Finite Group Databasebeta

← #11858039

Subgroups — #11858039

Order 1152.

1689 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2C2×#64157C211yesmaximal, characteristic, complemented
3C3×#5827C211yesmaximal, characteristic, complemented
4#10591087C213yesmaximal, complemented
5#10591085C213yesmaximal, complemented
6#10591083C213yesmaximal, complemented
7C2×#63562C213yesmaximal, complemented
8#84099—31nomaximal
9#82563—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C3×#1009—24no—
12C3×#1009C418yescomplemented
13C2×C3×#239—21no—
14C2×C3×D3×D4—23no—
15C2×C3×#235C2213yes—
16C22×C3×D12C2213yes—
17#64157—24no—
18C2×#3748C2213yescomplemented
19C22×C3⋊(C3⋊C8)C2213yescomplemented
20C3×Q8×Dic3—21no—
21C3×D4×Dic3—23no—
22C3×#926C2213yescomplemented
23C2×C3×C4⋊Dic3C2213yescomplemented
24#63565C2211yescharacteristic, complemented
25#63565C2213yescomplemented
26#63562C2213yescomplemented
27#63562C2216yescomplemented
28#63562C2213yescomplemented
29C2×C3×H(5,𝔽2)—31no—
30C2×#1009D311yescharacteristic
31C3×#520—31no—
32#5827D311yescharacteristic, complemented
33C2×#948—31no—
34C2×#948—31no—
35C2×#948—61no—
36#5233—33no—
37#5232—33no—
38#5215—33no—
39C2×#832—33no—
40#5002—33no—
41#5001—33no—
42#4966—33no—
43C2×#809—33no—
44C23×C3×D3—23no—
45C32×#41C2×C414yes—
46C32×#41D414yes—
47C2×C32×Q8D411yescharacteristic
48C2×C32×D4D413yes—
49C22×C32×C4C2313yes—
50C2×C3×#67—23no—
51C22×C3×Dic3—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#3748—26no—
63C2×C3⋊(C3⋊C8)—26no—
64C2×C3⋊(C3⋊C8)C2311yescharacteristic
65C2×C3⋊(C3⋊C8)C2313yes—
66C3×#217—23no—
67C3×C4⋊Dic3—23no—
68C3×C4⋊Dic3C2313yes—
69C3×C4⋊Dic3C2311yescharacteristic
70C3×C4×Dic3—23no—
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×C4×Q8—61no—
88C3×C4×D4—63no—
89C3×#117—33no—
90C2×C3×C4⋊C4—33no—
91#948—68no—
92#948—64no—
93#948—64no—
94Q8×Dic3—21no—
95D4×Dic3—23no—
96#926C2×D313yescomplemented
97C2×C4⋊Dic3C2×D313yescomplemented
98C2×#208—33no—
99C2×#208—33no—
100C2×#208—63no—
101C22×C3⋊C8—33no—
102C22×C3⋊C8—33no—
103C22×C3⋊C8—63no—
104#835—33no—
105#835—31no—
106#832—33no—
107#832—36no—
108#832—33no—
109#810—33no—
110#810—31no—
111#809—33no—
112#809—36no—
113#809—33no—
114C23×C32C2×D413yes—
115C22×C3×D3—23no—
116C22×C3×D3—212no—
117C22×C3×D3—83no—
118C22×C3×D3—83no—
119C32×Q8C22⋊C414yes—
120C32×D4C22⋊C4112yes—
121C2×C32×C4C22×C416yes—
122C2×C32×C4C2×D416yes—
123C2×C32×C4C2×D413yes—
124C2×C32×C4C2411yescharacteristic
125C3×#67—212no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—23no—
129C2×C3×Dic3—83no—
130C3×D12—212no—
131C3×D12—23no—
132C3×D12C22×C416yes—
133C3×C4×D3—212no—
134C3×Dic6—21no—
135C3×Dic6C22×C412yes—
136C3⋊(C3⋊C8)—21no—
137C3⋊(C3⋊C8)—23no—
138C2×H(5,𝔽2)—31no—
139C2×#131—91no—
140#520—31no—
141#418—93no—
142#417—93no—
143#416—93no—
144C2×#102—93no—
145C24×C3—63no—
146C23×D3—23no—
147C3×#41—24no—
148C3×#41—24no—
149C3×#41—312no—
150C3×#41—68no—
151C3×#41—66no—
152C3×#41C4×D314yes—
153C3×#41D1214yes—
154C3×#41C2×Dic314yes—
155C3×#41#6714yes—
156C2×C3×Q8—21no—
157C2×C3×Q8—31no—
158C2×C3×Q8#6711yescharacteristic
159C2×C3×Q8#6711yescharacteristic
