Finite Group Databasebeta

← #11920231

Subgroups — #11920231

Order 1152.

415 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 415 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×C4×Q8⋊C9C211yesmaximal, characteristic, complemented
2#10589523C212yesmaximal, complemented
3#10589496C212yesmaximal, complemented
4C4⋊#3689C211yesmaximal, characteristic, complemented
5#10589493C211yesmaximal, characteristic, complemented
6#82444—31nomaximal
7C22×Q8⋊C9C2211yescharacteristic
8C2×#3689C2212yes—
9#63492—41nomaximal
10C4×Q8⋊C9C2211yescharacteristic
11C4×Q8⋊C9C2211yescharacteristic
12#63421C2212yes—
13C2×C3×C4×Q8D311yescharacteristic
14#5477—31no—
15#5227—32no—
16#5027—31no—
17#5027—31no—
18#5026—32no—
19#5026—32no—
20#5021—31no—
21#5021—31no—
22#4967—32no—
23#4926—31no—
24C22×C4×C9—41no—
25C2×#611—42no—
26C2×D36—41no—
27C2×Q8⋊C9—21no—
28C2×Q8⋊C9C2311yescharacteristic
29#3689—22no—
30(C2×D9)⋊C4—42no—
31C4⋊Dic9—41no—
32#3112—91noSylow
33C22×C3×Q8C2×D311yescharacteristic
34C2×#235—61no—
35C3×C4×Q8—31no—
36C3×C4×Q8—31no—
37C3×C4×Q8C2×D311yescharacteristic
38C3×C4×Q8C2×D311yescharacteristic
39C2×C3×C4⋊C4—31no—
40C2×C3×C42—31no—
41C2×#215—32no—
42C2×#215—32no—
43#930—32no—
44#930—61no—
45#875—61no—
46#874—31no—
47C4×D12—32no—
48C4×D12—61no—
49#869—31no—
50#835—32no—
51#835—32no—
52#830—32no—
53#809—32no—
54#809—32no—
55#807—32no—
56#807—32no—
57C4⋊(C3⋊C8)—31no—
58C4⋊(C3⋊C8)—31no—
59#803—32no—
60C23×C9—41no—
61C22×D9—42no—
62C2×C4×C9—41no—
63C2×C4×C9—41no—
64C2×C4×C9—82no—
65#611—84no—
66C2×Dic9—42no—
67D36—82no—
68Q8⋊C9#4111yescharacteristic, complemented
69#532—91no—
70C2×C4×Q8D911yescharacteristic, complemented
71#480—92no—
72#477—91no—
73#477—91no—
74#460—91no—
75#460—91no—
76#448—92no—
77#440—92no—
78#440—92no—
79#432—91no—
80C2×C3×Q8—21no—
81C2×C3×Q8—31no—
82C2×C3×Q8—61no—
83C2×C3×Q8C22×D311yescharacteristic
84C22×C3×C4—31no—
85C22×C3×C4—31no—
86C22×C3×C4S411yescharacteristic
87C2×#67—62no—
88#235—124no—
89C2×D12—32no—
90C2×D12—61no—
91C2×D12—61no—
92C2×C4×D3—62no—
93C2×Dic6—61no—
94C3×C4⋊C4—31no—
95C3×C4⋊C4—31no—
96C3×C4⋊C4—61no—
97C3×C42—31no—
98C3×C42—31no—
99C3×C42—31no—
100C3×C42—31no—
101#215—62no—
102#215—64no—
103#215—62no—
104(C2×D3)⋊C4—62no—
105(C2×D3)⋊C4—62no—
106C4⋊Dic3—32no—
107C4⋊Dic3—61no—
108C2×C3⋊C8—32no—
109C2×C3⋊C8—32no—
110C22×C9—42no—
111C22×C9—41no—
112C22×C9—81no—
113C22×C9—81no—
114C2×D9—82no—
115C2×D9—82no—
116C2×D9—82no—
117C4×C9—42no—
118C4×C9—81no—
119Dic9—82no—
120C2×#41—181no—
121C22×Q8C2×D911yescharacteristic
122C2×SD16—92no—
123C2×SD16—92no—
124C4⋊Q8—91no—
125#127—91no—
126#124—181no—
127#121—92no—
128#121—181no—
129C4×Q8—31no—
130C4×Q8—31no—
131C4×Q8C2×D911yescharacteristic
132C4×Q8C2×D911yescharacteristic
133C4×D4—92no—
134C4×D4—181no—
135C2×C4⋊C4—31no—
136C2×C42—31no—
137#107—92no—
138#107—92no—
139C4⋊C8—91no—
140C4⋊C8—91no—
141#103—92no—
142#103—92no—
