Finite Group Databasebeta

← #11885752

Subgroups — #11885752

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#10595074C211yesmaximal, characteristic, complemented
2D12×#67C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic, complemented
4C2×D3×D24C211yesmaximal, characteristic, complemented
5#10592431C211yesmaximal, characteristic, complemented
6C3×#4732C211yesmaximal, characteristic, complemented
7C3×#67⋊C8C211yesmaximal, characteristic, complemented
8#10591164C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590880C211yesmaximal, characteristic, complemented
12#10590826C211yesmaximal, characteristic, complemented
13#10590765C211yesmaximal, characteristic, complemented
14#10590753C211yesmaximal, characteristic, complemented
15#10590745C211yesmaximal, characteristic, complemented
16#80024—31nomaximal
17D4×D24—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic, complemented
20C2×#3811—21no—
21C2×D3×#67—21no—
22C2×D3×D12C2211yescharacteristic, complemented
23C2×D3×D12C2211yescharacteristic, complemented
24#64139C2211yescharacteristic, complemented
25C2×#3745C2211yescharacteristic, complemented
26C2×#3745C2211yescharacteristic, complemented
27C3×#930C2211yescharacteristic, complemented
28C3×C4×#67C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic, complemented
30C2×C3×D24C2211yescharacteristic, complemented
31C2×C3×D24C2211yescharacteristic, complemented
32C2×C3×D3×C8C2211yescharacteristic, complemented
33#63981—21no—
34#63977—21no—
35#63923—21no—
36#63922—21no—
37#63911C2211yescharacteristic, complemented
38#63911C2211yescharacteristic, complemented
39#63910—21no—
40#63909C2211yescharacteristic, complemented
41#63908C2211yescharacteristic, complemented
42#63894C2211yescharacteristic, complemented
43Dic3×D12C2211yescharacteristic, complemented
44#63886—21no—
45C2×#3714—24no—
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51D3×D24—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×C8×Dic3C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#213—31no—
65C2×D3×D8—31no—
66C22×D24—31no—
67C22×D24—31no—
68#5609—31no—
69D4×D12—31no—
70D4×D12—31no—
71C3×#447—31no—
72C3×C8×D4—31no—
73#5156—31no—
74#5151—31no—
75#5150—31no—
76#5115—31no—
77#5115—31no—
78#5038—31no—
79#4843—31no—
80#4843—31no—
81#4786—31no—
82#4775—31no—
83#4773—31no—
84#4756—31no—
85#4732—31no—
86#4732—31no—
87#4732—31no—
88#4732—31no—
89#4732—61no—
90#4732D311yescharacteristic, complemented
91#67⋊C8D311yescharacteristic, complemented
92#4695—31no—
93C4×D24—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C22×D32—21no—
97C22×D32—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)—22no—
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67D411yescharacteristic
108C2×C3×D12—22no—
109C2×C3×D12—21no—
110C2×C3×D12—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115#3811—44no—
116D3×#67—44no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#625—21no—
125C2×#624—21no—
126C2×D3×Dic3—21no—
127D3×D12—22no—
128D3×D12—22no—
129D3×D12—41no—
130D3×D12—41no—
131C2×C32×C8C2311yescharacteristic
132C2×C32×C8C2311yescharacteristic
133#3752—21no—
134C4⋊(C3⋊Dic3)C2311yescharacteristic
135#3745—22no—
136#3745—41no—
