Finite Group Databasebeta

← #11896044

Subgroups — #11896044

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×#5671C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592754C211yesmaximal, characteristic
4C3×#5054C211yesmaximal, characteristic
5#10591623C211yesmaximal, characteristic, complemented
6#10591576C211yesmaximal, characteristic, complemented
7#10591574C211yesmaximal, characteristic, complemented
8#10591544C211yesmaximal, characteristic, complemented
9#10591488C211yesmaximal, characteristic
10#10591442C211yesmaximal, characteristic
11Dic3×#214C211yesmaximal, characteristic
12#10591408C211yesmaximal, characteristic
13#10590381C211yesmaximal, characteristic, complemented
14#10590301C211yesmaximal, characteristic, complemented
15#10590252C211yesmaximal, characteristic, complemented
16#83677—31nomaximal
17#80582—31nomaximal
18C32×#124C2211yescharacteristic
19#64078C2211yescharacteristic
20C3×Q8×Dic3C2211yescharacteristic
21C3×#944C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C3×#936C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C3×#879—21no—
27C3×#879—21no—
28C3×#878—21no—
29C3×#877—21no—
30C3×C4×Dic6C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63918—21no—
34#63918C2211yescharacteristic
35#63918C2211yescharacteristic
36Dic3×Dic6—21no—
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63840—21no—
40#63840—21no—
41C2×#3718C2211yescharacteristic
42#63662C2211yescharacteristic
43#63662C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63630C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50#63574C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#556—31no—
62#5671D311yescharacteristic
63Q8×Dic6—31no—
64Q8×Dic6—31no—
65C3×#464—31no—
66#5184—31no—
67#5182—31no—
68#5166—31no—
69Dic3×SD16—31no—
70#5090—31no—
71#5079—31no—
72#5055—31no—
73#5055—31no—
74#5055—31no—
75#5055—61no—
76#5054—31no—
77#5054D311yescharacteristic
78#5030—31no—
79#5030—31no—
80#5030—31no—
81#5024—31no—
82#5020—31no—
83#5020—31no—
84C4×#214—31no—
85#5008—31no—
86#4851—31no—
87#4828—31no—
88#4792—31no—
89#4791—31no—
90#4765—31no—
91#4761—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#634—21no—
95C22×C3×Dic3—21no—
96C2×C3×Dic6D411yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627—21no—
101C32×C22⋊C4—21no—
102C32×C22⋊C4—21no—
103C32×C42C2311yescharacteristic
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×#217—21no—
110C3×#217—21no—
111C3×#217—21no—
112C3×#216—22no—
113C3×#214—22no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3D411yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
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
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137#3718—22no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×C4⋊Q8—31no—
142C3×#126—61no—
143C3×#126—61no—
144C3×#124—21no—
145C3×#124—31no—
146C3×#124C2×D311yescharacteristic
147C3×#124C2×D311yescharacteristic
148C3×C22⋊Q8—61no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—31no—
154C3×#117—61no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—61no—
158Q8×Dic3C2×D311yescharacteristic
159#944C2×D311yescharacteristic
160C2×#216—31no—
161C2×#216—31no—
162C2×#216C2×D311yescharacteristic
163#936C2×D311yescharacteristic
164D4×Dic3C2×D311yescharacteristic
165C2×#214C2×D311yescharacteristic
166#888—31no—
167#888—31no—
168#888—61no—
169#888—61no—
170#888—61no—
171#888—61no—
172#888—61no—
173#879—21no—
174#879—21no—
175#878—21no—
176#877—21no—
177#869—31no—
178#869—31no—
179#869—31no—
180#869—31no—
181#869—61no—
182#869—61no—
183C4×Dic6—31no—
184C4×Dic6—31no—
185C4×Dic6—61no—
186C4×Dic6C2×D311yescharacteristic
187C4×Dic6C2×D311yescharacteristic
188C4×Dic6C2×D311yescharacteristic
