Finite Group Databasebeta

← #11878629

Subgroups — #11878629

Order 1152.

1596 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 241 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#10596187C211yesmaximal, characteristic, complemented
2C3⋊D3×#127C211yesmaximal, characteristic, complemented
3C32×#493C211yesmaximal, characteristic, complemented
4#10592855C214yesmaximal, complemented
5#10592849C214yesmaximal, complemented
6#10592772C211yesmaximal, characteristic, complemented
7#10592769C211yesmaximal, characteristic, complemented
8#10592393C211yesmaximal, characteristic, complemented
9#10592384C211yesmaximal, characteristic, complemented
10#81785—34nomaximal
11C2×#3830—21no—
12C2×D4×C3⋊D3—21no—
13C2×D4×C3⋊D3—21no—
14C2×D4×C3⋊D3C2212yes—
15C2×C32×D8C2214yescomplemented
16C32×#127C2211yescharacteristic
17C32×#127C2211yescharacteristic, complemented
18#64149—21no—
19#64149—21no—
20#64149C2212yes—
21#64147—21no—
22#64147C2212yes—
23#64145—21no—
24D4×C3⋊Dic3—21no—
25D4×C3⋊Dic3C2212yescomplemented
26C2×#3753C2214yescomplemented
27#64083C2211yescharacteristic
28C42×C3⋊D3C2211yescharacteristic
29#64078C2211yescharacteristic, complemented
30C32×C4×C8C2211yescharacteristic, complemented
31#63659C2214yescomplemented
32#63648C2214yescomplemented
33#63647C2212yes—
34#63641C2212yescomplemented
35C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
36#5716—34no—
37D3×#127—34no—
38C3×#493D314yescomplemented
39#5156—316no—
40#5150—316no—
41#5073—34no—
42#5070—34no—
43#4694—34no—
44#4685—34no—
45C23×C3⋊D3—22no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4C2312yes—
51C2×C32×D4C2312yes—
52C2×#638—22no—
53C2×#638—22no—
54C2×#638—22no—
55C2×#638—22no—
56C22×C3⋊Dic3—22no—
57#3830—44no—
58D4×C3⋊D3—44no—
59D4×C3⋊D3—44no—
60D4×C3⋊D3—44no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×#634—21no—
68C32×D8—44no—
69C2×C32×C8C2312yes—
70C32×C42C2311yescharacteristic
71#3757—22no—
72#3757—22no—
73#3753—44no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76C4×C3⋊Dic3D411yescharacteristic
77C4×C3⋊Dic3D411yescharacteristic
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2312yes—
80#3205—91noSylow
81C2×#237—64no—
82C2×D3×D4—38no—
83C2×D3×D4—64no—
84C2×D3×D4—64no—
85C2×C3×D8C2×D3116yescomplemented
86C3×#127C2×D314yes—
87C3×#127C2×D314yescomplemented
88#940—38no—
89#940—64no—
90#940—64no—
91#938—38no—
92#938—64no—
93#936—64no—
94D4×Dic3—38no—
95D4×Dic3—64no—
96C2×#213—316no—
97#874—34no—
98C42×D3—34no—
99#869—34no—
100C3×C4×C8C2×D314yescomplemented
101#832—316no—
102#821—316no—
103(C2×D3)⋊C8—38no—
104Dic3⋊C8—38no—
105C4×C3⋊C8—34no—
106C23×C32—22no—
107C23×C32—22no—
108C22×C3⋊D3—22no—
109C22×C3⋊D3—44no—
110C22×C3⋊D3—44no—
111C22×C3⋊D3—44no—
112C22×C3⋊D3C2×D411yescharacteristic
113C32×D4—24no—
114C32×D4—24no—
115C32×D4—42no—
116C32×D4—42no—
117C32×D4—42no—
118C32×D4—42no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2411yescharacteristic
122#638—44no—
123#638—44no—
124#638—44no—
