Finite Group Databasebeta

← #11865055

Subgroups — #11865055

Order 1152.

1655 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2#10596293C211yesmaximal, characteristic, complemented
3#10595042C211yesmaximal, characteristic, complemented
4#10594795C211yesmaximal, characteristic, complemented
5C3×#5236C211yesmaximal, characteristic, complemented
6#10591688C214yesmaximal, complemented
7#10591666C214yesmaximal, complemented
8#10591111C211yesmaximal, characteristic, complemented
9C2×#63558C211yesmaximal, characteristic, complemented
10#84104—31nomaximal
11#78993—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×#3828C2211yescharacteristic, complemented
14C3×#1009—22no—
15C3×#1009—22no—
16C3×#1009—22no—
17C3×#1009C2214yes—
18C2×C3×#239—21no—
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4—22no—
21C2×C3×#235—21no—
22C2×C3×#235C2211yescharacteristic
23C22×C3×D12—21no—
24C22×C3×D12C2211yescharacteristic
25#64160C2212yescomplemented
26#64159—22no—
27#64158C2212yescomplemented
28#64151—21no—
29#64141—21no—
30C2×#3748C2211yescharacteristic, complemented
31C3×#926C2211yescharacteristic, complemented
32C2×C3×#208C2211yescharacteristic, complemented
33#63977—22no—
34#63916—22no—
35#63911C2212yescomplemented
36#63860C2212yescomplemented
37#63833—21no—
38#63831C2212yescomplemented
39#63830—21no—
40#63829—22no—
41#63825C2212yescomplemented
42C3×#837C2214yescomplemented
43#63569C2214yescomplemented
44#63558C2214yescomplemented
45C2×C3×H(5,𝔽2)—31no—
46C2×#1009D311yescharacteristic, complemented
47#5822—31no—
48#5822—31no—
49#5822—31no—
50#5822—61no—
51#5805—31no—
52#5748—31no—
53#5525—31no—
54C3×#421—31no—
55#5242—34no—
56#5241—34no—
57#5236—31no—
58#5236D311yescharacteristic, complemented
59C2×#833—31no—
60C2×#823—31no—
61#5005—31no—
62#4825—34no—
63#4822—34no—
64C23×C3×D3—22no—
65C23×C3×D3D412yes—
66C32×#41—21no—
67C32×#41—21no—
68C32×#41D412yescomplemented
69C32×#41C2312yes—
70C2×C32×Q8D411yescharacteristic, complemented
71C2×C32×D4—21no—
72C2×C32×D4D411yescharacteristic, complemented
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76#3828—21no—
77#3828—21no—
78#3828—21no—
79#3828—21no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
81C2×C4×C3⋊D3—21no—
82C2×#634C2311yescharacteristic, complemented
83C2×C3×#67—22no—
84C2×C3×#67—21no—
85C3×#239—24no—
86C3×#239—24no—
87C3×D3×D4—28no—
88C3×D3×D4—24no—
89C3×D3×D4—28no—
90C3×D3×D4—24no—
91C3×#235—24no—
92C3×#235—21no—
93C3×#235—21no—
94C3×#235—24no—
95C3×#235D412yescomplemented
96C3×#235C2312yes—
97C2×C3×D12—22no—
98C2×C3×D12—24no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12—24no—
104C2×C3×D12D412yes—
105C2×C3×D12D411yescharacteristic, complemented
106C2×C3×D12C2312yes—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—21no—
109C2×C3×Dic6D411yescharacteristic, complemented
110C2×#626—24no—
111#3756—22no—
112#3755—22no—
113#3754—22no—
114#3753—22no—
115#3748—21no—
