Finite Group Databasebeta

← #11779558

Subgroups — #11779558

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#10589823C211yesmaximal, characteristic
2C9×#487C211yesmaximal, characteristic
3#10588764C211yesmaximal, characteristic
4#10588764C211yesmaximal, characteristic
5#10588224C211yesmaximal, characteristic
6#10588133C211yesmaximal, characteristic
7#10588133C211yesmaximal, characteristic
8#71236—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C9×C4⋊Q8C2211yescharacteristic
11Q8×Dic9—21no—
12#63506—21no—
13#63452—21no—
14#63451—22no—
15#63449—21no—
16C4×Dic18C2211yescharacteristic
17C4×Dic18C2211yescharacteristic
18C9×#103—22no—
19C4×C8×C9C2211yescharacteristic
20#63368—21no—
21#63368—21no—
22#63366—21no—
23#63366—21no—
24C4⋊(C9⋊C8)C2211yescharacteristic
25C4⋊(C9⋊C8)C2211yescharacteristic
26#5721—31no—
27C3×#487D311yescharacteristic
28#5091—31no—
29#5091—31no—
30#4547—31no—
31#4456—31no—
32#4456—31no—
33C2×Q8×C9—21no—
34C2×Q8×C9—21no—
35C2×Dic18D411yescharacteristic
36C2×Dic18D411yescharacteristic
37C2×C8×C9—21no—
38C9×C4⋊C4—21no—
39C9×C4⋊C4—21no—
40C9×C4⋊C4—21no—
41C9×C4⋊C4D412yes—
42C42×C9C2311yescharacteristic
43C4⋊Dic9—22no—
44C4⋊Dic9D411yescharacteristic
45C4⋊Dic9D411yescharacteristic
46Dic9⋊C4—22no—
47Dic9⋊C4—22no—
48Dic9⋊C4—21no—
49Dic9⋊C4—21no—
50C4×Dic9—22no—
51C4×Dic9—21no—
52C4×Dic9—21no—
53C2×C9⋊C8—21no—
54C2×C9⋊C8—21no—
55#1636—91noSylow
56C3×C4⋊Q8C2×D311yescharacteristic
57C3×C4⋊Q8C2×D311yescharacteristic
58Q8×Dic3—61no—
59#944—61no—
60#890—61no—
61#889—62no—
62#887—61no—
63C4×Dic6—31no—
64C4×Dic6—31no—
65C3×#103—22no—
66C3×C4×C8C2×D311yescharacteristic
67#810—61no—
68#810—61no—
69#807—61no—
70#807—61no—
71C4⋊(C3⋊C8)—31no—
72C4⋊(C3⋊C8)—31no—
73Q8×C9—42no—
74Q8×C9—41no—
75Q8×C9—41no—
76C2×C4×C9—22no—
77C2×C4×C9—41no—
78C2×C4×C9C2×D411yescharacteristic
79C2×C4×C9C2×D411yescharacteristic
80C2×C4×C9C2×D411yescharacteristic
81C2×Dic9—21no—
82C2×Dic9—21no—
83C2×Dic9—21no—
84C2×Dic9—21no—
85Dic18—21no—
86Dic18—21no—
87Dic18—21no—
88Dic18Q1612yes—
89C8×C9—41no—
90C9⋊C8—41no—
91C9⋊C8—41no—
92#557—91no—
93#487D911yescharacteristic
94#477—91no—
95#477—91no—
96#332—91no—
97Q8⋊C8—91no—
98Q8⋊C8—91no—
99C2×C3×Q8—21no—
100C2×C3×Q8—21no—
101C2×Dic6—31no—
102C2×Dic6—31no—
103C2×C3×C8—21no—
104C3×C4⋊C4—21no—
105C3×C4⋊C4—21no—
106C3×C4⋊C4—21no—
107C3×C4⋊C4#6712yes—
108C3×C42C22×D311yescharacteristic
109C4⋊Dic3—31no—
110C4⋊Dic3—31no—
111C4⋊Dic3—62no—
112Dic3⋊C4—62no—
113Dic3⋊C4—62no—
114Dic3⋊C4—61no—
115Dic3⋊C4—61no—
116C4×Dic3—62no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C2×C3⋊C8—61no—
120C2×C3⋊C8—61no—
121C22×C9#12011yescharacteristic
122C4×C9—21no—
123C4×C9—42no—
124C4×C9—81no—
125C4×C9C2×Q1611yescharacteristic
