Finite Group Databasebeta

← #11896058

Subgroups — #11896058

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2#10593932C211yesmaximal, characteristic
3#10592729C211yesmaximal, characteristic, complemented
4C3×#5028C211yesmaximal, characteristic
5#10591625C211yesmaximal, characteristic, complemented
6#10591604C211yesmaximal, characteristic
7#10591576C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic
9#10590560C211yesmaximal, characteristic, complemented
10#10590531C211yesmaximal, characteristic
11#10590486C211yesmaximal, characteristic, complemented
12#10590465C211yesmaximal, characteristic
13#10590307C211yesmaximal, characteristic, complemented
14#10590280C211yesmaximal, characteristic
15#10590252C211yesmaximal, characteristic, complemented
16#83704—31nomaximal
17#80582—31nomaximal
18C32×C4×Q8C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#888—21no—
26C3×#888—21no—
27C3×#888C2211yescharacteristic
28C3×#888C2211yescharacteristic
29C3×#875C2211yescharacteristic
30C3×#869—21no—
31C3×#869C2211yescharacteristic
32C3×C4×Dic6—21no—
33C3×C4×Dic6C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35#63887—21no—
36#63878—21no—
37#63866C2211yescharacteristic
38#63862—21no—
39#63860C2211yescharacteristic
40#63858—21no—
41Dic3×Dic6C2211yescharacteristic
42#63662C2211yescharacteristic
43#63637C2211yescharacteristic
44#63635C2211yescharacteristic
45#63630C2211yescharacteristic
46C3×#810C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×C4⋊(C3⋊C8)C2211yescharacteristic
49#63573C2211yescharacteristic
50#63573C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×Q82—31no—
62#5671—31no—
63#5584—31no—
64Q8×Dic6D311yescharacteristic, complemented
65C3×#464—31no—
66#5184—31no—
67#5182—31no—
68#5166—31no—
69Dic3×SD16—31no—
70#5094—31no—
71#5094—31no—
72#5093—31no—
73#5089—31no—
74#5089—31no—
75#5084—31no—
76#5055—31no—
77#5031—31no—
78#5030—31no—
79#5030—31no—
80#5030—31no—
81#5030—61no—
82#5028—31no—
83#5028D311yescharacteristic
84C4×#215—31no—
85#5024—31no—
86#4851—31no—
87#4828—31no—
88#4792—31no—
89#4791—31no—
90#4765—31no—
91#4761—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6D411yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×D3×Dic3—21no—
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C42—21no—
104C32×C42C2311yescharacteristic
105#3756—22no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×#215—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3D411yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4D411yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×C4⋊Q8—31no—
142C3×C4⋊Q8—31no—
143C3×C4⋊Q8—31no—
144C3×C4⋊Q8—61no—
145C3×C4⋊Q8—61no—
146C3×C4⋊Q8—61no—
147C3×#124—31no—
148C3×C4×Q8—21no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—31no—
152C3×C4×Q8—61no—
153C3×C4×Q8C2×D311yescharacteristic
154C3×C4×Q8C2×D311yescharacteristic
155#946—61no—
156Q8×Dic3—31no—
157Q8×Dic3C2×D311yescharacteristic
158Q8×Dic3C2×D311yescharacteristic
159#944—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#216—61no—
163C2×#216C2×D311yescharacteristic
164C2×#215C2×D311yescharacteristic
165#936—31no—
166D4×Dic3—31no—
167#898—61no—
168#898—61no—
169#892—61no—
170#888—21no—
171#888—21no—
172#888C2×D311yescharacteristic
173#888C2×D311yescharacteristic
174#879—61no—
175#879—61no—
176#878—61no—
177#877—61no—
178#875—31no—
179#875C2×D311yescharacteristic
180C4×D12—31no—
181#869—21no—
182#869—31no—
183#869C2×D311yescharacteristic
184C4×Dic6—21no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C4×Dic6C2×D311yescharacteristic
190C3×C4⋊C8—31no—
191C3×#103—31no—
192C3×#102—31no—
193#835—31no—
194#835—31no—
195#835—31no—
196#835—31no—
197#835—61no—
198#832—31no—
199#832—31no—
200#817—31no—
