Finite Group Databasebeta

← #11779751

Subgroups — #11779751

Order 1152.

318 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 72 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#10589687C211yesmaximal, characteristic
2C9×#462C211yesmaximal, characteristic, complemented
3#10588773C211yesmaximal, characteristic
4#10588767C211yesmaximal, characteristic, complemented
5#10588212C211yesmaximal, characteristic, complemented
6#10588163C211yesmaximal, characteristic
7#10588160C211yesmaximal, characteristic, complemented
8#71060—31nomaximal
9C2×C9×Q16—21no—
10C9×C4⋊Q8C2211yescharacteristic
11C4×Q8×C9C2211yescharacteristic
12#63509—21no—
13#63456—22no—
14#63455—21no—
15#63437—21no—
16#63436C2211yescharacteristic
17C4×D36—21no—
18C4×Dic18C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C9×#103—21no—
21#63369—22no—
22#63368—21no—
23#63367—21no—
24C4⋊(C9⋊C8)C2211yescharacteristic
25C4×C9⋊C8C2211yescharacteristic
26#5585—31no—
27C3×#462D311yescharacteristic
28#5094—31no—
29#5088—31no—
30#4535—31no—
31#4485—31no—
32#4484—31no—
33C2×Q8×C9—21no—
34C2×Q8×C9D411yescharacteristic
35C2×D36—21no—
36C2×D36—21no—
37C2×D36D412yes—
38C2×C4×D9—22no—
39C2×Dic18D411yescharacteristic
40C9×Q16—42no—
41C2×C8×C9—21no—
42C9×C4⋊C4—21no—
43C9×C4⋊C4—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4D411yescharacteristic
46C42×C9—21no—
47C42×C9C2311yescharacteristic
48(C2×D9)⋊C4—22no—
49(C2×D9)⋊C4—22no—
50(C2×D9)⋊C4—22no—
51C4⋊Dic9D411yescharacteristic
52Dic9⋊C4—21no—
53C4×Dic9—21no—
54C2×C9⋊C8—21no—
55C2×C9⋊C8—21no—
56#1640—91noSylow
57C2×C3×Q16—21no—
58C3×C4⋊Q8C2×D311yescharacteristic
59C3×C4×Q8C2×D311yescharacteristic
60#947—61no—
61#894—62no—
62#893—61no—
63#875—61no—
64#874—31no—
65C4×D12—61no—
66C4×Dic6—31no—
67C3×C4⋊C8C2×D311yescharacteristic
68C3×#103—21no—
69#810—61no—
70#809—62no—
71#808—61no—
72C4⋊(C3⋊C8)—31no—
73C4×C3⋊C8—31no—
74C22×D9—22no—
75Q8×C9—21no—
76Q8×C9—21no—
77Q8×C9—41no—
78Q8×C9—41no—
79C2×C4×C9—21no—
80C2×C4×C9—21no—
81C2×C4×C9—41no—
82C2×C4×C9C2×D411yescharacteristic
83C2×C4×C9C2×D411yescharacteristic
84C2×C4×C9C2×D411yescharacteristic
85C2×Dic9—21no—
86C2×Dic9—21no—
87D36—42no—
88D36—41no—
89D36—41no—
90D36—41no—
91D36—41no—
92C4×D9—82no—
93Dic18—21no—
94Dic18—21no—
95C8×C9—41no—
96C9⋊C8—41no—
97C9⋊C8—41no—
98#559—91no—
99#486—91no—
100#475—91no—
101#462D911yescharacteristic, complemented
102#331—91no—
103Q8⋊C8—91no—
104Q8⋊C8—91no—
105C2×C3×Q8—21no—
106C2×C3×Q8#6711yescharacteristic
107C2×D12—32no—
108C2×D12—61no—
109C2×D12—61no—
110C2×C4×D3—62no—
111C2×Dic6—31no—
112C3×Q16—42no—
113C2×C3×C8—21no—
114C3×C4⋊C4—21no—
115C3×C4⋊C4—21no—
116C3×C4⋊C4—21no—
117C3×C4⋊C4#6711yescharacteristic
118C3×C42—21no—
119C3×C42C22×D311yescharacteristic
120(C2×D3)⋊C4—62no—
121(C2×D3)⋊C4—62no—
122(C2×D3)⋊C4—62no—
123C4⋊Dic3—31no—
124Dic3⋊C4—61no—
125C4×Dic3—61no—
126C2×C3⋊C8—61no—
127C2×C3⋊C8—61no—
128C22×C9#12011yescharacteristic
129C2×D9—42no—
130C2×D9—42no—
131C2×D9—42no—
132C4×C9—21no—
133C4×C9—41no—
134C4×C9—41no—
135C4×C9—81no—
136C4×C9#13511yescharacteristic
137C4×C9#13511yescharacteristic
