Finite Group Databasebeta

← #25976472

Subgroups — #25976472

Order 11008.

1804 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148190C211yesmaximal, characteristic
2#19147437C214yesmaximal, complemented
3#19147398C212yesmaximal, complemented
4#19147363C214yesmaximal, complemented
5#19147324C212yesmaximal, complemented
6#19147291C212yesmaximal, complemented
7#19147280C212yesmaximal, complemented
8#19144998C212yesmaximal, complemented
9#19144991C211yesmaximal, characteristic, complemented
10#19144413C212yesmaximal, complemented
11#19144404C211yesmaximal, characteristic, complemented
12#19144067C211yesmaximal, characteristic, complemented
13#19144067C212yesmaximal, complemented
14Q8×#10621877C211yesmaximal, characteristic, complemented
15C4×#13063356C211yesmaximal, characteristic, complemented
16C4×#13063356C212yesmaximal, complemented
17C2×C43×#557C211yesmaximal, characteristic, complemented
18C2×#13063356C2211yescharacteristic
19C2×#13063356C2212yes—
20#14583634C2211yescharacteristic
21#14583634C2212yes—
22#14583628C2211yescharacteristic
23#14583622C2211yescharacteristic
24#14583622C2212yes—
25#14583597—21no—
26#14583597—22no—
27#14583571C2211yescharacteristic
28#14583560—21no—
29#14583449C2211yescharacteristic
30#14583449C2212yes—
31#14583436—22no—
32#14583436—21no—
33C4×#10621902—21no—
34C4×#10621898C2211yescharacteristic
35C4×#10621898C2212yes—
36#14583269C2214yes—
37#14583265C2214yes—
38#14583261C2214yes—
39#14583256C2214yes—
40#14583256C2214yes—
41#14583251C2212yes—
42#14583247C2212yes—
43#14583203C2214yes—
44#14583203C2214yes—
45#14583196C2214yes—
46#14583196C2214yes—
47#14583191C2212yes—
48#14583186C2212yes—
49#14583181C2212yes—
50#14583176C2212yes—
51#14583121C2214yes—
52#14583121C2214yes—
53#14583121C2214yes—
54#14583109C2212yes—
55#14583109C2214yes—
56#14583099C2212yes—
57#14583099C2214yes—
58#14583030C2212yes—
59#14583030C2214yes—
60Q8×C43⋊C8C2212yes—
61#14583004C2214yes—
62#14583004C2212yes—
63#14582997C2214yes—
64#14582997C2212yes—
65C4×#10621885C2214yes—
66C4×#10621885C2212yes—
67C4×#10621884C2212yes—
68C4×#10621884C2214yes—
69#14582939C2212yes—
70#14582939C2211yescharacteristic
71#14582923C2211yescharacteristic
72#14582923C2212yes—
73#14582908C2211yescharacteristic
74#14582898C2212yes—
75#14582898C2212yes—
76#14582898C2211yescharacteristic
77#14582898C2212yes—
78#14582898C2212yes—
79C4×#10621877C2211yescharacteristic
80C4×#10621877C2212yes—
81C43×#557—21no—
82C43×#557—21no—
83C43×#557—22no—
84C43×#557C2212yes—
85C43×#557C2212yes—
86C43×#557C2214yes—
87C2×C4⋊Q8×C43—21no—
88C2×C4⋊Q8×C43C2211yescharacteristic
89C2×#125×C43—22no—
90C2×#125×C43C2212yes—
91C2×C4×Q8×C43—21no—
92C2×C4×Q8×C43C2212yes—
