Finite Group Databasebeta

← #11885761

Subgroups — #11885761

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
1#10595297C211yesmaximal, characteristic, complemented
2#10595293C211yesmaximal, characteristic, complemented
3C2×#63926C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5#10592855C211yesmaximal, characteristic, complemented
6C3×#5156C211yesmaximal, characteristic, complemented
7C3×#5151C211yesmaximal, characteristic, complemented
8#10591498C211yesmaximal, characteristic, complemented
9#10591455C211yesmaximal, characteristic, complemented
10#10591429C211yesmaximal, characteristic, complemented
11#10591428C211yesmaximal, characteristic, complemented
12#10590945C211yesmaximal, characteristic, complemented
13#10590944C211yesmaximal, characteristic, complemented
14#10590745C211yesmaximal, characteristic, complemented
15#10590721C211yesmaximal, characteristic, complemented
16#81789—31nomaximal
17#80024—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic, complemented
20C2×#3811—21no—
21C2×D3×#67—21no—
22C2×#3802C2211yescharacteristic, complemented
23C2×D3×D12C2211yescharacteristic, complemented
24C2×C32×D8C2211yescharacteristic, complemented
25#64147C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic, complemented
28C3×#940C2211yescharacteristic, complemented
29C3×#938C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic, complemented
33C2×C3×D24C2211yescharacteristic, complemented
34#63983—21no—
35#63983—21no—
36#63981—21no—
37#63976—21no—
38#63970—21no—
39#63958—21no—
40#63926—24no—
41D3×#213—24no—
42#63916C2211yescharacteristic, complemented
43#63908C2211yescharacteristic, complemented
44C4×#626C2211yescharacteristic
45#63894C2211yescharacteristic, complemented
46Dic3×D12C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3710C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×C8×Dic3C2211yescharacteristic, complemented
59#63575C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#213—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67C2×D3×D8—31no—
68#5717—31no—
69#5717—31no—
70#5609—31no—
71C3×#493—31no—
72C3×#447—31no—
73#5157—31no—
74#5157—31no—
75#5156—31no—
76#5156—31no—
77#5156—31no—
78#5156—31no—
79#5156—61no—
80#5156D311yescharacteristic, complemented
81#5151D311yescharacteristic, complemented
82#5150—31no—
83#5072—31no—
84#5072—31no—
85#5038—31no—
86#4786—31no—
87#4775—31no—
88#4773—31no—
89#4756—31no—
90#4732—31no—
91#67⋊C8—31no—
92C4×D24—31no—
93C8×D12—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C22×D32—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—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C3×D3×D4—22no—
113C3×D3×D4—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118#3811—44no—
119D3×#67—44no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#626D411yescharacteristic
123C2×#625—21no—
124C2×#625—21no—
125C2×#624—21no—
126C2×D3×Dic3—21no—
127#3802—22no—
128#3802—41no—
129D3×D12—22no—
130D3×D12—41no—
131C32×D8—41no—
132C2×C32×C8C2311yescharacteristic
133#3757—21no—
134#3753—22no—
135C4⋊(C3⋊Dic3)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C3×#217—21no—
138C3×#213—22no—
139C3×#213—22no—
140C3×#213—22no—
141C3×C4⋊Dic3C2311yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×D24—41no—
146Dic3⋊Dic3D411yescharacteristic
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153#3714—22no—
154#3714D414yescomplemented
155#3713—22no—
