Finite Group Databasebeta

← #11898315

Subgroups — #11898315

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic, complemented
4C3×#5019C211yesmaximal, characteristic, complemented
5#10591490C212yesmaximal, complemented
6#10591438C212yesmaximal, complemented
7#10590559C212yesmaximal, complemented
8#10590475C212yesmaximal, complemented
9#10590377C211yesmaximal, characteristic, complemented
10#10590375C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83588—31nomaximal
13#80420—31nomaximal
14C2×C3×#235—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3754C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#940C2212yes—
19C2×C3×#214C2212yes—
20C3×#930—21no—
21C3×#893C2212yes—
22C3×#884—22no—
23C3×#874C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63872—21no—
27#63866C2212yes—
28#63846—22no—
29#63843—21no—
30Dic3×Dic6C2212yes—
31C2×#3716C2212yes—
32C2×#3715C2212yes—
33C2×#3715C2212yes—
34#63659C2211yescharacteristic
35#63637C2211yescharacteristic
36#63635C2211yescharacteristic
37C4×C3⋊(C3⋊C8)C2211yescharacteristic
38C3×#810C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41#63563C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5721—31no—
45#5570—31no—
46#5553D311yescharacteristic
47C3×#461—31no—
48#5175—32no—
49#5163—32no—
50#5085—31no—
51#5076—32no—
52#5076—31no—
53#5075—32no—
54#5075—31no—
55Q8×C3⋊C8—31no—
56#5019—32no—
57#5019D311yescharacteristic, complemented
58C4×#214—31no—
59C4×#214—31no—
60C4×#214—32no—
61C4×#214—61no—
62#4848—31no—
63#4830—31no—
64#4818—32no—
65#4788—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2311yescharacteristic
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C3×#235—44no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6D411yescharacteristic
77C2×C3×Dic6C2312yes—
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42C2311yescharacteristic
81#3754—22no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84C4×C3⋊Dic3—21no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×#214—42no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98Dic32—22no—
99#3716—42no—
100#3715—24no—
101#3715—42no—
102#3392—91noSylow
103C2×C3×#41—61no—
104C2×#235—21no—
105C2×C3×SD16—32no—
106C3×C4⋊Q8—31no—
107C3×#127—32no—
108C3×#127—31no—
109C3×#121—62no—
110C3×#121—61no—
111C3×C4×Q8—31no—
112C3×C4×D4—21no—
113C3×C4×D4—32no—
114C3×C4×D4C2×D311yescharacteristic
115C3×C4×D4C2×D311yescharacteristic
116Q8×Dic3—32no—
117Q8×Dic3—61no—
118#944—32no—
119C2×#215—32no—
120C2×#215—32no—
121#940C2×D312yes—
122C2×#214—31no—
123C2×#214—31no—
124C2×#214—32no—
125C2×#214—32no—
126C2×#214—32no—
127C2×#214—61no—
128C2×#214C2×D312yes—
129#930—21no—
130C2×#204—32no—
131#893C2×D312yes—
132#890—62no—
133#890—61no—
134#890—61no—
135#889—62no—
136#887—61no—
137#884—22no—
138#874C2×D311yescharacteristic
139#869—32no—
140#869C2×D311yescharacteristic
141C4×Dic6—32no—
142C4×Dic6—31no—
143C4×Dic6—31no—
144C4×Dic6—61no—
145C4×Dic6C2×D311yescharacteristic
146C3×C4⋊C8—31no—
147C3×#103—32no—
148#832—31no—
149#832—31no—
150#832—32no—
151#832—61no—
152#821—32no—
153Dic3⋊C8—32no—
154C8×Dic3—32no—
155#810—31no—
156#810—31no—
157#810—61no—
158#810C2×D312yes—
159#808—31no—
160#808—31no—
161#808—61no—
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8—31no—
165C4×C3⋊C8—31no—
166C4×C3⋊C8—32no—
167C4×C3⋊C8—61no—
168C23×C32—21no—
169C22×C3×D3—22no—
170C32×D4—21no—
171C32×D4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—42no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179#634—21no—
180#634—21no—
181C3×#67—44no—
182C3×#67—82no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×D412yes—
186C3×D12—22no—
