Finite Group Databasebeta

← #11909965

Subgroups — #11909965

Order 1152.

3090 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#550C211yesmaximal, characteristic, complemented
2#10596302C211yesmaximal, characteristic, complemented
3#10596302C211yesmaximal, characteristic, complemented
4#10596298C211yesmaximal, characteristic, complemented
5#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10596190C213yesmaximal, complemented
7#10596184C213yesmaximal, complemented
8#10596089C213yesmaximal, complemented
9#10596087C213yesmaximal, complemented
10#10596074C213yesmaximal, complemented
11#10596071C213yesmaximal, complemented
12#10596043C211yesmaximal, characteristic, complemented
13#10596040C211yesmaximal, characteristic, complemented
14#10596012C213yesmaximal, complemented
15#10596009C213yesmaximal, complemented
16#86777—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×C32×#41C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C32×#127C2213yes—
21C32×#121C2213yes—
22C32×#121C2213yes—
23C32×C4×Q8C2211yescharacteristic
24C32×C4×D4C2213yes—
25Q8×C3⋊Dic3C2211yescharacteristic
26Q8×C3⋊Dic3C2211yescharacteristic
27Q8×C3⋊Dic3C2211yescharacteristic
28#64148C2213yes—
29#64148C2216yes—
30#64147C2213yes—
31#64147C2213yes—
32#64145C2213yes—
33#64145C2213yes—
34#64145C2216yes—
35#64144C2213yes—
36#64144C2216yes—
37#64144C2216yes—
38D4×C3⋊Dic3C2213yes—
39D4×C3⋊Dic3C2213yes—
40D4×C3⋊Dic3C2216yes—
41D4×C3⋊Dic3C2213yes—
42D4×C3⋊Dic3C2213yes—
43C4×#638C2213yes—
44C4×#638C2213yes—
45#64135C2213yes—
46#64135C2213yes—
47C2×C4⋊(C3⋊Dic3)C2213yes—
48#64133C2213yes—
49#64133C2213yes—
50C2×C4×C3⋊Dic3C2213yes—
51#64107C2211yescharacteristic
52#64101C2213yes—
53#64099C2213yes—
54#64098C2213yes—
55#64097C2213yes—
56#64096C2213yes—
57#64095C2213yes—
58#64094C2213yes—
59#64088C2213yes—
60#64088C2216yes—
61#64087C2213yes—
62#64086C2216yes—
63#64081C2213yes—
64#64079C2213yes—
65C4×#634C2213yes—
66C4×#634C2213yes—
67C3×#550D314yescomplemented
68#5831—34no—
69#5831—34no—
70#5827—34no—
71Dic3×#41—34no—
72#5719—312no—
73#5713—312no—
74#5618—312no—
75#5616—312no—
76#5603—312no—
77#5600—312no—
78#5572—34no—
79#5569—34no—
80#5541—312no—
81#5538—312no—
82C32×#41—24no—
83C32×#41—24no—
84C2×C32×Q8C2311yescharacteristic
85C2×C32×D4C2313yes—
86C2×C32×D4C2313yes—
87C2×C32×D4C2316yes—
88C2×C32×D4C2313yes—
89C22×C32×C4C2313yes—
90C22×C32×C4C2313yes—
91C2×#638C2313yes—
92C2×#638C2313yes—
93C22×C3⋊Dic3C2316yes—
94C22×C3⋊Dic3C2313yes—
95C22×C3⋊Dic3C2313yes—
96Q8×C3⋊D3—24no—
97C2×C4×C3⋊D3C2313yes—
98C2×#634C2313yes—
99C2×#634C2313yes—
100C32×C4⋊C4C2313yes—
101C32×C4⋊C4C2311yescharacteristic
102C32×C22⋊C4C2313yes—
103C32×C22⋊C4C2313yes—
104C32×C42C2313yes—
105#3757C2316yes—
106#3757C2313yes—
107#3757C2316yes—
108#3757C2313yes—
109#3757C2316yes—
110#3757C2313yes—
111#3757C2313yes—
112#3752C2311yescharacteristic
113#3752C2313yes—
114#3752C2311yescharacteristic
