Finite Group Databasebeta

← #11861475

Subgroups — #11861475

Order 1152.

783 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595050C211yesmaximal, characteristic
2M16×C3⋊Dic3C211yesmaximal, characteristic
3C3×#5122C212yesmaximal
4C2×#63572C211yesmaximal, characteristic
5#10591116C212yesmaximal
6#10590787C212yesmaximal, complemented
7#10590784C214yesmaximal, complemented
8C8×#627C212yesmaximal, complemented
9#78544—32nomaximal
10C2×C32×M16C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2212yes—
14C22×C3×C3⋊C8C2212yes—
15#63982C412yes—
16#63982C412yes—
17#63919C411yescharacteristic
18#63919C411yescharacteristic
19C4×#627C2212yes—
20C4×#627C2212yes—
21#63872C412yes—
22#63642C2212yes—
23C8×C3⋊Dic3C2212yes—
24C3×#815C2214yes—
25C3×C8×Dic3C2214yes—
26#63572C2211yescharacteristic
27#63572C2212yes—
28#63572C2211yescharacteristic
29Dic3⋊(C3⋊C8)C2214yes—
30Dic3⋊(C3⋊C8)C2214yes—
31#5517—32no—
32C3×#405—32no—
33#5122D312yes—
34Dic3×M16—32no—
35Dic3×M16—61no—
36#5102—32no—
37C2×Dic3⋊C8—32no—
38#4999—32no—
39#4701—34no—
40#4701—34no—
41#4679—34no—
42C8×Dic6—34no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2×C411yescharacteristic
45C22×C3⋊Dic3C2×C411yescharacteristic
46C2×#627C2×C412yes—
47C2×#627C2×C412yes—
48C32×M16Q814yescomplemented
49C2×C32×C8C2312yes—
50C4×C3⋊Dic3C2×C411yescharacteristic
51C4×C3⋊Dic3C2×C411yescharacteristic
52C4×C3⋊Dic3C2311yescharacteristic
53C4×C3⋊Dic3C2311yescharacteristic
54#3748—22no—
55C2×C3⋊(C3⋊C8)C2312yes—
56C3×#217C2×C414yes—
57C3×C4⋊Dic3C2×C412yes—
58C3×C4⋊Dic3C2×C412yes—
59C3×C4×Dic3C2314yes—
60C2×C3×C3⋊C8—24no—
61C2×C3×C3⋊C8C2312yes—
62C2×C3×C3⋊C8C2312yes—
63#3724C2×C412yes—
64#3724C2×C412yes—
65Dic3⋊Dic3C2×C414yes—
66Dic3⋊Dic3C2×C414yes—
67#2962—91noSylow
68C2×C3×M16—21no—
69C2×C3×M16C2×D312yes—
70C22×C3×C8—32no—
71C3×#117—32no—
72#926C2×D312yes—
73C2×C4×Dic3—32no—
74C2×C4×Dic3—61no—
75C2×#208—32no—
76C2×#208—61no—
77C22×C3⋊C8C2×D312yes—
78#890—32no—
79#890—32no—
80#888—32no—
81#888—32no—
82#878—34no—
83#878—34no—
84C4×Dic6—34no—
85C4×Dic6—34no—
86C3×#97—34no—
87C3×C4×C8—34no—
88#815—34no—
89#815—62no—
90#815C2×D314yes—
91Dic3⋊C8—34no—
92Dic3⋊C8—34no—
93Dic3⋊C8—32no—
94Dic3⋊C8—32no—
95Dic3⋊C8—32no—
96Dic3⋊C8—32no—
97C8×Dic3—34no—
98C8×Dic3—62no—
99C8×Dic3C2×D314yes—
100C4⋊(C3⋊C8)—34no—
101C4⋊(C3⋊C8)—34no—
102C23×C32C22×C411yescharacteristic
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×Q812yes—
105C2×C32×C4#4112yes—
106C2×C32×C4C2411yescharacteristic
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3C22×C411yescharacteristic
110C2×C3⋊Dic3C22×C411yescharacteristic
111C2×C3⋊Dic3C22×C411yescharacteristic
112C2×C3⋊Dic3C22×C411yescharacteristic
113C2×C3×Dic3C22×C414yes—
114C2×C3×Dic3C22×C414yes—
115#627—24no—
116#627—42no—
117C32×C8C2×Q814yes—
118C3⋊(C3⋊C8)—22no—
119C3×C3⋊C8—22no—
120C3×C3⋊C8—22no—
121#533—91no—
122#446—94no—
123#446—92no—
124C8×Q8—92no—
125#424—92no—
126C2×C4⋊C8—91no—
127#405—32no—
128C4×M16—91no—
129C22×C3×C4—21no—
130C22×C3×C4C22×D312yes—
131C22×Dic3—32no—
132C22×Dic3—32no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C2×Dic6—34no—
136C2×Dic6—34no—
137C3×M16—24no—
138C3×M16Dic618yescomplemented
139C2×C3×C8—22no—
140C2×C3×C8—32no—
141C2×C3×C8—32no—
142C2×C3×C8—64no—
143C2×C3×C8C22×D314yes—
144C3×C4⋊C4—32no—
145C3×C4⋊C4—32no—
146C3×C22⋊C4—34no—
147C3×C42—34no—
148#217C4×D314yes—
149C4⋊Dic3—34no—
150C4⋊Dic3—34no—
151C4⋊Dic3C4×D312yes—
152C4⋊Dic3C4×D312yes—
153Dic3⋊C4—34no—
154Dic3⋊C4—34no—
155Dic3⋊C4—34no—
156Dic3⋊C4—34no—
157C4×Dic3—32no—
158C4×Dic3—32no—
159C4×Dic3—32no—
160C4×Dic3—32no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3C22×D314yes—
166#208—64no—
167#208—64no—
168C2×C3⋊C8—24no—
169C2×C3⋊C8—34no—
170C2×C3⋊C8—62no—
171C2×C3⋊C8C22×D312yes—
