Finite Group Databasebeta

← #11788172

Subgroups — #11788172

Order 1152.

979 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595034C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic, complemented
3#10592825C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70382—31nomaximal
9#68756—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×#624—21no—
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18#63981—21no—
19#63962—21no—
20C2×Dic32—21no—
21#63916C412yescomplemented
22C4×#626—22no—
23C4×#624—22no—
24C4×#624—22no—
25#63871C412yescomplemented
26#63647—22no—
27C3×#825—22no—
28#63569—22no—
29#5828—31no—
30#5524—31no—
31C2×C42×D3—31no—
32C2×C42×D3—31no—
33C2×C3×#104—31no—
34C2×#837—31no—
35C2×#825D311yescharacteristic, complemented
36#5126—31no—
37#5126—31no—
38#5126—61no—
39C2×#805—31no—
40C3×#339—31no—
41#4555D311yescharacteristic, complemented
42#4532—31no—
43#4523—31no—
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3C2×C412yes—
52C2×C4×C3⋊D3D412yes—
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C2×C3×D12C2×C411yescharacteristic, complemented
61C2×C3×C4×D3—21no—
62C2×C3×Dic6C2×C411yescharacteristic, complemented
63C2×#626—22no—
64C2×#624—28no—
65C2×#624—24no—
66C32×M16—21no—
67C32×M16—21no—
68C2×C32×C8—21no—
69#3748—21no—
70#3748—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C3×#217—21no—
73C3×C4⋊Dic3C2×C412yescomplemented
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3D412yescomplemented
78C3×C4×Dic3D412yescomplemented
79Dic3⋊Dic3—22no—
80#3722—22no—
81(C2×D3)⋊Dic3—22no—
82Dic32—24no—
83#1896—91noSylow
84C2×C3×#41—31no—
85C2×#235C2×D311yescharacteristic
86C22×C4×D3—31no—
87C22×C4×D3—31no—
88C22×C4×D3—61no—
89C22×C4×D3—61no—
90C22×C4×D3—61no—
91C2×C3×M16—21no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C3×#117—31no—
95C2×C3×C42—31no—
96C2×C3×C42—31no—
97#946—32no—
98#938—32no—
99#937—61no—
100#935—61no—
101C4×#67—62no—
102#926C2×D311yescharacteristic
103C2×C4×Dic3—61no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3C2×D311yescharacteristic
106C2×C4×Dic3C2×D311yescharacteristic
107C2×#208—31no—
108C2×#208—31no—
109C2×#208—61no—
110#897—32no—
111#895—32no—
112#886—61no—
113#882—61no—
114C4×D12—62no—
115C42×D3—62no—
116C42×D3—62no—
117C42×D3—62no—
118C42×D3—62no—
119C3×#104—62no—
120#837—62no—
121#825—22no—
122(C2×D3)⋊C8—62no—
123(C2×D3)⋊C8—62no—
124(C2×D3)⋊C8—64no—
125#805—62no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3—24no—
130C22×C3⋊D3C22⋊C412yes—
131C22×C3×D3—21no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3C22⋊C412yes—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—22no—
144C4×C3⋊D3—22no—
145C3×#67—41no—
146C3×#67—41no—
147C2×C3×Dic3—24no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—21no—
153C3×D12—21no—
154C3×D12—21no—
155C3×C4×D3—41no—
156C3×C4×D3—41no—
157C3×Dic6—21no—
158C3×Dic6—21no—
159#626—44no—
160#624—216no—
161C32×C8—41no—
162C3⋊(C3⋊C8)—41no—
163#525—91no—
164C22×C42—91no—
165C2×#104—31no—
166C2×#104—91no—
167#407—91no—
168#339—31no—
169#339—91no—
170C23×D3—31no—
171C23×D3—31no—
172C23×D3—61no—
173C3×#41—61no—
174C3×#41—61no—
175C3×#41—61no—
176C3×#41—61no—
177C2×C3×Q8—31no—
178C2×C3×D4—31no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C2×#67—21no—
187C2×#67—62no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—61no—
193#235—21no—
194#235—21no—
195#235—21no—
196#235—21no—
197C2×D12—62no—
198C2×D12C4×D311yescharacteristic, complemented
199C2×C4×D3—21no—
200C2×C4×D3—32no—
201C2×C4×D3—32no—
202C2×C4×D3—32no—
203C2×C4×D3—32no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—64no—
207C2×C4×D3—64no—
208C2×C4×D3—68no—
