Finite Group Databasebeta

← #11858840

Subgroups — #11858840

Order 1152.

1217 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3#10591120C212yesmaximal, complemented
4#10591066C214yesmaximal, complemented
5#10591061C214yesmaximal, complemented
6#10591060C212yesmaximal, complemented
7#78619—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C412yes—
10C2×C4×C3⋊Dic3C412yes—
11C2×C4×C3⋊Dic3C412yes—
12C2×C4×C3⋊Dic3C412yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×#208C2214yes—
18C3×#830C2218yes—
19#63572C2218yescomplemented
20#63555C2214yescomplemented
21#63553C2214yescomplemented
22C22×C4×Dic3—32no—
23C22×C4×Dic3—61no—
24C3×#407—32no—
25#5207D312yes—
26#5118—34no—
27Dic3×M16—34no—
28#4719—38no—
29#4718—38no—
30C24×C32C2×C411yescharacteristic
31C22×C32×C4—24no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C412yes—
34C22×C32×C4C2312yes—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—28no—
37C22×C3⋊Dic3C2×C412yes—
38C22×C3⋊Dic3C2×C412yes—
39C22×C3⋊Dic3C2×C412yes—
40C22×C3⋊Dic3C2×C412yes—
41C22×C3⋊Dic3C2×C412yes—
42C22×C3⋊Dic3C2×C412yes—
43C4×C3⋊Dic3C2×C412yes—
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3C2×C412yes—
46C4×C3⋊Dic3C2×C412yes—
47C4×C3⋊Dic3C2×C412yes—
48C4×C3⋊Dic3C2×C412yes—
49C4×C3⋊Dic3C2×C411yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51C4×C3⋊Dic3C2311yescharacteristic
52C4×C3⋊Dic3C2312yes—
53C3×#208—28no—
54C2×C3×C3⋊C8C2318yes—
55#2920—91noSylow
56C23×C3×C4—21no—
57C23×C3×C4C2×D312yes—
58C23×Dic3—34no—
59C23×Dic3—62no—
60C2×C3×M16—34no—
61C2×C4×Dic3—34no—
62C2×C4×Dic3—34no—
63C2×C4×Dic3—34no—
64C2×C4×Dic3—34no—
65C2×C4×Dic3—34no—
66C2×C4×Dic3—32no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—62no—
69C2×C4×Dic3—62no—
70C2×C4×Dic3—62no—
71C2×C4×Dic3—61no—
72C2×C4×Dic3—61no—
73C2×C4×Dic3—62no—
74C2×C4×Dic3—62no—
75C2×#208C2×D314yes—
76C3×C22⋊C8—38no—
77#830C2×D318yes—
78#815—38no—
79Dic3⋊C8—316no—
80C8×Dic3—38no—
81C23×C32—22no—
82C23×C32—24no—
83C23×C32C22×C411yescharacteristic
84C23×C32C22×C412yes—
85C2×C32×C4—22no—
86C2×C32×C4—24no—
87C2×C32×C4—24no—
88C2×C32×C4C22×C412yes—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4#4114yes—
91C2×C32×C4C2411yescharacteristic
92C2×C3⋊Dic3—24no—
93C2×C3⋊Dic3—24no—
94C2×C3⋊Dic3—24no—
95C2×C3⋊Dic3—24no—
96C2×C3⋊Dic3—24no—
97C2×C3⋊Dic3M1618yescomplemented
98C2×C3⋊Dic3C22×C412yes—
99C2×C3⋊Dic3C22×C412yes—
100C2×C3⋊Dic3C22×C412yes—
101C2×C3⋊Dic3C22×C412yes—
102C3×C3⋊C8—28no—
103C22×C42—91no—
104#432—94no—
105#431—94no—
106#423—92no—
107#407—32no—
108C4×M16—92no—
109C24×C3—21no—
110C24×C3C4×D312yes—
111C22×C3×C4—28no—
112C22×C3×C4—28no—
113C22×C3×C4—21no—
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—21no—
117C22×C3×C4C4×D312yes—
118C22×C3×C4C4×D314yes—
119C22×C3×C4C22×D314yes—
120C22×C3×C4C22×D312yes—
121C22×Dic3—34no—
122C22×Dic3—34no—
123C22×Dic3—34no—
124C22×Dic3—34no—
125C22×Dic3—34no—
126C22×Dic3—34no—
127C22×Dic3—62no—
128C22×Dic3—62no—
129C22×Dic3—62no—
130C22×Dic3—62no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C22×Dic3—616no—
134C22×Dic3—616no—
135C3×M16—68no—
136C2×C3×C8—38no—
137C4×Dic3—34no—
138C4×Dic3—32no—
139C4×Dic3—34no—
140C4×Dic3—34no—
141C4×Dic3—34no—
142C4×Dic3—34no—
143C4×Dic3—32no—
144C4×Dic3—32no—
145C4×Dic3—34no—
146C4×Dic3—32no—
147C4×Dic3—62no—
148C4×Dic3—61no—
149C4×Dic3—62no—
150C4×Dic3—62no—
151C4×Dic3—62no—
152C4×Dic3—62no—
153C4×Dic3—61no—
154C4×Dic3—61no—
155C4×Dic3—61no—
156C4×Dic3—62no—
157#208—28no—
158C2×C3⋊C8C22×D318yes—
159C22×C32—28no—
160C22×C32—22no—
161C22×C32—22no—
162C22×C32—22no—
163C22×C32#11712yes—
164C22×C32C2×M1614yes—
165C22×C32C23×C411yescharacteristic
166C32×C4—22no—
