Finite Group Databasebeta

← #11865113

Subgroups — #11865113

Order 1152.

1473 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3#10594855C211yesmaximal, characteristic, complemented
4#10594786C211yesmaximal, characteristic, complemented
5#10592935C211yesmaximal, characteristic, complemented
6#10591687C214yesmaximal, complemented
7#10591684C214yesmaximal, complemented
8#10591110C211yesmaximal, characteristic, complemented
9C2×#63560C211yesmaximal, characteristic, complemented
10#84116—31nomaximal
11#84006—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1010—22no—
14C3×#1010—22no—
15C3×#1010—22no—
16C3×#1010C2214yes—
17C2×C3×D3×Q8—21no—
18C2×C3×#237—21no—
19C2×C3×#237—22no—
20C2×C3×#235—21no—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23C22×C3×Dic6—21no—
24C22×C3×Dic6C2211yescharacteristic
25#64135C2211yescharacteristic
26C2×#3748C2211yescharacteristic
27C3×#951C2212yescomplemented
28C3×#950—22no—
29C3×#949C2212yescomplemented
30C3×#942—21no—
31C3×#932—21no—
32C2×C3×#208C2211yescharacteristic
33#63961—22no—
34#63873C2212yescomplemented
35#63863C2212yescomplemented
36#63856—22no—
37#63827—21no—
38#63827C2212yescomplemented
39#63823—21no—
40#63823C2212yescomplemented
41#63822—22no—
42#63664C2214yescomplemented
43#63568C2214yescomplemented
44#63560C2214yescomplemented
45C2×C3×2−1+4—31no—
46C2×#1010D311yescharacteristic, complemented
47C3×#575—31no—
48#5825—31no—
49#5822—31no—
50#5822—31no—
51#5822D311yescharacteristic, complemented
52#5816—31no—
53#5246—34no—
54#5245—34no—
55#5236—31no—
56#5236—31no—
57#5236—31no—
58#5236—61no—
59C2×#836—31no—
60#5205—34no—
61#5201—34no—
62#5139—31no—
63C2×#824—31no—
64C32×#41—21no—
65C32×#41—21no—
66C32×#41D412yes—
67C32×#41C2312yes—
68C2×C32×Q8D411yescharacteristic
69C2×C32×D4—21no—
70C2×C32×D4D411yescharacteristic
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—22no—
74C2×C3×#67—21no—
75C2×C3×#67—21no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3D412yes—
78C3×D3×Q8—24no—
79C3×D3×Q8—24no—
80C3×#237—28no—
81C3×#237—24no—
82C3×#237—24no—
83C3×#237—28no—
84C3×#235—24no—
85C3×#235—21no—
86C3×#235—21no—
87C3×#235—24no—
88C3×#235—21no—
89C3×#235—21no—
90C3×#235—21no—
91C3×#235—21no—
92C3×#235D412yes—
93C3×#235C2312yes—
94C2×C3×D12D411yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—22no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6—24no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—24no—
106C2×C3×Dic6D412yes—
107C2×C3×Dic6D411yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2312yes—
110#3757—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4×C3⋊Dic3C2312yes—
113#3748—21no—
114#3748C2312yes—
115C2×C3⋊(C3⋊C8)—21no—
116C3×#216—22no—
117C3×#215—22no—
118C3×#214—22no—
119C3×#213—22no—
120C3×#208—21no—
121C3×#208C2312yes—
122C2×C3×C3⋊C8—21no—
123#3724—24no—
124(C2×D3)⋊Dic3—24no—
125#3718—22no—
126#3715—22no—
127#3715—22no—
128#3713—22no—
129#3020—91noSylow
130C3×2−1+4—34no—
131C3×2−1+4—62no—
132C3×2−1+4—62no—
133C3×2−1+4—62no—
134C2×C3×#41—21no—
135C2×C3×#41—31no—
