Finite Group Databasebeta

← #11865053

Subgroups — #11865053

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×#64307C211yesmaximal, characteristic, complemented
2#10596293C211yesmaximal, characteristic, complemented
3C3×#5830C211yesmaximal, characteristic, complemented
4C3×#5822C211yesmaximal, characteristic, complemented
5#10591659C214yesmaximal, complemented
6#10591523C214yesmaximal, complemented
7#10591113C211yesmaximal, characteristic, complemented
8#10591111C211yesmaximal, characteristic, complemented
9C2×#63558C211yesmaximal, characteristic, complemented
10#84005—31nomaximal
11#83394—31nomaximal
12C2×C32×#41C2211yescharacteristic, complemented
13C2×#3828C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C2×D3×#67—22no—
17#64307—22no—
18#64307—22no—
19#64307—22no—
20#64307C2214yes—
21C2×#3802—21no—
22C2×D3×D12—21no—
23C2×#3796—21no—
24C2×#3795—21no—
25#64160—21no—
26#64159—22no—
27#64158—21no—
28#64151C2212yescomplemented
29#64141C2212yescomplemented
30C2×#3748C2211yescharacteristic, complemented
31C3×#951—21no—
32C3×#950—22no—
33C3×#949—21no—
34C3×#947C2212yescomplemented
35C3×#942C2212yescomplemented
36C3×#940C2212yescomplemented
37C3×#937—22no—
38C3×#932C2212yescomplemented
39C3×#930—22no—
40C3×#926C2211yescharacteristic, complemented
41C2×C3×#208C2211yescharacteristic, complemented
42#63570C2214yescomplemented
43#63569C2214yescomplemented
44#63558C2214yescomplemented
45C2×#1009—31no—
46C2×#1004—31no—
47C3×#575—31no—
48C3×#535—31no—
49#5830D311yescharacteristic, complemented
50#5822—31no—
51#5822—31no—
52#5822—61no—
53#5822D311yescharacteristic, complemented
54#5236—31no—
55C2×#833—31no—
56#5202—34no—
57#5198—34no—
58#5139—31no—
59C2×#823—31no—
60#5077—34no—
61#5061—34no—
62#5005—31no—
63#5005—31no—
64C23×C3×D3D412yes—
65C22×D32—22no—
66C32×#41—21no—
67C32×#41—21no—
68C32×#41—21no—
69C32×#41—21no—
70C2×C32×Q8C2311yescharacteristic, complemented
71C2×C32×D4—21no—
72C2×C32×D4C2311yescharacteristic, complemented
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×#638—21no—
76#3828—21no—
77#3828—21no—
78#3828D412yescomplemented
79#3828C2312yes—
80C2×C4⋊(C3⋊D3)D411yescharacteristic, complemented
81C2×C4×C3⋊D3—21no—
82C2×#634D411yescharacteristic, complemented
83C2×C3×#67—21no—
84C2×C3×#67—24no—
85C3×#235—21no—
86C3×#235—21no—
87C3×#235D412yescomplemented
88C3×#235C2312yes—
89C2×C3×D12—21no—
90C2×C3×D12—21no—
91C2×C3×D12—21no—
92C2×C3×D12—21no—
93C2×C3×D12D412yes—
94C2×C3×D12D411yescharacteristic, complemented
95C2×C3×D12C2312yes—
96C2×C3×C4×D3—21no—
97C2×C3×Dic6D411yescharacteristic, complemented
98D3×#67—28no—
99D3×#67—28no—
100C2×#626—22no—
101C2×#625—22no—
102C2×D3×Dic3—22no—
103#3802—24no—
104#3802—24no—
105D3×D12—24no—
106D3×D12—24no—
107#3796—24no—
108#3796—24no—
109#3795—24no—
110#3795—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×#216—22no—
120C3×#215—22no—
121C3×#214—22no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—24no—
124C3×C4⋊Dic3—21no—
125C3×C4×Dic3C2312yescomplemented
126C3×#208—21no—
127C3×#208C2312yescomplemented
128C2×C3×C3⋊C8—21no—
129#3019—91noSylow
130C2×C3×#41—21no—
131C2×C3×#41—31no—
132C2×C3×#41C2×D311yescharacteristic, complemented
133C2×C3×#41C2×D311yescharacteristic, complemented
134C22×C3×D4—31no—
135C22×#67—62no—
136#1009—34no—
137#1009—62no—
138#1009—62no—
139#1009—62no—
140C2×#239—61no—
141#1004—34no—
142#1004—62no—
