Finite Group Databasebeta

← #11801838

Subgroups — #11801838

Order 1152.

1477 conjugacy classes of subgroups.

The subgroup lattice has 383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic
2C2×#63957C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4C3×#4950C212yesmaximal
5#10591693C212yesmaximal
6#10591274C212yesmaximal, complemented
7#10591264C214yesmaximal, complemented
8#10591257C212yesmaximal, complemented
9#74378—32nomaximal
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16#64086C418yescomplemented
17C2×C3×#217C2212yes—
18C2×C3×C4⋊Dic3C2214yes—
19C2×#3724C2214yes—
20C2×#3724C2212yes—
21#63957—24no—
22C2×Dic32—24no—
23C2×Dic32C2211yescharacteristic
24C2×Dic32C2212yes—
25C2×Dic32C2212yes—
26C2×Dic32C2211yescharacteristic
27C3×C3⋊#95C2214yes—
28#63579C2214yes—
29C22×C4×Dic3—32no—
30C2×#877—32no—
31C2×#877—32no—
32C2×#877—61no—
33C3×#385—32no—
34#5210—32no—
35#4976—34no—
36Dic3×C4⋊C4—34no—
37#4950D312yes—
38#4946—32no—
39#4649—34no—
40#4647—34no—
41C24×C32C2311yescharacteristic
42C22×C32×C4C2312yes—
43C22×C3⋊Dic3C2×C414yes—
44C22×C3⋊Dic3D414yes—
45C22×C3⋊Dic3Q814yes—
46C22×C3⋊Dic3C2312yes—
47C22×C3⋊Dic3C2311yescharacteristic
48C22×C3⋊Dic3C2311yescharacteristic
49C22×C3×Dic3—24no—
50C22×C3×Dic3—28no—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2314yes—
54C32×C22⋊C4C2×C414yes—
55#3757C2×C414yes—
56#3750C2×C418yescomplemented
57C4×C3⋊Dic3C2×C418yescomplemented
58C3×#217—24no—
59C3×C4⋊Dic3—28no—
60#3724—24no—
61#3724—28no—
62Dic32—24no—
63Dic32—24no—
64Dic32—22no—
65Dic32—22no—
66#2296—91noSylow
67C23×C3×C4—32no—
68C23×Dic3—32no—
69C23×Dic3—61no—
70C23×Dic3C2×D312yes—
71C2×C3×C4⋊C4—34no—
72C2×C3×C22⋊C4—21no—
73C2×C3×C22⋊C4—32no—
74C2×C3×C22⋊C4C2×D312yes—
75C2×#217—32no—
76C2×#217—61no—
77C2×#217C2×D312yes—
78C2×C4⋊Dic3C2×D314yes—
79C2×Dic3⋊C4—34no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—34no—
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4—32no—
84C2×Dic3⋊C4—62no—
85C2×C4×Dic3—34no—
86C2×C4×Dic3—34no—
87C2×C4×Dic3—32no—
88C2×C4×Dic3—34no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—62no—
91C2×C4×Dic3—68no—
92#877—316no—
93#877—68no—
94#877—68no—
95C3×#95—34no—
96C3⋊#95—34no—
97C3⋊#95—34no—
98C3⋊#95C2×D314yes—
99C23×C32—24no—
100C23×C32C22×C412yes—
101C23×C32C2×D412yes—
102C23×C32C2×Q812yes—
103C23×C32C2411yescharacteristic
104C2×C32×C4—24no—
105C2×C32×C4C22×C414yes—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3C4⋊C4116yescomplemented
108C2×C3⋊Dic3C22×C414yes—
109C2×C3⋊Dic3C22×C412yes—
110C2×C3⋊Dic3C22×C412yes—
111C2×C3⋊Dic3C2×D412yes—
112C2×C3⋊Dic3C2×D412yes—
