Finite Group Databasebeta

← #25963122

Subgroups — #25963122

Order 11008.

5126 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063370C211yesmaximal, characteristic, complemented
2C2×#14583700C212yesmaximal, complemented
3#19148260C211yesmaximal, characteristic, complemented
4#19143904C212yesmaximal, complemented
5#19143894C214yesmaximal, complemented
6#19143859C212yesmaximal, complemented
7#19143858C214yesmaximal, complemented
8#19143845C211yesmaximal, characteristic, complemented
9#19143842C212yesmaximal, complemented
10#19143822C211yesmaximal, characteristic, complemented
11#19143819C212yesmaximal, complemented
12#19143817C211yesmaximal, characteristic, complemented
13#19143808C212yesmaximal, complemented
14#447×D43C212yesmaximal, complemented
15#19143116C212yesmaximal, complemented
16#19143041C211yesmaximal, characteristic, complemented
17C2×C43×#447C211yesmaximal, characteristic, complemented
18C2×#13063370—216no—
19C2×#13063370—21no—
20C2×#13063370—22no—
21C2×#13063370—21no—
22C2×#13063370C2212yes—
23C2×#13063370C2214yescomplemented
24C2×#13063370C2212yescomplemented
25C2×#13063370C2211yescharacteristic, complemented
26C22×#10621898C2211yescharacteristic
27C22×#10621898C2211yescharacteristic, complemented
28C22×#10621900—21no—
29C22×#10621900C2212yescomplemented
30C23×C22⋊D43—22no—
31C22×D4×D43—21no—
32C22×D4×D43C2212yescomplemented
33#14583700—216no—
34C2×#13063351C2212yescomplemented
35C2×#13063351C2212yescomplemented
36C2×#13063349C2214yescomplemented
37C2×#13063349C2214yescomplemented
38C2×#13063347C2212yescomplemented
39C2×#13063344C2214yescomplemented
40C2×D8×D43C2214yescomplemented
41C2×#13063331C2212yescomplemented
42#14583567—21no—
43#14583555—21no—
44#14583546—21no—
45#14583539—22no—
46#14583533—21no—
47D4×C22⋊D43—22no—
48#14583480C2211yescharacteristic, complemented
49#14583478C2212yescomplemented
50#14583466C2211yescharacteristic, complemented
51#14583465C2212yescomplemented
52#14583410C2211yescharacteristic, complemented
53#14583409C2212yescomplemented
54#121×D43C2212yescomplemented
55#14583380C2211yescharacteristic, complemented
56#14583063C2212yescomplemented
57#14583062C2214yescomplemented
58#14583057C2211yescharacteristic, complemented
59#14583052C2211yescharacteristic, complemented
60#14583051C2214yescomplemented
61#14583050C2212yescomplemented
62#14583050C2212yescomplemented
63#14583046C2212yescomplemented
64#14583045C2214yescomplemented
65#14583042C2214yescomplemented
66#14583041C2214yescomplemented
67#14583041C2214yescomplemented
68#14583040C2211yescharacteristic, complemented
69#14583037C2212yescomplemented
70#14583035C2211yescharacteristic, complemented
71#14583034C2214yescomplemented
72#14583033C2212yescomplemented
73#14583033C2212yescomplemented
74#14583032C2212yescomplemented
75#14583031C2214yescomplemented
76#14583031C2214yescomplemented
77#14582904C2212yescomplemented
78#14582902C2214yescomplemented
