Finite Group Databasebeta

← #11787687

Subgroups — #11787687

Order 1152.

753 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5827C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3C2×#63664C211yesmaximal, characteristic
4#10591221C211yesmaximal, characteristic, complemented
5#10591099C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#72100—31nomaximal
9#71666—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#951—22no—
15C3×#951C414yescomplemented
16C3×Q8×Dic3—21no—
17C2×C3×#216—21no—
18C3×D4×Dic3—21no—
19C3×D4×Dic3—22no—
20C2×C3×#214—21no—
21C3×#926—21no—
22C3×#926C2211yescharacteristic
23C2×C3×C4⋊Dic3—21no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26#63664—22no—
27#63579—22no—
28#63565—21no—
29#63565—21no—
30C2×C3×#137—31no—
31C3×#520—31no—
32#5827D311yescharacteristic
33C2×#951D311yescharacteristic
34C2×#837—31no—
35C2×#837—31no—
36C2×#837—61no—
37#5229—31no—
38#5225—31no—
39#5004—31no—
40#4973—31no—
41#4555—31no—
42#4554—31no—
43#4532—31no—
44#4530—31no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41C2×C412yes—
48C32×#41D412yes—
49C2×C32×Q8D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3D412yes—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6C2×C412yescomplemented
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—21no—
66#3748—21no—
67#3748—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C3×#217—22no—
70C3×#217—21no—
71C3×#216—24no—
72C3×#214—24no—
73C3×C4⋊Dic3—22no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3D411yescharacteristic
77C3×C4⋊Dic3D411yescharacteristic
78C3×C4×Dic3—22no—
79C3×C4×Dic3—21no—
80C3×#208—21no—
81C3×#208C2×C412yescomplemented
82C2×C3×C3⋊C8—21no—
83#1882—91noSylow
84C2×C3×#41—21no—
85C2×C3×#41C2×D311yescharacteristic
86C2×C3×#41C2×D311yescharacteristic
87C22×C3×Q8—31no—
88C22×Dic6C2×D311yescharacteristic
89C3×#137—34no—
90C3×#137—62no—
91C2×C3×Q16—61no—
92C2×C3×SD16—61no—
93C2×C3×M16—31no—
94C3×C4×Q8—61no—
95C3×C4×D4—62no—
96C3×C4×D4—61no—
97C3×#117—31no—
98C3×#117—61no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—61no—
101#951—22no—
102#951Dic314yescomplemented
103Q8×Dic3—21no—
104C2×#216—21no—
105D4×Dic3—21no—
106D4×Dic3—22no—
107C2×#214—21no—
108#926—21no—
109#926C2×D311yescharacteristic
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C2×#208—31no—
116C2×#208—31no—
117C2×#208—61no—
118C2×#208C2×D311yescharacteristic
119#837—64no—
120#837—62no—
121#837—62no—
122#835—61no—
123#835—61no—
124C3⋊#95—62no—
125C3⋊#95—62no—
126#810—61no—
127#810—61no—
128C23×C32—21no—
129C23×C32C2×D411yescharacteristic
130C32×Q8—21no—
131C32×Q8C22⋊C412yes—
132C32×D4—22no—
133C32×D4—22no—
134C32×D4—21no—
135C32×D4C22⋊C412yes—
136C2×C32×C4—21no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—41no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—82no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—41no—
159C3×Dic6—41no—
160C3⋊(C3⋊C8)—41no—
161C3×C3⋊C8—22no—
162C2×#137—31no—
163#520—31no—
164C2×#104—91no—
165#419—91no—
166#391—91no—
167#343—91no—
168#339—91no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41—41no—
176C3×#41—41no—
177C3×#41C4×D312yes—
178C3×#41D1212yes—
179C3×#41C2×Dic312yes—
180C3×#41#6712yes—
181C2×C3×Q8—21no—
182C2×C3×Q8—32no—
183C2×C3×Q8—61no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×Q8#6711yescharacteristic
189C2×C3×Q8#6711yescharacteristic
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—41no—
194C2×C3×D4#6711yescharacteristic
195C2×C3×D4#6711yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—32no—
