Finite Group Databasebeta

← #11865162

Subgroups — #11865162

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3#10595045C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5236C211yesmaximal, characteristic, complemented
6#10591685C214yesmaximal, complemented
7#10591666C214yesmaximal, complemented
8#10591111C211yesmaximal, characteristic, complemented
9#10591076C211yesmaximal, characteristic, complemented
10#84122—31nomaximal
11#78994—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
14C3×#1010—21no—
15C3×#1010C2212yescomplemented
16C3×#1009—21no—
17C3×#1009C2212yescomplemented
18C3×D3×#41—22no—
19C3×D3×#41—22no—
20C3×#1007—21no—
21C3×#1004—21no—
22C3×#1004—22no—
23C2×C3×#235—22no—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic
26#64158—22no—
27#64158C2214yescomplemented
28C2×#3755—21no—
29C2×#3753—21no—
30C2×#3748C2211yescharacteristic, complemented
31C3×#926C2211yescharacteristic, complemented
32C2×C3×#208C2211yescharacteristic, complemented
33#63981—22no—
34#63911C2212yescomplemented
35#63909—22no—
36#63864C2212yescomplemented
37C2×#3717—21no—
38#63825—22no—
39#63825C2214yescomplemented
40C2×#3714—21no—
41C3×#837C2214yescomplemented
42#63569C2214yescomplemented
43#63560C2212yescomplemented
44#63558C2212yescomplemented
45C3×#585—31no—
46#5964D311yescharacteristic, complemented
47#5830—31no—
48C2×#949—31no—
49C2×#949—31no—
50C2×#949—31no—
51C2×#949—61no—
52C2×#908—31no—
53#5525—31no—
54C3×#421—31no—
55#5245—34no—
56#5241—34no—
57#5237—31no—
58#5236—31no—
59#5236D311yescharacteristic, complemented
60#5132—31no—
61#5005—31no—
62#4827—34no—
63#4822—34no—
64C23×C3⋊D3—21no—
65C32×#41—21no—
66C32×#41—21no—
67C32×#41D412yescomplemented
68C32×#41C2312yes—
69C2×C32×Q8D411yescharacteristic, complemented
70C2×C32×D4—21no—
71C2×C32×D4D411yescharacteristic, complemented
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×C4⋊(C3⋊D3)—21no—
75C2×C4⋊(C3⋊D3)—21no—
76C2×C4⋊(C3⋊D3)—21no—
77C2×C4⋊(C3⋊D3)—21no—
78C2×C4⋊(C3⋊D3)—21no—
79C2×C4⋊(C3⋊D3)C2312yes—
80C2×C3×#67—24no—
81C2×C3×#67—21no—
82C2×C3×#67D412yes—
83C3×#239—22no—
84C3×#239—22no—
85C3×D3×Q8—22no—
86C3×D3×Q8—22no—
87C3×#237—24no—
88C3×#237—22no—
89C3×#237—22no—
90C3×#237—24no—
91C3×D3×D4—24no—
92C3×D3×D4—22no—
93C3×D3×D4—24no—
94C3×D3×D4—22no—
95C3×#235—24no—
96C3×#235—24no—
97C3×#235—21no—
98C3×#235—21no—
99C3×#235—21no—
100C3×#235—21no—
101C3×#235—21no—
102C3×#235—21no—
103C3×#235—22no—
104C3×#235—22no—
105C3×#235D412yescomplemented
106C3×#235C2312yes—
107C2×C3×D12—22no—
108C2×C3×D12D411yescharacteristic, complemented
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—24no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3D412yes—
113C2×C3×Dic6—22no—
114C2×C3×Dic6D411yescharacteristic, complemented
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—24no—
117#3755—24no—
118#3753—24no—
119#3748—21no—
120#3748C2312yes—
121C2×C3⋊(C3⋊C8)—21no—
122C3×#217—21no—
123C3×C4⋊Dic3—21no—
124C3×C4×Dic3C2312yes—
125C3×#208—21no—