79#14582898C2212yescomplemented
80#14582897C2214yescomplemented
81#14582896C2212yescomplemented
82#14582892C2214yescomplemented
83#102×D43C2214yescomplemented
84#14582865C2212yescomplemented
85#14582864C2214yescomplemented
86#14582863C2211yescharacteristic, complemented
87#14582861C2212yescomplemented
88C22⋊C8×D43C2212yescomplemented
89C23×D4×C43C2211yescharacteristic, complemented
90C22×D8×C43C2212yescomplemented
91C2×#121×C43C2211yescharacteristic, complemented
92C43×#447C2212yescomplemented
93C43×#447C2212yescomplemented
94C43×#447C2214yescomplemented
95C2×#102×C43C2212yescomplemented
96C2×C22⋊C8×C43C2211yescharacteristic, complemented
97C24×D43—22no—
98#13063370—232no—
99#13063370—216no—
100#13063370—216no—
101#13063370—28no—
102#13063370—216no—
103#13063370—216no—
104#13063370—28no—
105#13063370—28no—
106#13063370—28no—
107#13063370D4116yescomplemented
108C2×#10621898—21no—
109C2×#10621898—21no—
110C2×#10621898—28no—
111C2×#10621898—28no—
112C2×#10621898D411yescharacteristic
113C2×#10621898D412yes—
114C2×#10621898D411yescharacteristic
115C2×#10621898C2312yes—
116C2×#10621898C2311yescharacteristic
117C2×#10621898C2311yescharacteristic
118C2×#10621898C2312yes—
119C2×#10621898C2312yes—
120C2×#10621898C2311yescharacteristic, complemented
121C2×#10621900—216no—
122C2×#10621900—216no—
123C2×#10621900—22no—
124C2×#10621900—22no—
125C2×#10621900—22no—
126C2×#10621900—24no—
127C2×#10621900—22no—
128C2×#10621900—21no—
129C2×#10621900C2314yes—
130C2×#10621900C2314yes—
131C2×#10621900C2312yescomplemented
132C22×Dic86D411yescharacteristic
133C22×Dic86C2311yescharacteristic
134C22×D172D411yescharacteristic
135C22×D172C2311yescharacteristic
136C22×C22⋊D43—232no—
137C22×C22⋊D43—21no—
138C22×C22⋊D43—22no—
139C22×C22⋊D43—24no—
140C22×C22⋊D43—24no—
141C22×C22⋊D43—24no—
142C22×C22⋊D43—24no—
143C22×C22⋊D43—22no—
144C22×C22⋊D43—22no—
145C22×C22⋊D43D412yes—
146C2×D4×D43—216no—
147C2×D4×D43—216no—
148C2×D4×D43—22no—
149C2×D4×D43—22no—
150C2×D4×D43—24no—
151C2×D4×D43—22no—
152C2×D4×D43—21no—
153C2×D4×D43—22no—
154C2×D4×D43—22no—
155C2×D4×D43C2314yes—
156C2×D4×D43C2314yes—
157C2×D4×D43C2312yescomplemented
158C23×Dic43—22no—
159C22×C4×D43—21no—
160C22×C4×D43C2312yes—
161#13063351—28no—
162#13063351—28no—
163#13063349—216no—
164#13063349—216no—
165#13063347—28no—
166#13063344—216no—
167C2×Dic172C2312yescomplemented
168C2×#10621873C2312yescomplemented
169C2×#10621873C2312yescomplemented
170C2×#10621883C2314yescomplemented
171C2×#10621883C2314yescomplemented
172C2×D344C2312yescomplemented
173C2×#10621882C2314yescomplemented
174C2×#10621882C2314yescomplemented
175D8×D43—216no—
176#13063331—28no—
177C2×#10621877C2312yescomplemented
178C2×#10621872C2314yescomplemented
179C2×C8×D43C2314yescomplemented
180#13063321—22no—
181#13063321—21no—
182#13063312—21no—
183#13063311—22no—
184#13063308—21no—
185#13063307—22no—
186#13063305—21no—
187#13063305C2312yescomplemented
188#13063304C2311yescharacteristic
