Finite Group Databasebeta

← #11864135

Subgroups — #11864135

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
2D3×#930C211yesmaximal, characteristic, complemented
3C2×#63794C212yesmaximal, complemented
4#10592431C211yesmaximal, characteristic, complemented
5C3×#4738C211yesmaximal, characteristic, complemented
6C3×#4726C211yesmaximal, characteristic, complemented
7#10591174C211yesmaximal, characteristic, complemented
8#10591168C211yesmaximal, characteristic, complemented
9#10590967C212yesmaximal, complemented
10#10590823C212yesmaximal, complemented
11#10590671C212yesmaximal, complemented
12#80040—31nomaximal
13#78639—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic, complemented
17C2×D3×#67—21no—
18C22×#626—21no—
19C22×#624—21no—
20C2×D3×D12C2211yescharacteristic, complemented
21C2×#3799—21no—
22C2×#3799—21no—
23C2×#3799—28no—
24C2×#3799C2212yes—
25C2×#3799C2212yescomplemented
26#64139C2211yescharacteristic
27C2×#3745C2212yescomplemented
28C3×#930C2211yescharacteristic
29C2×C3×#204C2212yescomplemented
30C2×C3×ΓL(1,𝔽25)C2212yescomplemented
31#63978—21no—
32D3×(C2×D3)⋊C4—21no—
33#63909C2211yescharacteristic, complemented
34#63908C2211yescharacteristic, complemented
35#63906—21no—
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×#3717C2212yescomplemented
38C2×#3714C2212yescomplemented
39#63794—28no—
40C32×C22⋊C8C2211yescharacteristic, complemented
41#63648C2212yescomplemented
42C3×#830C2211yescharacteristic, complemented
43C3×(C2×D3)⋊C8C2212yescomplemented
44C3×#816C2212yescomplemented
45#63566C2212yescomplemented
46#63564C2212yescomplemented
47C22×#239—31no—
48C22×#235—31no—
49C2×#930—31no—
50C2×#914—32no—
51C2×#908—32no—
52D3×#121—31no—
53C3×#448—31no—
54C3×#407—31no—
55#5227—31no—
56#5172—32no—
57#5133—32no—
58#5036—31no—
59#4810—32no—
60#4803—32no—
61#4738—31no—
62#4738D311yescharacteristic, complemented
63#4734—32no—
64#4734—32no—
65#4732—31no—
66#4732—31no—
67#4732—31no—
68#4732—61no—
69#4726D311yescharacteristic, complemented
70C23×C3⋊D3—21no—
71C23×C3×D3D411yescharacteristic
72C22×D32—21no—
73C22×C32×C4C2311yescharacteristic
74C2×#638—21no—
75C2×C4⋊(C3⋊D3)—21no—
76C2×C4⋊(C3⋊D3)—24no—
77C2×C4⋊(C3⋊D3)C2311yescharacteristic
78C2×C4⋊(C3⋊D3)C2312yes—
79C2×C3×#67—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3D411yescharacteristic
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3D411yescharacteristic
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×C4×D3C2311yescharacteristic
87C2×C3×C4×D3C2311yescharacteristic
88C2×C3×Dic6—21no—
89C2×C3×Dic6—24no—
90C2×C3×Dic6C2312yes—
91D3×#67—44no—
92C2×#626—28no—
93C2×#626—22no—
94C2×#626—22no—
95C2×#626—21no—
96C2×#626—21no—
97C2×#625—21no—
98C2×#624—28no—
99C2×#624—22no—
100C2×#624—22no—
101C2×D3×Dic3—21no—
102D3×D12—24no—
103#3799—28no—
104#3799—28no—
105#3799—24no—
106#3799—24no—
107#3799—24no—
108#3799D418yescomplemented
109C2×C32×C8C2312yes—
110#3752—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3745—24no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊C8C2312yes—
116C3×#204—24no—
117C3×ΓL(1,𝔽25)—24no—
118Dic3⋊Dic3—21no—
119#3722—21no—
120(C2×D3)⋊Dic3—21no—
