Finite Group Databasebeta

← #11895424

Subgroups — #11895424

Order 1152.

838 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592707C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591487C212yesmaximal, complemented
6#10591438C212yesmaximal, complemented
7#10590558C212yesmaximal, complemented
8#10590475C212yesmaximal, complemented
9#10590364C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83586—31nomaximal
13#79622—31nomaximal
14C2×C3×#235—21no—
15C32×C4×D4C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#940C2212yes—
18C2×C3×#214C2211yescharacteristic
19C3×#930—21no—
20C3×#893C2212yes—
21C3×#884—22no—
22C3×#874C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918—21no—
26#63918C2212yes—
27Dic3×Dic6—21no—
28Dic3×Dic6C2212yes—
29#63840—22no—
30C2×#3715C2212yes—
31#63659C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#832C2211yescharacteristic
35C3×#810C2211yescharacteristic
36C3×#808C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44Q8×Dic6—31no—
45Q8×Dic6—31no—
46#5553D311yescharacteristic
47C3×C4×SD16—31no—
48#5163—32no—
49#5075—32no—
50#5075—31no—
51#5070—32no—
52#5070—31no—
53#5027—31no—
54Q8×C3⋊C8—31no—
55C4×#214—32no—
56C4×#214D311yescharacteristic, complemented
57#5008—31no—
58#5008—31no—
59#5008—32no—
60#5008—61no—
61#4870—32no—
62#4788—32no—
63#4760—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634—21no—
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×Dic6C2311yescharacteristic
78C2×#627—22no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C22⋊C4—21no—
81C32×C42C2311yescharacteristic
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#214—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3715—24no—
99#3362—91noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C2×C3×SD16—31no—
103C3×#127—32no—
104C3×#127—31no—
105C3×#121—62no—
106C3×#121—61no—
107C3×C4×Q8—31no—
108C3×C4×Q8—31no—
109C3×C4×D4—21no—
110C3×C4×D4—32no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113Q8×Dic3—32no—
114Q8×Dic3—61no—
115C2×#215—32no—
116#940C2×D312yes—
117C2×#214—32no—
118C2×#214C2×D311yescharacteristic
119#930—21no—
120#893C2×D312yes—
121#888—32no—
122#888—61no—
123#888—62no—
124#888—62no—
125#884—22no—
126#874C2×D311yescharacteristic
127#869—31no—
128#869—31no—
129#869—32no—
130#869—61no—
131#869—61no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#106—31no—
137C3×#103—31no—
138C3×#102—31no—
139C3×C4×C8—31no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—32no—
144#832—32no—
145#832—62no—
146#832C2×D311yescharacteristic
147#821—32no—
148#821—32no—
149Dic3⋊C8—32no—
150C8×Dic3—32no—
151#810C2×D311yescharacteristic
152#809—32no—
153#808—32no—
154#808—32no—
155#808—62no—
156#808C2×D311yescharacteristic
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C23×C32—21no—
164C22×C3×D3—22no—
165C32×D4—21no—
166C32×D4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—42no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173#634—81no—
174C3×#67—44no—
175C3×#67—82no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×C4×D3—44no—
185C3×Dic6—21no—
186C3×Dic6SD1614yescomplemented
187C3×Dic6#4112yescomplemented
188#627—82no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192Q82—91no—
193#550—31no—
194#486—91no—
195#486—92no—
196#476—92no—
197#476—91no—
198#460—91no—
199#460—92no—
200C8×Q8—91no—
201C4×SD16—31no—
202C4×SD16—92no—
203C3×#41—124no—
204C2×C3×Q8—31no—
205C2×C3×Q8—31no—
206C2×C3×D4—21no—
207C2×C3×D4—32no—
208C2×C3×D4—62no—
209C2×C3×D4—62no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C2×C3×D4C22×D311yescharacteristic
213C2×C3×D4C22×D311yescharacteristic
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—41no—
217C22×C3×C4—62no—
218C2×#67—22no—
219C2×#67—22no—
220#235—44no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12C22×D312yes—
224C2×C4×D3—22no—
225C2×Dic6—62no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—62no—
229C2×Dic6—121no—
230C2×Dic6#6711yescharacteristic
231C2×Dic6C22×D311yescharacteristic
232C3×SD16—62no—
233C2×C3×C8—31no—
234C2×C3×C8—31no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C22⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C22⋊C4—41no—
245C3×C22⋊C4—62no—
246C3×C42—21no—
247C3×C42—32no—
248C3×C42—61no—
249C3×C42C22×D311yescharacteristic
250C3×C42C22×D311yescharacteristic
251#215—64no—
252#214—22no—
253#214—64no—
254(C2×D3)⋊C4—22no—
255C4⋊Dic3—32no—
256C4⋊Dic3—32no—
257C4⋊Dic3—62no—
258C4⋊Dic3—62no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3—121no—
263C4⋊Dic3#6711yescharacteristic
264C4⋊Dic3C22×D311yescharacteristic
265Dic3⋊C4—21no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4#6712yes—
269C4×Dic3—21no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3C22×D312yes—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278C22×C32—41no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—21no—
286C32×C4—41no—
287C32×C4C2×SD1612yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3⋊Dic3—42no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3C2×SD1614yes—