200C22×C3×C4—41no—
201C22×C3×C4—61no—
202C22×C3×C4—62no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—21no—
206C22×Dic3—22no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—121no—
210C22×Dic3#6712yes—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6C2×Dic312yescomplemented
217C3×Q16—64no—
218C3×SD16—64no—
219C3×M16—32no—
220C3×M16—61no—
221C2×C3×C8—61no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C22⋊C4—62no—
228C3×C22⋊C4—61no—
229C3×C42—62no—
230C3×C42—61no—
231#217—22no—
232#217—21no—
233#216—24no—
234#214—24no—
235C4⋊Dic3—22no—
236C4⋊Dic3—21no—
237C4⋊Dic3—21no—
238C4⋊Dic3#6711yescharacteristic
239C4⋊Dic3#6711yescharacteristic
240C4×Dic3—22no—
241C4×Dic3—21no—
242C4×Dic3—62no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—121no—
248#208—21no—
249#208—62no—
250#208—61no—
251#208—61no—
252#208—61no—
253#208—61no—
254#208—121no—
255#208C2×Dic312yescomplemented
256C2×C3⋊C8—21no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—121no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32—22no—
263C22×C32—41no—
264C22×C32—41no—
265C22×C32C4×D411yescharacteristic
266C22×C32#12011yescharacteristic
267C22×C32#12111yescharacteristic
268C32×C4—22no—
269C32×C4C2×C22⋊C411yescharacteristic
270C32×C4C4×D411yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12311yescharacteristic
273C3⋊Dic3—42no—
274C3×Dic3—42no—
275C3×Dic3—42no—
276C3×Dic3—41no—
277C3×Dic3—41no—
278C2×#41D3211yescharacteristic
279C22×Q8—31no—
280#137—34no—
281#137—62no—
282C2×Q16—61no—
283C2×SD16—61no—
284C2×M16—31no—
285C2×M16—91no—
286C4×Q8—61no—
287C4×D4—62no—
288C4×D4—61no—
289#117—31no—
290#117—61no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—61no—
293C2×C42—91no—
294#104—182no—
295#103—181no—
296#103—181no—
297#95—182no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—41no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C3×Q8—21no—
305C3×Q8—21no—
306C3×Q8—22no—
307C3×Q8—41no—
308C3×Q8—62no—
309C3×Q8—62no—
310C3×Q8—121no—
311C3×Q8—121no—
312C3×Q8(C2×D3)⋊C412yes—
313C3×Q8#21712yes—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—21no—
319C3×D4—21no—
320C3×D4—22no—
321C3×D4—41no—
322C3×D4—42no—
323C3×D4—42no—
324C3×D4(C2×D3)⋊C412yes—
325C3×D4#21712yes—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—62no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4—122no—
348C2×C3×C4—242no—
349C2×C3×C4C2×C4×D311yescharacteristic
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4#23511yescharacteristic
352C2×C3×C4#23511yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4#23711yescharacteristic
356C2×C3×C4C22×Dic311yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×Dic3—22no—
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—21no—
365C2×Dic3—41no—
366C2×Dic3—41no—
367C2×Dic3—42no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—82no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3—122no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378Dic6—22no—
379Dic6—22no—
380Dic6—41no—
381Dic6—41no—
382C3×C8—62no—
383C3⋊C8—22no—
384C3⋊C8—122no—
385C3⋊C8—121no—
386C3⋊C8—121no—
387C2×C32—21no—
388C2×C32—21no—
389C2×C32—42no—
390C2×C32#38611yescharacteristic
391C2×C32#45511yescharacteristic
392C2×C32#45611yescharacteristic
393#41—21no—
394#41—21no—
395#41D3×Dic312yes—
396#41#62612yes—
397C2×Q8—32no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×Q8—61no—
403C2×Q8#62511yescharacteristic
404C2×D4—21no—
405C2×D4#62511yescharacteristic
406C22×C4—21no—
407C22×C4—32no—
408C22×C4—61no—
