Finite Group Databasebeta

← #11866167

Subgroups — #11866167

Order 1152.

1578 conjugacy classes of subgroups; only the 265 normal subgroups are shown.

normal subgroups only

This group has 1578 conjugacy classes of subgroups — too many to draw. Only its 265 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#10596276C211yesmaximal, characteristic, complemented
2C22×#3753C211yesmaximal, characteristic, complemented
3C2×#64117C211yesmaximal, characteristic, complemented
4#10595992C211yesmaximal, characteristic, complemented
5C32×#418C211yesmaximal, characteristic, complemented
6#10592818C211yesmaximal, characteristic, complemented
7#10592701C211yesmaximal, characteristic, complemented
8#10592486C214yesmaximal, complemented
9#10592485C214yesmaximal, complemented
10#78944—34nomaximal
11C22×C32×D4C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64162—22no—
17#64149C2212yescomplemented
18#64147—22no—
19#64145C2212yescomplemented
20C2×#3753—24no—
21C2×#3753C2214yes—
22#64135C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24#64117—24no—
25C2×#3745C2212yescomplemented
26C2×#3744C2212yescomplemented
27#64102C2214yescomplemented
28C22⋊C4×C3⋊D3—22no—
29C4×C4⋊(C3⋊D3)—22no—
30C32×#102C2214yescomplemented
31#63641C2214yescomplemented
32#63637C2212yescomplemented
33#63636C2212yescomplemented
34#5805—34no—
35C22×#213—34no—
36C2×#908—34no—
37#5521—34no—
38C3×#418D314yescomplemented
39#5119—34no—
40#5002—34no—
41#4787—316no—
42#4786—316no—
43C24×C32—21no—
44C23×C3⋊D3—21no—
45C2×C32×D4—22no—
46C2×C32×D4—21no—
47C2×C32×D4—22no—
48C2×C32×D4C2312yes—
49C22×C32×C4C2311yescharacteristic
50C2×#638—21no—
51C2×#638—24no—
52#3828—22no—
53#3828—22no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)D414yescomplemented
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—24no—
61C2×#634C2311yescharacteristic
62C32×M16—22no—
63C2×C32×C8C2312yes—
64C32×C4⋊C4C2312yes—
65C32×C22⋊C4—21no—
66C32×C42—21no—
67#3757—24no—
68#3757D412yes—
69#3753—28no—
70#3752—24no—
71C4⋊(C3⋊Dic3)D412yes—
72C4×C3⋊Dic3C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75#3745—24no—
76#3744—24no—
77#3041—91noSylow
78C22×C3×D4C2×D314yes—
79C2×#235—34no—
80C22×D12—34no—
81C2×C3×M16C2×D314yes—
82C3×#117C2×D314yes—
83#953—68no—
84#940—38no—
85#938—68no—
86#936—38no—
87C2×#213—316no—
88C2×#213—616no—
89#926—34no—
90C22×C3⋊C8—34no—
91#908—616no—
92C2×D24—38no—
93C2×#204—38no—
94#893—316no—
95D3×C22⋊C4—68no—
96C4×D12—68no—
97C3×#102C2×D3116yescomplemented
98Dic3⋊C8—316no—
99#810—38no—
100#809—38no—
101C23×C32—22no—
102C23×C32—42no—
103C23×C32—82no—
104C23×C32C2×D411yescharacteristic
105C22×C3⋊D3—22no—
106C22×C3⋊D3—24no—
107C22×C3⋊D3—21no—
108C22×C3⋊D3—82no—
109C32×D4—22no—
110C32×D4—22no—
111C32×D4—42no—
112C2×C32×C4—22no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D412yes—