137C3×#217D411yescharacteristic
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8—22no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C3×D24—22no—
147C3×D24—41no—
148C3×D3×C8—22no—
149#3722—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153#3714—22no—
154#3714—22no—
155#3714—22no—
156#3714—22no—
157#3714D414yescomplemented
158D4×D8—91noSylow
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—61no—
164C2×D3×D4—61no—
165C2×D3×D4—61no—
166C22×D12—31no—
167C22×D12—31no—
168C22×D12—31no—
169C22×D12—31no—
170C22×D12—61no—
171C22×D12C2×D311yescharacteristic, complemented
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C22×C3×C8—31no—
176C3×#121—31no—
177C3×C4×D4—31no—
178#953—61no—
179#940—31no—
180#940—31no—
181#939—61no—
182#938—31no—
183#937—61no—
184#937—61no—
185D4×Dic3—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—64no—
192#930—31no—
193#930—31no—
194#930—31no—
195#930—31no—
196#930—61no—
197#930C2×D311yescharacteristic, complemented
198C4×#67C2×D311yescharacteristic
199C22×C3⋊C8C2×D311yescharacteristic, complemented
200D3×D8—64no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—31no—
204C2×D24—31no—
205C2×D24—31no—
206C2×D24—31no—
207C2×D24—31no—
208C2×D24—31no—
209C2×D24—31no—
210C2×D24—61no—
211C2×D24—61no—
212C2×D24—64no—
213C2×D24—64no—
214C2×D24C2×D311yescharacteristic, complemented
215C2×D24C2×D311yescharacteristic, complemented
216C2×D3×C8C2×D311yescharacteristic, complemented
217#895—31no—
218#895—61no—
219#895—61no—
220#893—31no—
221#884—61no—
222#882—61no—
223#882—61no—
224#882—61no—
225#882—61no—
226#882—61no—
227#874—31no—
228#874—31no—
229C4×D12—31no—
230C4×D12—31no—
231C3×C4⋊C8—31no—
232C3×#102—31no—
233C3×#102—31no—
234C3×C22⋊C8—21no—
235C3×C22⋊C8—31no—
236C3×C22⋊C8C2×D311yescharacteristic, complemented
237C3×C22⋊C8C2×D311yescharacteristic, complemented
238C3×C4×C8—31no—
239#832—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244#821—31no—
245#821—31no—
246#821—61no—
247#821—61no—
248#821C2×D311yescharacteristic, complemented
249#821C2×D311yescharacteristic, complemented
250(C2×D3)⋊C8C2×D311yescharacteristic, complemented
251#818—31no—
252Dic3⋊C8C2×D311yescharacteristic, complemented
253C8×Dic3C2×D311yescharacteristic, complemented
254#809—31no—
255#807—31no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3—21no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—81no—
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—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4C2×D411yescharacteristic
279C2×C32×C4C2411yescharacteristic
280#638—42no—
281C2×C3⋊Dic3—21no—
282C4⋊(C3⋊D3)—21no—
283C4⋊(C3⋊D3)—21no—
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)—42no—
288C4⋊(C3⋊D3)C2×D412yescomplemented
289C3×#67—42no—
290C3×#67D814yescomplemented
291C2×C3×Dic3—21no—
292C2×C3×Dic3C2×D411yescharacteristic
293C2×C3×Dic3C2×D411yescharacteristic
294C2×C3×Dic3C2×D411yescharacteristic
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—42no—
301C3×D12C2×D412yescomplemented
302C3×C4×D3—21no—
303C3×C4×D3—21no—
304#626—42no—
305#626—42no—
306#626—42no—
307#626—42no—
308#626—42no—
309#626—81no—
310#626—81no—
311#625—42no—
312#624—42no—
