Finite Group Databasebeta

← #11788338

Subgroups — #11788338

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic
2C22×#3748C211yesmaximal, characteristic
3C2×#63663C212yesmaximal, complemented
4#10592906C211yesmaximal, characteristic
5#10589396C212yesmaximal, complemented
6#71698—34nomaximal
7C22×C32×Q8C2211yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C32×C22⋊Q8—21no—
10C32×C22⋊Q8—21no—
11C32×C22⋊Q8—21no—
12C32×C22⋊Q8—21no—
13C2×C32×C4⋊C4C412yes—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C22⋊C4C412yes—
16C2×#3748—21no—
17C2×#3748—24no—
18C2×#3748C2212yes—
19C2×#3748C2212yes—
20C22×C3⋊(C3⋊C8)—21no—
21#63663—24no—
22#63657—21no—
23#63657—21no—
24C2×C3×C22⋊Q8D314yes—
25C22×#208—34no—
26C2×#836—38no—
27#5207—34no—
28#4530—38no—
29C24×C32C2×C411yescharacteristic
30C2×C32×Q8—21no—
31C2×C32×Q8—21no—
32C2×C32×Q8—22no—
33C2×C32×Q8—22no—
34C22×C32×C4—22no—
35C22×C32×C4—22no—
36C22×C32×C4C2×C412yes—
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4C2×C412yes—
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C32×C4⋊C4—22no—
45C32×C4⋊C4—22no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C22⋊C4—22no—
49C32×C22⋊C4—22no—
50#3748—24no—
51#3748—22no—
52#3748—22no—
53#3748—22no—
54#3748D414yes—
55C2×C3⋊(C3⋊C8)—24no—
56C2×C3⋊(C3⋊C8)—22no—
57C2×C3⋊(C3⋊C8)—22no—
58#1901—91noSylow
59C22×C3×Q8C2×D314yes—
60C23×C3×C4C2×D314yes—
61C3×C22⋊Q8—24no—
62C3×C22⋊Q8—24no—
63C3×C22⋊Q8—24no—
64C3×C22⋊Q8—24no—
65C2×C3×C4⋊C4Dic318yes—
66C2×C3×C4⋊C4C2×D314yes—
67C2×C3×C22⋊C4Dic318yes—
68C2×#208—38no—
69C2×#208—38no—
70C2×#208—616no—
71C2×#208—64no—
72C22×C3⋊C8—64no—
73#836—616no—
74#830—64no—
75#830—64no—
76C23×C32—22no—
77C23×C32—22no—
78C23×C32—41no—
79C23×C32C22⋊C411yescharacteristic
80C23×C32C22⋊C411yescharacteristic
81C23×C32C22×C411yescharacteristic
82C32×Q8—41no—
83C32×Q8—42no—
84C32×Q8—41no—
85C2×C32×C4—22no—
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—24no—
95C2×C32×C4—42no—
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C2×D412yes—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4112yes—
102C3⋊(C3⋊C8)—24no—
103C3⋊(C3⋊C8)—42no—
104C22×M16—91no—
105C2×C22⋊Q8C3⋊D311yescharacteristic
106C2×#101—92no—
107#407—91no—
108#343—92no—
109C24×C3C2×Dic314yes—
110C2×C3×Q8—28no—
111C2×C3×Q8—28no—
112C2×C3×Q8—24no—
113C2×C3×Q8—24no—
114C22×C3×C4—28no—
115C22×C3×C4—28no—
116C22×C3×C4C2×Dic318yes—
117C22×C3×C4C2×Dic314yes—
118C22×C3×C4C2×Dic318yes—
119C22×C3×C4#6714yes—
120C22×C3×C4#6714yes—
121C22×C3×C4#6714yes—
122C22×C3×C4#6714yes—
123C22×C3×C4C22×D314yes—
124C3×C4⋊C4—28no—
125C3×C4⋊C4—28no—
126C3×C4⋊C4—24no—
127C3×C4⋊C4—24no—
128C3×C22⋊C4—28no—
129C3×C22⋊C4—28no—
130#208—316no—
131#208—616no—
132#208—68no—
133#208—68no—
134#208—68no—
135C2×C3⋊C8—616no—
136C2×C3⋊C8—68no—
137C2×C3⋊C8—68no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32—44no—
146C22×C32#10112yescomplemented
147C22×C32C2×C22⋊C411yescharacteristic
148C22×C32C4×D412yes—
149C32×C4—21no—
150C32×C4—21no—
151C32×C4—42no—
152C32×C4—42no—
153C32×C4#12011yescharacteristic
154C32×C4#12112yes—
155C32×C4#12311yescharacteristic
156C22×Q8C2×C3⋊D311yescharacteristic
157C23×C4C2×C3⋊D311yescharacteristic
158C2×M16—92no—
159C2×M16—92no—
160C2×M16—184no—
161C2×M16—181no—
162C22×C8—181no—
163C22⋊Q8—21no—