160C2×C3×D4—23no—
161C2×C3×D4—312no—
162C2×C3×D4—33no—
163C2×C3×D4—63no—
164C2×C3×D4—624no—
165C2×C3×D4—66no—
166C2×C3×D4—63no—
167C2×C3×D4#6713yes—
168C2×C3×D4#6713yes—
169C22×C3×C4—23no—
170C22×C3×C4—63no—
171C22×C3×C4—63no—
172C22×C3×C4C22×D313yes—
173C22×C3×C4C22×D313yes—
174C2×#67—23no—
175C22×Dic3—23no—
176#239—28no—
177D3×D4—224no—
178#235—26no—
179#235C2×Dic3112yescomplemented
180C2×D12—23no—
181C2×D12—26no—
182C2×D12C2×Dic3112yescomplemented
183C2×D12C22×D313yes—
184C2×C4×D3—23no—
185C2×Dic6C22×D311yescharacteristic
186C3×C4⋊C4—33no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—63no—
189C3×C22⋊C4—63no—
190C3×C42—63no—
191#217—23no—
192C4⋊Dic3—23no—
193C4⋊Dic3C22×D313yes—
194C4⋊Dic3C22×D311yescharacteristic
195C4×Dic3—23no—
196#208—612no—
197#208—66no—
198#208—66no—
199C2×C3⋊C8—31no—
200C2×C3⋊C8—33no—
201C2×C3⋊C8—31no—
202C2×C3⋊C8—33no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—63no—
205C2×C3⋊C8—612no—
206C2×C3⋊C8—66no—
207C2×C3⋊C8—66no—
208C22×C32—23no—
209C22×C32—23no—
210C22×C32C2×C22⋊C416yes—
211C22×C32C22×D411yescharacteristic
212C2×C3×D3—26no—
213C2×C3×D3—43no—
214C2×C3×D3—43no—
215C2×C3×D3—812no—
216C32×C4C2×C22⋊C416yes—
217C32×C4C23×C411yescharacteristic
218C32×C4C22×D411yescharacteristic
219C3×Dic3—22no—
220C3×Dic3—43no—
221C3×Dic3—41no—
222H(5,𝔽2)—38no—
223H(5,𝔽2)—64no—
224C2×#41—33no—
225C2×#41—61no—
226C2×#41D3211yescharacteristic
227C22×D4—33no—
228C22×D4—63no—
229#131—184no—
230C2×M16—93no—
231C22×C8—93no—
232C4×Q8—61no—
233C4×D4—63no—
234#117—33no—
235C2×C4⋊C4—33no—
236#103—91no—
237#103—93no—
238#102—93no—
239#102—96no—
240#102—93no—
241C23×C3—23no—
242C23×C3—63no—
243C23×C3—612no—
244C23×C3—243no—
245C23×C3—243no—
246C23×C3C2×#6713yes—
247C23×C3C2×#6713yes—
248C22×D3—23no—
249C22×D3—212no—
250C22×D3—83no—
251C22×D3—83no—
252C3×Q8—24no—
253C3×Q8—32no—
254C3×Q8—61no—
255C3×Q8(C2×D3)⋊C414yes—
256C3×Q8#21714yes—
257C3×D4—212no—
258C3×D4—36no—
259C3×D4—612no—
260C3×D4—612no—
261C3×D4—63no—
262C3×D4(C2×D3)⋊C4112yes—
263C3×D4#217112yes—
264C2×C3×C4—21no—
265C2×C3×C4—26no—
266C2×C3×C4—23no—
267C2×C3×C4—26no—
268C2×C3×C4—61no—
269C2×C3×C4—612no—
270C2×C3×C4—61no—
271C2×C3×C4—63no—
272C2×C3×C4—243no—
273C2×C3×C4C2×C4×D316yes—
274C2×C3×C4C2×D1216yes—
275C2×C3×C4C22×Dic316yes—
276C2×C3×C4C2×#6713yes—
277C2×C3×C4C2×#6713yes—
278C2×C3×C4C2×#6716yes—
279C2×C3×C4C23×D311yescharacteristic
280C2×C3×C4C23×D311yescharacteristic
281#67—212no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—23no—
285C2×Dic3—83no—
286D12—212no—
287D12—23no—
288D12C22×Dic316yes—
289C4×D3—212no—
290Dic6—21no—
291Dic6C22×Dic312yes—
292C3⋊C8—62no—
293C3⋊C8—66no—
294C3⋊C8—61no—
295C3⋊C8—63no—
296C3⋊C8—61no—
297C3⋊C8—63no—
298C2×C32—26no—
299C2×C32C22×C22⋊C411yescharacteristic
300C2×C32#57611yescharacteristic
301C2×C32#57711yescharacteristic
302C3×D3—46no—
303C24—63no—
304#41—312no—
305#41—68no—
306#41—66no—
307#41D3×Dic314yes—
308#41#62614yes—
309C2×Q8—31no—
310C2×Q8#62511yescharacteristic
311C2×D4—33no—
312C2×D4—312no—
313C2×D4—63no—
314C2×D4—624no—
315C2×D4—63no—
316C2×D4—66no—
317C2×D4#62513yes—
318C22×C4—63no—
319C22×C4—63no—
