Finite Group Databasebeta

← #11789936

Subgroups — #11789936

Order 1152.

690 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 183 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
1#10592828C211yesmaximal, characteristic
2#10592701C211yesmaximal, characteristic
3#10592698C211yesmaximal, characteristic, complemented
4C2×#63632C211yesmaximal, characteristic
5C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C32×#339C211yesmaximal, characteristic, complemented
7#10589424C211yesmaximal, characteristic, complemented
8#68745—34nomaximal
9C2×#3828C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16#63647—22no—
17#63637C412yescomplemented
18#63636C412yescomplemented
19#63632—22no—
20C4⋊(C3⋊(C3⋊C8))—22no—
21C4×C3⋊(C3⋊C8)—22no—
22#5129—34no—
23#5002—34no—
24#4999—34no—
25C2×#805—34no—
26C2×C4×C3⋊C8—34no—
27C3×#339D314yescomplemented
28#4558—34no—
29C22×C32×C4—21no—
30C22×C32×C4C2311yescharacteristic
31C2×#638—21no—
32#3828—21no—
33#3828—21no—
34#3828—21no—
35#3828—21no—
36C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×#634C2×C411yescharacteristic
39C32×M16—21no—
40C32×M16—21no—
41C2×C32×C8—21no—
42C32×C4⋊C4C2×C412yes—
43C32×C22⋊C4—21no—
44C32×C42—21no—
45C32×C42—21no—
46C32×C42D412yes—
47#3748—21no—
48#3748—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)C2×C412yes—
55C2×C3⋊(C3⋊C8)D412yes—
56#1937—91noSylow
57C2×#235—34no—
58C2×C3×M16C2×D314yes—
59C3×#117C2×D314yes—
60C2×C3×C42C2×D314yes—
61C2×#208—34no—
62C22×C3⋊C8—34no—
63C22×C3⋊C8—34no—
64(C2×D3)⋊C8—68no—
65#810—38no—
66#809—38no—
67#805—68no—
68C4⋊(C3⋊C8)—68no—
69C4×C3⋊C8—68no—
70C23×C32#4111yescharacteristic
71C22×C3⋊D3—21no—
72C2×C32×C4—24no—
73C2×C32×C4—22no—
74C2×C32×C4—22no—
75C2×C32×C4C22×C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4#4111yescharacteristic
79C2×C32×C4#4111yescharacteristic
80C2×C32×C4#4111yescharacteristic
81#638—41no—
82#638—41no—
83C2×C3⋊Dic3—21no—
84C4⋊(C3⋊D3)—21no—
85C4⋊(C3⋊D3)—21no—
86C4×C3⋊D3—41no—
87C4×C3⋊D3—41no—
88#634—21no—
89#634—21no—
90C32×C8—41no—
91C3⋊(C3⋊C8)—22no—
92C3⋊(C3⋊C8)—22no—
93C3⋊(C3⋊C8)—41no—
94#424—91no—
95C2×#104—91no—
96#416—91no—
97#408—91no—
98C2×C4×C8—91no—
99#341—91no—
100#339C3⋊D311yescharacteristic, complemented
101C22×C3×C4—24no—
102C22×C3×C4C22×D314yes—
103C2×#67—64no—
104#235—64no—
105#235—64no—
106#235—64no—
107#235—64no—
108C2×D12—34no—
109C2×C4×D3—64no—
110C2×Dic6—34no—
111C3×M16—24no—
112C3×M16—24no—
113C2×C3×C8—24no—
114C3×C4⋊C4C4×D318yes—
115C3×C22⋊C4—24no—
116C3×C42—24no—
117C3×C42—24no—
118C3×C42D1218yes—
119#208—64no—
120#208—64no—
121C2×C3⋊C8—38no—
122C2×C3⋊C8—38no—
123C2×C3⋊C8—64no—
124C2×C3⋊C8—64no—
125C2×C3⋊C8—64no—
126C2×C3⋊C8—64no—
127C2×C3⋊C8—64no—
128C22×C32—22no—
129C22×C32C4×D411yescharacteristic
130C22×C32#12311yescharacteristic
131C22×C32#12611yescharacteristic
132C2×C3⋊D3—41no—
133C2×C3⋊D3—42no—
134C32×C4—24no—
135C32×C4—42no—
136C32×C4#11711yescharacteristic
137C32×C4C4×D411yescharacteristic
138C32×C4#12111yescharacteristic
139C32×C4#12411yescharacteristic
140C3⋊Dic3—41no—
141C2×#41—91no—
142C2×M16—91no—
