Finite Group Databasebeta

← #11801153

Subgroups — #11801153

Order 1152.

1385 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic
2C3×#5212C212yesmaximal
3#10591705C212yesmaximal
4#10591697C212yesmaximal
5#10591274C212yesmaximal, complemented
6#10591252C212yesmaximal, complemented
7#10591230C212yesmaximal, complemented
8#10591229C212yesmaximal, complemented
9#73863—32nomaximal
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C418yescomplemented
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×#217C2214yes—
19C2×C3×C4⋊Dic3C2214yes—
20C2×Dic32C2214yes—
21C3×C3⋊#95C2214yes—
22#63579C2214yes—
23#63579C2214yes—
24#63579C2214yes—
25C22×C4×Dic3—32no—
26C22×C4×Dic3—61no—
27C3×#380—32no—
28#5212D312yes—
29#4977—34no—
30Dic3×C4⋊C4—34no—
31#4943—34no—
32Dic3×C22⋊C4—34no—
33#4651—34no—
34#4648—34no—
35C24×C32C2311yescharacteristic
36C22×C32×C4—24no—
37C22×C32×C4C2×C414yes—
38C22×C32×C4C2311yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3—24no—
41C22×C3⋊Dic3—24no—
42C22×C3⋊Dic3C2×C414yes—
43C22×C3⋊Dic3C2×C414yes—
44C22×C3⋊Dic3C2311yescharacteristic
45C22×C3⋊Dic3C2311yescharacteristic
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3⋊Dic3C2311yescharacteristic
48C22×C3×Dic3C2318yes—
49C4×C3⋊Dic3C2×C414yes—
50C4×C3⋊Dic3C2×C414yes—
51C4×C3⋊Dic3C2×C414yes—
52C4×C3⋊Dic3C2×C414yes—
53C3×#217—28no—
54C3×C4⋊Dic3—28no—
55Dic32—28no—
56#2283—91noSylow
57C23×C3×C4—21no—
58C23×C3×C4C2×D312yes—
59C23×Dic3—32no—
60C23×Dic3—32no—
61C23×Dic3—61no—
62C23×Dic3—61no—
63C2×C3×C4⋊C4—34no—
64C2×C3×C22⋊C4—34no—
65C2×#217C2×D314yes—
66C2×C4⋊Dic3C2×D314yes—
67C2×C4×Dic3—316no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—32no—
71C2×C4×Dic3—32no—
72C2×C4×Dic3—38no—
73C2×C4×Dic3—68no—
74C2×C4×Dic3—61no—
75C2×C4×Dic3—61no—
76C2×C4×Dic3—61no—
77C2×C4×Dic3—61no—
78C3×#95—34no—
79C3⋊#95—38no—
80C3⋊#95—38no—
81C3⋊#95—38no—
82C3⋊#95C2×D314yes—
83C23×C32—22no—
84C23×C32—22no—
85C23×C32C22×C412yes—
86C23×C32#4114yes—
87C23×C32C2411yescharacteristic
88C2×C32×C4—22no—
89C2×C32×C4—28no—
90C2×C32×C4C22×C412yes—
91C2×C32×C4C22×C412yes—
92C2×C32×C4#4114yes—
93C2×C3⋊Dic3—28no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—28no—
98C2×C3⋊Dic3C22×C412yes—
99C2×C3⋊Dic3C22×C412yes—
100C2×C3⋊Dic3C22×C412yes—
101C2×C3⋊Dic3C22×C412yes—
102C2×C3⋊Dic3#4114yes—
103C2×C3×Dic3—28no—
104C2×C3×Dic3—28no—
105C2×C3×Dic3—28no—
106C22×C42—91no—
107#383—92no—
108#382—92no—
109#381—92no—
110#380—32no—
111C4×C4⋊C4—92no—
112C4×C22⋊C4—92no—
113#376—92no—
114C24×C3—21no—
115C24×C3C22×D312yes—
116C22×C3×C4—28no—
117C22×C3×C4—28no—
118C22×C3×C4—24no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—38no—
122C22×C3×C4C4×D318yes—
123C22×C3×C4C22×D312yes—
124C22×C3×C4C22×D312yes—
125C22×Dic3—32no—
126C22×Dic3—38no—
127C22×Dic3—38no—
128C22×Dic3—32no—
129C22×Dic3—32no—
130C22×Dic3—32no—
131C22×Dic3—64no—
132C22×Dic3—64no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137C22×Dic3—68no—
138C22×Dic3—68no—
139C22×Dic3—68no—
140C22×Dic3—64no—
141C22×Dic3—64no—
142C22×Dic3C22×D318yes—
143C3×C4⋊C4—68no—
144C3×C22⋊C4—68no—
145#217—28no—
146C4⋊Dic3—28no—
147C4×Dic3—38no—
148C4×Dic3—38no—
149C4×Dic3—38no—
150C4×Dic3—38no—
151C4×Dic3—64no—
152C4×Dic3—64no—
153C4×Dic3—64no—
154C4×Dic3—64no—
155C4×Dic3—616no—
156C22×C32—22no—
157C22×C32—22no—
158C22×C32—28no—
159C22×C32#11714yes—
160C22×C32C23×C411yescharacteristic
161C22×C32C2×#4112yes—
162C22×C32C2×#4112yes—
163C22×C32C2×#4112yes—
164C32×C4—22no—
165C32×C4#11714yes—
166C3⋊Dic3—22no—
167C3⋊Dic3—22no—
168C3⋊Dic3—22no—
169C3⋊Dic3#11714yes—
170C3×Dic3—48no—
171C23×C4—91no—
