Finite Group Databasebeta

← #11858094

Subgroups — #11858094

Order 1152.

1849 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic
2C3×#5827C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4#10591107C213yesmaximal, complemented
5#10591106C213yesmaximal, complemented
6#10591105C213yesmaximal, complemented
7C2×#63567C213yesmaximal, complemented
8#83806—31nomaximal
9#82570—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64367—24no—
12#64367C418yescomplemented
13C2×Q8×C3⋊D3—21no—
14C2×#3830—23no—
15C2×#3828C2213yes—
16C22×#634C2213yes—
17C3×#948—24no—
18C3×Q8×Dic3—21no—
19C3×D4×Dic3—23no—
20C3×#926C2213yes—
21C2×C3×C4⋊Dic3C2213yes—
22C2×C3×#208C2213yes—
23C22×C3×C3⋊C8C2213yes—
24#63567C2213yes—
25#63567C2216yes—
26#63567C2213yes—
27#63564C2211yescharacteristic
28#63564C2213yes—
29C2×#1010—31no—
30C2×#1010—31no—
31C2×#1010—61no—
32C2×C3×#131—31no—
33C3×#520—31no—
34#5827D311yescharacteristic, complemented
35C2×#948D311yescharacteristic, complemented
36#5133—33no—
37#5120—33no—
38#5113—33no—
39C2×#816—33no—
40#5004—33no—
41#5002—33no—
42C2×#810—33no—
43#4966—33no—
44C32×#41C2×C414yes—
45C32×#41D414yes—
46C2×C32×Q8D411yescharacteristic
47C2×C32×D4D413yes—
48C22×C32×C4C2313yes—
49C2×#638—23no—
50C22×C3⋊Dic3—23no—
51Q8×C3⋊D3—28no—
52#3830—224no—
53#3828—26no—
54#3828C2×C4112yescomplemented
55C2×C4⋊(C3⋊D3)C2311yescharacteristic
56C2×C4×C3⋊D3—23no—
57C2×#634—23no—
58C2×#634—26no—
59C2×#634C2×C4112yescomplemented
60C2×#634C2313yes—
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#2898—91noSylow
72C2×C3×#41—21no—
73C2×C3×#41C2×D311yescharacteristic
74C2×C3×#41C2×D311yescharacteristic
75#1010—38no—
76#1010—38no—
77#1010—68no—
78#1010—68no—
79#1010—64no—
80#1010—64no—
81C2×D3×Q8—62no—
82C2×D3×Q8—61no—
83C2×D3×Q8—61no—
84C2×#237—66no—
85C2×#237—63no—
86C2×#237—63no—
87C2×#235—33no—
88C2×#235—33no—
89C2×#235—63no—
90C22×Dic6—33no—
91C22×Dic6—33no—
92C22×Dic6—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×D313yes—
104C2×C4⋊Dic3C2×D313yes—
105C2×#208C2×D313yes—
106C22×C3⋊C8C2×D313yes—
107#821—33no—
108#821—31no—
109#816—33no—
110#816—36no—
111#816—33no—
112#810—36no—
113#810—33no—
114#810—33no—
115#809—33no—
116#809—31no—
117C23×C32C2×D413yes—
118C22×C3⋊D3—21no—
119C32×Q8C22⋊C414yes—
120C32×D4C22⋊C4112yes—
121C2×C32×C4C22×C416yes—
122C2×C32×C4C2×D413yes—
123C2×C32×C4C2×D416yes—
124C2×C32×C4C2411yescharacteristic
125#638—212no—
126C2×C3⋊Dic3—212no—
127C2×C3⋊Dic3—23no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)C22×C412yes—
130C4×C3⋊D3—212no—
131#634—212no—
132#634—23no—
133#634C22×C416yes—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—23no—
136C2×C3×Dic3—83no—
137C3×C3⋊C8—21no—
138C3×C3⋊C8—23no—
139C2×2−1+4—91no—
140C2×#131—31no—
141#520—31no—
142#419—93no—
143#417—93no—
144#416—93no—
145C2×#103—93no—
146C3×#41—24no—
147C3×#41—24no—
148C3×#41C4×D314yes—
149C3×#41C4×D314yes—
150C3×#41D1214yes—
151C3×#41#6714yes—
152C2×C3×Q8—21no—
153C2×C3×Q8D1211yescharacteristic
154C2×C3×Q8#6711yescharacteristic
155C2×C3×D4—23no—