115#3752C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2313yes—
117C4⋊(C3⋊Dic3)C2313yes—
118C4⋊(C3⋊Dic3)C2313yes—
119C4⋊(C3⋊Dic3)C2313yes—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2313yes—
122#3750C2311yescharacteristic
123#3750C2313yes—
124#3750C2313yes—
125#3750C2316yes—
126#3750C2313yes—
127#3750C2313yes—
128#3750C2313yes—
129C4×C3⋊Dic3C2316yes—
130C4×C3⋊Dic3C2313yes—
131C4×C3⋊Dic3C2313yes—
132C4×C3⋊Dic3C2313yes—
133C4×C3⋊Dic3C2313yes—
134C4×C3⋊Dic3C2311yescharacteristic
135#3524—91noSylow
136C2×C3×#41C2×D314yes—
137C2×C3×#41C2×D314yes—
138C2×D3×Q8—34no—
139C3×#127C2×D3112yes—
140C3×#121C2×D3112yes—
141C3×#121C2×D3112yes—
142C3×C4×Q8C2×D314yes—
143C3×C4×D4C2×D3112yes—
144Q8×Dic3—34no—
145Q8×Dic3—34no—
146Q8×Dic3—34no—
147#939—312no—
148#939—324no—
149#938—312no—
150#938—312no—
151#936—312no—
152#936—312no—
153#936—324no—
154#935—312no—
155#935—324no—
156#935—324no—
157D4×Dic3—312no—
158D4×Dic3—312no—
159D4×Dic3—324no—
160D4×Dic3—312no—
161D4×Dic3—312no—
162C4×#67—312no—
163C4×#67—312no—
164#926—312no—
165#926—312no—
166C2×C4⋊Dic3—312no—
167#924—312no—
168#924—312no—
169C2×C4×Dic3—312no—
170#898—34no—
171#892—312no—
172#890—312no—
173#889—312no—
174#888—312no—
175#887—312no—
176#886—312no—
177#885—312no—
178#879—312no—
179#879—324no—
180#878—312no—
181#877—324no—
182#872—312no—
183#870—312no—
184C4×Dic6—312no—
185C4×Dic6—312no—
186C23×C32C2413yes—
187C23×C32C2413yes—
188C22×C3⋊D3C2411yescharacteristic
189C32×Q8#4114yes—
190C32×D4—26no—
191C32×D4—26no—
192C32×D4—46no—
193C32×D4—43no—
194C2×C32×C4—26no—
195C2×C32×C4—26no—
196C2×C32×C4C2411yescharacteristic
197C2×C32×C4C2413yes—
198C2×C32×C4C2411yescharacteristic
199C2×C32×C4C2411yescharacteristic
200C2×C32×C4C2413yes—
201#638—43no—
202#638—43no—
203C2×C3⋊Dic3—43no—
204C2×C3⋊Dic3—43no—
205C2×C3⋊Dic3—46no—
206C2×C3⋊Dic3C2411yescharacteristic
207C2×C3⋊Dic3C2413yes—
208C2×C3⋊Dic3C2411yescharacteristic
209C2×C3⋊Dic3C2411yescharacteristic
210C2×C3⋊Dic3C2413yes—
211C2×C3⋊Dic3C2413yes—
212C2×C3⋊Dic3C2413yes—
213C4×C3⋊D3—26no—
214#634—26no—
215#634—43no—
216#559—93no—
217#557—91no—
218#555—93no—
219#553—93no—
220#552—93no—
221#550C3⋊D311yescharacteristic, complemented
222#548—91no—
223#548—91no—
224#542—93no—
225#540—93no—
226#529—93no—
227#529—93no—
228#520—91no—
229#519—91no—
230C4×#41—91no—
231C3×#41—216no—
232C3×#41—216no—
233C2×C3×Q8C22×D314yes—
234C2×C3×D4C22×D3112yes—
235C2×C3×D4C22×D3112yes—
236C2×C3×D4C22×D3124yes—
237C2×C3×D4C22×D3112yes—
238C22×C3×C4C22×D3112yes—
239C22×C3×C4C22×D3112yes—
240C2×#67—312no—
241C2×#67—312no—
242C22×Dic3—324no—
243C22×Dic3—312no—
244C22×Dic3—312no—
245D3×Q8—616no—
246C2×C4×D3—312no—
247C2×Dic6—312no—
248C2×Dic6—312no—
249C3×C4⋊C4C22×D3112yes—
250C3×C4⋊C4C22×D314yes—
251C3×C22⋊C4C22×D3112yes—
252C3×C22⋊C4C22×D3112yes—
253C3×C42C22×D3112yes—
254#217—324no—
255#217—312no—
256#217—324no—
257#217—312no—
258#217—324no—