126C3×#208C2312yes—
127C2×C3×C3⋊C8—21no—
128#3722—24no—
129#3717—24no—
130#3714—24no—
131#3021—91noSylow
132C3×2−1+4—32no—
133C3×2−1+4—61no—
134C3×2−1+4—61no—
135C3×H(5,𝔽2)—32no—
136C3×H(5,𝔽2)—62no—
137C3×H(5,𝔽2)—61no—
138C3×H(5,𝔽2)—61no—
139C2×C3×#41—21no—
140C2×C3×#41—31no—
141C2×C3×#41—31no—
142C2×C3×#41—62no—
143C2×C3×#41—62no—
144C2×C3×#41—62no—
145C2×C3×#41C2×D311yescharacteristic
146C2×C3×#41C2×D311yescharacteristic
147#1010—21no—
148#1010C2×D312yescomplemented
149#1009—21no—
150#1009C2×D312yescomplemented
151D3×#41—22no—
152D3×#41—22no—
153#1007—21no—
154#1004—21no—
155#1004—22no—
156C2×#235—22no—
157C2×#235C2×D311yescharacteristic
158C2×#235C2×D311yescharacteristic
159C22×D12—31no—
160C22×D12—31no—
161C22×D12—61no—
162C2×C3×M16—31no—
163C3×#117—31no—
164#949—34no—
165#949—34no—
166#949—34no—
167#949—64no—
168#949—62no—
169#949—64no—
170#949—62no—
171#949—62no—
172#947—32no—
173C2×#215—61no—
174C2×#215—62no—
175C2×#215—61no—
176C2×#215—61no—
177#940—32no—
178#937—62no—
179C2×#213—61no—
180C2×#213—62no—
181C2×#213—61no—
182C2×#213—61no—
183#930—62no—
184#926C2×D311yescharacteristic, complemented
185C2×#208—31no—
186C2×#208—31no—
187C2×#208—61no—
188C2×#208C2×D311yescharacteristic, complemented
189#908—34no—
190#908—62no—
191C2×D24—61no—
192C2×#204—61no—
193#895—62no—
194#882—62no—
195#875—32no—
196#874—32no—
197C3×#104—34no—
198#837—34no—
199#837C2×D314yescomplemented
200#836—32no—
201#833—32no—
202#824—32no—
203#823—32no—
204#805—34no—
205C23×C32—21no—
206C23×C32C2×D411yescharacteristic
207C22×C3⋊D3—22no—
208C22×C3⋊D3—41no—
209C22×C3⋊D3—41no—
210C22×C3⋊D3—82no—
211C22×C3×D3—24no—
212C22×C3×D3—21no—
213C22×C3×D3C2×D412yes—
214C32×Q8—21no—
215C32×Q8C2×D412yes—
216C32×D4—22no—
217C32×D4—22no—
218C32×D4—21no—
219C32×D4C2×D412yes—
220C2×C32×C4—21no—
221C2×C32×C4—22no—
222C2×C32×C4—22no—
223C2×C32×C4C2×D411yescharacteristic
224C2×C32×C4C2×D411yescharacteristic
225C2×C32×C4C2×D411yescharacteristic
226C2×C32×C4C2×D411yescharacteristic
227C2×C32×C4C2×D411yescharacteristic
228C2×C32×C4C2411yescharacteristic
229C4⋊(C3⋊D3)—22no—
230C4⋊(C3⋊D3)—22no—
231C4⋊(C3⋊D3)—41no—
232C4⋊(C3⋊D3)—41no—
233C3×#67—24no—
234C3×#67—24no—
235C3×#67—22no—
236C3×#67—22no—
237C3×#67—22no—
238C3×#67—22no—
239C2×C3×Dic3—24no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3C2×D412yes—
243C3×D12—24no—
244C3×D12—21no—
245C3×D12—21no—
246C3×D12—21no—
247C3×D12C2×D412yes—
248C3×C4×D3—24no—
249C3×C4×D3—24no—
250C3×C4×D3—22no—
251C3×C4×D3—22no—
252C3×C4×D3—22no—
253C3×C4×D3—22no—
254C3×Dic6—24no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6C2×D412yes—
259#626—84no—
260C3⋊(C3⋊C8)—22no—
261C3×C3⋊C8—22no—
262#585—31no—
263C2×AGL(1,ℤ/8)—91no—
264C2×AGL(1,ℤ/8)—91no—
265#535—91no—
266#454—94no—
267#453—94no—
268#421—31no—
269#421—91no—
270#413—91no—
271C23×D3—61no—
272C23×D3—61no—
273C23×D3—121no—
274C3×#41—21no—
275C3×#41—21no—
276C3×#41—21no—
277C3×#41—21no—
278C3×#41—22no—
279C3×#41—22no—
280C3×#41—32no—
