Finite Group Databasebeta

← #11785726

Subgroups — #11785726

Order 1152.

727 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2#10592906C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4#10589167C214yesmaximal, complemented
5#71562—31nomaximal
6#69973—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C23×C3×Dic3C412yes—
9C2×#3748C2212yes—
10C2×C3×C4⋊Dic3—21no—
11C2×C3×C4⋊Dic3—21no—
12C2×C3×C4⋊Dic3—21no—
13C2×C3×C4⋊Dic3—21no—
14C2×C3×C4⋊Dic3C412yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×#208C2212yes—
17#63657—21no—
18#63657—21no—
19C3×#830—21no—
20C3×#830—21no—
21C22×C3×C4⋊C4—31no—
22C22×C4⋊Dic3D311yescharacteristic
23C3×#407—31no—
24#5207—31no—
25#5207—31no—
26#5207—61no—
27#5207D311yescharacteristic
28#4554—34no—
29#4530—34no—
30C24×C32C2×C411yescharacteristic
31C22×C32×C4—24no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3×Dic3—22no—
39C22×C3×Dic3—22no—
40C22×C3×Dic3—44no—
41C22×C3×Dic3C2×C414yes—
42#3748—24no—
43C2×C3⋊(C3⋊C8)—22no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3—22no—
48C3×#208—24no—
49C2×C3×C3⋊C8—22no—
50#1821—91noSylow
51C23×C3×C4—21no—
52C23×C3×C4—32no—
53C23×C3×C4C2×D311yescharacteristic
54C23×C3×C4C2×D311yescharacteristic
55C23×Dic3Dic312yes—
56C2×C3×M16—32no—
57C2×C3×C4⋊C4—32no—
58C2×C3×C4⋊C4—32no—
59C2×C3×C4⋊C4—61no—
60C2×C3×C4⋊C4—61no—
61C2×C3×C4⋊C4—61no—
62C2×C3×C4⋊C4—61no—
63C2×C4⋊Dic3—21no—
64C2×C4⋊Dic3—21no—
65C2×C4⋊Dic3—21no—
66C2×C4⋊Dic3—21no—
67C2×C4⋊Dic3Dic312yes—
68C2×C4⋊Dic3C2×D312yes—
69C2×#208—32no—
70C2×#208—32no—
71C2×#208—62no—
72C2×#208C2×D312yes—
73C3×C22⋊C8—61no—
74C3×C22⋊C8—61no—
75#830—21no—
76#830—21no—
77#830—62no—
78#830—62no—
79#830—61no—
80#830—61no—
81#830—61no—
82#830—61no—
83C23×C32—22no—
84C23×C32—22no—
85C23×C32—22no—
86C23×C32C22⋊C411yescharacteristic
87C23×C32C22⋊C411yescharacteristic
88C23×C32C22×C411yescharacteristic
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4114yes—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—44no—
101C2×C3×Dic3—44no—
102C2×C3×Dic3—44no—
103C3⋊(C3⋊C8)—42no—
104C3×C3⋊C8—42no—
105C22×C4⋊C4—31no—
106#407—31no—
107#407—91no—
108#343—94no—
109C24×C3—21no—
110C24×C3C4×D311yescharacteristic
111C24×C3C2×Dic311yescharacteristic
112C22×C3×C4—24no—
113C22×C3×C4—24no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—34no—
121C22×C3×C4—44no—
122C22×C3×C4—62no—
123C22×C3×C4—62no—
124C22×C3×C4—124no—
125C22×C3×C4C4×D311yescharacteristic
126C22×C3×C4D1211yescharacteristic
127C22×C3×C4D1211yescharacteristic
128C22×C3×C4C2×Dic311yescharacteristic
129C22×C3×C4#6711yescharacteristic
130C22×C3×C4#6711yescharacteristic
131C22×C3×C4#6711yescharacteristic
132C22×C3×C4#6711yescharacteristic
133C22×C3×C4#6711yescharacteristic
134C22×C3×C4#6711yescharacteristic
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C22×D311yescharacteristic
137C22×Dic3—22no—
138C22×Dic3—22no—
139C22×Dic3—44no—
140C22×Dic3C2×Dic314yes—
141C3×M16—64no—
142C2×C3×C8—62no—
143C3×C4⋊C4—62no—
144C3×C4⋊C4—62no—
145C3×C4⋊C4—62no—
146C3×C4⋊C4—62no—
147C4⋊Dic3—22no—
148C4⋊Dic3—22no—
149C4⋊Dic3—22no—
150C4⋊Dic3—22no—
151#208—24no—
152#208—64no—
153#208—64no—
154#208—124no—
155C2×C3⋊C8—22no—
156C2×C3⋊C8—64no—
157C2×C3⋊C8—62no—
158C2×C3⋊C8—62no—
159C22×C32—28no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32—21no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32#10012yes—
167C22×C32#10112yes—
168C22×C32C2×C22⋊C411yescharacteristic
169C22×C32#11712yes—
170C32×C4—21no—
171C32×C4—21no—
172C32×C4#12312yes—
173C32×C4#12312yes—
174C3×Dic3—44no—
175C23×C4—32no—
176C23×C4D3211yescharacteristic
177C2×M16—32no—
178C2×M16—92no—
179C2×C4⋊C4—32no—
180C2×C4⋊C4—32no—
181C2×C4⋊C4—61no—
182C2×C4⋊C4—61no—
183C2×C4⋊C4—61no—
184C2×C4⋊C4—61no—
185C22⋊C8—61no—
186C22⋊C8—61no—
187C22⋊C8—181no—
188C22⋊C8—181no—
189C23×C3—22no—
190C23×C3—22no—
191C23×C3—22no—
192C23×C3—22no—
