Finite Group Databasebeta

← #11896099

Subgroups — #11896099

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 693 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2#10593850C211yesmaximal, characteristic
3#10592788C211yesmaximal, characteristic
4C3×#5094C211yesmaximal, characteristic, complemented
5#10590561C211yesmaximal, characteristic, complemented
6#10590560C211yesmaximal, characteristic, complemented
7#10590536C211yesmaximal, characteristic
8#10590535C211yesmaximal, characteristic
9#10590487C211yesmaximal, characteristic, complemented
10#10590480C211yesmaximal, characteristic, complemented
11#10590466C211yesmaximal, characteristic
12#10590458C211yesmaximal, characteristic
13#10590381C211yesmaximal, characteristic, complemented
14#10590368C211yesmaximal, characteristic
15#10590252C211yesmaximal, characteristic, complemented
16#83704—31nomaximal
17#81004—31nomaximal
18C32×C4⋊Q8C2211yescharacteristic
19#64084C2211yescharacteristic
20C3×#944—21no—
21C3×#944—21no—
22C3×#888—21no—
23C3×#888C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887—21no—
26C3×#887C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31#63894C2211yescharacteristic
32#63888—21no—
33#63868—21no—
34#63866C2211yescharacteristic
35#63864C2211yescharacteristic
36#63848—21no—
37#63844C2211yescharacteristic
38#63836—21no—
39C2×#3719C2211yescharacteristic
40C2×#3718C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42#63637C2211yescharacteristic
43#63637C2211yescharacteristic
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63630C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×C4⋊(C3⋊C8)C2211yescharacteristic
52#63574C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×Q82—31no—
62#5722D311yescharacteristic, complemented
63#5584—31no—
64#5568—31no—
65C3×#475—31no—
66#5094—31no—
67#5094D311yescharacteristic, complemented
68#5093—31no—
69#5089—31no—
70#5089—31no—
71#5089—31no—
72#5089—61no—
73#5084—31no—
74#5031—31no—
75#5030—31no—
76#5030—31no—
77#5030—31no—
78#5028—31no—
79#5028—31no—
80C4×#215—31no—
81#5024—31no—
82#4870—31no—
83#4854—31no—
84#4853—31no—
85#4852—31no—
86#4845—31no—
87#4828—31no—
88#4798—31no—
89#4795—31no—
90#4794—31no—
91#4792—31no—
92C2×C32×Q8—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6D411yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#624—21no—
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C42C2311yescharacteristic
105#3752—21no—
106#3752—21no—
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×C4⋊Dic3D411yescharacteristic
110C3×C4⋊Dic3C2311yescharacteristic
111C3×C4⋊Dic3C2311yescharacteristic
112C3×Dic3⋊C4—21no—
113C3×Dic3⋊C4—21no—
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4D411yescharacteristic
119C3×Dic3⋊C4D411yescharacteristic
120C3×C4×Dic3—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134Dic32—21no—
135#3719—22no—
136#3718—22no—
137#3717—22no—
138#3369—91noSylow
139C3×C4⋊Q8—21no—
140C3×C4⋊Q8—31no—
141C3×C4⋊Q8—31no—
142C3×C4⋊Q8—61no—
143C3×C4⋊Q8—61no—
144C3×C4⋊Q8—61no—
145C3×C4⋊Q8C2×D311yescharacteristic
146C3×C4⋊Q8C2×D311yescharacteristic
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—31no—
152C3×C4×Q8—61no—
153#947—31no—
154#946—61no—
155#944—21no—
156#944—21no—
157#944—31no—
158C2×#216—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#215—31no—
162C2×Dic12—31no—
163C2×#204—31no—
164#898—61no—
165#898—61no—
166#898—61no—
167#896—61no—
168#893—31no—
169#892—61no—
170#888—21no—
171#888C2×D311yescharacteristic
172#888C2×D311yescharacteristic
173#887—21no—
174#887—31no—
175#887C2×D311yescharacteristic
176#887C2×D311yescharacteristic
177#876—61no—
178#875—31no—
179#875—31no—
180#875—31no—
181#875—61no—
182C4×D12—31no—
183#872—61no—
184#869—31no—
185C4×Dic6—31no—
186C4×Dic6C2×D311yescharacteristic
187C4×Dic6C2×D311yescharacteristic
188C4×Dic6C2×D311yescharacteristic
189C3×#106—31no—
190C3×#106—31no—
191C3×C4⋊C8—31no—
192C3×#103—31no—
193C3×#103—31no—
194#835—31no—
195#835—31no—
196#821—31no—
197#816—31no—
198#815—31no—
199Dic3⋊C8—31no—
200Dic3⋊C8—31no—
201C8×Dic3—31no—