156#3710—22no—
157D3×C3⋊C8—22no—
158D4×D8—91noSylow
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×D3×D4—61no—
168C2×D3×D4—61no—
169C2×D3×D4—61no—
170C2×D3×D4C2×D311yescharacteristic, complemented
171C22×D12—31no—
172C2×C3×D8—21no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8—31no—
177C2×C3×D8C2×D311yescharacteristic, complemented
178C2×C3×D8C2×D311yescharacteristic, complemented
179C3×#127—31no—
180C3×#127—31no—
181C3×#121—31no—
182#953—61no—
183#940C2×D311yescharacteristic, complemented
184#940C2×D311yescharacteristic, complemented
185#939—61no—
186#938—31no—
187#938—31no—
188#938—31no—
189#938—31no—
190#938—61no—
191#938—61no—
192#938—61no—
193#938C2×D311yescharacteristic, complemented
194#937—61no—
195#937—61no—
196#937—61no—
197#937—61no—
198#937—61no—
199#937—61no—
200D4×Dic3—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—61no—
208C2×#213—64no—
209C2×#213C2×D311yescharacteristic, complemented
210C2×#213C2×D311yescharacteristic, complemented
211C2×#213C2×D311yescharacteristic, complemented
212#930—31no—
213C4×#67—31no—
214C22×C3⋊C8—31no—
215D3×D8—64no—
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×C8—31no—
224#895—31no—
225#893—31no—
226#884—61no—
227#882—61no—
228C4×D12—31no—
229C4×D12—31no—
230C4×D12—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×C22⋊C8—31no—
234C3×C4×C8—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—31no—
239#832—61no—
240#832C2×D311yescharacteristic, complemented
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—61no—
249(C2×D3)⋊C8C2×D311yescharacteristic, complemented
250#818—31no—
251Dic3⋊C8—31no—
252C8×Dic3C2×D311yescharacteristic, complemented
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—81no—
269C22×C3×D3C2×D411yescharacteristic
270C2×D32—42no—
271C2×D32—42no—
272C2×D32—42no—
273C2×D32—42no—
274C2×D32—81no—
275C2×D32—81no—
276C32×D4—21no—
277C32×D4—21no—
278C32×D4—21no—
279C32×D4—21no—
280C2×C32×C4C2411yescharacteristic
281#638—42no—
282#638—42no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3C2×D411yescharacteristic
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)C2×D412yescomplemented
287C4×C3⋊D3—21no—
288C4×C3⋊D3—21no—
289C3×#67—42no—
290C3×#67—42no—
291C3×#67—42no—
292C3×#67—42no—
293C3×#67—81no—
294C3×#67—81no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3C2×D411yescharacteristic
297C2×C3×Dic3C2×D411yescharacteristic
298C2×C3×Dic3C2×D411yescharacteristic
299C3×D12—21no—
300C3×D12—21no—
301C3×D12—21no—
302C3×D12—21no—
303C3×D12—21no—
304C3×D12C2×D412yescomplemented
305C3×C4×D3—21no—
306C3×C4×D3—21no—
307#626—42no—
308#626—42no—
309#626D814yescomplemented
310#625—42no—
311#625—42no—
312#624—42no—
313D3×Dic3—42no—
314C32×C8—21no—
315C3⋊(C3⋊C8)—21no—
316C3×C3⋊C8—21no—
317C3×C3⋊C8C2×D412yescomplemented
318C22×D8—91no—
319C22×D8—91no—
320D42—91no—
321D42—91no—
322#493—31no—
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—
334C23×D3—21no—
335C23×D3—61no—
336C23×D3—61no—
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—61no—
352C2×C3×D4—62no—
353C2×C3×D4—61no—
354C2×C3×D4—121no—
355C2×C3×D4C22×D311yescharacteristic
356C2×C3×D4C22×D311yescharacteristic
357C2×C3×D4C22×D311yescharacteristic
358C2×C3×D4C22×D311yescharacteristic
359C22×C3×C4—31no—
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—21no—
366C2×#67—31no—
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—121no—
378C2×#67—121no—