116#3748C2312yescomplemented
117C2×C3⋊(C3⋊C8)—21no—
118C3×#217—21no—
119C3×C4⋊Dic3—21no—
120C3×C4×Dic3C2312yescomplemented
121C3×#208—21no—
122C3×#208C2312yescomplemented
123C2×C3×C3⋊C8—21no—
124(C2×D3)⋊Dic3—24no—
125#3719—22no—
126#3717—22no—
127#3716—22no—
128#3714—22no—
129#3019—91noSylow
130C3×H(5,𝔽2)—34no—
131C3×H(5,𝔽2)—62no—
132C3×H(5,𝔽2)—62no—
133C3×H(5,𝔽2)—62no—
134C2×C3×#41—21no—
135C2×C3×#41—31no—
136C2×C3×#41—61no—
137C2×C3×#41—61no—
138C2×C3×#41C2×D311yescharacteristic
139C2×C3×#41C2×D311yescharacteristic
140C22×C3×D4—31no—
141C22×C3×D4—61no—
142C22×C3×D4—62no—
143C22×C3×D4—61no—
144#1009—22no—
145#1009—22no—
146#1009—22no—
147#1009C2×D314yes—
148C2×#239—21no—
149C2×D3×D4—22no—
150C2×D3×D4—21no—
151C2×#235—21no—
152C2×#235—31no—
153C2×#235—31no—
154C2×#235—61no—
155C2×#235C2×D311yescharacteristic
156C22×D12—21no—
157C22×D12C2×D311yescharacteristic
158C2×C3×M16—31no—
159C3×#117—31no—
160#953—62no—
161#951—32no—
162#951—32no—
163#951—32no—
164#951—62no—
165#950—62no—
166#950—64no—
167#950—62no—
168#950—62no—
169#949—32no—
170#949—32no—
171#949—32no—
172#949—62no—
173#942—61no—
174#942—62no—
175#942—61no—
176#942—61no—
177#940—32no—
178#938—62no—
179#936—32no—
180#932—61no—
181#932—62no—
182#932—61no—
183#932—61no—
184#926C2×D311yescharacteristic, complemented
185C2×#208—31no—
186C2×#208—31no—
187C2×#208—61no—
188C2×#208C2×D311yescharacteristic, complemented
189#909—32no—
190#909—61no—
191#908—32no—
192#908—61no—
193#904—62no—
194#895—62no—
195#882—62no—
196#875—32no—
197#874—32no—
198C3×#104—34no—
199#837—34no—
200#837C2×D314yescomplemented
201#833—34no—
202#823—34no—
203#805—34no—
204C23×C32—21no—
205C23×C32C2×D411yescharacteristic
206C22×C3⋊D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—22no—
209C22×C3×D3—28no—
210C22×C3×D3—22no—
211C22×C3×D3—82no—
212C22×C3×D3—84no—
213C22×C3×D3C2×D414yes—
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
229#638—41no—
230#638—41no—
231C2×C3⋊Dic3—21no—
232C4⋊(C3⋊D3)—21no—
233C4⋊(C3⋊D3)—21no—
234C4×C3⋊D3—41no—
235C4×C3⋊D3—41no—
236#634—21no—
237#634—21no—
238C3×#67—28no—
239C3×#67—22no—
240C3×#67—22no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—22no—
243C3×D12—28no—
244C3×D12—22no—
245C3×D12—21no—
246C3×D12—22no—
247C3×D12—22no—
248C3×D12—22no—
249C3×D12C2×D412yes—
250C3×C4×D3—28no—
251C3×C4×D3—22no—
252C3×C4×D3—22no—
253C3×Dic6—21no—
254C3×Dic6C2×D412yes—
255#626—84no—
256C3⋊(C3⋊C8)—22no—
257C3×C3⋊C8—22no—
258C2×H(5,𝔽2)—31no—
259#575—91no—
260#575—91no—
261#535—91no—
262#455—94no—
263#453—94no—
264#421—31no—
265#421—91no—
266C2×#100—91no—
267C24×C3—32no—
268C24×C3—62no—
269C23×D3—22no—
270C23×D3#6712yes—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—21no—
275C3×#41—22no—
276C3×#41—22no—
277C3×#41—32no—
278C3×#41—32no—
279C3×#41—41no—
280C3×#41—41no—
281C3×#41—64no—
282C3×#41—64no—
283C3×#41—64no—
284C3×#41—64no—
285C3×#41—61no—
286C3×#41—61no—
287C3×#41D1212yescomplemented
