Finite Group Databasebeta

← #11858038

Subgroups — #11858038

Order 1152.

2005 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic
2C3×#5827C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4#10591106C213yesmaximal, complemented
5#10591105C213yesmaximal, complemented
6#10591096C213yesmaximal, complemented
7C2×#63564C213yesmaximal, complemented
8#83797—31nomaximal
9#82563—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64366—24no—
12#64366C418yescomplemented
13C2×#3832—21no—
14C2×D4×C3⋊D3—23no—
15C2×#3828C2213yes—
16C22×C4⋊(C3⋊D3)C2213yes—
17C3×#948—24no—
18C3×Q8×Dic3—21no—
19C3×D4×Dic3—23no—
20C3×#926C2213yescomplemented
21C2×C3×C4⋊Dic3C2213yescomplemented
22C2×C3×#208C2213yescomplemented
23C22×C3×C3⋊C8C2213yescomplemented
24#63567C2211yescharacteristic, complemented
25#63567C2213yescomplemented
26#63564C2213yescomplemented
27#63564C2216yescomplemented
28#63564C2213yescomplemented
29C2×#1009—31no—
30C2×#1009—31no—
31C2×#1009—61no—
32C2×C3×#131—31no—
33C3×#520—31no—
34#5827D311yescharacteristic, complemented
35C2×#948D311yescharacteristic, complemented
36#5133—33no—
37#5131—33no—
38#5113—33no—
39C2×#821—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×#638—23no—
51#3832—28no—
52D4×C3⋊D3—224no—
53#3828—26no—
54#3828C2×C4112yescomplemented
55C2×C4⋊(C3⋊D3)—23no—
56C2×C4⋊(C3⋊D3)—26no—
57C2×C4⋊(C3⋊D3)C2×C4112yescomplemented
58C2×C4⋊(C3⋊D3)C2313yes—
59C2×C4×C3⋊D3—23no—
60C2×#634C2311yescharacteristic
61C22×C3×Dic3—23no—
62C3×#217—23no—
63C3×C4⋊Dic3—23no—
64C3×C4⋊Dic3C2313yes—
65C3×C4⋊Dic3C2311yescharacteristic
66C3×C4×Dic3—23no—
67C3×#208—26no—
68C2×C3×C3⋊C8—26no—
69C2×C3×C3⋊C8C2311yescharacteristic
70C2×C3×C3⋊C8C2313yes—
71#2897—91noSylow
72C2×C3×#41—21no—
73C2×C3×#41C2×D311yescharacteristic
74C2×C3×#41C2×D311yescharacteristic
75#1009—38no—
76#1009—38no—
77#1009—68no—
78#1009—68no—
79#1009—64no—
80#1009—64no—
81C2×#239—62no—
82C2×#239—61no—
83C2×#239—61no—
84C2×D3×D4—66no—
85C2×D3×D4—63no—
86C2×D3×D4—63no—
87C2×#235—33no—
88C2×#235—33no—
89C2×#235—63no—
90C22×D12—33no—
91C22×D12—33no—
92C22×D12—63no—
93C3×#131—64no—
94C2×C3×M16—33no—
95C22×C3×C8—33no—
96C3×C4×Q8—61no—
97C3×C4×D4—63no—
98C3×#117—33no—
99C2×C3×C4⋊C4—33no—
100#948—24no—
101Q8×Dic3—21no—
102D4×Dic3—23no—
103#926C2×D313yescomplemented
104C2×C4⋊Dic3C2×D313yescomplemented
105C2×#208C2×D313yescomplemented
106C22×C3⋊C8C2×D313yescomplemented
107#821—33no—
108#821—36no—
109#821—33no—
110#816—33no—
111#816—31no—
112#810—33no—
113#810—31no—
114#809—33no—
