Finite Group Databasebeta

← #11780736

Subgroups — #11780736

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#10589774C211yesmaximal, characteristic
2C9×#489C211yesmaximal, characteristic
3#10588762C211yesmaximal, characteristic, complemented
4#10588761C211yesmaximal, characteristic, complemented
5#10588217C211yesmaximal, characteristic
6#10588141C211yesmaximal, characteristic, complemented
7#10588141C211yesmaximal, characteristic, complemented
8#71247—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C9×#124C2211yescharacteristic
11#63506—21no—
12#63497—21no—
13#63441—21no—
14#63441—21no—
15#63440—21no—
16#63440—21no—
17#63432C2211yescharacteristic
18#63432C2211yescharacteristic
19C9×#103—21no—
20C9×#102—21no—
21C9×#97C2211yescharacteristic
22#63395—21no—
23#63395—21no—
24#63367—21no—
25#63366—21no—
26#63362C2211yescharacteristic
27#63362C2211yescharacteristic
28#5672—31no—
29C3×#489D311yescharacteristic
30#5082—31no—
31#5081—31no—
32#4540—31no—
33#4465—31no—
34#4465—31no—
35C2×Q8×C9—21no—
36C2×Q8×C9D411yescharacteristic
37C2×D4×C9D411yescharacteristic
38C22×Dic9—21no—
39C2×Dic18—21no—
40C2×C8×C9—21no—
41C9×C4⋊C4—21no—
42C9×C4⋊C4—21no—
43C9×C22⋊C4—21no—
44C9×C22⋊C4—21no—
45C42×C9C2311yescharacteristic
46#3676—21no—
47#3676—21no—
48#3676—21no—
49C4⋊Dic9D411yescharacteristic
50C4⋊Dic9D411yescharacteristic
51C4⋊Dic9D411yescharacteristic
52C4⋊Dic9D411yescharacteristic
53Dic9⋊C4—21no—
54Dic9⋊C4—21no—
55Dic9⋊C4—21no—
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×#124C2×D311yescharacteristic
65#944—61no—
66#935—61no—
67#879—61no—
68#879—61no—
69#878—61no—
70#878—61no—
71#870—31no—
72#870—31no—
73C3×#103—21no—
74C3×#102—21no—
75C3×#97C2×D311yescharacteristic
76#835—61no—
77#835—61no—
78#808—61no—
79#807—61no—
80#803—31no—
81#803—31no—
82C23×C9—21no—
83Q8×C9—41no—
84Q8×C9—42no—
85D4×C9—41no—
86C2×C4×C9—21no—
87C2×C4×C9—41no—
88C2×C4×C9C2×D411yescharacteristic
89C2×C4×C9C2×D411yescharacteristic
90C2×C4×C9C2×D411yescharacteristic
91C2×Dic9—21no—
92C2×Dic9—21no—
93C2×Dic9—21no—
94C2×Dic9—21no—
95C2×Dic9—81no—
96Dic18—81no—
97C8×C9—41no—
98C9⋊C8—22no—
99C9⋊C8—41no—
100#563—91no—
101#501—91no—
102#491—91no—
103#489D911yescharacteristic
104#330—91no—
105#330—91no—
106#329—91no—
107C2×C3×Q8—21no—
108C2×C3×Q8#6711yescharacteristic
109C2×C3×D4#6711yescharacteristic
110C22×Dic3—61no—
111C2×Dic6—61no—
112C2×C3×C8—21no—
113C3×C4⋊C4—21no—
114C3×C4⋊C4—21no—
115C3×C22⋊C4—21no—
116C3×C22⋊C4—21no—
117C3×C42C22×D311yescharacteristic
118#217—61no—
119#217—61no—
120#217—61no—
121C4⋊Dic3—31no—
122C4⋊Dic3—31no—
123C4⋊Dic3—31no—
124C4⋊Dic3—31no—
125Dic3⋊C4—61no—
126Dic3⋊C4—61no—
127Dic3⋊C4—61no—
128Dic3⋊C4—61no—
129Dic3⋊C4—61no—
130Dic3⋊C4—61no—
131C4×Dic3—61no—
132C2×C3⋊C8—61no—
133C2×C3⋊C8—61no—
134C22×C9—41no—
135C22×C9—41no—
136C22×C9—41no—
137C22×C9#12011yescharacteristic
138C4×C9—21no—
