Finite Group Databasebeta

← #11884501

Subgroups — #11884501

Order 1152.

1096 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594919C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C2×#63807C211yesmaximal, characteristic, complemented
5#10592432C211yesmaximal, characteristic, complemented
6C3×#4732C211yesmaximal, characteristic, complemented
7C3×#4728C211yesmaximal, characteristic, complemented
8#10591176C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590962C211yesmaximal, characteristic, complemented
11#10590883C211yesmaximal, characteristic, complemented
12#10590861C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590753C211yesmaximal, characteristic, complemented
15#10590747C211yesmaximal, characteristic, complemented
16#80013—31nomaximal
17#79497—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22#64133C2211yescharacteristic
23C2×#3746C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic, complemented
25C3×#930C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C2×C3×D24C2211yescharacteristic
29C2×C3×D24C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic, complemented
31#63979—21no—
32#63976—21no—
33#63971—21no—
34D3×#217—21no—
35#63912—21no—
36#63911C2211yescharacteristic, complemented
37#63909C2211yescharacteristic, complemented
38#63908C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63885—21no—
41#63884—21no—
42#63881—21no—
43#63860C2211yescharacteristic
44#63844C2211yescharacteristic, complemented
45#63830—24no—
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63807—24no—
52C32×C22⋊C8C2211yescharacteristic
53#63648C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#5806—31no—
64C2×#932—31no—
65C2×#912—31no—
66C2×#908—31no—
67C2×#904—31no—
68#5599—31no—
69#5553—31no—
70#5550—31no—
71C3×#447—31no—
72C3×#435—31no—
73#5158—31no—
74#5154—31no—
75#5150—31no—
76#5134—31no—
77#5115—31no—
78#5042—31no—
79#4845—31no—
80#4843—31no—
81#4781—31no—
82#4775—31no—
83#4767—31no—
84#4757—31no—
85#4734—31no—
86#4734—31no—
87#4733—31no—
88#4733—31no—
89#4733—61no—
90#4732D311yescharacteristic, complemented
91#4728D311yescharacteristic, complemented
92#4712—31no—
93#4710—31no—
94C23×C3×D3—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97#3828—22no—
98#3828—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×#634C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C2×C3×D12—22no—
106C2×C3×D12—21no—
107C2×C3×D12—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×#625—21no—
117C2×#625—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120C2×D3×Dic3—21no—
121#3795—22no—
122#3795—22no—
123#3795—41no—
124#3795—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127#3757—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130#3746—22no—
131#3744—41no—
132C3×#217D411yescharacteristic
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C3×#208—22no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×D24—41no—
143C3×D3×C8—22no—
144#3724—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3716—22no—
152#3716—22no—
153#3716D414yescomplemented
154#3714—22no—
155#3714—22no—
156#3268—91noSylow
157C22×C3×D4—31no—
158C2×#237—31no—
159C2×#237—31no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—31no—
164C2×#235—61no—
165C22×D12C2×D311yescharacteristic
166C2×C3×D8—31no—
167C2×C3×D8—31no—
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×#121—31no—
171C3×C4×D4—31no—
172#953—61no—
173C2×#217—61no—
174#940—31no—
175#940—61no—
176#940—61no—
177#939—61no—
178#939—61no—
179#938—31no—
180#937—61no—
181#936—31no—
182#935—61no—
183D4×Dic3—31no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—31no—
187#932—64no—
188C2×#213—31no—
189C2×#213—31no—
190#930—31no—
191#930—31no—
192#930C2×D311yescharacteristic
193C4×#67C2×D311yescharacteristic
194#924—31no—
195#924—31no—
196#924—61no—
197C2×#208C2×D311yescharacteristic
198#912—64no—
199#908—64no—
200C2×Dic12—31no—
201C2×Dic12—31no—
202C2×Dic12—61no—
203#904—64no—
204C2×D24—31no—
205C2×D24—31no—
206C2×D24C2×D311yescharacteristic
207C2×D24C2×D311yescharacteristic
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—31no—
212C2×#204—31no—
213C2×#204—61no—
214C2×D3×C8C2×D311yescharacteristic, complemented
215#895—31no—
216#894—61no—
217#893—61no—
218#887—31no—
219#884—61no—
220#884—61no—
221#884—61no—
222#884—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226#874—31no—
227C4×D12—31no—
228C4×Dic6—31no—
229C3×C4⋊C8—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×C22⋊C8—21no—
233C3×C22⋊C8—31no—
234C3×C22⋊C8C2×D311yescharacteristic
235C3×C22⋊C8C2×D311yescharacteristic
236C3×#97—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242#821C2×D311yescharacteristic
243#821C2×D311yescharacteristic
244(C2×D3)⋊C8C2×D311yescharacteristic, complemented
245#818—31no—
246#816—31no—
247#816—31no—
248#816—31no—
249#816—61no—
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#810—31no—
253#807—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—42no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4×C3⋊D3—42no—
