Finite Group Databasebeta

← #11877039

Subgroups — #11877039

Order 1152.

787 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 787 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594810C212yesmaximal
2M16×C3⋊Dic3C211yesmaximal, characteristic
3C3×#5137C212yesmaximal
4#10591189C212yesmaximal
5#10590905C211yesmaximal, characteristic, complemented
6#10590901C212yesmaximal, complemented
7#10590900C211yesmaximal, characteristic, complemented
8#10590819C212yesmaximal, complemented
9#10590791C212yesmaximal, complemented
10#80893—32nomaximal
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#924C2214yes—
15C2×C3×Dic12C2212yes—
16#63982—22no—
17#63957—22no—
18#63919C2212yes—
19#63873C2212yes—
20#63870—22no—
21#63843C2214yes—
22#63838—22no—
23C2×#3718C2212yes—
24#63642C2211yescharacteristic
25#63642C2211yescharacteristic
26C8×C3⋊Dic3C2211yescharacteristic
27C8×C3⋊Dic3C2211yescharacteristic
28C3×#817C2212yes—
29C3×#816C2214yes—
30#63574C2212yes—
31#63565C2214yes—
32#5622—34no—
33C3×#470—32no—
34#5184—32no—
35#5183—32no—
36#5137D312yes—
37Dic3×M16—32no—
38Dic3×M16—61no—
39#5052—34no—
40#4855—32no—
41#4853—32no—
42#4792—34no—
43#4789—34no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D412yes—
46C2×C3×Dic6C2314yes—
47C2×#627—22no—
48C32×M16—22no—
49C2×C32×C8C2311yescharacteristic
50C2×C32×C8C2311yescharacteristic
51C4×C3⋊Dic3D412yes—
52C4×C3⋊Dic3C2311yescharacteristic
53C4×C3⋊Dic3C2311yescharacteristic
54#3748—22no—
55C2×C3⋊(C3⋊C8)C2311yescharacteristic
56C2×C3⋊(C3⋊C8)C2311yescharacteristic
57C3×#217—24no—
58C3×C4⋊Dic3C2314yes—
59C3×Dic3⋊C4—24no—
60C3×Dic12—24no—
61#3724—22no—
62#3724—22no—
63#3724—22no—
64Dic3⋊Dic3—24no—
65Dic32—24no—
66#3718—24no—
67#3185—91noSylow
68C2×C3×Q16—32no—
69C2×C3×M16—21no—
70C2×C3×M16C2×D312yes—
71C3×C22⋊Q8—34no—
72Q8×Dic3—34no—
73#944—34no—
74C2×#216—34no—
75#924C2×D314yes—
76C2×C4×Dic3—32no—
77C2×C4×Dic3—61no—
78C2×#208—32no—
79C2×#208—61no—
80C2×Dic12C2×D312yes—
81#889—64no—
82#888—34no—
83#887—34no—
84#887—64no—
85#878—64no—
86#877—64no—
87C3×#106—32no—
88C3×#103—34no—
89#835—34no—
90#817C2×D312yes—
91#816C2×D314yes—
92#815—32no—
93#815—32no—
94#815—61no—
95#815—61no—
96C8×Dic3—32no—
97C8×Dic3—32no—
98C8×Dic3—61no—
99C8×Dic3—61no—
100#810—34no—
101#808—34no—
102C23×C32C2×D411yescharacteristic
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2411yescharacteristic
107C2×C3⋊Dic3—24no—
108C2×C3⋊Dic3C2×D412yes—
109C2×C3⋊Dic3C2×D412yes—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C3×Dic6—24no—
113C3×Dic6—24no—
114#627—44no—
115C32×C8—21no—
116C32×C8#4112yes—
117C3⋊(C3⋊C8)—21no—
118C3⋊(C3⋊C8)#4112yes—
119#533—92no—
120#498—91no—
121#494—91no—
122#487—92no—
123#470—32no—
124#470—92no—
125#441—92no—
126#441—92no—
127C4×M16—91no—
128C2×C3×Q8—34no—
129C22×C3×C4—21no—
130C22×C3×C4C22×D312yes—
131C22×Dic3—34no—
132C22×Dic3—62no—
133C2×Dic6—64no—
134C2×Dic6C22×D314yes—
135C3×Q16—64no—
136C3×M16—24no—
137C3×M16—24no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8C22×D312yes—
141C2×C3×C8C22×D312yes—
142C3×C4⋊C4—34no—
143C3×C4⋊C4—64no—
144C3×C22⋊C4—64no—
145#217—24no—
146#216—68no—
147C4⋊Dic3—64no—
148C4⋊Dic3C22×D314yes—
149Dic3⋊C4—24no—
150Dic3⋊C4—64no—
151Dic3⋊C4—64no—
152Dic3⋊C4—64no—
153Dic3⋊C4—64no—
154C4×Dic3—34no—
155C4×Dic3—32no—
