Finite Group Databasebeta

← #11781328

Subgroups — #11781328

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#10588759C211yesmaximal, characteristic, complemented
3#10588525C211yesmaximal, characteristic
4#10588518C211yesmaximal, characteristic
5C9×#332C211yesmaximal, characteristic, complemented
6#10588161C211yesmaximal, characteristic, complemented
7#10588157C211yesmaximal, characteristic, complemented
8#68444—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C2×#3664—21no—
11C2×C8×D9—21no—
12C4×D36C2211yescharacteristic
13#63431C2211yescharacteristic
14C9×C4⋊C8C2211yescharacteristic
15C9×C4⋊C8C2211yescharacteristic
16#63395—21no—
17#63395—21no—
18(C2×D9)⋊C8—21no—
19#63376—21no—
20#63369—21no—
21#63366—21no—
22C4⋊(C9⋊C8)C2211yescharacteristic
23C4×C9⋊C8C2211yescharacteristic
24#5087—31no—
25#5079—31no—
26#4841—31no—
27#4834—31no—
28C3×#332D311yescharacteristic
29#4486—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(C2×D9)⋊C4—21no—
41C4⋊Dic9—21no—
42C4⋊Dic9—21no—
43C4⋊Dic9D411yescharacteristic
44C2×C9⋊C8—21no—
45C2×C9⋊C8D411yescharacteristic
46C2×C9⋊C8D411yescharacteristic
47#3664—42no—
48C8×D9—42no—
49#1679—91noSylow
50C3×C4⋊Q8C2×D311yescharacteristic
51C2×#204—61no—
52C2×D3×C8—61no—
53C4×D12—31no—
54#869—31no—
55C3×C4⋊C8C2×D311yescharacteristic
56C3×C4⋊C8C2×D311yescharacteristic
57#835—61no—
58#835—61no—
59(C2×D3)⋊C8—61no—
60#816—61no—
61#809—61no—
62#807—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—
75D36SD1612yes—
76C4×D9—41no—
77C4×D9—41no—
78Dic18—41no—
79Dic18—41no—
80C8×C9—41no—
81C8×C9—41no—
82C9⋊C8—21no—
83C9⋊C8—21no—
84C9⋊C8—41no—
85#487—91no—
86#474—91no—
87#461—91no—
88C8×D4—91no—
89#334—91no—
90#332—91no—
91#332D911yescharacteristic, complemented
92C2×C3×Q8—21no—
93C2×D12—31no—
94C2×C4×D3—61no—
95C2×Dic6—61no—
96C2×C3×C8—21no—
97C2×C3×C8—21no—
98C3×C4⋊C4—21no—
99C3×C4⋊C4—21no—
100C3×C42C22×D311yescharacteristic
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—
108#204—122no—
109D3×C8—122no—
110C22×C9#12111yescharacteristic
111C2×D9—22no—
112C2×D9—41no—
113C2×D9—41no—
114C4×C9—21no—
115C4×C9—81no—
116C4×C9C2×SD1611yescharacteristic
117C4×C9#13511yescharacteristic
118C4×C9#13511yescharacteristic
119C4×C9AGL(1,ℤ/8)11yescharacteristic
120Dic9—41no—
121Dic9—81no—
122C2×SD16—181no—
123C22×C8—181no—
124C4⋊Q8—91no—
125C4⋊Q8C2×D911yescharacteristic
126C4×D4—91no—
127#107—181no—
128C4⋊C8—91no—
129C4⋊C8C2×D911yescharacteristic
130C4⋊C8C2×D911yescharacteristic
131#103—181no—
132#103—181no—
133#103—181no—
134#102—181no—
135C22⋊C8—181no—
136C4×C8—91no—
137C22×D3—61no—
138C3×Q8—41no—
139C3×Q8—41no—
140C2×C3×C4—41no—
141C2×C3×C4#23511yescharacteristic
142C2×C3×C4D3×D411yescharacteristic
143C2×C3×C4D3×D411yescharacteristic
144C2×Dic3—61no—
145C2×Dic3—121no—
146D12—32no—
147D12—61no—
148C4×D3—121no—
149C4×D3—121no—
150Dic6—121no—
151Dic6—121no—
152C3×C8—41no—
153C3×C8—41no—
154C3⋊C8—61no—
155C3⋊C8—61no—
156C3⋊C8—121no—
157C2×C9#46311yescharacteristic
158C2×C9#46511yescharacteristic
159C2×C9#47311yescharacteristic
160D9—42no—
161C2×Q8—21no—
162C2×Q8—181no—
163C2×D4—91no—
164C22×C4—181no—
165SD16—362no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—91no—
169C2×C8—91no—
170C2×C8—181no—
171C2×C8—362no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—91no—
175C4⋊C4—181no—
176C4⋊C4—181no—
177C22⋊C4—181no—
178C42C22×D911yescharacteristic
179C22×C3#88411yescharacteristic
180C2×D3—62no—
181C2×D3—121no—
182C2×D3—121no—
183C3×C4—21no—
184C3×C4—81no—
185C3×C4#91111yescharacteristic
186C3×C4D3×SD1611yescharacteristic
187C3×C4#91611yescharacteristic
188C3×C4#91911yescharacteristic
189Dic3—121no—
190Dic3—241no—
191C9#167911yescharacteristic, complemented, Sylow
192C23—181no—
193Q8—41no—
194Q8—41no—
195Q8—361no—
196Q8—361no—
197D4—92no—
198D4—181no—
199C2×C4—41no—
200C2×C4—181no—
201C2×C4—361no—
202C2×C4—361no—
203C2×C4—361no—
204C2×C4#369711yescharacteristic
205C2×C4D4×D911yescharacteristic
206C2×C4D4×D911yescharacteristic
207C8—41no—
208C8—41no—
209C8—181no—
210C8—181no—
211C8—361no—
212C2×C3#475511yescharacteristic
213C2×C3#478711yescharacteristic
214C2×C3#480711yescharacteristic
215D3—122no—
216C22—182no—
217C22—361no—
218C22—361no—
219C22#6344611yescharacteristic
220C4—21no—
221C4—81no—
222C4—361no—
223C4—721no—
224C4#6347311yescharacteristic
225C4SD16×D911yescharacteristic
226C4#6347811yescharacteristic
227C4#6348111yescharacteristic
228C3#6844411yescharacteristic
229C2—362no—
230C2#1058843511yescharacteristic
231C2#1058846711yescharacteristic
232C2#1058848711yescharacteristic
subgroupG/H
centerC22#63446
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#332C2
socleC22×C3#884
prime radicalC2×D36D4
hypercenter#332D9
hypocenterC9#1679
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. #10588161C2semidirect
7. #10588157C2semidirect
91. #332D9semidirect
191. C9#1679semidirect

Maximal subgroups

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

subgroupindex
#105887722
#105887592
#105885252
#105885182
C9×#3322
#105881612
#105881572
#684443