Finite Group Databasebeta

← #11896056

Subgroups — #11896056

Order 1152.

732 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2#10593850C211yesmaximal, characteristic
3#10592727C211yesmaximal, characteristic
4C3×#5030C211yesmaximal, characteristic, complemented
5#10591625C211yesmaximal, characteristic, complemented
6#10591607C211yesmaximal, characteristic
7#10591541C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic
9#10590560C211yesmaximal, characteristic, complemented
10#10590535C211yesmaximal, characteristic
11#10590487C211yesmaximal, characteristic, complemented
12#10590466C211yesmaximal, characteristic
13#10590294C211yesmaximal, characteristic
14#10590285C211yesmaximal, characteristic, complemented
15#10590251C211yesmaximal, characteristic, complemented
16#83704—31nomaximal
17#79815—31nomaximal
18C32×C4×Q8C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21#64084C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#888—21no—
26C3×#888—21no—
27C3×#888C2211yescharacteristic
28C3×#888C2211yescharacteristic
29C3×#869—21no—
30C3×#869C2211yescharacteristic
31C3×C4×Dic6—21no—
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63894C2211yescharacteristic
35#63888—21no—
36#63868—21no—
37#63866C2211yescharacteristic
38#63864C2211yescharacteristic
39#63848—21no—
40#63844C2211yescharacteristic
41#63836—21no—
42#63637C2211yescharacteristic
43#63636C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#810C2211yescharacteristic
47C3×#808C2211yescharacteristic
48C3×#803C2211yescharacteristic
49#63574C2211yescharacteristic
50#63574C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×Q82—31no—
62#5584—31no—
63#5568—31no—
64Q8×Dic6D311yescharacteristic, complemented
65C3×#441—31no—
66#5185—31no—
67#5182—31no—
68#5094—31no—
69#5094—31no—
70#5093—31no—
71#5089—31no—
72#5089—31no—
73#5084—31no—
74#5031—31no—
75#5030—31no—
76#5030D311yescharacteristic, complemented
77#5028—31no—
78#5028—31no—
79#5028—31no—
80#5028—61no—
81C4×#215—31no—
82#5024—31no—
83#5020—31no—
84#4870—31no—
85#4854—31no—
86#4794—31no—
87#4792—31no—
88#4789—31no—
89#4788—31no—
90#4714—31no—
91#4701—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6D411yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#624—21no—
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C42—21no—
104C32×C42C2311yescharacteristic
105#3756—22no—
106#3755—22no—
107#3752—21no—
108#3752—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3D411yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4D411yescharacteristic
123C3×Dic3⋊C4D411yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137Dic32—21no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C3×C4⋊Q8—31no—
141C3×C4⋊Q8—31no—
142C3×C4⋊Q8—31no—
143C3×C4⋊Q8—61no—
144C3×C4⋊Q8—61no—
145C3×C4⋊Q8—61no—
146C3×C4×Q8—21no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—61no—
152C3×C4×Q8C2×D311yescharacteristic
153C3×C4×Q8C2×D311yescharacteristic
154#947—31no—
155#946—61no—
156Q8×Dic3C2×D311yescharacteristic
157Q8×Dic3C2×D311yescharacteristic
158#944—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#216—61no—
162C2×#216C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—61no—
166#898—61no—
167#898—61no—
168#898—61no—
169#896—61no—
170#893—31no—
171#892—61no—
172#888—21no—
173#888—21no—
174#888C2×D311yescharacteristic
175#888C2×D311yescharacteristic
176#887—31no—
177#876—61no—
178#875—31no—
179#875—31no—
180#875—31no—
181#875—61no—
182C4×D12—31no—
183#872—61no—
184#869—21no—
185#869—31no—
186#869C2×D311yescharacteristic
187C4×Dic6—21no—
188C4×Dic6—31no—
189C4×Dic6C2×D311yescharacteristic
190C4×Dic6C2×D311yescharacteristic
191C3×#106—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#97—31no—
195#835—31no—
196#835—31no—
197#835C2×D311yescharacteristic
198#821—31no—
199#821—31no—
200#816—31no—
201#816—31no—
202#815—31no—
203Dic3⋊C8—31no—
204Dic3⋊C8—31no—
205C8×Dic3—31no—
206#810—31no—
207#810—31no—
208#810—31no—
209#810—31no—
210#810—31no—