143#1004—62no—
144#1004—62no—
145C2×#237—61no—
146C2×#237—61no—
147C2×D3×D4—61no—
148C2×D3×D4—61no—
149C2×D3×D4—62no—
150C2×D3×D4—61no—
151C2×#235—31no—
152C2×#235—31no—
153C2×#235—61no—
154C2×#235—61no—
155C2×#235C2×D311yescharacteristic
156C22×D12—61no—
157C22×D12C2×D311yescharacteristic
158C3×#137—32no—
159C3×#137—61no—
160C3×AGL(1,ℤ/8)—32no—
161C3×AGL(1,ℤ/8)—61no—
162C3×#135—62no—
163C2×C3×M16—31no—
164C3×#127—32no—
165C3×#124—32no—
166C3×#121—62no—
167C3×#120—62no—
168C3×#117—31no—
169#951—21no—
170#951—61no—
171#951—61no—
172#951—62no—
173#950—22no—
174#950—62no—
175#950—62no—
176#950—64no—
177#949—21no—
178#949—61no—
179#949—61no—
180#949—62no—
181#947C2×D312yescomplemented
182#942—32no—
183#942—32no—
184#942—62no—
185#942C2×D312yescomplemented
186#940C2×D312yescomplemented
187#937—22no—
188#932—32no—
189#932—32no—
190#932—62no—
191#932C2×D312yescomplemented
192#930—22no—
193#926C2×D311yescharacteristic, complemented
194C2×#208—31no—
195C2×#208—31no—
196C2×#208—61no—
197C2×#208C2×D311yescharacteristic, complemented
198#837—34no—
199#833—34no—
200#825—34no—
201#823—34no—
202#805—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—22no—
210C22×C3×D3—82no—
211C22×C3×D3C2×D414yes—
212C2×D32—28no—
213C2×D32—84no—
214C32×Q8—21no—
215C32×Q8—21no—
216C32×D4—21no—
217C32×D4—21no—
218C32×D4—41no—
219C32×D4—41no—
220C2×C32×C4—21no—
221C2×C32×C4—41no—
222C2×C32×C4—41no—
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—22no—
230#638—22no—
231C2×C3⋊Dic3—21no—
232C4⋊(C3⋊D3)—21no—
233C4⋊(C3⋊D3)C2×D412yes—
234C4×C3⋊D3—22no—
235C4×C3⋊D3—22no—
236#634—21no—
237#634C2×D412yes—
238C3×#67—22no—
239C3×#67—22no—
240C3×#67—84no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—22no—
243C3×D12—22no—
244C3×D12—22no—
245C3×D12—21no—
246C3×D12—22no—
247C3×D12—22no—
248C3×D12C2×D412yes—
249C3×C4×D3—22no—
250C3×C4×D3—22no—
251C3×Dic6—21no—
252C3×Dic6C2×D412yes—
253#626—28no—
254#625—28no—
255D3×Dic3—28no—
256C3⋊(C3⋊C8)—22no—
257C3×C3⋊C8—22no—
258C2×H(5,𝔽2)—91no—
259#575—31no—
260#575—91no—
261#535—31no—
262#455—94no—
263#453—94no—
264#421—91no—
265#421—91no—
266C2×#100—91no—
267C24×C3—32no—
268C23×D3—62no—
269C23×D3—62no—
270C23×D3#6712yes—
271C3×#41—22no—
272C3×#41—22no—
273C3×#41—21no—
274C3×#41—21no—
275C3×#41—21no—
276C3×#41—21no—
277C3×#41—21no—
278C3×#41—21no—
279C3×#41—21no—
280C3×#41—21no—
281C3×#41—32no—
282C3×#41—32no—
283C3×#41—41no—
284C3×#41—41no—
285C3×#41—61no—
286C3×#41—61no—
287C2×C3×Q8—21no—
288C2×C3×Q8—31no—
289C2×C3×Q8C22×D311yescharacteristic, complemented
290C2×C3×Q8C22×D311yescharacteristic, complemented
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—32no—
296C2×C3×D4—32no—
297C2×C3×D4—41no—
298C2×C3×D4—61no—
299C2×C3×D4—64no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic, complemented
305C2×C3×D4C22×D311yescharacteristic, complemented
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—41no—
310C22×C3×C4—61no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C2×#67—21no—
314C2×#67—24no—
315C2×#67—62no—
316C2×#67—68no—
317C2×#67—68no—
318C2×#67—62no—
319C2×#67—62no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—121no—
323C22×Dic3—62no—
324#239—64no—
325#239—64no—
326#237—64no—
327#237—64no—
328#237—64no—
329#237—64no—
330D3×D4—64no—
331D3×D4—64no—
332D3×D4—64no—
333D3×D4—64no—
334D3×D4—64no—
335D3×D4—68no—
336D3×D4—68no—
337D3×D4—64no—
