Finite Group Databasebeta

← #11801113

Subgroups — #11801113

Order 1152.

1413 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#624C211yesmaximal, characteristic
2C3⋊D3×#95C211yesmaximal, characteristic
3C3×#4651C212yesmaximal, complemented
4#10591370C211yesmaximal, characteristic
5#10591370C212yesmaximal
6#10591370C212yesmaximal
7#10591248C214yesmaximal, complemented
8#10591223C212yesmaximal, complemented
9D3×#383—32nomaximal
10C22×C4×C3⋊D3C2212yes—
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#624C2212yes—
13C22×#624C2211yescharacteristic
14C22×#624C2211yescharacteristic
15C2×C3×C4×Dic3C2212yes—
16C2×Dic32C2212yes—
17C4×#624C418yescomplemented
18C32×#95C2211yescharacteristic
19#63658C2212yes—
20#63658C2211yescharacteristic
21C3×C3⋊#95C2214yes—
22C3×C3⋊#95C2214yes—
23C3×C3⋊#95C2212yes—
24#63579C2212yes—
25#63579C2214yes—
26#63579C2214yes—
27C2×C42×D3—32no—
28C3×#383—32no—
29#4937—32no—
30D3×#95—32no—
31D3×#95—32no—
32D3×#95—34no—
33D3×#95—34no—
34D3×#95—61no—
35#4651—32no—
36#4651—34no—
37#4651—34no—
38#4651D312yescomplemented
39C23×C3⋊D3C2311yescharacteristic
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C2×C4×C3⋊D3—24no—
45C2×C4×C3⋊D3—24no—
46C2×C4×C3⋊D3—24no—
47C2×C4×C3⋊D3—24no—
48C2×C4×C3⋊D3C2×C414yes—
49C22×C3×Dic3C2314yes—
50C22×C3×Dic3C2312yes—
51C22×C3×Dic3C2312yes—
52C2×#624—22no—
53C2×#624—24no—
54C2×#624—22no—
55C2×#624—24no—
56C2×#624—24no—
57C2×#624—24no—
58C2×#624C2×C414yes—
59C2×#624C2×C414yes—
60C3×C4×Dic3C2×C418yescomplemented
61Dic32C2×C418yescomplemented
62C2×#383—91noSylow
63C22×C4×D3—32no—
64C22×C4×D3—32no—
65C22×C4×D3—32no—
66C22×C4×D3—34no—
67C22×C4×D3—34no—
68C22×C4×D3—61no—
69C22×C4×D3—62no—
70C2×C3×C42—32no—
71C2×C4×Dic3—32no—
72C2×C4×Dic3—32no—
73C2×C4×Dic3C2×D312yes—
74C42×D3—316no—
75C3×#95—21no—
76C3×#95—34no—
77C3×#95—34no—
78C3×#95—32no—
79C3×#95C2×D312yes—
80C3⋊#95—34no—
81C3⋊#95—32no—
82C3⋊#95—34no—
83C3⋊#95—34no—
84C3⋊#95—34no—
85C3⋊#95—34no—
86C3⋊#95—34no—
87C3⋊#95—62no—
88C3⋊#95—61no—
89C3⋊#95C2×D314yes—
90C3⋊#95C2×D314yes—
91C3⋊#95C2×D312yes—
92C23×C32C2411yescharacteristic
93C22×C3⋊D3C22×C412yes—
94C22×C3⋊D3#4112yes—
95C22×C3⋊D3#4114yes—
96C22×C3⋊D3#4112yes—
97C22×C3⋊D3#4114yes—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4C22×C412yes—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3C22×C412yes—
108C4×C3⋊D3—28no—
109C4×C3⋊D3—48no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3C22×C414yes—
117C2×C3×Dic3C22×C414yes—
118#624—28no—
119#624—28no—
120#624—48no—
121C22×C42—91no—
122#383—32no—
123#383—94no—
124#383—92no—
125C2×#95—92no—
126C2×#95—92no—
