Finite Group Databasebeta

← #11898320

Subgroups — #11898320

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3#10592774C211yesmaximal, characteristic, complemented
4C3×#5076C211yesmaximal, characteristic, complemented
5#10591490C212yesmaximal, complemented
6#10591489C212yesmaximal, complemented
7#10591438C212yesmaximal, complemented
8Dic3×#214C212yesmaximal, complemented
9#10590363C211yesmaximal, characteristic, complemented
10C4×#3716C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83588—31nomaximal
13#81755—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16C2×#3754C2212yes—
17C4×#634C2211yescharacteristic
18C3×#940C2212yes—
19C3×#939—22no—
20C3×#938—21no—
21C3×D4×Dic3C2212yes—
22C2×C3×#214C2212yes—
23C2×C3×#214C2212yes—
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63872—21no—
28#63866C2212yes—
29#63846—22no—
30#63843—21no—
31Dic3×Dic6C2212yes—
32C2×#3716C2211yescharacteristic
33C2×#3715C2212yes—
34#63659C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2211yescharacteristic
40#63565C2212yes—
41#63563C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5721—31no—
45#5718D311yescharacteristic
46#5570—31no—
47C3×#492—31no—
48#5175—32no—
49#5163—32no—
50#5162—32no—
51Dic3×SD16—32no—
52#5083—31no—
53#5076—32no—
54#5076D311yescharacteristic, complemented
55#5075—31no—
56#5075—31no—
57#5075—32no—
58#5075—61no—
59Q8×C3⋊C8—31no—
60#5019—32no—
61#5019—31no—
62C4×#214—32no—
63C4×#214—31no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#634C2311yescharacteristic
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C22×C3×Dic3—22no—
73C3×#237—44no—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77C2×C3×Dic6C2312yes—
78C32×C42C2311yescharacteristic
79#3754—42no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C4×C3⋊Dic3—21no—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#217—22no—
85C3×#214—24no—
86C3×#214—42no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99Dic32—22no—
100#3716—22no—
101#3715—42no—
102#3392—91noSylow
103C2×C3×#41—61no—
104C2×#237—21no—
105C2×C3×SD16—32no—
106C2×C3×SD16—32no—
107C3×C4⋊Q8—31no—
108C3×#127—21no—
109C3×#127—32no—
110C3×#127C2×D311yescharacteristic
111C3×#127C2×D311yescharacteristic
112C3×#121—61no—
113C3×#121—62no—
114C3×C4×Q8—31no—
115C3×C4×D4—32no—
116C3×C4×D4—31no—
117Q8×Dic3—32no—
118Q8×Dic3—61no—
119#944—32no—
120C2×#215—32no—
121#940C2×D312yes—
122#939—22no—
123#938—21no—
124D4×Dic3C2×D312yes—
125C2×#214—32no—
126C2×#214—32no—
127C2×#214—32no—
128C2×#214—31no—
129C2×#214—62no—
130C2×#214C2×D312yes—
131C2×#214C2×D312yes—
132C2×#204—31no—
133#890—62no—
134#890—61no—
135#890—61no—
136#889—62no—
137#887—61no—
138C4×D12C2×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—
147#835—32no—
148#832—32no—
149#832—32no—
150#832—31no—
151#832—62no—
152#821—31no—
153#817—31no—
154#816—31no—
155Dic3⋊C8—32no—
156C8×Dic3—32no—
157#810—32no—
158#810—31no—
159#808—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)—61no—
164C4×C3⋊C8—32no—
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—22no—
167C22×C3×D3—21no—
168C32×D4—22no—
169C32×D4—22no—
170C32×D4—42no—
171C32×D4—81no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177#634—21no—
178#634—21no—
179C3×#67—44no—
180C3×#67—82no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—44no—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×D412yes—
186C3×D12—21no—
187C3×D12—21no—
188C3×C4×D3—42no—
189C3×Dic6—22no—
190C3×Dic6—22no—
191C3×Dic6SD1614yescomplemented
192C3⋊(C3⋊C8)—22no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8#4112yescomplemented