189#13063304C2311yescharacteristic, complemented
190#13063302—22no—
191#13063300—21no—
192#13063300C2312yescomplemented
193#13063299—22no—
194#13063299C2311yescharacteristic
195#13063299C2311yescharacteristic, complemented
196#13063298—22no—
197#13063298—22no—
198#13063297—22no—
199#13063297—22no—
200#13063296—22no—
201#13063296C2312yescomplemented
202#13063296C2312yescomplemented
203#13063295—22no—
204#13063294—21no—
205#13063294—22no—
206#13063293—22no—
207#13063293—22no—
208#13063290—21no—
209D4×Dic43—22no—
210#13063287—21no—
211C4×C22⋊D43—21no—
212C4×C22⋊D43—21no—
213C4×C22⋊D43—22no—
214(C22⋊D43)⋊C4—22no—
215#13063284C2311yescharacteristic, complemented
216#13063283C2312yescomplemented
217C4⋊C4×D43C2312yescomplemented
218C22⋊C4×D43—22no—
219#13063250C2312yescomplemented
220#13063250C2312yescomplemented
221#13063248C2314yescomplemented
222#13063247C2312yescomplemented
223#13063247C2312yescomplemented
224#13063246C2314yescomplemented
225#13063246C2314yescomplemented
226#13063245C2314yescomplemented
227C22⋊(C43⋊C8)C2312yes—
228C22⋊(C43⋊C8)C2312yescomplemented
229(C2×D43)⋊C8C2314yescomplemented
230(C2×D43)⋊C8C2314yescomplemented
231C25×C43—21no—
232C22×D4×C43—28no—
233C22×D4×C43—21no—
234C22×D4×C43—21no—
235C22×D4×C43—21no—
236C22×D4×C43—21no—
237C22×D4×C43C2312yes—
238C22×D4×C43C2312yes—
239C22×D4×C43C2312yes—
240C22×D4×C43C2311yescharacteristic, complemented
241C23×C4×C43C2311yescharacteristic
242C2×D8×C43—28no—
243C2×D8×C43C2314yescomplemented
244C2×D8×C43C2314yescomplemented
245C22×C8×C43C2312yescomplemented
246#121×C43—21no—
247#121×C43—21no—
248#121×C43C2312yes—
249#121×C43C2312yescomplemented
250C2×C4⋊C4×C43C2311yescharacteristic, complemented
251C2×C22⋊C4×C43—21no—
252#102×C43C2314yescomplemented
253#102×C43C2314yescomplemented
254C22⋊C8×C43C2311yescharacteristic
255C22⋊C8×C43C2311yescharacteristic
256C22⋊C8×C43C2312yescomplemented
257C24×C43—28no—
258C24×C43—22no—
259C24×C43—22no—
260C24×C43—22no—
261C24×C43—21no—
262C24×C43—82no—
263C24×C43—82no—
264C24×C43C2×D411yescharacteristic
265C23×D43—21no—
266C23×D43—216no—
267C23×D43—24no—
268C23×D43—24no—
269C23×D43—22no—
270C23×D43—84no—
271C23×D43—84no—
272C23×D43C2×D412yes—
273C2×D4×C43—28no—
274C2×D4×C43—28no—
275C2×D4×C43—28no—
276C2×D4×C43—28no—
277C2×D4×C43—28no—
278C2×D4×C43—22no—
279C2×D4×C43—22no—
280C2×D4×C43—22no—
281C2×D4×C43—24no—
282C2×D4×C43—21no—
283C2×D4×C43—22no—
284C2×D4×C43—22no—
285C2×D4×C43—24no—
286C2×D4×C43—82no—
287C2×D4×C43C2×D418yescomplemented
288C2×D4×C43C2412yes—
289C2×D4×C43C2414yes—
290C22×C4×C43—24no—
291C22×C4×C43—21no—
292C22×C4×C43C2×D411yescharacteristic
293C22×C4×C43C2×D411yescharacteristic
294C22×C4×C43C2×D411yescharacteristic
295C22×C4×C43C2411yescharacteristic
296C22×C4×C43C2411yescharacteristic
297C22×C4×C43C2411yescharacteristic
298C2×C22⋊D43—216no—
299C2×C22⋊D43—216no—
300C2×C22⋊D43—28no—
301C2×C22⋊D43—232no—
302C2×C22⋊D43—232no—
303C2×C22⋊D43—232no—