259#217—312no—
260#217—312no—
261(C2×D3)⋊C4—34no—
262(C2×D3)⋊C4—312no—
263(C2×D3)⋊C4—34no—
264(C2×D3)⋊C4—34no—
265C4⋊Dic3—312no—
266C4⋊Dic3—312no—
267C4⋊Dic3—312no—
268C4⋊Dic3—312no—
269C4⋊Dic3—34no—
270C4⋊Dic3—312no—
271Dic3⋊C4—34no—
272Dic3⋊C4—312no—
273Dic3⋊C4—312no—
274Dic3⋊C4—324no—
275Dic3⋊C4—312no—
276Dic3⋊C4—312no—
277Dic3⋊C4—312no—
278C4×Dic3—324no—
279C4×Dic3—312no—
280C4×Dic3—312no—
281C4×Dic3—312no—
282C4×Dic3—312no—
283C4×Dic3—34no—
284C22×C32—23no—
285C22×C32—23no—
286C22×C32—23no—
287C22×C32—23no—
288C22×C32—23no—
289C22×C32—23no—
290C22×C32C2511yescharacteristic
291C2×C3⋊D3—21no—
292C2×C3⋊D3—21no—
293C2×C3⋊D3—21no—
294C32×C4—21no—
295C32×C4—21no—
296C32×C4—23no—
297C32×C4—21no—
298C32×C4C2×#4116yes—
299C3⋊Dic3—23no—
300C3⋊Dic3—21no—
301C3⋊Dic3—23no—
302C3⋊Dic3—21no—
303C3⋊Dic3—23no—
304C3⋊Dic3—21no—
305C3⋊Dic3—23no—
306C2×#41C2×C3⋊D311yescharacteristic
307C2×#41C2×C3⋊D311yescharacteristic
308C22×Q8—91no—
309C4⋊Q8—93no—
310#127C2×C3⋊D313yes—
311#126—91no—
312#126—93no—
313#126—96no—
314#125—93no—
315#125—93no—
316#125—93no—
317#124—93no—
318#124—93no—
319#124—96no—
320#124—93no—
321#123—96no—
322#123—93no—
323#123—96no—
324#123—93no—
325C22⋊Q8—93no—
326C22⋊Q8—93no—
327C22⋊Q8—93no—
328#121—93no—
329#121—93no—
330#121—93no—
331#121—96no—
332#121C2×C3⋊D313yes—
333#121C2×C3⋊D313yes—
334C4×Q8—91no—
335C4×Q8—91no—
336C4×Q8—91no—
337C4×Q8—93no—
338C4×Q8—93no—
339C4×Q8—93no—
340C4×Q8C2×C3⋊D311yescharacteristic
341C4×D4—93no—
342C4×D4—93no—
343C4×D4—93no—
344C4×D4—93no—
345C4×D4—96no—
346C4×D4—93no—
347C4×D4—93no—
348C4×D4C2×C3⋊D313yes—
349#117—93no—
350#117—93no—
351#117—93no—
352#117—96no—
353#117—93no—
354C2×C4⋊C4—93no—
355C2×C42—93no—
356C23×C3C23×D3112yes—
357C23×C3C23×D3112yes—
358C22×D3—34no—
359C3×Q8#237116yes—
360C3×D4—224no—
361C3×D4—224no—
362C3×D4—412no—
363C3×D4—424no—
364C2×C3×C4—224no—
365C2×C3×C4—224no—
366C2×C3×C4C23×D314yes—
367C2×C3×C4C23×D3112yes—
368C2×C3×C4C23×D314yes—
369C2×C3×C4C23×D314yes—
370C2×C3×C4C23×D3112yes—
371#67—1212no—
372#67—1212no—
373C2×Dic3—34no—
374C2×Dic3—312no—
375C2×Dic3—34no—
376C2×Dic3—34no—
377C2×Dic3—312no—
378C2×Dic3—312no—
379C2×Dic3—312no—
380C2×Dic3—1212no—
381C2×Dic3—1224no—
382C2×Dic3—1212no—
383C4×D3—624no—
384Dic6—624no—
385Dic6—1212no—
386C2×C32—43no—
387C2×C32—43no—
388C2×C32C22×#4111yescharacteristic
389C2×C32#58511yescharacteristic
390C2×C32#58511yescharacteristic
391C3⋊D3—41no—
392#41—24no—
393#41—24no—
394C2×Q8—93no—
395C2×Q8—93no—
396C2×Q8—184no—
397C2×Q8C22×C3⋊D311yescharacteristic
398C2×D4—93no—
399C2×D4—93no—
400C2×D4C22×C3⋊D313yes—
401C2×D4C22×C3⋊D313yes—
402C2×D4C22×C3⋊D316yes—
403C2×D4C22×C3⋊D313yes—
404C22×C4—93no—
405C22×C4—93no—
406C22×C4—96no—
407C22×C4—93no—
408C22×C4C22×C3⋊D313yes—
409C22×C4C22×C3⋊D313yes—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—93no—
413C4⋊C4—91no—
414C4⋊C4—93no—
415C4⋊C4—93no—
416C4⋊C4—93no—
