Finite Group Databasebeta

← #11896042

Subgroups — #11896042

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×#5671C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592753C211yesmaximal, characteristic
4C3×#5055C211yesmaximal, characteristic
5#10591623C211yesmaximal, characteristic, complemented
6#10591575C211yesmaximal, characteristic, complemented
7#10591544C211yesmaximal, characteristic, complemented
8#10591541C211yesmaximal, characteristic, complemented
9#10591488C211yesmaximal, characteristic
10#10591441C211yesmaximal, characteristic
11#10591408C211yesmaximal, characteristic
12#10591401C211yesmaximal, characteristic
13#10590383C211yesmaximal, characteristic, complemented
14#10590285C211yesmaximal, characteristic, complemented
15#10590251C211yesmaximal, characteristic, complemented
16#83677—31nomaximal
17#81671—31nomaximal
18C32×#124C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C3×#936C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C3×#879—21no—
27C3×#879—21no—
28C3×#878—21no—
29C3×#877—21no—
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63919—21no—
34#63918C2211yescharacteristic
35#63918C2211yescharacteristic
36#63844C2211yescharacteristic
37#63844C2211yescharacteristic
38#63843—21no—
39#63839—21no—
40#63839—21no—
41C2×#3719C2211yescharacteristic
42#63662C2211yescharacteristic
43#63659C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#803C2211yescharacteristic
50#63574C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#556—31no—
62#5722—31no—
63#5671D311yescharacteristic
64Q8×Dic6—31no—
65C3×#489—31no—
66#5094—31no—
67#5090—31no—
68#5079—31no—
69#5055—31no—
70#5055D311yescharacteristic
71#5054—31no—
72#5054—31no—
73#5054—31no—
74#5054—61no—
75#5030—31no—
76#5030—31no—
77#5024—31no—
78#5020—31no—
79#5020—31no—
80C4×#214—31no—
81#5008—31no—
82#4795—31no—
83#4792—31no—
84#4791—31no—
85#4789—31no—
86#4767—31no—
87#4765—31no—
88#4761—31no—
89#4758—31no—
90#4716—31no—
91#4701—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C22×C3×Dic3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6D411yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627—21no—
101C32×C22⋊C4—21no—
102C32×C22⋊C4—21no—
103C32×C42C2311yescharacteristic
104#3756—22no—
105#3754—22no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×#217—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3D411yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
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
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137#3719—22no—
138#3369—91noSylow
139C3×C4⋊Q8—31no—
140C3×C4⋊Q8—31no—
141C3×#126—61no—
142C3×#126—61no—
143C3×#124—21no—
144C3×#124—31no—
145C3×#124C2×D311yescharacteristic
146C3×#124C2×D311yescharacteristic
147C3×C22⋊Q8—61no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×D4—31no—
152C3×#117—61no—
153Q8×Dic3—61no—
154Q8×Dic3C2×D311yescharacteristic
155#944—61no—
156#944—61no—
157#944C2×D311yescharacteristic
158C2×#216—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#216—61no—
162#936C2×D311yescharacteristic
163D4×Dic3C2×D311yescharacteristic
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—61no—
167C2×Dic12—31no—
168#888—31no—
169#888—31no—
170#888—61no—
171#888—61no—
172#888—61no—
173#888—61no—
174#887—31no—
175#887—31no—
176#887—61no—
177#879—21no—
178#879—21no—
179#878—21no—
180#877—21no—
181#869—31no—
182#869—31no—
183#869C2×D311yescharacteristic
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C4×Dic6C2×D311yescharacteristic
190C4×Dic6C2×D311yescharacteristic
191C3×#103—31no—
192C3×#103—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#97—31no—
196#835—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835C2×D311yescharacteristic
203#835C2×D311yescharacteristic
204#832—31no—
205#832—31no—
206#832—61no—
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic
209#817—31no—
210#816—31no—
211#816—31no—
212#815—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215C8×Dic3—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#808—31no—
220#808—31no—
221#808—31no—
222#808—31no—
223#808—31no—
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—
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—21no—
244#634#4112yes—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—42no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×Dic6—22no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—81no—
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—31no—
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—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×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—21no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6#6711yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C2×C3×C8—31no—
301C2×C3×C8—31no—
302C3×C4⋊C4—31no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—61no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C22⋊C4—21no—
314C3×C22⋊C4—21no—
315C3×C22⋊C4—21no—
316C3×C22⋊C4—21no—
317C3×C22⋊C4—41no—
318C3×C22⋊C4—41no—
319C3×C22⋊C4—61no—
320C3×C22⋊C4—61no—
321C3×C22⋊C4—61no—
322C3×C42—21no—
323C3×C42—31no—
324C3×C42—31no—
325C3×C42—61no—
326C3×C42—61no—
327C3×C42C22×D311yescharacteristic
328C3×C42C22×D311yescharacteristic
329#217—21no—
330#217—21no—
331#217—21no—
332#216—62no—
333#216—62no—
334#216—62no—
335#216—122no—
336#214—62no—
337#214—62no—
