Finite Group Databasebeta

← #11856254

Subgroups — #11856254

Order 1152.

3306 conjugacy classes of subgroups; only the 537 normal subgroups are shown.

normal subgroups only

This group has 3306 conjugacy classes of subgroups — too many to draw. Only its 537 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
1C24×C32×C4C211yesmaximal, characteristic, complemented
2C2×#64162C211yesmaximal, characteristic
3C2×#64138C212yesmaximal, complemented
4#10592946C211yesmaximal, characteristic, complemented
5#10592912C214yesmaximal, complemented
6#10592910C212yesmaximal, complemented
7#10592909C214yesmaximal, complemented
8#84033—34nomaximal
9C25×C32C2211yescharacteristic
10C23×C32×C4—28no—
11C23×C32×C4—24no—
12C23×C32×C4C2214yes—
13C23×C32×C4C2212yes—
14C22×#638C2212yes—
15C22×#638C2211yescharacteristic
16#64162—24no—
17C2×#3757C2212yes—
18C2×#3757C2214yes—
19C2×#3757C2211yescharacteristic
20C2×#3757C2212yes—
21#64138—28no—
22C2×#3752C2214yescomplemented
23C2×#3750C2214yescomplemented
24#63658C2218yescomplemented
25C24×C3×C4D314yescomplemented
26C2×#953—34no—
27C2×#929—38no—
28#5247—34no—
29#5213—316no—
30#5211—38no—
31#5210—316no—
32C24×C32—24no—
33C24×C32—28no—
34C24×C32D414yes—
35C24×C32C2311yescharacteristic
36C24×C32C2312yes—
37C23×C3⋊D3C2311yescharacteristic
38C22×C32×C4—232no—
39C22×C32×C4—28no—
40C22×C32×C4—24no—
41C22×C32×C4—24no—
42C22×C32×C4—216no—
43C22×C32×C4D418yescomplemented
44C22×C32×C4C2314yes—
45C2×#638—24no—
46C2×#638—22no—
47C2×#638—24no—
48C2×#638—28no—
49C22×C3⋊Dic3C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2314yes—
52#3757—24no—
53#3757—22no—
54#3757—24no—
55#3757—28no—
56#3752—28no—
57#3750—28no—
58#2849—91noSylow
59C25×C3C2×D314yes—
60C23×C3×C4—216no—
61C23×C3×C4—232no—
62C23×C3×C4C2×D3116yes—
63C23×C3×C4C2×D318yes—
64C22×#67—38no—
65C22×#67—34no—
66#953—616no—
67C2×#217—38no—
68C2×#217—316no—
69C2×#217—34no—
70C2×#217—38no—
71#929—632no—
72C2×(C2×D3)⋊C4—316no—
73C2×Dic3⋊C4—316no—
74C3⋊#95—332no—
75C23×C32—232no—
76C23×C32—28no—
77C23×C32—216no—
78C23×C32—24no—
79C23×C32—24no—
80C23×C32—24no—
81C23×C32C2×D414yes—
82C23×C32C2×D412yes—
83C23×C32C2×D414yes—
84C23×C32#4118yes—
85C23×C32C2411yescharacteristic
86C22×C3⋊D3—22no—
87C22×C3⋊D3—21no—
88C22×C3⋊D3—24no—
89C2×C32×C4—232no—
90C2×C32×C4—216no—
91C2×C32×C4—24no—
92C2×C32×C4—24no—
93C2×C32×C4C2×D418yes—
94#638—44no—
95#638—48no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—28no—
101C2×C3⋊Dic3—24no—
102C24×C4C3⋊D311yescharacteristic, complemented
103C2×#123—92no—
104C2×#120—91no—
105#386—94no—
106#385—94no—
107#381—92no—
108#379—91no—
109C24×C3—232no—
110C24×C3—216no—
111C24×C3#67116yes—
112C24×C3C22×D318yes—
113C24×C3C22×D314yes—
114C23×D3—34no—
115C22×C3×C4—2128no—
116C22×C3×C4—232no—
117C22×C3×C4—216no—
118C22×C3×C4—216no—
119C22×C3×C4—264no—
120C22×C3×C4#67132yescomplemented
121C22×C3×C4C22×D3116yes—
122C2×#67—632no—
123C2×#67—616no—
124C2×#67—616no—
125C2×#67—68no—
126C22×Dic3—38no—
127C22×Dic3—316no—
128C22×Dic3—34no—
129#217—632no—
130#217—616no—
131#217—616no—
132#217—68no—
133(C2×D3)⋊C4—632no—
134Dic3⋊C4—632no—
135C22×C32—232no—
136C22×C32—24no—
137C22×C32—24no—
138C22×C32—24no—
139C22×C32—28no—
140C22×C32—216no—
141C22×C32#12014yes—
142C22×C32#12318yescomplemented
143C22×C32C22×D411yescharacteristic
144C22×C32C22×D412yes—
145C22×C32C2×#4114yes—
146C2×C3⋊D3—41no—
147C2×C3⋊D3—42no—
148C2×C3⋊D3—44no—
149C32×C4—28no—
150C3⋊Dic3—41no—
151C3⋊Dic3—42no—
152C3⋊Dic3—44no—
153C25C2×C3⋊D311yescharacteristic
154C22×D4—91no—
155C22×D4—92no—
156C23×C4—24no—
157C23×C4—28no—
