Finite Group Databasebeta

← #11885740

Subgroups — #11885740

Order 1152.

1310 conjugacy classes of subgroups.

The subgroup lattice has 1005 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2#10595288C211yesmaximal, characteristic, complemented
3D4×#625C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5#10592849C211yesmaximal, characteristic, complemented
6C3×#5156C211yesmaximal, characteristic, complemented
7#10591498C211yesmaximal, characteristic, complemented
8#10591484C211yesmaximal, characteristic, complemented
9#10591448C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11#10591435C211yesmaximal, characteristic, complemented
12#10590944C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590749C211yesmaximal, characteristic, complemented
15#10590717C211yesmaximal, characteristic, complemented
16D8×#67—31nomaximal
17#80024—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C2×D3×#67—21no—
22C22×#625—21no—
23C2×D3×D12C2211yescharacteristic, complemented
24C2×C32×D8C2211yescharacteristic, complemented
25#64149C2211yescharacteristic, complemented
26D4×C3⋊Dic3C2211yescharacteristic, complemented
27C2×#3753C2211yescharacteristic, complemented
28C3×#938C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C3×D3×D8—24no—
33C2×C3×D24C2211yescharacteristic, complemented
34C2×C3×D3×C8C2211yescharacteristic, complemented
35#63983—21no—
36#63980—21no—
37#63977—21no—
38#63976—21no—
39#63976—21no—
40#63971—21no—
41D3×#213—24no—
42#63914C2211yescharacteristic, complemented
43#63909C2211yescharacteristic, complemented
44#63908C2211yescharacteristic, complemented
45#63908C2211yescharacteristic, complemented
46C4×#625C2211yescharacteristic
47#63898C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63553C2211yescharacteristic, complemented
63C22×C3×D8—31no—
64D4×#67—31no—
65D4×#67—31no—
66D4×#67—31no—
67C22×#213—31no—
68C2×D3×D8—31no—
69C2×D3×D8D311yescharacteristic, complemented
70#5609—31no—
71C3×#447—31no—
72#5217—31no—
73#5217—31no—
74#5157—31no—
75#5156—31no—
76#5156—31no—
77#5156D311yescharacteristic, complemented
78#5151—31no—
79#5151—31no—
80#5150—31no—
81#5150—31no—
82#5150—31no—
83#5150—61no—
84Dic3×D8—31no—
85#5115—31no—
86C8×#67—31no—
87#5038—31no—
88#4786—31no—
89#4775—31no—
90#4773—31no—
91#4756—31no—
92#4732—31no—
93#67⋊C8—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101C2×#638—21no—
102C22×C3⋊Dic3—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C3×D3×D4—22no—
109C3×D3×D4—22no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C3×D3×D4—41no—
113C3×D3×D4—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119D3×#67—44no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#625—21no—
123C2×#625—21no—
124C2×#625—21no—
125C2×#625—21no—
126C2×#625—44no—
127C2×#625D411yescharacteristic
128C2×D3×Dic3—21no—
129D3×D12—22no—
130D3×D12—41no—
131C32×D8—22no—
132C2×C32×C8C2311yescharacteristic
133#3757—21no—
134#3753—22no—
135C4⋊(C3⋊Dic3)C2311yescharacteristic
136C4×C3⋊Dic3C2311yescharacteristic
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C3×#217—21no—
139C3×#213—22no—
140C3×#213—41no—
141C3×#213D414yescomplemented
142C3×C4⋊Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×D24—22no—
146C3×D3×C8—22no—
147#3724D411yescharacteristic
