Finite Group Databasebeta

← #11778493

Subgroups — #11778493

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#10589704C211yesmaximal, characteristic
2C9×#480C211yesmaximal, characteristic
3#10588663C211yesmaximal, characteristic, complemented
4#10588647C211yesmaximal, characteristic, complemented
5#10588214C211yesmaximal, characteristic
6#10588145C211yesmaximal, characteristic, complemented
7#10588144C211yesmaximal, characteristic, complemented
8#71166—31nomaximal
9C9×#121C2211yescharacteristic
10C2×C9×C4⋊C4C2211yescharacteristic
11#63497—21no—
12#63497—21no—
13D4×Dic9—21no—
14#63486C2211yescharacteristic
15C2×Dic9⋊C4—21no—
16C2×Dic9⋊C4C2211yescharacteristic
17#63451—21no—
18#63441—21no—
19#63440—21no—
20C9×#107—21no—
21C9×#102—21no—
22C9×C22⋊C8C2211yescharacteristic
23C9⋊#95—21no—
24C9⋊#95C2211yescharacteristic
25#63389C2211yescharacteristic
26#63368—21no—
27#63367—21no—
28#5602—31no—
29C3×#480D311yescharacteristic
30#4983—31no—
31#4971—31no—
32#4537—31no—
33#4469—31no—
34#4467—31no—
35C2×D4×C9—21no—
36C2×D4×C9D411yescharacteristic
37C22×C4×C9—21no—
38C22×C4×C9C2311yescharacteristic
39C22×Dic9—21no—
40C22×Dic9—21no—
41C22×Dic9D411yescharacteristic
42C22×Dic9D411yescharacteristic
43C2×Dic18D411yescharacteristic
44C2×C8×C9—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4—21no—
47C9×C4⋊C4D411yescharacteristic
48C9×C22⋊C4—21no—
49#3676—21no—
50#3676—21no—
51#3676—21no—
52#3676—21no—
53C4⋊Dic9—21no—
54C4⋊Dic9D411yescharacteristic
55Dic9⋊C4—21no—
56Dic9⋊C4—21no—
57Dic9⋊C4—21no—
58Dic9⋊C4—21no—
59Dic9⋊C4—21no—
60Dic9⋊C4—42no—
61C4×Dic9—21no—
62C2×C9⋊C8—21no—
63#1609—91noSylow
64C3×#121C2×D311yescharacteristic
65C2×C3×C4⋊C4C2×D311yescharacteristic
66#935—61no—
67#935—61no—
68D4×Dic3—61no—
69#924—31no—
70C2×Dic3⋊C4—31no—
71C2×Dic3⋊C4—61no—
72#889—61no—
73#879—61no—
74#878—61no—
75C3×#107—21no—
76C3×#102—21no—
77C3×C22⋊C8C2×D311yescharacteristic
78C3⋊#95—31no—
79C3⋊#95—61no—
80#830—31no—
81#810—61no—
82#808—61no—
83C23×C9—21no—
84C23×C9C2×D411yescharacteristic
85D4×C9—41no—
86D4×C9—41no—
87D4×C9—41no—
88C2×C4×C9—21no—
89C2×C4×C9—41no—
90C2×C4×C9—41no—
91C2×C4×C9—41no—
92C2×C4×C9—41no—
93C2×C4×C9C2×D411yescharacteristic
94C2×C4×C9C2×D411yescharacteristic
95C2×Dic9—22no—
96C2×Dic9—21no—
97C2×Dic9—21no—
98C2×Dic9—21no—
99C2×Dic9—21no—
100C2×Dic9—21no—
101C2×Dic9—21no—
102C2×Dic9—41no—
103C2×Dic9—41no—
104C2×Dic9—41no—
105C2×Dic9—81no—
106Dic18—41no—
107C8×C9—41no—
108C9⋊C8—41no—
109#539—91no—
110#483—91no—
111#480D911yescharacteristic
112#398—91no—
113#328—91no—
114#327—91no—
115#324—91no—
116C2×C3×D4—21no—
117C2×C3×D4#6711yescharacteristic
118C22×C3×C4—21no—
119C22×C3×C4C22×D311yescharacteristic
120C22×Dic3—31no—
121C22×Dic3—31no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C2×Dic6—31no—
125C2×C3×C8—21no—
126C3×C4⋊C4—21no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4#6711yescharacteristic
129C3×C22⋊C4—21no—
130#217—61no—
131#217—61no—
132#217—61no—
133#217—61no—
134C4⋊Dic3—31no—
135C4⋊Dic3—61no—
136Dic3⋊C4—61no—
137Dic3⋊C4—61no—
138Dic3⋊C4—61no—
139Dic3⋊C4—61no—
140Dic3⋊C4—61no—
141Dic3⋊C4—122no—
142C4×Dic3—61no—
143C2×C3⋊C8—61no—
144C22×C9—21no—
145C22×C9—21no—
146C22×C9—41no—
147C22×C9—41no—
148C22×C9—41no—
149C22×C9#12011yescharacteristic
150C22×C9#13511yescharacteristic
151C22×C9AGL(1,ℤ/8)11yescharacteristic
152C4×C9—21no—
