Finite Group Databasebeta

← #25965088

Subgroups — #25965088

Order 11008.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147985C211yesmaximal, characteristic, complemented
2C2×#14583379C211yesmaximal, characteristic, complemented
3#19144874C214yesmaximal, complemented
4#19144859C214yesmaximal, complemented
5#19144811C214yesmaximal, complemented
6#19144796C214yesmaximal, complemented
7#19144520C212yesmaximal, complemented
8#19144402C211yesmaximal, characteristic, complemented
9#19144394C211yesmaximal, characteristic, complemented
10#19144069C211yesmaximal, characteristic, complemented
11#19144061C211yesmaximal, characteristic, complemented
12#19143840C212yesmaximal, complemented
13C4×#13063358C212yesmaximal, complemented
14C4×#13063353C212yesmaximal, complemented
15C43×#2921C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063358C2212yes—
18C2×#13063353C2212yes—
19#14583520C2212yescomplemented
20#14583520C2212yescomplemented
21#14583511C2212yescomplemented
22#14583504C2212yescomplemented
23#14583496—21no—
24#14583496—21no—
25#14583487—21no—
26#14583487—21no—
27#14583456C2211yescharacteristic
28#14583449C2211yescharacteristic
29#14583427—22no—
30#14583427—22no—
31#14583410C2212yes—
32#14583379—22no—
33#14583379—22no—
34#14583379C2214yes—
35#14583379C2214yes—
36C4×#10621898C2212yes—
37C2×C4×Dic86C2211yescharacteristic
38C2×C4×Dic86C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×(C22⋊D43)⋊C4—21no—
42C2×(C22⋊D43)⋊C4—21no—
43C2×#13063283—21no—
44C22×C4⋊Dic43C2211yescharacteristic
45C2×C4⋊C4×D43—21no—
46#14583235C2214yescomplemented
47#14583230C2214yescomplemented
48#14583218C2214yescomplemented
49#14583213C2214yescomplemented
50#14583207C2214yescomplemented
51#14583200C2214yescomplemented
52#14583195C2212yescomplemented
53#14583190C2212yescomplemented
54#14583185C2212yescomplemented
55#14583180C2212yescomplemented
56#14583122C2214yescomplemented
57#14583115C2214yescomplemented
58#14583110C2212yescomplemented
59#14583105C2212yescomplemented
60#14583100C2212yescomplemented
61#14583095C2212yescomplemented
62#14583063C2214yes—
63#14583063C2214yes—
64#14583046C2214yes—
65#14583046C2214yes—
66#14583012C2214yescomplemented
67#14583007C2214yescomplemented
68#14583001C2214yescomplemented
69#14583001C2214yescomplemented
70C4×Dic172C2214yescomplemented
71C4×#10621873C2214yescomplemented
72C4×#10621873C2214yescomplemented
73C4×D344C2214yescomplemented
74#14582941C2212yes—
75#14582941C2212yes—
76#14582909C2212yes—
77#14582905C2212yes—
78#14582901C2212yes—
79#14582901C2212yes—
80C2×#117×C43C2211yescharacteristic
81C43×#433C2214yescomplemented
82C43×#433C2214yescomplemented
83C43×#423C2211yescharacteristic
84C43×#423C2211yescharacteristic
85C43×#407C2212yes—
86C4×M16×C43C2212yes—
87C2×#10621898—22no—
88C2×#10621898—24no—
89C2×#10621898—24no—
90C2×#10621898C2314yes—
91C2×#10621898C2312yes—
92C22×Dic86C2311yescharacteristic
93C22×D172C2311yescharacteristic
94C22×C22⋊D43—21no—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C22×C4×D43—21no—
99#13063358—28no—
100#13063353—28no—
101C2×Dic172C2314yes—
102C2×#10621873C2314yes—
103C2×#10621873C2314yes—
104C2×D344C2314yes—