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153(C2×D3)⋊Dic3D411yescharacteristic
154#3714—22no—
155#3714—41no—
156#3713—22no—
157D3×C3⋊C8—22no—
158D4×D8—91noSylow
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×#67—61no—
163C22×#67—61no—
164C22×#67—61no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×D3×D4C2×D311yescharacteristic, complemented
168C2×D3×D4C2×D311yescharacteristic, complemented
169C2×D3×D4C2×D311yescharacteristic, complemented
170C22×D12—31no—
171C2×C3×D8—21no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8—64no—
177C2×C3×D8C2×D311yescharacteristic, complemented
178C2×C3×D8C2×D311yescharacteristic, complemented
179C22×C3×C8—31no—
180C3×#121—31no—
181#953—61no—
182#953—61no—
183#953—61no—
184#940—31no—
185#940—31no—
186#940—31no—
187#940—31no—
188#940—61no—
189#939—61no—
190#939—61no—
191#939—61no—
192#938—31no—
193#938—31no—
194#938C2×D311yescharacteristic, complemented
195#937—61no—
196#937—61no—
197#937—61no—
198#937—61no—
199D4×Dic3—31no—
200D4×Dic3—31no—
201D4×Dic3—31no—
202D4×Dic3—61no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—31no—
209C2×#213—61no—
210C2×#213—64no—
211C2×#213C2×D311yescharacteristic
212C2×#213C2×D311yescharacteristic, complemented
213C2×#213C2×D311yescharacteristic, complemented
214#930—31no—
215#930—31no—
216#930—31no—
217C4×#67—31no—
218C4×#67—31no—
219C22×C3⋊C8—31no—
220D3×D8—24no—
221D3×D8—64no—
222C2×D24—31no—
223C2×D24—31no—
224C2×D24C2×D311yescharacteristic, complemented
225C2×D3×C8—31no—
226C2×D3×C8C2×D311yescharacteristic, complemented
227#895—31no—
228#893—31no—
229#884—61no—
230#882—61no—
231C3×#102—31no—
232C3×#102—31no—
233C3×C22⋊C8—31no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#832C2×D311yescharacteristic, complemented
240#830—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244#821—61no—
245#821C2×D311yescharacteristic, complemented
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8C2×D311yescharacteristic, complemented
248#818—31no—
249Dic3⋊C8—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—61no—
252C8×Dic3—31no—
253C8×Dic3—31no—
254#809—31no—
255#807—31no—
256C23×C32—21no—
257C23×C32—21no—
258C22×C3⋊D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—42no—
266C22×C3×D3—42no—
267C22×C3×D3—42no—
268C22×C3×D3—81no—
269C22×C3×D3—81no—
270C22×C3×D3—81no—
271C22×C3×D3C2×D411yescharacteristic
272C22×C3×D3C2×D411yescharacteristic
273C2×D32—42no—
274C2×D32—42no—
275C2×D32—81no—
276C32×D4—21no—
277C32×D4—21no—
278C32×D4—21no—
279C32×D4C2×D412yescomplemented
280C2×C32×C4C2411yescharacteristic
281#638—42no—
282#638—81no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—42no—
285C2×C3⋊Dic3C2×D411yescharacteristic
286C2×C3⋊Dic3C2×D411yescharacteristic
287C4⋊(C3⋊D3)—21no—
288C4⋊(C3⋊D3)—21no—
289C3×#67—42no—
290C3×#67—42no—
291C3×#67—42no—
292C3×#67—42no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3C2×D411yescharacteristic
295C2×C3×Dic3C2×D411yescharacteristic
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—21no—
301C3×D12C2×D412yescomplemented
302C3×C4×D3—21no—
303C3×C4×D3—21no—
304C3×C4×D3—21no—
305C3×C4×D3—21no—
306#626—42no—
307#626—42no—
308#625—42no—
309#625—42no—
310#625—42no—
311#625—81no—
312#625D814yescomplemented
313D3×Dic3—42no—
314C32×C8—21no—
315C3⋊(C3⋊C8)—21no—