202#810—31no—
203#810—31no—
204#810—31no—
205#810—31no—
206#810—31no—
207#810—31no—
208#810—31no—
209#810—61no—
210#810—61no—
211#810C2×D311yescharacteristic
212#810C2×D311yescharacteristic
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—61no—
219#809—61no—
220#808—31no—
221#808—31no—
222#808C2×D311yescharacteristic
223#808C2×D311yescharacteristic
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)C2×D311yescharacteristic
227#803—31no—
228#803—31no—
229#803—31no—
230#803—61no—
231C4×C3⋊C8—31no—
232C22×C3⋊D3—21no—
233C32×Q8—81no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C4⋊(C3⋊D3)—21no—
241C4⋊(C3⋊D3)—21no—
242#634—21no—
243#634—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×Dic6—21no—
253C3×Dic6—22no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—81no—
257C3×Dic6—81no—
258C3×Dic6#4112yes—
259#624—42no—
260C3⋊(C3⋊C8)—21no—
261C3⋊(C3⋊C8)—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264Q82—31no—
265#556—91no—
266#489—91no—
267#489—91no—
268#487—91no—
269#476—91no—
270#475—31no—
271#475—91no—
272#464—91no—
273#464—91no—
274#462—91no—
275#446—91no—
276#441—91no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—21no—
280C2×C3×Q8—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—41no—
285C2×C3×Q8—61no—
286C2×C3×Q8—61no—
287C2×D12—31no—
288C2×D12—31no—
289C2×D12—61no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6—31no—
295C2×Dic6—31no—
296C2×Dic6—61no—
297C2×Dic6#6711yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C2×C3×C8—31no—
301C2×C3×C8—31no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—41no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4C22×D311yescharacteristic
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C4⋊C4C22×D311yescharacteristic
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C42—21no—
323C3×C42—31no—
324C3×C42—31no—
325C3×C42—61no—
326C3×C42—61no—
327C3×C42—61no—
328C3×C42—61no—
329C3×C42C22×D311yescharacteristic
330C3×C42C22×D311yescharacteristic
331#216—62no—
332#216—62no—
333#216—62no—
334#215—62no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—121no—
346(C2×D3)⋊C4—121no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3#6711yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4#6711yescharacteristic
363Dic3⋊C4#6711yescharacteristic
364C4×Dic3—21no—
365C4×Dic3—21no—
366C4×Dic3—21no—
367C4×Dic3—21no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3C22×D311yescharacteristic
371C4×Dic3C22×D311yescharacteristic
372C2×C3⋊C8—31no—
373C2×C3⋊C8—31no—
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—61no—
377C2×C3⋊C8—61no—
378C2×C3⋊C8C22×D311yescharacteristic
379C2×C3⋊C8C22×D311yescharacteristic
380Dic12—62no—
381#204—62no—
382C22×C32C22×D411yescharacteristic
383C2×C3⋊D3—41no—
384C2×C3⋊D3—41no—
385C2×C3⋊D3—41no—
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—41no—
389C32×C4—41no—
390C32×C4C2×#4111yescharacteristic
391C32×C42−1+411yescharacteristic
392C3⋊Dic3—41no—
393C3×Dic3—22no—
394C3×Dic3—21no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—41no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3#13712yes—
401C2×Q16—91no—
402C2×Q16—91no—
403C2×SD16—91no—
404C4⋊Q8—31no—
405C4⋊Q8—31no—
406C4⋊Q8—61no—
407C4⋊Q8—61no—
408C4⋊Q8—61no—
409C4⋊Q8—91no—
410C4⋊Q8D3211yescharacteristic
411#126—181no—
412#126—181no—
413#124—91no—
414#124—91no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—61no—
422C4×Q8—91no—
423C4×D4—91no—
424#117—181no—
425#106—31no—
426#106—31no—
427#106—91no—
428C4⋊C8—31no—
429C4⋊C8—91no—
430C4⋊C8—91no—
431#103—31no—
432#103—31no—
433#103—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—91no—
439#102—91no—
440#102—91no—
441#97—91no—
442#97—91no—
443C4×C8—91no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—121no—
447C3×Q8—32no—
448C3×Q8—62no—
449C3×Q8—61no—
450C3×Q8—61no—
451C3×Q8—61no—
452C3×Q8—81no—
453C3×Q8—81no—
454C3×Q8—82no—
455C3×Q8—241no—
456C3×Q8—241no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4D3×D411yescharacteristic
475C2×C3×C4D3×D411yescharacteristic
476C2×C3×C4C2×#6711yescharacteristic
