Finite Group Databasebeta

← #11778722

Subgroups — #11778722

Order 1152.

312 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 66 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#10589617C211yesmaximal, characteristic
2C9×#400C211yesmaximal, characteristic, complemented
3#10588651C211yesmaximal, characteristic
4#10588646C211yesmaximal, characteristic, complemented
5#10588205C211yesmaximal, characteristic, complemented
6#10588129C211yesmaximal, characteristic
7#10588128C211yesmaximal, characteristic, complemented
8#69717—31nomaximal
9C2×C9×C4⋊C4C2211yescharacteristic
10C2×C9×C4⋊C4C2211yescharacteristic
11#63492C2211yescharacteristic
12#63491—21no—
13C4×#611—21no—
14#63486C2211yescharacteristic
15#63460—21no—
16#63458—21no—
17#63456—21no—
18#63451—21no—
19C9×#95—21no—
20C9×#95—21no—
21C9×#95C2211yescharacteristic
22#63389C2211yescharacteristic
23#63389C2211yescharacteristic
24#63369—21no—
25#63368—21no—
26#63367—21no—
27#63366—21no—
28#5515—31no—
29C3×#400D311yescharacteristic
30#4970—31no—
31#4968—31no—
32#4528—31no—
33#4452—31no—
34#4451—31no—
35C22×C4×C9—21no—
36C22×C4×C9—21no—
37C22×C4×C9D411yescharacteristic
38C22×C4×C9D411yescharacteristic
39C22×C4×C9C2311yescharacteristic
40C2×#611—21no—
41C2×D36D411yescharacteristic
42C2×C4×D9—21no—
43C2×Dic18D411yescharacteristic
44C9×C4⋊C4—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4—21no—
47C9×C4⋊C4—21no—
48#3676—21no—
49(C2×D9)⋊C4—21no—
50(C2×D9)⋊C4—21no—
51(C2×D9)⋊C4—21no—
52(C2×D9)⋊C4—21no—
53C4⋊Dic9D411yescharacteristic
54C4⋊Dic9D411yescharacteristic
55Dic9⋊C4—21no—
56Dic9⋊C4—21no—
57Dic9⋊C4—21no—
58Dic9⋊C4—21no—
59C4×Dic9—21no—
60C2×C9⋊C8—21no—
61C2×C9⋊C8—21no—
62#1615—91noSylow
63C2×C3×C4⋊C4C2×D311yescharacteristic
64C2×C3×C4⋊C4C2×D311yescharacteristic
65#930—31no—
66#929—61no—
67C4×#67—61no—
68#924—31no—
69#898—61no—
70#896—61no—
71#894—61no—
72#889—61no—
73C3×#95—21no—
74C3×#95—21no—
75C3×#95C2×D311yescharacteristic
76#830—31no—
77#830—31no—
78#810—61no—
79#809—61no—
80#808—61no—
81#807—61no—
82C23×C9C2×D411yescharacteristic
83C22×D9—21no—
84C2×C4×C9—21no—
85C2×C4×C9—21no—
86C2×C4×C9—21no—
87C2×C4×C9—21no—
88C2×C4×C9—41no—
89C2×C4×C9—41no—
90C2×C4×C9—41no—
91C2×C4×C9—41no—
92C2×C4×C9—42no—
93C2×C4×C9—41no—
94C2×C4×C9—41no—
95C2×C4×C9C2×D411yescharacteristic
96C2×C4×C9C2×D411yescharacteristic
97#611—41no—
98#611—41no—
99C2×Dic9—21no—
100C2×Dic9—21no—
101C2×Dic9—21no—
102D36—41no—
103C4×D9—81no—
104Dic18—41no—
105C9⋊C8—41no—
106C9⋊C8—41no—
107#539—91no—
108#484—91no—
109#481—91no—
110#400D911yescharacteristic, complemented
111#328—91no—
112#327—91no—
113#324—91no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4#6711yescharacteristic
117C22×C3×C4#6711yescharacteristic
118C22×C3×C4C22×D311yescharacteristic
119C2×#67—61no—
120C2×D12—31no—
121C2×C4×D3—61no—
122C2×Dic6—31no—
123C3×C4⋊C4—21no—
124C3×C4⋊C4—21no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4—21no—
127#217—61no—
128(C2×D3)⋊C4—61no—
129(C2×D3)⋊C4—61no—
130(C2×D3)⋊C4—61no—
131(C2×D3)⋊C4—61no—
132C4⋊Dic3—31no—
133C4⋊Dic3—31no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136Dic3⋊C4—61no—
137Dic3⋊C4—61no—
138C4×Dic3—61no—
139C2×C3⋊C8—61no—
140C2×C3⋊C8—61no—
141C22×C9—21no—
142C22×C9—21no—
143C22×C9#12011yescharacteristic
144C22×C9#13511yescharacteristic