138C4×C9AGL(1,ℤ/8)11yescharacteristic
139C4×C9#13711yescharacteristic
140Dic9—41no—
141Dic9—41no—
142C2×Q16—21no—
143C4⋊Q8C2×D911yescharacteristic
144#127—91no—
145#124—181no—
146#124—181no—
147#123—182no—
148C4×Q8—91no—
149C4×Q8C2×D911yescharacteristic
150C4×D4—181no—
151C4×D4—181no—
152#106—181no—
153C4⋊C8—91no—
154C4⋊C8C2×D911yescharacteristic
155#103—21no—
156#103—181no—
157#102—182no—
158C4×C8—91no—
159C22×D3—62no—
160C3×Q8—21no—
161C3×Q8—21no—
162C3×Q8—41no—
163C3×Q8—41no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—41no—
167C2×C3×C4D3×D411yescharacteristic
168C2×C3×C4D3×D411yescharacteristic
169C2×C3×C4C2×#6711yescharacteristic
170C2×Dic3—61no—
171C2×Dic3—61no—
172D12—122no—
173D12—121no—
174D12—121no—
175D12—121no—
176D12—121no—
177C4×D3—242no—
178Dic6—61no—
179Dic6—61no—
180C3×C8—41no—
181C3⋊C8—121no—
182C3⋊C8—121no—
183C2×C9#44911yescharacteristic
184C2×C9#45211yescharacteristic
185C2×C9#45511yescharacteristic
186D9—82no—
187C2×Q8—21no—
188C2×Q8—91no—
189C2×Q8#61111yescharacteristic
190C2×D4—92no—
191C2×D4—181no—
192C2×D4—181no—
193C22×C4—182no—
194Q16—42no—
195C2×C8—21no—
196C2×C8—181no—
197C2×C8—181no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—91no—
202C4⋊C4—181no—
203C4⋊C4#61111yescharacteristic
204C22⋊C4—182no—
205C22⋊C4—182no—
206C22⋊C4—182no—
207C42—21no—
208C42—181no—
209C42C22×D911yescharacteristic
210C22×C3#93711yescharacteristic
211C2×D3—122no—
212C2×D3—122no—
213C2×D3—122no—
214C3×C4—21no—
215C3×C4—41no—
216C3×C4—41no—
217C3×C4—81no—
218C3×C4#91811yescharacteristic
219C3×C4#91911yescharacteristic
220C3×C4#93211yescharacteristic
221C3×C4#95011yescharacteristic
222Dic3—121no—
223Dic3—121no—
224C9#164011yescharacteristic, complemented, Sylow
225C23—182no—
226Q8—21no—
227Q8—21no—
228Q8—41no—
229Q8—41no—
230Q8—181no—
231Q8—181no—
232D4—362no—
233D4—361no—
234D4—361no—
235D4—361no—
236D4—361no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—722no—
243C2×C4D4×D911yescharacteristic
244C2×C4D4×D911yescharacteristic
245C2×C4C2×#61111yescharacteristic
246C8—41no—
247C8—361no—
248C8—361no—
249C2×C3#503711yescharacteristic
250C2×C3#518711yescharacteristic
251C2×C3#520211yescharacteristic
252D3—242no—
253C22—362no—
254C22—362no—
255C22—362no—
256C22#6349911yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—81no—
261C4—361no—
262C4—361no—
263C4#6348011yescharacteristic
264C4#6348111yescharacteristic
265C4#6349511yescharacteristic
266C4#6351311yescharacteristic
267C3#7106011yescharacteristic
268C2—722no—
269C2#1058872011yescharacteristic
270C2#1058886711yescharacteristic
271C2#1058888311yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#462C2
socleC22×C3#937
prime radical#63436C22
hypercenter#462D9
hypocenterC9#1640
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C9×#462C2semidirect
4. #10588767C2semidirect
5. #10588212C2semidirect
7. #10588160C2semidirect
101. #462D9semidirect
224. C9#1640semidirect

Maximal subgroups

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

subgroupindex
#105896872
C9×#4622
#105887732
#105887672
#105882122
#105881632
#105881602
#710603