379C2×#67—124no—
380C22×Dic3—61no—
381D3×D4—22no—
382D3×D4—41no—
383D3×D4—62no—
384D3×D4—62no—
385D3×D4—62no—
386D3×D4—62no—
387D3×D4—62no—
388D3×D4—122no—
389D3×D4—121no—
390D3×D4—121no—
391D3×D4—121no—
392D3×D4—121no—
393D3×D4—121no—
394D3×D4—124no—
395D3×D4—124no—
396D3×D4—124no—
397D3×D4—122no—
398C2×D12—31no—
399C2×D12—31no—
400C2×D12—31no—
401C2×D12—61no—
402C2×D12—62no—
403C2×D12—61no—
404C2×D12—61no—
405C2×D12—121no—
406C2×D12C22×D311yescharacteristic
407C2×D12C22×D311yescharacteristic
408C2×D12C22×D311yescharacteristic
409C2×C4×D3—31no—
410C2×C4×D3—31no—
411C2×C4×D3—61no—
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3C22×D311yescharacteristic
416C3×D8—41no—
417C3×D8—41no—
418C3×D8—42no—
419C3×D8—62no—
420C3×D8—62no—
421C3×D8—62no—
422C3×D8—121no—
423C2×C3×C8—21no—
424C2×C3×C8—31no—
425C2×C3×C8—31no—
426C2×C3×C8C22×D311yescharacteristic
427C2×C3×C8C22×D311yescharacteristic
428C3×C4⋊C4—31no—
429C3×C22⋊C4—61no—
430C3×C42—31no—
431#217—21no—
432#217—31no—
433#217—61no—
434#217—61no—
435#217—61no—
436#217—61no—
437#217—61no—
438#217—121no—
439#213—22no—
440#213—22no—
441#213—22no—
442#213—34no—
443#213—62no—
444#213—62no—
445#213—62no—
446#213—62no—
447#213—62no—
448#213—122no—
449(C2×D3)⋊C4—31no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—31no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—61no—
455(C2×D3)⋊C4—61no—
456(C2×D3)⋊C4—61no—
457C4⋊Dic3—31no—
458C4⋊Dic3—31no—
459C4⋊Dic3—31no—
460C4⋊Dic3—61no—
461C4⋊Dic3C22×D311yescharacteristic
462Dic3⋊C4—31no—
463C4×Dic3C22×D311yescharacteristic
464C2×C3⋊C8—31no—
465C2×C3⋊C8—31no—
466C2×C3⋊C8—61no—
467C2×C3⋊C8—62no—
468C2×C3⋊C8C22×D311yescharacteristic
469C2×C3⋊C8C22×D311yescharacteristic
470D24—34no—
471D24—41no—
472D24—62no—
473D3×C8—62no—
474D3×C8—62no—
475D3×C8—62no—
476C22×C32—41no—
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—22no—
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×D3C2×D812yescomplemented
503D32—84no—
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—91no—
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—91no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—91no—
527C2×D8—184no—
528C2×D8—184no—
529C2×D8D3211yescharacteristic, complemented
530C22×C8—91no—
531C22×C8—91no—
532#127—31no—
533#127—31no—
534#121—31no—
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—91no—
545C4×D4—91no—
546C4×D4—91no—
547#107—91no—
548C4⋊C8—91no—
549#102—31no—
550#102—31no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102—91no—
555C22⋊C8—31no—
556C22⋊C8—91no—
557C4×C8—31no—
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—241no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—31no—
575C22×D3—31no—
576C22×D3—42no—
577C22×D3—42no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—81no—
582C22×D3—121no—
583C22×D3—122no—
584C22×D3—122no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3—122no—
588C22×D3—122no—
589C22×D3—122no—
590C22×D3—122no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—124no—
595C22×D3—122no—
596C22×D3—242no—
597C22×D3—241no—
598C22×D3—241no—
599C22×D3—241no—
600C22×D3—241no—
601C22×D3—241no—
602C22×D3—241no—
603C22×D3—242no—
604C22×D3D3×D411yescharacteristic
605C3×D4—22no—
606C3×D4—21no—
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—32no—
615C3×D4—41no—
616C3×D4—41no—
617C3×D4—41no—
618C3×D4—61no—
619C3×D4—61no—
620C3×D4—61no—
621C3×D4—61no—
622C3×D4—61no—
623C3×D4—122no—