195#557—91no—
196#550—31no—
197#492—31no—
198#492—92no—
199#461—91no—
200#461—92no—
201#460—92no—
202#460—91no—
203C8×Q8—91no—
204C4×SD16—91no—
205C4×SD16—92no—
206C3×#41—124no—
207C2×C3×Q8—31no—
208C2×C3×Q8—32no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—22no—
214C2×C3×D4—31no—
215C2×C3×D4—41no—
216C2×C3×D4—41no—
217C2×C3×D4—62no—
218C2×C3×D4—62no—
219C2×C3×D4C22×D312yes—
220C2×C3×D4C22×D312yes—
221C22×C3×C4—62no—
222C22×C3×C4—61no—
223C2×#67—22no—
224C2×#67—22no—
225C22×Dic3—22no—
226#237—44no—
227C2×D12C22×D311yescharacteristic
228C2×C4×D3—21no—
229C2×Dic6—31no—
230C2×Dic6—31no—
231C2×Dic6—61no—
232C2×Dic6#6711yescharacteristic
233C2×Dic6C22×D312yes—
234C3×SD16—64no—
235C3×SD16—122no—
236C2×C3×C8—31no—
237C2×C3×C8—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—61no—
245C3×C42—21no—
246C3×C42—32no—
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249#217—22no—
250#215—122no—
251#214—24no—
252#214—42no—
253#214—62no—
254#214—122no—
255#214—122no—
256#214—122no—
257#214—124no—
258(C2×D3)⋊C4—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—61no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3#6711yescharacteristic
268C4⋊Dic3C22×D311yescharacteristic
269Dic3⋊C4—62no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—121no—
275Dic3⋊C4#6712yes—
276C4×Dic3—62no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C4×Dic3—62no—
280C4×Dic3—121no—
281C4×Dic3C22×D312yes—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—32no—
284C2×C3⋊C8—62no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287#204—62no—
288C22×C32—42no—
289C22×C32—42no—
290C22×C32—42no—
291C22×C32C22×D411yescharacteristic
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C32×C4—21no—
296C32×C4C2×SD1612yes—
297C32×C4C2×#4111yescharacteristic
298C32×C4H(5,𝔽2)11yescharacteristic
299C3⋊Dic3—41no—
300C3⋊Dic3—41no—
301C3×Dic3—22no—
302C3×Dic3—42no—
303C3×Dic3—41no—
304C3×Dic3C2×SD1614yes—
305C2×#41—61no—
306C2×SD16—32no—
307C2×SD16—32no—
308C2×SD16—91no—
309C2×SD16—92no—
310C2×SD16—92no—
311C4⋊Q8—31no—
312C4⋊Q8—92no—
313#127—32no—
314#127D3211yescharacteristic
315#125—182no—
316#125—181no—
317#121—61no—
318#121—62no—
319C4×Q8—31no—
320C4×Q8—92no—
321C4×Q8—91no—
322C4×Q8—181no—
323C4×D4—32no—
324C4×D4—31no—
325#106—91no—
326C4⋊C8—92no—
327C4⋊C8—91no—
328#103—91no—
329#103—92no—
330#102—91no—
331#102—92no—
332C4×C8—31no—
333C4×C8—92no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—42no—
337C23×C3—61no—
338C22×D3—21no—
339C3×Q8—34no—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×D4—22no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—22no—
346C3×D4—42no—
347C3×D4—42no—
348C3×D4—42no—
349C3×D4—42no—
350C3×D4—61no—
351C3×D4—61no—
352C3×D4—82no—
353C3×D4—81no—
354C3×D4—81no—
355C3×D4—82no—
356C3×D4—124no—
357C3×D4—242no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—32no—
362C2×C3×C4—32no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—124no—
366C2×C3×C4—122no—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—44no—
374#67—82no—
375C2×Dic3—22no—
376C2×Dic3—21no—
377C2×Dic3—44no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3C2×#6712yes—
385C2×Dic3C2×#6712yes—
386D12—21no—
387D12—21no—
388C4×D3—42no—
389Dic6—22no—
390Dic6—22no—
391Dic6—62no—
392Dic6—61no—
393Dic6—61no—
394Dic6—61no—
395Dic6—61no—
396Dic6—121no—
397Dic6#21414yescomplemented
398C3×C8—32no—
399C3×C8—61no—
400C3⋊C8—21no—
401C3⋊C8—62no—
402C3⋊C8—62no—
403C3⋊C8—122no—
404C3⋊C8#23712yescomplemented
405C2×C32—82no—
406C2×C32#55011yescharacteristic