136C2×C3×#41—31no—
137C2×C3×#41—61no—
138C2×C3×#41—62no—
139C2×C3×#41—61no—
140C2×C3×#41C2×D311yescharacteristic
141C2×C3×#41C2×D311yescharacteristic
142C22×C3×Q8—31no—
143C22×C3×Q8—61no—
144C22×C3×Q8—61no—
145#1010—22no—
146#1010—22no—
147#1010—22no—
148#1010C2×D314yes—
149C2×D3×Q8—21no—
150C2×#237—21no—
151C2×#237—22no—
152C2×#235—21no—
153C2×#235C2×D311yescharacteristic
154C2×#235C2×D311yescharacteristic
155C22×Dic6—21no—
156C22×Dic6C2×D311yescharacteristic
157C3×#137—32no—
158C3×#137—61no—
159C3×AGL(1,ℤ/8)—32no—
160C3×AGL(1,ℤ/8)—61no—
161C3×#135—62no—
162C2×C3×M16—31no—
163#951—32no—
164#951—61no—
165#951C2×D312yescomplemented
166#950—22no—
167#950—62no—
168#950—62no—
169#949—32no—
170#949—61no—
171#949C2×D312yescomplemented
172#947—32no—
173#946—62no—
174#944—32no—
175#944—32no—
176#942—21no—
177#942—32no—
178#942—61no—
179#936—32no—
180#935—62no—
181#932—21no—
182#932—32no—
183#932—61no—
184#929—62no—
185#926—31no—
186#926—31no—
187#926—61no—
188#924—62no—
189C2×#208—31no—
190C2×#208—31no—
191C2×#208—61no—
192C2×#208C2×D311yescharacteristic
193#837—34no—
194#837—34no—
195#837—34no—
196#837—64no—
197#836—34no—
198#825—34no—
199#824—34no—
200C23×C32—21no—
201C23×C32C2×D411yescharacteristic
202C22×C3×D3—21no—
203C22×C3×D3—21no—
204C32×Q8—21no—
205C32×Q8C2×D412yes—
206C32×D4—22no—
207C32×D4—22no—
208C32×D4—21no—
209C32×D4C2×D412yes—
210C2×C32×C4—21no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4C2×D411yescharacteristic
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2×D411yescharacteristic
216C2×C32×C4C2×D411yescharacteristic
217C2×C32×C4C2×D411yescharacteristic
218C2×C32×C4C2411yescharacteristic
219C2×C3⋊Dic3—22no—
220C3×#67—28no—
221C3×#67—22no—
222C3×#67—22no—
223C3×#67—41no—
224C3×#67—41no—
225C2×C3×Dic3—28no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3C2×D414yes—
231C3×D12—21no—
232C3×D12—21no—
233C3×D12—21no—
234C3×D12C2×D412yes—
235C3×C4×D3—28no—
236C3×C4×D3—22no—
237C3×C4×D3—22no—
238C3×C4×D3—41no—
239C3×C4×D3—41no—
240C3×Dic6—28no—
241C3×Dic6—22no—
242C3×Dic6—21no—
243C3×Dic6—22no—
244C3×Dic6—22no—
245C3×Dic6—22no—
246C3×Dic6—21no—
247C3×Dic6—21no—
248C3×Dic6C2×D412yes—
249C3⋊(C3⋊C8)—22no—
250C3×C3⋊C8—22no—
251C2×2−1+4—31no—
252#575—31no—
253#575—91no—
254#536—91no—
255#456—94no—
256#454—94no—
257#421—91no—
258#421—91no—
259C2×#101—91no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C3×#41—22no—
265C3×#41—22no—
266C3×#41—32no—
267C3×#41—32no—
268C3×#41—41no—
269C3×#41—41no—
270C3×#41—64no—
271C3×#41—64no—
272C3×#41—68no—
273C3×#41—68no—
274C3×#41—64no—
275C3×#41—64no—
276C3×#41—61no—
277C3×#41—61no—
278C3×#41—61no—
279C3×#41—61no—
280C3×#41—61no—
281C3×#41—61no—
282C3×#41#6712yes—
283C3×#41#6712yes—
284C3×#41C22×D312yes—
285C3×#41C22×D312yes—
286C2×C3×Q8—21no—
287C2×C3×Q8—32no—
288C2×C3×Q8—32no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×Q8—64no—
292C2×C3×Q8—62no—
293C2×C3×Q8—64no—
294C2×C3×Q8—64no—
295C2×C3×Q8—64no—
296C2×C3×Q8—61no—
297C2×C3×Q8—61no—
298C2×C3×Q8—61no—
299C2×C3×Q8—61no—
300C2×C3×Q8#6711yescharacteristic
