Finite Group Databasebeta

← #11885777

Subgroups — #11885777

Order 1152.

1307 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 1307 conjugacy classes of subgroups — too many to draw. Only its 178 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
1C2×#63797C212yesmaximal, complemented
2#10594004C212yesmaximal, complemented
3#10592533C211yesmaximal, characteristic, complemented
4C3×#4843C212yesmaximal, complemented
5#10590945C214yesmaximal, complemented
6#10590839C212yesmaximal, complemented
7#10590352C211yesmaximal, characteristic, complemented
8C4×#3713C211yesmaximal, characteristic, complemented
9#80350—32nomaximal
10C2×#3802C2214yescomplemented
11C2×D3×D12—22no—
12C2×C8×C3⋊D3C2212yescomplemented
13C4×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×D24C2214yescomplemented
15C3×#874C2212yescomplemented
16C3×C4×D12C2212yescomplemented
17#63922—24no—
18#63916C2214yescomplemented
19#63908—22no—
20C2×#3713C2211yescharacteristic
21C2×#3713C2212yescomplemented
22C2×#3713C2212yescomplemented
23#63797—28no—
24C32×C4⋊C8C2211yescharacteristic, complemented
25#63647C2212yescomplemented
26C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27C3×#821C2214yescomplemented
28#63576C2211yescharacteristic, complemented
29#63562C2212yescomplemented
30C2×D3×D8—34no—
31#5717—32no—
32D4×D12—32no—
33C3×#459—32no—
34#5156—34no—
35#5073—32no—
36C4×#213—32no—
37#4843D312yescomplemented
38#4834—32no—
39#4834—61no—
40#4775—34no—
41#4773—34no—
42C22×D32—24no—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3C2312yes—
45C2×C3×D12—22no—
46C2×C3×D12—22no—
47C2×C3×D12C2314yes—
48C2×C3×D12C2312yes—
49C2×C3×C4×D3—22no—
50C2×#626—24no—
51C2×#625—24no—
52#3802—28no—
53#3802—44no—
54D3×D12—48no—
55C2×C32×C8C2312yes—
56C32×C42C2311yescharacteristic
57#3752D412yes—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59C2×C3⋊(C3⋊C8)C2311yescharacteristic
60C2×C3⋊(C3⋊C8)C2311yescharacteristic
61C8×C3⋊D3—24no—
62C3×(C2×D3)⋊C4—22no—
63C3×C4⋊Dic3C2312yes—
64C3×D24—28no—
65(C2×D3)⋊Dic3—24no—
66#3713—24no—
67#3713—42no—
68#3713D414yescomplemented
69D4×D8—91noSylow
70C2×D3×D4—34no—
71C2×D3×D4—34no—
72C2×D3×D4—62no—
73C22×D12—62no—
74C2×C3×D8—34no—
75C3×#127—32no—
76C3×C4×D4—32no—
77#938—34no—
78#938—62no—
79#937—64no—
80C2×#213—32no—
81C2×#213—34no—
82C2×#213—34no—
83#930—62no—
84D3×D8—616no—
85C2×D24C2×D314yescomplemented
86C2×D3×C8—34no—
87C2×D3×C8—62no—
88#895—34no—
89#882—64no—
90#874C2×D312yescomplemented
91C4×D12—32no—
92C4×D12—61no—
93C4×D12C2×D312yescomplemented
94C3×C4⋊C8—21no—
95C3×C4⋊C8C2×D312yescomplemented
96C3×#102—34no—
97#832—32no—
98#821C2×D314yescomplemented
99(C2×D3)⋊C8—34no—
100(C2×D3)⋊C8—62no—
101#809—32no—
102#807—32no—
103C4×C3⋊C8—32no—
104C4×C3⋊C8—61no—
105C22×C3⋊D3C2×D412yes—
106C22×C3×D3—22no—
107C22×C3×D3—24no—
108C2×D32—48no—
109C2×D32—48no—
110C2×D32—84no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2411yescharacteristic
114C2×C3⋊Dic3C2×D412yes—
115C4⋊(C3⋊D3)D814yescomplemented
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118C2×C3×Dic3—22no—
119C3×D12—24no—
120C3×D12—22no—
121C3×D12—24no—
122C3×D12—44no—
