Finite Group Databasebeta

← #11885738

Subgroups — #11885738

Order 1152.

1339 conjugacy classes of subgroups.

The subgroup lattice has 1015 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2#10595293C211yesmaximal, characteristic, complemented
3D4×#626C211yesmaximal, characteristic, complemented
4C2×#63926C211yesmaximal, characteristic, complemented
5#10592855C211yesmaximal, characteristic, complemented
6C3×#5150C211yesmaximal, characteristic, complemented
7#10591482C211yesmaximal, characteristic, complemented
8#10591455C211yesmaximal, characteristic, complemented
9#10591448C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11Dic3×#213C211yesmaximal, characteristic, complemented
12#10590945C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590753C211yesmaximal, characteristic, complemented
15#10590720C211yesmaximal, characteristic, complemented
16D8×#67—31nomaximal
17#80350—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C2×D3×#67—21no—
22C22×#626—21no—
23C2×#3802C2211yescharacteristic, complemented
24C2×C32×D8C2211yescharacteristic, complemented
25#64147C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic, complemented
28C3×D4×Dic3C2211yescharacteristic, 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#63981—21no—
37#63978—21no—
38#63977—21no—
39#63976—21no—
40#63970—21no—
41#63926—24no—
42#63916C2211yescharacteristic, complemented
43#63911C2211yescharacteristic, complemented
44#63909C2211yescharacteristic, complemented
45#63908C2211yescharacteristic, complemented
46C4×#626C2211yescharacteristic
47Dic3×D12C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C22×C3×D8—31no—
64D4×#67—31no—
65D4×#67—31no—
66C2×D3×D8—31no—
67C2×D3×D8—31no—
68C2×D3×D8D311yescharacteristic, complemented
69#5717—31no—
70D4×D12—31no—
71C3×#459—31no—
72#5217—31no—
73#5217—31no—
74#5157—31no—
75#5156—31no—
76#5156—31no—
77#5156—31no—
78#5156—31no—
79#5156—61no—
80#5151—31no—
81#5150—31no—
82#5150D311yescharacteristic, complemented
83Dic3×D8—31no—
84#5115—31no—
85C8×#67—31no—
86#5073—31no—
87C4×#213—31no—
88#4843—31no—
89#4834—31no—
90#4775—31no—
91#4775—31no—
92#4773—31no—
93#4773—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—
102D4×C3⋊D3—22no—
103D4×C3⋊D3—41no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3—21no—
111C3×D3×D4—22no—
112C3×D3×D4—22no—
113C3×D3×D4—41no—
114C3×D3×D4—41no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119D3×#67—44no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#626—44no—
125C2×#626D411yescharacteristic
126C2×#625—21no—
127C2×#625—21no—
128C2×D3×Dic3—21no—
129#3802—22no—
130#3802—41no—
131C32×D8—22no—
132C2×C32×C8C2311yescharacteristic
133#3757—21no—
134#3753—41no—
135C4⋊(C3⋊Dic3)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C3×#217—21no—
138C3×#213—22no—
139C3×#213—22no—
140C3×#213D414yescomplemented
141C3×C4⋊Dic3C2311yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×D24—22no—
146C3×D3×C8—22no—
147Dic3⋊Dic3D411yescharacteristic
148#3722—21no—
149#3722D411yescharacteristic
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3714—22no—
155#3714—22no—
156#3713—41no—
157#3710—22no—
158D4×D8—91noSylow
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×#67—61no—
