Finite Group Databasebeta

← #11858037

Subgroups — #11858037

Order 1152.

1703 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2#10596298C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4#10591088C213yesmaximal, complemented
5#10591086C213yesmaximal, complemented
6#10591084C213yesmaximal, complemented
7C2×#63563C213yesmaximal, complemented
8#84099—31nomaximal
9#83797—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C3×#1009—24no—
12C3×#1009C418yescomplemented
13C2×C3×#239—21no—
14C2×C3×D3×D4—23no—
15C2×C3×#235C2213yes—
16C22×C3×D12C2213yes—
17Q8×C3⋊Dic3—21no—
18D4×C3⋊Dic3—23no—
19#64135C2213yescomplemented
20C2×C4⋊(C3⋊Dic3)C2213yescomplemented
21C3×#948—24no—
22C2×C3×#208C2213yescomplemented
23C22×C3×C3⋊C8C2213yescomplemented
24#63566C2211yescharacteristic, complemented
25#63566C2213yescomplemented
26#63563C2213yescomplemented
27#63563C2216yescomplemented
28#63563C2213yescomplemented
29C2×C3×H(5,𝔽2)—31no—
30C2×#1009D311yescharacteristic
31C2×C3×#131—31no—
32#5827—31no—
33#5827—31no—
34#5827—61no—
35C2×#948D311yescharacteristic, complemented
36#5233—33no—
37#5232—33no—
38#5215—33no—
39C2×#832—33no—
40#5133—33no—
41#5131—33no—
42#5113—33no—
43C2×#821—33no—
44C23×C3×D3—23no—
45C32×#41C2×C414yes—
46C32×#41D414yes—
47C2×C32×Q8D411yescharacteristic
48C2×C32×D4D413yes—
49C22×C32×C4C2313yes—
50C22×C3⋊Dic3—23no—
51C2×C3×#67—23no—
52C3×#239—28no—
53C3×D3×D4—224no—
54C3×#235—26no—
55C3×#235C2×C4112yescomplemented
56C2×C3×D12—23no—
57C2×C3×D12—26no—
58C2×C3×D12C2×C4112yescomplemented
59C2×C3×D12C2313yes—
60C2×C3×C4×D3—23no—
61C2×C3×Dic6C2311yescharacteristic
62#3757—23no—
63C4⋊(C3⋊Dic3)—23no—
64C4⋊(C3⋊Dic3)C2313yes—
65C4⋊(C3⋊Dic3)C2311yescharacteristic
66C4×C3⋊Dic3—23no—
67C3×#208—26no—
68C2×C3×C3⋊C8—26no—
69C2×C3×C3⋊C8C2311yescharacteristic
70C2×C3×C3⋊C8C2313yes—
71#2897—91noSylow
72C3×H(5,𝔽2)—38no—
73C3×H(5,𝔽2)—64no—
74C2×C3×#41—21no—
75C2×C3×#41—33no—
76C2×C3×#41—61no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C2×D311yescharacteristic
79C22×C3×D4—33no—
80C22×C3×D4—63no—
81#1009—24no—
82#1009Dic318yescomplemented
83C2×#239—21no—
84C2×D3×D4—23no—
85C2×#235C2×D313yes—
86C22×D12C2×D313yes—
87C3×#131—64no—
88C2×C3×M16—33no—
89C22×C3×C8—33no—
90#948—24no—
91Q8×Dic3—62no—
92Q8×Dic3—61no—
93Q8×Dic3—61no—
94D4×Dic3—66no—
95D4×Dic3—63no—
96D4×Dic3—63no—
97#926—33no—
98#926—33no—
99#926—63no—
100C2×C4⋊Dic3—33no—
101C2×C4⋊Dic3—33no—
102C2×C4⋊Dic3—63no—
103C2×#208C2×D313yescomplemented
104C22×C3⋊C8C2×D313yescomplemented