274#634—21no—
275#634—21no—
276#634—21no—
277#634C2×D412yes—
278C3×#67—41no—
279C3×#67—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—42no—
290C3×D12C2×D412yes—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293#626—42no—
294#626—81no—
295#626—81no—
296#625—42no—
297#625—42no—
298#625—81no—
299D3×Dic3—42no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C32×C8—21no—
303C32×C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—31no—
319#440—91no—
320#435—31no—
321C24×C3—61no—
322C23×D3—21no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—121no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—21no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—121no—
348C2×#67D1211yescharacteristic
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352#237—62no—
353#237—62no—
354#237—121no—
355#237—121no—
356#235—62no—
357#235—62no—
358#235—62no—
359#235—62no—
360#235—122no—
361#235—121no—
362#235—121no—
363#235—121no—
364#235—121no—
365#235—122no—
366C2×D12—22no—
367C2×D12—21no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—41no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—121no—
384C2×C4×D3C22×D311yescharacteristic
385C2×Dic6—31no—
386C2×Dic6—31no—
387C2×Dic6—31no—
388C2×Dic6—31no—
389C2×Dic6—61no—
390C2×Dic6—61no—
391C3×D8—62no—
392C3×D8—121no—
393C3×M16—62no—
394C2×C3×C8—21no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—62no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C3×C4⋊C4—31no—
404C3×C4⋊C4—31no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—61no—
408C3×C42—31no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—61no—
415#217—121no—
416#217D1211yescharacteristic
417#214—34no—
418#214—62no—
419#214—62no—
420#213—62no—
421#213—62no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4D1211yescharacteristic
430C4⋊Dic3—31no—
431C4⋊Dic3—31no—
432C4⋊Dic3—61no—
433C4⋊Dic3C22×D311yescharacteristic
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—121no—
439Dic3⋊C4D1211yescharacteristic
440C4×Dic3—61no—
441C4×Dic3—61no—
442C4×Dic3C22×D311yescharacteristic
443#208—22no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446Dic12—62no—
447Dic12—62no—
448Dic12—122no—
449D24—22no—
450D24—41no—
451D24—62no—
452D24—62no—
453#204—34no—
454#204—62no—
455#204—62no—
456#204—121no—
457#204—121no—
458#204—122no—
459D3×C8—22no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3×D3—22no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C32×C4—21no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—22no—
484C3⋊Dic3—41no—
485C3⋊Dic3—41no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C2×#41—91no—
491C2×#41—91no—
492C2×#41—91no—
493C22×D4—31no—
494AGL(1,ℤ/8)—184no—
495#135—184no—
496C2×Q16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—31no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—31no—
506C22×C8—31no—
507#127—91no—
508#127—181no—
509#124—91no—
510#123—181no—
511C22⋊Q8—91no—
512#121—31no—
513#121—91no—
514#121—91no—
515#121—181no—
516#121—181no—
517#121—181no—
518#120—181no—
519C4×Q8—91no—
520C4×D4—31no—
521C4×D4—91no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—91no—
525C4⋊C8—31no—
526#103—91no—
527#103—91no—
528#102—31no—
529#102—31no—
530#102—91no—
531#102—91no—
532C22⋊C8—31no—
533C22⋊C8D3211yescharacteristic
534#97—31no—
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3—241no—
543C23×C3C2×D1211yescharacteristic
544C23×C3D3×D411yescharacteristic
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—81no—
553C22×D3—121no—
554C22×D3C2×D1211yescharacteristic
555C3×D4—32no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—122no—
562C3×D4—121no—
563C3×D4—241no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4C2×D1211yescharacteristic
579C2×C3×C4D3×D411yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—41no—
583#67—81no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—124no—
592#67—241no—
593#67—241no—
594#67—241no—
595#67—241no—
596C2×Dic3—21no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—121no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—122no—
607C2×Dic3—122no—
608C2×Dic3—241no—
609C2×Dic3C2×D1211yescharacteristic
610C2×Dic3C2×D1211yescharacteristic
611C2×Dic3C2×D1211yescharacteristic
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—21no—
617D12—42no—
618D12—62no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—121no—
624D12—122no—
625D12—241no—
626D12—241no—
627D12D3×D412yes—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—122no—
631C4×D3—122no—
632C4×D3—122no—
633C4×D3—124no—
634C4×D3—122no—
635C4×D3—241no—
636Dic6—32no—
637Dic6—32no—
638Dic6—62no—
639Dic6—61no—
640Dic6—61no—
641Dic6—61no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—121no—
646Dic6—121no—
647Dic6—121no—
648C3×C8—21no—
649C3×C8—21no—
650C3×C8—21no—
651C3×C8—21no—
652C3×C8—32no—
653C3×C8—41no—
654C3×C8—41no—
655C3×C8—61no—
656C3⋊C8—21no—
657C3⋊C8D3×D412yes—
658C2×C32—41no—
659C2×C32D4211yescharacteristic
660C2×C32#57511yescharacteristic
