Finite Group Databasebeta

← #11887568

Subgroups — #11887568

Order 1152.

900 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5551C211yesmaximal, characteristic
2Dic6×D12C211yesmaximal, characteristic, complemented
3#10592718C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591517C212yesmaximal, complemented
6#10591460C212yesmaximal, complemented
7D3×#810C212yesmaximal, complemented
8#10590426C212yesmaximal, complemented
9C3⋊C8×D12C211yesmaximal, characteristic, complemented
10#10590288C211yesmaximal, characteristic, complemented
11#10590285C211yesmaximal, characteristic, complemented
12#83531—31nomaximal
13#79678—31nomaximal
14C2×C3×#235—21no—
15C2×D3×Dic6C2212yes—
16C32×C4×D4C2211yescharacteristic
17C2×#3754C2212yes—
18#64078C2211yescharacteristic
19C3×#938C2212yes—
20C2×C3×#214C2211yescharacteristic
21C3×#924—21no—
22C3×D3×C4⋊C4C2212yes—
23C3×#883—22no—
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63918—21no—
28#63893—22no—
29Dic3×D12—21no—
30#63857C2212yes—
31C2×D3×C3⋊C8C2212yes—
32#63637C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#832C2211yescharacteristic
35C3×#810C2211yescharacteristic
36C3×#808C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63574C2212yes—
39#63567C2212yes—
40#63567C2212yes—
41#63565C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×#547—31no—
44Q8×D12—31no—
45#5551D311yescharacteristic
46D4×Dic6—31no—
47C3×C4×SD16—31no—
48#5170—32no—
49#5094—31no—
50#5093—31no—
51#5041—32no—
52#5040—32no—
53#5020—31no—
54#5019—31no—
55#5019—31no—
56#5019—61no—
57C4×#214D311yescharacteristic, complemented
58D4×C3⋊C8—31no—
59#4971—32no—
60C2×#810—32no—
61#4862—32no—
62D3×#103—32no—
63#4778—32no—
64C8×D12—31no—
65#4681—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2312yes—
69C2×C3×#67—22no—
70C3×#235—44no—
71C2×C3×D12D411yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2312yes—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×#627—22no—
77C2×D3×Dic3—22no—
78D3×Dic6—24no—
79D3×Dic6—42no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83#3754—42no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)—21no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—22no—
88C3×#214—22no—
89C3×(C2×D3)⋊C4D412yes—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—21no—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99Dic3⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101D3×C3⋊C8—42no—
102#3298—91noSylow
103C2×C3×#41—61no—
104C2×D3×Q8—32no—
105C2×#235—21no—
106C22×Dic6—32no—
107C2×C3×SD16—31no—
108C3×C4⋊Q8—31no—
109C3×#123—62no—
110C3×C22⋊Q8—61no—
111C3×#121—32no—
112C3×C4×Q8—31no—
113C3×C4×D4—21no—
114C3×C4×D4—31no—
115C3×C4×D4C2×D311yescharacteristic
116C3×C4×D4C2×D311yescharacteristic
117C2×C3×C4⋊C4—32no—
118#938C2×D312yes—
119D4×Dic3—61no—
120C2×#214—32no—
121C2×#214—32no—
122C2×#214—62no—
123C2×#214C2×D311yescharacteristic
124#924—21no—
125#924—32no—
126C22×C3⋊C8—32no—
127C2×D3×C8—32no—
128#897—32no—
129#897—62no—
130D3×C4⋊C4C2×D312yes—
131#888—61no—
132#883—22no—
133#878—62no—
134C4×D12—61no—
135C4×D12C2×D311yescharacteristic
136#869—31no—
137#869—31no—
138#869—61no—
139#869—61no—
140#869C2×D311yescharacteristic
141C4×Dic6C2×D311yescharacteristic
142C3×#106—31no—
143C3×#103—31no—
144C3×#102—31no—
145C3×C4×C8—31no—
146#835—32no—
147#832C2×D311yescharacteristic
148#830—32no—
149(C2×D3)⋊C8—32no—
150#816—32no—
151#816—32no—
152#810—32no—
153#810—32no—
154#810—32no—
155#810—32no—
156#810—32no—
157#810—62no—
158#810C2×D311yescharacteristic
159#808—32no—
160#808—32no—
161#808C2×D311yescharacteristic
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—31no—
164C4⋊(C3⋊C8)—61no—
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—21no—
167C22×C3×D3C2×D412yes—
168C32×D4—21no—