105#13063325C2311yescharacteristic
106#13063325C2311yescharacteristic
107#13063325C2311yescharacteristic
108#13063322C2311yescharacteristic
109#13063320—22no—
110#13063320—22no—
111#13063318—22no—
112#13063318—22no—
113#13063317C2312yes—
114#13063315—22no—
115#13063315—22no—
116#13063313C2312yes—
117#13063311—22no—
118#13063311—22no—
119#13063310—22no—
120#13063310—22no—
121#13063308—22no—
122#13063307—22no—
123#13063307—22no—
124#13063304—21no—
125#13063304—21no—
126#13063304C2312yes—
127#13063304C2312yes—
128#13063303—22no—
129#13063303—22no—
130#13063299—21no—
131#13063299—21no—
132#13063299C2312yes—
133#13063299C2312yes—
134#13063298—22no—
135#13063298—22no—
136#13063294—22no—
137C4×Dic86—22no—
138C4×Dic86—21no—
139C4×Dic86—21no—
140C4×Dic86—21no—
141C4×Dic86—21no—
142C4×Dic86C2312yes—
143C4×Dic86C2312yes—
144C4×Dic86C2314yes—
145C4×Dic86C2312yes—
146C4×Dic86C2312yes—
147C4×D172—22no—
148C4×D172—21no—
149C4×D172—21no—
150C4×D172—21no—
151C4×D172—21no—
152C4×D172C2312yes—
153C4×D172C2312yes—
154C4×D172C2314yes—
155C4×D172C2312yes—
156C4×D172C2312yes—
157C4×C22⋊D43—22no—
158C4×C22⋊D43—22no—
159C4×C22⋊D43—22no—
160C4×C22⋊D43—22no—
161(C22⋊D43)⋊C4—24no—
162(C22⋊D43)⋊C4—24no—
163(C22⋊D43)⋊C4—24no—
164(C22⋊D43)⋊C4—24no—
165#13063284C2312yes—
166#13063283—24no—
167#13063283—24no—
168#13063282—22no—
169C2×C4⋊Dic43—21no—
170C2×C4⋊Dic43—22no—
171C2×C4⋊Dic43C2311yescharacteristic
172C2×C4⋊Dic43C2311yescharacteristic
173C2×C4⋊Dic43C2314yes—
174C2×Dic43⋊C4—21no—
175C2×Dic43⋊C4—21no—
176C4⋊C4×D43—24no—
177C4⋊C4×D43—24no—
178C2×(C2×D43)⋊C4—21no—
179C2×(C2×D43)⋊C4—21no—
180C2×C4×Dic43—21no—
181C2×C4×Dic43—21no—
182C42×D43—22no—
183#13063259C2314yes—
184#13063259C2314yes—
185#13063257C2314yes—
186#13063257C2314yes—
187#13063250C2314yes—
188#13063250C2314yes—
189#13063250C2314yes—
190#13063250C2314yes—
191#13063247C2314yes—
192#13063247C2314yes—
193#13063247C2314yes—
194#13063247C2314yes—
195C23×C4×C43C2311yescharacteristic
196C2×M16×C43C2312yes—
197C2×M16×C43C2312yes—
198#117×C43D412yes—
199#117×C43D412yes—
200#117×C43C2312yes—
201#117×C43C2312yes—
202C2×C4⋊C4×C43D411yescharacteristic
203C2×C4⋊C4×C43D411yescharacteristic
204C2×C22⋊C4×C43D411yescharacteristic
205C2×C22⋊C4×C43D411yescharacteristic
206C2×C42×C43C2311yescharacteristic
207C2×C42×C43C2311yescharacteristic
208C4⋊C8×C43C2312yes—
209C4⋊C8×C43C2312yes—
210C4⋊C8×C43C2312yes—
211C4⋊C8×C43C2312yes—
212C22⋊C8×C43C2314yes—
213C22⋊C8×C43C2314yes—
214#97×C43C2314yes—
215C4×C8×C43C2314yes—
216C24×C43C2×D411yescharacteristic
217C23×D43—21no—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2412yes—
227C22×C4×C43C2411yescharacteristic
228C2×C22⋊D43—28no—
229C2×C22⋊D43—24no—
230C2×C22⋊D43—22no—
231C2×C22⋊D43—22no—
232C2×C22⋊D43—22no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—24no—
237C22×Dic43—82no—
238#10621898—216no—
239#10621898—28no—
240#10621898—24no—
241#10621898—24no—
242#10621898—28no—
243C2×D172—21no—
244C2×D172—22no—
245C2×D172—21no—
246C2×D172—21no—
247C2×D172#4114yes—
248C2×D172C2412yes—
249C2×D172C2412yes—
250C2×C4×D43—28no—
251C2×C4×D43—24no—
252C2×C4×D43—22no—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—24no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—82no—