93C2×C4×Q8×C43C2211yescharacteristic
94C2×C4×Q8×C43C2211yescharacteristic
95C2×#10621902—21no—
96C2×#10621898C2311yescharacteristic
97C2×#10621898C2312yes—
98#13063356—24no—
99#13063356—28no—
100C2×#10621885C2314yes—
101C2×#10621885C2312yes—
102C2×#10621884C2314yes—
103C2×#10621884C2312yes—
104C2×#10621877C2311yescharacteristic
105C2×#10621877C2311yescharacteristic
106C2×#10621877C2312yes—
107#13063325C2311yescharacteristic
108#13063325C2312yes—
109#13063322C2311yescharacteristic
110#13063322C2312yes—
111#13063320—22no—
112#13063320—22no—
113#13063320—22no—
114#13063316—21no—
115#13063316—22no—
116#13063314—21no—
117#13063314—22no—
118#13063313C2312yes—
119#13063313C2312yes—
120#13063313C2312yes—
121#13063310—22no—
122#13063310—22no—
123#13063310—22no—
124#13063301—21no—
125#13063301—22no—
126#13063300—21no—
127#13063300—22no—
128#13063299—21no—
129#13063299—22no—
130#13063299—22no—
131#13063299—21no—
132Q8×Dic43—21no—
133C4×Dic86C2311yescharacteristic
134C4×Dic86C2312yes—
135C4×Dic86C2311yescharacteristic
136C4×Dic86C2312yes—
137C4×D172—22no—
138C4×D172—21no—
139C4×D172—22no—
140C4×D172—21no—
141C4×D172C2311yescharacteristic
142C4×D172C2312yes—
143C4×D172C2311yescharacteristic
144C4×D172C2312yes—
145#13063287—21no—
146#13063287—22no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—22no—
149C4×C22⋊D43—22no—
150C4×C22⋊D43—21no—
151#13063284C2311yescharacteristic
152#13063283—21no—
153#13063283—22no—
154#13063282—22no—
155#13063282—21no—
156C42×D43—22no—
157C42×D43—21no—
158#13063258C2314yes—
159#13063258C2312yes—
160#13063256C2314yes—
161#13063256C2312yes—
162C4⋊(C43⋊C8)C2312yes—
163C4⋊(C43⋊C8)C2314yes—
164C4⋊(C43⋊C8)C2312yes—
165C4⋊(C43⋊C8)C2314yes—
166#13063249C2312yes—
167#13063249C2312yes—
168#13063248C2314yes—
169#13063248C2314yes—
170#13063248C2314yes—
171#13063248C2314yes—
172#13063248C2312yes—
173#13063245C2314yes—
174#13063245C2314yes—
175#13063245C2314yes—
176#13063245C2314yes—
177#13063245C2312yes—
178#13063236C2312yes—
179#13063236C2314yes—
180C4×C43⋊C8C2312yes—
181C4×C43⋊C8C2314yes—
182C22×Q8×C43—21no—
183C22×Q8×C43D411yescharacteristic
184C22×Q8×C43C2311yescharacteristic
185C4⋊Q8×C43—22no—
186C4⋊Q8×C43—22no—
187C4⋊Q8×C43—24no—
188C4⋊Q8×C43—21no—
189C4⋊Q8×C43—21no—
190C4⋊Q8×C43C2312yes—
191C4⋊Q8×C43C2312yes—
192#125×C43—24no—
193#125×C43—24no—
194#125×C43—24no—
195#125×C43—24no—
196#125×C43—22no—
197#125×C43—22no—
198#125×C43C2314yes—
199#125×C43C2314yes—
200C4×Q8×C43—22no—
201C4×Q8×C43—22no—
202C4×Q8×C43—24no—
203C4×Q8×C43—22no—
204C4×Q8×C43—22no—
205C4×Q8×C43—21no—
206C4×Q8×C43—21no—
207C4×Q8×C43D411yescharacteristic
208C4×Q8×C43D412yes—
209C4×Q8×C43D411yescharacteristic
210C4×Q8×C43C2312yes—