338#235—21no—
339#235—21no—
340#235—32no—
341#235—32no—
342#235—32no—
343#235—32no—
344#235—62no—
345#235—62no—
346#235—64no—
347#235—64no—
348#235—61no—
349#235—61no—
350#235—61no—
351#235—61no—
352#235—121no—
353#235—121no—
354#235#6712yescomplemented
355#235C22×D312yes—
356C2×D12—21no—
357C2×D12—21no—
358C2×D12—21no—
359C2×D12—21no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—64no—
364C2×D12—64no—
365C2×D12—62no—
366C2×D12#6712yes—
367C2×D12#6711yescharacteristic, complemented
368C2×D12C22×D312yes—
369C2×C4×D3—21no—
370C2×C4×D3—62no—
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×Q16—62no—
379C3×SD16—62no—
380C3×SD16—62no—
381C3×D8—62no—
382C3×M16—32no—
383C3×M16—61no—
384C2×C3×C8—61no—
385C3×C4⋊C4—61no—
386C3×C22⋊C4—64no—
387C3×C22⋊C4—61no—
388C3×C42—32no—
389#217—21no—
390#216—22no—
391#216—62no—
392#216—62no—
393#216—64no—
394#215—22no—
395#215—62no—
396#215—62no—
397#215—64no—
398#214—22no—
399#214—62no—
400#214—62no—
401#214—64no—
402#213—22no—
403#213—62no—
404#213—62no—
405#213—64no—
406(C2×D3)⋊C4—24no—
407C4⋊Dic3—21no—
408C4×Dic3C22×D312yescomplemented
409#208—21no—
410#208—32no—
411#208—32no—
412#208—62no—
413#208—62no—
414#208—61no—
415#208—61no—
416#208C22×D312yescomplemented
417C2×C3⋊C8—21no—
418C2×C3⋊C8—62no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—61no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—42no—
424C22×C32#12011yescharacteristic
425C22×C32#12011yescharacteristic
426C22×C32C22×D411yescharacteristic
427C2×C3⋊D3—22no—
428C2×C3⋊D3—42no—
429C2×C3×D3—24no—
430C2×C3×D3—22no—
431C2×C3×D3—42no—
432C2×C3×D3—44no—
433C2×C3×D3—44no—
434C2×C3×D3—82no—
435D32—88no—
436C32×C4—41no—
437C32×C4#12011yescharacteristic
438C32×C4#12011yescharacteristic
439C32×C4C22×D411yescharacteristic
440C32×C4C22×D411yescharacteristic
441C3⋊Dic3—22no—
442C3×Dic3—22no—
443C3×Dic3—42no—
444H(5,𝔽2)—94no—
445H(5,𝔽2)—182no—
446H(5,𝔽2)—182no—
447H(5,𝔽2)—182no—
448C2×#41—31no—
449C2×#41—91no—
450C2×#41—181no—
451C2×#41—181no—
452C2×#41D3211yescharacteristic, complemented
453C22×D4—31no—
454C22×D4—181no—
455C22×D4—181no—
456C22×D4—182no—
457#137—32no—
458#137—61no—
459#137—92no—
460#137—181no—
461AGL(1,ℤ/8)—32no—
462AGL(1,ℤ/8)—61no—
463AGL(1,ℤ/8)—92no—
464AGL(1,ℤ/8)—181no—
465#135—62no—
466#135—182no—
467C2×M16—31no—
468C2×M16—91no—
469#127—32no—
470#124—32no—
471#121—62no—
472#120—62no—
473#117—31no—
474#104—94no—
475#104—94no—
476#100—94no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—34no—
481C23×C3—41no—
482C23×C3—62no—
483C23×C3—61no—
484C23×C3—62no—
485C23×C3—242no—
486C23×C3D3×D411yescharacteristic
487C23×C3C2×#6711yescharacteristic
488C22×D3—21no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—68no—
492C22×D3—68no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—82no—
496C22×D3—121no—
497C22×D3—244no—
498C22×D3—244no—
499C22×D3C2×#6714yes—
500C3×Q8—22no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—32no—
506C3×Q8—41no—
507C3×Q8—61no—
508C3×D4—22no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—32no—
514C3×D4—41no—
515C3×D4—42no—
516C3×D4—42no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—62no—
522C3×D4—62no—
523C3×D4—61no—
524C3×D4—62no—
525C3×D4—62no—
526C3×D4—62no—
527C3×D4—62no—
528C3×D4—244no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—41no—
538C2×C3×C4—42no—