624C3×D4—122no—
625C3×D4—122no—
626C3×D4—122no—
627C3×D4—241no—
628C3×D4—241no—
629C2×C3×C4—21no—
630C2×C3×C4—31no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638#67—34no—
639#67—42no—
640#67—42no—
641#67—42no—
642#67—42no—
643#67—81no—
644#67—81no—
645#67—122no—
646#67—122no—
647#67—122no—
648#67—122no—
649#67—122no—
650#67—122no—
651#67—122no—
652#67—122no—
653#67—122no—
654#67—124no—
655#67—122no—
656#67—242no—
657C2×Dic3—21no—
658C2×Dic3—31no—
659C2×Dic3—31no—
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—32no—
675D12—32no—
676D12—62no—
677D12—61no—
678D12—61no—
679D12—121no—
680D12—122no—
681D12—122no—
682D12D3×D412yescomplemented
683C4×D3—21no—
684C4×D3—21no—
685C4×D3—61no—
686C4×D3—61no—
687C4×D3—61no—
688C4×D3—61no—
689C4×D3—121no—
690C4×D3—121no—
691C4×D3—122no—
692C4×D3—122no—
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⋊C8D3×D412yescomplemented
704C2×C32—81no—
705C2×C32—81no—
706C2×C32D4211yescharacteristic
707C2×C32C22×D811yescharacteristic
708C2×C32#57611yescharacteristic
709C3⋊D3—22no—
710C3⋊D3—42no—
711C3×D3—22no—
712C3×D3—42no—
713C3×D3—81no—
714C3×D3—81no—
715C24—61no—
716C24—181no—
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—61no—
727C2×D4—62no—
728C2×D4—61no—
729C2×D4—91no—
730C2×D4—91no—
731C2×D4—121no—
732C2×D4—181no—
733C2×D4—182no—
734C2×D4—181no—
735C2×D4—181no—
736C2×D4—181no—
737C2×D4—182no—
738C2×D4—182no—
739C2×D4—181no—
740C2×D4—181no—
741C2×D4—361no—
742C2×D4—361no—
743C2×D4—361no—
744C2×D4—364no—
745C2×D4—364no—
746C2×D4C2×D3211yescharacteristic
747C2×D4C2×D3211yescharacteristic
748C22×C4—31no—
749C22×C4—91no—
750C22×C4—181no—
751C22×C4—181no—
752D8—41no—
753D8—62no—
754D8—62no—
755D8—62no—
756D8—94no—
757D8—121no—
758D8—182no—
759D8—182no—
760D8—182no—
761C2×C8—31no—
762C2×C8—31no—
763C2×C8—91no—
764C2×C8—182no—
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—21no—
780C22×C3—32no—
781C22×C3—42no—
782C22×C3—41no—
783C22×C3—41no—
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×C3C2×D3×D411yescharacteristic
812C22×C3C2×D3×D411yescharacteristic
813C2×D3—21no—
814C2×D3—21no—
815C2×D3—22no—
816C2×D3—32no—
817C2×D3—32no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—41no—
824C2×D3—41no—
825C2×D3—41no—
826C2×D3—62no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—62no—
832C2×D3—62no—
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—241no—
842C2×D3—241no—
843C2×D3—244no—
844C2×D3—244no—
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×C4C2×D3×D411yescharacteristic
859C3×C4#100411yescharacteristic
860C3×C4#100411yescharacteristic
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—181no—
882C23—241no—
883C23—362no—
884C23—362no—
885C23—362no—
886C23—362no—
887C23—362no—
888C23—362no—
889C23—721no—
890C23—721no—
891C23—721no—
892D4—21no—
893D4—21no—
894D4—21no—
895D4—21no—
896D4—32no—
897D4—61no—
898D4—61no—
899D4—61no—
900D4—61no—
901D4—61no—
902D4—94no—
903D4—92no—
904D4—122no—
905D4—122no—
906D4—122no—
907D4—122no—
908D4—181no—
909D4—241no—
910D4—241no—
911D4—362no—
912D4—362no—
913D4—362no—
914D4—362no—
915D4—362no—
916D4—362no—
917C2×C4—31no—
918C2×C4—31no—
919C2×C4—31no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—91no—
924C2×C4—181no—
925C2×C4—181no—
926C2×C4—181no—
927C2×C4—362no—
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—62no—
938C2×C3—82no—
939C2×C3—81no—
940C2×C3—81no—
941C2×C3—81no—
942C2×C3—81no—
