Finite Group Databasebeta

← #11794304

Subgroups — #11794304

Order 1152.

471 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 104 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#10589585C211yesmaximal, characteristic
2#10588630C212yesmaximal
3#10588626C211yesmaximal, characteristic
4C9×#342C211yesmaximal, characteristic
5#10588204C212yesmaximal
6#68958—31nomaximal
7C23×Dic9C2211yescharacteristic
8C2×C9×C22⋊C4C2211yescharacteristic
9C2×C9×C22⋊C4C2212yes—
10C2×#3676C2212yes—
11C2×#3676C2211yescharacteristic
12C2×C4⋊Dic9—22no—
13#63486—21no—
14#63486—21no—
15C2×Dic9⋊C4—21no—
16#63440—22no—
17#63440—22no—
18C9⋊#95—21no—
19C9⋊#95—22no—
20#5483—31no—
21#4950—32no—
22#4946—31no—
23C3×#342D311yescharacteristic
24#4527—32no—
25C24×C9C2311yescharacteristic
26C22×C4×C9—22no—
27C22×C4×C9D411yescharacteristic
28C22×C4×C9D411yescharacteristic
29C22×Dic9—21no—
30C22×Dic9—21no—
31C22×Dic9—22no—
32C22×Dic9—42no—
33C22×Dic9D412yes—
34C22×Dic9D412yes—
35C2×Dic18—21no—
36C2×Dic18—21no—
37C9×C22⋊C4—22no—
38C9×C22⋊C4—22no—
39C9×C22⋊C4Q814yescomplemented
40#3676—22no—
41#3676—22no—
42#3676—21no—
43#3676Q812yescomplemented
44C4⋊Dic9—21no—
45C4⋊Dic9—21no—
46C4⋊Dic9—44no—
47Dic9⋊C4—22no—
48Dic9⋊C4—22no—
49Dic9⋊C4—42no—
50#2062—91noSylow
51C23×Dic3—31no—
52C2×C3×C22⋊C4C2×D311yescharacteristic
53C2×C3×C22⋊C4C2×D312yes—
54C2×#217—31no—
55C2×#217—32no—
56C2×C4⋊Dic3—62no—
57#924—61no—
58#924—61no—
59C2×Dic3⋊C4—61no—
60#878—62no—
61#878—62no—
62C3⋊#95—62no—
63C3⋊#95—61no—
64C23×C9—41no—
65C23×C9—41no—
66C23×C9C2×D411yescharacteristic
67C23×C9C2×D412yes—
68C23×C9C2×Q812yes—
69C23×C9C2×Q811yescharacteristic
70C23×C9#4111yescharacteristic
71C2×C4×C9—21no—
72C2×C4×C9—21no—
73C2×C4×C9—24no—
74C2×C4×C9—42no—
75C2×C4×C9—42no—
76C2×C4×C9—41no—
77C2×C4×C9—41no—
78C2×Dic9—22no—
79C2×Dic9—24no—
80C2×Dic9—22no—
81C2×Dic9—22no—
82C2×Dic9—22no—
83C2×Dic9—41no—
84C2×Dic9—41no—
85C2×Dic9—41no—
86C2×Dic9—42no—
87C2×Dic9—41no—
88C2×Dic9—42no—
89C2×Dic9—42no—
90Dic18—81no—
91Dic18—81no—
92#543—91no—
93#385—91no—
94#385—92no—
95#342—92no—
96#342D911yescharacteristic
97C24×C3C22×D311yescharacteristic
98C22×C3×C4—22no—
99C22×C3×C4D1211yescharacteristic
100C22×C3×C4D1211yescharacteristic
101C22×Dic3—32no—
102C22×Dic3—32no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—62no—
106C22×Dic3—122no—
107C2×Dic6—61no—
108C2×Dic6—61no—
109C3×C22⋊C4—22no—
110C3×C22⋊C4—22no—
111C3×C22⋊C4Dic614yes—
112#217—32no—
113#217—62no—
114#217—62no—
115#217—61no—
116C4⋊Dic3—61no—
117C4⋊Dic3—61no—
118C4⋊Dic3—124no—
119Dic3⋊C4—62no—
120Dic3⋊C4—62no—
121Dic3⋊C4—122no—
122C22×C9—21no—
123C22×C9—22no—
124C22×C9—21no—
125C22×C9—22no—
126C22×C9—42no—
127C22×C9—41no—
128C22×C9—41no—
129C22×C9#12011yescharacteristic
130C22×C9C22⋊Q812yes—
131C22×C9C22⋊Q811yescharacteristic
132C22×C9C4⋊Q811yescharacteristic
133C22×C9C4⋊Q812yes—
134C4×C9—44no—
135C4×C9—41no—
136C4×C9—41no—
137Dic9—42no—
138Dic9—42no—
139Dic9—42no—
140Dic9—42no—
141C23×C4—91no—
142C22⋊Q8—182no—
143C22⋊Q8—182no—
144C22⋊Q8—181no—
145C22⋊Q8—181no—
146C2×C4⋊C4—182no—
147C2×C4⋊C4—181no—
148C2×C22⋊C4—91no—
149C2×C22⋊C4—92no—
150C2×C22⋊C4C2×D911yescharacteristic
151C2×C22⋊C4C2×D912yes—
152#95—182no—