259C2×C4×D43—82no—
260C2×Dic86—21no—
261C2×Dic86—22no—
262C2×Dic86—21no—
263C2×Dic86—21no—
264C2×Dic86#4114yes—
265C2×Dic86C2412yes—
266C2×Dic86C2412yes—
267M16×C43—24no—
268M16×C43—24no—
269C2×C8×C43C2414yes—
270C2×C8×C43C2414yes—
271C4⋊C4×C43C2×D412yes—
272C4⋊C4×C43C2×D412yes—
273C4⋊C4×C43C2×D412yes—
274C4⋊C4×C43C2×D412yes—
275C22⋊C4×C43C2×D412yes—
276C22⋊C4×C43C2×D412yes—
277C22⋊C4×C43C2×D412yes—
278C22⋊C4×C43C2×D412yes—
279C42×C43C2×D412yes—
280C42×C43C2×D411yescharacteristic
281C42×C43C2×D411yescharacteristic
282C42×C43C2412yes—
283C42×C43C2411yescharacteristic
284C42×C43C2411yescharacteristic
285C22⋊Dic43—22no—
286C22⋊Dic43—22no—
287C22⋊Dic43—22no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—22no—
294(C2×D43)⋊C4—22no—
295(C2×D43)⋊C4—22no—
296(C2×D43)⋊C4—22no—
297C4⋊Dic43—24no—
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43C2412yes—
305C4⋊Dic43C2412yes—
306C4⋊Dic43C2412yes—
307C4⋊Dic43C2412yes—
308Dic43⋊C4—24no—
309Dic43⋊C4—22no—
310Dic43⋊C4—22no—
311Dic43⋊C4—22no—
312Dic43⋊C4—22no—
313Dic43⋊C4—22no—
314Dic43⋊C4—22no—
315Dic43⋊C4—22no—
316Dic43⋊C4—22no—
317C4×Dic43—22no—
318C4×Dic43—22no—
319C4×Dic43—22no—
320C4×Dic43—24no—
321C4×Dic43—22no—
322C4×Dic43—22no—
323Dic172—28no—
324D344—28no—
325#10621873—28no—
326#10621873—28no—
327C23×C43—22no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43C22×D412yes—
331C23×C43C22×D411yescharacteristic
332C22×D43—24no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—42no—
336C22×D43—42no—
337C2×C4×C43—22no—
338C2×C4×C43—24no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43C22×D412yes—
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D412yes—
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D412yes—
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C2×#4112yes—
354C2×C4×C43C2×#4112yes—
355C2×C4×C43C2511yescharacteristic
356C22⋊D43—216no—
357C22⋊D43—44no—
358C22⋊D43—82no—
359C22⋊D43—82no—
360C2×Dic43—24no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—42no—
368C2×Dic43—42no—
369C2×Dic43—84no—
370D172—24no—
371D172—22no—
372D172—22no—
373D172—22no—
374D172—81no—
375D172—81no—
376D172C2×#4114yes—
377C4×D43—216no—
378C4×D43—44no—
379C4×D43—82no—
380C4×D43—82no—
381C4×D43—82no—
382C4×D43—84no—
383C4×D43—82no—
384Dic86—24no—
385Dic86—22no—
386Dic86—22no—
387Dic86—22no—
388Dic86—81no—
389Dic86—81no—
390Dic86C2×#4114yes—
391C8×C43—24no—
392C8×C43—24no—
393#60565—431nomaximal, Sylow
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—44no—
400C22×C43#52512yes—
401C22×C43C23×D411yescharacteristic
402C2×D43—24no—
403C2×D43—48no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C4×C43—21no—
410C4×C43—22no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—22no—
414C4×C43—21no—
415C4×C43—22no—
416C4×C43#52512yes—
417C4×C43C22×#4111yescharacteristic
418C4×C43C22×#4111yescharacteristic
419Dic43—24no—
420Dic43—42no—
421Dic43—42no—
422Dic43—42no—
423Dic43—42no—
424Dic43—42no—
425#3455—431no—
426C2×#520—431no—
427#3125—434no—
428#3124—434no—
429#3120—434no—
430#3119—434no—
431#3092—432no—
432#3078—431no—
433#3077—431no—
