Finite Group Databasebeta

← #11775164

Subgroups — #11775164

Order 1152.

342 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 80 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#10589724C211yesmaximal, characteristic
2#10588399C211yesmaximal, characteristic
3#10588328C211yesmaximal, characteristic
4C9×#328C211yesmaximal, characteristic
5#10588215C211yesmaximal, characteristic
6#10588144C211yesmaximal, characteristic
7#10588128C211yesmaximal, characteristic
8#68310—31nomaximal
9C9×C22⋊Q8C2211yescharacteristic
10Q8×Dic9C411yescharacteristic, complemented
11#63506C411yescharacteristic, complemented
12#63486C2211yescharacteristic
13C2×C4×Dic9—21no—
14C2×C4×Dic9C2211yescharacteristic
15#63451—21no—
16#63450C411yescharacteristic, complemented
17#63449—21no—
18#63449C411yescharacteristic, complemented
19#63440—21no—
20#63439—21no—
21C9×C22⋊C8C2211yescharacteristic
22C9×#95C2211yescharacteristic
23C9⋊#95—21no—
24C9⋊#95C2211yescharacteristic
25#63389C2211yescharacteristic
26#63375—21no—
27Dic9⋊C8—21no—
28#5622—31no—
29#4719—31no—
30#4648—31no—
31C3×#328D311yescharacteristic
32#4538—31no—
33#4467—31no—
34#4452—31no—
35C2×Q8×C9C2×C411yescharacteristic
36C22×C4×C9—21no—
37C22×C4×C9C2311yescharacteristic
38C22×Dic9—21no—
39C22×Dic9D411yescharacteristic
40C22×Dic9D411yescharacteristic
41C2×Dic18—21no—
42C2×Dic18C2×C411yescharacteristic
43C2×C8×C9—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4C2×C411yescharacteristic
46C9×C22⋊C4—21no—
47#3676—21no—
48C4⋊Dic9—21no—
49C4⋊Dic9C2×C411yescharacteristic
50Dic9⋊C4—21no—
51Dic9⋊C4—21no—
52Dic9⋊C4—21no—
53Dic9⋊C4—21no—
54Dic9⋊C4—21no—
55C4×Dic9—24no—
56C4×Dic9—21no—
57C4×Dic9—21no—
58C4×Dic9C2×C411yescharacteristic
59C4×Dic9C2×C411yescharacteristic
60C4×Dic9D411yescharacteristic
61C4×Dic9D411yescharacteristic
62C2×C9⋊C8—21no—
63#1506—91noSylow
64C3×C22⋊Q8C2×D311yescharacteristic
65Q8×Dic3—31no—
66#944—31no—
67#924—31no—
68C2×C4×Dic3—31no—
69C2×C4×Dic3—61no—
70#889—61no—
71#888—31no—
72#887—31no—
73#887—61no—
74#878—61no—
75#877—61no—
76C3×C22⋊C8C2×D311yescharacteristic
77C3×#95C2×D311yescharacteristic
78C3⋊#95—31no—
79C3⋊#95—61no—
80#830—31no—
81#815—61no—
82Dic3⋊C8—61no—
83C23×C9C2×D411yescharacteristic
84Q8×C9—41no—
85C2×C4×C9—22no—
86C2×C4×C9—21no—
87C2×C4×C9—21no—
88C2×C4×C9—41no—
89C2×C4×C9—41no—
90C2×C4×C9—41no—
91C2×C4×C9C22×C411yescharacteristic
92C2×C4×C9C2×D411yescharacteristic
93C2×Dic9—21no—
94C2×Dic9—21no—
95C2×Dic9—22no—
96C2×Dic9—22no—
97C2×Dic9—21no—
98C2×Dic9—21no—
99C2×Dic9—41no—
100C2×Dic9—41no—
101C2×Dic9C22⋊C411yescharacteristic
102C2×Dic9C22⋊C411yescharacteristic
103C2×Dic9C22⋊C411yescharacteristic
104C2×Dic9C22⋊C411yescharacteristic
105Dic18—42no—
106Dic18—41no—
107C8×C9—41no—
108C9⋊C8—41no—
109#533—91no—
110#432—91no—
111#376—91no—
112#328—91no—
113#328—91no—
114#328—91no—
115#328D911yescharacteristic
116C2×C3×Q8C4×D311yescharacteristic
117C22×C3×C4—21no—
118C22×C3×C4C22×D311yescharacteristic
119C22×Dic3—31no—
120C22×Dic3—31no—
121C22×Dic3—61no—
122C2×Dic6—31no—
123C2×Dic6—61no—
124C2×C3×C8—21no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4C4×D311yescharacteristic
127C3×C22⋊C4—21no—
128#217—61no—
129C4⋊Dic3—31no—
130C4⋊Dic3—61no—
131Dic3⋊C4—61no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136C4×Dic3—31no—
137C4×Dic3—31no—
138C4×Dic3—31no—
139C4×Dic3—31no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—64no—
143C2×C3⋊C8—61no—
144C22×C9—21no—
145C22×C9—21no—
146C22×C9C2×C22⋊C411yescharacteristic
