Finite Group Databasebeta

← #11901958

Subgroups — #11901958

Order 1152.

2157 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic
2C2×C3×#926C212yesmaximal
3#10595521C214yesmaximal
4#10595052C214yesmaximal, complemented
5#10595051C218yesmaximal, complemented
6#10595050C214yesmaximal, complemented
7#10595049C218yesmaximal, complemented
8#85725—32nomaximal
9C23×C32×C4C2211yescharacteristic
10C2×#3757C2212yes—
11#64135C2214yes—
12#64135C2214yes—
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×C4×C3⋊Dic3C2212yes—
15C2×C3×#217C2214yes—
16C3×#926C2214yes—
17C3×#926C2214yes—
18C3×#926C2214yes—
19C3×#926C2214yes—
20C2×C3×C4⋊Dic3C2214yes—
21C2×C3×C4×Dic3C2214yes—
22#63982C22116yes—
23#63964C22132yes—
24#63919C2218yescomplemented
25#63918C22116yescomplemented
26C4×#627C22116yescomplemented
27#63872C2218yescomplemented
28#63869C22116yescomplemented
29C2×C3×#117—32no—
30C2×#926—32no—
31C2×#926—61no—
32C2×#926D312yes—
33#5519—38no—
34#5519—38no—
35#5517—38no—
36#5517—38no—
37#5500—38no—
38#5483—38no—
39#5470—38no—
40C24×C32C2311yescharacteristic
41C22×C32×C4Q818yescomplemented
42C22×C32×C4C2312yes—
43C22×C32×C4C2312yes—
44C22×C32×C4C2311yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2314yes—
47C22×C3×Dic3C2318yes—
48C2×#627C23116yes—
49#3757C2318yes—
50C4⋊(C3⋊Dic3)C2318yes—
51C4×C3⋊Dic3C2314yes—
52C4×C3⋊Dic3C2314yes—
53C3×#217C2318yes—
54C3×#217C2318yes—
55C3×C4⋊Dic3C2318yes—
56C3×C4⋊Dic3C2318yes—
57C3×C4×Dic3C2318yes—
58C3×C4×Dic3C2318yes—
59#3724C23116yes—
60Dic3⋊Dic3C23132yes—
61#3458—91noSylow
62C23×C3×C4—21no—
63C23×C3×C4C2×D312yes—
64C3×#117—34no—
65C3×#117—34no—
66C3×#117—34no—
67C3×#117—34no—
68C2×C3×C4⋊C4—34no—
69C2×C3×C22⋊C4—34no—
70C2×C3×C42—34no—
71C2×#217—34no—
72C2×#217—62no—
73C2×#217C2×D314yes—
74#926—34no—
75#926—34no—
76#926—34no—
77#926—34no—
78#926—64no—
79#926—64no—
80#926C2×D314yes—
81#926C2×D314yes—
82#926C2×D314yes—
83#926C2×D314yes—
84C2×C4⋊Dic3—34no—
85C2×C4⋊Dic3—62no—
86C2×C4⋊Dic3C2×D314yes—
87#924—332no—
88C2×C4×Dic3—34no—
89C2×C4×Dic3—62no—
90C2×C4×Dic3C2×D314yes—
91#890—316no—
92#890—316no—
93#888—316no—
94#888—316no—
95#878—332no—
96#878—332no—
97#870—316no—
98#869—316no—
99C4×Dic6—332no—
100C23×C32—42no—
101C23×C32C2×Q814yes—
102C23×C32C2411yescharacteristic
103C23×C32C2412yes—
104C2×C32×C4C2×Q818yes—
105C2×C32×C4C2×Q818yes—
106C2×C32×C4C2×Q814yes—
107C2×C32×C4C2×Q814yes—
108C2×C32×C4C2411yescharacteristic
109C2×C32×C4C2412yes—
110C2×C32×C4C2411yescharacteristic
111C2×C3⋊Dic3—44no—
112C2×C3⋊Dic3C2418yes—
113C2×C3×Dic3—48no—
114C2×C3×Dic3C24116yes—
115#627—416no—
116#544—98no—
117#544—94no—
118#543—94no—
119#533—98no—
120#533—94no—
121C2×#117—32no—
122C2×#117—91no—
123C24×C3—21no—
124C24×C3C22×D312yes—
125C22×C3×C4—28no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—38no—
131C22×C3×C4Dic6116yescomplemented
132C22×C3×C4C22×D312yes—
133C22×C3×C4C22×D312yes—
134C22×C3×C4C22×D312yes—
135C22×C3×C4C22×D312yes—
136C22×C3×C4C22×D312yes—
137C22×C3×C4C22×D312yes—
138C22×Dic3—38no—
139C22×Dic3—64no—
140C22×Dic3C22×D318yes—
141C2×Dic6—332no—
142C3×C4⋊C4—38no—
143C3×C4⋊C4—38no—
144C3×C22⋊C4—38no—
145C3×C22⋊C4—38no—
146C3×C42—38no—
147C3×C42—38no—
148#217—38no—
149#217—38no—
150#217—68no—
151#217C22×D318yes—
152#217C22×D318yes—
153C4⋊Dic3—38no—
154C4⋊Dic3—38no—
155C4⋊Dic3—332no—
156C4⋊Dic3—68no—
157C4⋊Dic3C22×D318yes—
158C4⋊Dic3C22×D318yes—
159Dic3⋊C4—332no—
160Dic3⋊C4—332no—
161C4×Dic3—38no—
162C4×Dic3—38no—
163C4×Dic3—64no—
164C4×Dic3—64no—
165C4×Dic3C22×D318yes—
166C4×Dic3C22×D318yes—
167C22×C32—22no—
168C22×C32—24no—
169C22×C32—44no—
170C22×C32C22×Q812yes—