189C3×C4⋊C8—31no—
190C3×#103—31no—
191C3×#102—31no—
192#835—31no—
193#835—31no—
194#835—31no—
195#835—31no—
196#835—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—61no—
201#835—61no—
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—61no—
208#832—61no—
209#832C2×D311yescharacteristic
210#817—31no—
211#817—31no—
212#816—31no—
213#816—31no—
214#815—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217C8×Dic3—31no—
218#810—31no—
219#810—31no—
220#808—31no—
221#808—31no—
222#808—31no—
223#808—31no—
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—
232C23×C32—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C32×D4—21no—
236C32×D4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243#634—81no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—42no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×Dic6—21no—
254C3×Dic6—22no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6#4112yes—
258#627—81no—
259#627—81no—
260C3⋊(C3⋊C8)—21no—
261C3⋊(C3⋊C8)—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264Q82—91no—
265#556—31no—
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—31no—
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×D4—21no—
286C2×C3×D4C22×D311yescharacteristic
287C2×C3×D4C22×D311yescharacteristic
288C22×C3×C4—61no—
289C22×Dic3—21no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—121no—
297C2×Dic6#6711yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—62no—
301C3×SD16—62no—
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C22⋊C4—21no—
315C3×C22⋊C4—21no—
316C3×C22⋊C4—21no—
317C3×C22⋊C4—21no—
318C3×C22⋊C4—41no—
319C3×C22⋊C4—41no—
320C3×C22⋊C4—61no—
321C3×C22⋊C4—61no—
322C3×C22⋊C4—61no—
323C3×C42—21no—
324C3×C42—31no—
325C3×C42—31no—
326C3×C42—61no—
327C3×C42—61no—
328C3×C42—61no—
329C3×C42C22×D311yescharacteristic
330C3×C42C22×D311yescharacteristic
331#217—21no—
332#217—21no—
333#217—21no—
334#216—22no—
335#216—62no—
336#216—62no—
337#214—22no—
338C4⋊Dic3—21no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—121no—
352C4⋊Dic3#6711yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354C4⋊Dic3C22×D311yescharacteristic
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4#6711yescharacteristic
364Dic3⋊C4#6711yescharacteristic
365C4×Dic3—21no—
366C4×Dic3—21no—
367C4×Dic3—21no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3C22×D311yescharacteristic
373C4×Dic3C22×D311yescharacteristic
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32C22×D411yescharacteristic
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—41no—
389C32×C4C2×#4111yescharacteristic
390C32×C42−1+411yescharacteristic
391C3⋊Dic3—41no—
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—31no—
402C2×Q16—91no—
403C2×SD16—31no—
404C4⋊Q8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409C4⋊Q8—181no—
410C4⋊Q8—181no—
411#126—61no—
412#126—61no—
413#124—31no—
414#124D3211yescharacteristic
415C22⋊Q8—61no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—181no—
423C4×D4—31no—
424#117—61no—
425#106—91no—
426#106—91no—
427#106—91no—
428C4⋊C8—31no—
429C4⋊C8—91no—
430C4⋊C8—91no—
431#103—31no—
432#103—91no—
433#103—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—91no—
440#102—91no—
441#97—91no—
442#97—91no—
443C4×C8—91no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—41no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—32no—
452C3×Q8—41no—
453C3×Q8—41no—
454C3×Q8—62no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—41no—
463C3×D4—41no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—41no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—122no—
479C2×C3×C4D3×D411yescharacteristic
480C2×C3×C4D3×D411yescharacteristic