288C3×#41#6712yescomplemented
289C3×#41C22×D312yes—
290C3×#41C22×D312yes—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8D1211yescharacteristic, complemented
294C2×C3×Q8#6711yescharacteristic, complemented
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—32no—
300C2×C3×D4—32no—
301C2×C3×D4—41no—
302C2×C3×D4—64no—
303C2×C3×D4—62no—
304C2×C3×D4—64no—
305C2×C3×D4—68no—
306C2×C3×D4—68no—
307C2×C3×D4—64no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—64no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4D1211yescharacteristic, complemented
316C2×C3×D4#6711yescharacteristic, complemented
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—41no—
321C22×C3×C4—62no—
322C22×C3×C4—61no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—22no—
326C2×#67—21no—
327C2×#67—64no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—121no—
331#239—24no—
332#239—24no—
333D3×D4—28no—
334D3×D4—24no—
335D3×D4—28no—
336D3×D4—24no—
337#235—24no—
338#235—21no—
339#235—21no—
340#235—24no—
341#235—62no—
342#235—62no—
343#235—61no—
344#235—61no—
345#235—61no—
346#235—61no—
347#235—61no—
348#235—61no—
349#235—61no—
350#235—61no—
351#235—121no—
352#235—121no—
353#235#6712yescomplemented
354#235C22×D312yes—
355C2×D12—22no—
356C2×D12—24no—
357C2×D12—21no—
358C2×D12—21no—
359C2×D12—21no—
360C2×D12—21no—
361C2×D12—24no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—61no—
365C2×D12—64no—
366C2×D12#6712yes—
367C2×D12#6711yescharacteristic, complemented
368C2×D12C22×D312yes—
369C2×C4×D3—22no—
370C2×C4×D3—21no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—121no—
374C2×Dic6—31no—
375C2×Dic6—31no—
376C2×Dic6—61no—
377C2×Dic6#6711yescharacteristic, complemented
378C3×M16—32no—
379C3×M16—61no—
380C2×C3×C8—61no—
381C3×C4⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C42—32no—
384#217—21no—
385#217—64no—
386#216—62no—
387#216—64no—
388#216—62no—
389#216—62no—
390#215—62no—
391#215—64no—
392#215—62no—
393#215—62no—
394#214—62no—
395#214—64no—
396#214—62no—
397#214—62no—
398#213—62no—
399#213—64no—
400#213—62no—
401#213—62no—
402(C2×D3)⋊C4—64no—
403C4⋊Dic3—21no—
404C4×Dic3C22×D312yescomplemented
405#208—21no—
406#208—32no—
407#208—32no—
408#208—62no—
409#208—62no—
410#208—61no—
411#208—61no—
412#208C22×D312yescomplemented
413C2×C3⋊C8—21no—
414C2×C3⋊C8—62no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—61no—
417Dic12—62no—
418D24—62no—
419#204—62no—
420#204—62no—
421C22×C32—22no—
422C22×C32—41no—
423C22×C32—42no—
424C22×C32#12011yescharacteristic
425C22×C32#12011yescharacteristic
426C22×C32C22×D411yescharacteristic
427C2×C3⋊D3—41no—
428C2×C3⋊D3—42no—
429C2×C3×D3—24no—
430C2×C3×D3—22no—
431C2×C3×D3—44no—
432C2×C3×D3—42no—
433C2×C3×D3—44no—
434C2×C3×D3—82no—
435C2×C3×D3—88no—
436C32×C4—22no—
437C32×C4#12011yescharacteristic
438C32×C4#12011yescharacteristic
439C32×C4C22×D411yescharacteristic
440C32×C4C22×D411yescharacteristic