171C22×C32C22×Q814yes—
172C22×C32C2511yescharacteristic
173C32×C4C22×Q812yes—
174C32×C4C22×Q814yes—
175C32×C4C22×Q812yes—
176C3⋊Dic3—28no—
177C3×Dic3—216no—
178C23×C4D3211yescharacteristic
179C4⋊Q8—916no—
180C4⋊Q8—98no—
181#125—916no—
182#125—98no—
183C22⋊Q8—916no—
184C22⋊Q8—932no—
185C4×Q8—916no—
186#117—34no—
187#117—34no—
188#117—34no—
189#117—34no—
190#117—94no—
191#117—94no—
192C2×C4⋊C4—34no—
193C2×C4⋊C4—92no—
194C2×C22⋊C4—34no—
195C2×C22⋊C4—92no—
196C2×C42—34no—
197C2×C42—92no—
198C23×C3—21no—
199C23×C3—22no—
200C23×C3—24no—
201C23×C3—44no—
202C23×C3—44no—
203C23×C3C2×Dic618yes—
204C23×C3C23×D312yes—
205C23×C3C23×D312yes—
206C23×C3C23×D312yes—
207C2×C3×C4—21no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—24no—
211C2×C3×C4—24no—
212C2×C3×C4—28no—
213C2×C3×C4—28no—
214C2×C3×C4—316no—
215C2×C3×C4—128no—
216C2×C3×C4C2×Dic618yes—
217C2×C3×C4C2×Dic618yes—
218C2×C3×C4C2×Dic618yes—
219C2×C3×C4C2×Dic618yes—
220C2×C3×C4C2×Dic618yes—
221C2×C3×C4C2×Dic618yes—
222C2×C3×C4C23×D312yes—
223C2×C3×C4C23×D312yes—
224C2×C3×C4C23×D312yes—
225C2×C3×C4C23×D312yes—
226C2×Dic3—316no—
227C2×Dic3—48no—
228C2×Dic3—68no—
229C2×Dic3—128no—
230C2×Dic3—128no—
231C2×Dic3C23×D3116yes—
232Dic6—1232no—
233C2×C32—22no—
234C2×C32—24no—
235C2×C32C23×Q811yescharacteristic
236C2×C32#58512yes—
237C24C2×D3211yescharacteristic
238C2×Q8—916no—
239C22×C4—38no—
240C22×C4—94no—
241C22×C4#62718yescomplemented
242C22×C4C2×D3212yes—
243C22×C4C2×D3211yescharacteristic
244C22×C4C2×D3212yes—
245C22×C4C2×D3211yescharacteristic
246C4⋊C4—38no—
247C4⋊C4—38no—
248C4⋊C4—916no—
249C4⋊C4—932no—
250C4⋊C4—98no—
251C22⋊C4—38no—
252C22⋊C4—38no—
253C22⋊C4—98no—
254C42—38no—
255C42—38no—
256C42—94no—
257C42—94no—
258C22×C3—24no—
259C22×C3—24no—
260C22×C3—24no—
261C22×C3—24no—
262C22×C3—22no—
263C22×C3—24no—
264C22×C3—21no—
265C22×C3—44no—
266C22×C3—48no—
267C22×C3—48no—
268C22×C3C22×Dic614yes—
269C22×C3C22×Dic614yes—
270C22×C3C22×Dic614yes—
271C22×C3C24×D312yes—
272C3×C4—22no—
273C3×C4—24no—
274C3×C4—22no—
275C3×C4—616no—
276C3×C4C22×Dic614yes—
277C3×C4C22×Dic614yes—
278C3×C4C22×Dic614yes—
279C3×C4C22×Dic614yes—
280Dic3—216no—
281Dic3—616no—
282Dic3—128no—
283C32#345811yescharacteristic, complemented, Sylow
284C23—42no—
285C23C2×#62714yes—
286C23C22×D3211yescharacteristic
287C23C22×D3212yes—
288Q8—3616no—
289C2×C4—316no—
290C2×C4—98no—
291C2×C4—128no—
292C2×C4—364no—
293C2×C4C2×#62718yes—
294C2×C4C2×#62714yes—
295C2×C4C2×#62718yes—
296C2×C4C2×#62714yes—
297C2×C4C22×D3212yes—
298C2×C4C22×D3211yescharacteristic
299C2×C4C22×D3211yescharacteristic
300C2×C3—24no—
301C2×C3—24no—
302C2×C3—24no—
303C2×C3—24no—
304C2×C3—22no—
305C2×C3—21no—
306C2×C3—44no—
307C2×C3C23×Dic612yes—
308C2×C3#596414yes—
309C22—24no—
310C22—22no—
311C22—44no—
312C22C22×#62712yes—
313C22C22×#62714yes—
314C22C23×D3211yescharacteristic
315C4—616no—
316C4—188no—
317C4C22×#62714yes—
318C4C22×#62712yes—
319C4C22×#62712yes—
320C3—21no—
321C3#8572512yescomplemented
322C2—22no—
323C2—24no—
324C2#1059666912yes—
325C2C23×#62711yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#3458
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10595052C2semidirect
5. #10595051C2semidirect
6. #10595050C2semidirect
7. #10595049C2semidirect
24. #63919C22semidirect
25. #63918C22semidirect
26. C4×#627C22semidirect
27. #63872C22semidirect
28. #63869C22semidirect
41. C22×C32×C4Q8semidirect
131. C22×C3×C4Dic6semidirect
241. C22×C4#627semidirect
283. C32#3458semidirect
321. C3#85725semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×#9262
#105955212
#105950522
#105950512
#105950502
#105950492
#857253