105#835—33no—
106#835—31no—
107#832—33no—
108#832—36no—
109#832—33no—
110#821—33no—
111#821—36no—
112#821—33no—
113#816—33no—
114#816—31no—
115C23×C32C2×D413yes—
116C22×C3×D3—23no—
117C22×C3×D3—212no—
118C22×C3×D3—83no—
119C22×C3×D3—83no—
120C32×Q8C22⋊C414yes—
121C32×D4C22⋊C4112yes—
122C2×C32×C4C22×C416yes—
123C2×C32×C4C2×D413yes—
124C2×C32×C4C2×D416yes—
125C2×C32×C4C2411yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—23no—
128C2×C3⋊Dic3—83no—
129C3×#67—212no—
130C2×C3×Dic3—21no—
131C3×D12—212no—
132C3×D12—23no—
133C3×D12C22×C416yes—
134C3×C4×D3—212no—
135C3×Dic6—21no—
136C3×Dic6C22×C412yes—
137C3×C3⋊C8—21no—
138C3×C3⋊C8—23no—
139C2×H(5,𝔽2)—31no—
140C2×#131—31no—
141#520—91no—
142#418—93no—
143#417—93no—
144#416—93no—
145C2×#102—93no—
146C24×C3—63no—
147C23×D3—23no—
148C3×#41—24no—
149C3×#41—24no—
150C3×#41—312no—
151C3×#41—68no—
152C3×#41—66no—
153C3×#41C4×D314yes—
154C3×#41C2×Dic314yes—
155C3×#41#6714yes—
156C3×#41#6714yes—
157C2×C3×Q8—21no—
158C2×C3×Q8—31no—
159C2×C3×Q8D1211yescharacteristic
160C2×C3×Q8#6711yescharacteristic
161C2×C3×D4—23no—
162C2×C3×D4—312no—
163C2×C3×D4—33no—
164C2×C3×D4—63no—
165C2×C3×D4—624no—
166C2×C3×D4—63no—
167C2×C3×D4—66no—
168C2×C3×D4D1213yes—
169C2×C3×D4#6713yes—
170C22×C3×C4—23no—
171C22×C3×C4—63no—
172C22×C3×C4C22×D313yes—
173C22×C3×C4C22×D313yes—
174C2×#67—23no—
175C22×Dic3—66no—
176C22×Dic3—63no—
177C22×Dic3—63no—
178#239—28no—
179D3×D4—224no—
180#235—26no—
181#235C2×Dic3112yescomplemented
182C2×D12—23no—
183C2×D12—26no—
184C2×D12C2×Dic3112yescomplemented
185C2×D12C22×D313yes—
186C2×C4×D3—23no—
187C2×Dic6C22×D311yescharacteristic
188C3×M16—66no—
189C2×C3×C8—31no—
190C2×C3×C8—33no—
191C2×C3×C8—66no—
192#217—66no—
193#217—63no—
194#217—63no—
195C4⋊Dic3—33no—
196C4⋊Dic3—31no—
197C4⋊Dic3—33no—
198C4⋊Dic3—31no—
199C4⋊Dic3—63no—
200C4⋊Dic3—61no—
201C4⋊Dic3—66no—
202C4⋊Dic3—63no—
203C4⋊Dic3—63no—
204C4×Dic3—66no—
205C4×Dic3—63no—
206C4×Dic3—63no—
207#208—26no—
208C2×C3⋊C8—26no—
209C2×C3⋊C8C22×D311yescharacteristic
210C2×C3⋊C8C22×D313yes—
211C22×C32—23no—
212C22×C32—23no—
213C22×C32C2×C22⋊C416yes—
214C22×C32C22×D411yescharacteristic
215C2×C3×D3—26no—
216C2×C3×D3—43no—
217C2×C3×D3—43no—
218C2×C3×D3—812no—
219C32×C4C2×C22⋊C416yes—
220C32×C4C23×C411yescharacteristic
221C32×C4C22×D411yescharacteristic
222C3⋊Dic3—43no—
223C3⋊Dic3—41no—
224C3×Dic3—22no—
225H(5,𝔽2)—38no—
226H(5,𝔽2)—64no—
227C2×#41—33no—
228C2×#41—61no—
229C2×#41D3211yescharacteristic
230C22×D4—33no—
231C22×D4—63no—
