Finite Group Databasebeta

← #11920243

Subgroups — #11920243

Order 1152.

482 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 61 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×#63691C212yesmaximal, complemented
2C4×#41⋊C9C211yesmaximal, characteristic, complemented
3#10589497C212yesmaximal, complemented
4C4⋊#3689C211yesmaximal, characteristic, complemented
5C4⋊#3688C211yesmaximal, characteristic, complemented
6#82525—31nomaximal
7C2×#41⋊C9C2211yescharacteristic
8#63691—24no—
9C2×#3689C2212yes—
10C2×#3688C2212yes—
11C4×D36—41nomaximal
12C4×Q8⋊C9C2211yescharacteristic
13C4×Q8⋊C9C2211yescharacteristic
14C3×C4×#41D311yescharacteristic
15C2×#950—32no—
16#5477—31no—
17#5031—31no—
18#5028—32no—
19#5027—31no—
20#5019—31no—
21#5016—32no—
22#5015—31no—
23#5002—32no—
24C2×C4⋊(C3⋊C8)—31no—
25C2×D36—41no—
26C2×C4×D9—42no—
27#41⋊C9D412yescomplemented
28C2×Q8⋊C9C2311yescharacteristic
29#3689—22no—
30#3688—22no—
31C42×C9—41no—
32(C2×D9)⋊C4—42no—
33C4⋊Dic9—41no—
34#3035—91noSylow
35C2×C3×#41C2×D311yescharacteristic
36C2×#235—32no—
37C3×C4×Q8C2×D311yescharacteristic
38C3×C4×Q8C2×D311yescharacteristic
39C3×C4×D4—31no—
40C3×C4×D4—31no—
41C3×#117—31no—
42C2×C3×C42—31no—
43#950—64no—
44#950—64no—
45C2×#216—32no—
46C2×#215—32no—
47C2×#214—32no—
48C2×#213—32no—
49#930—61no—
50#930—61no—
51C22×C3⋊C8—32no—
52#875—32no—
53#874—31no—
54C4×D12—61no—
55C4×D12—61no—
56#869—31no—
57#810—32no—
58#810—32no—
59#809—32no—
60#809—32no—
61C4⋊(C3⋊C8)—31no—
62C4⋊(C3⋊C8)—32no—
63C4⋊(C3⋊C8)—31no—
64C22×D9—42no—
65C2×C4×C9—41no—
66C2×C4×C9—41no—
67C2×C4×C9—41no—
68C2×Dic9—42no—
69D36—44no—
70C4×D9—84no—
71Q8⋊C9C2×D411yescharacteristic
72C2×#135—92no—
73#532—91no—
74C4×#41D911yescharacteristic, complemented
75#464—92no—
76#463—92no—
77#462—91no—
78#461—91no—
79#460—91no—
80#459—91no—
81C2×C4⋊C8—91no—
82#416—92no—
83C3×#41—32no—
84C3×#41D1212yes—
85C2×C3×Q8C22×D311yescharacteristic
86C2×C3×D4—31no—
87C22×C3×C4—31no—
88C22×C3×C4—31no—
89C22×C3×C4—31no—
90C2×#67—62no—
91#235—64no—
92#235—64no—
93C2×D12—32no—
94C2×D12—61no—
95C2×D12—61no—
96C2×C4×D3—62no—
97C2×Dic6—32no—
98C3×C4⋊C4—31no—
99C3×C4⋊C4—31no—
100C3×C22⋊C4—61no—
101C3×C42—31no—
102C3×C42—31no—
103C3×C42—31no—
104C3×C42S411yescharacteristic
105#216—62no—
106#216—62no—
107#215—62no—
108#215—62no—
109#214—64no—
110#213—64no—
111(C2×D3)⋊C4—62no—
112(C2×D3)⋊C4—62no—
113C4⋊Dic3—61no—
114C4⋊Dic3—61no—
115C2×C3⋊C8—32no—
116C2×C3⋊C8—32no—
117C2×C3⋊C8—64no—
118C22×C9—41no—
119C2×D9—44no—
120C2×D9—82no—
121C2×D9—82no—
122C4×C9—42no—
123C4×C9—42no—
124C4×C9—81no—
125Dic9—82no—
126C2×#41—92no—
127C2×#41C2×D911yescharacteristic
128#135—184no—
129#135—184no—
130C2×Q16—92no—
131C2×SD16—92no—
132C2×SD16—92no—
133C2×D8—92no—
134C22×C8—92no—
135C4⋊Q8—91no—
136#127—91no—
137#124—92no—
138#121—181no—
139#121—181no—
140C4×Q8C2×D911yescharacteristic
141C4×Q8C2×D911yescharacteristic
142C4×D4—31no—
143C4×D4—31no—
144C4×D4—181no—
145C4×D4—181no—
146#117—31no—
147C2×C42—31no—
148C4⋊C8—91no—
149C4⋊C8—91no—
150C4⋊C8—92no—
151#103—92no—
152#103—92no—
153#102—92no—
154#102—92no—
155C23×C3—31no—
156C22×D3—62no—