539C2×C3×C4—42no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—61no—
545C2×C3×C4—62no—
546C2×C3×C4—62no—
547C2×C3×C4—62no—
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
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×C4C23×D311yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560#67—22no—
561#67—22no—
562#67—68no—
563#67—68no—
564#67—68no—
565#67—62no—
566#67—62no—
567#67—62no—
568#67—62no—
569#67—84no—
570#67—122no—
571#67—122no—
572C2×Dic3—21no—
573C2×Dic3—22no—
574C2×Dic3—68no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—121no—
578D12—22no—
579D12—22no—
580D12—21no—
581D12—22no—
582D12—22no—
583D12—32no—
584D12—32no—
585D12—62no—
586D12—68no—
587D12—61no—
588D12—61no—
589D12—121no—
590D12C2×#6712yes—
591C4×D3—22no—
592C4×D3—22no—
593C4×D3—68no—
594C4×D3—62no—
595C4×D3—62no—
596C4×D3—62no—
597C4×D3—62no—
598C4×D3—122no—
599C4×D3—122no—
600Dic6—21no—
601Dic6—32no—
602Dic6—32no—
603Dic6—62no—
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—81no—
617C2×C32C2×#12011yescharacteristic
618C3⋊D3—42no—
619C3×D3—42no—
620C3×D3—44no—
621C24—32no—
622C24—182no—
623#41—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627#41—32no—
628#41—32no—
629#41—61no—
630#41—61no—
631#41—92no—
632#41—92no—
633#41—184no—
634#41—184no—
635#41—184no—
636#41—184no—
637#41—181no—
638#41—181no—
639C2×Q8—31no—
640C2×Q8—91no—
641C2×Q8C2×D3211yescharacteristic, complemented
642C2×D4—21no—
643C2×D4—32no—
644C2×D4—31no—
645C2×D4—32no—
646C2×D4—61no—
647C2×D4—64no—
648C2×D4—61no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—61no—
652C2×D4—91no—
653C2×D4—184no—
654C2×D4—184no—
655C2×D4—182no—
656C2×D4—184no—
657C2×D4—184no—
658C2×D4—188no—
659C2×D4—188no—
660C2×D4—182no—
661C2×D4—181no—
662C2×D4C2×D3211yescharacteristic, complemented
663C22×C4—21no—
664C22×C4—61no—
665C22×C4—182no—
666C22×C4—181no—
667C22×C4C2×D3211yescharacteristic
668Q16—62no—
669Q16—182no—
670SD16—62no—
671SD16—62no—
672SD16—182no—
673SD16—182no—
674D8—62no—
675D8—182no—
676M16—32no—
677M16—61no—
678M16—92no—
679M16—181no—
680C2×C8—61no—
681C2×C8—181no—
682C4⋊C4—61no—
683C22⋊C4—64no—
684C22⋊C4—61no—
685C42—32no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—64no—
697C22×C3—62no—
698C22×C3—81no—
699C22×C3—82no—
700C22×C3—124no—
701C22×C3—122no—
702C22×C3—124no—
703C22×C3—242no—
704C22×C3#93711yescharacteristic
705C22×C3#93711yescharacteristic
706C22×C3#93711yescharacteristic
707C22×C3#93711yescharacteristic
708C22×C3C2×D3×D411yescharacteristic
709C22×C3C22×#6711yescharacteristic
710C2×D3—22no—
711C2×D3—24no—
712C2×D3—44no—
713C2×D3—42no—
714C2×D3—44no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—82no—
718C2×D3—122no—
719C2×D3—122no—
720C2×D3—122no—
721C2×D3—242no—
722C2×D3—248no—
723C2×D3—248no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—42no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—62no—
732C3×C4—122no—
733C3×C4#93711yescharacteristic
734C3×C4#93711yescharacteristic
735C3×C4#93711yescharacteristic
736C3×C4#93711yescharacteristic
737C3×C4C2×D3×D411yescharacteristic
738C3×C4C2×D3×D411yescharacteristic
739C3×C4C2×D3×D411yescharacteristic
740C3×C4C22×#6711yescharacteristic
741Dic3—22no—
742Dic3—42no—
743Dic3—62no—
744Dic3—62no—
745Dic3—122no—
746C32#301911yescharacteristic, complemented, Sylow
747C23—21no—
748C23—34no—
749C23—61no—
750C23—62no—
751C23—62no—
752C23—188no—
753C23—181no—
754C23—242no—