441C3⋊Dic3—41no—
442C3×Dic3—22no—
443C3×Dic3—42no—
444H(5,𝔽2)—34no—
445H(5,𝔽2)—62no—
446H(5,𝔽2)—62no—
447H(5,𝔽2)—62no—
448C2×#41—31no—
449C2×#41—61no—
450C2×#41—61no—
451C2×#41—91no—
452C2×#41D3211yescharacteristic
453C22×D4—31no—
454C22×D4—61no—
455C22×D4—62no—
456C22×D4—61no—
457#137—92no—
458#137—92no—
459#137—181no—
460#137—181no—
461AGL(1,ℤ/8)—92no—
462AGL(1,ℤ/8)—92no—
463AGL(1,ℤ/8)—181no—
464AGL(1,ℤ/8)—181no—
465#135—182no—
466#135—182no—
467C2×M16—31no—
468C2×M16—91no—
469#127—92no—
470#124—92no—
471#121—182no—
472#120—182no—
473#117—31no—
474#104—34no—
475#104—94no—
476#100—94no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—34no—
481C23×C3—41no—
482C23×C3—68no—
483C23×C3—61no—
484C23×C3—62no—
485C23×C3—62no—
486C23×C3—242no—
487C23×C3—244no—
488C23×C3D3×D411yescharacteristic
489C23×C3C2×#6711yescharacteristic
490C22×D3—22no—
491C22×D3—21no—
492C22×D3—28no—
493C22×D3—22no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—82no—
497C22×D3—84no—
498C22×D3—121no—
499C22×D3C2×#6714yes—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—22no—
503C3×Q8—32no—
504C3×Q8—41no—
505C3×Q8—61no—
506C3×Q8C2×D1212yes—
507C3×Q8C2×#6712yes—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—22no—
511C3×D4—22no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—22no—
515C3×D4—32no—
516C3×D4—41no—
517C3×D4—42no—
518C3×D4—42no—
519C3×D4—68no—
520C3×D4—68no—
521C3×D4—62no—
522C3×D4—62no—
523C3×D4—61no—
524C3×D4—62no—
525C3×D4—62no—
526C3×D4—62no—
527C3×D4—62no—
528C3×D4C2×D1212yes—
529C3×D4C2×#6712yes—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—42no—
543C2×C3×C4—42no—
544C2×C3×C4—41no—
545C2×C3×C4—68no—
546C2×C3×C4—61no—
547C2×C3×C4—62no—
548C2×C3×C4—62no—
549C2×C3×C4—62no—
550C2×C3×C4C2×D1211yescharacteristic
551C2×C3×C4C2×D1211yescharacteristic
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4C2×#6711yescharacteristic
556C2×C3×C4C2×#6711yescharacteristic
557C2×C3×C4C2×#6711yescharacteristic
558C2×C3×C4C2×#6711yescharacteristic
559C2×C3×C4C2×#6711yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—28no—
563#67—22no—
564#67—22no—
565#67—122no—
566#67—122no—
567#67—121no—
568#67—121no—
569#67—121no—
570#67—121no—
571#67—244no—
572C2×Dic3—21no—
573C2×Dic3—22no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—121no—
577D12—28no—
578D12—22no—
579D12—21no—
580D12—22no—
581D12—22no—
582D12—22no—
583D12—62no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—121no—
589D12—244no—
590D12C2×#6712yes—
591C4×D3—28no—
592C4×D3—22no—
593C4×D3—22no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3—121no—
597C4×D3—121no—
598C4×D3—121no—
599C4×D3—121no—
600Dic6—21no—
601Dic6—62no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—61no—
606Dic6—121no—
607Dic6C2×#6712yes—
608C3×C8—62no—
609C3⋊C8—22no—
610C3⋊C8—64no—
611C3⋊C8—62no—
612C3⋊C8—62no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—42no—
617C2×C32C2×#12011yescharacteristic