434#3037—431no—
435#3036—431no—
436#3005—432no—
437C4×#137—432no—
438C4×AGL(1,ℤ/8)—432no—
439#2921D4311yescharacteristic, complemented
440C2×C43—22no—
441C2×C43—42no—
442C2×C43C2×#52511yescharacteristic
443C2×C43#358511yescharacteristic
444C2×C43#358611yescharacteristic
445D43—44no—
446D43—82no—
447C22×#41—431no—
448C2×#137—432no—
449C2×AGL(1,ℤ/8)—432no—
450#542—432no—
451#542—432no—
452#541—432no—
453#540—432no—
454#539—861no—
455#539—861no—
456#538—861no—
457#538—861no—
458#533—431no—
459#532—431no—
460#529—862no—
461#529—862no—
462#525—432no—
463#520—434no—
464#520—434no—
465#520—862no—
466#520—862no—
467C4×#41—432no—
468C2×C4×Q8—431no—
469C2×C4×Q8—431no—
470C2×C4×D4—431no—
471C2×C4×D4—431no—
472C2×C4×D4—861no—
473C2×C4×D4—861no—
474C2×#117—861no—
475C2×#117C2×D4311yescharacteristic
476C22×C4⋊C4—431no—
477C22×C4⋊C4—861no—
478#484—434no—
479#483—434no—
480#481—434no—
481#480—434no—
482#479—434no—
483#478—434no—
484#477—432no—
485#476—432no—
486#475—432no—
487#474—432no—
488#464—434no—
489#463—434no—
490#462—432no—
491#461—432no—
492#460—432no—
493#459—432no—
494#452—434no—
495#452—434no—
496#449—434no—
497#449—434no—
498#442—434no—
499#441—434no—
500#440—434no—
501#440—434no—
502C4×Q16—434no—
503C4×SD16—434no—
504C4×SD16—434no—
505C4×D8—434no—
506#433C2×D4314yescomplemented
507#433C2×D4314yescomplemented
508#428—432no—
509#428—432no—
510#423C2×D4311yescharacteristic
511#423C2×D4311yescharacteristic
512#419—432no—
513#418—432no—
514#417—432no—
515#417—432no—
516#407C2×D4312yes—
517C4×M16C2×D4312yes—
518C43#6056511yescharacteristic, complemented, Sylow
519C2×#41—432no—
520C2×#41—434no—
521C2×#41—864no—
522C2×#41—864no—
523C2×#41—862no—
524C22×Q8—431no—
525C22×D4—431no—
526C22×D4—861no—
527C23×C4—861no—
528C23×C4—861no—
529C23×C4—861no—
530C23×C4—861no—
531C23×C4C22×D4311yescharacteristic
532#137—868no—
533AGL(1,ℤ/8)—868no—
534C2×Q16—434no—
535C2×SD16—434no—
536C2×SD16—434no—
537C2×D8—434no—
538C2×M16C22×D4312yes—
539C2×M16C22×D4312yes—
540C4⋊Q8—431no—
541C4⋊Q8—431no—
542C4⋊Q8—431no—
543#127—431no—
544#126—862no—
545#126—862no—
546#126—862no—
547#126—862no—
548#125—432no—
549#125—862no—
550#125—862no—
551#124—432no—
552#124—862no—
553#124—862no—
554#123—862no—
555#123—862no—
556#123—862no—
557#123—862no—
558#123—862no—
559C22⋊Q8—432no—
560C22⋊Q8—432no—
561C22⋊Q8—861no—
562C22⋊Q8—861no—
563C22⋊Q8—862no—
564C22⋊Q8—862no—
565#121—432no—
566#121—432no—
567#121—861no—
568#121—861no—
569#121—862no—
570#121—862no—
571#120—862no—
572C4×Q8—434no—
573C4×Q8—432no—
574C4×Q8—432no—
575C4×Q8—432no—
576C4×Q8—432no—
577C4×Q8—862no—
578C4×Q8—861no—
579C4×Q8—861no—
580C4×Q8—861no—
581C4×Q8—861no—
582C4×D4—434no—
583C4×D4—432no—
584C4×D4—432no—
585C4×D4—432no—
586C4×D4—432no—
587C4×D4—862no—
588C4×D4—862no—
589C4×D4—862no—
590C4×D4—862no—
591C4×D4—864no—
592C4×D4—864no—
593C4×D4—864no—
594C4×D4—864no—
595C4×D4—862no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4—861no—
600#117—432no—
601#117—864no—
602#117—864no—
603#117—862no—
604#117D17212yes—
605#117D17212yes—
606#117C22×D4312yes—
607#117C22×D4312yes—
608C2×C4⋊C4—431no—
609C2×C4⋊C4—431no—
610C2×C4⋊C4—434no—
611C2×C4⋊C4—861no—