162C22×#67—61no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—31no—
167C2×D3×D4—61no—
168C2×D3×D4—61no—
169C2×D3×D4C2×D311yescharacteristic, complemented
170C2×D3×D4C2×D311yescharacteristic, complemented
171C22×D12—61no—
172C2×C3×D8—21no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8—31no—
177C2×C3×D8—64no—
178C2×C3×D8C2×D311yescharacteristic, complemented
179C2×C3×D8C2×D311yescharacteristic, complemented
180C22×C3×C8—31no—
181C3×#127—31no—
182C3×C4×D4—31no—
183#953—61no—
184#953—61no—
185#940—31no—
186#940C2×D311yescharacteristic, complemented
187#939—61no—
188#939—61no—
189#938—31no—
190#938—31no—
191#938—31no—
192#938—31no—
193#938—61no—
194#938—61no—
195#937—61no—
196#937—61no—
197#937—61no—
198#937—61no—
199D4×Dic3—31no—
200D4×Dic3C2×D311yescharacteristic, complemented
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—61no—
208C2×#213C2×D311yescharacteristic
209C2×#213C2×D311yescharacteristic, complemented
210C2×#213C2×D311yescharacteristic, complemented
211#930—31no—
212#930—31no—
213#930—61no—
214C4×#67—31no—
215D3×D8—24no—
216D3×D8—64no—
217D3×D8—64no—
218C2×D24—31no—
219C2×D24—31no—
220C2×D24C2×D311yescharacteristic, complemented
221C2×D3×C8—31no—
222C2×D3×C8—31no—
223C2×D3×C8C2×D311yescharacteristic, complemented
224#895—31no—
225#895—31no—
226#882—61no—
227#882—61no—
228#874—31no—
229C4×D12—31no—
230C4×D12—31no—
231C3×C4⋊C8—31no—
232C3×#102—31no—
233C3×#102—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)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249(C2×D3)⋊C8—61no—
250#818—31no—
251Dic3⋊C8C2×D311yescharacteristic, complemented
252C8×Dic3—31no—
253#809—31no—
254#807—31no—
255C4×C3⋊C8—31no—
256C23×C32—21no—
257C23×C32—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—81no—
262C22×C3⋊D3C2×D411yescharacteristic
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—42no—
267C22×C3×D3—42no—
268C22×C3×D3—42no—
269C22×C3×D3—42no—
270C22×C3×D3—81no—
271C22×C3×D3—81no—
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—42no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3C2×D411yescharacteristic
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—21no—
287C4×C3⋊D3—21no—
288C4×C3⋊D3—21no—
289C3×#67—42no—
290C3×#67—42no—
291C3×#67—42no—
292C3×#67—81no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—42no—
295C2×C3×Dic3C2×D411yescharacteristic
296C2×C3×Dic3C2×D411yescharacteristic
297C2×C3×Dic3C2×D411yescharacteristic
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—21no—
301C3×D12—21no—
302C3×D12—21no—
303C3×D12C2×D412yescomplemented
304C3×C4×D3—21no—
305C3×C4×D3—21no—
306#626—42no—
307#626—42no—
308#626—42no—
309#626—81no—
310#626D814yescomplemented
311#625—42no—
312#625—42no—
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—31no—
326#459—91no—
327#447—91no—
328#447—91no—
329#447—91no—
330#447—91no—
331C4×D8—91no—
332C8×D4—91no—
333C24×C3—61no—
334C24×C3—61no—
335C23×D3—21no—
336C23×D3—21no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3—61no—
340C23×D3—61no—
341C23×D3—121no—
342C2×C3×D4—21no—
343C2×C3×D4—21no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—31no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—121no—
354C2×C3×D4—121no—
355C2×C3×D4C22×D311yescharacteristic