127C2×#95—91no—
128C2×#95—91no—
129C23×D3—32no—
130C23×D3—61no—
131C22×C3×C4—22no—
132C22×C3×C4—21no—
133C22×C3×C4—32no—
134C22×C3×C4—32no—
135C22×C3×C4—34no—
136C22×C3×C4C22×D314yes—
137C22×C3×C4C22×D312yes—
138C22×Dic3—32no—
139C22×Dic3—34no—
140C22×Dic3—61no—
141C22×Dic3—62no—
142C22×Dic3C22×D314yes—
143C22×Dic3C22×D312yes—
144C22×Dic3C22×D312yes—
145C2×C4×D3—38no—
146C2×C4×D3—38no—
147C2×C4×D3—38no—
148C2×C4×D3—64no—
149C2×C4×D3—68no—
150C2×C4×D3—64no—
151C2×C4×D3—64no—
152C2×C4×D3—68no—
153C2×C4×D3—68no—
154C2×C4×D3—68no—
155C2×C4×D3—68no—
156C2×C4×D3—68no—
157C2×C4×D3—68no—
158C2×C4×D3—68no—
159C2×C4×D3—68no—
160C2×C4×D3—124no—
161C2×C4×D3—124no—
162C2×C4×D3—124no—
163C3×C42—38no—
164C4×Dic3—38no—
165C4×Dic3—38no—
166C4×Dic3C4×D318yescomplemented
167C22×C32C23×C411yescharacteristic
168C22×C32C2×#4111yescharacteristic
169C22×C32C2×#4112yes—
170C22×C32C2×#4111yescharacteristic
171C22×C32C2×#4112yes—
172C2×C3⋊D3#11714yes—
173C2×C3⋊D3#11714yes—
174C2×C3⋊D3#11714yes—
175C2×C3⋊D3#12618yes—
176C2×C3⋊D3#12618yes—
177C32×C4—22no—
178C32×C4—42no—
179C3⋊Dic3—22no—
180C3⋊Dic3—42no—
181C3×Dic3—24no—
182C3×Dic3—24no—
183C3×Dic3—44no—
184C23×C4—91no—
185C23×C4—91no—
186C23×C4—92no—
187C23×C4—91no—
188C23×C4—92no—
189C2×C42—32no—
190C2×C42—98no—
191C2×C42—92no—
192#95—34no—
193#95—34no—
194#95—32no—
195#95—94no—
196#95—94no—
197#95—92no—
198#95—92no—
199#95—91no—
200#95D3211yescharacteristic
201C23×C3—21no—
202C23×C3C23×D312yes—
203C22×D3—34no—
204C22×D3—38no—
205C22×D3—34no—
206C22×D3—38no—
207C22×D3—34no—
208C22×D3—62no—
209C22×D3—64no—
210C22×D3—64no—
211C22×D3—62no—
212C22×D3—62no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—24no—
216C2×C3×C4—24no—
217C2×C3×C4—24no—
218C2×C3×C4—22no—
219C2×C3×C4—34no—
220C2×C3×C4—34no—
221C2×C3×C4—42no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4—64no—
225C2×C3×C4—62no—
226C2×C3×C4—62no—
227C2×C3×C4—64no—
228C2×C3×C4—64no—
229C2×C3×C4—64no—
230C2×C3×C4C2×C4×D314yes—
231C2×Dic3—24no—
232C2×Dic3—22no—
233C2×Dic3—22no—
234C2×Dic3—24no—
235C2×Dic3—24no—
236C2×Dic3—24no—
237C2×Dic3—34no—
238C2×Dic3—62no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—64no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246C2×Dic3—122no—
247C2×Dic3C2×C4×D314yes—
248C2×Dic3C2×C4×D314yes—
249C4×D3—616no—
250C4×D3—616no—
251C4×D3—616no—
252C4×D3—128no—
253C4×D3—1216no—
254C4×D3—1216no—
255C4×D3—1216no—
256C2×C32C2×#11711yescharacteristic
257C2×C32C2×#11711yescharacteristic
258C2×C32C2×#11711yescharacteristic
259C2×C32C2×#12612yes—
260C2×C32C2×#12612yes—
261C3⋊D3#38318yescomplemented
262C24—91no—
263C22×C4—32no—