409C22×C4—62no—
410C22×C4—181no—
411C22×C4C2×D3211yescharacteristic
412Q16—64no—
413SD16—64no—
414M16—32no—
415M16—61no—
416M16—181no—
417M16—181no—
418C2×C8—61no—
419C2×C8—181no—
420C4⋊C4—31no—
421C4⋊C4—31no—
422C4⋊C4—62no—
423C4⋊C4—61no—
424C4⋊C4—61no—
425C22⋊C4—62no—
426C22⋊C4—61no—
427C42—62no—
428C42—61no—
429C42—181no—
430C42—181no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—42no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—81no—
448C22×C3—81no—
449C22×C3C4×#6711yescharacteristic
450C22×C3#93011yescharacteristic
451C22×C3D4×Dic311yescharacteristic
452C22×C3#93711yescharacteristic
453C22×C3#93911yescharacteristic
454C22×C3#95311yescharacteristic
455C3×C4—22no—
456C3×C4—22no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—42no—
462C3×C4—122no—
463C3×C4—121no—
464C3×C4—121no—
465C3×C4—122no—
466C3×C4C2×(C2×D3)⋊C411yescharacteristic
467C3×C4C4×#6711yescharacteristic
468C3×C4#92911yescharacteristic
469C3×C4#93011yescharacteristic
470C3×C4D4×Dic311yescharacteristic
471C3×C4#93511yescharacteristic
472C3×C4#93911yescharacteristic
473C3×C4C2×#21711yescharacteristic
474Dic3—42no—
475Dic3—42no—
476Dic3—41no—
477Dic3—41no—
478Dic3—122no—
479Dic3—122no—
480Dic3—124no—
481C32#188211yescharacteristic, complemented, Sylow
482C23—21no—
483C23D3×#6711yescharacteristic
484Q8—21no—
485Q8—62no—
486Q8—62no—
487Q8—121no—
488Q8—121no—
489Q8(C2×D3)⋊Dic312yes—
490D4—22no—
491D4—22no—
492D4—21no—
493D4(C2×D3)⋊Dic312yes—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—62no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—62no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—122no—
504C2×C4—182no—
505C2×C4—242no—
506C2×C4—361no—
507C2×C4—361no—
508C2×C4C2×D3×Dic311yescharacteristic
509C2×C4#380411yescharacteristic
510C2×C4#380411yescharacteristic
511C2×C4C2×#62511yescharacteristic
512C2×C4C2×#62611yescharacteristic
513C2×C4D3×#6711yescharacteristic
514C8—62no—
515C8—361no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—42no—
526C2×C3—42no—
527C2×C3—82no—
528C2×C3#520211yescharacteristic
529C2×C3#520511yescharacteristic
530C2×C3#521311yescharacteristic
531C2×C3#522011yescharacteristic
532C2×C3#524211yescharacteristic
533C2×C3#524611yescharacteristic
534C22—21no—
535C22—21no—
536C22—22no—
537C22—41no—
538C22—41no—
539C22Dic3×#6711yescharacteristic
540C22#6397611yescharacteristic
541C22#6397811yescharacteristic
542C4—22no—
543C4—122no—
544C4—121no—
545C4—121no—
546C4—122no—
547C4—362no—
548C4C2×(C2×D3)⋊Dic311yescharacteristic
549C4#6396111yescharacteristic
550C4Dic3×#6711yescharacteristic
551C4#6397811yescharacteristic
552C3—21no—
553C3#7166611yescharacteristic, complemented
554C3#7210011yescharacteristic, complemented
555C2—21no—
556C2—21no—
557C2—42no—
558C2#1059166411yescharacteristic
559C2#1059168711yescharacteristic
560C2#1059171011yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#120
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1882
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591221C2semidirect
5. #10591099C2semidirect
6. #10589167C2semidirect
7. #10589160C2semidirect
15. C3×#951C4semidirect
63. C2×C3×Dic6C2×C4semidirect
81. C3×#208C2×C4semidirect
102. #951Dic3semidirect
216. C2×Dic6C2×Dic3semidirect
255. #208C2×Dic3semidirect
481. C32#1882semidirect
553. C3#71666semidirect
554. C3#72100semidirect

Maximal subgroups

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

subgroupindex
C3×#58272
C2×C3×#9512
C2×#636642
#105912212
#105910992
#105891672
#105891602
#721003
#716663