316C3×C3⋊C8—21no—
317C3×C3⋊C8C2×D412yescomplemented
318C22×D8—31no—
319C22×D8—91no—
320D42—91no—
321D42—91no—
322#493—91no—
323#466—91no—
324#466—91no—
325#459—91no—
326#459—91no—
327#447—31no—
328#447—91no—
329#447—91no—
330#447—91no—
331C4×D8—91no—
332C8×D4—91no—
333C24×C3—61no—
334C24×C3—61no—
335C24×C3—61no—
336C23×D3—21no—
337C23×D3—21no—
338C23×D3—21no—
339C23×D3—61no—
340C23×D3—61no—
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C2×C3×D4—61no—
353C2×C3×D4—121no—
354C2×C3×D4—121no—
355C2×C3×D4—121no—
356C2×C3×D4C22×D311yescharacteristic
357C2×C3×D4C22×D311yescharacteristic
358C2×C3×D4C22×D311yescharacteristic
359C2×C3×D4C22×D311yescharacteristic
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—21no—
366C2×#67—31no—
367C2×#67—31no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—121no—
383C2×#67—121no—
384C2×#67—124no—
385C2×#67—124no—
386C2×#67—124no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—121no—
391D3×D4—22no—
392D3×D4—22no—
393D3×D4—22no—
394D3×D4—41no—
395D3×D4—41no—
396D3×D4—41no—
397D3×D4—62no—
398D3×D4—121no—
399D3×D4—124no—
400C2×D12—31no—
401C2×D12—31no—
402C2×D12—61no—
403C2×D12—62no—
404C2×D12—61no—
405C2×D12—61no—
406C2×D12—121no—
407C2×D12C22×D311yescharacteristic
408C2×D12C22×D311yescharacteristic
409C2×D12C22×D311yescharacteristic
410C2×C4×D3—61no—
411C2×C4×D3C22×D311yescharacteristic
412C2×C4×D3C22×D311yescharacteristic
413C3×D8—22no—
414C3×D8—22no—
415C3×D8—34no—
416C3×D8—42no—
417C3×D8—62no—
418C3×D8—62no—
419C3×D8—121no—
420C2×C3×C8—21no—
421C2×C3×C8—31no—
422C2×C3×C8—31no—
423C2×C3×C8—62no—
424C2×C3×C8C22×D311yescharacteristic
425C2×C3×C8C22×D311yescharacteristic
426C3×C4⋊C4—31no—
427C3×C22⋊C4—61no—
428#217—21no—
429#217—31no—
430#217—31no—
431#217—61no—
432#217—61no—
433#217—61no—
434#217—61no—
435#217—61no—
436#217—121no—
437#213—22no—
438#213—41no—
439#213—62no—
440#213—62no—
441#213—62no—
442#213—62no—
443#213—62no—
444#213—122no—
445#213—121no—
446#213#6714yescomplemented
447(C2×D3)⋊C4—31no—
448(C2×D3)⋊C4—31no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454C4⋊Dic3—31no—
455C4⋊Dic3—31no—
456C4⋊Dic3—61no—
457C4⋊Dic3C22×D311yescharacteristic
458Dic3⋊C4—31no—
459Dic3⋊C4—31no—
460C4×Dic3—31no—
461C4×Dic3—31no—
462C4×Dic3—61no—
463C2×C3⋊C8—31no—
464C2×C3⋊C8—31no—
465C2×C3⋊C8—61no—
466C2×C3⋊C8—62no—
467C2×C3⋊C8C22×D311yescharacteristic
468C2×C3⋊C8C22×D311yescharacteristic
469D24—22no—
470D24—62no—
471D24—121no—
472D3×C8—22no—
473D3×C8—62no—
474C22×C32—22no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32C22×D411yescharacteristic
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3—22no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—84no—
498C2×C3×D3—84no—
499C2×C3×D3—84no—
500C2×C3×D3C2×D812yescomplemented
501C2×C3×D3C2×D812yescomplemented
502D32—84no—
503C32×C4C22×D411yescharacteristic
504C32×C4H(5,𝔽2)11yescharacteristic
505C3⋊Dic3—21no—
506C3⋊Dic3—41no—
507C3⋊Dic3C2×D812yescomplemented
508C3×Dic3—21no—
509C3×Dic3—21no—
510C3×Dic3—41no—
511C22×D4—31no—
512C22×D4—31no—
513C22×D4—31no—
514C22×D4—91no—
515C22×D4—181no—
516C22×D4—181no—
517C2×D8—31no—
518C2×D8—31no—
519C2×D8—31no—
520C2×D8—31no—
521C2×D8—64no—
522C2×D8—91no—
523C2×D8—91no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—184no—