169C32×D4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—22no—
176#634—22no—
177#634—22no—
178C3×#67—44no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3C2×D412yes—
183C3×D12SD1614yescomplemented
184C3×C4×D3—22no—
185C3×C4×D3—22no—
186C3×C4×D3—44no—
187C3×Dic6—21no—
188C3×Dic6—42no—
189C3×Dic6#4112yescomplemented
190#627—44no—
191D3×Dic3—44no—
192C3⋊(C3⋊C8)—22no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—21no—
195D4×Q8—91no—
196#547—31no—
197#487—91no—
198#483—92no—
199#475—91no—
200#465—92no—
201#461—91no—
202#448—92no—
203C4×SD16—31no—
204C8×D4—91no—
205C2×#103—92no—
206C3×#41—124no—
207C2×C3×Q8—31no—
208C2×C3×Q8—61no—
209C2×C3×D4—21no—
210C2×C3×D4—31no—
211C2×C3×D4—62no—
212C2×C3×D4C22×D311yescharacteristic
213C2×C3×D4C22×D311yescharacteristic
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—41no—
218C22×C3×C4—62no—
219C2×#67—22no—
220C22×Dic3—62no—
221D3×Q8—64no—
222D3×Q8—122no—
223#235—44no—
224C2×D12#6711yescharacteristic
225C2×C4×D3—22no—
226C2×C4×D3—62no—
227C2×C4×D3C22×D312yes—
228C2×Dic6—21no—
229C2×Dic6—32no—
230C2×Dic6—32no—
231C2×Dic6—62no—
232C2×Dic6—64no—
233C2×Dic6—62no—
234C2×Dic6—62no—
235C2×Dic6—122no—
236C2×Dic6C22×D311yescharacteristic
237C3×SD16—62no—
238C2×C3×C8—31no—
239C2×C3×C8—31no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C22⋊C4—21no—
250C3×C22⋊C4—21no—
251C3×C22⋊C4—32no—
252C3×C22⋊C4—41no—
253C3×C22⋊C4—62no—
254C3×C42—21no—
255C3×C42—61no—
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258#217—22no—
259#217—62no—
260#214—22no—
261#214—122no—
262#214—122no—
263#214—124no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4#6712yes—
266C4⋊Dic3—21no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—62no—
272C4⋊Dic3—121no—
273C4⋊Dic3—121no—
274C4⋊Dic3#6711yescharacteristic
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D312yes—
277Dic3⋊C4—21no—
278Dic3⋊C4—22no—
279Dic3⋊C4—62no—
280C4×Dic3—21no—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8—122no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287D3×C8—122no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32C22×D411yescharacteristic
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3C2×SD1614yes—
295C32×C4—21no—
296C32×C4—41no—
297C32×C4C2×SD1612yes—
298C32×C4C2×#4111yescharacteristic
299C32×C4H(5,𝔽2)11yescharacteristic
300C3⋊Dic3—42no—
301C3×Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C2×#41—61no—
306C22×Q8—92no—
307C2×SD16—31no—
308C2×SD16—92no—
309C22×C8—92no—
310C4⋊Q8—31no—
311C4⋊Q8—91no—
312C4⋊Q8—181no—
313#123—62no—
314C22⋊Q8—61no—
315C22⋊Q8—92no—
316C22⋊Q8—182no—
317#121—32no—
318C4×Q8—31no—
319C4×D4—31no—
320C4×D4—181no—
321C4×D4D3211yescharacteristic
322C2×C4⋊C4—32no—
323#106—31no—
324#106—92no—
325C4⋊C8—91no—
326#103—31no—
327#103—92no—
328#103—92no—
329#103—92no—
330#103—92no—
331#102—31no—
332C22⋊C8—92no—
333C4×C8—31no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—32no—
337C23×C3—41no—
338C22×D3C2×#6712yes—
339C3×Q8—32no—
340C3×Q8—61no—
341C3×Q8—122no—
342C3×D4—22no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4—34no—
348C3×D4—41no—
349C3×D4—124no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—32no—
356C2×C3×C4—41no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—61no—
364C2×C3×C4—82no—
365C2×C3×C4—124no—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372#67—44no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—22no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—122no—
379C2×Dic3—124no—
380C2×Dic3C2×#6712yes—
381D12#21414yescomplemented
382C4×D3—22no—
383C4×D3—22no—
384C4×D3—44no—
385C4×D3—124no—
386Dic6—21no—
387Dic6—42no—
388Dic6—62no—
389Dic6—62no—
390Dic6—62no—
391Dic6—62no—
392Dic6—122no—
393Dic6—122no—
394Dic6—124no—
395Dic6—124no—
396Dic6#23512yescomplemented
