Finite Group Databasebeta

← #11781955

Subgroups — #11781955

Order 1152.

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

normal subgroups only

This group has 228 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#10588763C211yesmaximal, characteristic
2#10588758C211yesmaximal, characteristic
3#10588513C211yesmaximal, characteristic
4#10588509C211yesmaximal, characteristic
5C9×#332C211yesmaximal, characteristic
6#10588161C211yesmaximal, characteristic
7#10588157C211yesmaximal, characteristic
8#68475—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C2×#3674—21no—
11C2×Dic36—21no—
12#63431C2211yescharacteristic
13C4×Dic18C2211yescharacteristic
14C9×C4⋊C8C2211yescharacteristic
15C9×C4⋊C8C2211yescharacteristic
16#63395—21no—
17#63376—21no—
18#63375—21no—
19Dic9⋊C8—21no—
20#63366—21no—
21#63366—21no—
22C4⋊(C9⋊C8)C2211yescharacteristic
23C4×C9⋊C8C2211yescharacteristic
24#5090—31no—
25#5078—31no—
26#4849—31no—
27#4831—31no—
28C3×#332D311yescharacteristic
29#4486—31no—
30#4480—31no—
31C2×Q8×C9—21no—
32C2×Dic18—21no—
33C2×Dic18D411yescharacteristic
34C2×C8×C9—21no—
35C2×C8×C9—21no—
36C9×C4⋊C4—21no—
37C9×C4⋊C4—21no—
38C42×C9C2311yescharacteristic
39#3674—42no—
40C4⋊Dic9—21no—
41C4⋊Dic9—21no—
42C4⋊Dic9D411yescharacteristic
43Dic9⋊C4—21no—
44C4×Dic9—21no—
45C2×C9⋊C8—21no—
46C2×C9⋊C8D411yescharacteristic
47C2×C9⋊C8D411yescharacteristic
48Dic36—42no—
49#1694—91noSylow
50C3×C4⋊Q8C2×D311yescharacteristic
51C2×#216—61no—
52C2×Dic12—61no—
53#869—31no—
54C4×Dic6—31no—
55C3×C4⋊C8C2×D311yescharacteristic
56C3×C4⋊C8C2×D311yescharacteristic
57#835—61no—
58#816—61no—
59#815—61no—
60Dic3⋊C8—61no—
61#807—61no—
62#807—61no—
63C4⋊(C3⋊C8)—31no—
64C4×C3⋊C8—31no—
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—21no—
73C2×Dic9—41no—
74Dic18—21no—
75Dic18—21no—
76Dic18—41no—
77Dic18—41no—
78C8×C9—41no—
79C8×C9—41no—
80C9⋊C8—21no—
81C9⋊C8—41no—
82C9⋊C8Q1612yescomplemented
83#500—91no—
84#462—91no—
85#462—91no—
86#446—91no—
87#334—91no—
88#332—91no—
89#332D911yescharacteristic
90C2×C3×Q8—21no—
91C2×Dic6—31no—
92C2×Dic6—61no—
93C2×C3×C8—21no—
94C2×C3×C8—21no—
95C3×C4⋊C4—21no—
96C3×C4⋊C4—21no—
97C3×C42C22×D311yescharacteristic
98#216—122no—
99C4⋊Dic3—31no—
100C4⋊Dic3—61no—
101C4⋊Dic3—61no—
102Dic3⋊C4—61no—
103C4×Dic3—61no—
104C2×C3⋊C8—31no—
105C2×C3⋊C8—31no—
106C2×C3⋊C8—61no—
107Dic12—122no—
108C22×C9#12111yescharacteristic
109C4×C9—21no—
110C4×C9—81no—
111C4×C9C2×Q1611yescharacteristic
112C4×C9AGL(1,ℤ/8)11yescharacteristic
113C4×C9AGL(1,ℤ/8)11yescharacteristic
114C4×C9#13711yescharacteristic
115Dic9—41no—
116Dic9—41no—
117Dic9—81no—
118C2×Q16—181no—
119C2×Q16—181no—
120C4⋊Q8—91no—
121C4⋊Q8C2×D911yescharacteristic
122C4×Q8—91no—
123#107—181no—
124#107—181no—
125C4⋊C8—91no—
126C4⋊C8—181no—
127C4⋊C8C2×D911yescharacteristic
128C4⋊C8C2×D911yescharacteristic
129#103—181no—
130#103—181no—
131#97—181no—
132C4×C8—91no—
133C3×Q8—41no—
134C3×Q8—41no—
135C2×C3×C4—41no—
136C2×C3×C4#23511yescharacteristic
137C2×C3×C4D3×D411yescharacteristic
138C2×C3×C4D3×D411yescharacteristic
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—121no—
142Dic6—61no—
143Dic6—61no—
144Dic6—121no—
145Dic6—121no—
146C3×C8—41no—
147C3×C8—41no—
148C3⋊C8—32no—
149C3⋊C8—61no—
150C3⋊C8—121no—
151C2×C9#46211yescharacteristic
152C2×C9#46911yescharacteristic
153C2×C9#47311yescharacteristic
154C2×Q8—21no—
155C2×Q8—91no—
156C2×Q8—181no—
157Q16—362no—
158Q16—362no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—91no—
162C2×C8—91no—
163C2×C8—181no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—91no—
167C4⋊C4—181no—
168C4⋊C4—181no—
169C4⋊C4—181no—
170C42—181no—
171C42C22×D911yescharacteristic
172C22×C3#88411yescharacteristic
173C3×C4—21no—
174C3×C4—81no—
175C3×C4#91111yescharacteristic
176C3×C4#91411yescharacteristic
177C3×C4#91511yescharacteristic
178C3×C4D3×Q1611yescharacteristic
179Dic3—121no—
180Dic3—121no—
181Dic3—241no—
182C9#169411yescharacteristic, complemented, Sylow
183Q8—41no—
184Q8—41no—
185Q8—181no—
186Q8—181no—
187Q8—361no—
188Q8—361no—
189C2×C4—41no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—361no—
193C2×C4#369711yescharacteristic
194C2×C4D4×D911yescharacteristic
195C2×C4D4×D911yescharacteristic
196C8—41no—
197C8—41no—
198C8—92no—
199C8—181no—
200C8—361no—
201C2×C3#475511yescharacteristic
202C2×C3#478211yescharacteristic
203C2×C3#479511yescharacteristic
204C22#6344611yescharacteristic
205C4—21no—
206C4—81no—
207C4—361no—
208C4—361no—
209C4—721no—
210C4#6347311yescharacteristic
211C4#6347611yescharacteristic
212C4#6347711yescharacteristic
213C4Q16×D911yescharacteristic
214C3#6847511yescharacteristic
215C2#1058843511yescharacteristic
216C2#1058846211yescharacteristic
217C2#1058847511yescharacteristic
subgroupG/H
centerC22#63446
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#332C2
socle, prime radicalC22×C3#884
hypercenter#332D9
hypocenterC9#1694
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
82. C9⋊C8Q16semidirect
182. C9#1694semidirect

Maximal subgroups

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

subgroupindex
#105887632
#105887582
#105885132
#105885092
C9×#3322
#105881612
#105881572
#684753