417C4⋊C4—93no—
418C4⋊C4—96no—
419C4⋊C4—93no—
420C4⋊C4—93no—
421C4⋊C4—91no—
422C4⋊C4—93no—
423C4⋊C4C22×C3⋊D313yes—
424C4⋊C4C22×C3⋊D311yescharacteristic
425C22⋊C4—93no—
426C22⋊C4—96no—
427C22⋊C4—93no—
428C22⋊C4—96no—
429C22⋊C4—93no—
430C22⋊C4—96no—
431C22⋊C4—93no—
432C22⋊C4—91no—
433C22⋊C4—93no—
434C22⋊C4—91no—
435C22⋊C4—91no—
436C22⋊C4C22×C3⋊D313yes—
437C22⋊C4C22×C3⋊D313yes—
438C42—91no—
439C42—93no—
440C42—93no—
441C42—93no—
442C42—96no—
443C42—93no—
444C42C22×C3⋊D313yes—
445C22×C3—212no—
446C22×C3—212no—
447C22×C3—212no—
448C22×C3—212no—
449C22×C3—212no—
450C22×C3—212no—
451C22×C3C24×D314yes—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—64no—
455C3×C4—24no—
456C3×C4—24no—
457C3×C4—24no—
458C3×C4—212no—
459C3×C4C2×#237124yes—
460Dic3—612no—
461Dic3—612no—
462Dic3—64no—
463Dic3—612no—
464Dic3—64no—
465Dic3—612no—
466Dic3—64no—
467C32#352411yescharacteristic, complemented, Sylow
468C23—91no—
469C23C23×C3⋊D313yes—
470C23C23×C3⋊D313yes—
471Q8—186no—
472Q8—363no—
473Q8#383014yes—
474D4—26no—
475D4—26no—
476D4—43no—
477D4—46no—
478D4—363no—
479D4—363no—
480C2×C4—26no—
481C2×C4—26no—
482C2×C4—91no—
483C2×C4—93no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—93no—
487C2×C4—93no—
488C2×C4—93no—
489C2×C4—186no—
490C2×C4—363no—
491C2×C4—366no—
492C2×C4—363no—
493C2×C4C23×C3⋊D311yescharacteristic
494C2×C4C23×C3⋊D313yes—
495C2×C4C23×C3⋊D311yescharacteristic
496C2×C4C23×C3⋊D311yescharacteristic
497C2×C4C23×C3⋊D313yes—
498C2×C3—412no—
499C2×C3—412no—
500C2×C3C22×#23714yes—
501C2×C3#596414yes—
502C2×C3#596614yes—
503D3—124no—
504C22—23no—
505C22—23no—
506C22—23no—
507C22—23no—
508C22—23no—
509C22—23no—
510C22—181no—
511C22—181no—
512C22—181no—
513C22C24×C3⋊D311yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—23no—
518C4—183no—
519C4—181no—
520C4—183no—
521C4—183no—
522C4—181no—
523C4—183no—
524C4—181no—
525C4C2×#383016yes—
526C3#8677714yescomplemented
527C2—43no—
528C2—43no—
529C2—361no—
530C2C22×#383011yescharacteristic
531C2#1059675611yescharacteristic
532C2#1059675811yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#550C2
hypercenter#550C3⋊D3
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C32×#550C2semidirect
2. #10596302C2semidirect
3. #10596302C2semidirect
4. #10596298C2semidirect
5. #41×C3⋊Dic3C2semidirect
6. #10596190C2semidirect
7. #10596184C2semidirect
8. #10596089C2semidirect
9. #10596087C2semidirect
10. #10596074C2semidirect
11. #10596071C2semidirect
12. #10596043C2semidirect
13. #10596040C2semidirect
14. #10596012C2semidirect
15. #10596009C2semidirect
67. C3×#550D3semidirect
221. #550C3⋊D3semidirect
467. C32#3524semidirect
526. C3#86777semidirect

Maximal subgroups

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

subgroupindex
C32×#5502
#105963022
#105962982
#41×C3⋊Dic32
#105961902
#105961842
#105960892
#105960872
#105960742
#105960712
#105960432
#105960402
#105960122
#105960092
#867773