156C2×C3×D4D1213yes—
157C2×C3×D4#6713yes—
158C22×C3×C4—23no—
159C22×C3×C4—63no—
160C22×C3×C4C22×D313yes—
161C22×C3×C4C22×D313yes—
162C2×#67—66no—
163C2×#67—63no—
164C2×#67—63no—
165C22×Dic3—23no—
166C22×Dic3—66no—
167C22×Dic3—63no—
168C22×Dic3—63no—
169D3×Q8—616no—
170D3×Q8—68no—
171D3×Q8—68no—
172#237—648no—
173#237—624no—
174#237—624no—
175#235—312no—
176#235—312no—
177#235—612no—
178#235—612no—
179#235—66no—
180#235—66no—
181C2×D12—31no—
182C2×D12—31no—
183C2×D12—61no—
184C2×C4×D3—66no—
185C2×C4×D3—63no—
186C2×C4×D3—63no—
187C2×Dic6—312no—
188C2×Dic6—312no—
189C2×Dic6—33no—
190C2×Dic6—33no—
191C2×Dic6—63no—
192C2×Dic6—612no—
193C2×Dic6—66no—
194C2×Dic6—612no—
195C2×Dic6—63no—
196C2×Dic6—66no—
197C2×Dic6—63no—
198C2×Dic6—66no—
199C3×M16—66no—
200C2×C3×C8—31no—
201C2×C3×C8—33no—
202C2×C3×C8—66no—
203C3×C4⋊C4—33no—
204C3×C4⋊C4—31no—
205C3×C4⋊C4—63no—
206C3×C22⋊C4—63no—
207C3×C42—63no—
208#217—23no—
209C4⋊Dic3—23no—
210C4⋊Dic3C22×D313yes—
211C4⋊Dic3C22×D311yescharacteristic
212C4×Dic3—23no—
213#208—26no—
214C2×C3⋊C8—26no—
215C2×C3⋊C8C22×D311yescharacteristic
216C2×C3⋊C8C22×D313yes—
217C22×C32—23no—
218C22×C32—23no—
219C22×C32C2×C22⋊C416yes—
220C22×C32C22×D411yescharacteristic
221C2×C3⋊D3—22no—
222C2×C3⋊D3—41no—
223C2×C3⋊D3—41no—
224C32×C4C2×C22⋊C416yes—
225C32×C4C23×C411yescharacteristic
226C32×C4C22×D411yescharacteristic
227C3⋊Dic3—26no—
228C3×Dic3—43no—
229C3×Dic3—41no—
2302−1+4—98no—
2312−1+4—184no—
232C2×#41—93no—
233C2×#41—183no—
234C2×#41D3211yescharacteristic
235C22×Q8—93no—
236C22×Q8—181no—
237#131—64no—
238C2×M16—33no—
239C22×C8—33no—
240C4×Q8—61no—
241C4×D4—63no—
242#117—33no—
243C2×C4⋊C4—33no—
244#103—93no—
245#103—96no—
246#103—93no—
247#102—91no—
248#102—93no—
249C23×C3—23no—
250C23×C3C2×D1213yes—
251C23×C3C2×#6713yes—
252C22×D3—62no—
253C22×D3—61no—
254C22×D3—61no—
255C3×Q8—24no—
256C3×Q8(C2×D3)⋊C414yes—
257C3×Q8(C2×D3)⋊C414yes—
258C3×D4—212no—
259C3×D4(C2×D3)⋊C4112yes—
260C3×D4(C2×D3)⋊C4112yes—
261C2×C3×C4—21no—
262C2×C3×C4—26no—
263C2×C3×C4—23no—
264C2×C3×C4—26no—
265C2×C3×C4—61no—
266C2×C3×C4—63no—
267C2×C3×C4—243no—
268C2×C3×C4C2×C4×D316yes—
269C2×C3×C4C2×C4×D316yes—
270C2×C3×C4C2×D1213yes—
271C2×C3×C4C2×D1216yes—
272C2×C3×C4C2×#6713yes—
273C2×C3×C4C2×#6716yes—
274C2×C3×C4C23×D311yescharacteristic
275C2×C3×C4C23×D311yescharacteristic
276#67—624no—
277#67—612no—
278#67—612no—
279C2×Dic3—21no—
280C2×Dic3—23no—
281C2×Dic3—66no—
282C2×Dic3—624no—
283C2×Dic3—612no—
284C2×Dic3—612no—
285C2×Dic3—63no—
286C2×Dic3—63no—
287C2×Dic3—83no—
288D12—32no—
289D12—32no—
290D12—62no—
291D12—62no—
292D12—61no—
293D12—61no—
294C4×D3—624no—
295C4×D3—612no—
296C4×D3—612no—
297Dic6—36no—
298Dic6—36no—
299Dic6—66no—
300Dic6—66no—
301Dic6—624no—
302Dic6—612no—
303Dic6—612no—
304Dic6—63no—
305Dic6—63no—
306C3×C8—61no—
307C3×C8—63no—
308C3⋊C8—21no—
309C3⋊C8—23no—
310C2×C32—26no—
311C2×C32C22×C22⋊C411yescharacteristic
312C2×C32#57711yescharacteristic
313C2×C32#57811yescharacteristic
314C3⋊D3—42no—
315#41—912no—
316#41—1824no—
317#41—186no—
318#41#62414yes—