264C22×C4—32no—
265C22×C4—34no—
266C22×C4—94no—
267C22×C4—94no—
268C22×C4—91no—
269C22×C4—94no—
270C22×C4—92no—
271C22×C4—184no—
272C22×C4—184no—
273C22×C4—184no—
274C22×C4—184no—
275C22×C4—184no—
276C22×C4—182no—
277C22×C4—182no—
278C22×C4—184no—
279C22×C4—184no—
280C22×C4—184no—
281C22×C4C2×D3212yes—
282C22×C4C2×D3211yescharacteristic
283C42—38no—
284C42—98no—
285C22×C3—21no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3C22×C4×D312yes—
291C22×C3D3×#4114yes—
292C22×C3D3×#4114yes—
293C22×C3D3×#4112yes—
294C22×C3D3×#4112yes—
295C2×D3—316no—
296C2×D3—316no—
297C2×D3—38no—
298C2×D3—38no—
299C2×D3—38no—
300C2×D3—64no—
301C2×D3—68no—
302C2×D3—64no—
303C2×D3—64no—
304C2×D3—68no—
305C3×C4—24no—
306C3×C4—42no—
307C3×C4—44no—
308C3×C4—44no—
309C3×C4—64no—
310C3×C4—64no—
311C3×C4—124no—
312Dic3—24no—
313Dic3—24no—
314Dic3—44no—
315Dic3—64no—
316Dic3—122no—
317Dic3—124no—
318Dic3—124no—
319C32C2×#38311yescharacteristic, complemented, Sylow
320C23—92no—
321C23—94no—
322C23—94no—
323C23—92no—
324C23—92no—
325C23C22×D3211yescharacteristic
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—34no—
331C2×C4—34no—
332C2×C4—64no—
333C2×C4—62no—
334C2×C4—62no—
335C2×C4—64no—
336C2×C4—64no—
337C2×C4—64no—
338C2×C4—92no—
339C2×C4—188no—
340C2×C4—188no—
341C2×C4—188no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—368no—
347C2×C4—368no—
348C2×C4C4×D3212yes—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—22no—
352C2×C3—22no—
353C2×C3—21no—
354C2×C3D3×#11712yes—
355C2×C3D3×#11712yes—
356C2×C3D3×#11712yes—
357C2×C3D3×#12614yes—
358C2×C3D3×#12614yes—
359D3—316no—
360D3—68no—
361C22—94no—
362C22—94no—
363C22—98no—
364C22—98no—
365C22—94no—
366C22C2×C4×D3211yescharacteristic
367C22#6430612yes—
368C22#6431212yes—
369C22#6431211yescharacteristic
370C22#6431911yescharacteristic
371C4—22no—
372C4—42no—
373C4—64no—
374C4—64no—
375C4—124no—
376C4—182no—
377C4—362no—
378C3—21no—
379C3D3×#38312yescomplemented
380C2—98no—
381C2#1059399211yescharacteristic
382C2#1059405211yescharacteristic
383C2#1059415412yes—
384C2#1059460211yescharacteristic
385C2#1059465612yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32C2×#383
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4651C2semidirect
7. #10591248C2semidirect
8. #10591223C2semidirect
17. C4×#624C4semidirect
38. #4651D3semidirect
60. C3×C4×Dic3C2×C4semidirect
61. Dic32C2×C4semidirect
166. C4×Dic3C4×D3semidirect
261. C3⋊D3#383semidirect
319. C32C2×#383semidirect
379. C3D3×#383semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6242
C3⋊D3×#952
C3×#46512
#105913702
#105912482
#105912232
D3×#3833