211C4×Q8×C43C2314yes—
212C4×Q8×C43C2314yes—
213C4×Q8×C43C2312yes—
214C4×Q8×C43C2311yescharacteristic
215C4×Q8×C43C2311yescharacteristic
216C4×Q8×C43C2312yes—
217C2×C4⋊C4×C43—22no—
218C2×C4⋊C4×C43—21no—
219C2×C4⋊C4×C43—22no—
220C2×C4⋊C4×C43—21no—
221C2×C4⋊C4×C43—22no—
222C2×C4⋊C4×C43D411yescharacteristic
223C2×C4⋊C4×C43D412yes—
224C2×C4⋊C4×C43C2311yescharacteristic
225C2×C4⋊C4×C43C2312yes—
226C2×C42×C43—22no—
227C2×C42×C43—21no—
228C2×C42×C43C2312yes—
229C2×C42×C43C2311yescharacteristic
230C2×Q8×C43—21no—
231C2×Q8×C43—22no—
232C2×Q8×C43—22no—
233C2×Q8×C43—22no—
234C2×Q8×C43—42no—
235C2×Q8×C43—44no—
236C2×Q8×C43C2×D411yescharacteristic
237C2×Q8×C43C2×D411yescharacteristic
238C2×Q8×C43C2×D412yes—
239C2×Q8×C43#4114yescomplemented
240C2×Q8×C43C2412yes—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—22no—
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D412yes—
248C22×C4×C43C2411yescharacteristic
249C2×C22⋊D43—21no—
250C2×C22⋊D43—22no—
251#10621902—44no—
252#10621898—22no—
253#10621898—24no—
254#10621898—22no—
255#10621898—24no—
256C2×D172—22no—
257C2×D172—21no—
258C2×D172—22no—
259C2×D172—21no—
260C2×D172C2411yescharacteristic
261C2×D172C2412yes—
262C2×C4×D43—22no—
263C2×C4×D43—21no—
264C2×C4×D43—22no—
265C2×C4×D43—21no—
266C2×C4×D43—22no—
267C2×C4×D43—21no—
268C2×Dic86C2411yescharacteristic
269C2×Dic86C2412yes—
270C4⋊C4×C43—24no—
271C4⋊C4×C43—24no—
272C4⋊C4×C43—22no—
273C4⋊C4×C43—22no—
274C4⋊C4×C43—24no—
275C4⋊C4×C43—24no—
276C4⋊C4×C43—22no—
277C4⋊C4×C43—22no—
278C4⋊C4×C43—24no—
279C4⋊C4×C43—24no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—22no—
282C4⋊C4×C43C2×D411yescharacteristic
283C4⋊C4×C43C2×D411yescharacteristic
284C4⋊C4×C43C2×D412yes—
285C4⋊C4×C43C2×D412yes—
286C4⋊C4×C43C2×D412yes—
287C4⋊C4×C43C2×D412yes—
288C4⋊C4×C43C2×D412yes—
289C4⋊C4×C43C2412yes—
290C4⋊C4×C43C2414yes—
291C42×C43—24no—
292C42×C43—24no—
293C42×C43—22no—
294C42×C43—22no—
295C42×C43C2×D412yes—
296C42×C43C2×D412yes—
297C42×C43C2×D411yescharacteristic
298C42×C43C2×D411yescharacteristic
299C42×C43C2412yes—
300C42×C43C2412yes—
301C42×C43C2411yescharacteristic
302C42×C43C2411yescharacteristic
303C22⋊Dic43—21no—
304#10621885—28no—
305#10621885—24no—
306#10621884—28no—
307#10621884—24no—
308(C2×D43)⋊C4—22no—
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—22no—
312(C2×D43)⋊C4—22no—
313(C2×D43)⋊C4—22no—
314(C2×D43)⋊C4—22no—
315(C2×D43)⋊C4—22no—
316(C2×D43)⋊C4—22no—
317(C2×D43)⋊C4—22no—
318C4⋊Dic43—22no—
319C4⋊Dic43—21no—
320C4⋊Dic43—22no—
321C4⋊Dic43—21no—
322C4⋊Dic43C2411yescharacteristic
323C4⋊Dic43C2411yescharacteristic
324Dic43⋊C4—21no—
325Dic43⋊C4—22no—
326Dic43⋊C4—22no—
327Dic43⋊C4—21no—
328C4×Dic43—21no—