139C4×C9—21no—
140C4×C9—21no—
141C4×C9—41no—
142C4×C9—81no—
143Dic9—41no—
144Dic9—41no—
145Dic9—41no—
146Dic9—41no—
147C4⋊Q8—181no—
148C4⋊Q8C2×D911yescharacteristic
149#126—181no—
150#126—181no—
151#125—91no—
152#125—91no—
153#124C2×D911yescharacteristic
154#123—181no—
155C22⋊Q8—181no—
156C22⋊Q8—181no—
157#107—181no—
158#106—181no—
159#103—21no—
160#103—181no—
161#103—181no—
162#102—21no—
163#97—91no—
164#97—91no—
165#97C2×D911yescharacteristic
166C23×C3—21no—
167C3×Q8—41no—
168C3×Q8—42no—
169C3×D4—41no—
170C2×C3×C4—21no—
171C2×C3×C4—41no—
172C2×C3×C4D3×D411yescharacteristic
173C2×C3×C4D3×D411yescharacteristic
174C2×C3×C4C2×#6711yescharacteristic
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—241no—
180Dic6—241no—
181C3×C8—41no—
182C3⋊C8—62no—
183C3⋊C8—121no—
184C2×C9—81no—
185C2×C9#45411yescharacteristic
186C2×C9#45511yescharacteristic
187C2×C9#45611yescharacteristic
188C2×Q8—21no—
189C2×Q8—181no—
190C2×Q8#61111yescharacteristic
191C2×D4#61111yescharacteristic
192C22×C4—181no—
193C2×C8—21no—
194C2×C8—181no—
195C2×C8—181no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—91no—
199C4⋊C4—91no—
200C4⋊C4—91no—
201C4⋊C4—91no—
202C4⋊C4—181no—
203C4⋊C4—181no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C4⋊C4—181no—
207C4⋊C4—181no—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—181no—
211C22⋊C4—181no—
212C22⋊C4—181no—
213C42—181no—
214C42C22×D911yescharacteristic
215C22×C3—41no—
216C22×C3—41no—
217C22×C3—41no—
218C22×C3#93711yescharacteristic
219C3×C4—21no—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4—41no—
223C3×C4—81no—
224Dic3—121no—
225Dic3—121no—
226Dic3—121no—
227Dic3—121no—
228C9#166411yescharacteristic, complemented, Sylow
229C23—21no—
230Q8—41no—
231Q8—42no—
232Q8—721no—
233D4—41no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—721no—
241C2×C4D4×D911yescharacteristic
242C2×C4D4×D911yescharacteristic
243C2×C4C2×#61111yescharacteristic
244C8—41no—
245C8—182no—
246C8—361no—
247C2×C3—81no—
248C2×C3#506111yescharacteristic
249C2×C3#520111yescharacteristic
250C2×C3#520511yescharacteristic
251C22—41no—
252C22—41no—
253C22—41no—
254C22#6349911yescharacteristic
255C4—21no—
256C4—21no—
257C4—21no—
258C4—41no—
259C4—81no—
260C4—361no—
261C4—361no—
262C4—361no—
263C4—361no—
264C3#7124711yescharacteristic
265C2—81no—
266C2#1058874111yescharacteristic
267C2#1058888111yescharacteristic
268C2#1058888511yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#489C2
socleC22×C3#937
prime radicalC2×C3×D4#67
hypercenter#489D9
hypocenterC9#1664
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
3. #10588762C2semidirect
4. #10588761C2semidirect
6. #10588141C2semidirect
7. #10588141C2semidirect
228. C9#1664semidirect

Maximal subgroups

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

subgroupindex
#105897742
C9×#4892
#105887622
#105887612
#105882172
#105881412
#712473