113C2×C3⋊Dic3C2×Q812yes—
114C2×C3⋊Dic3C2×Q812yes—
115C2×C3×Dic3—216no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3#4118yes—
123C2×#117—91no—
124C2×#117—91no—
125C22×C42—91no—
126#389—94no—
127#385—32no—
128#385—92no—
129C4×C4⋊C4—92no—
130C4×C4⋊C4—92no—
131C24×C3—21no—
132C24×C3C22×D312yes—
133C22×C3×C4—22no—
134C22×C3×C4—34no—
135C22×C3×C4—32no—
136C22×C3×C4—32no—
137C22×C3×C4—68no—
138C22×C3×C4—64no—
139C22×C3×C4C22×D314yes—
140C22×Dic3—24no—
141C22×Dic3—28no—
142C22×Dic3—38no—
143C22×Dic3—38no—
144C22×Dic3—38no—
145C22×Dic3—32no—
146C22×Dic3—32no—
147C22×Dic3—34no—
148C22×Dic3—64no—
149C22×Dic3—61no—
150C22×Dic3—61no—
151C22×Dic3—64no—
152C22×Dic3—64no—
153C22×Dic3—62no—
154C22×Dic3C22×D312yes—
155C22×Dic3C22×D312yes—
156C22×Dic3C22×D314yes—
157C3×C4⋊C4—68no—
158C3×C22⋊C4—24no—
159C3×C22⋊C4—64no—
160C3×C22⋊C4C4×D318yes—
161#217—24no—
162#217—38no—
163#217—64no—
164C4⋊Dic3—28no—
165Dic3⋊C4—316no—
166Dic3⋊C4—68no—
167Dic3⋊C4—64no—
168Dic3⋊C4—64no—
169Dic3⋊C4—68no—
170Dic3⋊C4—68no—
171C4×Dic3—316no—
172C4×Dic3—68no—
173C4×Dic3—64no—
174C4×Dic3—64no—
175C4×Dic3—68no—
176C4×Dic3—68no—
177C22×C32—24no—
178C22×C32—24no—
179C22×C32—24no—
180C22×C32C2×C4⋊C414yes—
181C22×C32C23×C411yescharacteristic
182C22×C32C22×D411yescharacteristic
183C22×C32C22×Q811yescharacteristic
184C22×C32C2×#4114yes—
185C32×C4—24no—
186C3⋊Dic3—24no—
187C3⋊Dic3C2×C4⋊C414yes—
188C3⋊Dic3C2×C4⋊C414yes—
189C3×Dic3—28no—
190C3×Dic3—42no—
191C3×Dic3—42no—
192C23×C4—32no—
193C23×C4—91no—
194#117—98no—
195#117—184no—
196C2×C4⋊C4—34no—
197C2×C4⋊C4—92no—
198C2×C4⋊C4—92no—
199C2×C4⋊C4—94no—
200C2×C22⋊C4—32no—
201C2×C22⋊C4—91no—
202C2×C22⋊C4D3211yescharacteristic
203C2×C42—92no—
204C2×C42—91no—
205C2×C42—91no—
206C2×C42—92no—
207C2×C42—92no—
208C2×C42—184no—
209#95—34no—
210#95—94no—
211C23×C3—24no—
212C23×C3—24no—
213C23×C3—21no—
214C23×C3—22no—
215C23×C3—22no—
216C23×C3—22no—
217C23×C3—44no—
218C23×C3C2×C4×D314yes—
219C23×C3D3×D414yes—
220C23×C3D3×Q814yes—
221C23×C3C23×D312yes—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—38no—
226C2×C3×C4—44no—
227C2×C3×C4—616no—
228C2×C3×C4—64no—
229C2×C3×C4—64no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—64no—
233C2×C3×C4—64no—
234C2×C3×C4C2×C4×D318yes—
235C2×Dic3—216no—
236C2×Dic3—24no—
237C2×Dic3—24no—
238C2×Dic3—22no—
239C2×Dic3—22no—
240C2×Dic3—24no—
241C2×Dic3—24no—
242C2×Dic3—332no—
243C2×Dic3—34no—
244C2×Dic3—34no—
245C2×Dic3—34no—
246C2×Dic3—34no—
247C2×Dic3—34no—
248C2×Dic3—34no—
249C2×Dic3—38no—
250C2×Dic3—616no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—124no—
261C2×Dic3#23718yes—
262C2×C32—24no—
