Finite Group Databasebeta

← #10944158

Subgroups — #10944158

Order 768.

1590 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#1009C211yesmaximal, characteristic, complemented
2C3×#3038C211yesmaximal, characteristic, complemented
3C2×#5198C212yesmaximal, complemented
4#83188C211yesmaximal, characteristic, complemented
5#83165C211yesmaximal, characteristic, complemented
6#72088C212yesmaximal, complemented
7#71646C211yesmaximal, characteristic, complemented
8#70529C211yesmaximal, characteristic, complemented
9#70527C211yesmaximal, characteristic, complemented
10#70328C212yesmaximal, complemented
11#70323C212yesmaximal, complemented
12#32920—31nomaximal, Sylow
13C2×#1009C2211yescharacteristic
14C2×C3×AGL(1,ℤ/8)C2212yes—
15C2×C3×#127C2211yescharacteristic, complemented
16C3×C4×#41C2211yescharacteristic
17#5827C2211yescharacteristic
18C2×#940C2212yes—
19C2×#938—22no—
20C2×#932C2212yes—
21#5574—21no—
22C4×#239—21no—
23#5545—21no—
24#5545—22no—
25C4×D3×D4—22no—
26C4×D3×D4—21no—
27#5523—21no—
28#5523C2211yescharacteristic
29#5521—21no—
30#5521C2211yescharacteristic
31C4×#235—21no—
32C4×#235C2211yescharacteristic
33C2×C4×D12—21no—
34C2×C4×D12C2211yescharacteristic
35C3×#460—21no—
36C3×#460—21no—
37C3×#459—21no—
38C3×#459—21no—
39C3×#423C2211yescharacteristic, complemented
40C3×#418C2212yescomplemented
41C2×#837C2212yes—
42#5223—22no—
43#5221C2212yescomplemented
44#5215C2212yescomplemented
45#5198—28no—
46C2×#825C2212yes—
47C2×#823C2212yes—
48#5075—21no—
49#5075—21no—
50#5072—21no—
51#5072—21no—
52C4×C4⋊Dic3C2211yescharacteristic, complemented
53#4924C2211yescharacteristic, complemented
54#4555C2212yescomplemented
55#4554C2212yescomplemented
56#4532C2212yescomplemented
57C4×H(5,𝔽2)—31no—
58#3038—31no—
59#3038D311yescharacteristic, complemented
60C2×#453—32no—
61#2541—31no—
62#1887—32no—
63#1883—32no—
64#1883—32no—
65#1806—31no—
66#1806—31no—
67#1800—31no—
68C2×C3×#41C2311yescharacteristic
69C22×C3×D4—21no—
70C22×C3×D4—21no—
71C22×C3×D4C2312yes—
72C22×#67—24no—
73#1009—22no—
74#1009—22no—
75#1009—22no—
76#1009D414yescomplemented
77C2×#239—21no—
78C2×D3×D4—22no—
79C2×D3×D4—21no—
80C2×#235—21no—
81C2×#235C2311yescharacteristic
82C22×D12—21no—
83C22×D12C2311yescharacteristic
84C22×C4×D3—22no—
85C22×C4×D3D412yes—
86C3×AGL(1,ℤ/8)—24no—
87C3×AGL(1,ℤ/8)—24no—
88C2×C3×SD16—22no—
89C2×C3×D8—22no—
90C2×C3×M16C2312yes—
91C3×#127—21no—
92C3×#127—21no—
93C3×#127—21no—
94C3×#127—21no—
95C3×C4×Q8D411yescharacteristic, complemented
96C3×C4×Q8D411yescharacteristic, complemented
97C3×C4×D4—21no—
98C3×C4×D4—21no—
99C3×C4×D4D411yescharacteristic, complemented
100C3×C4×D4D411yescharacteristic, complemented
101C3×#117—21no—
102C3×#117C2311yescharacteristic
103C2×C3×C42—21no—
104C2×C3×C42C2311yescharacteristic
105C2×#217—24no—
106Q8×Dic3—21no—
107#940—24no—
108#940—24no—
109#938—48no—
110D4×Dic3—21no—
111D4×Dic3—22no—
112C2×#214—22no—
113#932—24no—
114#932—24no—
115C2×#213—22no—
116C4×#67—22no—
117C4×#67—22no—
118C4×#67—21no—
119C4×#67—21no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4D412yes—
122#926—21no—
123#926C2311yescharacteristic
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4×Dic3C2312yes—
128C2×#208C2312yes—
129#893—22no—
130#893—22no—
131#893—21no—
132#893—21no—
133#892—22no—
134#892—21no—
135D3×C4⋊C4—22no—
136D3×C4⋊C4—21no—
137#67⋊C4—22no—
138#67⋊C4—22no—
139#67⋊C4—22no—
140D3×C22⋊C4—22no—