193C23×C3—22no—
194C23×C3—22no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—42no—
199C23×C3—42no—
200C23×C3—42no—
201C23×C3(C2×D3)⋊C411yescharacteristic
202C23×C3(C2×D3)⋊C411yescharacteristic
203C23×C3#21711yescharacteristic
204C23×C3#21711yescharacteristic
205C23×C3C2×C4×D311yescharacteristic
206C23×C3C22×Dic311yescharacteristic
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—24no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4—42no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—64no—
228C2×C3×C4—124no—
229C2×C3×C4—124no—
230C2×C3×C4—124no—
231C2×C3×C4(C2×D3)⋊C411yescharacteristic
232C2×C3×C4(C2×D3)⋊C411yescharacteristic
233C2×C3×C4#21711yescharacteristic
234C2×C3×C4#21711yescharacteristic
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4#23514yes—
237C2×C3×C4#23714yes—
238C2×C3×C4C2×#6711yescharacteristic
239C2×C3×C4C2×#6711yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×Dic3—24no—
242C2×Dic3—44no—
243C2×Dic3—44no—
244C2×Dic3—44no—
245C3×C8—122no—
246C3⋊C8—42no—
247C3⋊C8—124no—
248C3⋊C8—122no—
249C3⋊C8—122no—
250C2×C32—22no—
251C2×C32—22no—
252C2×C32—22no—
253C2×C32#38111yescharacteristic
254C2×C32C2×#10011yescharacteristic
255C2×C32C2×#10111yescharacteristic
256C24D3×Dic311yescharacteristic
257C22×C4—24no—
258C22×C4—34no—
259C22×C4—62no—
260C22×C4—62no—
261C22×C4—124no—
262C22×C4D3×Dic311yescharacteristic
263C22×C4#62511yescharacteristic
264C22×C4#62511yescharacteristic
265C22×C4#62611yescharacteristic
266C22×C4#62611yescharacteristic
267C22×C4C2×D3211yescharacteristic
268M16—64no—
269M16—184no—
270C2×C8—62no—
271C2×C8—182no—
272C4⋊C4—62no—
273C4⋊C4—62no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C22×C3—28no—
277C22×C3—28no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—22no—
293C22×C3—21no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—48no—
301C22×C3#82312yes—
302C22×C3#82412yes—
303C22×C3#83312yes—
304C22×C3#83612yes—
305C22×C3#87712yes—
306C22×C3#92612yes—
307C22×C3C2×(C2×D3)⋊C411yescharacteristic
308C22×C3C2×#21711yescharacteristic
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—124no—
318C3×C4#88612yes—
319C3×C4#92912yes—
320C3×C4#92912yes—
321C3×C4#93512yes—
322Dic3—44no—
323C32#182111yescharacteristic, complemented, Sylow
324C23—22no—
325C23—22no—
326C23—22no—
327C23(C2×D3)⋊Dic311yescharacteristic
328C23(C2×D3)⋊Dic311yescharacteristic
329C23C2×D3×Dic311yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—64no—
336C2×C4—124no—
337C2×C4—124no—
338C2×C4—124no—
339C2×C4(C2×D3)⋊Dic311yescharacteristic
340C2×C4(C2×D3)⋊Dic311yescharacteristic
341C2×C4#380414yes—
342C2×C4C2×#62511yescharacteristic
343C2×C4C2×#62611yescharacteristic
344C8—122no—
345C8—362no—
346C2×C3—22no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—22no—
351C2×C3—22no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—42no—
356C2×C3—42no—
357C2×C3—42no—
358C2×C3#494311yescharacteristic
359C2×C3C2×#82311yescharacteristic
360C2×C3C2×#82411yescharacteristic
361C2×C3#521111yescharacteristic
362C2×C3C2×#83311yescharacteristic
363C2×C3C2×#83611yescharacteristic
364C22—28no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22#6355812yes—
372C22#6356012yes—
373C22#6395512yes—
374C22C2×(C2×D3)⋊Dic311yescharacteristic
375C4—21no—
376C4—21no—
377C4—124no—
378C4#6396112yes—
379C4#6396612yes—
380C3—21no—
381C3#6997311yescharacteristic, complemented
382C3#7156211yescharacteristic, complemented
383C2—22no—
384C2—22no—
385C2—22no—
386C2C2×#6355811yescharacteristic
387C2C2×#6356011yescharacteristic
388C2#1059169611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1821
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10589167C2semidirect
323. C32#1821semidirect
381. C3#69973semidirect
382. C3#71562semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
#105929062
C3×#52072
#105891672
#715623
#699733