121#3717—24no—
122#3714—24no—
123#3006—91noSylow
124C22×C3×Q8—31no—
125C23×C3×C4—31no—
126C22×#67—61no—
127C22×#67—61no—
128C2×#239—32no—
129C2×#239—32no—
130C2×#239—68no—
131C2×#239—61no—
132C2×#239—61no—
133C2×D3×D4—31no—
134C2×D3×D4—61no—
135C2×#235—32no—
136C2×#235—32no—
137C2×#235—68no—
138C2×#235—61no—
139C2×#235—61no—
140C22×D12—31no—
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—
150C2×C3×M16—32no—
151C3×#121—31no—
152C2×#215—32no—
153#939—61no—
154#938—31no—
155C2×#213—32no—
156#930—31no—
157#930—31no—
158#930—31no—
159#930—31no—
160#930—61no—
161#930—61no—
162#930—61no—
163#930C2×D311yescharacteristic
164C2×(C2×D3)⋊C4—61no—
165C2×C4⋊Dic3—31no—
166#914—68no—
167#908—68no—
168C2×D24—32no—
169C2×D24—32no—
170C2×D24—32no—
171C2×D24—62no—
172C2×#204—32no—
173C2×#204C2×D312yescomplemented
174C2×ΓL(1,𝔽25)C2×D312yescomplemented
175#895—31no—
176D3×C4⋊C4—31no—
177#884—61no—
178D3×C22⋊C4—61no—
179C3×#103—32no—
180C3×C22⋊C8—21no—
181C3×C22⋊C8—31no—
182C3×C22⋊C8—32no—
183C3×C22⋊C8C2×D311yescharacteristic, complemented
184C3×C22⋊C8C2×D311yescharacteristic, complemented
185#835—32no—
186#830C2×D311yescharacteristic, complemented
187#821—32no—
188#821—32no—
189#821—32no—
190#821—62no—
191(C2×D3)⋊C8C2×D312yescomplemented
192#816—32no—
193#816C2×D312yescomplemented
194#809—32no—
195C23×C32C2×D411yescharacteristic
196C22×C3⋊D3—24no—
197C22×C3⋊D3—22no—
198C22×C3⋊D3—21no—
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×D3C2×D411yescharacteristic
206C22×C3×D3C2×D411yescharacteristic
207C2×D32—42no—
208C2×D32—42no—
209C2×D32—42no—
210C2×C32×C4—22no—
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2411yescharacteristic
213#638—42no—
214C2×C3⋊Dic3—21no—
215C4⋊(C3⋊D3)—24no—
216C4⋊(C3⋊D3)—22no—
217C4⋊(C3⋊D3)—22no—
218C4⋊(C3⋊D3)C2×D414yescomplemented
219C3×#67—42no—
220C2×C3×Dic3—24no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3C2×D411yescharacteristic
225C2×C3×Dic3C2×D411yescharacteristic
226C3×D12—22no—
227C3×C4×D3—22no—
228C3×C4×D3—22no—
229C3×C4×D3—22no—
230C3×C4×D3C2×D414yes—
231C3×Dic6—24no—
232C3×Dic6—22no—
233C3×Dic6C2×D414yescomplemented
234#626—28no—
235#626—28no—
236#626—42no—
237#626—42no—
238#625—42no—
239#624—28no—
240#624—28no—
241D3×Dic3—42no—
242C32×C8—22no—
243C3×C3⋊C8—22no—
244C22×#41—91no—
245C2×AGL(1,ℤ/8)—92no—
246C2×#121—91no—
247#449—92no—
248#449—92no—
249#448—31no—
250#448—91no—
251#447—91no—
252#447—91no—
253#417—92no—
254#407—31no—
255C24×C3—31no—
256C23×D3—61no—
257C23×D3—61no—
258C23×D3—61no—
259C23×D3—61no—
260C23×D3—121no—
261C23×D3D1211yescharacteristic
262C2×C3×Q8—32no—
263C2×C3×Q8—64no—
264C2×C3×Q8—61no—
265C2×C3×D4—31no—
266C2×C3×D4—61no—
267C22×C3×C4—21no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—64no—
274C22×C3×C4—61no—
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C2×#67—21no—
278C2×#67—62no—
279C2×#67—62no—
280C2×#67—68no—
281C2×#67—61no—
282C2×#67—61no—
283C2×#67—61no—
284C2×#67—61no—
285C2×#67—61no—
286C2×#67—61no—
287C2×#67—121no—
288C2×#67—124no—
289C22×Dic3—21no—
290C22×Dic3—61no—
291C22×Dic3D1211yescharacteristic
292#239—38no—
293#239—64no—
294#239—64no—