115#809—36no—
116#809—33no—
117C23×C32C2×D413yes—
118C22×C3⋊D3—23no—
119C22×C3⋊D3—212no—
120C22×C3⋊D3—83no—
121C22×C3⋊D3—83no—
122C32×Q8C22⋊C414yes—
123C32×D4C22⋊C4112yes—
124C2×C32×C4C22×C416yes—
125C2×C32×C4C2×D413yes—
126C2×C32×C4C2×D416yes—
127C2×C32×C4C2411yescharacteristic
128#638—212no—
129C2×C3⋊Dic3—21no—
130C4⋊(C3⋊D3)—212no—
131C4⋊(C3⋊D3)—23no—
132C4⋊(C3⋊D3)C22×C416yes—
133C4×C3⋊D3—212no—
134#634—21no—
135#634C22×C412yes—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—23no—
138C2×C3×Dic3—83no—
139C3×C3⋊C8—21no—
140C3×C3⋊C8—23no—
141C2×H(5,𝔽2)—91no—
142C2×#131—31no—
143#520—31no—
144#418—93no—
145#417—93no—
146#416—93no—
147C2×#102—93no—
148C23×D3—66no—
149C23×D3—63no—
150C23×D3—63no—
151C3×#41—24no—
152C3×#41—24no—
153C3×#41C4×D314yes—
154C3×#41C4×D314yes—
155C3×#41D1214yes—
156C3×#41#6714yes—
157C2×C3×Q8—21no—
158C2×C3×Q8D1211yescharacteristic
159C2×C3×Q8#6711yescharacteristic
160C2×C3×D4—23no—
161C2×C3×D4D1213yes—
162C2×C3×D4#6713yes—
163C22×C3×C4—23no—
164C22×C3×C4—63no—
165C22×C3×C4C22×D313yes—
166C22×C3×C4C22×D313yes—
167C2×#67—66no—
168C2×#67—63no—
169C2×#67—63no—
170C22×Dic3—23no—
171#239—616no—
172#239—68no—
173#239—68no—
174D3×D4—648no—
175D3×D4—624no—
176D3×D4—624no—
177#235—312no—
178#235—312no—
179#235—612no—
180#235—612no—
181#235—66no—
182#235—66no—
183C2×D12—312no—
184C2×D12—312no—
185C2×D12—33no—
186C2×D12—33no—
187C2×D12—63no—
188C2×D12—612no—
189C2×D12—66no—
190C2×D12—612no—
191C2×D12—63no—
192C2×D12—66no—
193C2×D12—63no—
194C2×D12—66no—
195C2×C4×D3—66no—
196C2×C4×D3—63no—
197C2×C4×D3—63no—
198C2×Dic6—31no—
199C2×Dic6—31no—
200C2×Dic6—61no—
201C3×M16—66no—
202C2×C3×C8—31no—
203C2×C3×C8—33no—
204C2×C3×C8—66no—
205C3×C4⋊C4—33no—
206C3×C4⋊C4—31no—
207C3×C4⋊C4—63no—
208C3×C22⋊C4—63no—
209C3×C42—63no—
210#217—23no—
211C4⋊Dic3—23no—
212C4⋊Dic3C22×D313yes—
213C4⋊Dic3C22×D311yescharacteristic
214C4×Dic3—23no—
215#208—26no—
216C2×C3⋊C8—26no—
217C2×C3⋊C8C22×D311yescharacteristic
218C2×C3⋊C8C22×D313yes—
219C22×C32—23no—
220C22×C32—23no—
221C22×C32C2×C22⋊C416yes—
222C22×C32C22×D411yescharacteristic
223C2×C3⋊D3—26no—
224C2×C3⋊D3—43no—
225C2×C3⋊D3—43no—
226C2×C3⋊D3—812no—
227C32×C4C2×C22⋊C416yes—
228C32×C4C23×C411yescharacteristic
229C32×C4C22×D411yescharacteristic
230C3⋊Dic3—22no—
231C3×Dic3—43no—
232C3×Dic3—41no—
233H(5,𝔽2)—98no—
234H(5,𝔽2)—184no—
235C2×#41—93no—
236C2×#41—181no—
237C2×#41D3211yescharacteristic
238C22×D4—93no—
239C22×D4—183no—
240#131—64no—
241C2×M16—33no—
242C22×C8—33no—
243C4×Q8—61no—
244C4×D4—63no—