943C2×C3—122no—
944C2×C3—161no—
945C2×C3—241no—
946C2×C3—241no—
947C2×C3#559011yescharacteristic
948C2×C3#571711yescharacteristic
949C2×C3C2×D3×D811yescharacteristic
950C2×C3C2×D3×D811yescharacteristic
951C2×C3#575711yescharacteristic
952C2×C3#577411yescharacteristic
953D3—22no—
954D3—42no—
955D3—62no—
956D3—62no—
957D3—81no—
958D3—81no—
959D3—122no—
960D3—122no—
961D3—122no—
962D3—242no—
963C22—32no—
964C22—41no—
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—182no—
985C22—244no—
986C22—361no—
987C22—361no—
988C22—724no—
989C22—724no—
990C22—724no—
991C22D32×D411yescharacteristic
992C4—32no—
993C4—61no—
994C4—61no—
995C4—121no—
996C4—181no—
997C4—361no—
998C4D32×D411yescharacteristic
999C4#6433011yescharacteristic
1000C3—21no—
1001C3#8002411yescharacteristic, complemented
1002C3#8178911yescharacteristic, complemented
1003C2—62no—
1004C2—81no—
1005C2—81no—
1006C2—122no—
1007C2—182no—
1008C2—241no—
1009C2—241no—
1010C2—362no—
1011C2D32×D811yescharacteristic
1012C2#1059473211yescharacteristic
1013C2#1059529511yescharacteristic
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. #10595297C2semidirect
2. #10595293C2semidirect
3. C2×#63926C2semidirect
4. C2×D3×#213C2semidirect
5. #10592855C2semidirect
6. C3×#5156C2semidirect
7. C3×#5151C2semidirect
8. #10591498C2semidirect
9. #10591455C2semidirect
10. #10591429C2semidirect
11. #10591428C2semidirect
12. #10590945C2semidirect
13. #10590944C2semidirect
14. #10590745C2semidirect
15. #10590721C2semidirect
18. C2×D4×C3⋊D3C22semidirect
19. C2×C3×D3×D4C22semidirect
22. C2×#3802C22semidirect
23. C2×D3×D12C22semidirect
24. C2×C32×D8C22semidirect
25. #64147C22semidirect
26. C2×#3753C22semidirect
27. C3×#940C22semidirect
28. C3×#940C22semidirect
29. C3×#938C22semidirect
30. C2×C3×#213C22semidirect
31. C2×C3×#213C22semidirect
32. C2×C3×#213C22semidirect
33. C2×C3×D24C22semidirect
42. #63916C22semidirect
43. #63908C22semidirect
45. #63894C22semidirect
46. Dic3×D12C22semidirect
48. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×#3710C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63659C22semidirect
53. #63648C22semidirect
54. #63647C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×C8×Dic3C22semidirect
59. #63575C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
80. #5156D3semidirect
81. #5151D3semidirect
154. #3714D4semidirect
170. C2×D3×D4C2×D3semidirect
177. C2×C3×D8C2×D3semidirect
178. C2×C3×D8C2×D3semidirect
183. #940C2×D3semidirect
184. #940C2×D3semidirect
193. #938C2×D3semidirect
209. C2×#213C2×D3semidirect
210. C2×#213C2×D3semidirect
211. C2×#213C2×D3semidirect
220. C2×D24C2×D3semidirect
240. #832C2×D3semidirect
245. #821C2×D3semidirect
249. (C2×D3)⋊C8C2×D3semidirect
252. C8×Dic3C2×D3semidirect
286. C4⋊(C3⋊D3)C2×D4semidirect
304. C3×D12C2×D4semidirect
309. #626D8semidirect
317. C3×C3⋊C8C2×D4semidirect
489. C2×C3⋊D3C2×D8semidirect
502. C2×C3×D3C2×D8semidirect
512. C3×Dic3C2×D8semidirect
529. C2×D8D32semidirect
682. D12D3×D4semidirect
703. C3⋊C8D3×D4semidirect
850. C2×D3D3×D8semidirect
870. Dic3D3×D8semidirect
871. C32D4×D8semidirect
1001. C3#80024semidirect
1002. C3#81789semidirect

Maximal subgroups

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

subgroupindex
#105952972
#105952932
C2×#639262
C2×D3×#2132
#105928552
C3×#51562
C3×#51512
#105914982
#105914552
#105914292
#105914282
#105909452
#105909442
#105907452
#105907212
#817893
#800243