141D3×C22⋊C4—22no—
142D3×C22⋊C4—22no—
143C4×D12—22no—
144C4×D12—22no—
145C4×D12—21no—
146C4×D12—21no—
147C4×D12—21no—
148C4×D12—21no—
149C4×D12—21no—
150C4×D12—21no—
151C4×D12—21no—
152C4×D12D411yescharacteristic, complemented
153C4×D12D411yescharacteristic, complemented
154#872—22no—
155#872—21no—
156C42×D3—22no—
157C42×D3—21no—
158C4×Dic6—21no—
159C4×Dic6D411yescharacteristic, complemented
160C4×Dic6D411yescharacteristic, complemented
161C3×C4⋊C8—21no—
162C3×C4⋊C8—21no—
163C3×#102—22no—
164C3×#102—22no—
165#837—24no—
166#832—22no—
167#832—22no—
168C3⋊#95—21no—
169#825—24no—
170#823—24no—
171C4⋊(C3⋊C8)—21no—
172C4⋊(C3⋊C8)—21no—
173C2×H(5,𝔽2)—31no—
174C2×AGL(1,ℤ/8)—32no—
175C2×AGL(1,ℤ/8)C2×D312yes—
176C2×#127—32no—
177C2×#127C2×D311yescharacteristic, complemented
178C2×#121—62no—
179#520—31no—
180#520—31no—
181#520—61no—
182#520—61no—
183#518—31no—
184#518—62no—
185#518—61no—
186#518—61no—
187C4×#41—31no—
188C4×#41—61no—
189C4×#41—61no—
190C4×#41C2×D311yescharacteristic
191C2×C4×D4—31no—
192C2×C4×D4—61no—
193C2×C4×D4—62no—
194C2×C4×D4—61no—
195#460—21no—
196#460—21no—
197#460—61no—
198#460—61no—
199#459—21no—
200#459—21no—
201#459—61no—
202#459—61no—
203#453—68no—
204#423—31no—
205#423C2×D311yescharacteristic, complemented
206C2×#104—32no—
207C2×#104—32no—
208#418—32no—
209#418C2×D312yescomplemented
210C2×#100—32no—
211#392—62no—
212#390—32no—
213C4×C4⋊C4—31no—
214#343—32no—
215#339—32no—
216#339—32no—
217C24×C3—22no—
218C23×D3—22no—
219C23×D3C2×D412yes—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41C2×D412yes—
223C3×#41#4112yes—
224C2×C3×Q8C2×D411yescharacteristic
225C2×C3×D4—21no—
226C2×C3×D4—22no—
227C2×C3×D4—22no—
228C2×C3×D4—22no—
229C2×C3×D4—22no—
230C2×C3×D4—22no—
231C2×C3×D4—22no—
232C2×C3×D4—44no—
233C2×C3×D4—41no—
234C2×C3×D4—41no—
235C2×C3×D4—41no—
236C2×C3×D4—41no—
237C2×C3×D4—82no—
238C2×C3×D4C2×D411yescharacteristic
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C2×#67—22no—
246C2×#67—21no—
247C2×#67—48no—
248C2×#67—48no—
249C2×#67—84no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3C2×D412yes—
253#239—24no—
254#239—24no—
255D3×D4—28no—
256D3×D4—24no—
257D3×D4—28no—
258D3×D4—24no—
259#235—24no—
260#235—21no—
261#235—21no—
262#235—24no—
263#235C2×D412yes—
264#235#4112yes—
265C2×D12—22no—
266C2×D12—24no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—24no—
272C2×D12C2×D412yes—
273C2×D12C2×D411yescharacteristic
274C2×D12#4112yes—
275C2×C4×D3—22no—
276C2×C4×D3—21no—
277C2×C4×D3—22no—
278C2×C4×D3—21no—
279C2×C4×D3—22no—
280C2×C4×D3—22no—
281C2×C4×D3—22no—
282C2×C4×D3—21no—
283C2×C4×D3—22no—
284C2×C4×D3—44no—
285C2×C4×D3—84no—
286C2×Dic6C2×D411yescharacteristic
287C3×SD16—44no—
288C3×D8—44no—
289C3×M16—22no—
290C3×M16—22no—
291C2×C3×C8—22no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4C2×D411yescharacteristic
295C3×C4⋊C4C2×D411yescharacteristic
296C3×C22⋊C4—21no—
297C3×C22⋊C4—21no—
298C3×C22⋊C4—21no—
299C3×C42—21no—
300C3×C42—21no—
301C3×C42—21no—
302C3×C42C2×D411yescharacteristic
303C3×C42C2×D411yescharacteristic
304C3×C42C2×D411yescharacteristic
305C3×C42C2×D411yescharacteristic
306#217—22no—
307#217—21no—
308#217—48no—
309#214—44no—
310#213—44no—
311(C2×D3)⋊C4—22no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—22no—
314(C2×D3)⋊C4—22no—
315(C2×D3)⋊C4—21no—
316(C2×D3)⋊C4—21no—
317(C2×D3)⋊C4—22no—
318C4⋊Dic3—22no—