320C22×C4C2×D3213yes—
321M16—186no—
322C2×C8—91no—
323C2×C8—93no—
324C2×C8—186no—
325C4⋊C4—33no—
326C4⋊C4—31no—
327C4⋊C4—63no—
328C22⋊C4—63no—
329C42—63no—
330C22×C3—23no—
331C22×C3—23no—
332C22×C3—23no—
333C22×C3—23no—
334C22×C3—21no—
335C22×C3—26no—
336C22×C3—43no—
337C22×C3—43no—
338C22×C3—66no—
339C22×C3—123no—
340C22×C3—123no—
341C22×C3—2412no—
342C22×C3C2×(C2×D3)⋊C416yes—
343C22×C3C2×#21716yes—
344C22×C3C22×#6711yescharacteristic
345C22×C3C22×#6711yescharacteristic
346C2×D3—26no—
347C2×D3—43no—
348C2×D3—43no—
349C2×D3—812no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—26no—
353C3×C4—62no—
354C3×C4—123no—
355C3×C4—121no—
356C3×C4C2×(C2×D3)⋊C416yes—
357C3×C4C2×#21716yes—
358C3×C4C22×C4×D311yescharacteristic
359C3×C4C22×D1211yescharacteristic
360C3×C4C23×Dic311yescharacteristic
361C3×C4C22×#6711yescharacteristic
362Dic3—22no—
363Dic3—43no—
364Dic3—41no—
365C32#289711yescharacteristic, complemented, Sylow
366C23—63no—
367C23—612no—
368C23—243no—
369C23—243no—
370C23C2×#62513yes—
371Q8—32no—
372Q8—61no—
373Q8(C2×D3)⋊Dic314yes—
374D4—36no—
375D4—612no—
376D4—63no—
377D4—612no—
378D4(C2×D3)⋊Dic3112yes—
379C2×C4—61no—
380C2×C4—612no—
381C2×C4—61no—
382C2×C4—63no—
383C2×C4—243no—
384C2×C4C2×D3×Dic316yes—
385C2×C4C2×#62513yes—
386C2×C4C2×#62616yes—
387C2×C4C22×D3211yescharacteristic
388C8—181no—
389C8—183no—
390C2×C3—26no—
391C2×C3—26no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—46no—
396C2×C3—126no—
397C2×C3C22×(C2×D3)⋊C411yescharacteristic
398C2×C3#583511yescharacteristic
399C2×C3#583511yescharacteristic
400C2×C3#583611yescharacteristic
401C2×C3#583711yescharacteristic
402C2×C3C22×#21711yescharacteristic
403D3—46no—
404C22—23no—
405C22—23no—
406C22—66no—
407C22—123no—
408C22—123no—
409C22—2412no—
410C22C2×(C2×D3)⋊Dic316yes—
411C22C22×#62511yescharacteristic
412C4—62no—
413C4—123no—
414C4—121no—
415C4C2×(C2×D3)⋊Dic316yes—
416C4C22×D3×Dic311yescharacteristic
417C4C22×#62611yescharacteristic
418C3—21no—
419C3#8256311yescharacteristic, complemented
420C3#8409911yescharacteristic, complemented
421C2—26no—
422C2—126no—
423C2#1059544411yescharacteristic
424C2#1059544611yescharacteristic
425C2C22×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC22C22×#625
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. C2×#64157C2semidirect
3. C3×#5827C2semidirect
4. #10591087C2semidirect
5. #10591085C2semidirect
6. #10591083C2semidirect
7. C2×#63562C2semidirect
12. C3×#1009C4semidirect
18. C2×#3748C22semidirect
19. C22×C3⋊(C3⋊C8)C22semidirect
22. C3×#926C22semidirect
23. C2×C3×C4⋊Dic3C22semidirect
24. #63565C22semidirect
25. #63565C22semidirect
26. #63562C22semidirect
27. #63562C22semidirect
28. #63562C22semidirect
32. #5827D3semidirect
55. C3×#235C2×C4semidirect
58. C2×C3×D12C2×C4semidirect
82. #1009Dic3semidirect
96. #926C2×D3semidirect
97. C2×C4⋊Dic3C2×D3semidirect
179. #235C2×Dic3semidirect
182. C2×D12C2×Dic3semidirect
365. C32#2897semidirect
419. C3#82563semidirect
420. 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
C2×#641572
C3×#58272
#105910872
#105910852
#105910832
C2×#635622
#840993
#825633