201#817—31no—
202#816—31no—
203#816—31no—
204#815—31no—
205Dic3⋊C8—31no—
206Dic3⋊C8—31no—
207C8×Dic3—31no—
208#810—31no—
209#810—31no—
210#810—31no—
211#810—31no—
212#810—31no—
213#810—31no—
214#810—61no—
215#810C2×D311yescharacteristic
216#809—31no—
217#809—31no—
218#809C2×D311yescharacteristic
219#808—31no—
220#808—31no—
221#808—31no—
222#808—31no—
223#808—61no—
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—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—
241C2×C3⋊Dic3—21no—
242#634—21no—
243#634—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12—21no—
253C3×Dic6—22no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—81no—
257C3×Dic6—81no—
258C3×Dic6—81no—
259D3×Dic3—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—31no—
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—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×C3×D4—31no—
288C22×Dic3—61no—
289C2×D12C22×D311yescharacteristic
290C2×C4×D3—61no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6—31no—
295C2×Dic6—31no—
296C2×Dic6—61no—
297C2×Dic6#6711yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C3×Q16—62no—
300C3×SD16—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—41no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C4⋊C4C22×D311yescharacteristic
319C3×C22⋊C4—61no—
320C3×C22⋊C4—61no—
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×C42C22×D311yescharacteristic
330C3×C42C22×D311yescharacteristic
331#217—61no—
332#217—61no—
333#217—61no—
334#216—22no—
335#216—64no—
336#216—62no—
337#216—62no—
338#215—22no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344C4⋊Dic3—21no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3#6711yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—121no—
364Dic3⋊C4#6711yescharacteristic
365Dic3⋊C4#6711yescharacteristic
366C4×Dic3—21no—
367C4×Dic3—21no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—121no—
373C4×Dic3C22×D311yescharacteristic
374C4×Dic3C22×D311yescharacteristic
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C32×C4—22no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—41no—
391C32×C4C2×#4111yescharacteristic
392C32×C42−1+411yescharacteristic
393C3⋊Dic3—41no—
394C3⋊Dic3—41no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3#13712yes—
402C2×Q16—31no—
403C2×Q16—91no—
404C2×SD16—31no—
405C4⋊Q8—31no—
406C4⋊Q8—31no—
407C4⋊Q8—31no—
408C4⋊Q8—61no—
409C4⋊Q8—61no—
410C4⋊Q8—61no—
411C4⋊Q8—91no—
412#126—181no—
413#126—181no—
414#124—31no—
415#124—91no—
416C22⋊Q8—181no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—61no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8D3211yescharacteristic
424C4×D4—91no—
425#117—181no—
426#106—91no—
427#106—91no—
428#106—91no—
429C4⋊C8—31no—
430C4⋊C8—91no—
431C4⋊C8—91no—
432#103—31no—
433#103—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#103—91no—
439#102—31no—
440#102—91no—
441#102—91no—
442#97—91no—
443#97—91no—
444C4×C8—91no—
445C23×C3—61no—
446C22×D3—21no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—22no—
450C3×Q8—41no—
451C3×Q8—62no—
452C3×Q8—61no—
453C3×Q8—61no—
454C3×Q8—241no—
455C3×Q8—241no—
456C3×Q8—241no—
457C3×Q8#23712yes—
458C3×Q8#23912yes—
459C3×D4—61no—
460C3×D4—61no—
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×C4D3×D411yescharacteristic
478C2×C3×C4D3×D411yescharacteristic
479C2×C3×C4C2×#6711yescharacteristic
480C2×C3×C4C2×#6711yescharacteristic
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C23×D311yescharacteristic
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—121no—
491C2×Dic3—121no—
492C2×Dic3—122no—
493C2×Dic3C2×#6711yescharacteristic
494C2×Dic3C2×#6711yescharacteristic
495C2×Dic3C2×#6711yescharacteristic
496C2×Dic3C2×#6711yescharacteristic
497D12—21no—