123C3×D12—82no—
124C3×D12C2×D414yescomplemented
125C3×C4×D3—44no—
126#626—48no—
127#625—48no—
128C32×C8—22no—
129C3⋊(C3⋊C8)—21no—
130C3⋊(C3⋊C8)C2×D412yescomplemented
131C22×D8—92no—
132D42—92no—
133#493—91no—
134#466—92no—
135#459—32no—
136#447—94no—
137C4×D8—91no—
138C8×D4—91no—
139C23×D3—64no—
140C23×D3—64no—
141C2×C3×D4—32no—
142C2×C3×D4—34no—
143C2×C3×D4—62no—
144C2×C3×D4—62no—
145C22×C3×C4—62no—
146C2×#67—64no—
147C2×#67—64no—
148C2×#67—64no—
149D3×D4—68no—
150D3×D4—68no—
151D3×D4—128no—
152D3×D4—124no—
153D3×D4—124no—
154C2×D12—22no—
155C2×D12—22no—
156C2×D12—32no—
157C2×D12—61no—
158C2×D12—64no—
159C2×D12—128no—
160C2×D12C22×D314yes—
161C2×D12C22×D312yes—
162C2×C4×D3—22no—
163C2×C4×D3—34no—
164C2×C4×D3—62no—
165C3×D8—68no—
166C2×C3×C8—22no—
167C2×C3×C8C22×D314yes—
168C3×C4⋊C4—32no—
169C3×C22⋊C4—62no—
170C3×C42—21no—
171C3×C42C22×D312yes—
172#217—64no—
173#213—38no—
174#213—68no—
175#213—124no—
176(C2×D3)⋊C4—22no—
177(C2×D3)⋊C4—34no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—64no—
180C4⋊Dic3—32no—
181C4⋊Dic3—61no—
182C4⋊Dic3C22×D312yes—
183C2×C3⋊C8—32no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187D24—28no—
188D3×C8—68no—
189D3×C8—124no—
190C22×C32C22×D411yescharacteristic
191C2×C3⋊D3—22no—
192C2×C3⋊D3—22no—
193C2×C3⋊D3C2×D814yescomplemented
194C2×C3×D3—24no—
195C2×C3×D3—42no—
196C2×C3×D3—42no—
197C2×C3×D3—44no—
198C2×C3×D3—44no—
199C2×C3×D3—44no—
200D32—816no—
201C32×C4—21no—
202C32×C4C2×D812yescomplemented
203C32×C4C22×D411yescharacteristic
204C32×C4H(5,𝔽2)11yescharacteristic
205C3⋊Dic3—22no—
206C3×Dic3—42no—
207C22×D4—94no—
208C22×D4—182no—
209C2×D8—34no—
210C2×D8—91no—
211C2×D8—92no—
212C2×D8—92no—
213C2×D8—188no—
214C22×C8—92no—
215#127—32no—
216#121—94no—
217#121—182no—
218#120—184no—
219C4×D4—32no—
220C4×D4—91no—
221#107—91no—
222C4⋊C8D3211yescharacteristic, complemented
223#102—34no—
224#102—92no—
225C22⋊C8—92no—
226C4×C8—91no—
227C23×C3—62no—
228C23×C3—64no—
229C22×D3—22no—
230C22×D3—24no—
231C22×D3—34no—
232C22×D3—62no—
233C22×D3—128no—
234C22×D3—128no—
235C22×D3—128no—
236C22×D3—128no—
237C22×D3—244no—
238C22×D3—244no—
239C3×D4—34no—
240C3×D4—64no—
241C3×D4—62no—
242C3×D4—64no—
243C3×D4—124no—
244C3×D4—242no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—62no—
249C2×C3×C4—124no—
250C2×C3×C4D3×D412yes—
251C2×C3×C4D3×D412yes—
252C2×C3×C4C23×D312yes—
253#67—128no—
254#67—128no—
255#67—128no—
256C2×Dic3—22no—
257C2×Dic3—34no—
258C2×Dic3—62no—
259D12—24no—
260D12—22no—
261D12—24no—
262D12—38no—
263D12—44no—
264D12—64no—
265D12—82no—
266D12—128no—
267D12D3×D414yescomplemented
268C4×D3—44no—
269C4×D3—64no—
270C4×D3—64no—
271C4×D3—122no—
272C4×D3—122no—
273C3×C8—24no—
274C3×C8—42no—
275C3⋊C8—34no—
276C3⋊C8—62no—
277C3⋊C8—62no—
278C3⋊C8—121no—
279C2×C32D4211yescharacteristic
280C2×C32C22×D811yescharacteristic
281C2×C32#57611yescharacteristic
282C3⋊D3—24no—
283C3×D3—44no—
284C3×D3—84no—
285C24—184no—
286C2×D4—32no—
287C2×D4—34no—
288C2×D4—62no—
289C2×D4—62no—
290C2×D4—91no—
291C2×D4—184no—
292C2×D4—184no—
293C2×D4—188no—
294C2×D4—368no—
295C2×D4—364no—
296C22×C4—62no—
297C22×C4—92no—
298D8—68no—