153C4×C9—21no—
154C4×C9—41no—
155C4×C9—81no—
156Dic9—42no—
157Dic9—41no—
158Dic9—41no—
159Dic9—41no—
160Dic9—41no—
161#126—181no—
162#125—181no—
163#123—181no—
164#123—181no—
165C22⋊Q8—91no—
166C22⋊Q8—181no—
167#121C2×D911yescharacteristic
168C4×D4—181no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—181no—
171C2×C4⋊C4C2×D911yescharacteristic
172#107—21no—
173#106—181no—
174#103—181no—
175#102—21no—
176C22⋊C8—91no—
177C22⋊C8C2×D911yescharacteristic
178#95—91no—
179#95—181no—
180C23×C3—21no—
181C23×C3D3×D411yescharacteristic
182C3×D4—41no—
183C3×D4—41no—
184C3×D4—41no—
185C2×C3×C4—21no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4C2×#6711yescharacteristic
192C2×Dic3—62no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—121no—
200C2×Dic3—121no—
201C2×Dic3—121no—
202C2×Dic3—241no—
203Dic6—121no—
204C3×C8—41no—
205C3⋊C8—121no—
206C2×C9—21no—
207C2×C9—21no—
208C2×C9—81no—
209C2×C9#44911yescharacteristic
210C2×C9#45611yescharacteristic
211C2×C9#45811yescharacteristic
212C2×Q8—91no—
213C2×D4—21no—
214C2×D4#61111yescharacteristic
215C22×C4—21no—
216C22×C4—91no—
217C22×C4—91no—
218C22×C4—181no—
219C22×C4—181no—
220C22×C4C22×D911yescharacteristic
221C2×C8—21no—
222C2×C8—181no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—91no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C4⋊C4—362no—
233C4⋊C4#61111yescharacteristic
234C22⋊C4—21no—
235C22⋊C4—181no—
236C22⋊C4—181no—
237C22⋊C4—181no—
238C22⋊C4—181no—
239C42—181no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—41no—
243C22×C3—41no—
244C22×C3—41no—
245C22×C3#91111yescharacteristic
246C22×C3#91211yescharacteristic
247C22×C3#93711yescharacteristic
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—41no—
251C3×C4—81no—
252Dic3—122no—
253Dic3—121no—
254Dic3—121no—
255Dic3—121no—
256Dic3—121no—
257C9#160911yescharacteristic, complemented, Sylow
258C23—21no—
259C23D4×D911yescharacteristic
260Q8—361no—
261D4—41no—
262D4—41no—
263D4—41no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—182no—
270C2×C4—181no—
271C2×C4—181no—
272C2×C4—181no—
273C2×C4—181no—
274C2×C4—181no—
275C2×C4—181no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—721no—
280C2×C4D4×D911yescharacteristic
281C2×C4C2×#61111yescharacteristic
282C8—41no—
283C8—361no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—81no—
287C2×C3#505311yescharacteristic
288C2×C3#515811yescharacteristic
289C2×C3#520511yescharacteristic
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22#6347311yescharacteristic
296C22#6347411yescharacteristic
297C22#6349911yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—81no—
302C4—362no—
303C4—361no—
304C4—361no—
305C4—361no—
306C4—361no—
307C3#7116611yescharacteristic
308C2—21no—
309C2—21no—
310C2—81no—
311C2#1058873311yescharacteristic
312C2#1058883811yescharacteristic
313C2#1058888511yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#480C2
socleC22×C3#937
prime radicalC3×#121C2×D3
hypercenter#480D9
hypocenterC9#1609
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
3. #10588663C2semidirect
4. #10588647C2semidirect
6. #10588145C2semidirect
7. #10588144C2semidirect
257. C9#1609semidirect

Maximal subgroups

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

subgroupindex
#105897042
C9×#4802
#105886632
#105886472
#105882142
#105881452
#105881442
#711663