211#810—31no—
212#810—61no—
213#810C2×D311yescharacteristic
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—61no—
219#808—31no—
220#808—31no—
221#808—31no—
222#808—31no—
223#808C2×D311yescharacteristic
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—61no—
229#803—31no—
230#803C2×D311yescharacteristic
231C4×C3⋊C8—31no—
232C22×C3⋊D3—21no—
233C32×Q8—21no—
234C32×Q8#4112yes—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)—21no—
243#634—21no—
244#634—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×Dic6—22no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—81no—
257C3×Dic6—81no—
258C3×Dic6—81no—
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—91no—
271#475—91no—
272#464—91no—
273#464—91no—
274#462—91no—
275#446—91no—
276#441—31no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—21no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×C3×Q8—61no—
284C2×C3×Q8—61no—
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C22×D311yescharacteristic
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—21no—
295C2×Dic6—31no—
296C2×Dic6—31no—
297C2×Dic6—61no—
298C2×Dic6#6711yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—62no—
301C2×C3×C8—31no—
302C2×C3×C8—31no—
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—31no—
312C3×C4⋊C4—41no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C4⋊C4C22×D311yescharacteristic
321C3×C42—21no—
322C3×C42—21no—
323C3×C42—21no—
324C3×C42—31no—
325C3×C42—31no—
326C3×C42—41no—
327C3×C42—61no—
328C3×C42—61no—
329C3×C42—61no—
330C3×C42C22×D311yescharacteristic
331C3×C42C22×D311yescharacteristic
332#216—22no—
333#216—62no—
334#216—62no—
335#216—122no—
336#215—62no—
337#215—62no—
338#215—122no—
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—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—121no—
350(C2×D3)⋊C4—121no—
351C4⋊Dic3—21no—
352C4⋊Dic3—21no—
353C4⋊Dic3—21no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3#6711yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358C4⋊Dic3C22×D311yescharacteristic
359C4⋊Dic3C22×D311yescharacteristic
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—21no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4#6711yescharacteristic
368Dic3⋊C4#6711yescharacteristic
369C4×Dic3—21no—
370C4×Dic3—21no—
371C4×Dic3—21no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8—61no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384C22×C32C22×D411yescharacteristic
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C32×C4—22no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—41no—
392C32×C4C2×#4111yescharacteristic
393C32×C42−1+411yescharacteristic
394C3⋊Dic3—41no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3#13712yes—
403C2×Q16—31no—
404C2×Q16—91no—
405C2×SD16—91no—
406C4⋊Q8—31no—
407C4⋊Q8—31no—
408C4⋊Q8—31no—
409C4⋊Q8—61no—
410C4⋊Q8—61no—
411C4⋊Q8—61no—
412C4⋊Q8—91no—
413#126—181no—
414#126—181no—
415#124—91no—
416#124—91no—
417C22⋊Q8—181no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—61no—
423C4×Q8—91no—
424C4×Q8D3211yescharacteristic
425C4×D4—91no—
426#117—181no—
427#106—31no—
428#106—91no—
429#106—91no—
430C4⋊C8—91no—
431C4⋊C8—91no—
432C4⋊C8—91no—
433#103—31no—
434#103—31no—
435#103—91no—
436#103—91no—
437#103—91no—
438#103—91no—
439#103—91no—
440#102—91no—
441#102—91no—
442#102—91no—
443#97—31no—
444#97—91no—
445C4×C8—91no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—121no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—22no—
452C3×Q8—41no—
453C3×Q8—62no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—241no—
457C3×Q8—241no—
458C3×Q8—241no—
459C3×Q8#23512yes—
460C3×Q8#23912yes—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4D3×D411yescharacteristic
479C2×C3×C4D3×D411yescharacteristic
480C2×C3×C4C2×#6711yescharacteristic
481C2×C3×C4C2×#6711yescharacteristic
482C2×C3×C4C23×D311yescharacteristic
483C2×C3×C4C23×D311yescharacteristic
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—121no—