187C3×D12—22no—
188C3×D12—42no—
189C3×D12—81no—
190C3×C4×D3—44no—
191C3×Dic6—22no—
192C3×Dic6—22no—
193C3×Dic6SD1614yescomplemented
194C3⋊(C3⋊C8)—21no—
195C3⋊(C3⋊C8)#4112yescomplemented
196C3×C3⋊C8—22no—
197#557—91no—
198#550—31no—
199#492—91no—
200#492—92no—
201#461—31no—
202#461—92no—
203#460—91no—
204#460—92no—
205C8×Q8—91no—
206C4×SD16—92no—
207C4×SD16—91no—
208C3×#41—124no—
209C2×C3×Q8—31no—
210C2×C3×Q8—32no—
211C2×C3×D4—21no—
212C2×C3×D4—32no—
213C2×C3×D4—62no—
214C2×C3×D4—62no—
215C2×C3×D4—61no—
216C2×C3×D4—61no—
217C2×C3×D4C22×D311yescharacteristic
218C2×C3×D4C22×D311yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—41no—
222C22×C3×C4—62no—
223C2×#67—22no—
224C2×#67—22no—
225#235—44no—
226C2×D12—21no—
227C2×D12—21no—
228C2×D12C22×D312yes—
229C2×C4×D3—22no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C2×Dic6—61no—
233C2×Dic6#6711yescharacteristic
234C2×Dic6C22×D312yes—
235C3×SD16—122no—
236C2×C3×C8—32no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—41no—
247C3×C22⋊C4—62no—
248C3×C42—21no—
249C3×C42—32no—
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252#215—64no—
253#215—122no—
254#214—42no—
255#214—64no—
256#214—62no—
257#214—62no—
258#214—64no—
259#214—122no—
260#214—122no—
261(C2×D3)⋊C4—22no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—61no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270C4⋊Dic3#6711yescharacteristic
271Dic3⋊C4—62no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—121no—
277Dic3⋊C4#6712yes—
278C4×Dic3—62no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C4×Dic3—62no—
282C4×Dic3—121no—
283C4×Dic3C22×D312yes—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—31no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—61no—
289C2×C3⋊C8—61no—
290C2×C3⋊C8C22×D312yes—
291#204—122no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32—41no—
295C22×C32C22×D411yescharacteristic
296C2×C3×D3—42no—
297C2×C3×D3—42no—
298C2×C3×D3—42no—
299C32×C4—21no—
300C32×C4—41no—
301C32×C4C2×SD1612yes—
302C32×C4C2×#4111yescharacteristic
303C32×C4H(5,𝔽2)11yescharacteristic
304C3⋊Dic3—41no—
305C3⋊Dic3—41no—
306C3×Dic3—22no—
307C3×Dic3—42no—
308C3×Dic3C2×SD1614yes—
309C2×#41—61no—
310C2×SD16—32no—
311C2×SD16—92no—
312C2×SD16—92no—
313C2×SD16—91no—
314C2×SD16—92no—
315C4⋊Q8—31no—
316C4⋊Q8—92no—
317#127—32no—
318#127—31no—
319#125—182no—
320#125—181no—
321#121—62no—
322#121—61no—
323C4×Q8—31no—
324C4×Q8—92no—
325C4×Q8—91no—
326C4×Q8—181no—
327C4×D4—32no—
328C4×D4D3211yescharacteristic
329#106—91no—
330C4⋊C8—31no—
331C4⋊C8—92no—
332#103—32no—
333#103—91no—
334#102—92no—
335#102—91no—
336C4×C8—92no—
337C4×C8—91no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—41no—
341C23×C3—62no—
342C22×D3—22no—
343C3×Q8—34no—
344C3×Q8—62no—
345C3×Q8—62no—
346C3×D4—22no—
347C3×D4—21no—
348C3×D4—21no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4—41no—
352C3×D4—62no—
353C3×D4—62no—
354C3×D4—124no—
355C3×D4—122no—
356C3×D4—241no—
357C3×D4—242no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—32no—
364C2×C3×C4—32no—
365C2×C3×C4—41no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—62no—
369C2×C3×C4—82no—
370C2×C3×C4—124no—
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377#67—44no—
378#67—82no—
379C2×Dic3—22no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3C2×#6712yes—
387C2×Dic3C2×#6712yes—
388D12—22no—
389D12—22no—
390D12—42no—
391D12—81no—
392C4×D3—44no—
393Dic6—22no—
394Dic6—22no—
395Dic6—62no—
396Dic6—61no—
397Dic6—61no—
398Dic6—61no—
399Dic6—61no—
400Dic6—121no—
401Dic6#21414yescomplemented
402C3×C8—62no—
403C3⋊C8—22no—
404C3⋊C8—32no—
405C3⋊C8—32no—
406C3⋊C8—62no—