157C3×Q8—31no—
158C3×Q8C2×D1211yescharacteristic
159C3×D4—32no—
160C3×D4—61no—
161C2×C3×C4—31no—
162C2×C3×C4—32no—
163C2×C3×C4—32no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—62no—
167C2×C3×C4—121no—
168C2×C3×C4C2×S411yescharacteristic
169C2×C3×C4C2×S411yescharacteristic
170C2×C3×C4C2×S411yescharacteristic
171#67—124no—
172C2×Dic3—62no—
173D12—62no—
174D12—62no—
175D12—122no—
176D12—122no—
177C4×D3—124no—
178Dic6—62no—
179Dic6—62no—
180C3⋊C8—62no—
181C3⋊C8—62no—
182C2×C9—41no—
183C2×C9—41no—
184C2×C9—41no—
185D9—84no—
186#41—32no—
187#41—184no—
188#41—184no—
189#41D3612yescomplemented
190C2×Q8—92no—
191C2×Q8C22×D911yescharacteristic
192C2×D4—31no—
193C2×D4—92no—
194C2×D4—181no—
195C2×D4—182no—
196C2×D4—181no—
197C22×C4—31no—
198C22×C4—31no—
199C22×C4—31no—
200C22×C4—182no—
201Q16—182no—
202Q16—182no—
203SD16—184no—
204SD16—182no—
205SD16—182no—
206D8—184no—
207C2×C8—92no—
208C2×C8—92no—
209C2×C8—184no—
210C4⋊C4—31no—
211C4⋊C4—31no—
212C4⋊C4—181no—
213C4⋊C4—181no—
214C22⋊C4—61no—
215C22⋊C4—182no—
216C22⋊C4—182no—
217C42—31no—
218C42—31no—
219C42—31no—
220C42(C22⋊C9)⋊C211yescharacteristic
221C22×C3—32no—
222C22×C3—61no—
223C22×C3—61no—
224C22×C3C22×S411yescharacteristic
225C2×D3—122no—
226C2×D3—122no—
227C2×D3—122no—
228C3×C4—21no—
229C3×C4—31no—
230C3×C4—31no—
231C3×C4—61no—
232C3×C4—61no—
233C3×C4C4⋊S412yes—
234C3×C4#98512yes—
235Dic3—122no—
236C9—41noSylow
237C23—31no—
238C23—182no—
239Q8—31no—
240Q8—182no—
241Q8—182no—
242Q8C2×D3611yescharacteristic
243D4—32no—
244D4—61no—
245D4—182no—
246D4—182no—
247D4—362no—
248D4—364no—
249D4—362no—
250C2×C4—31no—
251C2×C4—32no—
252C2×C4—32no—
253C2×C4—31no—
254C2×C4—31no—
255C2×C4—62no—
256C2×C4—121no—
257C2×C4—182no—
258C2×C4—364no—
259C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
260C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
261C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
262C8—182no—
263C8—182no—
264C2×C3—62no—
265C2×C3C2×C4⋊S411yescharacteristic
266C2×C3C2×#98511yescharacteristic
267C2×C3#592311yescharacteristic
268D3—242no—
269C22—32no—
270C22—61no—
271C22—61no—
272C22—362no—
273C22—362no—
274C22—362no—
275C22C22×(C22⋊C9)⋊C211yescharacteristic
276C4—21no—
277C4—31no—
278C4—31no—
279C4—61no—
280C4—61no—
281C4—362no—
282C4C4⋊((C22⋊C9)⋊C2)12yes—
283C4#6369112yescomplemented
284C3#8534411yescharacteristic
285C2—62no—
286C2—722no—
287C2C2×C4⋊((C22⋊C9)⋊C2)11yescharacteristic
288C2C2×#6369111yescharacteristic
289C2#1059309811yescharacteristic
subgroupG/H
centerC2×C4C2×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
FittingC3×C4×#41D3
hypercenterC42(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×D4
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×#63691C2semidirect
2. C4×#41⋊C9C2semidirect
3. #10589497C2semidirect
4. C4⋊#3689C2semidirect
5. C4⋊#3688C2semidirect
27. #41⋊C9D4semidirect
74. C4×#41D9semidirect
189. #41D36semidirect
283. C4#63691semidirect

Maximal subgroups

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

subgroupindex
C2×#636912
C4×#41⋊C92
#105894972
C4⋊#36892
C4⋊#36882
#825253
C4×D364