295C2×#41—61no—
296C2×SD16—31no—
297C2×SD16—92no—
298C4⋊Q8—92no—
299C4⋊Q8—91no—
300C4⋊Q8—181no—
301C4⋊Q8—182no—
302#127—32no—
303#127—31no—
304#121—62no—
305#121—61no—
306C4×Q8—31no—
307C4×Q8—31no—
308C4×Q8—92no—
309C4×Q8—181no—
310C4×D4—32no—
311C4×D4D3211yescharacteristic
312#106—31no—
313#106—92no—
314C4⋊C8—92no—
315C4⋊C8—91no—
316#103—31no—
317#102—31no—
318#102—92no—
319#102—92no—
320#102—92no—
321#102—92no—
322C4×C8—31no—
323C4×C8—92no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—41no—
327C23×C3—62no—
328C22×D3—22no—
329C3×Q8—34no—
330C3×Q8—32no—
331C3×Q8—61no—
332C3×D4—22no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—41no—
338C3×D4—62no—
339C3×D4—62no—
340C3×D4—124no—
341C3×D4—122no—
342C3×D4—241no—
343C3×D4—242no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—41no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—82no—
357C2×C3×C4—124no—
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364#67—44no—
365#67—82no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—122no—
371C2×Dic3C2×#6712yes—
372C2×Dic3C2×#6712yes—
373D12—22no—
374D12—22no—
375D12—42no—
376D12—81no—
377C4×D3—44no—
378Dic6—21no—
379Dic6—242no—
380Dic6—242no—
381Dic6—241no—
382Dic6—241no—
383Dic6—242no—
384Dic6#21414yescomplemented
385Dic6#23512yescomplemented
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—21no—
390C3⋊C8—62no—
391C3⋊C8—62no—
392C3⋊C8—122no—
393C2×C32—81no—
394C2×C32#54811yescharacteristic
395C2×C32C22×SD1611yescharacteristic
396C2×C32#57611yescharacteristic
397C3×D3—82no—
398#41—124no—
399C2×Q8—31no—
400C2×Q8—31no—
401C2×Q8—182no—
402C2×Q8—181no—
403C2×D4—32no—
404C2×D4—62no—
405C2×D4—62no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4C2×D3211yescharacteristic
409C22×C4—21no—
410C22×C4—62no—
411SD16—62no—
412SD16—184no—
413C2×C8—31no—
414C2×C8—31no—
415C2×C8—92no—
416C4⋊C4—32no—
417C4⋊C4—31no—
418C4⋊C4—31no—
419C4⋊C4—61no—
420C4⋊C4—92no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C4⋊C4—181no—
424C4⋊C4C2×D3211yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—62no—
427C42—32no—
428C42—61no—
429C42—182no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—42no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—81no—
440C22×C3—81no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C22×#6711yescharacteristic
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—42no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—34no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—62no—
459C3×C4—62no—
460C3×C4—81no—
461C3×C4—121no—
462C3×C4D3×SD1612yes—
463C3×C4C2×#21412yes—
464C3×C4C2×#23511yescharacteristic
465C3×C4D3×#4111yescharacteristic
466C3×C4#101011yescharacteristic
467C3×C4#101011yescharacteristic
468Dic3—22no—
469Dic3—22no—
470Dic3—41no—
471Dic3—122no—
472Dic3—122no—
473Dic3—242no—
474Dic3C2×#21414yes—
475C32#336211yescharacteristic, complemented, Sylow
476C23—21no—
477C23—62no—
478Q8—34no—
479Q8—32no—
480Q8—61no—
481Q8—721no—
482Q8—722no—
483D4—21no—
484D4—21no—
485D4—62no—
486D4—62no—
487D4—124no—
488D4—122no—
489D4—241no—
490D4—242no—
491C2×C4—21no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—42no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—124no—
498C2×C4—182no—
499C2×C4D3×#6711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—61no—
503C8—61no—
504C8—182no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—82no—
509C2×C3—81no—
510C2×C3—81no—
511C2×C3—242no—
512C2×C3#555211yescharacteristic
513C2×C3C2×D3×SD1611yescharacteristic
514C2×C3#576911yescharacteristic
515C2×C3C22×#21411yescharacteristic
516C2×C3#583111yescharacteristic
517C2×C3#583511yescharacteristic
518D3—82no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—122no—
523C22—122no—
524C22—122no—
525C22C2×D3×#6711yescharacteristic
526C4—21no—
527C4—34no—
528C4—41no—
529C4—62no—
530C4—62no—
531C4—121no—
532C4—362no—
533C4D3×#21412yes—
534C4#6429811yescharacteristic
535C4D3×#23511yescharacteristic
536C3—21no—
537C3#7962211yescharacteristic, complemented
538C3#8358611yescharacteristic, complemented
539C2—81no—
540C2—242no—
541C2#1059489911yescharacteristic
542C2C2×D3×#21411yescharacteristic
543C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC4×D4D32
hypocenterC32#3362
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. Dic62C2semidirect
3. #10592707C2semidirect
4. C3×C4×#214C2semidirect
5. #10591487C2semidirect
6. #10591438C2semidirect
7. #10590558C2semidirect
8. #10590475C2semidirect
9. #10590364C2semidirect
10. #10590273C2semidirect
11. C3⋊C8×Dic6C2semidirect
56. C4×#214D3semidirect
186. C3×Dic6SD16semidirect
187. C3×Dic6#41semidirect
384. Dic6#214semidirect
385. Dic6#235semidirect
475. C32#3362semidirect
537. C3#79622semidirect
538. C3#83586semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
Dic622
#105927072
C3×C4×#2142
#105914872
#105914382
#105905582
#105904752
#105903642
#105902732
C3⋊C8×Dic62
#835863
#796223