Finite Group Databasebeta

← #11781829

Subgroups — #11781829

Order 1152.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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#10588768C211yesmaximal, characteristic
2#10588760C211yesmaximal, characteristic, complemented
3#10588526C211yesmaximal, characteristic
4#10588522C211yesmaximal, characteristic
5C9×#332C211yesmaximal, characteristic, complemented
6#10588158C211yesmaximal, characteristic, complemented
7#10588156C211yesmaximal, characteristic, complemented
8#68450—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C2×#3675—21no—
11C2×#3663—21no—
12C4×D36C2211yescharacteristic
13#63431C2211yescharacteristic
14C9×C4⋊C8C2211yescharacteristic
15C9×C4⋊C8C2211yescharacteristic
16#63395—21no—
17#63380—21no—
18(C2×D9)⋊C8—21no—
19#63377—21no—
20#63367—21no—
21#63367—21no—
22C4⋊(C9⋊C8)C2211yescharacteristic
23C4×C9⋊C8C2211yescharacteristic
24#5083—31no—
25#5080—31no—
26#4842—31no—
27#4838—31no—
28C3×#332D311yescharacteristic
29#4481—31no—
30#4479—31no—
31C2×Q8×C9—21no—
32C2×D36D411yescharacteristic
33C2×C4×D9—21no—
34C2×Dic18—21no—
35C2×C8×C9—21no—
36C2×C8×C9—21no—
37C9×C4⋊C4—21no—
38C9×C4⋊C4—21no—
39C42×C9C2311yescharacteristic
40#3675—42no—
41(C2×D9)⋊C4—21no—
42C4⋊Dic9—21no—
43C4⋊Dic9—21no—
44C4⋊Dic9D411yescharacteristic
45C2×C9⋊C8—21no—
46C2×C9⋊C8D411yescharacteristic
47C2×C9⋊C8D411yescharacteristic
48#3663—42no—
49#1691—91noSylow
50C3×C4⋊Q8C2×D311yescharacteristic
51C2×#215—61no—
52C2×ΓL(1,𝔽25)—61no—
53C4×D12—31no—
54#869—31no—
55C3×C4⋊C8C2×D311yescharacteristic
56C3×C4⋊C8C2×D311yescharacteristic
57#835—61no—
58#821—61no—
59(C2×D3)⋊C8—61no—
60#817—61no—
61#808—61no—
62#808—61no—
63C4⋊(C3⋊C8)—31no—
64C4×C3⋊C8—31no—
65C22×D9—21no—
66Q8×C9—41no—
67Q8×C9—41no—
68C2×C4×C9—41no—
69C2×C4×C9C2×D411yescharacteristic
70C2×C4×C9C2×D411yescharacteristic
71C2×C4×C9#4111yescharacteristic
72C2×Dic9—21no—
73C2×Dic9—41no—
74D36—21no—
75D36—21no—
76C4×D9—41no—
77C4×D9—41no—
78Dic18—81no—
79C8×C9—41no—
80C8×C9—41no—
81C9⋊C8—21no—
82C9⋊C8—41no—
83C9⋊C8SD1612yescomplemented
84#498—91no—
85#476—91no—
86#461—91no—
87#436—91no—
88#335—91no—
89#333—91no—
90#332D911yescharacteristic, complemented
91C2×C3×Q8—21no—
92C2×D12—31no—
93C2×C4×D3—61no—
94C2×Dic6—61no—
95C2×C3×C8—21no—
96C2×C3×C8—21no—
97C3×C4⋊C4—21no—
98C3×C4⋊C4—21no—
99C3×C42C22×D311yescharacteristic
100#215—122no—
101(C2×D3)⋊C4—61no—
102C4⋊Dic3—31no—
103C4⋊Dic3—61no—
104C4⋊Dic3—61no—
105C2×C3⋊C8—31no—
106C2×C3⋊C8—31no—
107C2×C3⋊C8—61no—
108ΓL(1,𝔽25)—122no—
109C22×C9#12111yescharacteristic
110C2×D9—41no—
111C2×D9—41no—
112C2×D9—41no—
113C4×C9—21no—
114C4×C9—81no—
115C4×C9C2×SD1611yescharacteristic
116C4×C9AGL(1,ℤ/8)11yescharacteristic
117C4×C9#13711yescharacteristic
118C4×C9#13711yescharacteristic
119Dic9—41no—
120Dic9—81no—