143#102—92no—
144#102—92no—
145C22⋊C8—92no—
146#97—92no—
147C23×C3C2×S411yescharacteristic
148C22×D3—62no—
149C3×Q8—31no—
150C3×Q8—32no—
151C3×Q8—61no—
152C3×Q8#23511yescharacteristic
153C2×C3×C4—22no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—31no—
157C2×C3×C4—31no—
158C2×C3×C4—61no—
159C2×C3×C4—61no—
160C2×C3×C4—62no—
161C2×C3×C4C2×S411yescharacteristic
162C2×C3×C4C2×S411yescharacteristic
163#67—124no—
164C2×Dic3—62no—
165D12—62no—
166D12—62no—
167D12—122no—
168D12—122no—
169C4×D3—124no—
170Dic6—122no—
171C3⋊C8—62no—
172C3⋊C8—62no—
173C2×C9—41no—
174C2×C9—41no—
175C2×C9—41no—
176C2×C9—82no—
177D9—162no—
178#41—364no—
179C2×Q8—21no—
180C2×Q8—31no—
181C2×Q8—61no—
182C2×Q8—181no—
183C2×Q8C22×D911yescharacteristic
184C2×D4—92no—
185C2×D4—181no—
186C2×D4—182no—
187C2×D4—181no—
188C22×C4—31no—
189C22×C4—31no—
190C22×C4—182no—
191C22×C4(C22⋊C9)⋊C211yescharacteristic
192SD16—182no—
193SD16—184no—
194SD16—182no—
195C2×C8—92no—
196C2×C8—92no—
197C4⋊C4—31no—
198C4⋊C4—31no—
199C4⋊C4—61no—
200C4⋊C4—92no—
201C4⋊C4—181no—
202C22⋊C4—182no—
203C22⋊C4—182no—
204C42—31no—
205C42—31no—
206C42—31no—
207C42—31no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3#98612yes—
211C22×C3C22×S411yescharacteristic
212C2×D3—122no—
213C2×D3—122no—
214C2×D3—122no—
215C3×C4—21no—
216C3×C4—31no—
217C3×C4—31no—
218C3×C4—61no—
219C3×C4—61no—
220C3×C4—61no—
221C3×C4#98312yes—
222Dic3—122no—
223C9—41noSylow
224C23—182no—
225C23C2×(C22⋊C9)⋊C211yescharacteristic
226Q8—31no—
227Q8—32no—
228Q8—61no—
229Q8—362no—
230Q8#369711yescharacteristic
231D4—182no—
232D4—182no—
233D4—362no—
234D4—364no—
235D4—362no—
236C2×C4—22no—
237C2×C4—31no—
238C2×C4—31no—
239C2×C4—31no—
240C2×C4—31no—
241C2×C4—61no—
242C2×C4—61no—
243C2×C4—62no—
244C2×C4—182no—
245C2×C4—364no—
246C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
247C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
248C8—182no—
249C8—182no—
250C2×C3—22no—
251C2×C3#591211yescharacteristic
252C2×C3C2×#98311yescharacteristic
253C2×C3C2×#98611yescharacteristic
254D3—242no—
255C22—21no—
256C22—21no—
257C22—362no—
258C22—362no—
259C22—362no—
260C22#6369212yes—
261C22C22×(C22⋊C9)⋊C211yescharacteristic
262C4—21no—
263C4—31no—
264C4—31no—
265C4—61no—
266C4—61no—
267C4—61no—
268C4—362no—
269C4#6368912yes—
270C3#8533211yescharacteristic
271C2—22no—
272C2—722no—
273C2#1059308711yescharacteristic
274C2C2×#6368911yescharacteristic
275C2C2×#6369211yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
FittingC2×C3×C4×Q8D3
hypercenterC22×C4(C22⋊C9)⋊C2
hypocenterQ8⋊C9#41
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8⋊C9C2semidirect
2. #10589523C2semidirect
3. #10589496C2semidirect
4. C4⋊#3689C2semidirect
5. #10589493C2semidirect
68. Q8⋊C9#41semidirect
70. C2×C4×Q8D9semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8⋊C92
#105895232
#105894962
C4⋊#36892
#105894932
#824443
#634924