356C2×C3×D4C22×D311yescharacteristic
357C2×C3×D4C22×D311yescharacteristic
358C2×C3×D4C22×D311yescharacteristic
359C22×C3×C4—31no—
360C22×C3×C4—61no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—31no—
366C2×#67—61no—
367C2×#67—61no—
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—121no—
379C2×#67—121no—
380C2×#67—124no—
381C2×#67—124no—
382C22×Dic3—21no—
383C22×Dic3—61no—
384D3×D4—22no—
385D3×D4—22no—
386D3×D4—41no—
387D3×D4—41no—
388D3×D4—62no—
389D3×D4—62no—
390D3×D4—62no—
391D3×D4—62no—
392D3×D4—122no—
393D3×D4—121no—
394D3×D4—121no—
395D3×D4—121no—
396D3×D4—121no—
397D3×D4—124no—
398D3×D4—122no—
399C2×D12—31no—
400C2×D12—31no—
401C2×D12—31no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—61no—
405C2×D12—61no—
406C2×D12—61no—
407C2×D12—124no—
408C2×D12C22×D311yescharacteristic
409C2×D12C22×D311yescharacteristic
410C2×D12C22×D311yescharacteristic
411C2×C4×D3—31no—
412C2×C4×D3—31no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3C22×D311yescharacteristic
416C3×D8—22no—
417C3×D8—22no—
418C3×D8—34no—
419C3×D8—42no—
420C3×D8—62no—
421C3×D8—62no—
422C3×D8—62no—
423C2×C3×C8—21no—
424C2×C3×C8—31no—
425C2×C3×C8—31no—
426C2×C3×C8—62no—
427C2×C3×C8C22×D311yescharacteristic
428C2×C3×C8C22×D311yescharacteristic
429C3×C4⋊C4—31no—
430C3×C22⋊C4—61no—
431C3×C42—31no—
432#217—21no—
433#217—31no—
434#217—61no—
435#217—61no—
436#217—61no—
437#217—61no—
438#217—61no—
439#217—121no—
440#213—22no—
441#213—22no—
442#213—62no—
443#213—62no—
444#213—121no—
445#213—121no—
446#213—121no—
447#213—121no—
448#213—122no—
449#213#6714yescomplemented
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—31no—
452(C2×D3)⋊C4—31no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—61no—
455(C2×D3)⋊C4—61no—
456(C2×D3)⋊C4—61no—
457(C2×D3)⋊C4—61no—
458C4⋊Dic3—31no—
459C4⋊Dic3—31no—
460C4⋊Dic3—31no—
461C4⋊Dic3—61no—
462C4⋊Dic3C22×D311yescharacteristic
463Dic3⋊C4—31no—
464C4×Dic3C22×D311yescharacteristic
465C2×C3⋊C8—31no—
466C2×C3⋊C8—31no—
467C2×C3⋊C8—61no—
468C2×C3⋊C8C22×D311yescharacteristic
469C2×C3⋊C8C22×D311yescharacteristic
470D24—22no—
471D24—62no—
472D24—62no—
473D3×C8—22no—
474D3×C8—62no—
475D3×C8—62no—
476C22×C32—22no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32C22×D411yescharacteristic
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—84no—
489C2×C3⋊D3C2×D812yescomplemented
490C2×C3×D3—21no—
491C2×C3×D3—21no—
492C2×C3×D3—22no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—84no—
502C2×C3×D3—84no—
503C2×C3×D3C2×D812yescomplemented
504D32—84no—
505C32×C4C22×D411yescharacteristic
506C32×C4H(5,𝔽2)11yescharacteristic
507C3⋊Dic3—21no—
508C3⋊Dic3—41no—
509C3×Dic3—21no—
510C3×Dic3—21no—
511C3×Dic3—41no—
512C3×Dic3C2×D812yescomplemented
513C22×D4—31no—
514C22×D4—31no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—181no—
518C22×D4—181no—
519C2×D8—31no—
520C2×D8—31no—
521C2×D8—31no—
522C2×D8—31no—
523C2×D8—64no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—91no—
527C2×D8—91no—
528C2×D8—184no—
529C2×D8D3211yescharacteristic, complemented
530C22×C8—31no—
531C22×C8—91no—
532#127—31no—
533#127—91no—
534#121—91no—
535#121—91no—
536#121—91no—
537#121—91no—
538#121—181no—
539#121—181no—
540#120—181no—
541#120—181no—
542#120—181no—
543#120—181no—
544C4×D4—31no—