295#239—68no—
296#239—68no—
297#239—64no—
298D3×D4—64no—
299D3×D4—124no—
300#235—38no—
301#235—64no—
302#235—64no—
303#235—68no—
304#235—68no—
305#235—64no—
306C2×D12—32no—
307C2×D12—32no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—62no—
311C2×D12—61no—
312C2×D12—64no—
313C2×D12—64no—
314C2×D12—64no—
315C2×D12—68no—
316C2×D12—62no—
317C2×D12—62no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—124no—
323C2×D12—121no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—24no—
326C2×C4×D3—62no—
327C2×C4×D3—62no—
328C2×C4×D3—68no—
329C2×C4×D3—68no—
330C2×C4×D3—62no—
331C2×C4×D3—62no—
332C2×C4×D3—61no—
333C2×C4×D3D1211yescharacteristic
334C2×C4×D3D1211yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6—21no—
338C2×Dic6—24no—
339C2×Dic6C22×D312yes—
340C3×SD16—64no—
341C3×M16—64no—
342C2×C3×C8—22no—
343C2×C3×C8—32no—
344C2×C3×C8C22×D312yes—
345C2×C3×C8C22×D312yes—
346C3×C4⋊C4—31no—
347C3×C22⋊C4—61no—
348#217—61no—
349#215—64no—
350#213—64no—
351(C2×D3)⋊C4—21no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—121no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3C22×D311yescharacteristic
363Dic3⋊C4—61no—
364C2×C3⋊C8C22×D312yes—
365D24—64no—
366D24—64no—
367D24—64no—
368D24—124no—
369#204—24no—
370#204—64no—
371ΓL(1,𝔽25)—24no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32AGL(1,ℤ/8)12yescomplemented
375C22×C32C22×D411yescharacteristic
376C2×C3⋊D3—24no—
377C2×C3⋊D3—48no—
378C2×C3⋊D3—42no—
379C2×C3⋊D3—42no—
380C2×C3⋊D3—41no—
381C2×C3⋊D3—41no—
382C2×C3⋊D3—41no—
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#12012yes—
393D32—84no—
394C32×C4—21no—
395C32×C4C22×D412yes—
396C3⋊Dic3—41no—
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—91no—
408C22×D4—91no—
409C22×D4—181no—
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—32no—
419#121—31no—
420#121—91no—
421#121—91no—
422#121—91no—
423#121—181no—
424#121—181no—
425C2×C4⋊C4—91no—
426C2×C22⋊C4—181no—
427#103—32no—
428#103—92no—
429#102—92no—
430#102—92no—
431C22⋊C8—31no—
432C22⋊C8—32no—
433C22⋊C8D3211yescharacteristic, complemented
434C23×C3—21no—
435C23×C3—31no—
436C23×C3—31no—
437C23×C3—62no—
438C23×C3—62no—
439C23×C3—61no—
440C23×C3—121no—
441C23×C3C2×D1211yescharacteristic
442C23×C3D3×D411yescharacteristic
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—21no—
446C22×D3—41no—
447C22×D3—64no—
448C22×D3—64no—
449C22×D3—62no—
450C22×D3—62no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—122no—
454C22×D3—124no—
455C22×D3—121no—
456C22×D3—122no—
457C22×D3—122no—
458C22×D3—122no—
459C22×D3—122no—
460C22×D3—122no—
461C22×D3—122no—
462C22×D3—122no—
463C22×D3—122no—
464C22×D3—122no—
465C22×D3—122no—
466C22×D3—242no—
467C22×D3—242no—
468C22×D3C2×D1211yescharacteristic
469C22×D3C2×D1211yescharacteristic
470C3×Q8—34no—
471C3×Q8—64no—
472C3×Q8—62no—
473C3×D4—62no—
474C3×D4—122no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—31no—
480C2×C3×C4—34no—
481C2×C3×C4—31no—
482C2×C3×C4—42no—
483C2×C3×C4—62no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—64no—
487C2×C3×C4—62no—
488C2×C3×C4—62no—
489C2×C3×C4—61no—
490C2×C3×C4C2×D1211yescharacteristic