481C2×C3×C4C2×#6711yescharacteristic
482C2×C3×C4C2×#6711yescharacteristic
483C2×C3×C4C23×D311yescharacteristic
484C2×C3×C4C23×D311yescharacteristic
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—42no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—121no—
495C2×Dic3—121no—
496C2×Dic3C2×#6711yescharacteristic
497C2×Dic3C2×#6711yescharacteristic
498C2×Dic3C2×#6711yescharacteristic
499C2×Dic3C2×#6711yescharacteristic
500Dic6—21no—
501Dic6—22no—
502Dic6—21no—
503Dic6—21no—
504Dic6—241no—
505Dic6—241no—
506Dic6—241no—
507Dic6—241no—
508Dic6—241no—
509Dic6—241no—
510Dic6—242no—
511Dic6#23712yes—
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—81no—
523C2×C32#54811yescharacteristic
524C2×C32C2×#13711yescharacteristic
525C2×C32#57711yescharacteristic
526C2×Q8—31no—
527C2×Q8—31no—
528C2×Q8—31no—
529C2×Q8—181no—
530C2×Q8—181no—
531C2×Q8—181no—
532C2×Q8C2×D3211yescharacteristic
533C2×D4C2×D3211yescharacteristic
534C22×C4—61no—
535Q16—62no—
536Q16—182no—
537SD16—62no—
538C2×C8—31no—
539C2×C8—31no—
540C2×C8—91no—
541C2×C8—91no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—61no—
562C22⋊C4—61no—
563C22⋊C4—61no—
564C42—31no—
565C42—31no—
566C42—61no—
567C42—61no—
568C42—61no—
569C42—181no—
570C42—181no—
571C42C2×D3211yescharacteristic
572C22×C3—21no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3—81no—
582C22×C3C2×D3×D411yescharacteristic
583C22×C3C22×#6711yescharacteristic
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—61no—
596C3×C4—61no—
597C3×C4—61no—
598C3×C4—62no—
599C3×C4—81no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4C2×#23711yescharacteristic
604C3×C4D3×#4111yescharacteristic
605C3×C4#101011yescharacteristic
606C3×C4#101011yescharacteristic
607Dic3—21no—
608Dic3—21no—
609Dic3—21no—
610Dic3—22no—
611Dic3—41no—
612Dic3—41no—
613Dic3—41no—
614Dic3—121no—
615Dic3—121no—
616Dic3—121no—
617Dic3—121no—
618Dic3—241no—
619Dic3—241no—
620Dic3#95112yes—
621C32#336911yescharacteristic, complemented, Sylow
622C23—21no—
623Q8—21no—
624Q8—21no—
625Q8—32no—
626Q8—62no—
627Q8—61no—
628Q8—61no—
629Q8—61no—
630Q8—721no—
631Q8—721no—
632Q8—721no—
633D4—21no—
634D4—21no—
635C2×C4—21no—
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—122no—
645C2×C4—181no—
646C2×C4—181no—
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—81no—
658C2×C3—81no—
659C2×C3—161no—
660C2×C3#559811yescharacteristic
661C2×C3#577011yescharacteristic
662C2×C3D3×#13711yescharacteristic
663C2×C3C2×#95111yescharacteristic
664C2×C3#583111yescharacteristic
665C2×C3#583711yescharacteristic
666C22—41no—
667C22—41no—
668C22—41no—
669C22C2×D3×#6711yescharacteristic
670C4—21no—
671C4—21no—
672C4—32no—
673C4—41no—
674C4—62no—
675C4—61no—
676C4—61no—
677C4—61no—
678C4—121no—
679C4—121no—
680C4—121no—
681C4—361no—
682C4—361no—
683C4#6430911yescharacteristic
684C4D3×#23711yescharacteristic
685C3—21no—
686C3#8058211yescharacteristic, complemented
687C3#8367711yescharacteristic, complemented
688C2—81no—
689C2#1059515711yescharacteristic
690C2#1059545711yescharacteristic
691C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenter#124D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. Dic62C2semidirect
5. #10591623C2semidirect
6. #10591576C2semidirect
7. #10591574C2semidirect
8. #10591544C2semidirect
13. #10590381C2semidirect
14. #10590301C2semidirect
15. #10590252C2semidirect
621. C32#3369semidirect
686. C3#80582semidirect
687. C3#83677semidirect

Maximal subgroups

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

subgroupindex
C3×#56712
Dic622
#105927542
C3×#50542
#105916232
#105915762
#105915742
#105915442
#105914882
#105914422
Dic3×#2142
#105914082
#105903812
#105903012
#105902522
#836773
#805823