Finite Group Databasebeta

← #11778547

Subgroups — #11778547

Order 1152.

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

normal subgroups only

This group has 381 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
1C9×#537C211yesmaximal, characteristic
2#10588713C212yesmaximal, complemented
3#10588661C211yesmaximal, characteristic, complemented
4#10588214C212yesmaximal, complemented
5#10588205C211yesmaximal, characteristic, complemented
6#71874—31nomaximal
7C2×C9×#41—21no—
8C9×C22⋊Q8—22no—
9C9×#121—22no—
10C9×#121—21no—
11C9×#121C2212yes—
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic9C2211yescharacteristic
14C2×Dic9⋊C4—21no—
15#63392—22no—
16C9⋊#95—21no—
17C9⋊#95C2211yescharacteristic
18#63389C2212yes—
19#63366—22no—
20C3×#537D311yescharacteristic
21#5033—32no—
22#4981—31no—
23#4537—32no—
24#4528—31no—
25C9×#41—42no—
26C9×#41—42no—
27C2×Q8×C9—21no—
28C2×D4×C9—21no—
29C2×D4×C9—22no—
30C2×D4×C9—21no—
31C2×D4×C9D412yes—
32C22×C4×C9—22no—
33C22×C4×C9D411yescharacteristic
34C22×C4×C9D411yescharacteristic
35C22×C4×C9C2311yescharacteristic
36C22×Dic9—21no—
37C22×Dic9—21no—
38C9×C4⋊C4—21no—
39C9×C4⋊C4—22no—
40C9×C4⋊C4D412yes—
41C9×C22⋊C4—22no—
42C9×C22⋊C4—22no—
43C4⋊Dic9—22no—
44Dic9⋊C4—42no—
45C2×C9⋊C8—22no—
46#1610—91noSylow
47C2×C3×#41—21no—
48C3×C22⋊Q8—22no—
49C3×#121—22no—
50C3×#121—21no—
51C3×#121C2×D312yes—
52C2×C3×C4⋊C4C2×D311yescharacteristic
53C2×C4⋊Dic3—31no—
54C2×Dic3⋊C4—61no—
55#832—62no—
56C3⋊#95—31no—
57C3⋊#95—61no—
58#830—32no—
59#807—62no—
60C23×C9—22no—
61C23×C9C2×D411yescharacteristic
62Q8×C9—42no—
63D4×C9—42no—
64D4×C9—42no—
65D4×C9—42no—
66D4×C9—42no—
67D4×C9—81no—
68C2×C4×C9—21no—
69C2×C4×C9—21no—
70C2×C4×C9—21no—
71C2×C4×C9—22no—
72C2×C4×C9—41no—
73C2×C4×C9—44no—
74C2×C4×C9—41no—
75C2×C4×C9D812yes—
76C2×C4×C9C2×D412yes—
77C2×Dic9—22no—
78C2×Dic9—41no—
79C2×Dic9—41no—
80C2×Dic9—41no—
81C2×Dic9—41no—
82C2×Dic9—41no—
83C9⋊C8—42no—
84#537D911yescharacteristic
85#480—92no—
86#398—91no—
87#327—92no—
88#324—91no—
89C3×#41—42no—
90C3×#41—42no—
91C2×C3×Q8—21no—
92C2×C3×D4—21no—
93C2×C3×D4—22no—
94C2×C3×D4—21no—
95C2×C3×D4#6712yes—
96C22×C3×C4—22no—
97C22×C3×C4#6711yescharacteristic
98C22×C3×C4#6711yescharacteristic
99C22×C3×C4C22×D311yescharacteristic
100C22×Dic3—61no—
101C22×Dic3—61no—
102C3×C4⋊C4—21no—
103C3×C4⋊C4—22no—
104C3×C4⋊C4#6712yes—
105C3×C22⋊C4—22no—
106C3×C22⋊C4—22no—
107C4⋊Dic3—62no—
108Dic3⋊C4—122no—
109C2×C3⋊C8—62no—
110C22×C9—21no—
111C22×C9—21no—
112C22×C9—42no—
113C22×C9—42no—
114C22×C9—42no—
115C22×C9#12011yescharacteristic
116C22×C9C2×D811yescharacteristic
117C22×C9AGL(1,ℤ/8)11yescharacteristic
118C4×C9—22no—
119C4×C9—22no—
120C4×C9—42no—
121C4×C9—41no—
122Dic9—42no—
123Dic9—81no—
124C2×#41—21no—
125C22⋊Q8—22no—
126#121—22no—
127#121—21no—
128#121C2×D912yes—
129C2×C4⋊C4—91no—