125#638—44no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—44no—
128C2×C3⋊Dic3C2×D411yescharacteristic
129C2×C3⋊Dic3C2×D411yescharacteristic
130C2×C3⋊Dic3C2×D411yescharacteristic
131C4⋊(C3⋊D3)—24no—
132C4⋊(C3⋊D3)—42no—
133C4⋊(C3⋊D3)—42no—
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C4×C3⋊D3D814yescomplemented
137#634—42no—
138C32×C8—22no—
139C3⋊(C3⋊C8)—22no—
140#532—91no—
141C2×#127—91no—
142#493—91no—
143#493C3⋊D311yescharacteristic, complemented
144#486—91no—
145#486—91no—
146#459—94no—
147#447—94no—
148#431—91no—
149C23×D3—68no—
150C2×C3×D4—24no—
151C2×C3×D4—24no—
152C2×C3×D4—24no—
153C2×C3×D4—24no—
154C2×C3×D4C22×D318yes—
155C2×C3×D4C22×D318yes—
156C2×#67—68no—
157C2×#67—68no—
158C2×#67—68no—
159C2×#67—68no—
160C22×Dic3—68no—
161#237—1216no—
162D3×D4—1216no—
163D3×D4—1216no—
164D3×D4—1216no—
165C2×D12—38no—
166C2×D12—64no—
167C2×D12—64no—
168C2×C4×D3—34no—
169C2×C4×D3—34no—
170C2×C4×D3—34no—
171C2×Dic6—64no—
172C3×D8—416no—
173C2×C3×C8C22×D318yes—
174C3×C42C22×D314yes—
175#217—68no—
176#217—68no—
177#213—1216no—
178C4⋊Dic3—38no—
179C4⋊Dic3—64no—
180C4×Dic3—34no—
181C4×Dic3—34no—
182C4×Dic3—34no—
183C2×C3⋊C8—38no—
184C22×C32—42no—
185C22×C32—42no—
186C22×C32—42no—
187C22×C32—42no—
188C22×C32—42no—
189C22×C32—42no—
190C22×C32C22×D411yescharacteristic
191C2×C3⋊D3—21no—
192C2×C3⋊D3—21no—
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—42no—
196C2×C3⋊D3—88no—
197C2×C3⋊D3C2×D812yes—
198C32×C4C2×D812yes—
199C32×C4AGL(1,ℤ/8)12yes—
200C32×C4H(5,𝔽2)12yes—
201C3⋊Dic3—21no—
202C3⋊Dic3—21no—
203C3⋊Dic3—42no—
204C3⋊Dic3C2×D812yes—
205C2×#41—181no—
206C22×D4—92no—
207C22×D4—181no—
208C22×D4—181no—
209C2×D8—94no—
210C2×D8C2×C3⋊D314yescomplemented
211C4⋊Q8—91no—
212#127—92no—
213#127—91no—
214#127—181no—
215#127—181no—
216#127C2×C3⋊D311yescharacteristic
217#127C2×C3⋊D311yescharacteristic, complemented
218#124—181no—
219#121—92no—
220#121—181no—
221C4×D4—92no—
222C4×D4—181no—
223C2×C42—91no—
224C4⋊C8—92no—
225#102—94no—
226#102—94no—
227C22⋊C8—92no—
228C4×C8—91no—
229C4×C8C2×C3⋊D311yescharacteristic, complemented
230C23×C3—28no—
231C23×C3—28no—
232C22×D3—34no—
233C22×D3—68no—
234C22×D3—1216no—
235C22×D3—1216no—
236C22×D3—1216no—
237C3×D4—216no—
238C3×D4—216no—
239C3×D4—48no—
240C3×D4—48no—
241C3×D4—48no—
242C3×D4—48no—
243C2×C3×C4D3×D414yes—
244C2×C3×C4D3×D414yes—
245C2×C3×C4C23×D314yes—
246#67—1216no—
247#67—1216no—
248#67—1216no—
249#67—1216no—
250C2×Dic3—34no—
251C2×Dic3—34no—
252C2×Dic3—34no—
253C2×Dic3—68no—
254C2×Dic3—1216no—
255D12—616no—
256D12—128no—
257D12—128no—
258C4×D3—316no—
259C4×D3—68no—
260C4×D3—68no—
261Dic6—128no—
262C3×C8—28no—
263C3⋊C8—68no—
264C2×C32—82no—
265C2×C32—82no—
266C2×C32#53511yescharacteristic
267C2×C32C22×D811yescharacteristic
268C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
269C3⋊D3—22no—
270C3⋊D3—82no—
271C24—182no—
272#41—364no—
273C2×Q8—181no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—92no—
279C2×D4—182no—
280C2×D4—182no—
281C2×D4—182no—
282C2×D4—182no—
283C2×D4—181no—