281C3×#41—32no—
282C3×#41—41no—
283C3×#41—41no—
284C3×#41—62no—
285C3×#41—62no—
286C3×#41—64no—
287C3×#41—64no—
288C3×#41—64no—
289C3×#41—64no—
290C3×#41—62no—
291C3×#41—62no—
292C3×#41—62no—
293C3×#41—62no—
294C3×#41—61no—
295C3×#41—61no—
296C3×#41—61no—
297C3×#41—61no—
298C3×#41—61no—
299C3×#41—61no—
300C3×#41D1212yescomplemented
301C3×#41#6712yescomplemented
302C3×#41C22×D312yes—
303C3×#41C22×D312yes—
304C2×C3×Q8—21no—
305C2×C3×Q8—31no—
306C2×C3×Q8—31no—
307C2×C3×Q8—62no—
308C2×C3×Q8—62no—
309C2×C3×Q8—62no—
310C2×C3×Q8D1211yescharacteristic, complemented
311C2×C3×Q8#6711yescharacteristic, complemented
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—32no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—41no—
319C2×C3×D4—62no—
320C2×C3×D4—64no—
321C2×C3×D4—64no—
322C2×C3×D4—62no—
323C2×C3×D4—64no—
324C2×C3×D4—61no—
325C2×C3×D4—62no—
326C2×C3×D4D1211yescharacteristic, complemented
327C2×C3×D4#6711yescharacteristic, complemented
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—32no—
332C22×C3×C4—41no—
333C22×C3×C4—64no—
334C22×C3×C4—61no—
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C2×#67—24no—
338C2×#67—21no—
339C2×#67—64no—
340C2×#67#6712yes—
341#239—22no—
342#239—22no—
343D3×Q8—22no—
344D3×Q8—22no—
345#237—24no—
346#237—22no—
347#237—22no—
348#237—24no—
349D3×D4—24no—
350D3×D4—22no—
351D3×D4—24no—
352D3×D4—22no—
353#235—24no—
354#235—24no—
355#235—21no—
356#235—21no—
357#235—21no—
358#235—21no—
359#235—21no—
360#235—21no—
361#235—22no—
362#235—22no—
363#235#6712yescomplemented
364#235C22×D312yes—
365C2×D12—22no—
366C2×D12—32no—
367C2×D12—32no—
368C2×D12—62no—
369C2×D12—62no—
370C2×D12—62no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—64no—
382C2×D12—121no—
383C2×D12—121no—
384C2×D12—121no—
385C2×D12#6711yescharacteristic, complemented
386C2×D12C22×D311yescharacteristic
387C2×C4×D3—24no—
388C2×C4×D3—21no—
389C2×C4×D3#6712yes—
390C2×Dic6—22no—
391C2×Dic6#6711yescharacteristic, complemented
392C2×Dic6C22×D311yescharacteristic
393C3×M16—32no—
394C3×M16—61no—
395C2×C3×C8—61no—
396C3×C4⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C42—32no—
399#217—21no—
400#215—64no—
401#215—68no—
402#215—64no—
403#215—64no—
404#213—64no—
405#213—68no—
406#213—64no—
407#213—64no—
408(C2×D3)⋊C4—64no—
409(C2×D3)⋊C4—64no—
410C4⋊Dic3—21no—
411C4×Dic3C22×D312yes—
412#208—21no—
413#208—32no—
414#208—32no—
415#208—62no—
416#208—62no—
417#208—61no—
418#208—61no—
419#208C22×D312yes—
420C2×C3⋊C8—21no—
421C2×C3⋊C8—62no—
422C2×C3⋊C8—61no—
423C2×C3⋊C8—61no—
424D24—64no—
425#204—64no—
426C22×C32—22no—
427C22×C32—41no—
428C22×C32—81no—
429C22×C32#12011yescharacteristic
430C22×C32#12011yescharacteristic
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—42no—
433C2×C3⋊D3—44no—
434C2×C3⋊D3—82no—
435C2×C3⋊D3—82no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—42no—
439C2×C3×D3—81no—
440C2×C3×D3—84no—
441C32×C4—22no—
442C32×C4#12011yescharacteristic
443C32×C4#12011yescharacteristic
