Finite Group Databasebeta

← #11864130

Subgroups — #11864130

Order 1152.

1711 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic, complemented
2C3×D3×#121C211yesmaximal, characteristic, complemented
3C2×#63934C212yesmaximal, complemented
4#10592735C211yesmaximal, characteristic, complemented
5C3×#5040C211yesmaximal, characteristic, complemented
6#10591521C212yesmaximal, complemented
7#10591171C211yesmaximal, characteristic, complemented
8#10591168C211yesmaximal, characteristic, complemented
9#10591154C211yesmaximal, characteristic, complemented
10#10590615C212yesmaximal, complemented
11#10590609C212yesmaximal, complemented
12#82624—31nomaximal
13#80040—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
15C2×C3×D3×D4—21no—
16C2×C3×D3×D4C2211yescharacteristic, complemented
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic, complemented
19C22×#626—21no—
20C22×#624—21no—
21C2×#3799—21no—
22C2×#3799—21no—
23C2×#3799—28no—
24C2×#3799C2212yes—
25C2×#3799C2212yescomplemented
26C32×#121C2211yescharacteristic
27C2×#3753C2212yescomplemented
28C3×#939—21no—
29C3×#938C2211yescharacteristic, complemented
30C2×C3×#214C2212yescomplemented
31C3×#930C2211yescharacteristic
32C3×#895C2211yescharacteristic, complemented
33C3×D3×C4⋊C4C2211yescharacteristic, complemented
34C3×#884—21no—
35C3×D3×C22⋊C4—21no—
36#63934—28no—
37C2×#3715C2212yescomplemented
38C2×#3714C2212yescomplemented
39C2×#3711C2212yescomplemented
40#63657C2211yescharacteristic, complemented
41#63636C2212yescomplemented
42C3×#830C2211yescharacteristic, complemented
43C3×#810C2212yescomplemented
44#63565C2212yescomplemented
45#63564C2212yescomplemented
46(C2×D3)⋊(C3⋊C8)C2212yescomplemented
47C22×#239—31no—
48C22×#235—31no—
49C2×C3×#121—31no—
50C2×#932—32no—
51C2×#914—32no—
52D3×#121D311yescharacteristic, complemented
53C3×#448—31no—
54#5227—31no—
55#5207—31no—
56#5172—32no—
57#5040—31no—
58#5040D311yescharacteristic, complemented
59#5037—32no—
60#5037—32no—
61#5036—31no—
62#5036—31no—
63#5036—31no—
64#5036—61no—
65#4966—32no—
66#4810—32no—
67#4803—32no—
68#4732—31no—
69#4726—31no—
70C23×C3⋊D3—21no—
71C23×C3×D3—21no—
72C23×C3×D3D411yescharacteristic
73C2×C32×D4—21no—
74C2×C32×D4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C2×C4⋊(C3⋊D3)—21no—
77C2×C4⋊(C3⋊D3)—24no—
78C2×C4⋊(C3⋊D3)C2312yes—
79C2×C3×#67—21no—
80C2×C3×#67—21no—
81C2×C3×#67—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3D411yescharacteristic
84C3×D3×D4—24no—
85C3×D3×D4—44no—
86C2×C3×D12—21no—
87C2×C3×D12C2311yescharacteristic
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—21no—
90C2×C3×C4×D3D411yescharacteristic
91C2×C3×C4×D3D411yescharacteristic
92C2×C3×C4×D3C2311yescharacteristic
93C2×C3×C4×D3C2311yescharacteristic
94C2×C3×Dic6—21no—
95C2×C3×Dic6—24no—
96C2×C3×Dic6C2312yes—
97C2×#626—28no—
98C2×#626—22no—
99C2×#626—22no—
100C2×#624—28no—
101C2×#624—22no—
102C2×#624—22no—
103#3799—28no—
104#3799—28no—
105#3799—24no—
106#3799—24no—
107#3799—24no—
108#3799D418yescomplemented
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111#3753—24no—
112C2×C3⋊(C3⋊C8)C2312yes—
113C3×#217—21no—
114C3×#214—24no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C2×C3×C3⋊C8C2312yes—
120#3715—24no—
121#3714—24no—