319C4⋊Dic3—24no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3C2×D411yescharacteristic
323C4⋊Dic3C2×D411yescharacteristic
324Dic3⋊C4—22no—
325Dic3⋊C4—21no—
326Dic3⋊C4—21no—
327C4×Dic3—22no—
328C4×Dic3—22no—
329C4×Dic3—21no—
330C4×Dic3—21no—
331C4×Dic3—21no—
332C4×Dic3—22no—
333C4×Dic3—22no—
334#208—22no—
335#208—22no—
336C2×C3⋊C8—22no—
337H(5,𝔽2)—34no—
338H(5,𝔽2)—62no—
339H(5,𝔽2)—62no—
340H(5,𝔽2)—62no—
341C2×#41—31no—
342C2×#41—61no—
343C2×#41—61no—
344C2×#41C22×D311yescharacteristic
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—31no—
348C22×D4—61no—
349C22×D4—62no—
350C22×D4—61no—
351C22×D4—64no—
352C22×D4C22×D312yes—
353C23×C4—32no—
354C23×C4—62no—
355AGL(1,ℤ/8)—24no—
356AGL(1,ℤ/8)—24no—
357AGL(1,ℤ/8)—64no—
358AGL(1,ℤ/8)—64no—
359C2×SD16—22no—
360C2×SD16—62no—
361C2×D8—22no—
362C2×D8—62no—
363C2×M16—32no—
364C2×M16C22×D312yes—
365#127—21no—
366#127—21no—
367#127—21no—
368#127—21no—
369#127—64no—
370#127—64no—
371#121—128no—
372C4×Q8—31no—
373C4×Q8—31no—
374C4×Q8—61no—
375C4×Q8—61no—
376C4×Q8#6711yescharacteristic, complemented
377C4×Q8#6711yescharacteristic, complemented
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—31no—
381C4×D4—31no—
382C4×D4—61no—
383C4×D4—61no—
384C4×D4—61no—
385C4×D4—62no—
386C4×D4—62no—
387C4×D4—62no—
388C4×D4—62no—
389C4×D4—62no—
390C4×D4—62no—
391C4×D4—62no—
392C4×D4—62no—
393C4×D4—62no—
394C4×D4—62no—
395C4×D4—61no—
396C4×D4—61no—
397C4×D4—61no—
398C4×D4—61no—
399C4×D4—61no—
400C4×D4—61no—
401C4×D4—61no—
402C4×D4—61no—
403C4×D4—61no—
404C4×D4#6711yescharacteristic, complemented
405C4×D4#6711yescharacteristic, complemented
406#117—21no—
407#117—31no—
408#117—62no—
409#117—62no—
410#117—61no—
411#117—61no—
412#117—61no—
413#117C22×D311yescharacteristic
414C2×C4⋊C4—31no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—64no—
425C2×C42—21no—
426C2×C42—32no—
427C2×C42—62no—
428C2×C42—61no—
429C2×C42C22×D311yescharacteristic
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8—61no—
433C4⋊C8—61no—
434#104—64no—
435#104—64no—
436#102—22no—
437#102—22no—
438#102—62no—
439#102—62no—
440#100—64no—
441#95—61no—
442C23×C3—21no—
443C23×C3—44no—
444C23×C3—44no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—42no—
448C23×C3C22×D411yescharacteristic
449C22×D3—22no—
450C22×D3—21no—
451C22×D3—28no—
452C22×D3—22no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—82no—
456C22×D3—82no—
457C22×D3#12114yes—
458C3×Q8—21no—
459C3×Q8#12112yescomplemented
460C3×D4—22no—
461C3×D4—22no—
462C3×D4—21no—
463C3×D4—42no—
464C3×D4—42no—
465C3×D4—42no—
466C3×D4—42no—
467C3×D4—82no—
468C3×D4—82no—
469C3×D4—82no—
470C3×D4—82no—
471C3×D4#12112yescomplemented
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—41no—
479C2×C3×C4—42no—
480C2×C3×C4—81no—
481C2×C3×C4#12011yescharacteristic
482C2×C3×C4#12011yescharacteristic
483C2×C3×C4#12011yescharacteristic
484C2×C3×C4#12011yescharacteristic
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4C2×#4111yescharacteristic
490C2×C3×C4C2×#4111yescharacteristic
491#67—28no—
492#67—22no—
493#67—22no—
494#67—816no—
495C2×Dic3—21no—
496C2×Dic3—24no—
497C2×Dic3—21no—
498C2×Dic3—22no—
499C2×Dic3—21no—
500C2×Dic3—42no—
501C2×Dic3—42no—
502C2×Dic3—42no—
503C2×Dic3—82no—
504D12—28no—
505D12—22no—
506D12—22no—
507D12—21no—
508D12—22no—
509D12—22no—
510D12#12112yescomplemented
511C4×D3—28no—
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—44no—