444C32×C4C22×D411yescharacteristic
445C32×C4C22×D411yescharacteristic
446C3×Dic3—22no—
447C3×Dic3—22no—
448C3×Dic3—42no—
4492−1+4—32no—
4502−1+4—61no—
4512−1+4—61no—
452H(5,𝔽2)—32no—
453H(5,𝔽2)—62no—
454H(5,𝔽2)—61no—
455H(5,𝔽2)—61no—
456C2×#41—31no—
457C2×#41—31no—
458C2×#41—62no—
459C2×#41—62no—
460C2×#41—62no—
461C2×#41D3211yescharacteristic
462C22×D4—91no—
463AGL(1,ℤ/8)—94no—
464AGL(1,ℤ/8)—94no—
465AGL(1,ℤ/8)—182no—
466AGL(1,ℤ/8)—182no—
467C2×SD16—181no—
468C2×SD16—181no—
469C2×D8—181no—
470C2×D8—181no—
471C2×M16—31no—
472C2×M16—91no—
473#127—92no—
474#124—92no—
475#121—182no—
476#120—182no—
477#117—31no—
478#104—34no—
479#104—94no—
480#101—92no—
481#100—92no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—32no—
486C23×C3—41no—
487C23×C3—64no—
488C23×C3—61no—
489C23×C3D3×D411yescharacteristic
490C23×C3C2×#6711yescharacteristic
491C22×D3—24no—
492C22×D3—21no—
493C22×D3—62no—
494C22×D3—62no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—121no—
499C22×D3—121no—
500C22×D3—121no—
501C22×D3—121no—
502C22×D3—242no—
503C22×D3—242no—
504C22×D3—244no—
505C22×D3C2×#6712yes—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—22no—
509C3×Q8—32no—
510C3×Q8—41no—
511C3×Q8—64no—
512C3×Q8—61no—
513C3×Q8—61no—
514C3×Q8—61no—
515C3×Q8C2×D1212yes—
516C3×Q8C2×#6712yes—
517C3×D4—22no—
518C3×D4—22no—
519C3×D4—22no—
520C3×D4—22no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—22no—
524C3×D4—32no—
525C3×D4—41no—
526C3×D4—42no—
527C3×D4—42no—
528C3×D4—64no—
529C3×D4—64no—
530C3×D4—64no—
531C3×D4—62no—
532C3×D4—62no—
533C3×D4—62no—
534C3×D4—62no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4C2×D1212yes—
539C3×D4C2×#6712yes—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—32no—
553C2×C3×C4—42no—
554C2×C3×C4—42no—
555C2×C3×C4—41no—
556C2×C3×C4—64no—
557C2×C3×C4—64no—
558C2×C3×C4—64no—
559C2×C3×C4—61no—
560C2×C3×C4—62no—
561C2×C3×C4—62no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—62no—
565C2×C3×C4C2×D1211yescharacteristic
566C2×C3×C4C2×D1211yescharacteristic
567C2×C3×C4D3×D411yescharacteristic
568C2×C3×C4D3×D411yescharacteristic
569C2×C3×C4D3×D411yescharacteristic
570C2×C3×C4C2×#6711yescharacteristic
571C2×C3×C4C2×#6711yescharacteristic
572C2×C3×C4C2×#6711yescharacteristic
573C2×C3×C4C2×#6711yescharacteristic
574C2×C3×C4C2×#6711yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—24no—
578#67—24no—
579#67—22no—
580#67—22no—
581#67—22no—
582#67—22no—
583#67—244no—
584C2×Dic3—24no—
585C2×Dic3—21no—
586C2×Dic3—22no—
587C2×Dic3C2×#6712yes—
588D12—24no—
589D12—21no—
590D12—21no—
591D12—21no—
592D12—64no—
593D12—62no—
594D12—62no—
595D12—62no—
596D12—62no—
597D12—122no—
598D12—122no—
599D12—122no—
600D12—121no—
601D12—121no—
602D12—121no—
603D12—121no—
604D12—244no—
605D12C2×#6712yes—
606C4×D3—24no—
607C4×D3—24no—
608C4×D3—22no—
609C4×D3—22no—
610C4×D3—22no—
611C4×D3—22no—
612Dic6—24no—
613Dic6—21no—
614Dic6—21no—
615Dic6—21no—
616Dic6C2×#6712yes—
617C3×C8—62no—
618C3⋊C8—22no—