209C2×C4×D3—68no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—121no—
219C2×C4×D3—121no—
220C2×C4×D3—121no—
221C2×C4×D3—121no—
222C2×Dic6C4×D311yescharacteristic, complemented
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—21no—
226C3×M16—21no—
227C3×M16—41no—
228C3×M16—41no—
229C2×C3×C8—22no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C3×C4⋊C4—32no—
233C3×C22⋊C4—61no—
234C3×C42—32no—
235C3×C42—32no—
236C3×C42—61no—
237C3×C42—61no—
238C3×C42—61no—
239#217—21no—
240#217—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3C4×D312yescomplemented
246Dic3⋊C4—62no—
247C4×Dic3—21no—
248C4×Dic3—21no—
249C4×Dic3—21no—
250C4×Dic3—64no—
251C4×Dic3—64no—
252C4×Dic3D1212yescomplemented
253C4×Dic3#6712yescomplemented
254#208—61no—
255#208—61no—
256#208—61no—
257#208—61no—
258#208—121no—
259#208—121no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C22×C32—22no—
264C22×C32C2×C22⋊C411yescharacteristic
265C22×C32#12011yescharacteristic
266C22×C32#12311yescharacteristic
267C2×C3⋊D3—24no—
268C2×C3⋊D3—24no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3#10414yescomplemented
272C2×C3×D3—41no—
273C2×C3×D3—42no—
274C32×C4C4×D411yescharacteristic
275C32×C4C4×D411yescharacteristic
276C32×C4#12111yescharacteristic
277C32×C4#12111yescharacteristic
278C3⋊Dic3—22no—
279C3×Dic3—24no—
280C3×Dic3—24no—
281C3×Dic3—41no—
282C3×Dic3—42no—
283C2×#41—31no—
284C23×C4—91no—
285C23×C4—181no—
286C2×M16—91no—
287C2×M16D3211yescharacteristic
288#123—181no—
289C22⋊Q8—92no—
290#121—92no—
291#120—181no—
292C4×D4—182no—
293#117—31no—
294C2×C42—31no—
295C2×C42—31no—
296C2×C42—182no—
297C2×C42—182no—
298C2×C42—181no—
299#104—62no—
300#104—182no—
301C22⋊C8—182no—
302C23×C3—21no—
303C23×C3—61no—
304C23×C3D3×D411yescharacteristic
305C23×C3D3×D411yescharacteristic
306C22×D3—21no—
307C22×D3—32no—
308C22×D3—32no—
309C22×D3—62no—
310C22×D3—64no—
311C22×D3—64no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—61no—
315C22×D3—61no—
316C22×D3—124no—
317C22×D3—121no—
318C22×D3—121no—
319C3×Q8—61no—
320C3×Q8—61no—
321C3×D4—61no—
322C3×D4—61no—
323C3×D4—121no—
324C3×D4—121no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—64no—
332C2×C3×C4—64no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4C2×C4×D311yescharacteristic
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4#23511yescharacteristic
343C2×C3×C4#23511yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4#23711yescharacteristic
349C2×C3×C4#23911yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351#67—41no—
352#67—41no—
353#67—124no—
354C2×Dic3—24no—
355C2×Dic3—24no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—21no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—62no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—121no—
368C2×Dic3—121no—
369D12—21no—
370D12—21no—
371D12—124no—
372C4×D3—41no—
373C4×D3—41no—
374C4×D3—616no—
375C4×D3—616no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—122no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—122no—
388Dic6—21no—
389Dic6—21no—
390C3×C8—42no—
391C3×C8—41no—
392C3×C8—41no—
393C3⋊C8—122no—
394C3⋊C8—121no—
395C3⋊C8—121no—
396C2×C32—21no—
397C2×C32—21no—
398C2×C32#38611yescharacteristic
399C2×C32C2×#10412yes—
400C3⋊D3—24no—
401C3×D3—81no—
402C24—91no—
403#41—61no—
404#41—61no—
405#41—61no—
406#41—61no—
407C2×Q8—31no—
408C2×D4—31no—
409C2×D4—61no—
410C2×D4—182no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—91no—
415C22×C4—92no—
416C22×C4—92no—
417C22×C4—184no—
418C22×C4—188no—
419C22×C4—181no—
420C22×C4—181no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4C2×D3211yescharacteristic
424M16—21no—
425M16—21no—