299D8—94no—
300D8—184no—
301D8—362no—
302C2×C8—91no—
303C2×C8—91no—
304C2×C8—184no—
305C2×C8C2×D3212yes—
306C4⋊C4—32no—
307C4⋊C4—91no—
308C22⋊C4—62no—
309C22⋊C4—92no—
310C22⋊C4—184no—
311C42C2×D3211yescharacteristic
312C22×C3—21no—
313C22×C3—64no—
314C22×C3—122no—
315C22×C3—122no—
316C22×C3—124no—
317C22×C3—124no—
318C22×C3—124no—
319C22×C3C2×D3×D412yes—
320C2×D3—24no—
321C2×D3—38no—
322C2×D3—42no—
323C2×D3—42no—
324C2×D3—44no—
325C2×D3—44no—
326C2×D3—44no—
327C2×D3—64no—
328C2×D3—64no—
329C2×D3—64no—
330C2×D3—122no—
331C2×D3—122no—
332C2×D3—2416no—
333C2×D3—2416no—
334C3×C4—22no—
335C3×C4—22no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—122no—
340C3×C4D3×D814yescomplemented
341C3×C4C2×D3×D412yes—
342C3×C4#100912yes—
343Dic3—42no—
344Dic3—64no—
345Dic3—122no—
346C32D4×D811yescharacteristic, complemented, Sylow
347C23—62no—
348C23—64no—
349C23—92no—
350C23—368no—
351C23—368no—
352C23—724no—
353D4—34no—
354D4—64no—
355D4—62no—
356D4—64no—
357D4—94no—
358D4—124no—
359D4—242no—
360D4—368no—
361D4—368no—
362C2×C4—62no—
363C2×C4—92no—
364C2×C4—124no—
365C2×C4—182no—
366C2×C4—182no—
367C2×C4#380211yescharacteristic
368C2×C4#380211yescharacteristic
369C2×C4C22×D3211yescharacteristic
370C8—22no—
371C8—92no—
372C8—181no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—124no—
377C2×C3—244no—
378C2×C3#560912yes—
379C2×C3C2×D3×D812yes—
380C2×C3#577412yes—
381D3—44no—
382D3—68no—
383D3—84no—
384D3—124no—
385C22—64no—
386C22—94no—
387C22—122no—
388C22—122no—
389C22—124no—
390C22—124no—
391C22—124no—
392C22—182no—
393C22—182no—
394C22—7216no—
395C22C2×#380211yescharacteristic
396C4—21no—
397C4—122no—
398C4—182no—
399C4#6379712yescomplemented
400C4D32×D411yescharacteristic
401C4#6432011yescharacteristic
402C3—21no—
403C3#8035012yescomplemented
404C2—124no—
405C2—184no—
406C2—244no—
407C2#1059461811yescharacteristic
408C2C2×#6379711yescharacteristic
409C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63797C2semidirect
2. #10594004C2semidirect
3. #10592533C2semidirect
4. C3×#4843C2semidirect
5. #10590945C2semidirect
6. #10590839C2semidirect
7. #10590352C2semidirect
8. C4×#3713C2semidirect
10. C2×#3802C22semidirect
12. C2×C8×C3⋊D3C22semidirect
14. C2×C3×D24C22semidirect
15. C3×#874C22semidirect
16. C3×C4×D12C22semidirect
18. #63916C22semidirect
21. C2×#3713C22semidirect
22. C2×#3713C22semidirect
24. C32×C4⋊C8C22semidirect
25. #63647C22semidirect
26. C4×C3⋊(C3⋊C8)C22semidirect
27. C3×#821C22semidirect
28. #63576C22semidirect
29. #63562C22semidirect
37. #4843D3semidirect
68. #3713D4semidirect
85. C2×D24C2×D3semidirect
90. #874C2×D3semidirect
93. C4×D12C2×D3semidirect
95. C3×C4⋊C8C2×D3semidirect
98. #821C2×D3semidirect
115. C4⋊(C3⋊D3)D8semidirect
124. C3×D12C2×D4semidirect
130. C3⋊(C3⋊C8)C2×D4semidirect
193. C2×C3⋊D3C2×D8semidirect
202. C32×C4C2×D8semidirect
222. C4⋊C8D32semidirect
267. D12D3×D4semidirect
340. C3×C4D3×D8semidirect
346. C32D4×D8semidirect
399. C4#63797semidirect
403. C3#80350semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
#105940042
#105925332
C3×#48432
#105909452
#105908392
#105903522
C4×#37132
#803503