263C2×C32C22×C4⋊C411yescharacteristic
264C2×C32C4×#4112yes—
265C2×C32#52512yes—
266C2×C32#53312yes—
267C24C2×D3211yescharacteristic
268C22×C4—34no—
269C22×C4—32no—
270C22×C4—32no—
271C22×C4—68no—
272C22×C4—64no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—94no—
276C22×C4—94no—
277C22×C4—94no—
278C22×C4—92no—
279C22×C4C2×D3212yes—
280C4⋊C4—68no—
281C4⋊C4—98no—
282C4⋊C4—188no—
283C4⋊C4—184no—
284C22⋊C4—64no—
285C22⋊C4—94no—
286C22⋊C4#62414yes—
287C42—98no—
288C42—184no—
289C42—184no—
290C42—182no—
291C42—182no—
292C22×C3—24no—
293C22×C3—28no—
294C22×C3—24no—
295C22×C3—28no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—24no—
299C22×C3—21no—
300C22×C3—24no—
301C22×C3—44no—
302C22×C3—44no—
303C22×C3—44no—
304C22×C3D3×C4⋊C418yes—
305C22×C3C22×C4×D312yes—
306C22×C3C2×D3×D412yes—
307C22×C3C2×#23714yes—
308C22×C3C2×D3×Q812yes—
309C22×C3D3×#4114yes—
310C3×C4—28no—
311C3×C4—44no—
312C3×C4—68no—
313C3×C4—122no—
314C3×C4—122no—
315Dic3—28no—
316Dic3—38no—
317Dic3—38no—
318Dic3—42no—
319Dic3—42no—
320Dic3—64no—
321Dic3—64no—
322Dic3—68no—
323Dic3—124no—
324C32#229611yescharacteristic, complemented, Sylow
325C23—24no—
326C23#379712yes—
327C23#380212yes—
328C23C2×#62412yes—
329C23C22×D3211yescharacteristic
330C2×C4—24no—
331C2×C4—38no—
332C2×C4—616no—
333C2×C4—64no—
334C2×C4—64no—
335C2×C4—62no—
336C2×C4—62no—
337C2×C4—64no—
338C2×C4—64no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—92no—
342C2×C4—92no—
343C2×C4—92no—
344C2×C4—92no—
345C2×C4—916no—
346C2×C4—94no—
347C2×C4—184no—
348C2×C4C2×#62414yes—
349C2×C3—28no—
350C2×C3—22no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—22no—
354C2×C3—44no—
355C2×C3C2×D3×C4⋊C412yes—
356C2×C3C4×#23714yes—
357C2×C3#558612yes—
358C2×C3#562214yes—
359C2×C3#565612yes—
360C22—24no—
361C22—24no—
362C22—24no—
363C22#6390014yes—
364C22C2×#379711yescharacteristic
365C22C2×#380211yescharacteristic
366C22D3×#23714yes—
367C22C22×#62411yescharacteristic
368C4—24no—
369C4—68no—
370C4—94no—
371C4—94no—
372C4—122no—
373C4—122no—
374C4—184no—
375C3—21no—
376C3#7437812yescomplemented
377C2—24no—
378C2#1059403012yes—
379C2#1059408212yes—
380C2C2×#6390011yescharacteristic
381C2#1059519012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10591274C2semidirect
7. #10591264C2semidirect
8. #10591257C2semidirect
16. #64086C4semidirect
56. #3750C2×C4semidirect
57. C4×C3⋊Dic3C2×C4semidirect
107. C2×C3⋊Dic3C4⋊C4semidirect
324. C32#2296semidirect
376. C3#74378semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C2×#639572
C22×Dic322
C3×#49502
#105916932
#105912742
#105912642
#105912572
#743783