Finite Group Databasebeta

← #11878856

Subgroups — #11878856

Order 1152.

1087 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 1087 conjugacy classes of subgroups — too many to draw. Only its 166 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#10596093C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic
3C3×#5046C212yesmaximal, complemented
4#10591622C212yesmaximal, complemented
5#10591620C212yesmaximal, complemented
6#10591172C212yesmaximal, complemented
7#10591061C211yesmaximal, characteristic, complemented
8#10590553C212yesmaximal, complemented
9#10590552C212yesmaximal, complemented
10#80138—32nomaximal
11C22×C3×D12C2212yes—
12C22×#625—21no—
13C22×#625—21no—
14C32×C22⋊Q8C2211yescharacteristic
15Q8×C3⋊Dic3C2211yescharacteristic, complemented
16#64153C2211yescharacteristic, complemented
17#64133C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19#64098—21no—
20#64097C2211yescharacteristic, complemented
21#64096—21no—
22#64096C2211yescharacteristic, complemented
23#64087—21no—
24#64086—21no—
25C2×C3×#215C2214yescomplemented
26#63914—21no—
27#63914—21no—
28#63914C2212yes—
29#63914C2212yes—
30C2×#3716C2214yescomplemented
31C3×#830C2212yes—
32C3×#809C2214yescomplemented
33#63572C2212yescomplemented
34#63563C2214yescomplemented
35#63553C2212yescomplemented
36C2×#940—32no—
37#5622—32no—
38#5622—61no—
39C3×#450—32no—
40#5218—32no—
41#5175—34no—
42#5163—34no—
43#5046D312yescomplemented
44#4762—34no—
45#4760—34no—
46#4731—32no—
47#4718—32no—
48C23×C3×D3—22no—
49C2×C32×Q8C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C2×#634—21no—
54C2×#634C2311yescharacteristic
55C2×C3×D12—22no—
56C2×C3×D12—44no—
57C2×C3×D12C2314yes—
58C2×#625—22no—
59C2×#625—22no—
60C2×#625—22no—
61C2×#625—22no—
62C2×#625—44no—
63C2×#625—44no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2311yescharacteristic
66C32×C22⋊C4—21no—
67#3757—21no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)C2311yescharacteristic
70#3750—21no—
71#3750—21no—
72#3750—21no—
73#3750—21no—
74#3750—21no—
75C4×C3⋊Dic3—21no—
76C4×C3⋊Dic3—21no—
77C4×C3⋊Dic3D411yescharacteristic
78C4×C3⋊Dic3D411yescharacteristic
79C4×C3⋊Dic3C2311yescharacteristic
80C4×C3⋊Dic3C2311yescharacteristic
81C3×#215—44no—
82C2×C3×C3⋊C8C2314yes—
83#3716—44no—
84#3208—91noSylow
85C22×C3×D4—32no—
86C22×#67—62no—
87C22×#67—62no—
88C22×D12C2×D312yes—
89C2×C3×SD16—34no—
90C3×C22⋊Q8—21no—
91C3×C22⋊Q8C2×D312yes—
92Q8×Dic3—32no—
93Q8×Dic3—61no—
94#944—32no—
95#944—61no—
96C2×#215C2×D314yescomplemented
97#940—34no—
98#940—34no—
99#940—62no—
100#940—62no—
101C2×#214—34no—
102#924—32no—
103#924—61no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—61no—
106C2×#204—34no—
107#889—62no—
108#889—62no—
109#888—32no—
110#888—61no—
111#887—32no—
112#887—61no—
113#887—62no—
114#887—62no—
115#878—62no—
116#878—62no—
117#877—62no—
118#877—62no—
119C3×#102—34no—
120C3×C22⋊C8—32no—
121#832—34no—
122#830C2×D312yes—
123#821—34no—
124Dic3⋊C8—34no—
125C8×Dic3—34no—
126#809C2×D314yescomplemented
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—24no—
129C22×C3×D3—44no—
130C22×C3×D3—44no—
131C22×C3×D3—44no—
132C32×Q8—22no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—22no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3SD1614yescomplemented