115C2×C32×C4#4112yes—
116C2×C32×C4C2411yescharacteristic
117#638—42no—
118#638—84no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3C2×D414yes—
121C4⋊(C3⋊D3)—24no—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)—22no—
124C4⋊(C3⋊D3)—21no—
125C4⋊(C3⋊D3)C2×D414yes—
126C4×C3⋊D3—42no—
127C4×C3⋊D3—84no—
128#634—21no—
129#634—21no—
130C32×C8—22no—
131C3⋊(C3⋊C8)—22no—
132C2×AGL(1,ℤ/8)—91no—
133C22×D8—91no—
134#535—91no—
135#518—91no—
136#463—94no—
137#459—94no—
138#424—91no—
139#418C3⋊D311yescharacteristic, complemented
140#416—91no—
141C24×C3—24no—
142C23×D3—64no—
143C2×C3×D4—28no—
144C2×C3×D4—28no—
145C2×C3×D4—24no—
146C2×C3×D4C22×D318yes—
147C22×C3×C4C22×D314yes—
148C2×#67—616no—
149C2×#67—64no—
150#235—68no—
151#235—68no—
152C2×D12—316no—
153C2×D12—38no—
154C2×D12—34no—
155C2×D12—68no—
156C2×D12—64no—
157C2×C4×D3—64no—
158C2×C4×D3—616no—
159C2×Dic6—34no—
160C3×M16—28no—
161C2×C3×C8C22×D318yes—
162C3×C4⋊C4C22×D318yes—
163C3×C22⋊C4—24no—
164C3×C42—24no—
165#217—38no—
166#217—616no—
167#213—632no—
168(C2×D3)⋊C4—616no—
169C4⋊Dic3—38no—
170C4×Dic3—38no—
171C2×C3⋊C8—38no—
172C2×C3⋊C8—68no—
173D24—616no—
174#204—616no—
175C22×C32—22no—
176C22×C32—42no—
177C22×C32—44no—
178C22×C32—84no—
179C22×C32#12112yes—
180C22×C32C22×D411yescharacteristic
181C2×C3⋊D3—24no—
182C2×C3⋊D3—44no—
183C2×C3⋊D3—41no—
184C2×C3⋊D3—42no—
185C2×C3⋊D3—84no—
186C32×C4—42no—
187C32×C4#12112yes—
188C32×C4C22×D411yescharacteristic
189C32×C4C2×#4111yescharacteristic
190C3⋊Dic3—24no—
191C3⋊Dic3—41no—
192C2×#41—91no—
193C22×D4—91no—
194C22×D4C2×C3⋊D311yescharacteristic
195AGL(1,ℤ/8)—184no—
196C2×SD16—92no—
197C2×D8—94no—
198C2×D8—92no—
199C2×D8—184no—
200C2×M16C2×C3⋊D311yescharacteristic
201C22×C8—91no—
202#127—92no—
203#124—92no—
204#121—182no—
205#120—182no—
206C4×D4—94no—
207C4×D4—182no—
208#117—91no—
209#117C2×C3⋊D311yescharacteristic
210C2×C22⋊C4—182no—
211C4⋊C8—94no—
212#103—92no—
213#102—92no—
214#102C2×C3⋊D314yescomplemented
215C23×C3—28no—
216C23×C3—48no—
217C23×C3—88no—
218C23×C3D3×D414yes—
219C22×D3—68no—
220C22×D3—616no—
221C22×D3—64no—
222C22×D3—248no—
223C3×D4—28no—
224C3×D4—28no—
225C3×D4—48no—
226C2×C3×C4—28no—
227C2×C3×C4#23518yes—
228C2×C3×C4D3×D414yes—
229C2×C3×C4D3×D418yes—
230C2×C3×C4C23×D314yes—
231#67—128no—
232#67—2416no—
233C2×Dic3—316no—
234C2×Dic3—64no—
235D12—316no—
236D12—616no—
237D12—68no—
238D12—64no—
239D12—64no—
240C4×D3—128no—
241C4×D3—2416no—
242Dic6—64no—
243Dic6—64no—
244C3×C8—28no—
245C3⋊C8—68no—
246C2×C32—22no—
247C2×C32—82no—
248C2×C32C2×#12111yescharacteristic
249C2×C32#57612yes—
250C3⋊D3—44no—
251C3⋊D3—81no—
252C24—21no—
253C24—181no—
254#41—182no—
255#41—182no—
256C2×Q8—91no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—92no—
261C2×D4—91no—
262C2×D4—94no—