545C4×D4—91no—
546C4×D4—91no—
547#107—91no—
548C4⋊C8—31no—
549#102—31no—
550#102—31no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102—91no—
555C22⋊C8—91no—
556C22⋊C8—91no—
557C4×C8—91no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—31no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—122no—
569C23×C3—122no—
570C23×C3—122no—
571C23×C3—122no—
572C23×C3—241no—
573C23×C3—241no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—31no—
578C22×D3—31no—
579C22×D3—42no—
580C22×D3—42no—
581C22×D3—42no—
582C22×D3—42no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—81no—
587C22×D3—81no—
588C22×D3—121no—
589C22×D3—122no—
590C22×D3—122no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—122no—
595C22×D3—122no—
596C22×D3—122no—
597C22×D3—124no—
598C22×D3—242no—
599C22×D3—241no—
600C22×D3—241no—
601C22×D3—241no—
602C22×D3—241no—
603C22×D3—242no—
604C22×D3D3×D411yescharacteristic
605C3×D4—21no—
606C3×D4—21no—
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—22no—
612C3×D4—32no—
613C3×D4—41no—
614C3×D4—41no—
615C3×D4—41no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4—61no—
619C3×D4—61no—
620C3×D4—61no—
621C3×D4—122no—
622C3×D4—122no—
623C3×D4—122no—
624C3×D4—241no—
625C3×D4D3×D412yescomplemented
626C3×D4C2×#6712yescomplemented
627C2×C3×C4—21no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—31no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—122no—
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D311yescharacteristic
637#67—34no—
638#67—42no—
639#67—42no—
640#67—42no—
641#67—81no—
642#67—122no—
643#67—122no—
644#67—122no—
645#67—122no—
646#67—122no—
647#67—122no—
648#67—122no—
649#67—122no—
650#67—122no—
651#67—124no—
652#67—122no—
653#67—122no—
654#67—242no—
655#67—241no—
656C2×Dic3—21no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—42no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—121no—
664C2×Dic3—122no—
665C2×Dic3D3×D411yescharacteristic
666C2×Dic3D3×D411yescharacteristic
667C2×Dic3D3×D411yescharacteristic
668D12—21no—
669D12—21no—
670D12—21no—
671D12—21no—
672D12—21no—
673D12—34no—
674D12—62no—
675D12—61no—
676D12—61no—
677D12—61no—
678D12—61no—
679D12—121no—
680D12—122no—
681D12—122no—
682D12—122no—
683D12—241no—
684D12C2×#6712yescomplemented
685C4×D3—21no—
686C4×D3—21no—
687C4×D3—61no—
688C4×D3—61no—
689C4×D3—61no—
690C4×D3—61no—
691C4×D3—121no—
692C4×D3—121no—
693C4×D3—122no—
694C3×C8—21no—
695C3×C8—21no—
696C3×C8—32no—
697C3×C8—41no—
698C3×C8—61no—
699C3⋊C8—21no—
700C3⋊C8—61no—
701C3⋊C8—61no—
702C3⋊C8—121no—
703C3⋊C8C2×#6712yescomplemented
704C2×C32—42no—
705C2×C32—81no—
706C2×C32D4211yescharacteristic
707C2×C32C22×D811yescharacteristic
708C2×C32#57611yescharacteristic
709C3⋊D3—22no—
710C3⋊D3—81no—
711C3×D3—22no—
712C3×D3—42no—
713C3×D3—81no—
714C3×D3—81no—
715C24—61no—
716C24—61no—
717C24—181no—
718C24—181no—
719C2×D4—31no—
720C2×D4—31no—
721C2×D4—31no—
722C2×D4—61no—
723C2×D4—61no—
724C2×D4—61no—
725C2×D4—61no—
726C2×D4—62no—
727C2×D4—62no—
728C2×D4—91no—
729C2×D4—91no—
730C2×D4—121no—
731C2×D4—121no—
732C2×D4—181no—
733C2×D4—181no—
734C2×D4—181no—
735C2×D4—181no—
736C2×D4—181no—
737C2×D4—181no—
738C2×D4—182no—
739C2×D4—182no—
740C2×D4—181no—
741C2×D4—181no—
742C2×D4—364no—