619C3⋊C8—64no—
620C3⋊C8—62no—
621C3⋊C8—62no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—42no—
626C2×C32C2×#12011yescharacteristic
627C3⋊D3—82no—
628C3×D3—42no—
629C3×D3—42no—
630C24—181no—
631#41—21no—
632#41—21no—
633#41—32no—
634#41—32no—
635#41—62no—
636#41—62no—
637#41—64no—
638#41—64no—
639#41—64no—
640#41—64no—
641#41—62no—
642#41—62no—
643#41—62no—
644#41—62no—
645#41—61no—
646#41—61no—
647#41—61no—
648#41—61no—
649#41—61no—
650#41—61no—
651#41#62612yescomplemented
652#41C2×D3212yes—
653C2×Q8—31no—
654C2×Q8—31no—
655C2×Q8—62no—
656C2×Q8—62no—
657C2×Q8—62no—
658C2×Q8#62611yescharacteristic, complemented
659C2×D4—21no—
660C2×D4—32no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—62no—
664C2×D4—64no—
665C2×D4—64no—
666C2×D4—62no—
667C2×D4—64no—
668C2×D4—61no—
669C2×D4—62no—
670C2×D4—92no—
671C2×D4—184no—
672C2×D4—181no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—181no—
676C2×D4—181no—
677C2×D4#62611yescharacteristic, complemented
678C22×C4—21no—
679C22×C4—32no—
680C22×C4—64no—
681C22×C4—61no—
682C22×C4C2×D3211yescharacteristic
683SD16—184no—
684SD16—184no—
685D8—184no—
686D8—184no—
687M16—32no—
688M16—61no—
689M16—92no—
690M16—181no—
691C2×C8—61no—
692C2×C8—181no—
693C4⋊C4—61no—
694C22⋊C4—61no—
695C22⋊C4—184no—
696C42—32no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—42no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—42no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—82no—
711C22×C3—122no—
712C22×C3—241no—
713C22×C3—244no—
714C22×C3#88211yescharacteristic
715C22×C3#88211yescharacteristic
716C22×C3#95311yescharacteristic
717C22×C3#95311yescharacteristic
718C22×C3C2×D3×D411yescharacteristic
719C22×C3C22×#6711yescharacteristic
720C2×D3—22no—
721C2×D3—22no—
722C2×D3—42no—
723C2×D3—81no—
724C2×D3—84no—
725C2×D3—124no—
726C2×D3—124no—
727C2×D3—124no—
728C2×D3—122no—
729C2×D3—122no—
730C2×D3—244no—
731C2×D3—244no—
732C2×D3—242no—
733C2×D3—242no—
734C2×D3—242no—
735C2×D3—242no—
736C2×D3—244no—
737C3×C4—22no—
738C3×C4—22no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—42no—
744C3×C4—62no—
745C3×C4—62no—
746C3×C4—122no—
747C3×C4#88211yescharacteristic
748C3×C4#88211yescharacteristic
749C3×C4#95311yescharacteristic
750C3×C4#95311yescharacteristic
751C3×C4C22×D1211yescharacteristic
752C3×C4C2×D3×D411yescharacteristic
753C3×C4C22×#6711yescharacteristic
754C3×C4C22×#6711yescharacteristic
755Dic3—22no—
756Dic3—22no—
757Dic3—42no—
758C32#302111yescharacteristic, complemented, Sylow
759C23—21no—
760C23—32no—
761C23—64no—
762C23—61no—
763C23—182no—
764C23—361no—
765C23—361no—
766C23—722no—
767C23D3×#6711yescharacteristic
768Q8—21no—
769Q8—32no—
770Q8—64no—
771Q8—61no—
772Q8—61no—
773Q8—61no—
774Q8C2×#62612yes—
775D4—22no—
776D4—22no—
777D4—21no—
778D4—32no—
779D4—64no—
780D4—64no—
781D4—64no—
782D4—62no—
783D4—62no—
784D4—62no—
785D4—62no—
786D4—61no—
787D4—61no—
788D4—61no—
789D4—182no—
790D4—182no—
791D4—361no—
792D4—361no—
793D4—724no—