143C2×M16C2×C3⋊D311yescharacteristic
144C22×C8—91no—
145C22×C8—91no—
146#117C2×C3⋊D311yescharacteristic
147C2×C42C2×C3⋊D311yescharacteristic
148C4⋊C8—182no—
149#104—182no—
150#103—92no—
151#102—92no—
152C22⋊C8—182no—
153C4×C8—182no—
154C23×C3#23714yes—
155C22×D3—64no—
156C2×C3×C4—216no—
157C2×C3×C4—28no—
158C2×C3×C4—28no—
159C2×C3×C4C2×C4×D314yes—
160C2×C3×C4C2×D1214yes—
161C2×C3×C4#23514yes—
162C2×C3×C4D3×D414yes—
163C2×C3×C4#23714yes—
164C2×C3×C4#23914yes—
165#67—124no—
166#67—124no—
167C2×Dic3—64no—
168D12—64no—
169D12—64no—
170C4×D3—124no—
171C4×D3—124no—
172Dic6—64no—
173Dic6—64no—
174C3×C8—44no—
175C3⋊C8—68no—
176C3⋊C8—68no—
177C3⋊C8—124no—
178C2×C32—21no—
179C2×C32—21no—
180C2×C32#38811yescharacteristic
181C2×C32#44312yes—
182C3⋊D3—81no—
183#41—181no—
184#41—181no—
185#41—181no—
186#41—181no—
187C2×Q8—91no—
188C2×D4—91no—
189C2×D4—181no—
190C22×C4—21no—
191C22×C4—181no—
192C22×C4C22×C3⋊D311yescharacteristic
193M16—21no—
194M16—21no—
195M16—181no—
196M16—181no—
197C2×C8—21no—
198C2×C8—92no—
199C2×C8—92no—
200C2×C8—181no—
201C2×C8—181no—
202C2×C8—181no—
203C2×C8—181no—
204C2×C8—181no—
205C4⋊C4C4×C3⋊D312yes—
206C22⋊C4—21no—
207C42—21no—
208C42—21no—
209C42C4⋊(C3⋊D3)12yes—
210C22×C3—28no—
211C22×C3#67⋊C414yes—
212C22×C3#88614yes—
213C22×C3#89814yes—
214C2×D3—124no—
215C2×D3—128no—
216C3×C4—216no—
217C3×C4—48no—
218C3×C4C4×D1214yes—
219C3×C4#88514yes—
220C3×C4#89214yes—
221C3×C4#89514yes—
222Dic3—124no—
223C32#193711yescharacteristic, complemented, Sylow
224C23—181no—
225C23#383011yescharacteristic
226Q8—181no—
227Q8—181no—
228D4—181no—
229D4—181no—
230D4—361no—
231D4—361no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—181no—
236C2×C4—361no—
237C2×C4—361no—
238C2×C4C2×C4×C3⋊D311yescharacteristic
239C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
240C2×C4#382811yescharacteristic
241C2×C4D4×C3⋊D311yescharacteristic
242C2×C4#383011yescharacteristic
243C2×C4#383211yescharacteristic
244C8—41no—
245C8—182no—
246C8—182no—
247C8—361no—
248C2×C3—24no—
249C2×C3—24no—
250C2×C3#467014yes—
251C2×C3#482418yes—
252D3—244no—
253C22—22no—
254C22—362no—
255C22—361no—
256C22#6409011yescharacteristic
257C22#6409511yescharacteristic
258C22#6410711yescharacteristic
259C4—24no—
260C4—42no—
261C4—361no—
262C4C4×C4⋊(C3⋊D3)11yescharacteristic
263C4#6409411yescharacteristic
264C4#6410111yescharacteristic
265C4#6410411yescharacteristic
266C3#6874514yescomplemented
267C2—21no—
268C2—21no—
269C2—721no—
270C2#1059236911yescharacteristic
271C2#1059252312yes—
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1937
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
3. #10592698C2semidirect
5. C2×C4×C3⋊(C3⋊C8)C2semidirect
6. C32×#339C2semidirect
7. #10589424C2semidirect
17. #63637C4semidirect
18. #63636C4semidirect
27. C3×#339D3semidirect
100. #339C3⋊D3semidirect
223. C32#1937semidirect
266. C3#68745semidirect

Maximal subgroups

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

subgroupindex
#105928282
#105927012
#105926982
C2×#636322
C2×C4×C3⋊(C3⋊C8)2
C32×#3392
#105894242
#687453