329C4×Dic43—22no—
330C4×Dic43—21no—
331C4×Dic43—22no—
332C4×Dic43—21no—
333#10621877—22no—
334#10621877—24no—
335#10621877—22no—
336C2×C43⋊C8C2412yes—
337C2×C43⋊C8C2412yes—
338C2×C43⋊C8C2414yes—
339C23×C43C22×D411yescharacteristic
340C22×D43—22no—
341C22×D43—21no—
342Q8×C43—24no—
343Q8×C43—22no—
344Q8×C43—22no—
345Q8×C43—22no—
346Q8×C43—42no—
347Q8×C43—44no—
348Q8×C43—44no—
349Q8×C43C2×#4114yes—
350C2×C4×C43—24no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—24no—
355C2×C4×C43—42no—
356C2×C4×C43—41no—
357C2×C4×C43—42no—
358C2×C4×C43—42no—
359C2×C4×C43—44no—
360C2×C4×C43C22×D412yes—
361C2×C4×C43C22×D412yes—
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D412yes—
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D412yes—
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C2×#4112yes—
370C2×C4×C432−1+412yes—
371C2×C4×C43C2511yescharacteristic
372C22⋊D43—42no—
373C22⋊D43—44no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—22no—
377C2×Dic43—21no—
378D172—21no—
379D172—22no—
380D172—21no—
381D172—22no—
382D172—44no—
383D172—42no—
384D172—82no—
385D172—81no—
386C4×D43—44no—
387C4×D43—44no—
388C4×D43—42no—
389C4×D43—42no—
390C4×D43—82no—
391C4×D43—81no—
392Dic86—21no—
393Dic86—22no—
394Dic86—21no—
395Dic86—22no—
396C43⋊C8—22no—
397C43⋊C8—24no—
398C43⋊C8—22no—
399#61320—431nomaximal, Sylow
400C22×C43—21no—
401C22×C43—21no—
402C22×C43#54812yes—
403C22×C43C23×D411yescharacteristic
404C2×D43—42no—
405C2×D43—41no—
406C2×D43—42no—
407C2×D43—41no—
408C2×D43—42no—
409C2×D43—41no—
410C4×C43—22no—
411C4×C43—21no—
412C4×C43—22no—
413C4×C43—21no—
414C4×C43—24no—
415C4×C43—22no—
416C4×C43—21no—
417C4×C43—22no—
418C4×C43—42no—
419C4×C43—44no—
420C4×C43#54812yes—
421C4×C43#57512yes—
422C4×C43C22×#4111yescharacteristic
423C4×C43C2×2−1+411yescharacteristic
424Dic43—41no—
425Dic43—41no—
426Dic43—42no—
427Dic43—41no—
428#3480—431no—
429C2×#557D4311yescharacteristic, complemented
430#3377—434no—
431#3374—432no—
432#3371—434no—
433#3368—432no—
434#3365—432no—
435#3364—432no—
436#3142—432no—
437#3141—431no—
438#3080—432no—
439#3079—431no—
440#3037—431no—
441#3037—432no—
442Q8×M16—431no—
443C4×#137—431no—
444C4×#137—432no—
445C2×C43—22no—
446C2×C43C2×#54811yescharacteristic
447C2×C43C2×#57511yescharacteristic
448C2×C43#358611yescharacteristic
449D43—82no—
450D43—81no—
451C2×#137—431no—
452C2×#137—432no—
453#559—431no—
454#559—432no—
455#557—21no—
456#557—21no—
457#557—22no—
458#557—431no—
459#557C2×D4312yes—
460#557C2×D4312yes—
461#557C2×D4314yes—
462#556—431no—
463#556—432no—
464#553—861no—
465#553—862no—
466#550—431no—
467#548—861no—
468#532—431no—
469#532—432no—
470C2×C4⋊Q8—21no—
471C2×C4⋊Q8C2×D4311yescharacteristic