612C2×C4⋊C4—862no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—864no—
616C2×C4⋊C4—864no—
617C2×C4⋊C4D17211yescharacteristic
618C2×C4⋊C4D17211yescharacteristic
619C2×C22⋊C4—861no—
620C2×C22⋊C4—861no—
621C2×C22⋊C4D17211yescharacteristic
622C2×C22⋊C4D17211yescharacteristic
623C2×C42—861no—
624C2×C42—861no—
625C2×C42—862no—
626C2×C42C22×D4311yescharacteristic
627C2×C42C22×D4311yescharacteristic
628#107—434no—
629#107—434no—
630#106—434no—
631#106—434no—
632C4⋊C8C22×D4312yes—
633C4⋊C8C22×D4312yes—
634C4⋊C8C22×D4312yes—
635C4⋊C8C22×D4312yes—
636#103—434no—
637#103—434no—
638#103—434no—
639#103—434no—
640#102—434no—
641#102—434no—
642#102—434no—
643#102—434no—
644C22⋊C8C22×D4314yes—
645C22⋊C8C22×D4314yes—
646#97C22×D4314yes—
647C4×C8C22×D4314yes—
648C24—861no—
649C24C2×D17211yescharacteristic
650#41—868no—
651#41—868no—
652#41—8616no—
653#41—864no—
654#41—864no—
655C2×Q8—434no—
656C2×Q8—432no—
657C2×Q8—432no—
658C2×Q8—861no—
659C2×Q8—861no—
660C2×Q8—861no—
661C2×Q8—862no—
662C2×D4—434no—
663C2×D4—432no—
664C2×D4—432no—
665C2×D4—868no—
666C2×D4—864no—
667C2×D4—862no—
668C2×D4—862no—
669C2×D4—862no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4—862no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—868no—
677C22×C4—861no—
678C22×C4—864no—
679C22×C4—864no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—862no—
683C22×C4—862no—
684C22×C4—864no—
685C22×C4—862no—
686C22×C4—862no—
687C22×C4—862no—
688C22×C4—3442no—
689C22×C4—3442no—
690C22×C4—3442no—
691C22×C4C2×D17211yescharacteristic
692C22×C4C2×D17212yes—
693C22×C4C2×D17211yescharacteristic
694C22×C4C2×D17211yescharacteristic
695C22×C4C2×D17211yescharacteristic
696C22×C4C2×D17211yescharacteristic
697C22×C4C23×D4312yes—
698C22×C4C23×D4311yescharacteristic
699Q16—868no—
700SD16—868no—
701SD16—868no—
702D8—868no—
703M16—24no—
704M16—24no—
705C2×C8C23×D4314yes—
706C2×C8C23×D4314yes—
707C4⋊C4—432no—
708C4⋊C4—432no—
709C4⋊C4—432no—
710C4⋊C4—432no—
711C4⋊C4—864no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—864no—
715C4⋊C4—862no—
716C4⋊C4—862no—
717C4⋊C4—862no—
718C4⋊C4—862no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—862no—
722C4⋊C4—862no—
723C4⋊C4—862no—
724C4⋊C4—862no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4C2×D17212yes—
728C4⋊C4C2×D17212yes—
729C4⋊C4C2×D17212yes—
730C4⋊C4C2×D17212yes—
731C22⋊C4—862no—
732C22⋊C4—862no—
733C22⋊C4—862no—
734C22⋊C4—864no—
735C22⋊C4—862no—
736C22⋊C4—862no—
737C22⋊C4—862no—
738C22⋊C4—862no—
739C22⋊C4—862no—
740C22⋊C4—862no—
741C22⋊C4—862no—
742C22⋊C4—862no—
743C22⋊C4C2×D17212yes—
744C22⋊C4C2×D17212yes—
745C22⋊C4C2×D17212yes—
746C22⋊C4C2×D17212yes—
747C42—862no—
748C42—864no—
749C42—862no—
750C42—862no—
751C42—862no—
752C42—862no—
753C42C2×D17212yes—
754C42C2×D17211yescharacteristic
755C42C2×D17211yescharacteristic
756C42C23×D4312yes—
757C42C23×D4311yescharacteristic
758C42C23×D4311yescharacteristic
759C23—22no—
760C23—41no—
761C23—41no—
762C23—864no—
763C23—862no—
764C23—862no—
765C23—1722no—
766C23—1722no—
767C23C22×D17212yes—
768C23C22×D17211yescharacteristic
769Q8—434no—
770Q8—864no—
771Q8—862no—
772Q8—862no—
773Q8—862no—
774Q8—3441no—
775Q8—3441no—
776D4—434no—