755C23—724no—
756C23D3×#6711yescharacteristic
757Q8—21no—
758Q8—21no—
759Q8—32no—
760Q8—61no—
761Q8—92no—
762Q8—181no—
763D4—21no—
764D4—21no—
765D4—32no—
766D4—41no—
767D4—41no—
768D4—62no—
769D4—62no—
770D4—62no—
771D4—62no—
772D4—62no—
773D4—62no—
774D4—61no—
775D4—92no—
776D4—188no—
777D4—188no—
778D4—182no—
779D4—182no—
780D4—181no—
781D4—244no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—61no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—188no—
790C2×C4—181no—
791C2×C4—182no—
792C2×C4—182no—
793C2×C4D3×#6711yescharacteristic
794C2×C4D3×#6711yescharacteristic
795C2×C4D3×#6711yescharacteristic
796C2×C4#381111yescharacteristic
797C2×C4#381111yescharacteristic
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—82no—
812C2×C3—81no—
813C2×C3—81no—
814C2×C3—124no—
815C2×C3—122no—
816C2×C3C2×#93711yescharacteristic
817C2×C3C2×#93711yescharacteristic
818D3—42no—
819D3—44no—
820D3—122no—
821D3—122no—
822D3—242no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—62no—
827C22—64no—
828C22—124no—
829C22—124no—
830C22—122no—
831C22—182no—
832C22—242no—
833C22—362no—
834C22—728no—
835C22#6398311yescharacteristic
836C22#6398311yescharacteristic
837C22C2×D3×#6711yescharacteristic
838C4—41no—
839C4—62no—
840C4—122no—
841C4—182no—
842C4#6398311yescharacteristic
843C4#6398311yescharacteristic
844C4C2×D3×#6711yescharacteristic
845C4C2×#381111yescharacteristic
846C3—21no—
847C3#8339411yescharacteristic, complemented
848C3#8400511yescharacteristic, complemented
849C2—21no—
850C2—21no—
851C2—21no—
852C2—81no—
853C2—124no—
854C2—122no—
855C2—362no—
856C2C2×#6398311yescharacteristic
subgroupG/H
centerC2C2×#63983
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×#64307C2semidirect
2. #10596293C2semidirect
3. C3×#5830C2semidirect
4. C3×#5822C2semidirect
5. #10591659C2semidirect
6. #10591523C2semidirect
7. #10591113C2semidirect
8. #10591111C2semidirect
9. C2×#63558C2semidirect
12. C2×C32×#41C22semidirect
28. #64151C22semidirect
29. #64141C22semidirect
30. C2×#3748C22semidirect
34. C3×#947C22semidirect
35. C3×#942C22semidirect
36. C3×#940C22semidirect
38. C3×#932C22semidirect
40. C3×#926C22semidirect
41. C2×C3×#208C22semidirect
42. #63570C22semidirect
43. #63569C22semidirect
44. #63558C22semidirect
49. #5830D3semidirect
53. #5822D3semidirect
70. C2×C32×Q8C23semidirect
72. C2×C32×D4C23semidirect
78. #3828D4semidirect
80. C2×C4⋊(C3⋊D3)D4semidirect
82. C2×#634D4semidirect
87. C3×#235D4semidirect
94. C2×C3×D12D4semidirect
97. C2×C3×Dic6D4semidirect
116. #3748C23semidirect
125. C3×C4×Dic3C23semidirect
127. C3×#208C23semidirect
132. C2×C3×#41C2×D3semidirect
133. C2×C3×#41C2×D3semidirect
181. #947C2×D3semidirect
185. #942C2×D3semidirect
186. #940C2×D3semidirect
191. #932C2×D3semidirect
193. #926C2×D3semidirect
197. C2×#208C2×D3semidirect
289. C2×C3×Q8C22×D3semidirect
290. C2×C3×Q8C22×D3semidirect
304. C2×C3×D4C22×D3semidirect
305. C2×C3×D4C22×D3semidirect
354. #235#67semidirect
367. C2×D12#67semidirect
377. C2×Dic6#67semidirect
408. C4×Dic3C22×D3semidirect
416. #208C22×D3semidirect
452. C2×#41D32semidirect
641. C2×Q8C2×D32semidirect
662. C2×D4C2×D32semidirect
746. C32#3019semidirect
847. C3#83394semidirect
848. C3#84005semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
#105962932
C3×#58302
C3×#58222
#105916592
#105915232
#105911132
#105911112
C2×#635582
#840053
#833943