313D3×Dic3—42no—
314C32×C8—21no—
315C32×C8—21no—
316C3×C3⋊C8—21no—
317C3×C3⋊C8C2×D412yescomplemented
318C22×D8—91no—
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—31no—
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—31no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—62no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—121no—
350C22×C3×C4—21no—
351C22×C3×C4—31no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—21no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—121no—
367C2×#67—124no—
368C2×#67D1211yescharacteristic
369C22×Dic3—61no—
370D3×D4—62no—
371D3×D4—62no—
372D3×D4—121no—
373D3×D4—121no—
374D3×D4—124no—
375D3×D4—124no—
376D3×D4—124no—
377C2×D12—22no—
378C2×D12—21no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—31no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—31no—
385C2×D12—41no—
386C2×D12—61no—
387C2×D12—61no—
388C2×D12—61no—
389C2×D12—62no—
390C2×D12—62no—
391C2×D12—62no—
392C2×D12—62no—
393C2×D12—61no—
394C2×D12—61no—
395C2×D12—61no—
396C2×D12—61no—
397C2×D12—61no—
398C2×D12—61no—
399C2×D12—61no—
400C2×D12—61no—
401C2×D12—61no—
402C2×D12—122no—
403C2×D12—121no—
404C2×D12—121no—
405C2×D12—121no—
406C2×D12—121no—
407C2×D12—121no—
408C2×D12—122no—
409C2×D12C22×D311yescharacteristic
410C2×D12C22×D311yescharacteristic
411C2×D12C22×D311yescharacteristic
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3C22×D311yescharacteristic
416C3×D8—62no—
417C3×D8—121no—
418C2×C3×C8—21no—
419C2×C3×C8—21no—
420C2×C3×C8—31no—
421C2×C3×C8—31no—
422C2×C3×C8—62no—
423C2×C3×C8—62no—
424C2×C3×C8C22×D311yescharacteristic
425C2×C3×C8C22×D311yescharacteristic
426C2×C3×C8C22×D311yescharacteristic
427C2×C3×C8C22×D311yescharacteristic
428C3×C4⋊C4—31no—
429C3×C4⋊C4—31no—
430C3×C22⋊C4—31no—
431C3×C22⋊C4—31no—
432C3×C22⋊C4—61no—
433C3×C42—31no—
434#217—61no—
435#217—61no—
436#217D1211yescharacteristic
437#213—34no—
438#213—62no—
439#213—62no—
440#213—62no—
441#213—62no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—61no—
448(C2×D3)⋊C4—61no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4D1211yescharacteristic
453C4⋊Dic3—31no—
454C4⋊Dic3—31no—
455C4⋊Dic3—61no—
456C4⋊Dic3C22×D311yescharacteristic
457Dic3⋊C4D1211yescharacteristic
458C4×Dic3C22×D311yescharacteristic
459C2×C3⋊C8—22no—
460C2×C3⋊C8C22×D311yescharacteristic
461C2×C3⋊C8C22×D311yescharacteristic
462D24—22no—
463D24—34no—
464D24—41no—
465D24—62no—
466D24—62no—
467D24—62no—
468D24—62no—
469D24—62no—
470D24—62no—
471D24—122no—
472D24—121no—
473D24—121no—
474D24—122no—
475D3×C8—22no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32C2×D812yescomplemented
479C22×C32C22×D411yescharacteristic
480C2×C3⋊D3—22no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—84no—
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×C4—21no—
506C32×C4C22×D411yescharacteristic
507C32×C4H(5,𝔽2)11yescharacteristic
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—91no—
522C2×D8—91no—
523C2×D8—91no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—91no—
527C2×D8—91no—
528C2×D8—184no—
529C2×D8—184no—
530C22×C8—31no—
531C22×C8—31no—
532#127—91no—
533#127—91no—
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—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—31no—