167C32×C4#11712yes—
168C32×C4C2×#4112yes—
169C3⋊Dic3—22no—
170C3⋊Dic3—22no—
171C3⋊Dic3C2×M1614yes—
172C3⋊Dic3C2×M1614yes—
173C23×C4—92no—
174C23×C4D3211yescharacteristic
175C2×M16—34no—
176C2×C42—92no—
177C2×C42—92no—
178C2×C42—92no—
179C2×C42—91no—
180C2×C42—91no—
181C2×C42—92no—
182C2×C42—92no—
183C4⋊C8—98no—
184C22⋊C8—38no—
185#97—94no—
186C4×C8—94no—
187C23×C3—28no—
188C23×C3—24no—
189C23×C3—24no—
190C23×C3—28no—
191C23×C3—22no—
192C23×C3—21no—
193C23×C3C2×C4×D312yes—
194C23×C3C2×C4×D314yes—
195C2×C3×C4—24no—
196C2×C3×C4—28no—
197C2×C3×C4—28no—
198C2×C3×C4—24no—
199C2×C3×C4—28no—
200C2×C3×C4—28no—
201C2×C3×C4—21no—
202C2×C3×C4—24no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4C2×C4×D314yes—
206C2×C3×C4C2×C4×D312yes—
207C2×C3×C4#23718yes—
208C2×C3×C4C23×D312yes—
209C2×Dic3—316no—
210C2×Dic3—34no—
211C2×Dic3—34no—
212C2×Dic3—34no—
213C2×Dic3—34no—
214C2×Dic3—68no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—68no—
220C2×Dic3—68no—
221C2×Dic3—68no—
222C2×Dic3—68no—
223C2×Dic3—68no—
224C2×Dic3—68no—
225C2×Dic3—68no—
226C2×Dic3—68no—
227C2×Dic3—68no—
228C2×Dic3—68no—
229C3×C8—68no—
230C3⋊C8—28no—
231C2×C32—22no—
232C2×C32—24no—
233C2×C32C2×#11711yescharacteristic
234C2×C32C22×M1612yes—
235C24#62411yescharacteristic
236C22×C4—24no—
237C22×C4—92no—
238C22×C4—92no—
239C22×C4—92no—
240C22×C4—92no—
241C22×C4—92no—
242C22×C4—92no—
243C22×C4—188no—
244C22×C4#62411yescharacteristic
245C22×C4#62412yes—
246C22×C4C2×D3212yes—
247C22×C4C2×D3211yescharacteristic
248M16—68no—
249C2×C8—38no—
250C42—91no—
251C42—91no—
252C42—92no—
253C42—92no—
254C42—91no—
255C42—92no—
256C42—92no—
257C42—92no—
258C42—92no—
259C42—91no—
260C22×C3—24no—
261C22×C3—24no—
262C22×C3—24no—
263C22×C3—216no—
264C22×C3—216no—
265C22×C3—24no—
266C22×C3—24no—
267C22×C3—24no—
268C22×C3—21no—
269C22×C3—24no—
270C22×C3—22no—
271C22×C3#87714yes—
272C22×C3D3×M1618yes—
273C22×C3C22×C4×D312yes—
274C3×C4—24no—
275C3×C4—24no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4#87714yes—
279C3×C4C2×#23714yes—
280Dic3—38no—
281Dic3—38no—
282Dic3—64no—
283Dic3—64no—
284Dic3—64no—
285Dic3—64no—
286Dic3—64no—
287Dic3—64no—
288C32#292011yescharacteristic, complemented, Sylow
289C23—24no—
290C23—22no—
291C23C2×#62412yes—
292C23C2×#62411yescharacteristic
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—92no—
297C2×C4—92no—
298C2×C4—98no—
299C2×C4—92no—
300C2×C4—92no—
301C2×C4—184no—
302C2×C4—184no—
303C2×C4—184no—
304C2×C4—184no—
305C2×C4—184no—
306C2×C4#380514yes—
307C2×C4C2×#62412yes—
308C2×C4C2×#62411yescharacteristic
309C2×C4C22×D3211yescharacteristic
310C8—68no—
311C2×C3—28no—
312C2×C3—24no—
313C2×C3—24no—
314C2×C3—28no—
315C2×C3—21no—
316C2×C3—22no—
317C2×C3C2×#87712yes—
318C2×C3C2×D3×M1614yes—
319C22—28no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22#6381814yes—
324C22#6395712yes—
325C22C22×#62411yescharacteristic
326C4—22no—
327C4—94no—
328C4—94no—
329C4—182no—
330C4—182no—
331C4#6395712yes—
332C4C2×#380512yes—
333C3—21no—
334C3#7861912yescomplemented
335C2—24no—
336C2—22no—
337C2C2×#6381812yes—
338C2C2×#6395711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC23×C32×C4C22
prime radicalC24×C32C2×C4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32#2920
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10591120C2semidirect
4. #10591066C2semidirect
5. #10591061C2semidirect
6. #10591060C2semidirect
19. #63572C22semidirect
20. #63555C22semidirect
21. #63553C22semidirect
97. C2×C3⋊Dic3M16semidirect
288. C32#2920semidirect
334. C3#78619semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C3×#52072
#105911202
#105910662
#105910612
#105910602
#786193