Finite Group Databasebeta

← #11781764

Subgroups — #11781764

Order 1152.

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

normal subgroups only

This group has 249 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#10588765C211yesmaximal, characteristic, complemented
3#10588530C211yesmaximal, characteristic
4#10588522C211yesmaximal, characteristic
5C9×#332C211yesmaximal, characteristic, complemented
6#10588159C211yesmaximal, characteristic, complemented
7#10588157C211yesmaximal, characteristic, complemented
8#68449—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C2×#3674—21no—
11C2×#3674—21no—
12C2×#3663—21no—
13C4×D36C2211yescharacteristic
14#63431C2211yescharacteristic
15C9×C4⋊C8C2211yescharacteristic
16C9×C4⋊C8C2211yescharacteristic
17#63380—21no—
18(C2×D9)⋊C8—21no—
19#63378—21no—
20#63369—21no—
21#63366—21no—
22C4⋊(C9⋊C8)C2211yescharacteristic
23C4×C9⋊C8C2211yescharacteristic
24#5092—31no—
25#5087—31no—
26#4846—31no—
27#4838—31no—
28C3×#332D311yescharacteristic
29#4482—31no—
30#4480—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#3674—42no—
41#3674—42no—
42(C2×D9)⋊C4—21no—
43C4⋊Dic9—21no—
44C4⋊Dic9—21no—
45C4⋊Dic9D411yescharacteristic
46C2×C9⋊C8—21no—
47C2×C9⋊C8D411yescharacteristic
48C2×C9⋊C8D411yescharacteristic
49#3663—42no—
50#1689—91noSylow
51C3×C4⋊Q8C2×D311yescharacteristic
52C2×#216—61no—
53C2×#216—61no—
54C2×ΓL(1,𝔽25)—61no—
55C4×D12—31no—
56#869—31no—
57C3×C4⋊C8C2×D311yescharacteristic
58C3×C4⋊C8C2×D311yescharacteristic
59#821—61no—
60(C2×D3)⋊C8—61no—
61#818—61no—
62#809—61no—
63#807—61no—
64C4⋊(C3⋊C8)—31no—
65C4×C3⋊C8—31no—
66C22×D9—21no—
67Q8×C9—41no—
68Q8×C9—41no—
69C2×C4×C9—41no—
70C2×C4×C9C2×D411yescharacteristic
71C2×C4×C9C2×D411yescharacteristic
72C2×C4×C9#4111yescharacteristic
73C2×Dic9—21no—
74C2×Dic9—41no—
75D36—21no—
76D36—21no—
77C4×D9—41no—
78C4×D9—41no—
79Dic18—41no—
80Dic18—41no—
81C8×C9—41no—
82C8×C9—41no—
83C9⋊C8—21no—
84C9⋊C8—41no—
85C9⋊C8D812yes—
86#494—91no—
87#474—91no—
88#474—91no—
89#436—91no—
90#334—91no—
91#332—91no—
92#332D911yescharacteristic, complemented
93C2×C3×Q8—21no—
94C2×D12—31no—
95C2×C4×D3—61no—
96C2×Dic6—61no—
97C2×C3×C8—21no—
98C2×C3×C8—21no—
99C3×C4⋊C4—21no—
100C3×C4⋊C4—21no—
101C3×C42C22×D311yescharacteristic
102#216—122no—
103#216—122no—
104(C2×D3)⋊C4—61no—
105C4⋊Dic3—31no—
106C4⋊Dic3—61no—
107C4⋊Dic3—61no—
108C2×C3⋊C8—31no—
109C2×C3⋊C8—31no—
110C2×C3⋊C8—61no—
111ΓL(1,𝔽25)—122no—
112C22×C9#12111yescharacteristic
113C2×D9—41no—
114C2×D9—41no—
115C2×D9—41no—
116C4×C9—21no—
117C4×C9—81no—
118C4×C9C2×D811yescharacteristic
119C4×C9AGL(1,ℤ/8)11yescharacteristic
120C4×C9#13711yescharacteristic
121C4×C9#13711yescharacteristic
122Dic9—41no—
123Dic9—81no—
124C2×Q16—181no—
125C2×Q16—181no—
126C2×M16—181no—
127C4⋊Q8—91no—
