Finite Group Databasebeta

← #11867166

Subgroups — #11867166

Order 1152.

1261 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596262C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic, complemented
5#10591176C212yesmaximal, complemented
6#10591175C212yesmaximal, complemented
7#10591165C212yesmaximal, complemented
8#10591164C212yesmaximal, complemented
9#10591130C211yesmaximal, characteristic, complemented
10#10591106C211yesmaximal, characteristic, complemented
11#10591086C211yesmaximal, characteristic, complemented
12#83772—31nomaximal
13#82621—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C22×C3×#67—21no—
17C22×C3×D12C2211yescharacteristic
18#64162—21no—
19#64139C2211yescharacteristic, complemented
20#64139C2211yescharacteristic, complemented
21#64138—21no—
22C4×#638—21no—
23C4×#638—21no—
24#64135C2211yescharacteristic
25#64133C2211yescharacteristic, complemented
26#64133C2211yescharacteristic, complemented
27C3×#930—21no—
28C3×#930—21no—
29C3×#930C2212yes—
30C3×#930C2212yes—
31C2×C3×(C2×D3)⋊C4—21no—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×#208—24no—
34C2×C3×#208C2211yescharacteristic
35C2×C3×#208C2211yescharacteristic
36C2×C3×#208C2212yescomplemented
37C22×C3×C3⋊C8C2212yescomplemented
38#63830—24no—
39C2×#3716C2212yescomplemented
40C2×#3714C2212yescomplemented
41#63575C2212yescomplemented
42#63573C2212yescomplemented
43#63567C2212yescomplemented
44#63564C2212yescomplemented
45#63563C2212yescomplemented
46#63563C2212yescomplemented
47C22×C3×M16—31no—
48C2×C3×#121—31no—
49C2×#932—31no—
50#5791—31no—
51#5791—31no—
52#5791—61no—
53C2×#930D311yescharacteristic, complemented
54C22×#208D311yescharacteristic, complemented
55C2×#908—31no—
56#5215—31no—
57#5135—32no—
58#5134—32no—
59#5133—31no—
60#5131—31no—
61#5121—31no—
62#5115—32no—
63#5114—32no—
64#5042—32no—
65#5041—32no—
66#5039—32no—
67#5038—32no—
68#4966—31no—
69#4964—31no—
70C24×C32D411yescharacteristic
71C23×C3×D3—21no—
72C22×C32×C4—22no—
73C22×C32×C4—22no—
74C22×C32×C4D411yescharacteristic
75C22×C32×C4D411yescharacteristic
76C22×C32×C4D411yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C2×#638—21no—
81C2×#638—21no—
82C2×#638—21no—
83#3828—22no—
84#3828—22no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×#634C2311yescharacteristic
88C2×C3×#67—22no—
89C2×C3×#67—22no—
90C2×C3×#67—44no—
91C22×C3×Dic3—21no—
92C2×C3×D12—22no—
93C2×C3×D12—22no—
94C2×C3×D12—21no—
95C2×C3×D12C2312yes—
96#3757—21no—
97#3757—21no—
98#3757—21no—
99#3752—21no—
100#3752—21no—
101C4⋊(C3⋊Dic3)C2311yescharacteristic
102C4⋊(C3⋊Dic3)C2311yescharacteristic
103#3750—21no—
104#3750—21no—
105C4×C3⋊Dic3—21no—
106C3×(C2×D3)⋊C4—22no—
107C3×(C2×D3)⋊C4—22no—
108C3×C4⋊Dic3—21no—
109C3×C4⋊Dic3C2312yes—
110C3×#208—22no—
111C3×#208—24no—
112C3×#208D414yescomplemented
113C2×C3×C3⋊C8—24no—
114C2×C3×C3⋊C8C2312yes—
115C2×C3×C3⋊C8C2312yes—
116#3716—24no—
117#3714—24no—
118#3055—91noSylow
119C22×C3×D4—31no—
120C22×C3×D4—61no—
121C23×C3×C4—21no—
122C23×C3×C4C2×D311yescharacteristic
123C23×C3×C4C2×D311yescharacteristic
124C22×#67—21no—
125C2×#235—31no—
126C2×#235—31no—
127C2×#235—61no—
128C22×D12C2×D311yescharacteristic
129C2×C3×M16—31no—
130C2×C3×M16—31no—
131C2×C3×M16—32no—
132C2×C3×M16—64no—
133C22×C3×C8—32no—
134C3×#121—32no—
135C3×#121—32no—
136C3×#121—61no—
137C3×#121—61no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C22⋊C4—61no—
140#953—62no—
141#953—61no—
142#953—61no—
143C2×#214—32no—
144#932—64no—
145C2×#213—32no—
146#930—21no—
147#930—21no—
148#930—31no—
149#930—31no—
150#930—31no—
151#930—31no—
152#930—61no—
153#930—61no—
154#930C2×D312yes—
155#930C2×D312yes—
156#929—62no—
157#929—61no—
158#929—61no—
159C4×#67—62no—
160C4×#67—62no—
161C4×#67—61no—
162C4×#67—61no—
163C4×#67—61no—
164C4×#67—61no—