122#3711—24no—
123#3006—91noSylow
124C22×C3×Q8—31no—
125C22×C3×D4—31no—
126C22×C3×D4—61no—
127C23×C3×C4—31no—
128C22×#67—61no—
129C2×#239—32no—
130C2×#239—32no—
131C2×#239—68no—
132C2×#239—61no—
133C2×#239—61no—
134C2×D3×D4—21no—
135C2×D3×D4C2×D311yescharacteristic, complemented
136C2×#235—32no—
137C2×#235—32no—
138C2×#235—68no—
139C2×#235—61no—
140C2×#235—61no—
141C22×D12—31no—
142C22×D12—31no—
143C22×D12—61no—
144C22×D12—61no—
145C22×C4×D3—61no—
146C22×C4×D3—61no—
147C22×C4×D3C2×D311yescharacteristic
148C22×Dic6C2×D311yescharacteristic, complemented
149C2×C3×SD16—32no—
150C3×#121—21no—
151C3×#121—31no—
152C3×#121—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#121—61no—
156C3×#121C2×D311yescharacteristic
157C3×#121C2×D311yescharacteristic
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—61no—
160C2×#215—32no—
161#939—21no—
162#938C2×D311yescharacteristic, complemented
163C2×#214—32no—
164C2×#214C2×D312yescomplemented
165#932—68no—
166C2×#213—32no—
167C2×#213—32no—
168C2×#213—32no—
169C2×#213—62no—
170#930C2×D311yescharacteristic
171C2×#208—32no—
172#914—68no—
173C2×D24—32no—
174C2×ΓL(1,𝔽25)—32no—
175#895C2×D311yescharacteristic, complemented
176D3×C4⋊C4C2×D311yescharacteristic, complemented
177#884—21no—
178D3×C22⋊C4—21no—
179C3×#103—32no—
180C3×C22⋊C8—31no—
181#835—32no—
182#830—31no—
183#830—31no—
184#830—32no—
185#830—61no—
186#830C2×D311yescharacteristic, complemented
187#821—32no—
188(C2×D3)⋊C8—32no—
189#810—32no—
190#810C2×D312yescomplemented
191#809—32no—
192#809—32no—
193#809—32no—
194#809—62no—
195C23×C32—21no—
196C23×C32C2×D411yescharacteristic
197C22×C3⋊D3—24no—
198C22×C3⋊D3—22no—
199C22×C3⋊D3—42no—
200C22×C3⋊D3—42no—
201C22×C3×D3—22no—
202C22×C3×D3—22no—
203C22×C3×D3—21no—
204C22×C3×D3—41no—
205C22×C3×D3—42no—
206C22×C3×D3—42no—
207C22×C3×D3—42no—
208C22×C3×D3C2×D411yescharacteristic
209C22×C3×D3C2×D411yescharacteristic
210C32×D4—22no—
211C32×D4—42no—
212C2×C32×C4—22no—
213C2×C32×C4—21no—
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2411yescharacteristic
216C4⋊(C3⋊D3)—24no—
217C4⋊(C3⋊D3)—22no—
218C4⋊(C3⋊D3)C2×D414yescomplemented
219C3×#67—42no—
220C3×#67—42no—
221C3×#67—42no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3C2×D411yescharacteristic
227C2×C3×Dic3C2×D411yescharacteristic
228C3×D12—22no—
229C3×D12—42no—
230C3×C4×D3—22no—
231C3×C4×D3—22no—
232C3×C4×D3—22no—
233C3×C4×D3—42no—
234C3×C4×D3C2×D414yes—
235C3×Dic6—24no—
236C3×Dic6—22no—
237C3×Dic6C2×D414yescomplemented
238#626—28no—
239#626—28no—
240#624—28no—
241#624—28no—
242C3⋊(C3⋊C8)—22no—
243C3×C3⋊C8—22no—
244C22×#41—91no—
245C2×AGL(1,ℤ/8)—92no—
246C2×#121—31no—
247#449—92no—
248#449—92no—
249#448—31no—
250#448—91no—
251#447—91no—
252#447—91no—
253#417—92no—
254#407—91no—
255C24×C3—31no—
256C24×C3—61no—
257C23×D3—21no—
258C23×D3—61no—
259C23×D3—61no—
260C23×D3—121no—
261C23×D3#6711yescharacteristic
262C2×C3×Q8—32no—
263C2×C3×Q8—64no—
264C2×C3×Q8—61no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—31no—
269C2×C3×D4—41no—
270C2×C3×D4—61no—
271C2×C3×D4—64no—
272C2×C3×D4—61no—
273C2×C3×D4—61no—
274C2×C3×D4—61no—
275C2×C3×D4—124no—
276C2×C3×D4C22×D311yescharacteristic
277C2×C3×D4C22×D311yescharacteristic
278C22×C3×C4—21no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—64no—