777D4—8616no—
778D4—864no—
779D4—862no—
780D4—862no—
781D4—862no—
782D4—3441no—
783D4—3441no—
784D4—3442no—
785D4—3442no—
786D4—1724no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—8616no—
796C2×C4—864no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—3444no—
804C2×C4—3442no—
805C2×C4—3442no—
806C2×C4—3442no—
807C2×C4—3442no—
808C2×C4—3444no—
809C2×C4—1722no—
810C2×C4—1722no—
811C2×C4—1724no—
812C2×C4C22×D17212yes—
813C2×C4C22×D17211yescharacteristic
814C2×C4C22×D17211yescharacteristic
815C2×C4C22×D17212yes—
816C2×C4C22×D17211yescharacteristic
817C2×C4C22×D17211yescharacteristic
818C2×C4C22×D17212yes—
819C2×C4C22×D17211yescharacteristic
820C2×C4#41×D4312yes—
821C2×C4#41×D4312yes—
822C2×C4C24×D4311yescharacteristic
823C8—24no—
824C8—24no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—44no—
831C22—864no—
832C22—1728no—
833C22—1722no—
834C22—1722no—
835C22—1722no—
836C22—1722no—
837C22—1722no—
838C22#1458341112yes—
839C22C23×D17211yescharacteristic
840C4—22no—
841C4—22no—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—21no—
846C4—21no—
847C4—864no—
848C4—1722no—
849C4—1722no—
850C4—1722no—
851C4—1722no—
852C4—1722no—
853C4#1458341112yes—
854C4C2×#41×D4311yescharacteristic
855C4C2×#41×D4311yescharacteristic
856C2—22no—
857C2—42no—
858C2—3442no—
859C2—1724no—
860C2C2×#1458341111yescharacteristic
861C2#1914937611yescharacteristic
862C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2921C2
socleC22×C43C23×D4
hypercenter#2921D43
hypocenterC43#60565
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. #19147985C2semidirect
2. C2×#14583379C2semidirect
3. #19144874C2semidirect
4. #19144859C2semidirect
5. #19144811C2semidirect
6. #19144796C2semidirect
7. #19144520C2semidirect
8. #19144402C2semidirect
9. #19144394C2semidirect
10. #19144069C2semidirect
11. #19144061C2semidirect
12. #19143840C2semidirect
13. C4×#13063358C2semidirect
14. C4×#13063353C2semidirect
15. C43×#2921C2semidirect
19. #14583520C22semidirect
20. #14583520C22semidirect
21. #14583511C22semidirect
22. #14583504C22semidirect
46. #14583235C22semidirect
47. #14583230C22semidirect
48. #14583218C22semidirect
49. #14583213C22semidirect
50. #14583207C22semidirect
51. #14583200C22semidirect
52. #14583195C22semidirect
53. #14583190C22semidirect
54. #14583185C22semidirect
55. #14583180C22semidirect
56. #14583122C22semidirect
57. #14583115C22semidirect
58. #14583110C22semidirect
59. #14583105C22semidirect
60. #14583100C22semidirect
61. #14583095C22semidirect
66. #14583012C22semidirect
67. #14583007C22semidirect
68. #14583001C22semidirect
69. #14583001C22semidirect
70. C4×Dic172C22semidirect
71. C4×#10621873C22semidirect
72. C4×#10621873C22semidirect
73. C4×D344C22semidirect
81. C43×#433C22semidirect
82. C43×#433C22semidirect
439. #2921D43semidirect
506. #433C2×D43semidirect
507. #433C2×D43semidirect
518. C43#60565semidirect

Maximal subgroups

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

subgroupindex
#191479852
C2×#145833792
#191448742
#191448592
#191448112
#191447962
#191445202
#191444022
#191443942
#191440692
#191440612
#191438402
C4×#130633582
C4×#130633532
C43×#29212
#6056543