515C4×D3—42no—
516C4×D3—81no—
517C4×D3—82no—
518C4×D3—82no—
519C4×D3—82no—
520C4×D3—82no—
521Dic6—21no—
522Dic6#12112yescomplemented
523C3×C8—42no—
524C3⋊C8—42no—
525C24—22no—
526C24—32no—
527C24—62no—
528#41—21no—
529#41—21no—
530#41—32no—
531#41—32no—
532#41—64no—
533#41—64no—
534#41—64no—
535#41—64no—
536#41—61no—
537#41—61no—
538#41D3×D412yes—
539#41#23712yes—
540C2×Q8—31no—
541C2×Q8C2×#6711yescharacteristic
542C2×D4—21no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—31no—
550C2×D4—32no—
551C2×D4—32no—
552C2×D4—44no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—64no—
558C2×D4—62no—
559C2×D4—64no—
560C2×D4—68no—
561C2×D4—68no—
562C2×D4—64no—
563C2×D4—62no—
564C2×D4—61no—
565C2×D4—64no—
566C2×D4—61no—
567C2×D4—61no—
568C2×D4—61no—
569C2×D4—61no—
570C2×D4—82no—
571C2×D4—128no—
572C2×D4—128no—
573C2×D4—244no—
574C2×D4C2×#6711yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—32no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—61no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—61no—
587C22×C4—62no—
588C22×C4—61no—
589C22×C4—62no—
590C22×C4—124no—
591C22×C4—244no—
592C22×C4D3×D411yescharacteristic
593C22×C4D3×D411yescharacteristic
594C22×C4C23×D311yescharacteristic
595SD16—44no—
596SD16—124no—
597D8—44no—
598D8—124no—
599M16—22no—
600M16—22no—
601M16—62no—
602M16—62no—
603C2×C8—22no—
604C2×C8—62no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—62no—
610C4⋊C4—62no—
611C4⋊C4—64no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4C2×#6711yescharacteristic
617C4⋊C4C2×#6711yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—62no—
622C22⋊C4—62no—
623C22⋊C4—62no—
624C22⋊C4—62no—
625C22⋊C4—61no—
626C22⋊C4—62no—
627C22⋊C4—62no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—128no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—62no—
635C42—62no—
636C42—61no—
637C42—61no—
638C42—61no—
639C42—62no—
640C42—62no—
641C42D3×D411yescharacteristic
642C42D3×D411yescharacteristic
643C42C2×#6711yescharacteristic
644C42C2×#6711yescharacteristic
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—22no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—84no—
651C22×C3—84no—
652C22×C3—82no—
653C22×C3—82no—
654C22×C3—82no—
655C22×C3C2×#12011yescharacteristic
656C22×C3C2×#12111yescharacteristic
657C22×C3#52511yescharacteristic
658C2×D3—24no—
659C2×D3—22no—
660C2×D3—42no—
661C2×D3—41no—
662C2×D3—42no—
663C2×D3—41no—
664C2×D3—44no—
665C2×D3—82no—
666C2×D3—88no—
667C3×C4—22no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4#45312yescomplemented
674C3×C4C2×#12111yescharacteristic
675C3×C4C2×#12111yescharacteristic
676C3×C4#52511yescharacteristic
677C3×C4#52511yescharacteristic
678Dic3—22no—
679Dic3—44no—
680Dic3—42no—
681Dic3—41no—
682Dic3—41no—
683C23—21no—
684C23—34no—
685C23—44no—
686C23—44no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—68no—
691C23—61no—
692C23—62no—
693C23—62no—
694C23—122no—
695C23—122no—
696C23—242no—
697C23—242no—
698C23C2×D3×D411yescharacteristic
699Q8—21no—
700Q8—32no—
701Q8—61no—
702Q8#93812yescomplemented
703D4—22no—
704D4—22no—
705D4—21no—
706D4—32no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—68no—
712D4—68no—
713D4—62no—
714D4—62no—
715D4—62no—
716D4—62no—
717D4—62no—
718D4—61no—
719D4—62no—
720D4—82no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—2416no—
725D4#93812yescomplemented