121C2×SD16—181no—
122C2×M16—181no—
123C4⋊Q8—91no—
124C4⋊Q8C2×D911yescharacteristic
125C4×D4—91no—
126#106—181no—
127#106—181no—
128#106—181no—
129C4⋊C8—91no—
130C4⋊C8C2×D911yescharacteristic
131C4⋊C8C2×D911yescharacteristic
132#103—181no—
133#102—181no—
134C22⋊C8—181no—
135C4×C8—91no—
136C22×D3—61no—
137C3×Q8—41no—
138C3×Q8—41no—
139C2×C3×C4—41no—
140C2×C3×C4#23511yescharacteristic
141C2×C3×C4D3×D411yescharacteristic
142C2×C3×C4D3×D411yescharacteristic
143C2×Dic3—61no—
144C2×Dic3—121no—
145D12—61no—
146D12—61no—
147C4×D3—121no—
148C4×D3—121no—
149Dic6—241no—
150C3×C8—41no—
151C3×C8—41no—
152C3⋊C8—32no—
153C3⋊C8—61no—
154C3⋊C8—121no—
155C2×C9#46111yescharacteristic
156C2×C9#46811yescharacteristic
157C2×C9#47111yescharacteristic
158D9—81no—
159C2×Q8—21no—
160C2×Q8—181no—
161C2×D4—91no—
162C22×C4—181no—
163SD16—362no—
164M16—362no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—91no—
168C2×C8—91no—
169C2×C8—181no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—91no—
173C4⋊C4—181no—
174C4⋊C4—181no—
175C22⋊C4—181no—
176C42C22×D911yescharacteristic
177C22×C3#88411yescharacteristic
178C2×D3—121no—
179C2×D3—121no—
180C2×D3—121no—
181C3×C4—21no—
182C3×C4—81no—
183C3×C4#91111yescharacteristic
184C3×C4D3×SD1611yescharacteristic
185C3×C4#91511yescharacteristic
186C3×C4#91811yescharacteristic
187Dic3—121no—
188Dic3—241no—
189C9#169111yescharacteristic, complemented, Sylow
190C23—181no—
191Q8—41no—
192Q8—41no—
193Q8—721no—
194D4—181no—
195D4—181no—
196C2×C4—41no—
197C2×C4—181no—
198C2×C4—361no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4#369711yescharacteristic
202C2×C4D4×D911yescharacteristic
203C2×C4D4×D911yescharacteristic
204C8—41no—
205C8—41no—
206C8—92no—
207C8—181no—
208C8—361no—
209C2×C3#475411yescharacteristic
210C2×C3#478011yescharacteristic
211C2×C3#481811yescharacteristic
212D3—241no—
213C22—361no—
214C22—361no—
215C22—361no—
216C22#6344611yescharacteristic
217C4—21no—
218C4—81no—
219C4—361no—
220C4—721no—
221C4#6347311yescharacteristic
222C4SD16×D911yescharacteristic
223C4#6347711yescharacteristic
224C4#6348011yescharacteristic
225C3#6845011yescharacteristic
226C2—721no—
227C2#1058843411yescharacteristic
228C2#1058846011yescharacteristic
229C2#1058849811yescharacteristic
subgroupG/H
centerC22#63446
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#332C2
socleC22×C3#884
prime radicalC2×D36D4
hypercenter#332D9
hypocenterC9#1691
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #10588760C2semidirect
5. C9×#332C2semidirect
6. #10588158C2semidirect
7. #10588156C2semidirect
83. C9⋊C8SD16semidirect
90. #332D9semidirect
189. C9#1691semidirect

Maximal subgroups

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

subgroupindex
#105887682
#105887602
#105885262
#105885222
C9×#3322
#105881582
#105881562
#684503