661C2×C32#57611yescharacteristic
662C3⋊D3—81no—
663C3×D3—41no—
664C3×D3—42no—
665C3×D3—81no—
666C3×D3—81no—
667C24—61no—
668#41—182no—
669#41—182no—
670#41—182no—
671#41—361no—
672#41—361no—
673#41—361no—
674C2×Q8—91no—
675C2×Q8—91no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—62no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—91no—
684C2×D4—121no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C22×C4—31no—
693C22×C4—181no—
694C22×C4—181no—
695C22×C4—181no—
696C22×C4—181no—
697C22×C4C2×D3211yescharacteristic
698Q16—182no—
699SD16—94no—
700SD16—182no—
701SD16—182no—
702SD16—361no—
703D8—62no—
704D8—121no—
705D8—182no—
706D8—182no—
707M16—62no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8C2×D3211yescharacteristic
712C2×C8C2×D3211yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—91no—
716C4⋊C4—181no—
717C4⋊C4—181no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C42—31no—
728C42—181no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—62no—
742C22×C3—61no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—244no—
752C22×C3C22×D1211yescharacteristic
753C22×C3C2×D3×D411yescharacteristic
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—22no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—84no—
767C2×D3—122no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—241no—
775C2×D3—241no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—41no—
781C3×C4—61no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—121no—
785C3×C4C2×D3×D411yescharacteristic
786C3×C4C2×D3×D411yescharacteristic
787C3×C4#100411yescharacteristic
788C3×C4#100911yescharacteristic
789Dic3—21no—
790Dic3—21no—
791Dic3—21no—
792Dic3—41no—
793Dic3—62no—
794Dic3—62no—
795Dic3—122no—
796Dic3—121no—
797Dic3—121no—
798Dic3—121no—
799Dic3—121no—
800Dic3—241no—
801Dic3—241no—
802C32#326811yescharacteristic, complemented, Sylow
803C23—31no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—122no—
808C23—122no—
809C23—181no—
810C23—241no—
811C23D3×D1211yescharacteristic
812Q8—92no—
813Q8—181no—
814Q8—181no—
815Q8—181no—
816D4—32no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—61no—
821D4—61no—
822D4—122no—
823D4—121no—
824D4—181no—
825D4—181no—
826D4—241no—
827D4—362no—
828D4—362no—
829D4—362no—
830D4—362no—
831D4—721no—
832D4—721no—
833D4—721no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—31no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—181no—
843C2×C4—181no—
844C2×C4—181no—
845C2×C4—362no—
846C2×C4—362no—
847C2×C4—362no—
848C2×C4—721no—
849C2×C4D3×D1211yescharacteristic
850C2×C4C22×D3211yescharacteristic
851C8—21no—
852C8—21no—
853C8—32no—
854C8—61no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—41no—
859C2×C3—41no—
860C2×C3—81no—
861C2×C3—122no—
862C2×C3—121no—
863C2×C3—241no—
864C2×C3—241no—
865C2×C3D4×D1211yescharacteristic
866C2×C3#559011yescharacteristic
867C2×C3#574811yescharacteristic
868C2×C3#575211yescharacteristic
869C2×C3#575711yescharacteristic
870C2×C3#577311yescharacteristic
871D3—41no—
872D3—42no—
873D3—81no—
874D3—81no—
875D3—242no—
876D3—241no—
877D3—241no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—62no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—244no—
894C22—361no—
895C22—361no—
896C22—361no—
897C22C2×D3×D1211yescharacteristic
898C4—21no—
899C4—61no—
900C4—61no—
901C4—61no—
902C4—121no—
903C4—182no—
904C4—361no—
905C4—361no—
906C4D32×D411yescharacteristic
907C4#6431411yescharacteristic
908C3—21no—
909C3#7949711yescharacteristic, complemented
910C3#8001311yescharacteristic, complemented
911C2—41no—
912C2—121no—
913C2—122no—
914C2—241no—
915C2—241no—
916C2—721no—
917C2#1059427711yescharacteristic
918C2#1059467811yescharacteristic
919C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594919C2semidirect
2. #10594886C2semidirect
3. C2×#63830C2semidirect
4. C2×#63807C2semidirect
5. #10592432C2semidirect
6. C3×#4732C2semidirect
7. C3×#4728C2semidirect
8. #10591176C2semidirect
9. #10590968C2semidirect
10. #10590962C2semidirect
11. #10590883C2semidirect
12. #10590861C2semidirect
13. #10590826C2semidirect
14. #10590753C2semidirect
15. #10590747C2semidirect
21. C2×#3795C22semidirect
23. C2×#3746C22semidirect
24. C2×#3744C22semidirect
30. C2×C3×D3×C8C22semidirect
36. #63911C22semidirect
37. #63909C22semidirect
44. #63844C22semidirect
48. C2×#3716C22semidirect
53. #63648C22semidirect
54. #63643C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63567C22semidirect
62. #63563C22semidirect
90. #4732D3semidirect
91. #4728D3semidirect
153. #3716D4semidirect
214. C2×D3×C8C2×D3semidirect
244. (C2×D3)⋊C8C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
802. C32#3268semidirect
909. C3#79497semidirect
910. C3#80013semidirect

Maximal subgroups

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

subgroupindex
#105949192
#105948862
C2×#638302
C2×#638072
#105924322
C3×#47322
C3×#47282
#105911762
#105909682
#105909622
#105908832
#105908612
#105908262
#105907532
#105907472
#800133
#794973