472#529—862no—
473#529—861no—
474C2×#125—22no—
475C2×#125C2×D4312yes—
476C4×#41—431no—
477C4×#41—432no—
478C4×#41—861no—
479C2×C4×Q8—21no—
480C2×C4×Q8C2×D4312yes—
481C2×C4×Q8C2×D4311yescharacteristic
482C2×C4×Q8C2×D4311yescharacteristic
483#491—434no—
484#490—434no—
485#489—434no—
486#488—434no—
487#488—434no—
488#487—432no—
489#486—432no—
490#479—434no—
491#479—434no—
492#478—434no—
493#478—434no—
494#477—432no—
495#476—432no—
496#475—432no—
497#474—432no—
498#464—434no—
499#464—434no—
500#464—434no—
501#462—432no—
502#462—434no—
503#460—432no—
504#460—434no—
505#446—432no—
506#446—434no—
507C8×Q8—432no—
508#441—434no—
509#441—432no—
510#440—434no—
511#440—432no—
512C4×Q16—434no—
513C4×Q16—432no—
514C4×SD16—432no—
515C4×SD16—434no—
516#428—432no—
517#428—431no—
518#423—431no—
519#423—432no—
520#419—431no—
521#417—432no—
522#417—432no—
523#417—432no—
524#417—432no—
525#417—431no—
526C4×M16—431no—
527C4×M16—432no—
528C43#6132011yescharacteristic, complemented, Sylow
529C2×#41—431no—
530C2×#41—432no—
531C2×#41—861no—
532C22×Q8—21no—
533C22×Q8C22⋊D4311yescharacteristic
534C22×Q8C22×D4311yescharacteristic
535#137—864no—
536#137—868no—
537C2×Q16—434no—
538C2×Q16—432no—
539C2×SD16—432no—
540C2×SD16—434no—
541C2×M16—431no—
542C2×M16—432no—
543C2×M16—431no—
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—24no—
547C4⋊Q8—21no—
548C4⋊Q8—21no—
549C4⋊Q8—431no—
550C4⋊Q8—432no—
551C4⋊Q8C22×D4312yes—
552C4⋊Q8C22×D4312yes—
553#127—431no—
554#127—432no—
555#126—862no—
556#126—862no—
557#126—862no—
558#125—24no—
559#125—24no—
560#125—24no—
561#125—24no—
562#125—22no—
563#125—22no—
564#125—861no—
565#125—862no—
566#125C22×D4314yes—
567#125C22×D4314yes—
568#124—432no—
569#124—432no—
570#124—432no—
571#124—861no—
572#124—862no—
573#123—862no—
574#123—862no—
575#123—862no—
576C22⋊Q8—861no—
577C22⋊Q8—862no—
578#121—861no—
579#121—862no—
580#121—862no—
581#121—861no—
582#121—861no—
583#121—862no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—24no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—21no—
590C4×Q8—21no—
591C4×Q8—432no—
592C4×Q8—431no—
593C4×Q8—431no—
594C4×Q8—432no—
595C4×Q8—861no—
596C4×Q8C22⋊D4311yescharacteristic
597C4×Q8C22⋊D4312yes—
598C4×Q8C22⋊D4311yescharacteristic
599C4×Q8C22×D4312yes—
600C4×Q8C22×D4314yes—
601C4×Q8C22×D4314yes—
602C4×Q8C22×D4312yes—
603C4×Q8C22×D4311yescharacteristic
604C4×Q8C22×D4311yescharacteristic
605C4×Q8C22×D4312yes—
606C4×D4—431no—
607C4×D4—432no—
608C4×D4—432no—
609C4×D4—431no—
610C4×D4—861no—
611C4×D4—862no—
612C4×D4—862no—
613C4×D4—861no—
614C4×D4—861no—
615C4×D4—862no—
616C4×D4—862no—
617C4×D4—861no—
618C4×D4—862no—
619C4×D4—861no—
620#117—431no—
621#117—861no—