556C22⋊C8D3211yescharacteristic, complemented
557C4×C8—31no—
558C23×C3—21no—
559C23×C3—31no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—122no—
564C23×C3—122no—
565C23×C3—241no—
566C23×C3C2×D1211yescharacteristic
567C23×C3D3×D411yescharacteristic
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—42no—
572C22×D3—42no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—81no—
580C22×D3—121no—
581C22×D3—121no—
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—124no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—122no—
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×D3C2×D1211yescharacteristic
605C3×D4—34no—
606C3×D4—32no—
607C3×D4—61no—
608C3×D4—61no—
609C3×D4—61no—
610C3×D4—61no—
611C3×D4—61no—
612C3×D4—122no—
613C3×D4—122no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—31no—
621C2×C3×C4—31no—
622C2×C3×C4—31no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4C2×D1211yescharacteristic
629C2×C3×C4D3×D411yescharacteristic
630C2×C3×C4C23×D311yescharacteristic
631C2×C3×C4C23×D311yescharacteristic
632#67—42no—
633#67—122no—
634#67—122no—
635#67—122no—
636#67—122no—
637#67—122no—
638#67—122no—
639#67—122no—
640#67—122no—
641#67—122no—
642#67—242no—
643#67—241no—
644#67—241no—
645#67D2414yescomplemented
646C2×Dic3—21no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—121no—
650C2×Dic3—122no—
651C2×Dic3C2×D1211yescharacteristic
652C2×Dic3C2×D1211yescharacteristic
653C2×Dic3C2×D1211yescharacteristic
654D12—21no—
655D12—21no—
656D12—21no—
657D12—21no—
658D12—21no—
659D12—32no—
660D12—32no—
661D12—42no—
662D12—62no—
663D12—62no—
664D12—61no—
665D12—61no—
666D12—61no—
667D12—61no—
668D12—61no—
669D12—61no—
670D12—61no—
671D12—61no—
672D12—61no—
673D12—61no—
674D12—121no—
675D12—121no—
676D12—121no—
677D12—121no—
678D12—122no—
679D12—122no—
680D12—122no—
681D12—122no—
682D12—124no—
683D12—122no—
684D12—122no—
685D12—122no—
686D12—241no—
687D12—241no—
688D12D3×D412yescomplemented
689C4×D3—21no—
690C4×D3—21no—
691C4×D3—122no—
692C4×D3—122no—
693C4×D3—122no—
694C3×C8—21no—
695C3×C8—21no—
696C3×C8—21no—
697C3×C8—21no—
698C3×C8—32no—
699C3×C8—41no—
700C3×C8—41no—
701C3×C8—61no—
702C3⋊C8—21no—
703C3⋊C8D3×D412yescomplemented
704C2×C32—22no—
705C2×C32D4211yescharacteristic
706C2×C32C22×D811yescharacteristic
707C2×C32#57611yescharacteristic
708C3⋊D3—42no—
709C3⋊D3—81no—
710C3⋊D3—81no—
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—31no—
723C2×D4—62no—
724C2×D4—61no—
725C2×D4—61no—
726C2×D4—91no—
727C2×D4—91no—
728C2×D4—91no—
729C2×D4—121no—
730C2×D4—182no—
731C2×D4—181no—
732C2×D4—181no—
733C2×D4—181no—
734C2×D4—181no—
735C2×D4—181no—
736C2×D4—181no—
737C2×D4—182no—
738C2×D4—182no—
739C2×D4—181no—
740C2×D4—181no—
741C2×D4—181no—
742C2×D4—181no—
743C2×D4—361no—
744C2×D4—361no—
745C2×D4—361no—
746C2×D4—364no—
747C2×D4—364no—
748C22×C4—31no—
749C22×C4—181no—
750C22×C4—181no—
751C22×C4C2×D3211yescharacteristic
752D8—62no—
753D8—94no—
754D8—121no—
755D8—182no—
756D8—182no—
757D8—182no—
758D8—182no—
759D8—182no—
760D8—361no—
761C2×C8—31no—
762C2×C8—31no—
763C2×C8—62no—
764C2×C8—62no—
765C2×C8C2×D3211yescharacteristic