498D12—21no—
499C4×D3—122no—
500Dic6—22no—
501Dic6—21no—
502Dic6—21no—
503Dic6—62no—
504Dic6—61no—
505Dic6—61no—
506Dic6—61no—
507Dic6—61no—
508Dic6—81no—
509Dic6—81no—
510Dic6—81no—
511Dic6—121no—
512C3×C8—61no—
513C3×C8—61no—
514C3⋊C8—21no—
515C3⋊C8—21no—
516C3⋊C8—62no—
517C3⋊C8—61no—
518C3⋊C8—61no—
519C3⋊C8—61no—
520C3⋊C8—61no—
521C3⋊C8—121no—
522C2×C32#54811yescharacteristic
523C2×C32C2×#13711yescharacteristic
524C2×C32#57711yescharacteristic
525C3×D3—81no—
526C2×Q8—31no—
527C2×Q8—31no—
528C2×Q8—61no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—91no—
532C2×Q8C2×D3211yescharacteristic
533C2×D4—31no—
534C22×C4—181no—
535Q16—62no—
536Q16—182no—
537SD16—62no—
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—91no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4C2×D3211yescharacteristic
559C22⋊C4—61no—
560C22⋊C4—61no—
561C22⋊C4—181no—
562C22⋊C4—181no—
563C22⋊C4—181no—
564C42—21no—
565C42—31no—
566C42—31no—
567C42—61no—
568C42—61no—
569C42—181no—
570C42—181no—
571C42C2×D3211yescharacteristic
572C22×C3—21no—
573C22×C3—121no—
574C22×C3—121no—
575C22×C3—121no—
576C22×C3C2×D3×D411yescharacteristic
577C22×C3C22×#6711yescharacteristic
578C2×D3—41no—
579C2×D3—41no—
580C2×D3—41no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—22no—
585C3×C4—21no—
586C3×C4—22no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—32no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—42no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—61no—
598C3×C4—81no—
599C3×C4—121no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4C2×#23711yescharacteristic
603C3×C4C2×#23911yescharacteristic
604C3×C4#100711yescharacteristic
605C3×C4#101011yescharacteristic
606Dic3—21no—
607Dic3—21no—
608Dic3—21no—
609Dic3—41no—
610Dic3—41no—
611Dic3—41no—
612Dic3—122no—
613Dic3—121no—
614Dic3—121no—
615Dic3—121no—
616Dic3—121no—
617Dic3—241no—
618Dic3#94212yes—
619C32#336911yescharacteristic, complemented, Sylow
620C23—61no—
621Q8—21no—
622Q8—62no—
623Q8—61no—
624Q8—61no—
625Q8—181no—
626Q8—181no—
627Q8—241no—
628Q8—241no—
629Q8—241no—
630Q8#379612yes—
631D4—61no—
632D4—61no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—181no—
643C2×C4—181no—
644C2×C4—362no—
645C2×C4D3×#6711yescharacteristic
646C2×C4D3×#6711yescharacteristic
647C2×C4C22×D3211yescharacteristic
648C8—61no—
649C8—61no—
650C8—181no—
651C8—181no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—241no—
656C2×C3#559811yescharacteristic
657C2×C3#577011yescharacteristic
658C2×C3D3×#13711yescharacteristic
659C2×C3C2×#94211yescharacteristic
660C2×C3#581711yescharacteristic
661C2×C3#583611yescharacteristic
662D3—81no—
663C22—121no—
664C22—121no—
665C22—121no—
666C22C2×D3×#6711yescharacteristic
667C4—22no—
668C4—21no—
669C4—21no—
670C4—32no—
671C4—41no—
672C4—61no—
673C4—61no—
674C4—61no—
675C4—121no—
676C4—121no—
677C4—121no—
678C4—361no—
679C4—361no—
680C4C2×#379611yescharacteristic
681C4#6429711yescharacteristic
682C3—21no—
683C3#8058211yescharacteristic, complemented
684C3#8370411yescharacteristic, complemented
685C2—241no—
686C2#1059490011yescharacteristic
687C2D3×#94211yescharacteristic
688C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
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
3. #10592729C2semidirect
5. #10591625C2semidirect
7. #10591576C2semidirect
9. #10590560C2semidirect
11. #10590486C2semidirect
13. #10590307C2semidirect
15. #10590252C2semidirect
64. Q8×Dic6D3semidirect
619. C32#3369semidirect
683. C3#80582semidirect
684. 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
#105939322
#105927292
C3×#50282
#105916252
#105916042
#105915762
Dic3×#2152
#105905602
#105905312
#105904862
#105904652
#105903072
#105902802
#105902522
#837043
#805823