—
157C32×C4—21no—
158C32×C4—22no—
159C32×C4AGL(1,ℤ/8)14yes—
160C32×C4C2×#4112yes—
161C3×Dic3—44no—
162C2×#41—62no—
163C2×D8—94no—
164C2×M16—92no—
165C4⋊Q8—32no—
166#127—32no—
167#124—62no—
168#121—34no—
169#121—62no—
170C4×D4—34no—
171C4×D4—62no—
172C2×C42D3211yescharacteristic
173#106—94no—
174#102—98no—
175#97—92no—
176C4×C8—91no—
177C4×C8—91no—
178C23×C3—21no—
179C23×C3—64no—
180C23×C3C2×#6712yes—
181C22×D3—24no—
182C3×Q8—124no—
183C3×D4—68no—
184C3×D4—128no—
185C3×D4—124no—
186C3×D4—124no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—24no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—44no—
196C2×C3×C4—64no—
197C2×C3×C4—128no—
198C2×C3×C4C2×#6712yes—
199C2×C3×C4C2×#6712yes—
200C2×C3×C4C2×#6712yes—
201C2×C3×C4C2×#6712yes—
202C2×C3×C4C2×#6712yes—
203C2×C3×C4C23×D312yes—
204#67—48no—
205C2×Dic3—24no—
206D12—28no—
207D12—44no—
208D12—44no—
209C4×D3—48no—
210Dic6—44no—
211C3⋊C8—38no—
212C3⋊C8—64no—
213C3⋊C8—64no—
214C3⋊C8—64no—
215C2×C32—41no—
216C2×C32#53211yescharacteristic
217C2×C32C2×AGL(1,ℤ/8)12yes—
218C3×D3—84no—
219#41—128no—
220C2×Q8—62no—
221C2×D4—34no—
222C2×D4—64no—
223C2×D4—62no—
224C2×D4—62no—
225C22×C4—64no—
226C22×C4#62512yes—
227C22×C4C2×D3211yescharacteristic
228D8—188no—
229M16—184no—
230C2×C8—92no—
231C2×C8—92no—
232C4⋊C4—34no—
233C4⋊C4—62no—
234C22⋊C4—64no—
235C22⋊C4—64no—
236C42#62512yes—
237C42C2×D3211yescharacteristic
238C42C2×D3211yescharacteristic
239C22×C3—22no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—22no—
243C22×C3—21no—
244C22×C3—42no—
245C22×C3—124no—
246C22×C3—124no—
247C22×C3—124no—
248C22×C3C22×#6712yes—
249C2×D3—44no—
250C2×D3—44no—
251C2×D3—44no—
252C3×C4—22no—
253C3×C4—22no—
254C3×C4—22no—
255C3×C4—22no—
256C3×C4—22no—
257C3×C4—24no—
258C3×C4—42no—
259C3×C4—124no—
260C3×C4#93214yes—
261C3×C4#94914yes—
262C3×C4D3×#4114yes—
263Dic3—44no—
264C32#318411yescharacteristic, complemented, Sylow
265C23—64no—
266C23C2×#62511yescharacteristic
267Q8—124no—
268D4—68no—
269D4—128no—
270D4—124no—
271D4—124no—
272C2×C4—22no—
273C2×C4—24no—
274C2×C4—64no—
275C2×C4—128no—
276C2×C4C2×#62511yescharacteristic
277C2×C4C2×#62512yes—
278C2×C4C2×#62512yes—
279C2×C4C22×D3211yescharacteristic
280C8—94no—
281C8—182no—
282C2×C3—21no—
283C2×C3—22no—
284C2×C3—42no—
285C2×C3—42no—
286C2×C3—244no—
287C2×C3C2×#93212yes—
288C2×C3C2×#94912yes—
289C2×C3#583212yes—
290D3—84no—
291C22—21no—
292C22—22no—
293C22—124no—
294C22—124no—
295C22—124no—
296C22C22×#62511yescharacteristic
297C4—21no—
298C4—22no—
299C4—124no—
300C4#6382314yes—
301C4#6430612yes—
302C3—21no—
303C3#8329512yescomplemented
304C2—41no—
305C2—244no—
306C2C2×#6382312yes—
307C2#1059503211yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5477C2semidirect
2. C4×#3748C2semidirect
3. #10591167C2semidirect
4. #10590352C2semidirect
5. #10590344C2semidirect
6. #10590309C2semidirect
7. #10590277C2semidirect
26. #5477D3semidirect
102. C3⋊(C3⋊C8)#41semidirect
264. C32#3184semidirect
303. C3#83295semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
C4×#37482
#105911672
#105903522
#105903442
#105903092
#105902772
#832953