491C2×C3×C4D3×D411yescharacteristic
492C2×C3×C4C23×D311yescharacteristic
493C2×C3×C4C23×D311yescharacteristic
494#67—42no—
495#67—68no—
496#67—68no—
497#67—122no—
498#67—122no—
499#67—122no—
500#67—122no—
501#67—122no—
502#67—122no—
503#67—242no—
504C2×Dic3—24no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—121no—
511C2×Dic3—122no—
512C2×Dic3C2×D1211yescharacteristic
513C2×Dic3C2×D1211yescharacteristic
514D12—22no—
515D12—34no—
516D12—34no—
517D12—64no—
518D12—64no—
519D12—64no—
520D12—68no—
521D12—68no—
522D12—62no—
523D12—62no—
524D12—62no—
525D12—62no—
526D12—122no—
527D12—122no—
528D12—124no—
529D12—122no—
530D12—122no—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—22no—
534C4×D3—68no—
535C4×D3—68no—
536C4×D3—68no—
537C4×D3—68no—
538C4×D3—122no—
539C4×D3D3×D414yes—
540Dic6—24no—
541Dic6—22no—
542Dic6D3×D414yescomplemented
543C3×C8—22no—
544C3×C8—22no—
545C3×C8—42no—
546C3×C8—62no—
547C3⋊C8—22no—
548C2×C32—22no—
549C2×C32C2×#12011yescharacteristic
550C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
551C2×C32#57511yescharacteristic
552C3⋊D3—44no—
553C3⋊D3—81no—
554C3×D3—22no—
555C3×D3—41no—
556C3×D3—81no—
557C24—31no—
558C24—181no—
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—31no—
570C2×D4—61no—
571C2×D4—92no—
572C2×D4—91no—
573C2×D4—184no—
574C2×D4—184no—
575C2×D4—181no—
576C2×D4—182no—
577C2×D4—182no—
578C2×D4—188no—
579C2×D4—181no—
580C2×D4—181no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4—364no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—64no—
590C22×C4—61no—
591C22×C4—182no—
592C22×C4—182no—
593C22×C4—188no—
594C22×C4—181no—
595C22×C4C2×D3211yescharacteristic
596SD16—64no—
597SD16—184no—
598D8—184no—
599D8—184no—
600M16—64no—
601C2×C8—32no—
602C2×C8C2×D3212yes—
603C4⋊C4—31no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
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—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—124no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3#90812yescomplemented
629C22×C3#91412yescomplemented
630C22×C3C22×D1211yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—44no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—124no—
644C2×D3—128no—
645C2×D3—128no—
646C2×D3—122no—
647C2×D3—122no—
648C2×D3—122no—
649C2×D3—122no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—242no—
657C2×D3—242no—
658C2×D3—248no—
659C2×D3—241no—
660C2×D3—241no—
661C2×D3—241no—
662C2×D3—244no—
663C2×D3—244no—
664C2×D3#88212yes—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—22no—
668C3×C4—32no—
669C3×C4—41no—
670C3×C4—64no—
671C3×C4—61no—
672C3×C4—121no—
673C3×C4C2×D3×D412yes—
674C3×C4C2×D3×D412yes—
675Dic3—21no—
676Dic3—24no—
677Dic3—41no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3#88212yes—
682C32#300611yescharacteristic, complemented, Sylow
683C23—31no—
684C23—31no—
685C23—62no—
686C23—62no—
687C23—61no—
688C23—121no—
689C23—184no—
690C23—182no—
691C23—181no—
692C23—362no—
693C23—362no—
694C23—362no—
695C23—362no—
696C23—362no—
697C23D3×D1211yescharacteristic
698Q8—34no—
699Q8—64no—
700Q8—62no—
701D4—62no—
702D4—94no—
703D4—122no—
