Finite Group Databasebeta

← #11794057

Subgroups — #11794057

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#215C211yesmaximal, characteristic
2C2×#63662C211yesmaximal, characteristic, complemented
3C3×#5229C211yesmaximal, characteristic, complemented
4#10591318C211yesmaximal, characteristic
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7#10589164C211yesmaximal, characteristic, complemented
8#72051—31nomaximal
9#69680—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#215—22no—
15C2×C3×#215—22no—
16C2×C3×#215—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×(C2×D3)⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63662—22no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25Dic3⋊(C3⋊C8)—22no—
26#63562—22no—
27C22×C3×SD16—31no—
28C22×#215D311yescharacteristic
29C3×#391—31no—
30#5229D311yescharacteristic, complemented
31C2×#835—31no—
32C2×#835—31no—
33C2×#835—61no—
34#5221—31no—
35C2×#832—31no—
36C2×Dic3⋊C8—31no—
37C2×#809—31no—
38#4939—31no—
39C2×C4⋊(C3⋊C8)—31no—
40#4551—31no—
41#4529—31no—
42C23×C3×D3—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8D412yes—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#215—28no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8D412yes—
74(C2×D3)⋊Dic3—42no—
75(C2×D3)⋊Dic3—42no—
76#2055—91noSylow
77C22×C3×Q8—21no—
78C22×C3×Q8C2×D311yescharacteristic
79C22×C3×Q8C2×D311yescharacteristic
80C22×C3×D4—31no—
81C22×D12C2×D311yescharacteristic
82C2×C3×SD16—62no—
83C2×C3×SD16—62no—
84C2×C3×SD16—62no—
85C22×C3×C8—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C42—31no—
88C2×#217—61no—
89C2×#217—61no—
90C2×#215—22no—
91C2×#215—22no—
92C2×#215—22no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4×Dic3C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103C22×C3⋊C8C2×D311yescharacteristic
104C3×#95—61no—
105C3×#95—61no—
106#835—64no—
107#835—62no—
108#835—62no—
109#832—62no—
110C3⋊#95—21no—
111C3⋊#95—21no—
112Dic3⋊C8—62no—
113#809—62no—
114C4⋊(C3⋊C8)—62no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C32×Q8—22no—
124C32×Q8—22no—
125C32×Q8—41no—
126C32×Q8—41no—
127C2×C32×C4—22no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3SD1612yescomplemented
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C3⋊(C3⋊C8)—41no—
153C3×C3⋊C8—22no—
154C22×SD16—31no—
155C2×C4⋊C8—91no—
156C2×#103—91no—
157C2×#102—91no—
158#391—31no—
159#390—91no—
160#340—91no—
161C24×C3—61no—
162C23×D3—21no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—22no—
166C2×C3×Q8—22no—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—22no—
176C2×C3×Q8—41no—
177C2×C3×Q8—41no—
178C2×C3×Q8—41no—
179C2×C3×Q8D1212yes—
180C2×C3×Q8#6712yes—
181C2×C3×D4—32no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—41no—
193C22×C3×C4—61no—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—121no—
200C22×Dic3#6711yescharacteristic
201C22×Dic3#6711yescharacteristic
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12#6712yes—
208C3×SD16—68no—
209C2×C3×C8—32no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4—61no—
214C3×C42—61no—
215C3×C42—61no—
216#217—122no—
217#217—122no—
218#215—28no—
219(C2×D3)⋊C4—122no—
220(C2×D3)⋊C4—122no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223C4⋊Dic3—62no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3—61no—
228C4⋊Dic3—121no—
229C4×Dic3—21no—
230C4×Dic3—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—62no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—121no—
241C2×C3⋊C8—121no—
242C2×C3⋊C8#6712yes—
243C22×C32#12111yescharacteristic
244C22×C32#12111yescharacteristic
245C22×C32#12111yescharacteristic
246C22×C32C2×SD1611yescharacteristic
247C22×C32#13511yescharacteristic
248C22×C32AGL(1,ℤ/8)11yescharacteristic
249C22×C32#13711yescharacteristic
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—81no—
254C2×C3×D3—81no—
255C2×C3×D3—81no—
256C2×C3×D3—81no—
257C32×C4—42no—
258C32×C4#12011yescharacteristic
259C32×C4#12311yescharacteristic
260C32×C4#12311yescharacteristic
261C32×C4#12411yescharacteristic
262C3⋊Dic3—81no—
263C3×Dic3—22no—
264C3×Dic3—41no—
265C3×Dic3—81no—
266C22×Q8D3211yescharacteristic
267C22×D4—31no—
268C2×SD16—62no—
269C2×SD16—62no—
270C2×SD16—62no—
271C22×C8—31no—
272C22×C8—91no—
273C2×C4⋊C4—31no—
274C2×C4⋊C4—91no—
275C2×C22⋊C4—181no—
276C2×C22⋊C4—181no—
277C2×C42—31no—
278C4⋊C8—182no—
279#103—182no—
280#102—182no—
281#95—61no—
282#95—61no—
283C23×C3—21no—
284C23×C3—62no—
285C23×C3—121no—
286C23×C3—121no—
287C23×C3—121no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3D3×D411yescharacteristic
292C23×C3C2×#6711yescharacteristic
293C22×D3—22no—
294C22×D3—41no—
295C22×D3—41no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C3×Q8—24no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—42no—
306C3×Q8—42no—
307C3×Q8—42no—
308C3×Q8—41no—
309C3×Q8—41no—
310C3×Q8—41no—
311C3×Q8—41no—
312C3×D4—62no—
313C3×D4—62no—
314C3×D4—121no—