142C2×C3⋊Dic3C2×D411yescharacteristic
143C2×C3⋊Dic3C2×D411yescharacteristic
144C2×C3⋊Dic3C2×D411yescharacteristic
145C2×C3⋊Dic3C2×D411yescharacteristic
146#634—22no—
147#634—42no—
148C3×D12—24no—
149C3×D12—24no—
150C3×D12—44no—
151#625—44no—
152#625—44no—
153#625—44no—
154#625—44no—
155C3×C3⋊C8—24no—
156#533—91no—
157C2×#127—91no—
158#492—92no—
159#486—92no—
160#460—92no—
161#460—92no—
162#450—32no—
163#450—92no—
164#431—91no—
165C24×C3—62no—
166C23×D3—22no—
167C2×C3×Q8—21no—
168C2×C3×Q8C22×D312yes—
169C2×C3×D4—34no—
170C2×C3×D4—62no—
171C2×C3×D4—124no—
172C22×C3×C4—21no—
173C22×C3×C4C22×D312yes—
174C2×#67—64no—
175C2×#67—64no—
176C2×#67—64no—
177C2×#67—64no—
178C2×#67—128no—
179C2×#67—128no—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C2×D12—22no—
185C2×D12—44no—
186C2×D12C22×D314yes—
187C2×Dic6—32no—
188C2×Dic6—61no—
189C2×Dic6—62no—
190C2×Dic6—62no—
191C3×SD16—124no—
192C2×C3×C8—34no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4C22×D312yes—
197C3×C22⋊C4—22no—
198C3×C22⋊C4—22no—
199#217—62no—
200#217—62no—
201#215—44no—
202#214—124no—
203C4⋊Dic3—32no—
204C4⋊Dic3—61no—
205C4⋊Dic3—62no—
206C4⋊Dic3—62no—
207Dic3⋊C4—62no—
208Dic3⋊C4—62no—
209Dic3⋊C4—62no—
210Dic3⋊C4—62no—
211Dic3⋊C4—62no—
212Dic3⋊C4—62no—
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215Dic3⋊C4—62no—
216Dic3⋊C4—62no—
217C4×Dic3—32no—
218C4×Dic3—32no—
219C4×Dic3—32no—
220C4×Dic3—32no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—62no—
226C4×Dic3—62no—
227C4×Dic3—62no—
228C4×Dic3—62no—
229C2×C3⋊C8C22×D314yes—
230#204—124no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32C2×SD1612yes—
234C22×C32C22×D411yescharacteristic
235C2×C3×D3—44no—
236C2×C3×D3—44no—
237C2×C3×D3—44no—
238C2×C3×D3—88no—
239C32×C4—21no—
240C32×C4—41no—
241C32×C4—41no—
242C32×C4H(5,𝔽2)12yes—
243C3⋊Dic3—21no—
244C3⋊Dic3—41no—
245C3⋊Dic3—41no—
246C3⋊Dic3C2×SD1612yes—
247C3⋊Dic3C2×SD1612yes—
248C3⋊Dic3AGL(1,ℤ/8)12yes—
249C22×D4—32no—
250C22×D4—181no—
251C22×D4—181no—
252C2×SD16—34no—
253C2×SD16—94no—
254C4⋊Q8—91no—
255C4⋊Q8—91no—
256#127—92no—
257#127—92no—
258#127—181no—
259#127—181no—
260#125—181no—
261C22⋊Q8—91no—
262C22⋊Q8—181no—
263C22⋊Q8D3211yescharacteristic
264C4×Q8—91no—
265C4×Q8—91no—
266C4×Q8—181no—
267#117—181no—
268C2×C42—91no—
269C4⋊C8—92no—
270#102—34no—
271#102—94no—
272C22⋊C8—32no—
273C4×C8—92no—
274C23×C3—21no—
275C23×C3—64no—
276C23×C3—124no—
277C23×C3—124no—
278C23×C3—124no—
279C23×C3D3×D412yes—
280C22×D3—24no—
281C22×D3—44no—
282C22×D3—44no—
283C22×D3—44no—
284C3×Q8—24no—
285C3×Q8—42no—
286C3×D4—64no—
287C3×D4—64no—
288C3×D4—124no—
289C2×C3×C4—24no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—42no—
297C2×C3×C4D3×D412yes—
298C2×C3×C4C23×D312yes—
299#67—128no—
300#67—128no—
301#67—128no—
302#67—128no—
303C2×Dic3—38no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—32no—
308C2×Dic3—64no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—64no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—122no—
319D12—24no—
320D12—24no—
321D12—44no—
322Dic6—64no—
323Dic6—122no—
324Dic6—124no—
325Dic6—124no—
326C3×C8—64no—
327C3⋊C8—24no—
328C2×C32—22no—
329C2×C32#53511yescharacteristic
330C2×C32C22×SD1611yescharacteristic
331C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
332C3×D3—84no—