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—68no—
735C2×C4—61no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—64no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—62no—
742C2×C4—81no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—124no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—242no—
749C2×C4—241no—
750C2×C4—242no—
751C2×C4—242no—
752C2×C4—242no—
753C2×C4—242no—
754C2×C4#93711yescharacteristic
755C2×C4#93711yescharacteristic
756C2×C4#93711yescharacteristic
757C2×C4#93711yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4C2×D3×D411yescharacteristic
760C2×C4C2×#23711yescharacteristic
761C2×C4D3×#4111yescharacteristic
762C2×C4D3×#4111yescharacteristic
763C2×C4C22×#6711yescharacteristic
764C8—42no—
765C8—122no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—162no—
770C2×C3#284711yescharacteristic
771C2×C3C2×#45311yescharacteristic
772C2×C3#302111yescharacteristic
773D3—44no—
774D3—42no—
775C22—21no—
776C22—21no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—62no—
781C22—64no—
782C22—84no—
783C22—84no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—124no—
788C22—122no—
789C22—121no—
790C22—122no—
791C22—121no—
792C22—242no—
793C22—248no—
794C22D3×#12111yescharacteristic
795C22#560611yescharacteristic
796C22C2×#93711yescharacteristic
797C4—22no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—41no—
802C4—41no—
803C4—62no—
804C4—124no—
805C4—122no—
806C4—121no—
807C4—121no—
808C4#519812yescomplemented
809C4D3×#12111yescharacteristic
810C4#560611yescharacteristic
811C4C2×#93811yescharacteristic
812C4#582811yescharacteristic
813C3#3292011yescharacteristic, complemented, Sylow
814C2—21no—
815C2—21no—
816C2—42no—
817C2—124no—
818C2—122no—
819C2—162no—
820C2#8272311yescharacteristic
821C2C2×#519811yescharacteristic
822C2#8395711yescharacteristic
subgroupG/H
centerC22C2×#937
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3038C2
socleC22×C3C2×#120
hypercenter#3038D3
hypocenterC3#32920
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. C4×#1009C2semidirect
2. C3×#3038C2semidirect
3. C2×#5198C2semidirect
4. #83188C2semidirect
5. #83165C2semidirect
6. #72088C2semidirect
7. #71646C2semidirect
8. #70529C2semidirect
9. #70527C2semidirect
10. #70328C2semidirect
11. #70323C2semidirect
15. C2×C3×#127C22semidirect
39. C3×#423C22semidirect
40. C3×#418C22semidirect
43. #5221C22semidirect
44. #5215C22semidirect
52. C4×C4⋊Dic3C22semidirect
53. #4924C22semidirect
54. #4555C22semidirect
55. #4554C22semidirect
56. #4532C22semidirect
59. #3038D3semidirect
76. #1009D4semidirect
95. C3×C4×Q8D4semidirect
96. C3×C4×Q8D4semidirect
99. C3×C4×D4D4semidirect
100. C3×C4×D4D4semidirect
152. C4×D12D4semidirect
153. C4×D12D4semidirect
159. C4×Dic6D4semidirect
160. C4×Dic6D4semidirect
177. C2×#127C2×D3semidirect
205. #423C2×D3semidirect
209. #418C2×D3semidirect
376. C4×Q8#67semidirect
377. C4×Q8#67semidirect
404. C4×D4#67semidirect
405. C4×D4#67semidirect
459. C3×Q8#121semidirect
471. C3×D4#121semidirect
510. D12#121semidirect
522. Dic6#121semidirect
673. C3×C4#453semidirect
702. Q8#938semidirect
725. D4#938semidirect
808. C4#5198semidirect
813. C3#32920semidirect

Maximal subgroups

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

subgroupindex
C4×#10092
C3×#30382
C2×#51982
#831882
#831652
#720882
#716462
#705292
#705272
#703282
#703232
#329203