172C2×C3⋊C8C22×D312yes—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32C4×Q812yes—
176C22×C32C23×C411yescharacteristic
177C32×C4C4×Q812yes—
178C32×C4C22×Q811yescharacteristic
179C32×C4C2×#4111yescharacteristic
180C3⋊Dic3—21no—
181C3⋊Dic3—21no—
182C3⋊Dic3—21no—
183C3⋊Dic3#13112yes—
184C3×Dic3—24no—
185C3×Dic3—24no—
186C2×M16—91no—
187C2×M16D3211yescharacteristic
188C22×C8—32no—
189C4⋊Q8—91no—
190C4⋊Q8—91no—
191#125—92no—
192C22⋊Q8—92no—
193C22⋊Q8—92no—
194C4×Q8—92no—
195C4×Q8—92no—
196#117—32no—
197C2×C42—91no—
198C4⋊C8—94no—
199C4⋊C8—94no—
200C4⋊C8—91no—
201C4⋊C8—91no—
202C4⋊C8—92no—
203#97—34no—
204#97—92no—
205C4×C8—34no—
206C4×C8—92no—
207C23×C3—21no—
208C23×C3C2×C4×D312yes—
209C2×C3×C4—21no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—34no—
214C2×C3×C4—34no—
215C2×C3×C4C2×Dic614yes—
216C2×C3×C4C2×C4×D312yes—
217C2×C3×C4#23514yes—
218C2×C3×C4C23×D312yes—
219C2×Dic3—32no—
220C2×Dic3—32no—
221C2×Dic3—32no—
222C2×Dic3—32no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—64no—
228C2×Dic3—122no—
229C2×Dic3—122no—
230C2×Dic3—122no—
231C2×Dic3C2×C4×D314yes—
232C2×Dic3C2×C4×D314yes—
233Dic6—68no—
234Dic6—124no—
235C3×C8—24no—
236C3×C8—62no—
237C3×C8—62no—
238C3×C8C2×Dic618yes—
239C3⋊C8—22no—
240C3⋊C8—22no—
241C3⋊C8—64no—
242C3⋊C8—64no—
243C2×C32—22no—
244C2×C32C2×C4×Q811yescharacteristic
245C2×C32C2×#13111yescharacteristic
246C2×C32#56811yescharacteristic
247C2×Q8—92no—
248C2×Q8—92no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4C2×D3211yescharacteristic
252M16—182no—
253M16#62714yescomplemented
254C2×C8—32no—
255C2×C8—32no—
256C2×C8—64no—
257C2×C8—92no—
258C2×C8C2×D3212yes—
259C4⋊C4—32no—
260C4⋊C4—32no—
261C4⋊C4—94no—
262C4⋊C4—94no—
263C4⋊C4—92no—
264C4⋊C4—92no—
265C22⋊C4—34no—
266C42—34no—
267C42—91no—
268C42—91no—
269C42—91no—
270C42—91no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—21no—
274C22×C3—22no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3C4×Dic614yes—
278C22×C3C22×C4×D312yes—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—22no—
282C3×C4—64no—
283C3×C4—64no—
284C3×C4C4×Dic614yes—
285C3×C4C22×Dic612yes—
286C3×C4C2×#23512yes—
287Dic3—24no—
288Dic3—24no—
289Dic3—34no—
290Dic3—62no—
291Dic3—62no—
292Dic3—62no—
293Dic3—62no—
294Dic3—62no—
295Dic3—121no—
296Dic3—121no—
297C32#296211yescharacteristic, complemented, Sylow
298C23C4×D3211yescharacteristic
299Q8—184no—
300Q8—362no—
301C2×C4—34no—
302C2×C4—34no—
303C2×C4—91no—
304C2×C4—91no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—182no—
308C2×C4—361no—
309C2×C4#379812yes—
310C2×C4C4×D3211yescharacteristic
311C2×C4C2×#62712yes—
312C2×C4C22×D3211yescharacteristic
313C8—62no—
314C8—62no—
315C8—182no—
316C8C2×#62714yes—
317C2×C3—24no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—42no—
322C2×C3C2×C4×Dic612yes—
323C2×C3D3×#13112yes—
324C2×C3#575012yes—
325C22—21no—
326C22—21no—
327C22C4×#62712yes—
328C22C2×C4×D3211yescharacteristic
329C4—64no—
330C4—64no—
331C4—92no—
332C4—181no—
333C4—181no—
334C4—181no—
335C4C4×#62712yes—
336C4C2×#379811yescharacteristic
337C4C22×#62711yescharacteristic
338C3—21no—
339C3#7854412yescomplemented
340C2—22no—
341C2#1059470711yescharacteristic
342C2#1059470811yescharacteristic
343C2C2×C4×#62711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC23×C32C22×C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2962
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
6. #10590787C2semidirect
7. #10590784C2semidirect
8. C8×#627C2semidirect
48. C32×M16Q8semidirect
138. C3×M16Dic6semidirect
253. M16#627semidirect
297. C32#2962semidirect
339. C3#78544semidirect

Maximal subgroups

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

subgroupindex
#105950502
M16×C3⋊Dic32
C3×#51222
C2×#635722
#105911162
#105907872
#105907842
C8×#6272
#785443