Finite Group Databasebeta

← #11778508

Subgroups — #11778508

Order 1152.

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

normal subgroups only

This group has 324 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
2#10588661C211yesmaximal, characteristic, complemented
3#10588418C211yesmaximal, characteristic
4#10588401C211yesmaximal, characteristic, complemented
5C9×#324C211yesmaximal, characteristic, complemented
6#10588147C211yesmaximal, characteristic
7#10588144C211yesmaximal, characteristic, complemented
8#68134—31nomaximal
9C2×C9×C4⋊C4C2211yescharacteristic
10#63492C2211yescharacteristic
11#63491—21no—
12C4×#611—21no—
13C2×C4⋊Dic9C2211yescharacteristic
14#63486C2211yescharacteristic
15C2×Dic9⋊C4—21no—
16#63460—21no—
17#63458—21no—
18#63456—21no—
19#63451—21no—
20C9×C22⋊C8C2211yescharacteristic
21C9×C22⋊C8C2211yescharacteristic
22C9⋊#95—21no—
23C9⋊#95C2211yescharacteristic
24#63380—21no—
25#63378—21no—
26#63377—21no—
27#63376—21no—
28#5515—31no—
29#4981—31no—
30#4736—31no—
31#4721—31no—
32C3×#324D311yescharacteristic
33#4470—31no—
34#4467—31no—
35C22×C4×C9D411yescharacteristic
36C22×C4×C9D411yescharacteristic
37C22×C4×C9C2311yescharacteristic
38C2×#611—21no—
39C22×Dic9—21no—
40C22×Dic9—21no—
41C2×D36D411yescharacteristic
42C2×C4×D9—21no—
43C2×Dic18D411yescharacteristic
44C2×C8×C9—21no—
45C2×C8×C9—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⋊Dic9—21no—
54C4⋊Dic9—21no—
55C4⋊Dic9D411yescharacteristic
56C4⋊Dic9D411yescharacteristic
57Dic9⋊C4—21no—
58Dic9⋊C4—21no—
59Dic9⋊C4—21no—
60Dic9⋊C4—21no—
61Dic9⋊C4—42no—
62C4×Dic9—21no—
63#1609—91noSylow
64C2×C3×C4⋊C4C2×D311yescharacteristic
65#930—31no—
66#929—61no—
67C4×#67—61no—
68C2×C4⋊Dic3—31no—
69#924—31no—
70C2×Dic3⋊C4—61no—
71#898—61no—
72#896—61no—
73#894—61no—
74#889—61no—
75C3×C22⋊C8C2×D311yescharacteristic
76C3×C22⋊C8C2×D311yescharacteristic
77C3⋊#95—31no—
78C3⋊#95—61no—
79#821—61no—
80#818—61no—
81#817—61no—
82#816—61no—
83C23×C9C2×D411yescharacteristic
84C22×D9—21no—
85C2×C4×C9—21no—
86C2×C4×C9—21no—
87C2×C4×C9—21no—
88C2×C4×C9—21no—
89C2×C4×C9—41no—
90C2×C4×C9—41no—
91C2×C4×C9C2×D411yescharacteristic
92C2×C4×C9C2×D411yescharacteristic
93#611—41no—
94#611—41no—
95C2×Dic9—22no—
96C2×Dic9—21no—
97C2×Dic9—21no—
98C2×Dic9—21no—
99C2×Dic9—41no—
100C2×Dic9—41no—
101C2×Dic9—41no—
102C2×Dic9—41no—
103C2×Dic9—41no—
104D36—41no—
105C4×D9—81no—
106Dic18—41no—
107C8×C9—41no—
108C8×C9—41no—
109#539—91no—
110#483—91no—
111#480—91no—
112#398—91no—
113#328—91no—
114#327—91no—
115#324D911yescharacteristic, complemented
116C22×C3×C4D1211yescharacteristic
117C22×C3×C4D1211yescharacteristic
118C22×C3×C4C22×D311yescharacteristic
119C2×#67—61no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C2×D12—31no—
123C2×C4×D3—61no—
124C2×Dic6—31no—
125C2×C3×C8—21no—
126C2×C3×C8—21no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129#217—61no—
130(C2×D3)⋊C4—61no—
131(C2×D3)⋊C4—61no—
132(C2×D3)⋊C4—61no—
133(C2×D3)⋊C4—61no—
134C4⋊Dic3—31no—
135C4⋊Dic3—31no—
136C4⋊Dic3—61no—
137C4⋊Dic3—61no—
138Dic3⋊C4—61no—
139Dic3⋊C4—61no—
140Dic3⋊C4—61no—
141Dic3⋊C4—61no—
142Dic3⋊C4—122no—
143C4×Dic3—61no—
144C22×C9—21no—
145C22×C9—21no—
146C22×C9#12011yescharacteristic
147C22×C9#13511yescharacteristic
148C22×C9AGL(1,ℤ/8)11yescharacteristic
149C2×D9—41no—
150C2×D9—41no—
151C2×D9—41no—
152C4×C9—21no—
153C4×C9—21no—
154C4×C9—41no—
155C4×C9—41no—