165C2×(C2×D3)⋊C4—21no—
166#926—31no—
167#926—31no—
168#926—61no—
169C2×C4⋊Dic3C2×D311yescharacteristic
170#924—31no—
171#924—31no—
172#924—31no—
173#924—31no—
174#924—61no—
175#924—61no—
176C2×#208—24no—
177C2×#208C2×D311yescharacteristic
178C2×#208C2×D311yescharacteristic
179C2×#208C2×D312yescomplemented
180C22×C3⋊C8C2×D312yescomplemented
181#908—64no—
182C2×D24—32no—
183C2×#204—32no—
184#832—32no—
185#832—32no—
186#821—32no—
187#821—32no—
188#821—32no—
189#818—32no—
190#817—32no—
191#816—32no—
192#810—32no—
193#809—32no—
194#808—32no—
195#807—32no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32—41no—
199C23×C32C2×D411yescharacteristic
200C23×C32C2×D411yescharacteristic
201C23×C32C2×D411yescharacteristic
202C22×C3⋊D3—21no—
203C22×C3×D3—22no—
204C22×C3×D3—42no—
205C22×C3×D3—42no—
206C22×C3×D3—42no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2×D411yescharacteristic
216C2×C32×C4C2×D411yescharacteristic
217C2×C32×C4C2×D412yes—
218C2×C32×C4#4112yes—
219C2×C32×C4C2411yescharacteristic
220#638—42no—
221#638—42no—
222#638—42no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C4⋊(C3⋊D3)—21no—
227C4⋊(C3⋊D3)—21no—
228C4×C3⋊D3—42no—
229#634—21no—
230#634—21no—
231C3×#67—44no—
232C3×#67—44no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—42no—
235C3×D12—22no—
236C3×D12—22no—
237C3×D12—42no—
238C3×C3⋊C8—22no—
239C3×C3⋊C8C2×D414yescomplemented
240C2×AGL(1,ℤ/8)—91no—
241C22×M16—31no—
242#525—91no—
243C2×#121—31no—
244#469—92no—
245#468—92no—
246#466—92no—
247#465—92no—
248#428—91no—
249#418—91no—
250#417—91no—
251C24×C3—21no—
252C24×C3—61no—
253C24×C3D1211yescharacteristic
254C24×C3#6711yescharacteristic
255C23×D3—21no—
256C2×C3×D4—32no—
257C2×C3×D4—62no—
258C2×C3×D4—62no—
259C2×C3×D4—61no—
260C2×C3×D4—62no—
261C2×C3×D4—62no—
262C2×C3×D4—124no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4—61no—
276C22×C3×C4D1211yescharacteristic
277C22×C3×C4D1211yescharacteristic
278C22×C3×C4D1211yescharacteristic
279C22×C3×C4#6711yescharacteristic
280C22×C3×C4#6711yescharacteristic
281C22×C3×C4#6711yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C2×#67—22no—
289C2×#67—22no—
290C2×#67—44no—
291C2×#67—62no—
292C2×#67—62no—
293C2×#67—62no—
294C2×#67—61no—
295C2×#67—61no—
296C2×#67—61no—
297C2×#67—61no—
298C2×#67—61no—
299C2×#67—61no—
300C22×Dic3—21no—
301#235—62no—
302#235—62no—
303#235—62no—
304#235—62no—
305#235—122no—
306#235—122no—
307C2×D12—22no—
308C2×D12—22no—
309C2×D12—21no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×D12C22×D312yes—
314C2×C4×D3—62no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C3×M16—34no—
321C3×M16—64no—
322C3×M16—62no—
323C2×C3×C8—32no—
324C2×C3×C8—32no—
325C2×C3×C8—64no—
326C3×C4⋊C4—32no—
327C3×C4⋊C4—61no—
328C3×C22⋊C4—62no—
329C3×C22⋊C4—62no—
330#217—62no—
331#217—62no—
332#217—62no—
333#217—61no—
334#217—61no—
335#217—61no—
336#217—61no—
337#217—61no—
338#217—61no—
339#214—64no—
340#213—64no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4—62no—
344(C2×D3)⋊C4—62no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349C4⋊Dic3—21no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D312yes—
357Dic3⋊C4—62no—
358Dic3⋊C4—62no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363C4×Dic3—62no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366#208—22no—
367#208—24no—
368#208#6714yescomplemented
369C2×C3⋊C8—24no—
370C2×C3⋊C8C22×D312yes—
371C2×C3⋊C8C22×D312yes—
372D24—64no—
373#204—64no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—44no—
382C22×C32#12112yes—
383C22×C32AGL(1,ℤ/8)12yescomplemented
384C22×C32C22×D411yescharacteristic
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C2×C3×D3—42no—
389C2×C3×D3—42no—
390C2×C3×D3—42no—
391C2×C3×D3—84no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4#12112yes—