766C2×C8C2×D3211yescharacteristic
767C4⋊C4—31no—
768C4⋊C4—31no—
769C4⋊C4—91no—
770C22⋊C4—31no—
771C22⋊C4—31no—
772C22⋊C4—61no—
773C22⋊C4—181no—
774C22⋊C4—181no—
775C22⋊C4—181no—
776C22⋊C4—181no—
777C22⋊C4—181no—
778C42—31no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—22no—
785C22×C3—32no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—61no—
789C22×C3—61no—
790C22×C3—62no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3—121no—
797C22×C3—121no—
798C22×C3—121no—
799C22×C3—244no—
800C22×C3C2×D2412yescomplemented
801C22×C3D3×D812yescomplemented
802C22×C3C22×D1211yescharacteristic
803C22×C3C2×D3×D411yescharacteristic
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—22no—
807C2×D3—41no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—62no—
816C2×D3—62no—
817C2×D3—84no—
818C2×D3—122no—
819C2×D3—121no—
820C2×D3—121no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—122no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—241no—
837C2×D3—241no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3—241no—
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×D3C2×D2412yescomplemented
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—21no—
854C3×C4—21no—
855C3×C4—32no—
856C3×C4—41no—
857C3×C4—61no—
858C3×C4—61no—
859C3×C4—121no—
860C3×C4C2×D3×D411yescharacteristic
861C3×C4C2×D3×D411yescharacteristic
862C3×C4#100411yescharacteristic
863C3×C4#100911yescharacteristic
864Dic3—21no—
865Dic3—21no—
866Dic3—41no—
867Dic3—121no—
868Dic3—121no—
869Dic3—241no—
870Dic3C2×D2412yescomplemented
871C32D4×D811yescharacteristic, complemented, Sylow
872C23—31no—
873C23—61no—
874C23—61no—
875C23—61no—
876C23—122no—
877C23—122no—
878C23—181no—
879C23—181no—
880C23—181no—
881C23—241no—
882C23—362no—
883C23—362no—
884C23—362no—
885C23—362no—
886C23—362no—
887C23—362no—
888C23—721no—
889C23—721no—
890C23—721no—
891C23D3×D1211yescharacteristic
892D4—34no—
893D4—32no—
894D4—61no—
895D4—61no—
896D4—61no—
897D4—61no—
898D4—61no—
899D4—92no—
900D4—122no—
901D4—122no—
902D4—181no—
903D4—181no—
904D4—181no—
905D4—181no—
906D4—181no—
907D4—362no—
908D4—362no—
909D4—362no—
910D4—362no—
911D4—362no—
912D4—362no—
913D4—362no—
914D4—362no—
915D4—721no—
916D4—721no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—31no—
920C2×C4—31no—
921C2×C4—31no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—181no—
926C2×C4—362no—
927C2×C4—362no—
928C2×C4D3×D1211yescharacteristic
929C2×C4C22×D3211yescharacteristic
930C8—21no—
931C8—21no—
932C8—32no—
933C8—61no—
934C2×C3—22no—
935C2×C3—22no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—42no—
940C2×C3—62no—
941C2×C3—122no—
942C2×C3—241no—
943C2×C3—241no—
944C2×C3D4×D1211yescharacteristic
945C2×C3#559011yescharacteristic
946C2×C3C22×D2411yescharacteristic
947C2×C3#575211yescharacteristic
948C2×C3C2×D3×D811yescharacteristic
949C2×C3#577411yescharacteristic
950D3—22no—
951D3—42no—
952D3—81no—
953D3—81no—
954D3—122no—
955D3—122no—
956D3—242no—
957D3—242no—
958D3—241no—
959D3—241no—
960D3—241no—
961D3—241no—
962D3—481no—
963C22—21no—
964C22—21no—
965C22—32no—
966C22—61no—
967C22—61no—
968C22—62no—
969C22—121no—
970C22—121no—
971C22—121no—