285C22×C3×C4—61no—
286C22×C3×C4—61no—
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C2×#67—21no—
290C2×#67—21no—
291C2×#67—21no—
292C2×#67—62no—
293C2×#67—62no—
294C2×#67—68no—
295C22×Dic3—21no—
296C22×Dic3#6711yescharacteristic
297#239—38no—
298#239—64no—
299#239—64no—
300#239—68no—
301#239—68no—
302#239—64no—
303D3×D4—24no—
304D3×D4—44no—
305#235—38no—
306#235—64no—
307#235—64no—
308#235—68no—
309#235—68no—
310#235—64no—
311C2×D12—21no—
312C2×D12—32no—
313C2×D12—32no—
314C2×D12—62no—
315C2×D12—64no—
316C2×D12—64no—
317C2×D12—68no—
318C2×D12—62no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—124no—
323C2×D12—121no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—24no—
326C2×C4×D3—21no—
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—68no—
330C2×C4×D3—68no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3#6711yescharacteristic
334C2×C4×D3#6711yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6—21no—
338C2×Dic6—24no—
339C2×Dic6C22×D312yes—
340C3×SD16—64no—
341C2×C3×C8—32no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353#217—21no—
354#215—64no—
355#214—24no—
356#214—64no—
357#213—64no—
358#213—64no—
359#213—64no—
360#213—124no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363C4⋊Dic3C22×D311yescharacteristic
364Dic3⋊C4—21no—
365#208—64no—
366C2×C3⋊C8—32no—
367C2×C3⋊C8—32no—
368C2×C3⋊C8—62no—
369C2×C3⋊C8C22×D312yes—
370D24—64no—
371ΓL(1,𝔽25)—64no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32AGL(1,ℤ/8)12yescomplemented
378C22×C32C22×D411yescharacteristic
379C2×C3⋊D3—24no—
380C2×C3⋊D3—48no—
381C2×C3⋊D3—42no—
382C2×C3⋊D3—42no—
383C2×C3×D3—21no—
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3—44no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—84no—
393C2×C3×D3#12012yes—
394C32×C4—21no—
395C32×C4—41no—
396C32×C4C22×D412yes—
397C3×Dic3—21no—
398C3×Dic3—24no—
399C3×Dic3—41no—
400C3×Dic3#12012yes—
401C2×#41—92no—
402C2×#41—92no—
403C2×#41—181no—
404C2×#41—181no—
405C2×#41—188no—
406C22×Q8—31no—
407C22×D4—31no—
408C22×D4—61no—
409C22×D4—91no—
410C22×D4—181no—
411C23×C4—31no—
412C23×C4—181no—
413AGL(1,ℤ/8)—188no—
414C2×SD16—32no—
415C2×SD16—92no—
416C2×D8—92no—
417C2×D8—92no—
418C2×M16—92no—
419#121—31no—
420#121—31no—
421#121—31no—
422#121—61no—
423#121—61no—
424#121D3211yescharacteristic
425C2×C4⋊C4—31no—
426C2×C22⋊C4—61no—
427#103—32no—
428#103—92no—
429#102—92no—
430#102—92no—
431C22⋊C8—31no—
432C22⋊C8—92no—
433C22⋊C8—91no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—31no—
438C23×C3—31no—
439C23×C3—41no—
440C23×C3—62no—
441C23×C3—62no—
442C23×C3—61no—
443C23×C3—121no—
444C23×C3—122no—
445C23×C3—122no—
446C23×C3—122no—
447C23×C3D3×D411yescharacteristic
448C23×C3C2×#6711yescharacteristic
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—21no—
452C22×D3—41no—
453C22×D3—42no—
454C22×D3—42no—
455C22×D3—42no—
456C22×D3—64no—
457C22×D3—64no—
458C22×D3—62no—
459C22×D3—62no—
460C22×D3—122no—
461C22×D3—124no—
462C22×D3—122no—
463C22×D3—122no—
464C22×D3—122no—
465C22×D3—122no—
466C22×D3—242no—
467C22×D3—242no—
468C22×D3C2×#6711yescharacteristic
469C22×D3C2×#6711yescharacteristic
470C3×Q8—34no—
471C3×Q8—64no—
472C3×Q8—62no—
473C3×D4—22no—
474C3×D4—22no—
475C3×D4—42no—