156Dic9—42no—
157Dic9—41no—
158Dic9—41no—
159Dic9—41no—
160Dic9—81no—
161#126—181no—
162#125—181no—
163#123—181no—
164#123—181no—
165C22⋊Q8—91no—
166C22⋊Q8—181no—
167#121—91no—
168C4×D4—181no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—181no—
171C2×C4⋊C4C2×D911yescharacteristic
172#107—181no—
173#106—181no—
174#103—181no—
175#102—181no—
176C22⋊C8C2×D911yescharacteristic
177C22⋊C8C2×D911yescharacteristic
178#95—91no—
179#95—181no—
180C23×C3C2×D1211yescharacteristic
181C22×D3—61no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4D3×D411yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190#67—121no—
191#67—121no—
192C2×Dic3—62no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—121no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199C2×Dic3—121no—
200C2×Dic3—121no—
201D12—121no—
202C4×D3—241no—
203Dic6—121no—
204C3×C8—41no—
205C3×C8—41no—
206C2×C9—21no—
207C2×C9—21no—
208C2×C9#44911yescharacteristic
209C2×C9#45611yescharacteristic
210C2×C9#45811yescharacteristic
211D9—81no—
212C2×Q8—91no—
213C2×D4—91no—
214C2×D4—181no—
215C22×C4—181no—
216C22×C4—181no—
217C22×C4—181no—
218C22×C4D3611yescharacteristic
219C22×C4D3611yescharacteristic
220C22×C4C22×D911yescharacteristic
221C2×C8—21no—
222C2×C8—21no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—91no—
226C4⋊C4—91no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C4⋊C4—181no—
233C4⋊C4—362no—
234C22⋊C4—181no—
235C22⋊C4—181no—
236C22⋊C4—181no—
237C22⋊C4—181no—
238C22⋊C4—181no—
239C42—181no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3#88211yescharacteristic
243C22×C3#90411yescharacteristic
244C22×C3#90811yescharacteristic
245C2×D3—121no—
246C2×D3—121no—
247C2×D3—121no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—41no—
251C3×C4—41no—
252Dic3—122no—
253Dic3—121no—
254Dic3—121no—
255Dic3—121no—
256Dic3—241no—
257C9#160911yescharacteristic, complemented, Sylow
258C23—181no—
259C23C2×D3611yescharacteristic
260Q8—361no—
261D4—361no—
262D4—361no—
263D4—361no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—182no—
271C2×C4—181no—
272C2×C4—181no—
273C2×C4—181no—
274C2×C4—361no—
275C2×C4—361no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—721no—
280C2×C4D4×D911yescharacteristic
281C2×C4D4×D911yescharacteristic
282C8—41no—
283C8—41no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3#473411yescharacteristic
287C2×C3#474211yescharacteristic
288C2×C3#475211yescharacteristic
289D3—241no—
290C22—21no—
291C22—21no—
292C22—361no—
293C22—361no—
294C22—361no—
295C22#6344411yescharacteristic
296C22#6346711yescharacteristic
297C22#6347011yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—362no—
303C4—361no—
304C4—361no—
305C4—361no—
306C4—721no—
307C3#6813411yescharacteristic
308C2—21no—
309C2—21no—
310C2—721no—
311C2#1058841611yescharacteristic
312C2#1058842211yescharacteristic
313C2#1058843211yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#324C2
socleC22×C3#882
prime radical#63492C22
hypercenter#324D9
hypocenterC9#1609
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #10588661C2semidirect
4. #10588401C2semidirect
5. C9×#324C2semidirect
7. #10588144C2semidirect
115. #324D9semidirect
257. C9#1609semidirect

Maximal subgroups

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

subgroupindex
#105896172
#105886612
#105884182
#105884012
C9×#3242
#105881472
#105881442
#681343