618C3⋊D3—81no—
619C3×D3—44no—
620C3×D3—42no—
621C24—32no—
622C24—62no—
623#41—21no—
624#41—21no—
625#41—32no—
626#41—32no—
627#41—64no—
628#41—64no—
629#41—64no—
630#41—64no—
631#41—61no—
632#41—61no—
633#41—181no—
634#41—181no—
635#41—181no—
636#41—181no—
637#41#62612yescomplemented
638#41C2×D3212yes—
639C2×Q8—31no—
640C2×Q8—91no—
641C2×Q8#62611yescharacteristic, complemented
642C2×D4—21no—
643C2×D4—32no—
644C2×D4—31no—
645C2×D4—32no—
646C2×D4—64no—
647C2×D4—62no—
648C2×D4—64no—
649C2×D4—68no—
650C2×D4—68no—
651C2×D4—64no—
652C2×D4—62no—
653C2×D4—61no—
654C2×D4—64no—
655C2×D4—61no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—61no—
659C2×D4—91no—
660C2×D4—184no—
661C2×D4—181no—
662C2×D4#62611yescharacteristic, complemented
663C22×C4—21no—
664C22×C4—62no—
665C22×C4—61no—
666C22×C4—181no—
667C22×C4C2×D3211yescharacteristic
668Q16—182no—
669Q16—182no—
670SD16—182no—
671SD16—182no—
672SD16—182no—
673SD16—182no—
674D8—182no—
675D8—182no—
676M16—32no—
677M16—61no—
678M16—92no—
679M16—181no—
680C2×C8—61no—
681C2×C8—181no—
682C4⋊C4—61no—
683C22⋊C4—61no—
684C22⋊C4—184no—
685C42—32no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—42no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—62no—
697C22×C3—64no—
698C22×C3—81no—
699C22×C3—82no—
700C22×C3—124no—
701C22×C3—124no—
702C22×C3—122no—
703C22×C3—242no—
704C22×C3—248no—
705C22×C3#88211yescharacteristic
706C22×C3#88211yescharacteristic
707C22×C3#95311yescharacteristic
708C22×C3#95311yescharacteristic
709C22×C3C2×D3×D411yescharacteristic
710C22×C3C22×#6711yescharacteristic
711C2×D3—24no—
712C2×D3—22no—
713C2×D3—44no—
714C2×D3—42no—
715C2×D3—44no—
716C2×D3—82no—
717C2×D3—88no—
718C2×D3—122no—
719C2×D3—122no—
720C2×D3—122no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—242no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—42no—
731C3×C4—62no—
732C3×C4—122no—
733C3×C4#88211yescharacteristic
734C3×C4#88211yescharacteristic
735C3×C4#95311yescharacteristic
736C3×C4#95311yescharacteristic
737C3×C4C22×D1211yescharacteristic
738C3×C4C2×D3×D411yescharacteristic
739C3×C4C22×#6711yescharacteristic
740C3×C4C22×#6711yescharacteristic
741Dic3—22no—
742Dic3—42no—
743Dic3—122no—
744Dic3—121no—
745Dic3—121no—
746C32#301911yescharacteristic, complemented, Sylow
747C23—21no—
748C23—34no—
749C23—68no—
750C23—61no—
751C23—62no—
752C23—62no—
753C23—181no—
754C23—242no—
755C23—244no—
756C23D3×#6711yescharacteristic
757Q8—21no—
758Q8—32no—
759Q8—61no—
760Q8—181no—
761Q8—181no—
762Q8C2×#62612yes—
763D4—22no—
764D4—22no—
765D4—21no—
766D4—32no—
767D4—68no—
768D4—68no—
769D4—62no—
770D4—62no—
771D4—62no—
772D4—62no—
773D4—61no—
774D4—62no—
775D4—62no—
776D4—181no—
777D4—181no—
778D4—361no—
779D4—361no—
780D4—724no—
781D4C2×#62612yes—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—68no—
786C2×C4—61no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—181no—
791C2×C4—361no—