704D4—184no—
705D4—188no—
706D4—188no—
707D4—182no—
708D4—182no—
709D4—362no—
710D4—362no—
711D4—362no—
712D4—362no—
713C2×C4—22no—
714C2×C4—31no—
715C2×C4—34no—
716C2×C4—31no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—64no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—61no—
724C2×C4—188no—
725C2×C4—188no—
726C2×C4—181no—
727C2×C4—362no—
728C2×C4D3×D1211yescharacteristic
729C2×C4C22×D3211yescharacteristic
730C8—22no—
731C8—62no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—62no—
739C2×C3—121no—
740C2×C3—241no—
741C2×C3C2×#88211yescharacteristic
742C2×C3D3×#12011yescharacteristic
743C2×C3C2×#90811yescharacteristic
744C2×C3#574811yescharacteristic
745C2×C3C2×#91411yescharacteristic
746C2×C3#577711yescharacteristic
747D3—22no—
748D3—41no—
749D3—81no—
750D3—124no—
751D3—124no—
752D3—244no—
753D3—241no—
754D3—241no—
755D3—481no—
756C22—21no—
757C22—21no—
758C22—32no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—124no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—184no—
769C22—368no—
770C22—362no—
771C22—362no—
772C22—361no—
773C22—361no—
774C22—361no—
775C22—724no—
776C22#6379412yescomplemented
777C22C2×D3×D1211yescharacteristic
778C4—21no—
779C4—32no—
780C4—61no—
781C4—64no—
782C4—121no—
783C4—361no—
784C4D32×D412yes—
785C3—21no—
786C3#7863911yescharacteristic, complemented
787C3#8004011yescharacteristic, complemented
788C2—22no—
789C2—62no—
790C2—121no—
791C2—241no—
792C2—364no—
793C2—721no—
794C2D3×#88211yescharacteristic
795C2C2×#6379411yescharacteristic
796C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. D3×#930C2semidirect
3. C2×#63794C2semidirect
4. #10592431C2semidirect
5. C3×#4738C2semidirect
6. C3×#4726C2semidirect
7. #10591174C2semidirect
8. #10591168C2semidirect
9. #10590967C2semidirect
10. #10590823C2semidirect
11. #10590671C2semidirect
14. C22×C4⋊(C3⋊D3)C22semidirect
16. C22×C3×Dic6C22semidirect
20. C2×D3×D12C22semidirect
25. C2×#3799C22semidirect
27. C2×#3745C22semidirect
29. C2×C3×#204C22semidirect
30. C2×C3×ΓL(1,𝔽25)C22semidirect
33. #63909C22semidirect
34. #63908C22semidirect
36. D3×C4⋊Dic3C22semidirect
37. C2×#3717C22semidirect
38. C2×#3714C22semidirect
40. C32×C22⋊C8C22semidirect
41. #63648C22semidirect
42. C3×#830C22semidirect
43. C3×(C2×D3)⋊C8C22semidirect
44. C3×#816C22semidirect
45. #63566C22semidirect
46. #63564C22semidirect
62. #4738D3semidirect
69. #4726D3semidirect
108. #3799D4semidirect
148. C22×Dic6C2×D3semidirect
173. C2×#204C2×D3semidirect
174. C2×ΓL(1,𝔽25)C2×D3semidirect
183. C3×C22⋊C8C2×D3semidirect
184. C3×C22⋊C8C2×D3semidirect
186. #830C2×D3semidirect
191. (C2×D3)⋊C8C2×D3semidirect
193. #816C2×D3semidirect
218. C4⋊(C3⋊D3)C2×D4semidirect
233. C3×Dic6C2×D4semidirect
374. C22×C32AGL(1,ℤ/8)semidirect
433. C22⋊C8D32semidirect
542. Dic6D3×D4semidirect
628. C22×C3#908semidirect
629. C22×C3#914semidirect
682. C32#3006semidirect
776. C22#63794semidirect
786. C3#78639semidirect
787. C3#80040semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
D3×#9302
C2×#637942
#105924312
C3×#47382
C3×#47262
#105911742
#105911682
#105909672
#105908232
#105906712
#800403
#786393