232#131—64no—
233C2×M16—33no—
234C22×C8—33no—
235C4×Q8—181no—
236C4×D4—183no—
237#117—93no—
238C2×C4⋊C4—93no—
239#103—91no—
240#103—93no—
241#102—93no—
242#102—96no—
243#102—93no—
244C23×C3—23no—
245C23×C3—63no—
246C23×C3—612no—
247C23×C3—243no—
248C23×C3—243no—
249C23×C3C2×D1213yes—
250C23×C3C2×#6713yes—
251C22×D3—23no—
252C22×D3—212no—
253C22×D3—83no—
254C22×D3—83no—
255C3×Q8—24no—
256C3×Q8—32no—
257C3×Q8—61no—
258C3×Q8(C2×D3)⋊C414yes—
259C3×Q8#21714yes—
260C3×D4—212no—
261C3×D4—36no—
262C3×D4—612no—
263C3×D4—612no—
264C3×D4—63no—
265C3×D4(C2×D3)⋊C4112yes—
266C3×D4#217112yes—
267C2×C3×C4—21no—
268C2×C3×C4—26no—
269C2×C3×C4—26no—
270C2×C3×C4—23no—
271C2×C3×C4—61no—
272C2×C3×C4—612no—
273C2×C3×C4C2×C4×D316yes—
274C2×C3×C4C2×D1213yes—
275C2×C3×C4C22×Dic316yes—
276C2×C3×C4C2×#6716yes—
277C2×C3×C4C2×#6716yes—
278C2×C3×C4C2×#6713yes—
279C2×C3×C4C23×D311yescharacteristic
280C2×C3×C4C23×D311yescharacteristic
281#67—212no—
282C2×Dic3—21no—
283C2×Dic3—62no—
284C2×Dic3—66no—
285C2×Dic3—61no—
286C2×Dic3—63no—
287C2×Dic3—61no—
288C2×Dic3—63no—
289C2×Dic3—243no—
290C2×Dic3—243no—
291C2×Dic3—246no—
292D12—212no—
293D12—23no—
294D12C22×Dic316yes—
295C4×D3—212no—
296Dic6—21no—
297Dic6C22×Dic312yes—
298C3×C8—61no—
299C3×C8—63no—
300C3⋊C8—21no—
301C3⋊C8—23no—
302C2×C32—26no—
303C2×C32C22×C22⋊C411yescharacteristic
304C2×C32#57611yescharacteristic
305C2×C32#57711yescharacteristic
306C3×D3—46no—
307C24—63no—
308#41—312no—
309#41—68no—
310#41—66no—
311#41D3×Dic314yes—
312#41#62514yes—
313C2×Q8—31no—
314C2×Q8#62611yescharacteristic
315C2×D4—33no—
316C2×D4—312no—
317C2×D4—63no—
318C2×D4—624no—
319C2×D4—66no—
320C2×D4—63no—
321C2×D4#62613yes—
322C22×C4—63no—
323C22×C4—183no—
324C22×C4C2×D3213yes—
325M16—66no—
326C2×C8—31no—
327C2×C8—33no—
328C2×C8—66no—
329C4⋊C4—93no—
330C4⋊C4—91no—
331C4⋊C4—183no—
332C22⋊C4—183no—
333C42—183no—
334C22×C3—23no—
335C22×C3—23no—
336C22×C3—23no—
337C22×C3—23no—
338C22×C3—21no—
339C22×C3—26no—
340C22×C3—43no—
341C22×C3—43no—
342C22×C3—66no—
343C22×C3—123no—
344C22×C3—123no—
345C22×C3—2412no—
346C22×C3C2×(C2×D3)⋊C416yes—
347C22×C3C2×#21716yes—
348C22×C3C22×D1211yescharacteristic
349C22×C3C22×#6711yescharacteristic
350C2×D3—26no—
351C2×D3—43no—
352C2×D3—43no—
353C2×D3—812no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—26no—
357C3×C4—62no—
358C3×C4C2×(C2×D3)⋊C416yes—
359C3×C4C2×#21716yes—
360C3×C4C22×C4×D311yescharacteristic
361C3×C4C23×Dic311yescharacteristic
362C3×C4C22×#6711yescharacteristic