245#117—33no—
246C2×C4⋊C4—33no—
247#103—91no—
248#103—93no—
249#102—93no—
250#102—96no—
251#102—93no—
252C23×C3—23no—
253C23×C3C2×D1213yes—
254C23×C3C2×#6713yes—
255C22×D3—66no—
256C22×D3—63no—
257C22×D3—63no—
258C22×D3—624no—
259C22×D3—612no—
260C22×D3—612no—
261C22×D3—243no—
262C22×D3—243no—
263C22×D3—243no—
264C22×D3—243no—
265C22×D3—246no—
266C22×D3—246no—
267C3×Q8—24no—
268C3×Q8(C2×D3)⋊C414yes—
269C3×Q8(C2×D3)⋊C414yes—
270C3×D4—212no—
271C3×D4(C2×D3)⋊C4112yes—
272C3×D4(C2×D3)⋊C4112yes—
273C2×C3×C4—21no—
274C2×C3×C4—26no—
275C2×C3×C4—23no—
276C2×C3×C4—26no—
277C2×C3×C4—61no—
278C2×C3×C4—63no—
279C2×C3×C4—243no—
280C2×C3×C4C2×C4×D316yes—
281C2×C3×C4C2×C4×D316yes—
282C2×C3×C4C2×D1213yes—
283C2×C3×C4C2×D1216yes—
284C2×C3×C4C2×#6713yes—
285C2×C3×C4C2×#6716yes—
286C2×C3×C4C23×D311yescharacteristic
287C2×C3×C4C23×D311yescharacteristic
288#67—624no—
289#67—612no—
290#67—612no—
291C2×Dic3—21no—
292C2×Dic3—23no—
293C2×Dic3—62no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—83no—
297D12—36no—
298D12—36no—
299D12—66no—
300D12—66no—
301D12—624no—
302D12—612no—
303D12—612no—
304D12—63no—
305D12—63no—
306C4×D3—624no—
307C4×D3—612no—
308C4×D3—612no—
309Dic6—32no—
310Dic6—32no—
311Dic6—62no—
312Dic6—62no—
313Dic6—61no—
314Dic6—61no—
315C3×C8—61no—
316C3×C8—63no—
317C3⋊C8—21no—
318C3⋊C8—23no—
319C2×C32—26no—
320C2×C32C22×C22⋊C411yescharacteristic
321C2×C32#57611yescharacteristic
322C2×C32#57711yescharacteristic
323C3⋊D3—46no—
324C24—183no—
325#41—912no—
326#41—188no—
327#41—186no—
328#41#62414yes—
329#41#62614yes—
330C2×Q8—91no—
331C2×Q8#62611yescharacteristic
332C2×D4—93no—
333C2×D4—912no—
334C2×D4—183no—
335C2×D4—1824no—
336C2×D4—183no—
337C2×D4—186no—
338C2×D4#62613yes—
339C22×C4—63no—
340C22×C4—183no—
341C22×C4C2×D3213yes—
342M16—66no—
343C2×C8—31no—
344C2×C8—33no—
345C2×C8—66no—
346C4⋊C4—33no—
347C4⋊C4—31no—
348C4⋊C4—63no—
349C22⋊C4—63no—
350C42—63no—
351C22×C3—23no—
352C22×C3—23no—
353C22×C3—23no—
354C22×C3—23no—
355C22×C3—21no—
356C22×C3—26no—
357C22×C3—43no—
358C22×C3—43no—
359C22×C3C2×(C2×D3)⋊C416yes—
360C22×C3C2×(C2×D3)⋊C416yes—
361C22×C3C22×D1211yescharacteristic
362C22×C3C22×#6711yescharacteristic
363C2×D3—612no—
364C2×D3—66no—
365C2×D3—66no—
366C2×D3—126no—
367C2×D3—126no—
368C2×D3—123no—
369C2×D3—123no—
370C2×D3—123no—
371C2×D3—123no—
372C2×D3—2412no—
373C2×D3—2412no—
374C2×D3—2424no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—26no—
378C3×C4—121no—
379C3×C4—123no—
380C3×C4C2×(C2×D3)⋊C416yes—