426M16—181no—
427M16—181no—
428C2×C8—21no—
429C2×C8—181no—
430C4⋊C4—32no—
431C4⋊C4—182no—
432C22⋊C4—61no—
433C22⋊C4—182no—
434C22⋊C4—182no—
435C42—32no—
436C42—32no—
437C42—61no—
438C42—61no—
439C42—61no—
440C42—184no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—42no—
447C22×C3—121no—
448C22×C3—122no—
449C22×C3D3×C22⋊C411yescharacteristic
450C22×C3D3×C22⋊C411yescharacteristic
451C22×C3#88211yescharacteristic
452C22×C3#88311yescharacteristic
453C22×C3#89411yescharacteristic
454C22×C3#93711yescharacteristic
455C2×D3—34no—
456C2×D3—34no—
457C2×D3—41no—
458C2×D3—42no—
459C2×D3—64no—
460C2×D3—64no—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—122no—
469C2×D3—122no—
470C2×D3—124no—
471C2×D3—124no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—64no—
477C3×C4—64no—
478C3×C4—121no—
479C3×C4—122no—
480C3×C4C4×D1211yescharacteristic
481C3×C4#67⋊C411yescharacteristic
482C3×C4#88411yescharacteristic
483C3×C4#88411yescharacteristic
484C3×C4#89311yescharacteristic
485C3×C4#89511yescharacteristic
486C3×C4C4×#6711yescharacteristic
487C3×C4#93811yescharacteristic
488Dic3—24no—
489Dic3—24no—
490Dic3—41no—
491Dic3—42no—
492Dic3—62no—
493Dic3—62no—
494Dic3—122no—
495C32#189611yescharacteristic, complemented, Sylow
496C23—61no—
497C23—92no—
498C23—184no—
499C23—181no—
500C23—181no—
501C23#380211yescharacteristic
502Q8—61no—
503Q8—61no—
504D4—61no—
505D4—61no—
506D4—121no—
507D4—121no—
508D4—364no—
509C2×C4—64no—
510C2×C4—64no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—61no—
515C2×C4—92no—
516C2×C4—121no—
517C2×C4—121no—
518C2×C4—1816no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4#379911yescharacteristic
526C2×C4C4×D3211yescharacteristic
527C2×C4D3×D1211yescharacteristic
528C2×C4#380411yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4#381111yescharacteristic
531C8—41no—
532C8—361no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—22no—
538C2×C3—21no—
539C2×C3—41no—
540C2×C3—41no—
541C2×C3—241no—
542C2×C3#466511yescharacteristic
543C2×C3D3×#10412yes—
544C2×C3D3×#10412yes—
545C2×C3#495611yescharacteristic
546D3—64no—
547D3—64no—
548D3—81no—
549D3—124no—
550C22—22no—
551C22—94no—
552C22—122no—
553C22—121no—
554C22—184no—
555C22—184no—
556C22—182no—
557C22—182no—
558C22#6385411yescharacteristic
559C22#6392111yescharacteristic
560C22#6392211yescharacteristic
561C4—64no—
562C4—64no—
563C4—122no—
564C4—121no—
565C4—182no—
566C4#6388011yescharacteristic
567C4#6390411yescharacteristic
568C4#6391011yescharacteristic
569C4#6395811yescharacteristic
570C3—21no—
571C3#6875611yescharacteristic, complemented
572C3#7038211yescharacteristic, complemented
573C2—21no—
574C2—21no—
575C2—184no—
576C2—241no—
577C2#1059100812yes—
578C2#1059127511yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595034C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#624C2semidirect
3. #10592825C2semidirect
4. C2×C3×#825C2semidirect
5. C2×#63569C2semidirect
6. C3×#4555C2semidirect
7. #10589161C2semidirect
21. #63916C4semidirect
25. #63871C4semidirect
35. C2×#825D3semidirect
41. #4555D3semidirect
60. C2×C3×D12C2×C4semidirect
62. C2×C3×Dic6C2×C4semidirect
73. C3×C4⋊Dic3C2×C4semidirect
77. C3×C4×Dic3D4semidirect
78. C3×C4×Dic3D4semidirect
198. C2×D12C4×D3semidirect
222. C2×Dic6C4×D3semidirect
245. C4⋊Dic3C4×D3semidirect
252. C4×Dic3D12semidirect
253. C4×Dic3#67semidirect
271. C2×C3⋊D3#104semidirect
495. C32#1896semidirect
571. C3#68756semidirect
572. C3#70382semidirect

Maximal subgroups

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

subgroupindex
#105950342
C2×C4×#6242
#105928252
C2×C3×#8252
C2×#635692
C3×#45552
#105891612
#703823
#687563