301C2×C3×Q8#6711yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4#6711yescharacteristic
312C2×C3×D4#6711yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—32no—
317C22×C3×C4—41no—
318C22×C3×C4—62no—
319C22×C3×C4—62no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C2×#67—22no—
325C2×#67—21no—
326C2×#67—21no—
327C22×Dic3—22no—
328C22×Dic3#6712yes—
329D3×Q8—24no—
330D3×Q8—24no—
331#237—28no—
332#237—24no—
333#237—24no—
334#237—28no—
335#235—24no—
336#235—21no—
337#235—21no—
338#235—24no—
339#235—21no—
340#235—21no—
341#235—21no—
342#235—21no—
343#235#6712yes—
344#235C22×D312yes—
345C2×D12#6711yescharacteristic
346C2×D12C22×D311yescharacteristic
347C2×C4×D3—22no—
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×Dic6—22no—
351C2×Dic6—24no—
352C2×Dic6—21no—
353C2×Dic6—21no—
354C2×Dic6—21no—
355C2×Dic6—21no—
356C2×Dic6—24no—
357C2×Dic6#6712yes—
358C2×Dic6#6711yescharacteristic
359C2×Dic6C22×D311yescharacteristic
360C2×Dic6C22×D312yes—
361C3×Q16—62no—
362C3×SD16—62no—
363C3×SD16—62no—
364C3×D8—62no—
365C3×M16—32no—
366C3×M16—61no—
367C2×C3×C8—61no—
368#217—61no—
369#217—61no—
370#217—64no—
371#217—121no—
372#216—22no—
373#216—62no—
374#216—62no—
375#215—22no—
376#215—62no—
377#215—62no—
378#214—22no—
379#214—62no—
380#214—62no—
381#213—22no—
382#213—62no—
383#213—62no—
384(C2×D3)⋊C4—64no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—121no—
388Dic3⋊C4—64no—
389Dic3⋊C4—64no—
390C4×Dic3—32no—
391C4×Dic3—32no—
392C4×Dic3—62no—
393#208—21no—
394#208—32no—
395#208—32no—
396#208—62no—
397#208—61no—
398#208—61no—
399#208—121no—
400#208C22×D312yes—
401C2×C3⋊C8—21no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C22×C32—22no—
406C22×C32—41no—
407C22×C32—42no—
408C22×C32#12011yescharacteristic
409C22×C32#12011yescharacteristic
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—22no—
412C2×C3×D3—42no—
413C2×C3×D3—42no—
414C2×C3×D3—41no—
415C32×C4—22no—
416C32×C4#12011yescharacteristic
417C32×C4#12011yescharacteristic
418C32×C4C22×D411yescharacteristic
419C32×C4C22×D411yescharacteristic
420C3⋊Dic3—42no—
421C3×Dic3—24no—
422C3×Dic3—22no—
423C3×Dic3—41no—
4242−1+4—34no—
4252−1+4—62no—
4262−1+4—62no—
4272−1+4—62no—
428C2×#41—31no—
429C2×#41—31no—
430C2×#41—61no—
431C2×#41—62no—
432C2×#41—61no—
433C2×#41D3211yescharacteristic
434C22×Q8—31no—
435C22×Q8—61no—
436C22×Q8—61no—
437#137—32no—
438#137—61no—
439#137—92no—
440#137—181no—
441AGL(1,ℤ/8)—32no—
442AGL(1,ℤ/8)—61no—
443AGL(1,ℤ/8)—92no—
444AGL(1,ℤ/8)—181no—
445#135—62no—
446#135—182no—
447C2×M16—31no—
448C2×M16—91no—
449C4⋊Q8—92no—
450#124—92no—
451#123—182no—
452C22⋊Q8—182no—
453#117—91no—
454#104—94no—
455#104—94no—
456#101—94no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—41no—
461C23×C3—61no—
462C23×C3—61no—
463C23×C3D3×D411yescharacteristic
464C23×C3C2×#6711yescharacteristic
465C22×D3—21no—
466C22×D3—21no—
467C3×Q8—21no—
468C3×Q8—21no—
469C3×Q8—22no—
470C3×Q8—32no—
471C3×Q8—41no—
472C3×Q8—68no—
473C3×Q8—62no—
474C3×Q8—62no—
475C3×Q8—61no—
476C3×Q8—62no—
