Finite Group Databasebeta

← #11878866

Subgroups — #11878866

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#10596049C211yesmaximal, characteristic, complemented
2#10594008C211yesmaximal, characteristic
3C3×#5027C212yesmaximal, complemented
4#10591652C212yesmaximal, complemented
5#10591620C212yesmaximal, complemented
6#10590597C212yesmaximal, complemented
7#10590552C212yesmaximal, complemented
8#10590377C212yesmaximal, complemented
9#10590256C211yesmaximal, characteristic, complemented
10#80387—32nomaximal
11C2×#3802—21no—
12C2×#3802—21no—
13C2×#3802C2212yes—
14C32×C4×Q8C2211yescharacteristic, complemented
15#64155C2211yescharacteristic
16#64153C2211yescharacteristic, complemented
17#64106C2211yescharacteristic
18#64105—21no—
19#64098—21no—
20#64097C2211yescharacteristic, complemented
21#64081—21no—
22C42×C3⋊D3C2211yescharacteristic
23C4×#634—21no—
24C4×#634C2211yescharacteristic, complemented
25C2×C3×#215C2214yescomplemented
26C3×#874C2212yes—
27#63914—21no—
28#63914—21no—
29#63914C2212yes—
30C2×#3716C2214yescomplemented
31C3×#809C2214yescomplemented
32C3×C4⋊(C3⋊C8)C2212yescomplemented
33#63563C2214yescomplemented
34#63557C2212yes—
35#63553C2212yescomplemented
36D3×#127—32no—
37#5578—32no—
38#5578—61no—
39C3×#460—32no—
40#5175—34no—
41#5169—34no—
42#5075—32no—
43#5027D312yescomplemented
44#4848—32no—
45#4833—32no—
46#4776—34no—
47#4760—34no—
48C22×D32—22no—
49C2×C32×Q8C2311yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3C2311yescharacteristic
53C2×#634—21no—
54C2×#634C2311yescharacteristic
55C2×C3×D12—22no—
56C2×C3×D12—22no—
57C2×C3×D12C2314yes—
58C2×#625—22no—
59C2×#625—22no—
60C2×#625—22no—
61#3802—44no—
62#3802—44no—
63#3802—44no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2311yescharacteristic
66C32×C42—21no—
67C32×C42C2311yescharacteristic
68#3752—21no—
69#3752—21no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)C2311yescharacteristic
72#3750—21no—
73#3750—21no—
74#3750—21no—
75#3750—21no—
76#3750—21no—
77C4×C3⋊Dic3—21no—
78C4×C3⋊Dic3D411yescharacteristic
79C4×C3⋊Dic3D411yescharacteristic
80C4×C3⋊Dic3C2311yescharacteristic
81C3×#215—44no—
82C2×C3×C3⋊C8C2314yes—
83#3716—44no—
84#3208—91noSylow
85C2×D3×D4—34no—
86C2×D3×D4—62no—
87C2×D3×D4—62no—
88C2×C3×SD16—34no—
89C3×#127—32no—
90C3×C4×Q8—21no—
91C3×C4×Q8C2×D312yescomplemented
92#946—32no—
93#946—61no—
94#944—32no—
95#944—61no—
96C2×#215C2×D314yescomplemented
97#940—34no—
98#940—62no—
99#940—62no—
100C2×#214—34no—
101C2×#204—34no—
102#897—32no—
103#897—61no—
104#896—62no—
105#896—62no—
106#889—62no—
107#889—62no—
108#888—32no—
109#888—61no—
110#874C2×D312yes—
111#872—62no—
112#872—62no—
113C42×D3—32no—
114C42×D3—61no—
115C4×Dic6—32no—
116C4×Dic6—61no—
117C4×Dic6—62no—
118C4×Dic6—62no—
119C3×C4⋊C8—32no—
120C3×#102—34no—
121#832—34no—
122#821—34no—
123(C2×D3)⋊C8—34no—
124C8×Dic3—34no—
125#809C2×D314yescomplemented
126C4⋊(C3⋊C8)C2×D312yescomplemented
127C22×C3⋊D3C2×D411yescharacteristic
128C22×C3×D3—24no—
129C2×D32—44no—
130C2×D32—44no—
131C2×D32—44no—
132C32×Q8—22no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C2×C3⋊Dic3C2×D411yescharacteristic
143C4×C3⋊D3—22no—