363C3×C4C22×#6711yescharacteristic
364Dic3—22no—
365Dic3—126no—
366Dic3—122no—
367Dic3—121no—
368Dic3—123no—
369Dic3—123no—
370Dic3—121no—
371C32#289711yescharacteristic, complemented, Sylow
372C23—63no—
373C23—612no—
374C23—243no—
375C23—243no—
376C23C2×#62613yes—
377Q8—32no—
378Q8—61no—
379Q8(C2×D3)⋊Dic314yes—
380D4—36no—
381D4—612no—
382D4—63no—
383D4—612no—
384D4(C2×D3)⋊Dic3112yes—
385C2×C4—61no—
386C2×C4—612no—
387C2×C4—181no—
388C2×C4—183no—
389C2×C4—723no—
390C2×C4C2×D3×Dic316yes—
391C2×C4C2×#62516yes—
392C2×C4C2×#62613yes—
393C2×C4C22×D3211yescharacteristic
394C8—61no—
395C8—63no—
396C2×C3—26no—
397C2×C3—26no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—46no—
402C2×C3—126no—
403C2×C3#575111yescharacteristic
404C2×C3#575211yescharacteristic
405C2×C3C22×(C2×D3)⋊C411yescharacteristic
406C2×C3#583511yescharacteristic
407C2×C3#583611yescharacteristic
408C2×C3C22×#21711yescharacteristic
409D3—46no—
410C22—23no—
411C22—23no—
412C22—66no—
413C22—123no—
414C22—123no—
415C22—2412no—
416C22C2×(C2×D3)⋊Dic316yes—
417C22C22×#62611yescharacteristic
418C4—62no—
419C4—361no—
420C4—363no—
421C4C2×(C2×D3)⋊Dic316yes—
422C4C22×D3×Dic311yescharacteristic
423C4C22×#62511yescharacteristic
424C3—21no—
425C3#8379711yescharacteristic, complemented
426C3#8409911yescharacteristic, complemented
427C2—26no—
428C2—126no—
429C2#1059544711yescharacteristic
430C2#1059544911yescharacteristic
431C2C22×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC22C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#1009C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2897
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10596298C2semidirect
3. C2×C3×#948C2semidirect
4. #10591088C2semidirect
5. #10591086C2semidirect
6. #10591084C2semidirect
7. C2×#63563C2semidirect
12. C3×#1009C4semidirect
19. #64135C22semidirect
20. C2×C4⋊(C3⋊Dic3)C22semidirect
22. C2×C3×#208C22semidirect
23. C22×C3×C3⋊C8C22semidirect
24. #63566C22semidirect
25. #63566C22semidirect
26. #63563C22semidirect
27. #63563C22semidirect
28. #63563C22semidirect
35. C2×#948D3semidirect
55. C3×#235C2×C4semidirect
58. C2×C3×D12C2×C4semidirect
82. #1009Dic3semidirect
103. C2×#208C2×D3semidirect
104. C22×C3⋊C8C2×D3semidirect
181. #235C2×Dic3semidirect
184. C2×D12C2×Dic3semidirect
371. C32#2897semidirect
425. C3#83797semidirect
426. C3#84099semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
#105962982
C2×C3×#9482
#105910882
#105910862
#105910842
C2×#635632
#840993
#837973