477C2×C3×C4C2×#6711yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—121no—
487C2×Dic3C2×#6711yescharacteristic
488C2×Dic3C2×#6711yescharacteristic
489C2×Dic3C2×#6711yescharacteristic
490C2×Dic3C2×#6711yescharacteristic
491D12—61no—
492D12—61no—
493D12—61no—
494D12—61no—
495D12—121no—
496D12—121no—
497C4×D3—122no—
498C4×D3—122no—
499Dic6—21no—
500Dic6—22no—
501Dic6—21no—
502Dic6—21no—
503Dic6—61no—
504Dic6—61no—
505Dic6—61no—
506Dic6—61no—
507Dic6—81no—
508Dic6—81no—
509Dic6—121no—
510Dic6—121no—
511Dic6#23912yes—
512C3×C8—61no—
513C3×C8—61no—
514C3⋊C8—21no—
515C3⋊C8—21no—
516C3⋊C8—61no—
517C3⋊C8—61no—
518C3⋊C8—61no—
519C3⋊C8—61no—
520C3⋊C8—121no—
521C3⋊C8—121no—
522C2×C32#54811yescharacteristic
523C2×C32C2×#13711yescharacteristic
524C2×C32#57711yescharacteristic
525C3⋊D3—81no—
526C2×Q8—21no—
527C2×Q8—31no—
528C2×Q8—31no—
529C2×Q8—31no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—91no—
533C2×D4—91no—
534C22×C4—181no—
535Q16—182no—
536Q16—182no—
537SD16—182no—
538C2×C8—31no—
539C2×C8—31no—
540C2×C8—91no—
541C2×C8—91no—
542C4⋊C4—21no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4C2×D3211yescharacteristic
558C4⋊C4C2×D3211yescharacteristic
559C22⋊C4—181no—
560C22⋊C4—181no—
561C22⋊C4—181no—
562C22⋊C4—181no—
563C22⋊C4—181no—
564C42—31no—
565C42—31no—
566C42—61no—
567C42—61no—
568C42—61no—
569C42—61no—
570C42—181no—
571C42C2×D3211yescharacteristic
572C22×C3—21no—
573C22×C3C2×D3×D411yescharacteristic
574C22×C3C22×#6711yescharacteristic
575C2×D3—121no—
576C2×D3—121no—
577C2×D3—121no—
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—241no—
582C2×D3—241no—
583C2×D3—241no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—32no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—62no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—81no—
602C3×C4—81no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4—121no—
606C3×C4C2×#23911yescharacteristic
607C3×C4#100711yescharacteristic
608C3×C4#100711yescharacteristic
609C3×C4D3×#4111yescharacteristic
610Dic3—21no—
611Dic3—22no—
612Dic3—21no—
613Dic3—21no—
614Dic3—41no—
615Dic3—41no—
616Dic3—41no—
617Dic3—121no—
618Dic3—121no—
619Dic3—241no—
620Dic3#94212yes—
621C32#336911yescharacteristic, complemented, Sylow
622C23—181no—
623Q8—32no—
624Q8—62no—
625Q8—61no—
626Q8—61no—
627Q8—61no—
628Q8—81no—
629Q8—181no—
630Q8—181no—
631Q8—241no—
632Q8—241no—
633D4—181no—
634D4—181no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—181no—
646C2×C4—362no—
647C2×C4D3×#6711yescharacteristic
648C2×C4D3×#6711yescharacteristic
649C2×C4C22×D3211yescharacteristic
650C8—61no—
651C8—61no—
652C8—181no—
653C8—181no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3#563311yescharacteristic
658C2×C3#576211yescharacteristic
659C2×C3D3×#13711yescharacteristic
660C2×C3C2×#94211yescharacteristic
661C2×C3#581711yescharacteristic
662C2×C3#583611yescharacteristic
663D3—241no—
664D3—241no—
665D3—481no—
666C22—361no—
667C22—361no—
668C22—361no—
669C22C2×D3×#6711yescharacteristic
670C4—21no—
671C4—21no—
672C4—32no—
673C4—41no—
674C4—41no—
675C4—61no—
676C4—61no—
677C4—62no—
678C4—61no—
679C4—121no—
680C4—121no—
681C4—121no—
682C4—361no—
683C4#6431611yescharacteristic
684C4D3×#23911yescharacteristic
685C3—21no—
686C3#8100411yescharacteristic, complemented
687C3#8370411yescharacteristic, complemented
688C2—721no—
689C2#1059510511yescharacteristic
690C2D3×#94211yescharacteristic
691C2#1059540211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4⋊Q8D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5722C2semidirect
4. C3×#5094C2semidirect
5. #10590561C2semidirect
6. #10590560C2semidirect
9. #10590487C2semidirect
10. #10590480C2semidirect
13. #10590381C2semidirect
15. #10590252C2semidirect
62. #5722D3semidirect
67. #5094D3semidirect
621. C32#3369semidirect
686. C3#81004semidirect
687. C3#83704semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
#105938502
#105927882
C3×#50942
#105905612
#105905602
#105905362
#105905352
#105904872
#105904802
#105904662
#105904582
#105903812
#105903682
#105902522
#837043
#810043