284C2×D4—181no—
285C2×D4—364no—
286C2×D4—364no—
287C2×D4—364no—
288C2×D4C22×C3⋊D312yes—
289C2×D4C22×C3⋊D312yes—
290C22×C4—91no—
291C22×C4—91no—
292C22×C4—91no—
293C22×C4—182no—
294D8—44no—
295D8—364no—
296C2×C8—92no—
297C2×C8C22×C3⋊D312yes—
298C4⋊C4—92no—
299C4⋊C4—181no—
300C22⋊C4—182no—
301C22⋊C4—182no—
302C42—91no—
303C42—91no—
304C42—91no—
305C42C22×C3⋊D311yescharacteristic
306C22×C3—48no—
307C22×C3—48no—
308C22×C3—48no—
309C22×C3—48no—
310C22×C3—48no—
311C22×C3—48no—
312C22×C3C2×D3×D414yes—
313C2×D3—38no—
314C2×D3—64no—
315C2×D3—64no—
316C2×D3—128no—
317C2×D3—128no—
318C2×D3—128no—
319C2×D3—2432no—
320C3×C4D3×D818yes—
321C3×C4#91118yes—
322C3×C4#100418yes—
323Dic3—38no—
324Dic3—64no—
325Dic3—64no—
326Dic3—128no—
327C32#320511yescharacteristic, complemented, Sylow
328C23—22no—
329C23—22no—
330C23—91no—
331C23—182no—
332C23—364no—
333C23—364no—
334C23—364no—
335Q8—362no—
336D4—24no—
337D4—24no—
338D4—42no—
339D4—42no—
340D4—42no—
341D4—42no—
342D4—184no—
343D4—364no—
344D4—364no—
345D4—364no—
346D4—364no—
347D4—362no—
348D4—362no—
349C2×C4—91no—
350C2×C4—94no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—364no—
357C2×C4D4×C3⋊D311yescharacteristic
358C2×C4D4×C3⋊D311yescharacteristic
359C2×C4C23×C3⋊D311yescharacteristic
360C8—22no—
361C8—182no—
362C2×C3—88no—
363C2×C3—88no—
364C2×C3#571514yes—
365C2×C3C2×D3×D814yes—
366C2×C3C2×#91114yes—
367D3—68no—
368D3—248no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—92no—
376C22—181no—
377C22—181no—
378C22—362no—
379C22—362no—
380C22—362no—
381C22—728no—
382C22C2×D4×C3⋊D311yescharacteristic
383C4—92no—
384C4—181no—
385C4—181no—
386C4—362no—
387C4D8×C3⋊D312yes—
388C4#6412012yes—
389C4#6436112yes—
390C3#8178514yescomplemented
391C2—82no—
392C2—82no—
393C2—182no—
394C2—722no—
395C2#1059618611yescharacteristic
396C2C2×D8×C3⋊D311yescharacteristic
397C2C2×#6412011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#493C2
socleC22×C32C22×D4
hypercenter#493C3⋊D3
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #10596187C2semidirect
2. C3⋊D3×#127C2semidirect
3. C32×#493C2semidirect
4. #10592855C2semidirect
5. #10592849C2semidirect
6. #10592772C2semidirect
7. #10592769C2semidirect
8. #10592393C2semidirect
9. #10592384C2semidirect
15. C2×C32×D8C22semidirect
17. C32×#127C22semidirect
25. D4×C3⋊Dic3C22semidirect
26. C2×#3753C22semidirect
29. #64078C22semidirect
30. C32×C4×C8C22semidirect
31. #63659C22semidirect
32. #63648C22semidirect
34. #63641C22semidirect
35. C4×C3⋊(C3⋊C8)C22semidirect
38. C3×#493D3semidirect
85. C2×C3×D8C2×D3semidirect
87. C3×#127C2×D3semidirect
100. C3×C4×C8C2×D3semidirect
136. C4×C3⋊D3D8semidirect
143. #493C3⋊D3semidirect
210. C2×D8C2×C3⋊D3semidirect
217. #127C2×C3⋊D3semidirect
229. C4×C8C2×C3⋊D3semidirect
327. C32#3205semidirect
390. C3#81785semidirect

Maximal subgroups

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

subgroupindex
#105961872
C3⋊D3×#1272
C32×#4932
#105928552
#105928492
#105927722
#105927692
#105923932
#105923842
#817853