476C3×D4—42no—
477C3×D4—42no—
478C3×D4—62no—
479C3×D4—82no—
480C3×D4—122no—
481C3×D4—122no—
482C3×D4—122no—
483C3×D4—122no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—34no—
492C2×C3×C4—31no—
493C2×C3×C4—42no—
494C2×C3×C4—41no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—64no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—61no—
502C2×C3×C4—122no—
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4C2×#6711yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—42no—
508#67—42no—
509#67—42no—
510#67—68no—
511#67—68no—
512C2×Dic3—24no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—21no—
516C2×Dic3C2×#6711yescharacteristic
517C2×Dic3C2×#6711yescharacteristic
518D12—22no—
519D12—34no—
520D12—34no—
521D12—42no—
522D12—64no—
523D12—64no—
524D12—64no—
525D12—68no—
526D12—68no—
527D12—62no—
528D12—62no—
529D12—122no—
530D12—124no—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—22no—
534C4×D3—42no—
535C4×D3—68no—
536C4×D3—68no—
537C4×D3—68no—
538C4×D3—68no—
539C4×D3D3×D414yes—
540Dic6—24no—
541Dic6—22no—
542Dic6D3×D414yescomplemented
543C3×C8—62no—
544C3⋊C8—22no—
545C3⋊C8—62no—
546C3⋊C8—62no—
547C3⋊C8—122no—
548C2×C32—22no—
549C2×C32—81no—
550C2×C32C2×#12011yescharacteristic
551C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
552C2×C32#57511yescharacteristic
553C3⋊D3—44no—
554C3×D3—22no—
555C3×D3—41no—
556C3×D3—81no—
557C24—31no—
558C24—61no—
559C24—181no—
560#41—98no—
561#41—184no—
562#41—184no—
563#41—184no—
564#41—188no—
565#41—188no—
566C2×Q8—32no—
567C2×Q8—64no—
568C2×Q8—61no—
569C2×D4—21no—
570C2×D4—31no—
571C2×D4—61no—
572C2×D4—64no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—92no—
577C2×D4—124no—
578C2×D4—184no—
579C2×D4—182no—
580C2×D4—182no—
581C2×D4—188no—
582C2×D4—181no—
583C2×D4C2×D3211yescharacteristic
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—64no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—182no—
593C22×C4—182no—
594C22×C4—188no—
595C22×C4C2×D3211yescharacteristic
596SD16—64no—
597SD16—184no—
598D8—184no—
599D8—184no—
600M16—184no—
601C2×C8—32no—
602C2×C8—92no—
603C4⋊C4—31no—
604C4⋊C4—61no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—22no—
616C22×C3—32no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—124no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—244no—
638C22×C3#91412yescomplemented
639C22×C3#93212yescomplemented
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×#6711yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—44no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—64no—
652C2×D3—64no—
653C2×D3—84no—
654C2×D3—124no—
655C2×D3—128no—
656C2×D3—128no—
657C2×D3—122no—
658C2×D3—122no—
659C2×D3—122no—
660C2×D3—122no—
661C2×D3—242no—
662C2×D3—242no—
663C2×D3—248no—
664C2×D3#93712yes—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—22no—
668C3×C4—32no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—64no—
673C3×C4—61no—
674C3×C4—81no—
675C3×C4—121no—
676C3×C4C2×D3×D412yes—
677C3×C4C2×D3×D412yes—
678Dic3—21no—
679Dic3—24no—
680Dic3—41no—
681Dic3#93712yes—
682C32#300611yescharacteristic, complemented, Sylow
683C23—21no—
684C23—31no—
685C23—31no—
686C23—62no—
687C23—62no—
688C23—61no—
689C23—121no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—184no—