338#214—122no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3#6711yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349C4⋊Dic3C22×D311yescharacteristic
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—121no—
362Dic3⋊C4#6711yescharacteristic
363Dic3⋊C4#6711yescharacteristic
364C4×Dic3—21no—
365C4×Dic3—21no—
366C4×Dic3—61no—
367C4×Dic3—61no—
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
383Dic12—62no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32C22×D411yescharacteristic
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—41no—
391C32×C4C2×#4111yescharacteristic
392C32×C42−1+411yescharacteristic
393C3⋊Dic3—22no—
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—91no—
404C2×Q16—91no—
405C2×SD16—91no—
406C4⋊Q8—31no—
407C4⋊Q8—31no—
408C4⋊Q8—91no—
409C4⋊Q8—91no—
410C4⋊Q8—181no—
411C4⋊Q8—181no—
412C4⋊Q8—181no—
413#126—61no—
414#126—61no—
415#124—31no—
416#124D3211yescharacteristic
417C22⋊Q8—61no—
418C4×Q8—31no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—181no—
425C4×D4—31no—
426#117—61no—
427#106—91no—
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—31no—
441#102—31no—
442#102—91no—
443#97—31no—
444#97—91no—
445C4×C8—91no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—41no—
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—21no—
452C3×Q8—21no—
453C3×Q8—41no—
454C3×Q8—41no—
455C3×Q8—62no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—241no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—21no—
463C3×D4—41no—
464C3×D4—41no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—41no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—122no—
480C2×C3×C4D3×D411yescharacteristic
481C2×C3×C4D3×D411yescharacteristic
482C2×C3×C4C2×#6711yescharacteristic
483C2×C3×C4C2×#6711yescharacteristic
484C2×C3×C4C23×D311yescharacteristic
485C2×C3×C4C23×D311yescharacteristic
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—42no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—121no—
496C2×Dic3—121no—
497C2×Dic3C2×#6711yescharacteristic
498C2×Dic3C2×#6711yescharacteristic
499C2×Dic3C2×#6711yescharacteristic
500C2×Dic3C2×#6711yescharacteristic
501Dic6—22no—
502Dic6—21no—
503Dic6—21no—
504Dic6—32no—
505Dic6—32no—
506Dic6—62no—
507Dic6—61no—
508Dic6—61no—
509Dic6—81no—
510Dic6—121no—
511Dic6—241no—
512Dic6—241no—
513Dic6—241no—
514Dic6—241no—
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—81no—
526C2×C32#54811yescharacteristic
527C2×C32C2×#13711yescharacteristic
528C2×C32#57711yescharacteristic
529C2×Q8—31no—
530C2×Q8—31no—
531C2×Q8—61no—
532C2×Q8—91no—
533C2×Q8—181no—
534C2×Q8—181no—
535C2×Q8C2×D3211yescharacteristic
536C2×D4C2×D3211yescharacteristic
537C22×C4—61no—
538Q16—182no—
539Q16—182no—
540SD16—182no—
541C2×C8—31no—
542C2×C8—31no—
543C2×C8—91no—
544C2×C8—91no—
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—91no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—61no—
565C22⋊C4—61no—
566C22⋊C4—61no—
567C42—31no—
568C42—31no—
569C42—61no—
570C42—61no—
571C42—181no—
572C42—181no—
573C42—181no—
574C42C2×D3211yescharacteristic
575C22×C3—21no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C22×#6711yescharacteristic
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—32no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—81no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4—121no—
606C3×C4D3×#4111yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4#101011yescharacteristic
609C3×C4#101011yescharacteristic
610Dic3—21no—
611Dic3—21no—
612Dic3—21no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—41no—
617Dic3—62no—
618Dic3—62no—
619Dic3—122no—
620Dic3—121no—
621Dic3—121no—
622Dic3—241no—
623Dic3#95112yes—
624C32#336911yescharacteristic, complemented, Sylow
625C23—21no—
626Q8—21no—
627Q8—21no—
628Q8—62no—
629Q8—61no—
630Q8—61no—
631Q8—92no—
632Q8—181no—
633Q8—241no—
634Q8—721no—
635Q8—721no—
636D4—21no—
637D4—21no—
638C2×C4—21no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—122no—
648C2×C4—181no—
649C2×C4—181no—
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—81no—
661C2×C3—81no—
662C2×C3—161no—
663C2×C3#567711yescharacteristic
664C2×C3#577511yescharacteristic
665C2×C3D3×#13711yescharacteristic
666C2×C3C2×#95111yescharacteristic
667C2×C3#583111yescharacteristic
668C2×C3#583711yescharacteristic
669C22—41no—
670C22—41no—
671C22—41no—
672C22C2×D3×#6711yescharacteristic
673C4—21no—
674C4—21no—
675C4—32no—
676C4—41no—
677C4—61no—
678C4—61no—
679C4—61no—
680C4—121no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—182no—
685C4—361no—
686C4#6430911yescharacteristic
687C4#6431211yescharacteristic
688C3—21no—
689C3#8167111yescharacteristic, complemented
690C3#8367711yescharacteristic, complemented
691C2—81no—
692C2#1059523711yescharacteristic
693C2#1059545511yescharacteristic
694C2D3×#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. #10593856C2semidirect
5. #10591623C2semidirect
6. #10591575C2semidirect
7. #10591544C2semidirect
8. #10591541C2semidirect
13. #10590383C2semidirect
14. #10590285C2semidirect
15. #10590251C2semidirect
624. C32#3369semidirect
689. C3#81671semidirect
690. C3#83677semidirect

Maximal subgroups

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

subgroupindex
C3×#56712
#105938562
#105927532
C3×#50552
#105916232
#105915752
#105915442
#105915412
#105914882
#105914412
#105914082
#105914012
#105903832
#105902852
#105902512
#836773
#816713