Finite Group Databasebeta

← #11780733

Subgroups — #11780733

Order 1152.

276 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 60 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#10589801C211yesmaximal, characteristic
2C9×#501C211yesmaximal, characteristic, complemented
3#10588774C211yesmaximal, characteristic
4#10588762C211yesmaximal, characteristic, complemented
5#10588220C211yesmaximal, characteristic, complemented
6#10588142C211yesmaximal, characteristic
7#10588141C211yesmaximal, characteristic, complemented
8#71394—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C9×#125C2211yescharacteristic
11#63460—21no—
12#63460—21no—
13#63459—21no—
14#63458—21no—
15#63456—21no—
16#63450—21no—
17#63437C2211yescharacteristic
18#63432C2211yescharacteristic
19C9×#107—21no—
20C9×#106—21no—
21C9×#97C2211yescharacteristic
22#63395—21no—
23#63395—21no—
24#63369—21no—
25#63368—21no—
26#63362C2211yescharacteristic
27#63362C2211yescharacteristic
28#5699—31no—
29C3×#501D311yescharacteristic
30#5089—31no—
31#5082—31no—
32#4543—31no—
33#4465—31no—
34#4464—31no—
35C2×Q8×C9—21no—
36C2×D36D411yescharacteristic
37C2×C4×D9—21no—
38C2×Dic18—21no—
39C2×Dic18D411yescharacteristic
40C2×C8×C9—21no—
41C9×C4⋊C4—21no—
42C9×C4⋊C4—21no—
43C9×C4⋊C4—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4D411yescharacteristic
46C9×C4⋊C4D411yescharacteristic
47C42×C9C2311yescharacteristic
48(C2×D9)⋊C4—21no—
49(C2×D9)⋊C4—21no—
50(C2×D9)⋊C4—21no—
51(C2×D9)⋊C4—21no—
52(C2×D9)⋊C4—21no—
53C4⋊Dic9—21no—
54C4⋊Dic9D411yescharacteristic
55C4⋊Dic9D411yescharacteristic
56Dic9⋊C4—21no—
57Dic9⋊C4—21no—
58Dic9⋊C4—21no—
59C4×Dic9—21no—
60C2×C9⋊C8—21no—
61C2×C9⋊C8—21no—
62#1664—91noSylow
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×#125C2×D311yescharacteristic
65#898—61no—
66#898—61no—
67#897—61no—
68#896—61no—
69#894—61no—
70#888—61no—
71#875—31no—
72#870—31no—
73C3×#107—21no—
74C3×#106—21no—
75C3×#97C2×D311yescharacteristic
76#835—61no—
77#835—61no—
78#810—61no—
79#809—61no—
80#803—31no—
81#803—31no—
82C22×D9—21no—
83Q8×C9—42no—
84C2×C4×C9—21no—
85C2×C4×C9—21no—
86C2×C4×C9—41no—
87C2×C4×C9C2×D411yescharacteristic
88C2×C4×C9C2×D411yescharacteristic
89C2×C4×C9C2×D411yescharacteristic
90C2×Dic9—21no—
91C2×Dic9—21no—
92C2×Dic9—21no—
93D36—41no—
94C4×D9—81no—
95Dic18—41no—
96Dic18—81no—
97C8×C9—22no—
98C9⋊C8—41no—
99C9⋊C8—41no—
100#563—91no—
101#501D911yescharacteristic, complemented
102#491—91no—
103#489—91no—
104#330—91no—
105#330—91no—
106#329—91no—
107C2×C3×Q8—21no—
108C2×D12—31no—
109C2×C4×D3—61no—
110C2×Dic6—31no—
111C2×Dic6—61no—
112C2×C3×C8—21no—
113C3×C4⋊C4—21no—
114C3×C4⋊C4—21no—
115C3×C4⋊C4—21no—
116C3×C4⋊C4—21no—
117C3×C4⋊C4#6711yescharacteristic
118C3×C4⋊C4#6711yescharacteristic
119C3×C42C22×D311yescharacteristic
120(C2×D3)⋊C4—61no—
121(C2×D3)⋊C4—61no—
122(C2×D3)⋊C4—61no—
123(C2×D3)⋊C4—61no—
124(C2×D3)⋊C4—61no—
125C4⋊Dic3—31no—
126C4⋊Dic3—31no—
127C4⋊Dic3—61no—
128Dic3⋊C4—61no—
129Dic3⋊C4—61no—
130Dic3⋊C4—61no—
131C4×Dic3—61no—
132C2×C3⋊C8—61no—
133C2×C3⋊C8—61no—