622#117—862no—
623#117—862no—
624#117—861no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4C22⋊D4311yescharacteristic
631C2×C4⋊C4C22⋊D4312yes—
632C2×C4⋊C4C22×D4311yescharacteristic
633C2×C4⋊C4C22×D4312yes—
634C2×C42—22no—
635C2×C42—21no—
636C2×C42—862no—
637C2×C42—861no—
638C2×C42C22×D4312yes—
639C2×C42C22×D4311yescharacteristic
640#107—434no—
641#107—432no—
642#106—434no—
643#106—432no—
644C4⋊C8—432no—
645C4⋊C8—434no—
646C4⋊C8—434no—
647C4⋊C8—432no—
648#103—432no—
649#103—432no—
650#103—434no—
651#103—432no—
652#103—434no—
653#103—434no—
654#103—434no—
655#102—434no—
656#102—432no—
657#102—434no—
658#102—434no—
659#102—434no—
660#97—432no—
661#97—434no—
662C4×C8—432no—
663C4×C8—434no—
664#41—862no—
665#41—864no—
666#41—862no—
667#41—864no—
668#41—1724no—
669C2×Q8—21no—
670C2×Q8—22no—
671C2×Q8—22no—
672C2×Q8—22no—
673C2×Q8—42no—
674C2×Q8—44no—
675C2×Q8—432no—
676C2×Q8—431no—
677C2×Q8#1062190214yescomplemented
678C2×Q8C2×C22⋊D4311yescharacteristic
679C2×Q8C2×C22⋊D4311yescharacteristic
680C2×Q8C2×C22⋊D4312yes—
681C2×Q8C23×D4312yes—
682C2×D4—432no—
683C2×D4—431no—
684C2×D4—861no—
685C2×D4—862no—
686C2×D4—862no—
687C2×D4—861no—
688C2×D4—862no—
689C2×D4—861no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—862no—
694C22×C4—861no—
695C22×C4—862no—
696C22×C4—861no—
697C22×C4—862no—
698C22×C4—861no—
699C22×C4C2×C22⋊D4311yescharacteristic
700C22×C4C2×C22⋊D4312yes—
701C22×C4C2×C22⋊D4311yescharacteristic
702C22×C4C2×C22⋊D4312yes—
703C22×C4C23×D4311yescharacteristic
704Q16—868no—
705Q16—864no—
706SD16—864no—
707SD16—868no—
708M16—862no—
709M16—864no—
710M16—862no—
711C2×C8—432no—
712C2×C8—432no—
713C2×C8—434no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—22no—
721C4⋊C4—22no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—21no—
725C4⋊C4—22no—
726C4⋊C4—431no—
727C4⋊C4—431no—
728C4⋊C4—861no—
729C4⋊C4—862no—
730C4⋊C4—862no—
731C4⋊C4—861no—
732C4⋊C4—862no—
733C4⋊C4—861no—
734C4⋊C4—862no—
735C4⋊C4—861no—
736C4⋊C4C2×C22⋊D4311yescharacteristic
737C4⋊C4C2×C22⋊D4312yes—
738C4⋊C4C2×C22⋊D4311yescharacteristic
739C4⋊C4C2×C22⋊D4312yes—
740C4⋊C4C2×C22⋊D4312yes—
741C4⋊C4C2×C22⋊D4312yes—
742C4⋊C4C2×C22⋊D4312yes—
743C4⋊C4C23×D4312yes—
744C4⋊C4C23×D4314yes—
745C22⋊C4—861no—
746C22⋊C4—862no—
747C22⋊C4—861no—
748C22⋊C4—861no—
749C22⋊C4—862no—
750C22⋊C4—862no—
751C22⋊C4—862no—
752C22⋊C4—862no—
753C22⋊C4—862no—
754C22⋊C4—862no—
755C22⋊C4—862no—
756C42—24no—
757C42—24no—
758C42—22no—
759C42—22no—
760C42—861no—
761C42—862no—
762C42—861no—
763C42—862no—
764C42—861no—
765C42C2×C22⋊D4312yes—
766C42C2×C22⋊D4311yescharacteristic
767C42C2×C22⋊D4312yes—
768C42C2×C22⋊D4311yescharacteristic
769C42C23×D4312yes—
770C42C23×D4311yescharacteristic