407C2×C32C22×SD1611yescharacteristic
408C2×C32#57711yescharacteristic
409C3×D3—81no—
410#41—124no—
411C2×Q8—31no—
412C2×Q8—32no—
413C2×Q8—91no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—31no—
417C2×D4—62no—
418C2×D4—62no—
419C2×D4C2×D3212yes—
420C22×C4—62no—
421C22×C4—61no—
422SD16—64no—
423SD16—122no—
424SD16—182no—
425SD16—362no—
426SD16—362no—
427C2×C8—31no—
428C2×C8—31no—
429C2×C8—92no—
430C4⋊C4—32no—
431C4⋊C4—31no—
432C4⋊C4—31no—
433C4⋊C4—61no—
434C4⋊C4—61no—
435C4⋊C4—91no—
436C4⋊C4—182no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C4⋊C4—181no—
440C22⋊C4—62no—
441C22⋊C4—61no—
442C42—32no—
443C42—182no—
444C42—181no—
445C42C2×D3211yescharacteristic
446C22×C3—21no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—82no—
454C22×C3—82no—
455C22×C3—82no—
456C22×C3—121no—
457C22×C3—121no—
458C22×C3—121no—
459C22×C3C2×D3×D411yescharacteristic
460C22×C3C22×#6711yescharacteristic
461C2×D3—41no—
462C2×D3—41no—
463C2×D3—41no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—22no—
469C3×C4—34no—
470C3×C4—41no—
471C3×C4—62no—
472C3×C4—121no—
473C3×C4—122no—
474C3×C4D3×SD1612yes—
475C3×C4C2×#21412yes—
476C3×C4C2×#23711yescharacteristic
477C3×C4#100411yescharacteristic
478C3×C4D3×#4111yescharacteristic
479C3×C4#100911yescharacteristic
480Dic3—22no—
481Dic3—42no—
482Dic3—41no—
483Dic3—122no—
484Dic3—121no—
485Dic3—121no—
486Dic3—121no—
487Dic3—121no—
488Dic3—241no—
489Dic3C2×#21414yes—
490C32#339211yescharacteristic, complemented, Sylow
491C23—22no—
492C23—61no—
493Q8—34no—
494Q8—62no—
495Q8—62no—
496Q8—181no—
497Q8—181no—
498D4—22no—
499D4—22no—
500D4—42no—
501D4—61no—
502D4—61no—
503D4—81no—
504D4—124no—
505D4—242no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—62no—
509C2×C4—61no—
510C2×C4—124no—
511C2×C4—122no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4D3×#6711yescharacteristic
515C2×C4D3×#6711yescharacteristic
516C2×C4C22×D3211yescharacteristic
517C8—32no—
518C8—61no—
519C8—182no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—82no—
524C2×C3—82no—
525C2×C3—162no—
526C2×C3—241no—
527C2×C3#571811yescharacteristic
528C2×C3C2×D3×SD1611yescharacteristic
529C2×C3#576211yescharacteristic
530C2×C3C22×#21411yescharacteristic
531C2×C3#583411yescharacteristic
532C2×C3#583611yescharacteristic
533D3—81no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—121no—
538C22—121no—
539C22—121no—
540C22C2×D3×#6711yescharacteristic
541C4—21no—
542C4—34no—
543C4—62no—
544C4—121no—
545C4—122no—
546C4—361no—
547C4—361no—
548C4D3×#21412yes—
549C4D3×#23711yescharacteristic
550C4#6431411yescharacteristic
551C3—21no—
552C3#8175511yescharacteristic, complemented
553C3#8358811yescharacteristic, complemented
554C2—82no—
555C2—241no—
556C2C2×D3×#21411yescharacteristic
557C2#1059510511yescharacteristic
558C2#1059515811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5718C2
hypercenter#127D32
hypocenterC32#3392
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593861C2semidirect
3. #10592774C2semidirect
4. C3×#5076C2semidirect
5. #10591490C2semidirect
6. #10591489C2semidirect
7. #10591438C2semidirect
8. Dic3×#214C2semidirect
9. #10590363C2semidirect
10. C4×#3716C2semidirect
11. C3⋊C8×Dic6C2semidirect
54. #5076D3semidirect
191. C3×Dic6SD16semidirect
194. C3×C3⋊C8#41semidirect
397. Dic6#214semidirect
404. C3⋊C8#237semidirect
490. C32#3392semidirect
552. C3#81755semidirect
553. C3#83588semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
#105938612
#105927742
C3×#50762
#105914902
#105914892
#105914382
Dic3×#2142
#105903632
C4×#37162
C3⋊C8×Dic62
#835883
#817553