397C3×C8—61no—
398C3×C8—61no—
399C3⋊C8—21no—
400C3⋊C8—21no—
401C3⋊C8—62no—
402C3⋊C8—62no—
403C3⋊C8—122no—
404C2×C32—81no—
405C2×C32#54611yescharacteristic
406C2×C32C22×SD1611yescharacteristic
407C2×C32#57811yescharacteristic
408C3×D3—24no—
409#41—124no—
410C2×Q8—31no—
411C2×Q8—61no—
412C2×Q8—92no—
413C2×Q8—182no—
414C2×Q8—184no—
415C2×Q8—362no—
416C2×D4—31no—
417C2×D4—62no—
418C2×D4C2×D3211yescharacteristic
419C22×C4—21no—
420C22×C4—32no—
421C22×C4—62no—
422C22×C4—182no—
423SD16—62no—
424SD16—362no—
425C2×C8—31no—
426C2×C8—31no—
427C2×C8—92no—
428C2×C8—362no—
429C4⋊C4—31no—
430C4⋊C4—31no—
431C4⋊C4—32no—
432C4⋊C4—62no—
433C4⋊C4—61no—
434C4⋊C4—61no—
435C4⋊C4—182no—
436C4⋊C4—181no—
437C4⋊C4—181no—
438C4⋊C4C2×D3211yescharacteristic
439C22⋊C4—21no—
440C22⋊C4—32no—
441C22⋊C4—62no—
442C22⋊C4—182no—
443C42—61no—
444C42C2×D3211yescharacteristic
445C22×C3—21no—
446C22×C3—34no—
447C22×C3—42no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—62no—
455C22×C3—62no—
456C22×C3—81no—
457C22×C3—81no—
458C22×C3C2×D3×D411yescharacteristic
459C22×C3C22×#6711yescharacteristic
460C2×D3—22no—
461C2×D3—22no—
462C2×D3C2×#21414yes—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—22no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—41no—
471C3×C4—62no—
472C3×C4—62no—
473C3×C4—81no—
474C3×C4—122no—
475C3×C4—121no—
476C3×C4D3×SD1612yes—
477C3×C4C2×#21412yes—
478C3×C4C2×#23511yescharacteristic
479C3×C4D3×#4111yescharacteristic
480C3×C4#100911yescharacteristic
481C3×C4#100911yescharacteristic
482Dic3—22no—
483Dic3—22no—
484Dic3—41no—
485Dic3—42no—
486Dic3—122no—
487Dic3—122no—
488Dic3—242no—
489C32#329811yescharacteristic, complemented, Sylow
490C23—21no—
491C23—32no—
492Q8—32no—
493Q8—61no—
494Q8—122no—
495Q8—182no—
496Q8—182no—
497Q8—364no—
498D4—21no—
499D4—21no—
500D4—34no—
501D4—124no—
502C2×C4—21no—
503C2×C4—32no—
504C2×C4—42no—
505C2×C4—61no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—61no—
509C2×C4—62no—
510C2×C4—124no—
511C2×C4—182no—
512C2×C4—364no—
513C2×C4D3×#6711yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C2×C4C22×D3211yescharacteristic
516C8—61no—
517C8—61no—
518C8—182no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—64no—
523C2×C3—82no—
524C2×C3—81no—
525C2×C3—81no—
526C2×C3#555011yescharacteristic
527C2×C3C2×D3×SD1611yescharacteristic
528C2×C3#577111yescharacteristic
529C2×C3C22×#21411yescharacteristic
530C2×C3#582911yescharacteristic
531C2×C3#583811yescharacteristic
532D3—24no—
533C22—34no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—62no—
538C22—62no—
539C22C2×D3×#6711yescharacteristic
540C4—21no—
541C4—41no—
542C4—62no—
543C4—62no—
544C4—122no—
545C4—121no—
546C4—362no—
547C4D3×#21412yes—
548C4D3×#23511yescharacteristic
549C4#6430811yescharacteristic
550C3—21no—
551C3#7967811yescharacteristic, complemented
552C3#8353111yescharacteristic, complemented
553C2—64no—
554C2—81no—
555C2#1059506711yescharacteristic
556C2C2×D3×#21411yescharacteristic
557C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5551C2
hypercenterC4×D4D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. Dic6×D12C2semidirect
3. #10592718C2semidirect
4. C3×C4×#214C2semidirect
5. #10591517C2semidirect
6. #10591460C2semidirect
7. D3×#810C2semidirect
8. #10590426C2semidirect
9. C3⋊C8×D12C2semidirect
10. #10590288C2semidirect
11. #10590285C2semidirect
57. C4×#214D3semidirect
183. C3×D12SD16semidirect
189. C3×Dic6#41semidirect
381. D12#214semidirect
396. Dic6#235semidirect
489. C32#3298semidirect
551. C3#79678semidirect
552. C3#83531semidirect

Maximal subgroups

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

subgroupindex
C3×#55512
Dic6×D122
#105927182
C3×C4×#2142
#105915172
#105914602
D3×#8102
#105904262
C3⋊C8×D122
#105902882
#105902852
#835313
#796783