477C3×Q8—62no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8C2×#6712yes—
481C3×Q8C2×#6712yes—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—22no—
485C3×D4—22no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—22no—
489C3×D4—32no—
490C3×D4—41no—
491C3×D4—42no—
492C3×D4—42no—
493C3×D4—68no—
494C3×D4—62no—
495C3×D4—62no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—121no—
500C3×D4—121no—
501C3×D4C2×#6712yes—
502C3×D4C2×#6712yes—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—34no—
516C2×C3×C4—42no—
517C2×C3×C4—42no—
518C2×C3×C4—41no—
519C2×C3×C4—68no—
520C2×C3×C4—68no—
521C2×C3×C4—62no—
522C2×C3×C4—62no—
523C2×C3×C4—61no—
524C2×C3×C4—62no—
525C2×C3×C4—62no—
526C2×C3×C4—61no—
527C2×C3×C4—121no—
528C2×C3×C4—121no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C2×#6711yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—28no—
542#67—22no—
543#67—22no—
544#67—41no—
545#67—41no—
546C2×Dic3—28no—
547C2×Dic3—22no—
548C2×Dic3—21no—
549C2×Dic3—22no—
550C2×Dic3—21no—
551C2×Dic3—62no—
552C2×Dic3—62no—
553C2×Dic3—122no—
554C2×Dic3C2×#6714yes—
555D12—21no—
556D12—21no—
557D12—21no—
558D12C2×#6712yes—
559C4×D3—28no—
560C4×D3—22no—
561C4×D3—22no—
562C4×D3—41no—
563C4×D3—41no—
564Dic6—28no—
565Dic6—22no—
566Dic6—21no—
567Dic6—22no—
568Dic6—22no—
569Dic6—22no—
570Dic6—21no—
571Dic6—21no—
572Dic6C2×#6712yes—
573C3×C8—62no—
574C3⋊C8—22no—
575C3⋊C8—62no—
576C3⋊C8—62no—
577C3⋊C8—122no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—42no—
582C2×C32C2×#12011yescharacteristic
583C3×D3—42no—
584C3×D3—81no—
585#41—21no—
586#41—21no—
587#41—32no—
588#41—32no—
589#41—64no—
590#41—64no—
591#41—68no—
592#41—68no—
593#41—64no—
594#41—64no—
595#41—61no—
596#41—61no—
597#41—61no—
598#41—61no—
599#41—61no—
600#41—61no—
601#41#62512yes—
602#41C2×D3212yes—
603C2×Q8—32no—
604C2×Q8—32no—
605C2×Q8—31no—
606C2×Q8—31no—
607C2×Q8—64no—
608C2×Q8—62no—
609C2×Q8—64no—
610C2×Q8—64no—
611C2×Q8—64no—
612C2×Q8—61no—
613C2×Q8—61no—
614C2×Q8—61no—
615C2×Q8—61no—
616C2×Q8#62511yescharacteristic
617C2×D4—21no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—62no—
621C2×D4—61no—
622C2×D4—61no—
623C2×D4#62511yescharacteristic
624C22×C4—21no—
625C22×C4—32no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4C2×D3211yescharacteristic
631Q16—62no—
632Q16—182no—
633SD16—62no—
634SD16—62no—
635SD16—182no—
636SD16—182no—
637D8—62no—
638D8—182no—
639M16—32no—
640M16—61no—
641M16—92no—
642M16—181no—
643C2×C8—61no—
644C2×C8—181no—
645C4⋊C4—184no—
646C4⋊C4—181no—
647C22⋊C4—184no—
648C22⋊C4—181no—
649C42—92no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—62no—
661C22×C3—81no—
662C22×C3—82no—
663C22×C3—122no—
664C22×C3—122no—
665C22×C3—121no—
666C22×C3#93711yescharacteristic
667C22×C3#93711yescharacteristic
668C22×C3#95311yescharacteristic
669C22×C3#95311yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C22×#6711yescharacteristic
672C2×D3—22no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—41no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—42no—
683C3×C4—64no—
684C3×C4—62no—