315C3×D4—121no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—32no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4#23511yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4#23711yescharacteristic
345C2×C3×C4#23711yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4#23711yescharacteristic
348C2×C3×C4#23711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—122no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—241no—
368C2×Dic3—241no—
369C2×Dic3#21512yescomplemented
370D12—22no—
371D12—22no—
372D12—41no—
373D12—41no—
374C3×C8—62no—
375C3⋊C8—22no—
376C3⋊C8—122no—
377C3⋊C8—121no—
378C3⋊C8—121no—
379C2×C32#39411yescharacteristic
380C2×C32#46011yescharacteristic
381C2×C32#46111yescharacteristic
382C2×C32#46311yescharacteristic
383C2×C32#46411yescharacteristic
384C2×C32#46511yescharacteristic
385C2×C32#46811yescharacteristic
386C3×D3—82no—
387C24—61no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8#62612yes—
394C2×D4—32no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C22×C4—21no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—61no—
404C22×C4—181no—
405C22×C4C2×D3211yescharacteristic
406SD16—68no—
407C2×C8—32no—
408C2×C8—61no—
409C2×C8—61no—
410C2×C8—181no—
411C2×C8—181no—
412C2×C8—181no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C22⋊C4—362no—
418C22⋊C4—362no—
419C42—61no—
420C42—61no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—122no—
431C22×C3—241no—
432C22×C3—241no—
433C22×C3—241no—
434C22×C3—241no—
435C22×C3D3×SD1611yescharacteristic
436C22×C3#91411yescharacteristic
437C22×C3#91511yescharacteristic
438C22×C3#91611yescharacteristic
439C22×C3#93011yescharacteristic
440C22×C3#93811yescharacteristic
441C22×C3#93811yescharacteristic
442C22×C3#93911yescharacteristic
443C22×C3#93911yescharacteristic
444C22×C3#93911yescharacteristic
445C22×C3C2×#21511yescharacteristic
446C22×C3#94211yescharacteristic
447C22×C3#94911yescharacteristic
448C22×C3#95011yescharacteristic
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—81no—
453C2×D3—81no—
454C2×D3—81no—
455C2×D3—81no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—44no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—62no—
464C3×C4—121no—
465C3×C4—241no—
466C3×C4#88211yescharacteristic
467C3×C4#88311yescharacteristic
468C3×C4#88511yescharacteristic
469C3×C4#88611yescharacteristic
470C3×C4#93511yescharacteristic
471C3×C4#93511yescharacteristic
472C3×C4#93611yescharacteristic
473C3×C4#95311yescharacteristic
474Dic3—22no—
475Dic3—41no—
476Dic3—81no—
477Dic3—242no—
478Dic3—241no—
479Dic3—241no—
480C32#205511yescharacteristic, complemented, Sylow
481C23—62no—
482C23—121no—
483C23—121no—
484C23—121no—
485C23—121no—
486C23—121no—
487C23—121no—
488C23D3×#6711yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493D4—62no—
494D4—62no—
495D4—121no—
496D4—121no—
497C2×C4—22no—
498C2×C4—32no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—121no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—361no—
510C2×C4—361no—
511C2×C4—361no—
512C2×C4#380411yescharacteristic
513C2×C4#380511yescharacteristic
514C2×C4#380511yescharacteristic
515C2×C4C2×#62611yescharacteristic
516C2×C4D3×#6711yescharacteristic
517C2×C4D3×#6711yescharacteristic
518C8—62no—
519C8—361no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—242no—
528C2×C3#496111yescharacteristic
529C2×C3#502711yescharacteristic
530C2×C3#502811yescharacteristic
531C2×C3#504811yescharacteristic
532C2×C3#504911yescharacteristic
533C2×C3#505711yescharacteristic
534C2×C3#508311yescharacteristic
535C2×C3#516211yescharacteristic
536C2×C3#516311yescharacteristic
537C2×C3#516511yescharacteristic
538C2×C3#516611yescharacteristic
539C2×C3#517111yescharacteristic
540C2×C3#517411yescharacteristic
541C2×C3#522211yescharacteristic
542D3—82no—
543C22—122no—
544C22—122no—
545C22—122no—
546C22—241no—
547C22—241no—
548C22—241no—
549C22—241no—
550C22D3×#21511yescharacteristic
551C22#6393911yescharacteristic
552C22#6394611yescharacteristic
553C22#6394711yescharacteristic
554C22#6397011yescharacteristic
555C22#6397011yescharacteristic
556C22#6397811yescharacteristic
557C4—42no—
558C4—62no—
559C4—121no—
560C4—241no—
561C4—721no—
562C4#6395911yescharacteristic
563C4#6396211yescharacteristic
564C4#6396911yescharacteristic
565C4#6397711yescharacteristic
566C3—21no—
567C3#6968011yescharacteristic, complemented
568C3#7205111yescharacteristic, complemented
569C2—242no—
570C2#1059156411yescharacteristic
571C2#1059156711yescharacteristic
572C2#1059158711yescharacteristic
573C2#1059160411yescharacteristic
574C2#1059161711yescharacteristic
575C2#1059163411yescharacteristic
576C2#1059170911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63662C2semidirect
3. C3×#5229C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
7. #10589164C2semidirect
30. #5229D3semidirect
147. C2×C3×Dic3SD16semidirect
369. C2×Dic3#215semidirect
480. C32#2055semidirect
567. C3#69680semidirect
568. C3#72051semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2152
C2×#636622
C3×#52292
#105913182
C2×Dic3⋊(C3⋊C8)2
C2×#635622
#105891642
#720513
#696803