395C32×C4C22×D411yescharacteristic
396C32×C4C2×#4111yescharacteristic
397C3⋊Dic3—41no—
398C3⋊Dic3—41no—
399C3⋊Dic3—41no—
400C3×Dic3—42no—
401C2×#41—91no—
402C22×D4—31no—
403C22×D4—61no—
404C23×C4D3211yescharacteristic
405AGL(1,ℤ/8)—184no—
406C2×SD16—92no—
407C2×D8—92no—
408C2×M16—31no—
409C2×M16—31no—
410C2×M16—32no—
411C2×M16—64no—
412C22×C8—32no—
413#123—181no—
414C22⋊Q8—91no—
415C22⋊Q8—91no—
416#121—32no—
417#121—32no—
418#121—61no—
419#121—61no—
420#121—91no—
421#121—91no—
422#120—181no—
423C4×D4—181no—
424C4×D4—181no—
425#117—91no—
426C2×C4⋊C4—31no—
427C2×C22⋊C4—61no—
428#107—92no—
429#106—92no—
430#103—92no—
431#102—92no—
432#102—92no—
433#102—92no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—42no—
446C23×C3—62no—
447C23×C3—122no—
448C23×C3—122no—
449C23×C3—122no—
450C23×C3C2×D1211yescharacteristic
451C23×C3C2×D1211yescharacteristic
452C23×C3C2×D1211yescharacteristic
453C23×C3C2×#6711yescharacteristic
454C23×C3C2×#6711yescharacteristic
455C23×C3C2×#6711yescharacteristic
456C22×D3—22no—
457C22×D3—42no—
458C22×D3—42no—
459C22×D3—42no—
460C22×D3—62no—
461C22×D3—61no—
462C22×D3—61no—
463C3×D4—62no—
464C3×D4—62no—
465C3×D4—124no—
466C3×D4—124no—
467C3×D4—122no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—22no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—42no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4—62no—
496C2×C3×C4—122no—
497C2×C3×C4C2×D1211yescharacteristic
498C2×C3×C4C2×D1211yescharacteristic
499C2×C3×C4C2×D1211yescharacteristic
500C2×C3×C4#23512yes—
501C2×C3×C4D3×D412yes—
502C2×C3×C4#23712yes—
503C2×C3×C4C2×#6711yescharacteristic
504C2×C3×C4C2×#6711yescharacteristic
505C2×C3×C4C2×#6711yescharacteristic
506C2×C3×C4C2×#6712yes—
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—44no—
510#67—44no—
511#67—124no—
512#67—124no—
513#67—122no—
514#67—122no—
515#67—124no—
516#67—122no—
517#67—122no—
518#67—122no—
519#67—122no—
520C2×Dic3—22no—
521C2×Dic3—42no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—62no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531D12—22no—
532D12—22no—
533D12—42no—
534D12—61no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—121no—
539D12—121no—
540C4×D3—124no—
541C4×D3—122no—
542C4×D3—122no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—121no—
548Dic6—121no—
549C3×C8—34no—
550C3×C8—62no—
551C3⋊C8—22no—
552C3⋊C8C2×#6714yescomplemented
553C2×C32—22no—
554C2×C32—22no—
555C2×C32—41no—
556C2×C32C2×#12111yescharacteristic
557C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
558C2×C32#57511yescharacteristic
559C3⋊D3—81no—
560C3×D3—82no—
561C24—61no—
562C24#62611yescharacteristic
563#41—182no—
564#41—182no—
565C2×Q8—91no—
566C2×D4—32no—
567C2×D4—62no—
568C2×D4—62no—
569C2×D4—62no—
570C2×D4—61no—
571C2×D4—62no—
572C2×D4—91no—
573C2×D4—124no—
574C2×D4—181no—
575C2×D4—181no—
576C2×D4—181no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—61no—
580C22×C4—181no—
581C22×C4#62611yescharacteristic
582C22×C4#62611yescharacteristic
583C22×C4#62611yescharacteristic
584C22×C4C2×D3211yescharacteristic
585C22×C4C2×D3211yescharacteristic
586C22×C4C2×D3211yescharacteristic
587SD16—184no—
588D8—184no—
589M16—34no—
590M16—64no—
591M16—62no—
592C2×C8—32no—
593C2×C8—32no—
594C2×C8—64no—
595C4⋊C4—32no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C22⋊C4—62no—
602C22⋊C4—62no—
603C22⋊C4—181no—
604C22⋊C4—181no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C42—181no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—22no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—48no—
636C22×C3—122no—
637C22×C3—122no—
638C22×C3—122no—
639C22×C3—244no—
640C22×C3#90812yescomplemented
641C22×C3#93012yes—
642C22×C3#93212yescomplemented
643C22×C3#93912yes—