319#41#62614yes—
320C2×Q8—93no—
321C2×Q8—912no—
322C2×Q8—188no—
323C2×Q8—183no—
324C2×Q8—186no—
325C2×Q8#62611yescharacteristic
326C2×D4—91no—
327C2×D4—183no—
328C2×D4#62613yes—
329C22×C4—63no—
330C22×C4—183no—
331C22×C4—183no—
332C22×C4C2×D3213yes—
333M16—66no—
334C2×C8—31no—
335C2×C8—33no—
336C2×C8—66no—
337C4⋊C4—33no—
338C4⋊C4—31no—
339C4⋊C4—63no—
340C22⋊C4—63no—
341C42—63no—
342C22×C3—23no—
343C22×C3—23no—
344C22×C3—23no—
345C22×C3—23no—
346C22×C3—21no—
347C22×C3—26no—
348C22×C3—43no—
349C22×C3—43no—
350C22×C3C2×(C2×D3)⋊C416yes—
351C22×C3C2×(C2×D3)⋊C416yes—
352C22×C3C22×D1211yescharacteristic
353C22×C3C22×#6711yescharacteristic
354C2×D3—64no—
355C2×D3—62no—
356C2×D3—62no—
357C2×D3—122no—
358C2×D3—122no—
359C2×D3—121no—
360C2×D3—121no—
361C2×D3—121no—
362C2×D3—121no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—26no—
366C3×C4—123no—
367C3×C4—121no—
368C3×C4C2×(C2×D3)⋊C416yes—
369C3×C4C2×(C2×D3)⋊C416yes—
370C3×C4C22×C4×D311yescharacteristic
371C3×C4C22×C4×D311yescharacteristic
372C3×C4C22×D1211yescharacteristic
373C3×C4C22×#6711yescharacteristic
374Dic3—43no—
375Dic3—41no—
376Dic3—612no—
377Dic3—66no—
378Dic3—66no—
379C32#289811yescharacteristic, complemented, Sylow
380C23—181no—
381C23C2×#62613yes—
382Q8—96no—
383Q8—183no—
384Q8—1812no—
385Q8#372214yes—
386D4—92no—
387D4—1812no—
388D4—181no—
389D4#3722112yes—
390C2×C4—61no—
391C2×C4—63no—
392C2×C4—183no—
393C2×C4—1812no—
394C2×C4—1812no—
395C2×C4—243no—
396C2×C4C2×#62416yes—
397C2×C4C2×#62616yes—
398C2×C4C2×#62613yes—
399C2×C4C22×D3211yescharacteristic
400C8—61no—
401C8—63no—
402C2×C3—26no—
403C2×C3—26no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—46no—
408C2×C3#575111yescharacteristic
409C2×C3#575311yescharacteristic
410C2×C3C22×(C2×D3)⋊C411yescharacteristic
411C2×C3C22×(C2×D3)⋊C411yescharacteristic
412C2×C3#583611yescharacteristic
413C2×C3#583811yescharacteristic
414D3—124no—
415D3—122no—
416D3—122no—
417C22—23no—
418C22—23no—
419C22—182no—
420C22—361no—
421C22—361no—
422C22C2×#372216yes—
423C22C22×#62611yescharacteristic
424C4—123no—
425C4—121no—
426C4—186no—
427C4C2×#372216yes—
428C4C22×#62411yescharacteristic
429C4C22×#62611yescharacteristic
430C3—21no—
431C3#8257011yescharacteristic, complemented
432C3#8380611yescharacteristic, complemented
433C2—26no—
434C2—362no—
435C2#1059544711yescharacteristic
436C2#1059545011yescharacteristic
437C2C22×#372211yescharacteristic
subgroupG/H
centerC22C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×#64367C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2898
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. #10591107C2semidirect
5. #10591106C2semidirect
6. #10591105C2semidirect
7. C2×#63567C2semidirect
12. #64367C4semidirect
34. #5827D3semidirect
35. C2×#948D3semidirect
54. #3828C2×C4semidirect
59. C2×#634C2×C4semidirect
379. C32#2898semidirect
431. C3#82570semidirect
432. C3#83806semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C3×#58272
C2×C3×#9482
#105911072
#105911062
#105911052
C2×#635672
#838063
#825703