Finite Group Databasebeta

← #11779561

Subgroups — #11779561

Order 1152.

282 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 74 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#10589669C211yesmaximal, characteristic
2C9×#477C211yesmaximal, characteristic
3#10588764C211yesmaximal, characteristic
4#10588759C211yesmaximal, characteristic
5#10588212C211yesmaximal, characteristic
6#10588160C211yesmaximal, characteristic
7#10588159C211yesmaximal, characteristic
8#71162—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C4×Q8×C9C2211yescharacteristic
11#63506—21no—
12#63451—22no—
13#63449—21no—
14#63432—21no—
15#63431C2211yescharacteristic
16C4×Dic18—21no—
17C4×Dic18C2211yescharacteristic
18C9×#107—21no—
19C9×C4⋊C8C2211yescharacteristic
20C9×#103—21no—
21#63395—22no—
22#63368—21no—
23#63366—21no—
24C4⋊(C9⋊C8)C2211yescharacteristic
25C4×C9⋊C8C2211yescharacteristic
26#5567—31no—
27C3×#477D311yescharacteristic
28#5091—31no—
29#5079—31no—
30#4535—31no—
31#4484—31no—
32#4482—31no—
33C2×Q8×C9—21no—
34C2×Q8×C9D411yescharacteristic
35C2×Dic18—21no—
36C2×Dic18D411yescharacteristic
37C2×C8×C9—21no—
38C9×C4⋊C4—21no—
39C9×C4⋊C4—21no—
40C9×C4⋊C4—21no—
41C9×C4⋊C4D411yescharacteristic
42C42×C9—21no—
43C42×C9C2311yescharacteristic
44C4⋊Dic9—21no—
45C4⋊Dic9D411yescharacteristic
46C4⋊Dic9D412yes—
47Dic9⋊C4—22no—
48Dic9⋊C4—22no—
49Dic9⋊C4—22no—
50Dic9⋊C4—21no—
51C4×Dic9—22no—
52C4×Dic9—21no—
53C2×C9⋊C8—21no—
54C2×C9⋊C8—21no—
55#1636—91noSylow
56C3×C4⋊Q8C2×D311yescharacteristic
57C3×C4×Q8C2×D311yescharacteristic
58#944—61no—
59#889—62no—
60#887—61no—
61#870—61no—
62#869—31no—
63C4×Dic6—31no—
64C4×Dic6—61no—
65C3×#107—21no—
66C3×C4⋊C8C2×D311yescharacteristic
67C3×#103—21no—
68#835—62no—
69#810—61no—
70#807—61no—
71C4⋊(C3⋊C8)—31no—
72C4×C3⋊C8—31no—
73Q8×C9—21no—
74Q8×C9—21no—
75Q8×C9—42no—
76C2×C4×C9—21no—
77C2×C4×C9—21no—
78C2×C4×C9—41no—
79C2×C4×C9C2×D411yescharacteristic
80C2×C4×C9C2×D411yescharacteristic
81C2×C4×C9C2×D411yescharacteristic
82C2×Dic9—21no—
83C2×Dic9—21no—
84C2×Dic9—22no—
85Dic18—21no—
86Dic18—41no—
87Dic18—41no—
88Dic18Q1612yes—
89C8×C9—41no—
90C9⋊C8—41no—
91C9⋊C8—41no—
92#557—91no—
93#487—91no—
94#477—91no—
95#477D911yescharacteristic
96#332—91no—
97Q8⋊C8—91no—
98Q8⋊C8—91no—
99C2×C3×Q8—21no—
100C2×C3×Q8#6711yescharacteristic
101C2×Dic6—31no—
102C2×Dic6—61no—
103C2×C3×C8—21no—
104C3×C4⋊C4—21no—
105C3×C4⋊C4—21no—
106C3×C4⋊C4—21no—
107C3×C4⋊C4#6711yescharacteristic
108C3×C42—21no—
109C3×C42C22×D311yescharacteristic
110C4⋊Dic3—31no—
111C4⋊Dic3—32no—
112C4⋊Dic3—61no—
113Dic3⋊C4—62no—
114Dic3⋊C4—62no—
115Dic3⋊C4—62no—
116Dic3⋊C4—61no—
117C4×Dic3—62no—
118C4×Dic3—61no—
119C2×C3⋊C8—61no—
120C2×C3⋊C8—61no—
121C22×C9#12011yescharacteristic
122C4×C9—21no—
123C4×C9—41no—
124C4×C9—41no—
125C4×C9—81no—
126C4×C9C2×Q1611yescharacteristic