144C4×C3⋊D3—22no—
145C4×C3⋊D3SD1614yescomplemented
146#634—22no—
147#634—42no—
148C3×D12—24no—
149C3×D12—24no—
150C3×D12—44no—
151C3×D12—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—32no—
161#460—92no—
162#450—92no—
163#450—92no—
164#431—91no—
165C23×D3—64no—
166C2×C3×Q8—21no—
167C2×C3×Q8C22×D312yes—
168C2×C3×D4—34no—
169C2×C3×D4—62no—
170C2×C3×D4—62no—
171C2×#67—64no—
172C2×#67—64no—
173C2×#67—64no—
174D3×D4—128no—
175D3×D4—124no—
176D3×D4—124no—
177D3×D4—128no—
178C2×D12—22no—
179C2×D12—22no—
180C2×D12C22×D314yes—
181C2×C4×D3—32no—
182C2×C4×D3—32no—
183C2×C4×D3—32no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
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×C42—22no—
198C3×C42—22no—
199C3×C42—21no—
200C3×C42C22×D312yes—
201#215—44no—
202#214—124no—
203(C2×D3)⋊C4—62no—
204(C2×D3)⋊C4—62no—
205(C2×D3)⋊C4—62no—
206(C2×D3)⋊C4—62no—
207C4⋊Dic3—32no—
208C4⋊Dic3—61no—
209C4⋊Dic3—62no—
210C4⋊Dic3—62no—
211Dic3⋊C4—62no—
212Dic3⋊C4—62no—
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215Dic3⋊C4—62no—
216Dic3⋊C4—62no—
217Dic3⋊C4—62no—
218Dic3⋊C4—62no—
219Dic3⋊C4—62no—
220Dic3⋊C4—62no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—62no—
228C4×Dic3—62no—
229C2×C3⋊C8C22×D314yes—
230#204—124no—
231C22×C32C22×D411yescharacteristic
232C2×C3⋊D3—21no—
233C2×C3⋊D3—21no—
234C2×C3⋊D3C2×SD1612yes—
235C2×C3×D3—44no—
236C2×C3×D3—44no—
237C2×C3×D3—44no—
238D32—88no—
239C32×C4—21no—
240C32×C4—41no—
241C32×C4—41no—
242C32×C4C2×SD1612yes—
243C32×C4H(5,𝔽2)12yes—
244C3⋊Dic3—21no—
245C3⋊Dic3—41no—
246C3⋊Dic3—41no—
247C3⋊Dic3C2×SD1612yes—
248C3⋊Dic3AGL(1,ℤ/8)12yes—
249C22×D4—92no—
250C22×D4—181no—
251C22×D4—181no—
252C2×SD16—34no—
253C2×SD16—94no—
254C4⋊Q8—91no—
255C4⋊Q8—91no—
256#127—32no—
257#127—92no—
258#127—181no—
259#127—181no—
260#125—181no—
261C22⋊Q8—91no—
262C22⋊Q8—91no—
263C22⋊Q8—181no—
264C4×Q8—91no—
265C4×Q8—181no—
266C4×Q8D3211yescharacteristic, complemented
267#117—181no—
268C2×C42—91no—
269C4⋊C8—32no—
270#102—34no—
271#102—94no—
272C22⋊C8—92no—
273C4×C8—92no—
274C23×C3—64no—
275C22×D3—24no—
276C22×D3—32no—
277C22×D3—61no—
278C22×D3—128no—
279C22×D3—128no—
280C22×D3—128no—
281C3×Q8—22no—
282C3×Q8—22no—
283C3×Q8—42no—
284C3×D4—64no—
285C3×D4—64no—
286C3×D4—124no—
287C3×D4—124no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4D3×D412yes—
296C2×C3×C4D3×D412yes—
297C2×C3×C4C23×D312yes—
298#67—128no—
299#67—128no—
300#67—128no—
301C2×Dic3—32no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311D12—24no—
312D12—24no—
313D12—44no—
314D12—44no—
315C4×D3—38no—
316C4×D3—64no—
317C4×D3—64no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—122no—
321C4×D3—122no—
322Dic6—62no—
323Dic6—62no—
324Dic6—122no—
325Dic6—124no—
326Dic6—124no—
327C3×C8—64no—
328C3⋊C8—24no—
329C2×C32#53511yescharacteristic
330C2×C32C22×SD1611yescharacteristic
331C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
332C3⋊D3—22no—
333C3×D3—84no—
334C24—182no—
335C2×Q8—91no—
336C2×Q8—181no—
337C2×Q8C2×D3211yescharacteristic
338C2×D4—34no—
339C2×D4—62no—
340C2×D4—62no—
341C2×D4—182no—
342C2×D4—182no—
343C2×D4—182no—
344C2×D4—364no—
345C2×D4—364no—