792C2×C4—361no—
793C2×C4C2×#62611yescharacteristic
794C2×C4C2×#62611yescharacteristic
795C2×C4D3×#6711yescharacteristic
796C2×C4D3×#6711yescharacteristic
797C2×C4D3×#6711yescharacteristic
798C2×C4C22×D3211yescharacteristic
799C8—62no—
800C8—182no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—41no—
809C2×C3—41no—
810C2×C3—41no—
811C2×C3—42no—
812C2×C3—42no—
813C2×C3—82no—
814C2×C3—124no—
815C2×C3—122no—
816C2×C3C2×#88211yescharacteristic
817C2×C3C2×#95311yescharacteristic
818D3—44no—
819D3—42no—
820D3—242no—
821D3—241no—
822D3—241no—
823C22—22no—
824C22—41no—
825C22—42no—
826C22—62no—
827C22—64no—
828C22—124no—
829C22—124no—
830C22—122no—
831C22—242no—
832C22—248no—
833C22—362no—
834C22—361no—
835C22#6397711yescharacteristic
836C22#6397711yescharacteristic
837C22C2×D3×#6711yescharacteristic
838C4—22no—
839C4—62no—
840C4—122no—
841C4—361no—
842C4#6397711yescharacteristic
843C4#6397711yescharacteristic
844C4C22×#62611yescharacteristic
845C4C2×D3×#6711yescharacteristic
846C3—21no—
847C3#7899311yescharacteristic, complemented
848C3#8410411yescharacteristic, complemented
849C2—21no—
850C2—21no—
851C2—21no—
852C2—42no—
853C2—124no—
854C2—122no—
855C2—721no—
856C2C2×#6397711yescharacteristic
subgroupG/H
centerC2C2×#63977
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3019
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. C2×C3×#1009C2semidirect
2. #10596293C2semidirect
3. #10595042C2semidirect
4. #10594795C2semidirect
5. C3×#5236C2semidirect
6. #10591688C2semidirect
7. #10591666C2semidirect
8. #10591111C2semidirect
9. C2×#63558C2semidirect
13. C2×#3828C22semidirect
25. #64160C22semidirect
27. #64158C22semidirect
30. C2×#3748C22semidirect
31. C3×#926C22semidirect
32. C2×C3×#208C22semidirect
35. #63911C22semidirect
36. #63860C22semidirect
38. #63831C22semidirect
41. #63825C22semidirect
42. C3×#837C22semidirect
43. #63569C22semidirect
44. #63558C22semidirect
46. C2×#1009D3semidirect
58. #5236D3semidirect
68. C32×#41D4semidirect
70. C2×C32×Q8D4semidirect
72. C2×C32×D4D4semidirect
80. C2×C4⋊(C3⋊D3)C23semidirect
82. C2×#634C23semidirect
95. C3×#235D4semidirect
105. C2×C3×D12D4semidirect
109. C2×C3×Dic6D4semidirect
116. #3748C23semidirect
120. C3×C4×Dic3C23semidirect
122. C3×#208C23semidirect
184. #926C2×D3semidirect
188. C2×#208C2×D3semidirect
200. #837C2×D3semidirect
287. C3×#41D12semidirect
288. C3×#41#67semidirect
293. C2×C3×Q8D12semidirect
294. C2×C3×Q8#67semidirect
315. C2×C3×D4D12semidirect
316. C2×C3×D4#67semidirect
353. #235#67semidirect
367. C2×D12#67semidirect
377. C2×Dic6#67semidirect
404. C4×Dic3C22×D3semidirect
412. #208C22×D3semidirect
637. #41#626semidirect
641. C2×Q8#626semidirect
662. C2×D4#626semidirect
746. C32#3019semidirect
847. C3#78993semidirect
848. C3#84104semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
#105962932
#105950422
#105947952
C3×#52362
#105916882
#105916662
#105911112
C2×#635582
#841043
#789933