333C24—62no—
334C2×Q8—91no—
335C2×Q8—181no—
336C2×Q8C2×D3211yescharacteristic
337C2×D4—34no—
338C2×D4—62no—
339C2×D4—124no—
340C2×D4—182no—
341C2×D4—182no—
342C2×D4—182no—
343C2×D4—182no—
344C2×D4—364no—
345C2×D4—364no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4C2×D3211yescharacteristic
349SD16—124no—
350SD16—364no—
351C2×C8—34no—
352C4⋊C4—21no—
353C4⋊C4—91no—
354C4⋊C4—181no—
355C4⋊C4—181no—
356C4⋊C4—181no—
357C4⋊C4—181no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4C2×D3211yescharacteristic
361C22⋊C4—21no—
362C22⋊C4—181no—
363C42—91no—
364C42—91no—
365C42—91no—
366C42—91no—
367C42—181no—
368C42—181no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—21no—
372C22×C3—22no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—124no—
376C22×C3—124no—
377C22×C3—124no—
378C22×C3—248no—
379C22×C3D3×SD1614yes—
380C22×C3C2×D3×D412yes—
381C2×D3—44no—
382C2×D3—44no—
383C2×D3—44no—
384C2×D3—88no—
385C3×C4—22no—
386C3×C4—22no—
387C3×C4—41no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4#100414yes—
393Dic3—34no—
394Dic3—34no—
395Dic3—34no—
396Dic3—62no—
397Dic3—62no—
398Dic3—62no—
399Dic3—62no—
400Dic3—121no—
401Dic3—122no—
402Dic3—122no—
403Dic3—122no—
404Dic3—122no—
405C32#320811yescharacteristic, complemented, Sylow
406C23—64no—
407C23—124no—
408C23—124no—
409C23—124no—
410C23#381111yescharacteristic
411Q8—22no—
412Q8—182no—
413Q8—362no—
414D4—64no—
415D4—64no—
416D4—124no—
417D4—364no—
418D4—364no—
419D4—364no—
420D4—364no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—91no—
425C2×C4—91no—
426C2×C4—91no—
427C2×C4—94no—
428C2×C4—91no—
429C2×C4—182no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4#381111yescharacteristic
433C2×C4C22×D3211yescharacteristic
434C8—64no—
435C2×C3—24no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—42no—
440C2×C3—244no—
441C2×C3#559212yes—
442C2×C3C2×D3×SD1612yes—
443C2×C3D3×AGL(1,ℤ/8)12yes—
444D3—84no—
445C22—21no—
446C22—21no—
447C22—124no—
448C22—124no—
449C22—124no—
450C22—248no—
451C22#6394012yes—
452C22C2×#381111yescharacteristic
453C4—21no—
454C4—41no—
455C4—41no—
456C4—92no—
457C4—92no—
458C4—92no—
459C4—181no—
460C4—361no—
461C4—361no—
462C4#6431312yes—
463C3—21no—
464C3#8013812yescomplemented
465C2—22no—
466C2—244no—
467C2#1059523911yescharacteristic
468C2C2×#6394011yescharacteristic
469C2#1059545811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#63914C2
hypercenterC22⋊Q8D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596093C2semidirect
3. C3×#5046C2semidirect
4. #10591622C2semidirect
5. #10591620C2semidirect
6. #10591172C2semidirect
7. #10591061C2semidirect
8. #10590553C2semidirect
9. #10590552C2semidirect
15. Q8×C3⋊Dic3C22semidirect
16. #64153C22semidirect
20. #64097C22semidirect
22. #64096C22semidirect
25. C2×C3×#215C22semidirect
30. C2×#3716C22semidirect
32. C3×#809C22semidirect
33. #63572C22semidirect
34. #63563C22semidirect
35. #63553C22semidirect
43. #5046D3semidirect
96. C2×#215C2×D3semidirect
126. #809C2×D3semidirect
141. C2×C3⋊Dic3SD16semidirect
405. C32#3208semidirect
464. C3#80138semidirect

Maximal subgroups

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

subgroupindex
#105960932
C2×#639142
C3×#50462
#105916222
#105916202
#105911722
#105910612
#105905532
#105905522
#801383