743C2×D4—361no—
744C2×D4—361no—
745C2×D4—364no—
746C2×D4C2×D3211yescharacteristic
747C2×D4C2×D3211yescharacteristic
748C22×C4—31no—
749C22×C4—61no—
750C22×C4—91no—
751C22×C4—181no—
752D8—22no—
753D8—34no—
754D8—62no—
755D8—62no—
756D8—62no—
757D8—182no—
758D8—182no—
759D8—361no—
760D8—361no—
761C2×C8—31no—
762C2×C8—31no—
763C2×C8—62no—
764C2×C8—91no—
765C2×C8—182no—
766C2×C8C2×D3211yescharacteristic
767C4⋊C4—31no—
768C4⋊C4—91no—
769C4⋊C4—91no—
770C22⋊C4—61no—
771C22⋊C4—91no—
772C22⋊C4—91no—
773C22⋊C4—181no—
774C22⋊C4—181no—
775C22⋊C4—181no—
776C22⋊C4—181no—
777C22⋊C4—181no—
778C42—31no—
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—21no—
782C22×C3—32no—
783C22×C3—42no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—61no—
795C22×C3—61no—
796C22×C3—62no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—244no—
811C22×C3—244no—
812C22×C3C2×D3×D411yescharacteristic
813C22×C3C2×D3×D411yescharacteristic
814C2×D3—21no—
815C2×D3—21no—
816C2×D3—22no—
817C2×D3—32no—
818C2×D3—32no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—41no—
824C2×D3—41no—
825C2×D3—41no—
826C2×D3—41no—
827C2×D3—62no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—84no—
833C2×D3—84no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—122no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—121no—
843C2×D3—241no—
844C2×D3—241no—
845C2×D3—244no—
846C2×D3—244no—
847C2×D3—244no—
848C2×D3—244no—
849C2×D3—248no—
850C2×D3D3×D812yescomplemented
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—32no—
854C3×C4—61no—
855C3×C4—61no—
856C3×C4—121no—
857C3×C4C2×D3×D411yescharacteristic
858C3×C4#100411yescharacteristic
859C3×C4#100911yescharacteristic
860C3×C4C22×#6711yescharacteristic
861Dic3—21no—
862Dic3—21no—
863Dic3—41no—
864Dic3—61no—
865Dic3—61no—
866Dic3—121no—
867Dic3—121no—
868Dic3—121no—
869Dic3—241no—
870Dic3D3×D812yescomplemented
871C32D4×D811yescharacteristic, complemented, Sylow
872C23—21no—
873C23—21no—
874C23—31no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—91no—
879C23—122no—
880C23—122no—
881C23—122no—
882C23—122no—
883C23—181no—
884C23—241no—
885C23—241no—
886C23—362no—
887C23—362no—
888C23—362no—
889C23—362no—
890C23—721no—
891C23—721no—
892D4—21no—
893D4—21no—
894D4—21no—
895D4—32no—
896D4—61no—
897D4—61no—
898D4—61no—
899D4—61no—
900D4—61no—
901D4—94no—
902D4—122no—
903D4—122no—
904D4—122no—
905D4—181no—
906D4—181no—
907D4—241no—
908D4—362no—
909D4—362no—
910D4—362no—
911D4—362no—
912D4—362no—
913D4—362no—
914D4—362no—
915D4—721no—
916D4D3×#6712yescomplemented
917C2×C4—31no—
918C2×C4—31no—
919C2×C4—31no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—91no—
924C2×C4—122no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—181no—
928C2×C4—362no—
929C2×C4C22×D3211yescharacteristic
930C8—21no—
931C8—32no—
932C8—61no—
933C8—181no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—42no—
938C2×C3—42no—
939C2×C3—62no—
940C2×C3—82no—
941C2×C3—81no—
942C2×C3—81no—
943C2×C3—122no—
944C2×C3—161no—
945C2×C3—241no—
946C2×C3—241no—
947C2×C3#560911yescharacteristic
948C2×C3C2×D3×D811yescharacteristic
949C2×C3C2×D3×D811yescharacteristic
950C2×C3#575711yescharacteristic
951C2×C3#577411yescharacteristic
952C2×C3D4×#6711yescharacteristic
953D3—22no—