145C22×C9#13711yescharacteristic
146C2×D9—41no—
147C2×D9—41no—
148C2×D9—41no—
149C4×C9—21no—
150C4×C9—21no—
151C4×C9—41no—
152C4×C9—41no—
153C4×C9—81no—
154C4×C9—81no—
155Dic9—41no—
156Dic9—41no—
157Dic9—41no—
158#126—181no—
159#125—181no—
160#123—181no—
161#123—181no—
162C22⋊Q8—91no—
163C22⋊Q8—181no—
164#121—91no—
165C4×D4—181no—
166C2×C4⋊C4C2×D911yescharacteristic
167C2×C4⋊C4C2×D911yescharacteristic
168#107—181no—
169#106—181no—
170#103—181no—
171#102—181no—
172C22⋊C8—91no—
173C22⋊C8—91no—
174#95—21no—
175#95—21no—
176#95C2×D911yescharacteristic
177C23×C3C2×#6711yescharacteristic
178C22×D3—61no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—41no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—42no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192#67—121no—
193#67—121no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197D12—121no—
198C4×D3—241no—
199Dic6—121no—
200C3⋊C8—121no—
201C3⋊C8—121no—
202C2×C9—21no—
203C2×C9—21no—
204C2×C9#45211yescharacteristic
205C2×C9#45411yescharacteristic
206C2×C9#45811yescharacteristic
207D9—81no—
208C2×Q8—91no—
209C2×D4—91no—
210C2×D4—181no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—181no—
214C22×C4#61111yescharacteristic
215C22×C4#61111yescharacteristic
216C22×C4C22×D911yescharacteristic
217C2×C8—181no—
218C2×C8—181no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—91no—
224C4⋊C4—91no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C22⋊C4—181no—
230C22⋊C4—181no—
231C22⋊C4—181no—
232C22⋊C4—181no—
233C22⋊C4—181no—
234C42—181no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3#93711yescharacteristic
238C22×C3#94211yescharacteristic
239C22×C3#95011yescharacteristic
240C2×D3—121no—
241C2×D3—121no—
242C2×D3—121no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—41no—
246C3×C4—41no—
247C3×C4—81no—
248C3×C4—81no—
249Dic3—121no—
250Dic3—121no—
251Dic3—121no—
252C9#161511yescharacteristic, complemented, Sylow
253C23—181no—
254C23C2×#61111yescharacteristic
255Q8—361no—
256D4—361no—
257D4—361no—
258D4—361no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—181no—
271C2×C4—181no—
272C2×C4—181no—
273C2×C4—721no—
274C2×C4D4×D911yescharacteristic
275C2×C4D4×D911yescharacteristic
276C8—361no—
277C8—361no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3#504711yescharacteristic
281C2×C3#505311yescharacteristic
282C2×C3#506211yescharacteristic
283D3—241no—
284C22—21no—
285C22—21no—
286C22—361no—
287C22—361no—
288C22—361no—
289C22#6349911yescharacteristic
290C22#6350511yescharacteristic
291C22#6351311yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—81no—
297C4—81no—
298C4—361no—
299C4—361no—
300C4—361no—
301C3#6971711yescharacteristic
302C2—21no—
303C2—21no—
304C2—721no—
305C2#1058873011yescharacteristic
306C2#1058873311yescharacteristic
307C2#1058874211yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#400C2
socleC22×C3#937
prime radical#63492C22
hypercenter#400D9
hypocenterC9#1615
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C9×#400C2semidirect
4. #10588646C2semidirect
5. #10588205C2semidirect
7. #10588128C2semidirect
110. #400D9semidirect
252. C9#1615semidirect

Maximal subgroups

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

subgroupindex
#105896172
C9×#4002
#105886512
#105886462
#105882052
#105881292
#105881282
#697173