527C2×D8D3211yescharacteristic, complemented
528C22×C8—31no—
529C22×C8—91no—
530#127—91no—
531#127—91no—
532#121—31no—
533#121—91no—
534#121—91no—
535#121—91no—
536#121—181no—
537#121—181no—
538#120—181no—
539#120—181no—
540#120—181no—
541#120—181no—
542C4×D4—91no—
543C4×D4—91no—
544C4×D4—91no—
545#107—91no—
546C4⋊C8—91no—
547#102—31no—
548#102—31no—
549#102—91no—
550#102—91no—
551#102—91no—
552#102—91no—
553C22⋊C8—31no—
554C22⋊C8—91no—
555C4×C8—91no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—31no—
561C23×C3—31no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—122no—
568C23×C3—122no—
569C23×C3—122no—
570C23×C3—122no—
571C23×C3—122no—
572C23×C3—122no—
573C23×C3—241no—
574C23×C3—241no—
575C23×C3—241no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—42no—
580C22×D3—42no—
581C22×D3—42no—
582C22×D3—42no—
583C22×D3—42no—
584C22×D3—42no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—81no—
588C22×D3—81no—
589C22×D3—81no—
590C22×D3—121no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—122no—
595C22×D3—241no—
596C22×D3—241no—
597C22×D3D3×D411yescharacteristic
598C22×D3D3×D411yescharacteristic
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—21no—
602C3×D4—21no—
603C3×D4—21no—
604C3×D4—21no—
605C3×D4—22no—
606C3×D4—32no—
607C3×D4—41no—
608C3×D4—41no—
609C3×D4—41no—
610C3×D4—61no—
611C3×D4—61no—
612C3×D4—61no—
613C3×D4—61no—
614C3×D4—61no—
615C3×D4—122no—
616C3×D4—122no—
617C3×D4—122no—
618C3×D4—122no—
619C3×D4D3×D412yescomplemented
620C3×D4C2×#6712yescomplemented
621C2×C3×C4—21no—
622C2×C3×C4—31no—
623C2×C3×C4—31no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4C23×D311yescharacteristic
630C2×C3×C4C23×D311yescharacteristic
631#67—34no—
632#67—34no—
633#67—42no—
634#67—42no—
635#67—42no—
636#67—42no—
637#67—122no—
638#67—122no—
639#67—122no—
640#67—122no—
641#67—122no—
642#67—122no—
643#67—122no—
644#67—122no—
645#67—122no—
646#67—122no—
647#67—242no—
648#67—241no—
649#67—241no—
650#67—241no—
651#67—241no—
652#67—242no—
653C2×Dic3—21no—
654C2×Dic3—31no—
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—31no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—121no—
663C2×Dic3—122no—
664C2×Dic3—122no—
665C2×Dic3—122no—
666C2×Dic3—242no—
667C2×Dic3D3×D411yescharacteristic
668C2×Dic3D3×D411yescharacteristic
669D12—21no—
670D12—21no—
671D12—21no—
672D12—21no—
673D12—21no—
674D12—61no—
675D12—61no—
676D12—61no—
677D12—61no—
678D12—121no—
679D12—121no—
680D12—122no—
681D12—122no—
682D12C2×#6712yescomplemented
683C4×D3—21no—
684C4×D3—21no—
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—122no—
688C3×C8—21no—
689C3×C8—21no—
690C3×C8—32no—
691C3×C8—41no—
692C3×C8—61no—
693C3⋊C8—21no—
694C3⋊C8—61no—
695C3⋊C8—61no—
696C3⋊C8—121no—
697C3⋊C8C2×#6712yescomplemented
698C2×C32—42no—
699C2×C32—81no—
700C2×C32D4211yescharacteristic
701C2×C32C22×D811yescharacteristic
702C2×C32#57611yescharacteristic
703C3⋊D3—81no—
704C3×D3—22no—
705C3×D3—22no—
706C3×D3—42no—
707C3×D3—81no—
708C3×D3—81no—
709C24—61no—
710C24—61no—
711C24—61no—
712C24—181no—
713C2×D4—31no—
714C2×D4—31no—
715C2×D4—31no—
716C2×D4—61no—
717C2×D4—61no—
718C2×D4—61no—
719C2×D4—62no—
720C2×D4—62no—
721C2×D4—62no—
722C2×D4—61no—
723C2×D4—91no—
724C2×D4—91no—
725C2×D4—121no—
726C2×D4—121no—
727C2×D4—121no—
728C2×D4—181no—