153#95—181no—
154C23×C3—41no—
155C23×C3—41no—
156C23×C3C2×Dic612yes—
157C23×C3C2×D1211yescharacteristic
158C23×C3D3×D412yes—
159C23×C3#23711yescharacteristic
160C23×C3D3×Q811yescharacteristic
161C2×C3×C4—24no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—42no—
165C2×C3×C4—42no—
166C2×C3×C4—41no—
167C2×C3×C4—41no—
168C2×Dic3—62no—
169C2×Dic3—64no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—121no—
174C2×Dic3—121no—
175C2×Dic3—121no—
176C2×Dic3—122no—
177C2×Dic3—121no—
178C2×Dic3—122no—
179C2×Dic3—122no—
180Dic6—241no—
181Dic6—241no—
182C2×C9—21no—
183C2×C9—22no—
184C2×C9—21no—
185C2×C9—22no—
186C2×C9#39511yescharacteristic
187C2×C9B(4,𝔽2)11yescharacteristic
188C2×C9#45811yescharacteristic
189C24C22×D911yescharacteristic
190C2×Q8—181no—
191C2×Q8—181no—
192C22×C4—22no—
193C22×C4—92no—
194C22×C4—92no—
195C22×C4—181no—
196C22×C4—181no—
197C22×C4—182no—
198C22×C4—362no—
199C22×C4D3611yescharacteristic
200C22×C4D3611yescharacteristic
201C4⋊C4—182no—
202C4⋊C4—182no—
203C4⋊C4—181no—
204C4⋊C4—181no—
205C4⋊C4—362no—
206C4⋊C4—364no—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—92no—
210C22⋊C4—182no—
211C22⋊C4—182no—
212C22⋊C4—181no—
213C22⋊C4Dic1814yescomplemented
214C22×C3—21no—
215C22×C3—22no—
216C22×C3—21no—
217C22×C3—22no—
218C22×C3—42no—
219C22×C3—41no—
220C22×C3—41no—
221C22×C3#86911yescharacteristic
222C22×C3#87812yes—
223C22×C3#88211yescharacteristic
224C22×C3#88812yes—
225C22×C3#89711yescharacteristic
226C3×C4—44no—
227C3×C4—41no—
228C3×C4—41no—
229Dic3—122no—
230Dic3—122no—
231Dic3—122no—
232Dic3—122no—
233C9#206211yescharacteristic, complemented, Sylow
234C23—41no—
235C23—41no—
236C23C2×Dic1812yes—
237C23C2×D3611yescharacteristic
238C23D4×D912yes—
239C23#369911yescharacteristic
240C23Q8×D911yescharacteristic
241Q8—721no—
242Q8—721no—
243C2×C4—24no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—182no—
251C2×C4—184no—
252C2×C4—182no—
253C2×C4—182no—
254C2×C4—182no—
255C2×C4—361no—
256C2×C4—361no—
257C2×C4—362no—
258C2×C4—361no—
259C2×C4—361no—
260C2×C4—362no—
261C2×C4—362no—
262C2×C3—21no—
263C2×C3—22no—
264C2×C3—21no—
265C2×C3—22no—
266C2×C3#465611yescharacteristic
267C2×C3#474111yescharacteristic
268C2×C3#474211yescharacteristic
269C22—21no—
270C22—22no—
271C22—21no—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22#6343111yescharacteristic
277C22#6344012yes—
278C22#6344411yescharacteristic
279C22#6345012yes—
280C22#6345911yescharacteristic
281C4—44no—
282C4—41no—
283C4—41no—
284C4—362no—
285C4—362no—
286C4—362no—
287C4—362no—
288C3#6895811yescharacteristic
289C2—22no—
290C2—21no—
291C2—21no—
292C2—22no—
293C2#1058833611yescharacteristic
294C2#1058842111yescharacteristic
295C2#1058842211yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC24×C9C23
Frattini, prime radicalC24×C3C22×D3
FittingC9×#342C2
socleC22×C3#882
hypercenter#342D9
hypocenterC9#2062
LCSG ▷ C24×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
39. C9×C22⋊C4Q8semidirect
43. #3676Q8semidirect
213. C22⋊C4Dic18semidirect
233. C9#2062semidirect

Maximal subgroups

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

subgroupindex
#105895852
#105886302
#105886262
C9×#3422
#105882042
#689583