158C23×C4C2×C3⋊D314yes—
159C23×C4C2×C3⋊D312yes—
160#123—188no—
161#120—184no—
162C2×C4⋊C4—94no—
163C2×C22⋊C4—91no—
164C2×C22⋊C4—92no—
165C2×C22⋊C4—92no—
166C2×C22⋊C4—94no—
167C2×C22⋊C4—94no—
168#95—98no—
169C23×C3—2128no—
170C23×C3—264no—
171C23×C3—232no—
172C23×C3—216no—
173C23×C3—216no—
174C23×C3—216no—
175C23×C3#235132yes—
176C23×C3C2×#67116yes—
177C23×C3C2×#6718yes—
178C23×C3C2×#67116yes—
179C23×C3C23×D314yes—
180C22×D3—616no—
181C22×D3—68no—
182C22×D3—64no—
183C2×C3×C4—2128no—
184C2×C3×C4—264no—
185C2×C3×C4—216no—
186C2×C3×C4—216no—
187C2×C3×C4C2×#67132yes—
188#67—1232no—
189#67—1216no—
190C2×Dic3—632no—
191C2×Dic3—616no—
192C2×Dic3—68no—
193C2×Dic3—616no—
194C2×Dic3—68no—
195C2×Dic3—64no—
196C2×C32—24no—
197C2×C32—28no—
198C2×C32C2×#12011yescharacteristic
199C2×C32C2×#12312yes—
200C2×C32#52514yes—
201C3⋊D3—81no—
202C24—28no—
203C24—24no—
204C24—91no—
205C24#63814yes—
206C24C22×C3⋊D312yes—
207C24C22×C3⋊D311yescharacteristic
208C2×D4—188no—
209C2×D4—184no—
210C2×D4—182no—
211C2×D4—184no—
212C22×C4—232no—
213C22×C4—28no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—216no—
217C22×C4—92no—
218C22×C4—94no—
219C22×C4—91no—
220C22×C4#63818yescomplemented
221C22×C4C22×C3⋊D314yes—
222C4⋊C4—188no—
223C22⋊C4—188no—
224C22⋊C4—184no—
225C22⋊C4—182no—
226C22⋊C4—184no—
227C22⋊C4—188no—
228C22×C3—2128no—
229C22×C3—216no—
230C22×C3—216no—
231C22×C3—264no—
232C22×C3—232no—
233C22×C3—216no—
234C22×C3#929132yescomplemented
235C22×C3#953116yes—
236C22×C3C2×#235116yes—
237C22×C3C22×#6714yes—
238C22×C3C22×#6718yes—
239C2×D3—128no—
240C2×D3—1216no—
241C2×D3—124no—
242C3×C4—232no—
243Dic3—128no—
244Dic3—1216no—
245Dic3—124no—
246C32#284911yescharacteristic, complemented, Sylow
247C23—232no—
248C23—24no—
249C23—24no—
250C23—24no—
251C23—216no—
252C23—28no—
253C23—184no—
254C23—182no—
255C23—181no—
256C23#382818yes—
257C23C2×#63814yes—
258C23C2×#63812yes—
259C23C2×#63814yes—
260C23C23×C3⋊D311yescharacteristic
261D4—368no—
262D4—364no—
263C2×C4—232no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—216no—
267C2×C4—188no—
268C2×C4—184no—
269C2×C4—184no—
270C2×C4—182no—
271C2×C4—181no—
272C2×C4—182no—
273C2×C4C2×#63818yes—
274C2×C3—232no—
275C2×C3—216no—
276C2×C3C2×#92918yes—
277C2×C3#5791116yes—
278C2×C3C2×#95314yes—
279D3—244no—
280C22—232no—
281C22—24no—
282C22—24no—
283C22—216no—
284C22—28no—
285C22—24no—
286C22—362no—
287C22—364no—
288C22—361no—
289C22#6413818yescomplemented
290C22#6416214yes—
291C22C2×#382814yes—
292C22C22×#63811yescharacteristic
293C22C22×#63812yes—
294C4—28no—
295C4—362no—
296C4—364no—
297C4—361no—
298C3#8403314yescomplemented
299C2—28no—
300C2—24no—
301C2—721no—
302C2C2×#6413812yes—
303C2#1059626214yes—
304C2C2×#6416211yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC24×C32×C4C2
prime radicalC2×#64162C2
hypercenterC24×C4C3⋊D3
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C24×C32×C4C2semidirect
3. C2×#64138C2semidirect
4. #10592946C2semidirect
5. #10592912C2semidirect
6. #10592910C2semidirect
7. #10592909C2semidirect
22. C2×#3752C22semidirect
23. C2×#3750C22semidirect
24. #63658C22semidirect
25. C24×C3×C4D3semidirect
43. C22×C32×C4D4semidirect
102. C24×C4C3⋊D3semidirect
120. C22×C3×C4#67semidirect
142. C22×C32#123semidirect
220. C22×C4#638semidirect
234. C22×C3#929semidirect
246. C32#2849semidirect
289. C22#64138semidirect
298. C3#84033semidirect

Maximal subgroups

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

subgroupindex
C24×C32×C42
C2×#641622
C2×#641382
#105929462
#105929122
#105929102
#105929092
#840333