134C22×C9#12011yescharacteristic
135C2×D9—41no—
136C2×D9—41no—
137C2×D9—41no—
138C4×C9—21no—
139C4×C9—21no—
140C4×C9—21no—
141C4×C9—41no—
142C4×C9—41no—
143C4×C9—81no—
144Dic9—41no—
145Dic9—41no—
146Dic9—41no—
147C4⋊Q8—181no—
148C4⋊Q8C2×D911yescharacteristic
149#126—181no—
150#126—181no—
151#125—91no—
152#125C2×D911yescharacteristic
153#124—91no—
154#123—181no—
155C22⋊Q8—181no—
156C22⋊Q8—181no—
157#107—21no—
158#106—21no—
159#103—181no—
160#103—181no—
161#103—181no—
162#102—181no—
163#97—91no—
164#97—91no—
165#97C2×D911yescharacteristic
166C22×D3—61no—
167C3×Q8—42no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—41no—
171C2×C3×C4D3×D411yescharacteristic
172C2×C3×C4D3×D411yescharacteristic
173C2×C3×C4C2×#6711yescharacteristic
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177D12—121no—
178C4×D3—241no—
179Dic6—121no—
180Dic6—241no—
181C3×C8—22no—
182C3⋊C8—121no—
183C3⋊C8—121no—
184C2×C9#45411yescharacteristic
185C2×C9#45511yescharacteristic
186C2×C9#45611yescharacteristic
187D9—81no—
188C2×Q8—21no—
189C2×Q8—91no—
190C2×Q8—181no—
191C2×D4—91no—
192C22×C4—181no—
193C2×C8—21no—
194C2×C8—181no—
195C2×C8—181no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—91no—
201C4⋊C4—91no—
202C4⋊C4—181no—
203C4⋊C4—181no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C4⋊C4#61111yescharacteristic
207C4⋊C4#61111yescharacteristic
208C22⋊C4—181no—
209C22⋊C4—181no—
210C22⋊C4—181no—
211C22⋊C4—181no—
212C22⋊C4—181no—
213C42—181no—
214C42C22×D911yescharacteristic
215C22×C3#93711yescharacteristic
216C2×D3—121no—
217C2×D3—121no—
218C2×D3—121no—
219C3×C4—21no—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4—41no—
223C3×C4—41no—
224C3×C4—81no—
225Dic3—121no—
226Dic3—121no—
227Dic3—121no—
228C9#166411yescharacteristic, complemented, Sylow
229C23—181no—
230Q8—42no—
231Q8—361no—
232Q8—721no—
233D4—361no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—181no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—721no—
241C2×C4D4×D911yescharacteristic
242C2×C4D4×D911yescharacteristic
243C2×C4C2×#61111yescharacteristic
244C8—22no—
245C8—361no—
246C8—361no—
247C2×C3#509511yescharacteristic
248C2×C3#520111yescharacteristic
249C2×C3#520211yescharacteristic
250D3—241no—
251C22—361no—
252C22—361no—
253C22—361no—
254C22#6349911yescharacteristic
255C4—21no—
256C4—21no—
257C4—21no—
258C4—41no—
259C4—41no—
260C4—81no—
261C4—361no—
262C4—361no—
263C4—361no—
264C3#7139411yescharacteristic
265C2—721no—
266C2#1058877511yescharacteristic
267C2#1058888111yescharacteristic
268C2#1058888311yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#501C2
socleC22×C3#937
prime radicalC2×D36D4
hypercenter#501D9
hypocenterC9#1664
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. C9×#501C2semidirect
4. #10588762C2semidirect
5. #10588220C2semidirect
7. #10588141C2semidirect
101. #501D9semidirect
228. C9#1664semidirect

Maximal subgroups

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

subgroupindex
#105898012
C9×#5012
#105887742
#105887622
#105882202
#105881422
#105881412
#713943