685C3×C4—121no—
686C3×C4#93711yescharacteristic
687C3×C4#93711yescharacteristic
688C3×C4#95311yescharacteristic
689C3×C4#95311yescharacteristic
690C3×C4C2×D3×D411yescharacteristic
691C3×C4C22×#6711yescharacteristic
692C3×C4C22×#6711yescharacteristic
693C3×C4C22×#6711yescharacteristic
694Dic3—24no—
695Dic3—22no—
696Dic3—41no—
697Dic3—122no—
698Dic3—122no—
699Dic3—242no—
700C32#302011yescharacteristic, complemented, Sylow
701C23—21no—
702C23—61no—
703C23—61no—
704C23D3×#6711yescharacteristic
705Q8—21no—
706Q8—32no—
707Q8—68no—
708Q8—62no—
709Q8—62no—
710Q8—62no—
711Q8—62no—
712Q8—61no—
713Q8—61no—
714Q8—61no—
715Q8C2×#62512yes—
716D4—22no—
717D4—22no—
718D4—21no—
719D4—32no—
720D4—68no—
721D4—62no—
722D4—62no—
723D4—61no—
724D4—61no—
725D4—61no—
726D4—121no—
727D4—121no—
728D4C2×#62512yes—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—34no—
733C2×C4—68no—
734C2×C4—68no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—61no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—61no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—182no—
744C2×C4C2×#62511yescharacteristic
745C2×C4C2×#62511yescharacteristic
746C2×C4D3×#6711yescharacteristic
747C2×C4D3×#6711yescharacteristic
748C2×C4D3×#6711yescharacteristic
749C2×C4C22×D3211yescharacteristic
750C8—62no—
751C8—182no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—41no—
762C2×C3—42no—
763C2×C3—42no—
764C2×C3—82no—
765C2×C3—122no—
766C2×C3—241no—
767C2×C3C2×#93711yescharacteristic
768C2×C3C2×#95311yescharacteristic
769D3—42no—
770D3—81no—
771C22—22no—
772C22—41no—
773C22—42no—
774C22—62no—
775C22—122no—
776C22—122no—
777C22—121no—
778C22#6397611yescharacteristic
779C22#6397611yescharacteristic
780C22C2×D3×#6711yescharacteristic
781C4—22no—
782C4—64no—
783C4—62no—
784C4—121no—
785C4—362no—
786C4#6397611yescharacteristic
787C4#6397611yescharacteristic
788C4C22×#62511yescharacteristic
789C4C2×D3×#6711yescharacteristic
790C3—21no—
791C3#8400611yescharacteristic, complemented
792C3#8411611yescharacteristic, complemented
793C2—21no—
794C2—21no—
795C2—21no—
796C2—42no—
797C2—122no—
798C2—241no—
799C2C2×#6397611yescharacteristic
subgroupG/H
centerC2C2×#63976
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3020
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×#1010C2semidirect
2. C3×#5822C2semidirect
3. #10594855C2semidirect
4. #10594786C2semidirect
5. #10592935C2semidirect
6. #10591687C2semidirect
7. #10591684C2semidirect
8. #10591110C2semidirect
9. C2×#63560C2semidirect
27. C3×#951C22semidirect
29. C3×#949C22semidirect
34. #63873C22semidirect
35. #63863C22semidirect
38. #63827C22semidirect
40. #63823C22semidirect
42. #63664C22semidirect
43. #63568C22semidirect
44. #63560C22semidirect
46. C2×#1010D3semidirect
51. #5822D3semidirect
165. #951C2×D3semidirect
171. #949C2×D3semidirect
700. C32#3020semidirect
791. C3#84006semidirect
792. C3#84116semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C3×#58222
#105948552
#105947862
#105929352
#105916872
#105916842
#105911102
C2×#635602
#841163
#840063