771C42C23×D4311yescharacteristic
772C42C23×D4312yes—
773C23—862no—
774C23—861no—
775C23C22×C22⋊D4311yescharacteristic
776Q8—24no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—42no—
781Q8—44no—
782Q8—44no—
783Q8—862no—
784Q8—861no—
785Q8—862no—
786Q8—861no—
787Q8C2×#1062190214yes—
788D4—862no—
789D4—861no—
790D4—862no—
791D4—861no—
792D4—3442no—
793D4—3441no—
794D4—1724no—
795D4—1722no—
796D4—1724no—
797D4—1722no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—861no—
809C2×C4—861no—
810C2×C4—862no—
811C2×C4—861no—
812C2×C4—3442no—
813C2×C4—3441no—
814C2×C4—1724no—
815C2×C4—1724no—
816C2×C4—1722no—
817C2×C4—1722no—
818C2×C4C22×C22⋊D4312yes—
819C2×C4C22×C22⋊D4311yescharacteristic
820C2×C4C22×C22⋊D4312yes—
821C2×C4C22×C22⋊D4311yescharacteristic
822C2×C4C22×C22⋊D4312yes—
823C2×C4C22×C22⋊D4312yes—
824C2×C4C22×C22⋊D4311yescharacteristic
825C2×C4C22×C22⋊D4311yescharacteristic
826C2×C4C22×C22⋊D4311yescharacteristic
827C2×C4C2×#1062190212yes—
828C2×C4#1306337312yes—
829C2×C4C24×D4311yescharacteristic
830C8—862no—
831C8—864no—
832C8—862no—
833C22—21no—
834C22—21no—
835C22—1722no—
836C22—1721no—
837C22—1722no—
838C22—1721no—
839C22—1722no—
840C22—1721no—
841C22#1458356012yes—
842C22C23×C22⋊D4311yescharacteristic
843C4—21no—
844C4—22no—
845C4—22no—
846C4—24no—
847C4—22no—
848C4—21no—
849C4—22no—
850C4—21no—
851C4—44no—
852C4—42no—
853C4—1721no—
854C4—1722no—
855C4—1721no—
856C4—1721no—
857C4#1458356012yes—
858C4#1458369712yes—
859C4C22×#1062190211yescharacteristic
860C4C2×#1306337311yescharacteristic
861C2—22no—
862C2—3442no—
863C2—3441no—
864C2C2×#1458356011yescharacteristic
865C2C2×#1458369711yescharacteristic
866C2#1914938211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#557C2
socleC22×C43C23×D4
prime radical#19148190C2
hypercenterC2×#557D43
hypocenterC43#61320
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #19147437C2semidirect
3. #19147398C2semidirect
4. #19147363C2semidirect
5. #19147324C2semidirect
6. #19147291C2semidirect
7. #19147280C2semidirect
8. #19144998C2semidirect
9. #19144991C2semidirect
10. #19144413C2semidirect
11. #19144404C2semidirect
12. #19144067C2semidirect
13. #19144067C2semidirect
14. Q8×#10621877C2semidirect
15. C4×#13063356C2semidirect
16. C4×#13063356C2semidirect
17. C2×C43×#557C2semidirect
239. C2×Q8×C43#41semidirect
429. C2×#557D43semidirect
528. C43#61320semidirect
677. C2×Q8#10621902semidirect

Maximal subgroups

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

subgroupindex
#191481902
#191474372
#191473982
#191473632
#191473242
#191472912
#191472802
#191449982
#191449912
#191444132
#191444042
#191440672
Q8×#106218772
C4×#130633562
C2×C43×#5572
#6132043