491C2×Dic3C2×#6711yescharacteristic
492C2×Dic3C2×#6711yescharacteristic
493C2×Dic3C2×#6711yescharacteristic
494C2×Dic3C2×#6711yescharacteristic
495D12—61no—
496D12—61no—
497D12—61no—
498D12—61no—
499D12—121no—
500D12—121no—
501C4×D3—122no—
502C4×D3—122no—
503Dic6—22no—
504Dic6—21no—
505Dic6—21no—
506Dic6—61no—
507Dic6—61no—
508Dic6—61no—
509Dic6—61no—
510Dic6—81no—
511Dic6—81no—
512Dic6—81no—
513Dic6—121no—
514Dic6—121no—
515C3×C8—61no—
516C3×C8—61no—
517C3⋊C8—21no—
518C3⋊C8—21no—
519C3⋊C8—61no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—121no—
524C3⋊C8—121no—
525C2×C32#54811yescharacteristic
526C2×C32C2×#13711yescharacteristic
527C2×C32#57711yescharacteristic
528C3⋊D3—81no—
529C2×Q8—31no—
530C2×Q8—31no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—91no—
535C2×Q8C2×D3211yescharacteristic
536C2×D4—91no—
537C22×C4—181no—
538Q16—62no—
539Q16—182no—
540SD16—182no—
541C2×C8—31no—
542C2×C8—31no—
543C2×C8—91no—
544C2×C8—91no—
545C4⋊C4—21no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4C2×D3211yescharacteristic
562C22⋊C4—181no—
563C22⋊C4—181no—
564C22⋊C4—181no—
565C22⋊C4—181no—
566C22⋊C4—181no—
567C42—21no—
568C42—31no—
569C42—31no—
570C42—61no—
571C42—61no—
572C42—61no—
573C42—181no—
574C42C2×D3211yescharacteristic
575C22×C3—21no—
576C22×C3C2×D3×D411yescharacteristic
577C22×C3C22×#6711yescharacteristic
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—121no—
582C2×D3—121no—
583C2×D3—121no—
584C2×D3—241no—
585C2×D3—241no—
586C2×D3—241no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—22no—
590C3×C4—21no—
591C3×C4—22no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—32no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—42no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—81no—
605C3×C4—121no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4C2×#23511yescharacteristic
610C3×C4C2×#23911yescharacteristic
611C3×C4#100711yescharacteristic
612C3×C4#101011yescharacteristic
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3—41no—
617Dic3—41no—
618Dic3—41no—
619Dic3—41no—
620Dic3—121no—
621Dic3—121no—
622Dic3—241no—
623Dic3#94212yes—
624C32#336911yescharacteristic, complemented, Sylow
625C23—181no—
626Q8—21no—
627Q8—62no—
628Q8—61no—
629Q8—61no—
630Q8—181no—
631Q8—181no—
632Q8—241no—
633Q8—241no—
634Q8—241no—
635Q8#379912yes—
636D4—181no—
637D4—181no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—181no—
649C2×C4—362no—
650C2×C4D3×#6711yescharacteristic
651C2×C4D3×#6711yescharacteristic
652C2×C4C22×D3211yescharacteristic
653C8—61no—
654C8—61no—
655C8—181no—
656C8—181no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3#555211yescharacteristic
661C2×C3D3×#13711yescharacteristic
662C2×C3#577811yescharacteristic
663C2×C3C2×#94211yescharacteristic
664C2×C3#581711yescharacteristic
665C2×C3#583611yescharacteristic
666D3—241no—
667D3—241no—
668D3—481no—
669C22—361no—
670C22—361no—
671C22—361no—
672C22C2×D3×#6711yescharacteristic
673C4—22no—
674C4—21no—
675C4—21no—
676C4—32no—
677C4—41no—
678C4—61no—
679C4—61no—
680C4—61no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—121no—
685C4—361no—
686C4#6429711yescharacteristic
687C4C2×#379911yescharacteristic
688C3—21no—
689C3#7981511yescharacteristic, complemented
690C3#8370411yescharacteristic, complemented
691C2—721no—
692C2#1059490211yescharacteristic
693C2D3×#94211yescharacteristic
694C2#1059546411yescharacteristic
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×Q8×Dic6C2semidirect
4. C3×#5030C2semidirect
5. #10591625C2semidirect
7. #10591541C2semidirect
9. #10590560C2semidirect
11. #10590487C2semidirect
14. #10590285C2semidirect
15. #10590251C2semidirect
64. Q8×Dic6D3semidirect
76. #5030D3semidirect
624. C32#3369semidirect
689. C3#79815semidirect
690. C3#83704semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
#105938502
#105927272
C3×#50302
#105916252
#105916072
#105915412
#105915362
#105905602
#105905352
#105904872
#105904662
#105902942
#105902852
#105902512
#837043
#798153