172C23×C4—91no—
173C23×C4D3211yescharacteristic
174C2×C4⋊C4—34no—
175C2×C22⋊C4—34no—
176C2×C42—98no—
177C2×C42—91no—
178C2×C42—91no—
179C2×C42—91no—
180C2×C42—91no—
181C2×C42—94no—
182#95—34no—
183#95—94no—
184#95—94no—
185#95—94no—
186C23×C3—24no—
187C23×C3—24no—
188C23×C3—24no—
189C23×C3—24no—
190C23×C3—21no—
191C23×C3—24no—
192C23×C3—22no—
193C23×C3C2×C4×D314yes—
194C23×C3#23714yes—
195C23×C3#23914yes—
196C23×C3C23×D312yes—
197C2×C3×C4—24no—
198C2×C3×C4—216no—
199C2×C3×C4—24no—
200C2×C3×C4—216no—
201C2×C3×C4—24no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—68no—
205C2×C3×C4—68no—
206C2×C3×C4—68no—
207C2×C3×C4C2×C4×D314yes—
208C2×C3×C4C2×C4×D314yes—
209C2×C3×C4#23718yes—
210C2×Dic3—28no—
211C2×Dic3—28no—
212C2×Dic3—28no—
213C2×Dic3—34no—
214C2×Dic3—38no—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—64no—
223C2×Dic3—616no—
224C2×Dic3—616no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3—616no—
229C2×Dic3—616no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—64no—
235C2×C32—24no—
236C2×C32C2×#11711yescharacteristic
237C2×C32C2×#11711yescharacteristic
238C2×C32C2×#11711yescharacteristic
239C2×C32#52914yes—
240C24C2×D3211yescharacteristic
241C22×C4—24no—
242C22×C4—38no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—94no—
248C22×C4—94no—
249C22×C4—184no—
250C22×C4—184no—
251C22×C4#62414yes—
252C22×C4C2×D3211yescharacteristic
253C22×C4C2×D3211yescharacteristic
254C4⋊C4—68no—
255C22⋊C4—68no—
256C42—94no—
257C42—94no—
258C42—94no—
259C42—94no—
260C42—188no—
261C22×C3—24no—
262C22×C3—24no—
263C22×C3—216no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—28no—
267C22×C3—28no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3—24no—
273C22×C3#89218yes—
274C22×C3C22×C4×D312yes—
275C22×C3C2×#23712yes—
276C22×C3C2×#23714yes—
277C22×C3C2×#23912yes—
278C22×C3D3×#4114yes—
279C3×C4—24no—
280C3×C4—24no—
281C3×C4—24no—
282C3×C4—128no—
283C3×C4#87718yes—
284Dic3—38no—
285Dic3—48no—
286Dic3—64no—
287Dic3—64no—
288Dic3—64no—
289Dic3—64no—
290Dic3—64no—
291Dic3—64no—
292Dic3—64no—
293C32#228311yescharacteristic, complemented, Sylow
294C23—22no—
295C23—22no—
296C23#379614yes—
297C23C2×#62412yes—
298C23C22×D3211yescharacteristic
299C2×C4—22no—
300C2×C4—28no—
301C2×C4—68no—
302C2×C4—68no—
303C2×C4—68no—
304C2×C4—94no—
305C2×C4—92no—
306C2×C4—92no—
307C2×C4—92no—
308C2×C4—92no—
309C2×C4—188no—
310C2×C4—182no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4—188no—
314C2×C4#380514yes—
315C2×C4C2×#62412yes—
316C2×C4C2×#62412yes—
317C2×C3—28no—
318C2×C3—28no—
319C2×C3—21no—
320C2×C3—24no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3C2×#87712yes—
324C2×C3C2×#89212yes—
325C2×C3D3×#11712yes—
326C2×C3#560014yes—
327C2×C3#562414yes—
328C22—28no—
329C22—22no—
330C22—22no—
331C22#6384914yes—
332C22C2×#379612yes—
333C22#6430612yes—
334C22C2×#380512yes—
335C22C22×#62411yescharacteristic
336C4—22no—
337C4—94no—
338C4—128no—
339C4—182no—
340C4—182no—
341C4—182no—
342C4#6395714yes—
343C3—21no—
344C3#7386312yescomplemented
345C2—24no—
346C2C2×#6384911yescharacteristic
347C2#1059496514yes—
348C2#1059496911yescharacteristic
349C2C2×#6395711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2283
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
5. #10591274C2semidirect
6. #10591252C2semidirect
7. #10591230C2semidirect
8. #10591229C2semidirect
13. C2×C4×C3⋊Dic3C4semidirect
293. C32#2283semidirect
344. C3#73863semidirect

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×#52122
#105917052
#105916972
#105912742
#105912522
#105912302
#105912292
#738633