127C4×C9#13511yescharacteristic
128C4×C9#13711yescharacteristic
129C4×C9#13711yescharacteristic
130Dic9—22no—
131Dic9—42no—
132Dic9—41no—
133C4⋊Q8—91no—
134C4⋊Q8—181no—
135C4⋊Q8C2×D911yescharacteristic
136#125—181no—
137#125—182no—
138C4×Q8—91no—
139C4×Q8—181no—
140C4×Q8—181no—
141C4×Q8C2×D911yescharacteristic
142#107—21no—
143#107—181no—
144C4⋊C8—91no—
145C4⋊C8C2×D911yescharacteristic
146#103—21no—
147#103—181no—
148#103—182no—
149C4×C8—91no—
150C3×Q8—21no—
151C3×Q8—21no—
152C3×Q8—42no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—41no—
156C2×C3×C4D3×D411yescharacteristic
157C2×C3×C4D3×D411yescharacteristic
158C2×C3×C4C2×#6711yescharacteristic
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—62no—
162Dic6—32no—
163Dic6—61no—
164Dic6—121no—
165Dic6—121no—
166C3×C8—41no—
167C3⋊C8—121no—
168C3⋊C8—121no—
169C2×C9#45111yescharacteristic
170C2×C9#45211yescharacteristic
171C2×C9#45411yescharacteristic
172C2×Q8—21no—
173C2×Q8—91no—
174C2×Q8—181no—
175C2×Q8#61111yescharacteristic
176C2×C8—21no—
177C2×C8—181no—
178C2×C8—181no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—92no—
183C4⋊C4—91no—
184C4⋊C4—182no—
185C4⋊C4—182no—
186C4⋊C4—182no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C4⋊C4#61111yescharacteristic
190C42—21no—
191C42—182no—
192C42—181no—
193C42C22×D911yescharacteristic
194C22×C3#93711yescharacteristic
195C3×C4—21no—
196C3×C4—41no—
197C3×C4—41no—
198C3×C4—81no—
199C3×C4D3×Q1611yescharacteristic
200C3×C4#91811yescharacteristic
201C3×C4#94211yescharacteristic
202C3×C4#95011yescharacteristic
203Dic3—62no—
204Dic3—121no—
205Dic3—122no—
206C9#163611yescharacteristic, complemented, Sylow
207Q8—21no—
208Q8—21no—
209Q8—42no—
210Q8—92no—
211Q8—181no—
212Q8—361no—
213Q8—361no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—181no—
218C2×C4—181no—
219C2×C4—182no—
220C2×C4D4×D911yescharacteristic
221C2×C4D4×D911yescharacteristic
222C2×C4C2×#61111yescharacteristic
223C8—41no—
224C8—361no—
225C8—361no—
226C2×C3#504711yescharacteristic
227C2×C3#518611yescharacteristic
228C2×C3#520111yescharacteristic
229C22#6349911yescharacteristic
230C4—21no—
231C4—41no—
232C4—41no—
233C4—81no—
234C4—182no—
235C4—362no—
236C4—361no—
237C4Q16×D911yescharacteristic
238C4#6348011yescharacteristic
239C4#6350511yescharacteristic
240C4#6351311yescharacteristic
241C3#7116211yescharacteristic
242C2#1058873011yescharacteristic
243C2#1058886611yescharacteristic
244C2#1058888111yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#477C2
socle, prime radicalC22×C3#937
hypercenter#477D9
hypocenterC9#1636
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
206. C9#1636semidirect

Maximal subgroups

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

subgroupindex
#105896692
C9×#4772
#105887642
#105887592
#105882122
#105881602
#105881592
#711623