147C22×C9#13711yescharacteristic
148C22×C9#13711yescharacteristic
149C4×C9—21no—
150C4×C9—21no—
151C4×C9—42no—
152C4×C9—41no—
153C4×C9—41no—
154Dic9—21no—
155Dic9—21no—
156Dic9—21no—
157Dic9—42no—
158Dic9—41no—
159Dic9—41no—
160Dic9#10412yes—
161C4⋊Q8—91no—
162C4⋊Q8—91no—
163#125—181no—
164C22⋊Q8—91no—
165C22⋊Q8—181no—
166C22⋊Q8C2×D911yescharacteristic
167C4×Q8—91no—
168C4×Q8—91no—
169C4×Q8—181no—
170#117—181no—
171C2×C42—91no—
172C2×C42—181no—
173C4⋊C8—181no—
174C22⋊C8—91no—
175C22⋊C8C2×D911yescharacteristic
176#97—181no—
177#95—91no—
178#95—181no—
179#95C2×D911yescharacteristic
180C23×C3D3×D411yescharacteristic
181C3×Q8—41no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4C2×C4×D311yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×Dic3—31no—
191C2×Dic3—31no—
192C2×Dic3—31no—
193C2×Dic3—31no—
194C2×Dic3—62no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—62no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—121no—
201C2×Dic3—121no—
202Dic6—122no—
203Dic6—121no—
204C3×C8—41no—
205C3⋊C8—121no—
206C2×C9—21no—
207C2×C9—21no—
208C2×C9#41011yescharacteristic
209C2×C9#41911yescharacteristic
210C2×C9C2×#10411yescharacteristic
211C2×Q8—91no—
212C2×Q8—181no—
213C2×Q8C4×D911yescharacteristic
214C22×C4—21no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—181no—
218C22×C4C22×D911yescharacteristic
219C2×C8—21no—
220C2×C8—181no—
221C4⋊C4—21no—
222C4⋊C4—91no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C4⋊C4C4×D911yescharacteristic
230C22⋊C4—21no—
231C22⋊C4—181no—
232C42—91no—
233C42—91no—
234C42—91no—
235C42—91no—
236C42—181no—
237C42—181no—
238C42—184no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3D3×C22⋊C411yescharacteristic
242C22×C3#91511yescharacteristic
243C22×C3#91811yescharacteristic
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—42no—
247C3×C4—41no—
248C3×C4—41no—
249Dic3—32no—
250Dic3—61no—
251Dic3—61no—
252Dic3—61no—
253Dic3—122no—
254Dic3—121no—
255Dic3—121no—
256C9#150611yescharacteristic, complemented, Sylow
257C23D4×D911yescharacteristic
258Q8—41no—
259Q8—361no—
260Q8—362no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—91no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—182no—
272C2×C4—181no—
273C2×C4—181no—
274C2×C4—182no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4C2×C4×D911yescharacteristic
280C2×C4D4×D911yescharacteristic
281C8—41no—
282C8—361no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3#474011yescharacteristic
286C2×C3#480211yescharacteristic
287C2×C3D3×#10411yescharacteristic
288C22—21no—
289C22—21no—
290C22C22⋊C4×D911yescharacteristic
291C22#6347711yescharacteristic
292C22#6348011yescharacteristic
293C4—21no—
294C4—21no—
295C4—42no—
296C4—41no—
297C4—41no—
298C4—92no—
299C4—181no—
300C4—181no—
301C4—181no—
302C4—362no—
303C4—361no—
304C4—361no—
305C3#6831011yescharacteristic
306C2—21no—
307C2—21no—
308C2#1058842011yescharacteristic
309C2#1058848211yescharacteristic
310C2D9×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#328C2
socleC22×C3D3×C22⋊C4
prime radicalC23×C3D3×D4
cosocleC22×C4×C9C23
hypercenter#328D9
hypocenterC9#1506
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
10. Q8×Dic9C4semidirect
11. #63506C4semidirect
16. #63450C4semidirect
18. #63449C4semidirect
256. C9#1506semidirect

Maximal subgroups

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

subgroupindex
#105897242
#105883992
#105883282
C9×#3282
#105882152
#105881442
#105881282
#683103