164C22⋊Q8—21no—
165C22⋊Q8—21no—
166C22⋊Q8—21no—
167C2×C4⋊C4C3⋊Dic312yes—
168C2×C4⋊C4C2×C3⋊D311yescharacteristic
169C2×C22⋊C4C3⋊Dic312yes—
170#101—184no—
171C22⋊C8—181no—
172C22⋊C8—181no—
173C23×C3—28no—
174C23×C3—28no—
175C23×C3—44no—
176C23×C3#21714yes—
177C23×C3#21714yes—
178C23×C3C22×Dic314yes—
179C3×Q8—44no—
180C3×Q8—44no—
181C3×Q8—48no—
182C2×C3×C4—28no—
183C2×C3×C4—24no—
184C2×C3×C4—24no—
185C2×C3×C4—24no—
186C2×C3×C4—24no—
187C2×C3×C4—28no—
188C2×C3×C4—28no—
189C2×C3×C4—216no—
190C2×C3×C4—28no—
191C2×C3×C4—28no—
192C2×C3×C4—48no—
193C2×C3×C4#21714yes—
194C2×C3×C4#21714yes—
195C2×C3×C4D3×D418yes—
196C2×C3×C4#23718yes—
197C2×C3×C4C2×#6714yes—
198C2×C3×C4C2×#6714yes—
199C3⋊C8—616no—
200C3⋊C8—128no—
201C2×C32—22no—
202C2×C32—22no—
203C2×C32—41no—
204C2×C32#38611yescharacteristic
205C2×C32C2×#10111yescharacteristic
206C2×C32#41311yescharacteristic
207C24C2×C3⋊Dic311yescharacteristic
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—21no—
211C2×Q8—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4C2×C3⋊Dic312yes—
215C22×C4C2×C3⋊Dic311yescharacteristic
216C22×C4C2×C3⋊Dic312yes—
217C22×C4#63811yescharacteristic
218C22×C4#63811yescharacteristic
219C22×C4#63811yescharacteristic
220C22×C4#63811yescharacteristic
221C22×C4C22×C3⋊D311yescharacteristic
222M16—94no—
223M16—184no—
224M16—182no—
225M16—182no—
226M16—182no—
227C2×C8—184no—
228C2×C8—182no—
229C2×C8—182no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C22⋊C4—22no—
235C22⋊C4—22no—
236C22×C3—24no—
237C22×C3—24no—
238C22×C3—24no—
239C22×C3—24no—
240C22×C3—24no—
241C22×C3—24no—
242C22×C3—24no—
243C22×C3—416no—
244C22×C3#83618yescomplemented
245C22×C3D4×Dic318yes—
246C22×C3C2×#21714yes—
247C3×C4—24no—
248C3×C4—24no—
249C3×C4—48no—
250C3×C4—48no—
251C3×C4#93514yes—
252C3×C4#93714yes—
253C3×C4#93918yes—
254C32#190111yescharacteristic, complemented, Sylow
255C23—22no—
256C23—22no—
257C23—41no—
258C23#375711yescharacteristic
259C23#375711yescharacteristic
260C23C22×C3⋊Dic311yescharacteristic
261Q8—41no—
262Q8—41no—
263Q8—42no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4#375711yescharacteristic
276C2×C4#375711yescharacteristic
277C2×C4D4×C3⋊D312yes—
278C2×C4#383012yes—
279C2×C4C2×#63811yescharacteristic
280C2×C4C2×#63811yescharacteristic
281C8—184no—
282C8—362no—
283C2×C3—28no—
284C2×C3—28no—
285C2×C3—44no—
286C2×C3#522014yes—
287C2×C3C2×#83614yes—
288C2×C3#523714yes—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—44no—
297C22#6366312yescomplemented
298C22D4×C3⋊Dic312yes—
299C22C2×#375711yescharacteristic
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4#6414411yescharacteristic
305C4#6414611yescharacteristic
306C4#6414812yes—
307C3#7169814yescomplemented
308C2—22no—
309C2—22no—
310C2—41no—
311C2#1059291911yescharacteristic
312C2C2×#6366311yescharacteristic
313C2#1059293611yescharacteristic
subgroupG/H
centerC22C2×#3757
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C22⋊Q8C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#63663C2semidirect
5. #10589396C2semidirect
146. C22×C32#101semidirect
244. C22×C3#836semidirect
254. C32#1901semidirect
297. C22#63663semidirect
307. C3#71698semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C22×#37482
C2×#636632
#105929062
#105893962
#716983