694C23—182no—
695C23—362no—
696C23—362no—
697C23D3×#6711yescharacteristic
698Q8—34no—
699Q8—64no—
700Q8—62no—
701D4—22no—
702D4—42no—
703D4—62no—
704D4—94no—
705D4—122no—
706D4—122no—
707D4—122no—
708D4—122no—
709D4—184no—
710D4—188no—
711D4—188no—
712D4—182no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—31no—
716C2×C4—34no—
717C2×C4—31no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—64no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—61no—
725C2×C4—122no—
726C2×C4—188no—
727C2×C4—188no—
728C2×C4D3×#6711yescharacteristic
729C2×C4C22×D3211yescharacteristic
730C8—62no—
731C8—182no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—62no—
739C2×C3—81no—
740C2×C3—81no—
741C2×C3—121no—
742C2×C3—161no—
743C2×C3—241no—
744C2×C3D3×#12011yescharacteristic
745C2×C3C2×#91411yescharacteristic
746C2×C3#577711yescharacteristic
747C2×C3C2×#93211yescharacteristic
748C2×C3C2×#93711yescharacteristic
749C2×C3#582211yescharacteristic
750D3—22no—
751D3—41no—
752D3—81no—
753D3—124no—
754D3—124no—
755D3—244no—
756C22—21no—
757C22—21no—
758C22—32no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—124no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—184no—
772C22—244no—
773C22—368no—
774C22—362no—
775C22—362no—
776C22#6393412yescomplemented
777C22C2×D3×#6711yescharacteristic
778C4—21no—
779C4—32no—
780C4—41no—
781C4—61no—
782C4—64no—
783C4—121no—
784C4D32×D412yes—
785C3—21no—
786C3#8004011yescharacteristic, complemented
787C3#8262411yescharacteristic, complemented
788C2—22no—
789C2—62no—
790C2—81no—
791C2—121no—
792C2—241no—
793C2—364no—
794C2C2×#6393411yescharacteristic
795C2D3×#93711yescharacteristic
796C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C3×D3×#121C2semidirect
3. C2×#63934C2semidirect
4. #10592735C2semidirect
5. C3×#5040C2semidirect
6. #10591521C2semidirect
7. #10591171C2semidirect
8. #10591168C2semidirect
9. #10591154C2semidirect
10. #10590615C2semidirect
11. #10590609C2semidirect
14. C22×C4⋊(C3⋊D3)C22semidirect
16. C2×C3×D3×D4C22semidirect
18. C22×C3×Dic6C22semidirect
25. C2×#3799C22semidirect
27. C2×#3753C22semidirect
29. C3×#938C22semidirect
30. C2×C3×#214C22semidirect
32. C3×#895C22semidirect
33. C3×D3×C4⋊C4C22semidirect
37. C2×#3715C22semidirect
38. C2×#3714C22semidirect
39. C2×#3711C22semidirect
40. #63657C22semidirect
41. #63636C22semidirect
42. C3×#830C22semidirect
43. C3×#810C22semidirect
44. #63565C22semidirect
45. #63564C22semidirect
46. (C2×D3)⋊(C3⋊C8)C22semidirect
52. D3×#121D3semidirect
58. #5040D3semidirect
108. #3799D4semidirect
135. C2×D3×D4C2×D3semidirect
148. C22×Dic6C2×D3semidirect
162. #938C2×D3semidirect
164. C2×#214C2×D3semidirect
175. #895C2×D3semidirect
176. D3×C4⋊C4C2×D3semidirect
186. #830C2×D3semidirect
190. #810C2×D3semidirect
218. C4⋊(C3⋊D3)C2×D4semidirect
237. C3×Dic6C2×D4semidirect
377. C22×C32AGL(1,ℤ/8)semidirect
542. Dic6D3×D4semidirect
638. C22×C3#914semidirect
639. C22×C3#932semidirect
682. C32#3006semidirect
776. C22#63934semidirect
786. C3#80040semidirect
787. C3#82624semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
C3×D3×#1212
C2×#639342
#105927352
C3×#50402
#105915212
#105911712
#105911682
#105911542
#105906152
#105906092
#826243
#800403