Finite Group Databasebeta

← #11781514

Subgroups — #11781514

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#10588772C211yesmaximal, characteristic
2#10588759C211yesmaximal, characteristic, complemented
3#10588526C211yesmaximal, characteristic
4#10588518C211yesmaximal, characteristic
5C9×#332C211yesmaximal, characteristic, complemented
6#10588158C211yesmaximal, characteristic, complemented
7#10588156C211yesmaximal, characteristic, complemented
8#68447—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C2×C8×D9—21no—
11C4×D36C2211yescharacteristic
12#63431C2211yescharacteristic
13C9×C4⋊C8C2211yescharacteristic
14C9×C4⋊C8C2211yescharacteristic
15#63395—21no—
16#63395—21no—
17#63380—21no—
18(C2×D9)⋊C8—21no—
19#63377—21no—
20#63369—21no—
21#63366—21no—
22C4⋊(C9⋊C8)C2211yescharacteristic
23C4×C9⋊C8C2211yescharacteristic
24#5087—31no—
25#5079—31no—
26#4842—31no—
27#4834—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(C2×D9)⋊C4—21no—
41C4⋊Dic9—21no—
42C4⋊Dic9—21no—
43C4⋊Dic9D411yescharacteristic
44C2×C9⋊C8—21no—
45C2×C9⋊C8D411yescharacteristic
46C2×C9⋊C8D411yescharacteristic
47C8×D9—42no—
48#1683—91noSylow
49C3×C4⋊Q8C2×D311yescharacteristic
50C2×D3×C8—61no—
51C4×D12—31no—
52#869—31no—
53C3×C4⋊C8C2×D311yescharacteristic
54C3×C4⋊C8C2×D311yescharacteristic
55#835—61no—
56#835—61no—
57#821—61no—
58(C2×D3)⋊C8—61no—
59#817—61no—
60#809—61no—
61#807—61no—
62C4⋊(C3⋊C8)—31no—
63C4×C3⋊C8—31no—
64C22×D9—21no—
65Q8×C9—41no—
66Q8×C9—41no—
67C2×C4×C9—41no—
68C2×C4×C9C2×D411yescharacteristic
69C2×C4×C9C2×D411yescharacteristic
70C2×C4×C9#4111yescharacteristic
71C2×Dic9—21no—
72C2×Dic9—41no—
73D36—21no—
74D36Q1612yes—
75C4×D9—41no—
76C4×D9—41no—
77Dic18—81no—
78C8×C9—41no—
79C8×C9—41no—
80C9⋊C8—21no—
81C9⋊C8—21no—
82C9⋊C8—41no—
83#487—91no—
84#476—91no—
85#474—91no—
86C8×D4—91no—
87#335—91no—
88#333—91no—
89#332D911yescharacteristic, complemented
90C2×C3×Q8—21no—
91C2×D12—31no—
92C2×C4×D3—61no—
93C2×Dic6—61no—
94C2×C3×C8—21no—
95C2×C3×C8—21no—
96C3×C4⋊C4—21no—
97C3×C4⋊C4—21no—
98C3×C42C22×D311yescharacteristic
99(C2×D3)⋊C4—61no—
100C4⋊Dic3—31no—
101C4⋊Dic3—61no—
102C4⋊Dic3—61no—
103C2×C3⋊C8—31no—
104C2×C3⋊C8—31no—
105C2×C3⋊C8—61no—
106D3×C8—122no—
107C22×C9#12111yescharacteristic
108C2×D9—22no—
109C2×D9—41no—
110C2×D9—41no—
111C4×C9—21no—
112C4×C9—81no—
113C4×C9C2×Q1611yescharacteristic
114C4×C9#13511yescharacteristic
115C4×C9#13511yescharacteristic
116C4×C9AGL(1,ℤ/8)11yescharacteristic
117Dic9—41no—
118Dic9—81no—
119C22×C8—181no—
120C4⋊Q8—91no—
121C4⋊Q8C2×D911yescharacteristic
122C4×D4—91no—
123#107—181no—
124#106—181no—
125C4⋊C8—91no—
126C4⋊C8C2×D911yescharacteristic
127C4⋊C8C2×D911yescharacteristic
128#103—181no—
129#103—181no—
130#102—181no—
131#102—181no—
132C22⋊C8—181no—
133C4×C8—91no—
134C22×D3—61no—
135C3×Q8—41no—
136C3×Q8—41no—
137C2×C3×C4—41no—
138C2×C3×C4#23511yescharacteristic
139C2×C3×C4D3×D411yescharacteristic
140C2×C3×C4D3×D411yescharacteristic
141C2×Dic3—61no—
142C2×Dic3—121no—
143D12—32no—
144D12—61no—
145C4×D3—121no—
146C4×D3—121no—
147Dic6—241no—
148C3×C8—41no—
149C3×C8—41no—
150C3⋊C8—61no—
151C3⋊C8—61no—
152C3⋊C8—121no—
153C2×C9#46311yescharacteristic
154C2×C9#46711yescharacteristic
155C2×C9#47111yescharacteristic
156D9—42no—
157C2×Q8—21no—
158C2×Q8—181no—
159C2×D4—91no—
160C22×C4—181no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—91no—
164C2×C8—91no—
165C2×C8—181no—
166C2×C8—362no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—91no—
170C4⋊C4—181no—
171C4⋊C4—181no—
172C22⋊C4—181no—
173C42C22×D911yescharacteristic
174C22×C3#88411yescharacteristic
175C2×D3—62no—
176C2×D3—121no—
177C2×D3—121no—
178C3×C4—21no—
179C3×C4—81no—
180C3×C4#91111yescharacteristic
181C3×C4#91611yescharacteristic
182C3×C4#91611yescharacteristic
183C3×C4D3×Q1611yescharacteristic
184Dic3—121no—
185Dic3—241no—
186C9#168311yescharacteristic, complemented, Sylow
187C23—181no—
188Q8—41no—
189Q8—41no—
190Q8—721no—
191D4—92no—
192D4—181no—
193C2×C4—41no—
194C2×C4—181no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—361no—
198C2×C4#369711yescharacteristic
199C2×C4D4×D911yescharacteristic
200C2×C4D4×D911yescharacteristic
201C8—41no—
202C8—41no—
203C8—181no—
204C8—181no—
205C8—361no—
206C2×C3#475411yescharacteristic
207C2×C3#478711yescharacteristic
208C2×C3#481311yescharacteristic
209D3—122no—
210C22—182no—
211C22—361no—
212C22—361no—
213C22#6344611yescharacteristic
214C4—21no—
215C4—81no—
216C4—361no—
217C4—721no—
218C4#6347311yescharacteristic
219C4#6347811yescharacteristic
220C4#6347811yescharacteristic
221C4Q16×D911yescharacteristic
222C3#6844711yescharacteristic
223C2—362no—
224C2#1058843411yescharacteristic
225C2#1058846711yescharacteristic
226C2#1058849311yescharacteristic
subgroupG/H
centerC22#63446
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#332C2
socleC22×C3#884
prime radicalC2×D36D4
hypercenter#332D9
hypocenterC9#1683
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. #10588759C2semidirect
5. C9×#332C2semidirect
6. #10588158C2semidirect
7. #10588156C2semidirect
89. #332D9semidirect
186. C9#1683semidirect

Maximal subgroups

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

subgroupindex
#105887722
#105887592
#105885262
#105885182
C9×#3322
#105881582
#105881562
#684473