972C22—121no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—182no—
978C22—244no—
979C22—361no—
980C22—361no—
981C22—361no—
982C22—361no—
983C22—361no—
984C22—361no—
985C22—361no—
986C22—361no—
987C22—724no—
988C22—724no—
989C22—724no—
990C22D3×D2412yescomplemented
991C22C2×D3×D1211yescharacteristic
992C4—21no—
993C4—32no—
994C4—61no—
995C4—61no—
996C4—121no—
997C4—361no—
998C4D32×D411yescharacteristic
999C4#6431411yescharacteristic
1000C3—21no—
1001C3D4×D2411yescharacteristic, complemented
1002C3#8002411yescharacteristic, complemented
1003C2—22no—
1004C2—62no—
1005C2—122no—
1006C2—241no—
1007C2—241no—
1008C2—362no—
1009C2—721no—
1010C2—721no—
1011C2#1059427711yescharacteristic
1012C2C2×D3×D2411yescharacteristic
1013C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32D4×D8
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. #10595074C2semidirect
2. D12×#67C2semidirect
3. C22×#3714C2semidirect
4. C2×D3×D24C2semidirect
5. #10592431C2semidirect
6. C3×#4732C2semidirect
7. C3×#67⋊C8C2semidirect
8. #10591164C2semidirect
9. #10590947C2semidirect
10. #10590944C2semidirect
11. #10590880C2semidirect
12. #10590826C2semidirect
13. #10590765C2semidirect
14. #10590753C2semidirect
15. #10590745C2semidirect
18. C22×C4⋊(C3⋊D3)C22semidirect
19. C22×C3×D12C22semidirect
22. C2×D3×D12C22semidirect
23. C2×D3×D12C22semidirect
24. #64139C22semidirect
25. C2×#3745C22semidirect
26. C2×#3745C22semidirect
27. C3×#930C22semidirect
29. C22×C3×C3⋊C8C22semidirect
30. C2×C3×D24C22semidirect
31. C2×C3×D24C22semidirect
32. C2×C3×D3×C8C22semidirect
37. #63911C22semidirect
38. #63911C22semidirect
40. #63909C22semidirect
41. #63908C22semidirect
42. #63894C22semidirect
43. Dic3×D12C22semidirect
47. C2×#3714C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
52. C32×C22⋊C8C22semidirect
53. #63648C22semidirect
54. #63648C22semidirect
55. C3×#821C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×C8×Dic3C22semidirect
60. #63575C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
90. #4732D3semidirect
91. #67⋊C8D3semidirect
157. #3714D4semidirect
171. C22×D12C2×D3semidirect
197. #930C2×D3semidirect
199. C22×C3⋊C8C2×D3semidirect
214. C2×D24C2×D3semidirect
215. C2×D24C2×D3semidirect
216. C2×D3×C8C2×D3semidirect
236. C3×C22⋊C8C2×D3semidirect
237. C3×C22⋊C8C2×D3semidirect
248. #821C2×D3semidirect
249. #821C2×D3semidirect
250. (C2×D3)⋊C8C2×D3semidirect
252. Dic3⋊C8C2×D3semidirect
253. C8×Dic3C2×D3semidirect
288. C4⋊(C3⋊D3)C2×D4semidirect
290. C3×#67D8semidirect
301. C3×D12C2×D4semidirect
317. C3×C3⋊C8C2×D4semidirect
478. C22×C32C2×D8semidirect
502. C2×C3×D3C2×D8semidirect
512. C3×Dic3C2×D8semidirect
556. C22⋊C8D32semidirect
645. #67D24semidirect
688. D12D3×D4semidirect
703. C3⋊C8D3×D4semidirect
800. C22×C3C2×D24semidirect
801. C22×C3D3×D8semidirect
850. C2×D3C2×D24semidirect
870. Dic3C2×D24semidirect
871. C32D4×D8semidirect
990. C22D3×D24semidirect
1001. C3D4×D24semidirect
1002. C3#80024semidirect

Maximal subgroups

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

subgroupindex
#105950742
D12×#672
C22×#37142
C2×D3×D242
#105924312
C3×#47322
C3×#67⋊C82
#105911642
#105909472
#105909442
#105908802
#105908262
#105907652
#105907532
#105907452
#800243
D4×D243