729C2×D4—182no—
730C2×D4—181no—
731C2×D4—181no—
732C2×D4—181no—
733C2×D4—181no—
734C2×D4—181no—
735C2×D4—181no—
736C2×D4—181no—
737C2×D4—361no—
738C2×D4—364no—
739C2×D4—364no—
740C2×D4C2×D3211yescharacteristic
741C2×D4C2×D3211yescharacteristic
742C22×C4—31no—
743C22×C4—31no—
744C22×C4—181no—
745C22×C4—181no—
746D8—22no—
747D8—34no—
748D8—62no—
749D8—62no—
750D8—121no—
751D8—182no—
752D8—182no—
753D8—182no—
754D8—361no—
755C2×C8—31no—
756C2×C8—31no—
757C2×C8—62no—
758C2×C8—91no—
759C2×C8—182no—
760C2×C8C2×D3211yescharacteristic
761C4⋊C4—31no—
762C4⋊C4—91no—
763C4⋊C4—91no—
764C22⋊C4—61no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4—181no—
768C22⋊C4—181no—
769C22⋊C4—181no—
770C22⋊C4—181no—
771C22⋊C4—181no—
772C42—91no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—21no—
776C22×C3—32no—
777C22×C3—32no—
778C22×C3—42no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—61no—
790C22×C3—61no—
791C22×C3—61no—
792C22×C3—61no—
793C22×C3—62no—
794C22×C3—81no—
795C22×C3—81no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—121no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—244no—
808C22×C3—244no—
809C22×C3—244no—
810C22×C3C2×D3×D411yescharacteristic
811C22×C3C2×D3×D411yescharacteristic
812C2×D3—21no—
813C2×D3—21no—
814C2×D3—21no—
815C2×D3—21no—
816C2×D3—22no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—41no—
824C2×D3—41no—
825C2×D3—84no—
826C2×D3—84no—
827C2×D3—84no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—241no—
835C2×D3—241no—
836C2×D3—241no—
837C2×D3—244no—
838C2×D3—244no—
839C2×D3D3×D812yescomplemented
840C2×D3D3×D812yescomplemented
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—61no—
844C3×C4—61no—
845C3×C4—121no—
846C3×C4C2×D3×D411yescharacteristic
847C3×C4#100411yescharacteristic
848C3×C4#100411yescharacteristic
849C3×C4C22×#6711yescharacteristic
850Dic3—21no—
851Dic3—21no—
852Dic3—32no—
853Dic3—32no—
854Dic3—41no—
855Dic3—62no—
856Dic3—61no—
857Dic3—61no—
858Dic3—121no—
859Dic3—121no—
860Dic3—121no—
861Dic3—241no—
862C32D4×D811yescharacteristic, complemented, Sylow
863C23—21no—
864C23—21no—
865C23—31no—
866C23—31no—
867C23—61no—
868C23—61no—
869C23—61no—
870C23—122no—
871C23—122no—
872C23—122no—
873C23—122no—
874C23—122no—
875C23—122no—
876C23—181no—
877C23—241no—
878C23—241no—
879C23—241no—
880C23—362no—
881C23—362no—
882C23—721no—
883D4—21no—
884D4—21no—
885D4—21no—
886D4—32no—
887D4—61no—
888D4—61no—
889D4—61no—
890D4—61no—
891D4—61no—
892D4—94no—
893D4—122no—
894D4—122no—
895D4—122no—
896D4—122no—
897D4—181no—
898D4—181no—
899D4—362no—
900D4—362no—
901D4—362no—
902D4—362no—
903D4—362no—
904D4—362no—
905D4—721no—
906D4—721no—
907D4D3×#6712yescomplemented
908C2×C4—31no—
909C2×C4—31no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—91no—
916C2×C4—91no—
917C2×C4—181no—
918C2×C4—362no—
919C2×C4—362no—
920C2×C4C22×D3211yescharacteristic
921C8—21no—
922C8—32no—
923C8—61no—
924C8—181no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—42no—
929C2×C3—42no—
930C2×C3—62no—
931C2×C3—62no—
932C2×C3—82no—
933C2×C3—81no—
934C2×C3—81no—
935C2×C3—122no—
936C2×C3—161no—
937C2×C3—241no—
938C2×C3—241no—
939C2×C3#559011yescharacteristic
940C2×C3C2×D3×D811yescharacteristic
941C2×C3C2×D3×D811yescharacteristic
942C2×C3#575711yescharacteristic