130C2×C4⋊C4—181no—
131C2×C4⋊C4C2×D911yescharacteristic
132#107—182no—
133#102—182no—
134C22⋊C8—92no—
135#95—91no—
136#95—181no—
137C23×C3—22no—
138C23×C3C2×#6711yescharacteristic
139C3×Q8—42no—
140C3×D4—42no—
141C3×D4—42no—
142C3×D4—42no—
143C3×D4—42no—
144C3×D4—81no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—22no—
149C2×C3×C4—41no—
150C2×C3×C4—44no—
151C2×C3×C4—41no—
152C2×C3×C4#21312yes—
153C2×C3×C4C2×#6712yes—
154C2×Dic3—62no—
155C2×Dic3—121no—
156C2×Dic3—121no—
157C2×Dic3—121no—
158C2×Dic3—121no—
159C2×Dic3—121no—
160C3⋊C8—122no—
161C2×C9—21no—
162C2×C9—21no—
163C2×C9—82no—
164C2×C9#44711yescharacteristic
165C2×C9#45611yescharacteristic
166C2×C9#45811yescharacteristic
167#41—42no—
168#41—42no—
169C2×Q8—21no—
170C2×D4—21no—
171C2×D4—22no—
172C2×D4—21no—
173C2×D4#61112yes—
174C22×C4—22no—
175C22×C4—181no—
176C22×C4—181no—
177C22×C4#61111yescharacteristic
178C22×C4#61111yescharacteristic
179C22×C4C22×D911yescharacteristic
180C2×C8—182no—
181C4⋊C4—21no—
182C4⋊C4—22no—
183C4⋊C4—182no—
184C4⋊C4—362no—
185C4⋊C4#61112yes—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—42no—
191C22×C3—42no—
192C22×C3—42no—
193C22×C3C2×#21311yescharacteristic
194C22×C3#93211yescharacteristic
195C22×C3#95311yescharacteristic
196C3×C4—22no—
197C3×C4—22no—
198C3×C4—42no—
199C3×C4—41no—
200Dic3—122no—
201Dic3—241no—
202C9#161011yescharacteristic, complemented, Sylow
203C23—22no—
204C23C2×#61111yescharacteristic
205Q8—42no—
206D4—42no—
207D4—42no—
208D4—42no—
209D4—42no—
210D4—81no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—44no—
217C2×C4—41no—
218C2×C4—182no—
219C2×C4—361no—
220C2×C4—361no—
221C2×C4—361no—
222C2×C4—361no—
223C2×C4—361no—
224C2×C4#367312yes—
225C2×C4C2×#61112yes—
226C8—362no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—82no—
230C2×C3#521711yescharacteristic
231C2×C3#524311yescharacteristic
232C2×C3#524611yescharacteristic
233C22—21no—
234C22—21no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22C2×#367311yescharacteristic
239C22#6349511yescharacteristic
240C22#6351511yescharacteristic
241C4—22no—
242C4—22no—
243C4—42no—
244C4—41no—
245C4—362no—
246C4—721no—
247C3#7187411yescharacteristic
248C2—21no—
249C2—21no—
250C2—82no—
251C2#1058889811yescharacteristic
252C2#1058892311yescharacteristic
253C2#1058892511yescharacteristic
subgroupG/H
centerC22#63515
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#537C2
socleC22×C3#953
prime radicalC3×#537D3
hypercenter#537D9
hypocenterC9#1610
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
2. #10588713C2semidirect
3. #10588661C2semidirect
4. #10588214C2semidirect
5. #10588205C2semidirect
202. C9#1610semidirect

Maximal subgroups

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

subgroupindex
C9×#5372
#105887132
#105886612
#105882142
#105882052
#718743