126C4×C9#13511yescharacteristic
127C4×C9#13711yescharacteristic
128C4×C9#13711yescharacteristic
129Dic9—22no—
130Dic9—41no—
131Dic9—41no—
132Dic9—41no—
133C4⋊Q8—181no—
134C4⋊Q8C2×D911yescharacteristic
135C4⋊Q8C2×D911yescharacteristic
136#125—181no—
137#125—182no—
138C4×Q8—91no—
139C4×Q8—91no—
140C4×Q8—181no—
141C4×Q8—181no—
142#107—181no—
143#107—181no—
144C4⋊C8—91no—
145C4⋊C8—91no—
146#103—22no—
147#103—181no—
148#103—181no—
149C4×C8C2×D911yescharacteristic
150C3×Q8—42no—
151C3×Q8—41no—
152C3×Q8—41no—
153C2×C3×C4—22no—
154C2×C3×C4—41no—
155C2×C3×C4D3×D411yescharacteristic
156C2×C3×C4D3×D411yescharacteristic
157C2×C3×C4C2×#6711yescharacteristic
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162Dic6—32no—
163Dic6—61no—
164Dic6—61no—
165Dic6—61no—
166C3×C8—41no—
167C3⋊C8—121no—
168C3⋊C8—121no—
169C2×C9#45111yescharacteristic
170C2×C9#45211yescharacteristic
171C2×C9#45411yescharacteristic
172C2×Q8—21no—
173C2×Q8—21no—
174C2×Q8—91no—
175C2×Q8—91no—
176C2×C8—21no—
177C2×C8—181no—
178C2×C8—181no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—91no—
183C4⋊C4—91no—
184C4⋊C4—182no—
185C4⋊C4—182no—
186C4⋊C4—182no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C4⋊C4#61112yes—
190C42—182no—
191C42—181no—
192C42—181no—
193C42C22×D911yescharacteristic
194C22×C3#93711yescharacteristic
195C3×C4—21no—
196C3×C4—42no—
197C3×C4—81no—
198C3×C4#91511yescharacteristic
199C3×C4#91611yescharacteristic
200C3×C4D3×Q1611yescharacteristic
201C3×C4#91811yescharacteristic
202Dic3—62no—
203Dic3—121no—
204Dic3—121no—
205Dic3—121no—
206C9#163611yescharacteristic, complemented, Sylow
207Q8—42no—
208Q8—41no—
209Q8—41no—
210Q8—92no—
211Q8—181no—
212Q8—181no—
213Q8—181no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—181no—
217C2×C4—181no—
218C2×C4—181no—
219C2×C4—181no—
220C2×C4D4×D911yescharacteristic
221C2×C4D4×D911yescharacteristic
222C2×C4C2×#61111yescharacteristic
223C8—41no—
224C8—361no—
225C8—361no—
226C2×C3#506211yescharacteristic
227C2×C3#517311yescharacteristic
228C2×C3#518611yescharacteristic
229C22#6349911yescharacteristic
230C4—21no—
231C4—42no—
232C4—81no—
233C4—182no—
234C4—361no—
235C4—361no—
236C4—361no—
237C4#6347711yescharacteristic
238C4#6347811yescharacteristic
239C4Q16×D911yescharacteristic
240C4#6348011yescharacteristic
241C3#7123611yescharacteristic
242C2#1058874211yescharacteristic
243C2#1058885311yescharacteristic
244C2#1058886611yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#487C2
socle, prime radicalC22×C3#937
hypercenter#487D9
hypocenterC9#1636
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #487

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
#105898232
C9×#4872
#105887642
#105882242
#105881332
#712363