644C22×C3C22×D1211yescharacteristic
645C22×C3C22×#6711yescharacteristic
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—42no—
649C2×D3—84no—
650C2×D3—122no—
651C2×D3—122no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—22no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—122no—
669C3×C4#93012yes—
670C3×C4#93912yes—
671C3×C4C2×#23511yescharacteristic
672C3×C4C2×D3×D411yescharacteristic
673C3×C4C2×#23711yescharacteristic
674C3×C4C22×#6711yescharacteristic
675Dic3—42no—
676Dic3—122no—
677Dic3—122no—
678Dic3—122no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685C32#305511yescharacteristic, complemented, Sylow
686C23—22no—
687C23—22no—
688C23—41no—
689C23—62no—
690C23—122no—
691C23—122no—
692C23—122no—
693C23—181no—
694C23C2×#62611yescharacteristic
695C23C2×#62611yescharacteristic
696C23C2×#62611yescharacteristic
697Q8—181no—
698Q8—181no—
699D4—62no—
700D4—62no—
701D4—124no—
702D4—124no—
703D4—122no—
704D4—181no—
705D4—181no—
706D4—362no—
707D4—362no—
708D4—362no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—62no—
717C2×C4—122no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—362no—
722C2×C4#380412yes—
723C2×C4C2×#62611yescharacteristic
724C2×C4C2×#62611yescharacteristic
725C2×C4C2×#62611yescharacteristic
726C2×C4D3×#6712yes—
727C2×C4C22×D3211yescharacteristic
728C8—34no—
729C8—62no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—42no—
739C2×C3—42no—
740C2×C3—41no—
741C2×C3—41no—
742C2×C3—242no—
743C2×C3C2×#90811yescharacteristic
744C2×C3#574811yescharacteristic
745C2×C3C2×#93011yescharacteristic
746C2×C3C2×#93211yescharacteristic
747C2×C3C2×#93911yescharacteristic
748C2×C3#582211yescharacteristic
749D3—82no—
750D3—242no—
751D3—241no—
752D3—241no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—44no—
761C22—122no—
762C22—122no—
763C22—122no—
764C22—244no—
765C22—361no—
766C22—361no—
767C22—361no—
768C22#6383012yescomplemented
769C22#6397812yes—
770C22C22×#62611yescharacteristic
771C4—21no—
772C4—21no—
773C4—122no—
774C4—361no—
775C4—361no—
776C4—361no—
777C4#6397812yes—
778C4C2×#380411yescharacteristic
779C4C2×D3×#6711yescharacteristic
780C3—21no—
781C3#8262111yescharacteristic, complemented
782C3#8377211yescharacteristic, complemented
783C2—22no—
784C2—22no—
785C2—41no—
786C2—242no—
787C2—721no—
788C2C2×#6383011yescharacteristic
789C2#1059479511yescharacteristic
790C2C2×#6397811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
hypercenterC23×C4D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #10596262C2semidirect
2. C2×C3×#930C2semidirect
3. C22×C3×#208C2semidirect
4. C2×#63830C2semidirect
5. #10591176C2semidirect
6. #10591175C2semidirect
7. #10591165C2semidirect
8. #10591164C2semidirect
9. #10591130C2semidirect
10. #10591106C2semidirect
11. #10591086C2semidirect
19. #64139C22semidirect
20. #64139C22semidirect
25. #64133C22semidirect
26. #64133C22semidirect
36. C2×C3×#208C22semidirect
37. C22×C3×C3⋊C8C22semidirect
39. C2×#3716C22semidirect
40. C2×#3714C22semidirect
41. #63575C22semidirect
42. #63573C22semidirect
43. #63567C22semidirect
44. #63564C22semidirect
45. #63563C22semidirect
46. #63563C22semidirect
53. C2×#930D3semidirect
54. C22×#208D3semidirect
112. C3×#208D4semidirect
179. C2×#208C2×D3semidirect
180. C22×C3⋊C8C2×D3semidirect
239. C3×C3⋊C8C2×D4semidirect
368. #208#67semidirect
383. C22×C32AGL(1,ℤ/8)semidirect
552. C3⋊C8C2×#67semidirect
640. C22×C3#908semidirect
642. C22×C3#932semidirect
685. C32#3055semidirect
768. C22#63830semidirect
781. C3#82621semidirect
782. C3#83772semidirect

Maximal subgroups

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

subgroupindex
#105962622
C2×C3×#9302
C22×C3×#2082
C2×#638302
#105911762
#105911752
#105911652
#105911642
#105911302
#105911062
#105910862
#837723
#826213