346C2×D4—364no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—91no—
350SD16—124no—
351SD16—364no—
352C2×C8—34no—
353C4⋊C4—21no—
354C4⋊C4—91no—
355C4⋊C4—181no—
356C4⋊C4—181no—
357C4⋊C4—181no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C4⋊C4C2×D3211yescharacteristic
362C22⋊C4—181no—
363C22⋊C4—181no—
364C42—21no—
365C42—91no—
366C42—91no—
367C42—91no—
368C42—181no—
369C42C2×D3211yescharacteristic
370C22×C3—21no—
371C22×C3—124no—
372C22×C3—124no—
373C22×C3—124no—
374C22×C3C2×D3×D412yes—
375C2×D3—34no—
376C2×D3—44no—
377C2×D3—44no—
378C2×D3—44no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—62no—
382C2×D3—121no—
383C2×D3—121no—
384C2×D3—2416no—
385C3×C4—22no—
386C3×C4—22no—
387C3×C4—22no—
388C3×C4—41no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4—42no—
393C3×C4D3×SD1614yes—
394C3×C4#100412yes—
395C3×C4#100912yes—
396Dic3—34no—
397Dic3—34no—
398Dic3—62no—
399Dic3—62no—
400Dic3—62no—
401Dic3—121no—
402Dic3—122no—
403Dic3—122no—
404Dic3—122no—
405Dic3—122no—
406C32#320811yescharacteristic, complemented, Sylow
407C23—64no—
408C23—91no—
409C23—364no—
410C23—364no—
411C23—364no—
412Q8—22no—
413Q8—182no—
414Q8—362no—
415D4—64no—
416D4—64no—
417D4—124no—
418D4—124no—
419D4—364no—
420D4—364no—
421D4—364no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—91no—
425C2×C4—91no—
426C2×C4—94no—
427C2×C4—91no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4#381111yescharacteristic
433C2×C4#381111yescharacteristic
434C2×C4C22×D3211yescharacteristic
435C8—64no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—244no—
440C2×C3#560712yes—
441C2×C3C2×D3×SD1612yes—
442C2×C3D3×AGL(1,ℤ/8)12yes—
443D3—64no—
444D3—84no—
445D3—122no—
446C22—92no—
447C22—124no—
448C22—124no—
449C22—124no—
450C22—181no—
451C22—181no—
452C22—728no—
453C22C2×#381111yescharacteristic
454C4—21no—
455C4—41no—
456C4—41no—
457C4—92no—
458C4—92no—
459C4—181no—
460C4—361no—
461C4—361no—
462C4#6394012yes—
463C4#6430712yes—
464C3—21no—
465C3#8038712yescomplemented
466C2—182no—
467C2—244no—
468C2#1059508211yescharacteristic
469C2C2×#6394011yescharacteristic
470C2#1059545811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594008C2
hypercenterC4×Q8D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596049C2semidirect
3. C3×#5027C2semidirect
4. #10591652C2semidirect
5. #10591620C2semidirect
6. #10590597C2semidirect
7. #10590552C2semidirect
8. #10590377C2semidirect
9. #10590256C2semidirect
14. C32×C4×Q8C22semidirect
16. #64153C22semidirect
20. #64097C22semidirect
24. C4×#634C22semidirect
25. C2×C3×#215C22semidirect
30. C2×#3716C22semidirect
31. C3×#809C22semidirect
32. C3×C4⋊(C3⋊C8)C22semidirect
33. #63563C22semidirect
35. #63553C22semidirect
43. #5027D3semidirect
91. C3×C4×Q8C2×D3semidirect
96. C2×#215C2×D3semidirect
125. #809C2×D3semidirect
126. C4⋊(C3⋊C8)C2×D3semidirect
145. C4×C3⋊D3SD16semidirect
266. C4×Q8D32semidirect
406. C32#3208semidirect
465. C3#80387semidirect

Maximal subgroups

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

subgroupindex
#105960492
#105940082
C3×#50272
#105916522
#105916202
#105905972
#105905522
#105903772
#105902562
#803873