156C4×Dic3—32no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—62no—
160C4×Dic3—64no—
161C4×Dic3—64no—
162#208—64no—
163#208—64no—
164C2×C3⋊C8—32no—
165C2×C3⋊C8—32no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8—61no—
168Dic12—24no—
169C22×C32—21no—
170C22×C32—22no—
171C22×C32C22×D411yescharacteristic
172C32×C4—21no—
173C32×C4C2×#4111yescharacteristic
174C32×C4C2×#4111yescharacteristic
175C3⋊Dic3—22no—
176C3⋊Dic3#13714yes—
177C3×Dic3—44no—
178C3×Dic3—44no—
179C2×Q16—32no—
180C2×Q16—92no—
181C2×M16—91no—
182C2×M16D3211yescharacteristic
183C4⋊Q8—92no—
184C4⋊Q8—92no—
185#125—182no—
186C22⋊Q8—34no—
187C22⋊Q8—182no—
188C4×Q8—94no—
189C4×Q8—182no—
190#117—182no—
191C2×C42—91no—
192#106—32no—
193#106—92no—
194#103—34no—
195#103—94no—
196#97—91no—
197#97—91no—
198C4×C8—91no—
199C4×C8—91no—
200C23×C3—21no—
201C23×C3D3×D412yes—
202C3×Q8—64no—
203C3×Q8—64no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—64no—
211C2×C3×C4—64no—
212C2×C3×C4D3×D412yes—
213C2×C3×C4C23×D312yes—
214C2×Dic3—24no—
215C2×Dic3—24no—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—68no—
221C2×Dic3—124no—
222Dic6—24no—
223Dic6—24no—
224Dic6—128no—
225C3×C8—22no—
226C3×C8—22no—
227C3×C8—22no—
228C3×C8#23714yes—
229C3⋊C8—34no—
230C3⋊C8—62no—
231C3⋊C8—62no—
232C3⋊C8—62no—
233C2×C32—41no—
234C2×C32#53211yescharacteristic
235C2×C32C2×#13712yes—
236C2×Q8—34no—
237C2×Q8—182no—
238C22×C4—92no—
239C22×C4C2×D3211yescharacteristic
240Q16—64no—
241Q16—184no—
242M16—22no—
243M16—182no—
244C2×C8—91no—
245C2×C8—91no—
246C2×C8C2×D3211yescharacteristic
247C2×C8C2×D3211yescharacteristic
248C4⋊C4—34no—
249C4⋊C4—64no—
250C4⋊C4—182no—
251C4⋊C4—182no—
252C4⋊C4—184no—
253C4⋊C4—182no—
254C22⋊C4—64no—
255C42—91no—
256C42—91no—
257C42—92no—
258C42—184no—
259C22×C3—22no—
260C22×C3—24no—
261C22×C3—22no—
262C22×C3—21no—
263C22×C3—42no—
264C22×C3C2×D3×D412yes—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—124no—
270C3×C4—124no—
271C3×C4C2×#23712yes—
272C3×C4D3×#4112yes—
273Dic3—38no—
274Dic3—44no—
275Dic3—44no—
276Dic3—64no—
277Dic3—64no—
278Dic3—122no—
279C32#318511yescharacteristic, complemented, Sylow
280C23#380211yescharacteristic
281Q8—64no—
282Q8—64no—
283Q8—364no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—64no—
287C2×C4—64no—
288C2×C4—92no—
289C2×C4—92no—
290C2×C4—184no—
291C2×C4#380211yescharacteristic
292C2×C4C22×D3211yescharacteristic
293C8—21no—
294C8—92no—
295C8—181no—
296C8#380512yes—
297C2×C3—21no—
298C2×C3—22no—
299C2×C3—42no—
300C2×C3—42no—
301C2×C3#559612yes—
302C2×C3D3×#13714yes—
303C22—21no—
304C22—22no—
305C22C2×#380211yescharacteristic
306C4—21no—
307C4—94no—
308C4—124no—
309C4—124no—
310C4—182no—
311C4#6430611yescharacteristic
312C4C2×#380511yescharacteristic
313C3—21no—
314C3#8089312yescomplemented
315C2—41no—
316C2#1059471712yes—
317C2#1059492911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC2×M16D32
hypocenterC32#3185
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
5. #10590905C2semidirect
6. #10590901C2semidirect
7. #10590900C2semidirect
8. #10590819C2semidirect
9. #10590791C2semidirect
279. C32#3185semidirect
314. C3#80893semidirect

Maximal subgroups

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

subgroupindex
#105948102
M16×C3⋊Dic32
C3×#51372
#105911892
#105909052
#105909012
#105909002
#105908192
#105907912
#808933