943C2×C3#577411yescharacteristic
944C2×C3D4×#6711yescharacteristic
945D3—22no—
946D3—22no—
947D3—42no—
948D3—81no—
949D3—81no—
950D3—241no—
951D3—241no—
952D3—481no—
953C22—22no—
954C22—32no—
955C22—32no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—61no—
962C22—61no—
963C22—61no—
964C22—61no—
965C22—62no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—121no—
972C22—121no—
973C22—121no—
974C22—244no—
975C22—244no—
976C22—244no—
977C22—361no—
978C22—361no—
979C22—361no—
980C22—724no—
981C22D32×D411yescharacteristic
982C4—61no—
983C4—61no—
984C4—92no—
985C4—121no—
986C4—181no—
987C4—361no—
988C4#6431311yescharacteristic
989C4C2×D3×#6711yescharacteristic
990C3—21no—
991C3#8002411yescharacteristic, complemented
992C3D8×#6711yescharacteristic, complemented
993C2—42no—
994C2—62no—
995C2—62no—
996C2—81no—
997C2—122no—
998C2—241no—
999C2—241no—
1000C2—721no—
1001C2D32×D811yescharacteristic
1002C2#1059473211yescharacteristic
1003C2#1059528711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D8C2semidirect
2. #10595288C2semidirect
3. D4×#625C2semidirect
4. C2×D3×#213C2semidirect
5. #10592849C2semidirect
6. C3×#5156C2semidirect
7. #10591498C2semidirect
8. #10591484C2semidirect
9. #10591448C2semidirect
10. #10591447C2semidirect
11. #10591435C2semidirect
12. #10590944C2semidirect
13. #10590826C2semidirect
14. #10590749C2semidirect
15. #10590717C2semidirect
18. C2×C3×D3×D4C22semidirect
19. C2×C3×D3×D4C22semidirect
20. C2×C3×D3×D4C22semidirect
23. C2×D3×D12C22semidirect
24. C2×C32×D8C22semidirect
25. #64149C22semidirect
26. D4×C3⋊Dic3C22semidirect
27. C2×#3753C22semidirect
28. C3×#938C22semidirect
30. C2×C3×#213C22semidirect
31. C2×C3×#213C22semidirect
33. C2×C3×D24C22semidirect
34. C2×C3×D3×C8C22semidirect
42. #63914C22semidirect
43. #63909C22semidirect
44. #63908C22semidirect
45. #63908C22semidirect
47. #63898C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63659C22semidirect
53. #63648C22semidirect
54. #63641C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. #63575C22semidirect
59. #63563C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63553C22semidirect
69. C2×D3×D8D3semidirect
77. #5156D3semidirect
141. C3×#213D4semidirect
167. C2×D3×D4C2×D3semidirect
168. C2×D3×D4C2×D3semidirect
169. C2×D3×D4C2×D3semidirect
177. C2×C3×D8C2×D3semidirect
178. C2×C3×D8C2×D3semidirect
194. #938C2×D3semidirect
212. C2×#213C2×D3semidirect
213. C2×#213C2×D3semidirect
224. C2×D24C2×D3semidirect
226. C2×D3×C8C2×D3semidirect
239. #832C2×D3semidirect
245. #821C2×D3semidirect
247. (C2×D3)⋊C8C2×D3semidirect
279. C32×D4C2×D4semidirect
301. C3×D12C2×D4semidirect
312. #625D8semidirect
317. C3×C3⋊C8C2×D4semidirect
446. #213#67semidirect
500. C2×C3×D3C2×D8semidirect
501. C2×C3×D3C2×D8semidirect
507. C3⋊Dic3C2×D8semidirect
527. C2×D8D32semidirect
619. C3×D4D3×D4semidirect
620. C3×D4C2×#67semidirect
682. D12C2×#67semidirect
697. C3⋊C8C2×#67semidirect
839. C2×D3D3×D8semidirect
840. C2×D3D3×D8semidirect
862. C32D4×D8semidirect
907. D4D3×#67semidirect
991. C3#80024semidirect
992. C3D8×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
#105952882
D4×#6252
C2×D3×#2132
#105928492
C3×#51562
#105914982
#105914842
#105914482
#105914472
#105914352
#105909442
#105908262
#105907492
#105907172
D8×#673
#800243