128C4⋊Q8C2×D911yescharacteristic
129C4×D4—91no—
130#107—181no—
131#107—181no—
132C4⋊C8—91no—
133C4⋊C8C2×D911yescharacteristic
134C4⋊C8C2×D911yescharacteristic
135#102—181no—
136#102—181no—
137C22⋊C8—181no—
138C4×C8—91no—
139C22×D3—61no—
140C3×Q8—41no—
141C3×Q8—41no—
142C2×C3×C4—41no—
143C2×C3×C4#23511yescharacteristic
144C2×C3×C4D3×D411yescharacteristic
145C2×C3×C4D3×D411yescharacteristic
146C2×Dic3—61no—
147C2×Dic3—121no—
148D12—61no—
149D12—61no—
150C4×D3—121no—
151C4×D3—121no—
152Dic6—121no—
153Dic6—121no—
154C3×C8—41no—
155C3×C8—41no—
156C3⋊C8—32no—
157C3⋊C8—61no—
158C3⋊C8—121no—
159C2×C9#45911yescharacteristic
160C2×C9#47011yescharacteristic
161C2×C9#47311yescharacteristic
162D9—81no—
163C2×Q8—21no—
164C2×Q8—181no—
165C2×D4—91no—
166C22×C4—181no—
167Q16—362no—
168Q16—362no—
169M16—362no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—91no—
173C2×C8—91no—
174C2×C8—181no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—91no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C22⋊C4—181no—
181C42C22×D911yescharacteristic
182C22×C3#88411yescharacteristic
183C2×D3—121no—
184C2×D3—121no—
185C2×D3—121no—
186C3×C4—21no—
187C3×C4—81no—
188C3×C4D3×D811yescharacteristic
189C3×C4#91411yescharacteristic
190C3×C4#91511yescharacteristic
191C3×C4#91811yescharacteristic
192Dic3—121no—
193Dic3—241no—
194C9#168911yescharacteristic, complemented, Sylow
195C23—181no—
196Q8—41no—
197Q8—41no—
198Q8—361no—
199Q8—361no—
200D4—181no—
201D4—181no—
202C2×C4—41no—
203C2×C4—181no—
204C2×C4—361no—
205C2×C4—361no—
206C2×C4—361no—
207C2×C4#369711yescharacteristic
208C2×C4D4×D911yescharacteristic
209C2×C4D4×D911yescharacteristic
210C8—41no—
211C8—41no—
212C8—92no—
213C8—181no—
214C8—361no—
215C2×C3#475511yescharacteristic
216C2×C3#478611yescharacteristic
217C2×C3#481611yescharacteristic
218D3—241no—
219C22—361no—
220C22—361no—
221C22—361no—
222C22#6344611yescharacteristic
223C4—21no—
224C4—81no—
225C4—361no—
226C4—721no—
227C4D8×D911yescharacteristic
228C4#6347611yescharacteristic
229C4#6347711yescharacteristic
230C4#6348011yescharacteristic
231C3#6844911yescharacteristic
232C2—721no—
233C2#1058843511yescharacteristic
234C2#1058846611yescharacteristic
235C2#1058849611yescharacteristic
subgroupG/H
centerC22#63446
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#332C2
socleC22×C3#884
prime radicalC2×D36D4
hypercenter#332D9
hypocenterC9#1689
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. #10588765C2semidirect
5. C9×#332C2semidirect
6. #10588159C2semidirect
7. #10588157C2semidirect
92. #332D9semidirect
194. C9#1689semidirect

Maximal subgroups

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

subgroupindex
#105887722
#105887652
#105885302
#105885222
C9×#3322
#105881592
#105881572
#684493