381C3×C4C2×(C2×D3)⋊C416yes—
382C3×C4C22×C4×D311yescharacteristic
383C3×C4C22×C4×D311yescharacteristic
384C3×C4C22×D1211yescharacteristic
385C3×C4C22×#6711yescharacteristic
386Dic3—43no—
387Dic3—41no—
388Dic3—64no—
389Dic3—62no—
390Dic3—62no—
391C32#289711yescharacteristic, complemented, Sylow
392C23—183no—
393C23—1812no—
394C23—723no—
395C23—723no—
396C23C2×#62613yes—
397Q8—92no—
398Q8—181no—
399Q8#372214yes—
400D4—96no—
401D4—1812no—
402D4—183no—
403D4—1812no—
404D4#3722112yes—
405C2×C4—61no—
406C2×C4—63no—
407C2×C4—181no—
408C2×C4—1812no—
409C2×C4—243no—
410C2×C4C2×#62416yes—
411C2×C4C2×#62616yes—
412C2×C4C2×#62613yes—
413C2×C4C22×D3211yescharacteristic
414C8—61no—
415C8—63no—
416C2×C3—26no—
417C2×C3—26no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—46no—
422C2×C3#575111yescharacteristic
423C2×C3#575211yescharacteristic
424C2×C3C22×(C2×D3)⋊C411yescharacteristic
425C2×C3C22×(C2×D3)⋊C411yescharacteristic
426C2×C3#583511yescharacteristic
427C2×C3#583711yescharacteristic
428D3—1212no—
429D3—126no—
430D3—126no—
431C22—23no—
432C22—23no—
433C22—186no—
434C22—363no—
435C22—363no—
436C22—7212no—
437C22C2×#372216yes—
438C22C22×#62611yescharacteristic
439C4—121no—
440C4—123no—
441C4—182no—
442C4C2×#372216yes—
443C4C22×#62411yescharacteristic
444C4C22×#62611yescharacteristic
445C3—21no—
446C3#8256311yescharacteristic, complemented
447C3#8379711yescharacteristic, complemented
448C2—26no—
449C2—366no—
450C2#1059544811yescharacteristic
451C2#1059544911yescharacteristic
452C2C22×#372211yescharacteristic
subgroupG/H
centerC22C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×#64366C2
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. C3×#5827C2semidirect
3. C2×C3×#948C2semidirect
4. #10591106C2semidirect
5. #10591105C2semidirect
6. #10591096C2semidirect
7. C2×#63564C2semidirect
12. #64366C4semidirect
20. C3×#926C22semidirect
21. C2×C3×C4⋊Dic3C22semidirect
22. C2×C3×#208C22semidirect
23. C22×C3×C3⋊C8C22semidirect
24. #63567C22semidirect
25. #63567C22semidirect
26. #63564C22semidirect
27. #63564C22semidirect
28. #63564C22semidirect
34. #5827D3semidirect
35. C2×#948D3semidirect
54. #3828C2×C4semidirect
57. C2×C4⋊(C3⋊D3)C2×C4semidirect
103. #926C2×D3semidirect
104. C2×C4⋊Dic3C2×D3semidirect
105. C2×#208C2×D3semidirect
106. C22×C3⋊C8C2×D3semidirect
391. C32#2897semidirect
446. C3#82563semidirect
447. C3#83797semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C3×#58272
C2×C3×#9482
#105911062
#105911052
#105910962
C2×#635642
#837973
#825633