263C2×D4—184no—
264C2×D4—181no—
265C2×D4—182no—
266C2×D4—181no—
267C2×D4C22×C3⋊D312yes—
268C22×C4—184no—
269C22×C4—181no—
270C22×C4C22×C3⋊D311yescharacteristic
271SD16—184no—
272D8—184no—
273D8—188no—
274M16—22no—
275C2×C8—92no—
276C2×C8—182no—
277C2×C8C22×C3⋊D312yes—
278C4⋊C4—92no—
279C4⋊C4C22×C3⋊D312yes—
280C22⋊C4—21no—
281C22⋊C4—92no—
282C22⋊C4—184no—
283C22⋊C4—184no—
284C42—21no—
285C42—92no—
286C22×C3—28no—
287C22×C3—48no—
288C22×C3—416no—
289C22×C3—816no—
290C22×C3#88418yes—
291C22×C3C2×D3×D414yes—
292C2×D3—616no—
293C2×D3—1216no—
294C2×D3—124no—
295C2×D3—128no—
296C2×D3—2416no—
297C3×C4—48no—
298C3×C4#88418yes—
299C3×C4C2×#23514yes—
300C3×C4C2×D3×D414yes—
301Dic3—616no—
302Dic3—124no—
303C32#304111yescharacteristic, complemented, Sylow
304C23—22no—
305C23—42no—
306C23—82no—
307C23—182no—
308C23—184no—
309C23—181no—
310C23—722no—
311C23D4×C3⋊D311yescharacteristic
312Q8—181no—
313Q8—181no—
314D4—22no—
315D4—22no—
316D4—42no—
317D4—94no—
318D4—184no—
319D4—182no—
320D4—181no—
321D4—181no—
322D4—362no—
323D4—724no—
324C2×C4—22no—
325C2×C4—94no—
326C2×C4—181no—
327C2×C4—362no—
328C2×C4—724no—
329C2×C4#382812yes—
330C2×C4D4×C3⋊D311yescharacteristic
331C2×C4D4×C3⋊D312yes—
332C2×C4C23×C3⋊D311yescharacteristic
333C8—22no—
334C8—182no—
335C2×C3—28no—
336C2×C3—88no—
337C2×C3C2×#88414yes—
338C2×C3#577418yes—
339D3—1216no—
340D3—244no—
341C22—22no—
342C22—42no—
343C22—44no—
344C22—84no—
345C22—184no—
346C22—364no—
347C22—361no—
348C22—362no—
349C22—724no—
350C22#6409312yes—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—42no—
353C4—184no—
354C4—361no—
355C4#6409312yes—
356C4C2×#382811yescharacteristic
357C4C2×D4×C3⋊D311yescharacteristic
358C3#7894414yescomplemented
359C2—22no—
360C2—82no—
361C2—364no—
362C2—721no—
363C2C2×#6409311yescharacteristic
364C2#1059624512yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#418C2
socleC22×C32C22×D4
hypercenter#418C3⋊D3
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #10596276C2semidirect
2. C22×#3753C2semidirect
3. C2×#64117C2semidirect
4. #10595992C2semidirect
5. C32×#418C2semidirect
6. #10592818C2semidirect
7. #10592701C2semidirect
8. #10592486C2semidirect
9. #10592485C2semidirect
17. #64149C22semidirect
19. #64145C22semidirect
25. C2×#3745C22semidirect
26. C2×#3744C22semidirect
27. #64102C22semidirect
30. C32×#102C22semidirect
31. #63641C22semidirect
32. #63637C22semidirect
33. #63636C22semidirect
38. C3×#418D3semidirect
56. C2×C4⋊(C3⋊D3)D4semidirect
97. C3×#102C2×D3semidirect
139. #418C3⋊D3semidirect
214. #102C2×C3⋊D3semidirect
303. C32#3041semidirect
358. C3#78944semidirect

Maximal subgroups

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

subgroupindex
#105962762
C22×#37532
C2×#641172
#105959922
C32×#4182
#105928182
#105927012
#105924862
#105924852
#789443