794D4C2×#62612yes—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—32no—
799C2×C4—64no—
800C2×C4—64no—
801C2×C4—64no—
802C2×C4—61no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—62no—
807C2×C4—62no—
808C2×C4C2×#62611yescharacteristic
809C2×C4C2×#62611yescharacteristic
810C2×C4D3×#6711yescharacteristic
811C2×C4D3×#6711yescharacteristic
812C2×C4D3×#6711yescharacteristic
813C2×C4C22×D3211yescharacteristic
814C8—62no—
815C8—182no—
816C2×C3—22no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—41no—
825C2×C3—41no—
826C2×C3—42no—
827C2×C3—42no—
828C2×C3—82no—
829C2×C3—122no—
830C2×C3—122no—
831C2×C3C2×#88211yescharacteristic
832C2×C3C2×#95311yescharacteristic
833D3—42no—
834D3—42no—
835D3—244no—
836D3—242no—
837D3—242no—
838C22—22no—
839C22—41no—
840C22—62no—
841C22—62no—
842C22—81no—
843C22—122no—
844C22—241no—
845C22—244no—
846C22—364no—
847C22—362no—
848C22—722no—
849C22—722no—
850C22#6397711yescharacteristic
851C22#6397711yescharacteristic
852C22C2×D3×#6711yescharacteristic
853C4—22no—
854C4—62no—
855C4—62no—
856C4—122no—
857C4#6397711yescharacteristic
858C4#6397711yescharacteristic
859C4C22×#62611yescharacteristic
860C4C2×D3×#6711yescharacteristic
861C3—21no—
862C3#7899411yescharacteristic, complemented
863C3#8412211yescharacteristic, complemented
864C2—21no—
865C2—21no—
866C2—21no—
867C2—42no—
868C2—122no—
869C2—122no—
870C2—722no—
871C2C2×#6397711yescharacteristic
subgroupG/H
centerC2C2×#63977
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3021
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. C2×#64158C2semidirect
3. #10595045C2semidirect
4. C2×#63825C2semidirect
5. C3×#5236C2semidirect
6. #10591685C2semidirect
7. #10591666C2semidirect
8. #10591111C2semidirect
9. #10591076C2semidirect
13. C22×C4⋊(C3⋊D3)C22semidirect
15. C3×#1010C22semidirect
17. C3×#1009C22semidirect
27. #64158C22semidirect
30. C2×#3748C22semidirect
31. C3×#926C22semidirect
32. C2×C3×#208C22semidirect
34. #63911C22semidirect
36. #63864C22semidirect
39. #63825C22semidirect
41. C3×#837C22semidirect
42. #63569C22semidirect
43. #63560C22semidirect
44. #63558C22semidirect
46. #5964D3semidirect
59. #5236D3semidirect
67. C32×#41D4semidirect
69. C2×C32×Q8D4semidirect
71. C2×C32×D4D4semidirect
105. C3×#235D4semidirect
108. C2×C3×D12D4semidirect
114. C2×C3×Dic6D4semidirect
148. #1010C2×D3semidirect
150. #1009C2×D3semidirect
184. #926C2×D3semidirect
188. C2×#208C2×D3semidirect
199. #837C2×D3semidirect
300. C3×#41D12semidirect
301. C3×#41#67semidirect
310. C2×C3×Q8D12semidirect
311. C2×C3×Q8#67semidirect
326. C2×C3×D4D12semidirect
327. C2×C3×D4#67semidirect
363. #235#67semidirect
385. C2×D12#67semidirect
391. C2×Dic6#67semidirect
651. #41#626semidirect
658. C2×Q8#626semidirect
677. C2×D4#626semidirect
758. C32#3021semidirect
862. C3#78994semidirect
863. C3#84122semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C2×#641582
#105950452
C2×#638252
C3×#52362
#105916852
#105916662
#105911112
#105910762
#841223
#789943