954D3—42no—
955D3—62no—
956D3—62no—
957D3—81no—
958D3—81no—
959D3—122no—
960D3—242no—
961D3—241no—
962D3—241no—
963C22—22no—
964C22—32no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—61no—
971C22—61no—
972C22—62no—
973C22—92no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—121no—
982C22—181no—
983C22—181no—
984C22—244no—
985C22—244no—
986C22—361no—
987C22—361no—
988C22—361no—
989C22—724no—
990C22—724no—
991C22D32×D411yescharacteristic
992C4—32no—
993C4—61no—
994C4—61no—
995C4—121no—
996C4—181no—
997C4—361no—
998C4#6431411yescharacteristic
999C4C2×D3×#6711yescharacteristic
1000C3—21no—
1001C3#8035011yescharacteristic, complemented
1002C3D8×#6711yescharacteristic, complemented
1003C2—42no—
1004C2—62no—
1005C2—81no—
1006C2—122no—
1007C2—182no—
1008C2—241no—
1009C2—241no—
1010C2—721no—
1011C2D32×D811yescharacteristic
1012C2#1059473211yescharacteristic
1013C2#1059529111yescharacteristic
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. #10595293C2semidirect
3. D4×#626C2semidirect
4. C2×#63926C2semidirect
5. #10592855C2semidirect
6. C3×#5150C2semidirect
7. #10591482C2semidirect
8. #10591455C2semidirect
9. #10591448C2semidirect
10. #10591447C2semidirect
11. Dic3×#213C2semidirect
12. #10590945C2semidirect
13. #10590826C2semidirect
14. #10590753C2semidirect
15. #10590720C2semidirect
18. C2×D4×C3⋊D3C22semidirect
19. C2×C3×D3×D4C22semidirect
20. C2×C3×D3×D4C22semidirect
23. C2×#3802C22semidirect
24. C2×C32×D8C22semidirect
25. #64147C22semidirect
26. C2×#3753C22semidirect
27. C3×#940C22semidirect
28. C3×D4×Dic3C22semidirect
30. C2×C3×#213C22semidirect
31. C2×C3×#213C22semidirect
33. C2×C3×D24C22semidirect
34. C2×C3×D3×C8C22semidirect
42. #63916C22semidirect
43. #63911C22semidirect
44. #63909C22semidirect
45. #63908C22semidirect
47. Dic3×D12C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3710C22semidirect
52. #63659C22semidirect
53. #63648C22semidirect
54. #63647C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63575C22semidirect
59. #63563C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. Dic3×C3⋊C8C22semidirect
68. C2×D3×D8D3semidirect
82. #5150D3semidirect
140. C3×#213D4semidirect
169. C2×D3×D4C2×D3semidirect
170. C2×D3×D4C2×D3semidirect
178. C2×C3×D8C2×D3semidirect
179. C2×C3×D8C2×D3semidirect
186. #940C2×D3semidirect
200. D4×Dic3C2×D3semidirect
209. C2×#213C2×D3semidirect
210. C2×#213C2×D3semidirect
220. C2×D24C2×D3semidirect
223. C2×D3×C8C2×D3semidirect
239. #832C2×D3semidirect
245. #821C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
279. C32×D4C2×D4semidirect
303. C3×D12C2×D4semidirect
310. #626D8semidirect
317. C3×C3⋊C8C2×D4semidirect
449. #213#67semidirect
489. C2×C3⋊D3C2×D8semidirect
503. C2×C3×D3C2×D8semidirect
512. C3×Dic3C2×D8semidirect
529. C2×D8D32semidirect
625. C3×D4D3×D4semidirect
626. C3×D4C2×#67semidirect
684. D12C2×#67semidirect
703. C3⋊C8C2×#67semidirect
850. C2×D3D3×D8semidirect
870. Dic3D3×D8semidirect
871. C32D4×D8semidirect
916. D4D3×#67semidirect
1001. C3#80350semidirect
1002. 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
#105952932
D4×#6262
C2×#639262
#105928552
C3×#51502
#105914822
#105914552
#105914482
#105914472
Dic3×#2132
#105909452
#105908262
#105907532
#105907202
D8×#673
#803503