407C3⋊C8—61no—
408C3⋊C8—61no—
409C3⋊C8—121no—
410C2×C32—81no—
411C2×C32#55011yescharacteristic
412C2×C32C22×SD1611yescharacteristic
413C2×C32#57711yescharacteristic
414C3×D3—82no—
415#41—124no—
416C2×Q8—31no—
417C2×Q8—32no—
418C2×Q8—91no—
419C2×D4—32no—
420C2×D4—62no—
421C2×D4—62no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4C2×D3211yescharacteristic
425C22×C4—21no—
426C22×C4—62no—
427SD16—122no—
428SD16—182no—
429SD16—184no—
430SD16—362no—
431SD16—362no—
432C2×C8—32no—
433C2×C8—91no—
434C2×C8—91no—
435C4⋊C4—32no—
436C4⋊C4—31no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—91no—
440C4⋊C4—182no—
441C4⋊C4—182no—
442C4⋊C4—182no—
443C4⋊C4—181no—
444C4⋊C4C2×D3211yescharacteristic
445C22⋊C4—21no—
446C22⋊C4—62no—
447C42—32no—
448C42—182no—
449C42—181no—
450C42C2×D3211yescharacteristic
451C22×C3—21no—
452C22×C3—42no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—122no—
462C22×C3—122no—
463C22×C3—122no—
464C22×C3C2×D3×D411yescharacteristic
465C22×C3C22×#6711yescharacteristic
466C2×D3—42no—
467C2×D3—42no—
468C2×D3—42no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—22no—
474C3×C4—34no—
475C3×C4—41no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4—62no—
479C3×C4—81no—
480C3×C4—122no—
481C3×C4D3×SD1612yes—
482C3×C4C2×#21412yes—
483C3×C4#100411yescharacteristic
484C3×C4D3×#4111yescharacteristic
485C3×C4D3×#4111yescharacteristic
486C3×C4#100911yescharacteristic
487Dic3—22no—
488Dic3—42no—
489Dic3—122no—
490Dic3—121no—
491Dic3—121no—
492Dic3—121no—
493Dic3—121no—
494Dic3—241no—
495Dic3C2×#21414yes—
496C32#339211yescharacteristic, complemented, Sylow
497C23—21no—
498C23—62no—
499Q8—34no—
500Q8—62no—
501Q8—62no—
502Q8—181no—
503Q8—181no—
504D4—21no—
505D4—21no—
506D4—62no—
507D4—62no—
508D4—124no—
509D4—122no—
510D4—241no—
511D4—242no—
512C2×C4—21no—
513C2×C4—32no—
514C2×C4—32no—
515C2×C4—42no—
516C2×C4—62no—
517C2×C4—124no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4D3×#6711yescharacteristic
521C2×C4D3×#6711yescharacteristic
522C2×C4C22×D3211yescharacteristic
523C8—62no—
524C8—92no—
525C8—181no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—82no—
530C2×C3—81no—
531C2×C3—81no—
532C2×C3—242no—
533C2×C3#559911yescharacteristic
534C2×C3C2×D3×SD1611yescharacteristic
535C2×C3#577811yescharacteristic
536C2×C3C22×#21411yescharacteristic
537C2×C3#583411yescharacteristic
538C2×C3#583611yescharacteristic
539D3—82no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—122no—
544C22—122no—
545C22—122no—
546C22C2×D3×#6711yescharacteristic
547C4—21no—
548C4—34no—
549C4—41no—
550C4—62no—
551C4—122no—
552C4—361no—
553C4—361no—
554C4D3×#21412yes—
555C4#6430611yescharacteristic
556C4#6430711yescharacteristic
557C3—21no—
558C3#8042011yescharacteristic, complemented
559C3#8358811yescharacteristic, complemented
560C2—81no—
561C2—242no—
562C2#1059500611yescharacteristic
563C2C2×D3×#21411yescharacteristic
564C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC4×D4D32
hypocenterC32#3392
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. #10593861C2semidirect
3. C4×#3754C2semidirect
4. C3×#5019C2semidirect
5. #10591490C2semidirect
6. #10591438C2semidirect
7. #10590559C2semidirect
8. #10590475C2semidirect
9. #10590377C2semidirect
10. #10590375C2semidirect
11. #10590250C2semidirect
57. #5019D3semidirect
193. C3×Dic6SD16semidirect
195. C3⋊(C3⋊C8)#41semidirect
401. Dic6#214semidirect
496. C32#3392semidirect
558. C3#80420semidirect
559. C3#83588semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105938612
C4×#37542
C3×#50192
#105914902
#105914382
#105905592
#105904752
#105903772
#105903752
#105902502
#835883
#804203