304C2×C22⋊D43—28no—
305C2×C22⋊D43—232no—
306C2×C22⋊D43—24no—
307C2×C22⋊D43—24no—
308C2×C22⋊D43—22no—
309C2×C22⋊D43—22no—
310C2×C22⋊D43—22no—
311C2×C22⋊D43—21no—
312C2×C22⋊D43—21no—
313C2×C22⋊D43—21no—
314C2×C22⋊D43—24no—
315C2×C22⋊D43—24no—
316C2×C22⋊D43—22no—
317C2×C22⋊D43—22no—
318C2×C22⋊D43—22no—
319C2×C22⋊D43—48no—
320C2×C22⋊D43C2×D412yes—
321C2×C22⋊D43C2×D412yes—
322C2×C22⋊D43C2×D412yes—
323C2×C22⋊D43C2×D412yes—
324C22×Dic43—216no—
325C22×Dic43—24no—
326C22×Dic43—24no—
327C22×Dic43—22no—
328C22×Dic43—21no—
329C22×Dic43C2×D412yes—
330#10621900—216no—
331#10621900—216no—
332#10621900—216no—
333#10621900—232no—
334#10621900—28no—
335#10621900—28no—
336#10621900—28no—
337#10621900—216no—
338#10621900—28no—
339#10621900—44no—
340#10621900C2×D4116yescomplemented
341D4×D43—216no—
342D4×D43—216no—
343D4×D43—232no—
344D4×D43—216no—
345D4×D43—28no—
346D4×D43—216no—
347D4×D43—28no—
348D4×D43—28no—
349D4×D43—28no—
350D4×D43—44no—
351D4×D43—84no—
352D4×D43C2×D4116yescomplemented
353#10621898—28no—
354#10621898—28no—
355#10621898—24no—
356#10621898—24no—
357#10621898—28no—
358#10621898—24no—
359#10621898—24no—
360#10621898—28no—
361#10621898—24no—
362#10621898—24no—
363#10621898—24no—
364#10621898C2×D418yes—
365#10621898C2×D418yescomplemented
366C2×D172—21no—
367C2×D172—24no—
368C2×D172—24no—
369C2×D172—22no—
370C2×D172C2×D412yes—
371C2×D172C2×D411yescharacteristic
372C2×D172C2×D411yescharacteristic
373C2×D172C2411yescharacteristic
374C2×D172C2412yes—
375C2×C4×D43—28no—
376C2×C4×D43—22no—
377C2×C4×D43—22no—
378C2×C4×D43—28no—
379C2×C4×D43—21no—
380C2×C4×D43—22no—
381C2×C4×D43C2×D412yes—
382C2×C4×D43C2×D412yes—
383C2×C4×D43C2412yes—
384C2×C4×D43C2412yes—
385C2×Dic86—21no—
386C2×Dic86—24no—
387C2×Dic86—24no—
388C2×Dic86C2×D412yes—
389C2×Dic86C2×D411yescharacteristic
390C2×Dic86C2×D411yescharacteristic
391C2×Dic86C2411yescharacteristic
392C2×Dic86C2412yes—
393D8×C43—28no—
394D8×C43—28no—
395C2×C8×C43—24no—
396C2×C8×C43C2412yes—
397C2×C8×C43C2412yes—
398C4⋊C4×C43—21no—
399C4⋊C4×C43C2412yes—
400C22⋊C4×C43—22no—
401C22⋊C4×C43—22no—
402C22⋊Dic43—22no—
403C22⋊Dic43—22no—
404C22⋊Dic43—21no—
405C22⋊Dic43—21no—
406C22⋊Dic43—21no—
407#10621883—28no—
408#10621883—28no—
409#10621882—28no—
410#10621882—28no—
411(C2×D43)⋊C4—21no—
412(C2×D43)⋊C4—21no—
413(C2×D43)⋊C4—22no—
414(C2×D43)⋊C4—22no—
415(C2×D43)⋊C4—22no—
416C4⋊Dic43—22no—
417C4⋊Dic43C2411yescharacteristic
418C4⋊Dic43C2411yescharacteristic
419Dic43⋊C4—21no—
420Dic43⋊C4—21no—
421Dic43⋊C4—22no—
422C4×Dic43—21no—
423C4×Dic43—22no—
424#10621877—24no—
425C2×C43⋊C8C2414yes—
426Dic172—24no—
427D344—24no—
428#10621873—24no—
429#10621873—24no—
430#10621872—28no—
431C8×D43—28no—
432C23×C43—28no—
433C23×C43—28no—
434C23×C43—22no—
435C23×C43—22no—
436C23×C43—24no—
437C23×C43—28no—
438C23×C43—22no—
439C23×C43—41no—
440C23×C43—44no—
441C23×C43—44no—
442C23×C43—42no—
443C23×C43—82no—
444C23×C43—82no—
445C23×C43—82no—
446C23×C43—82no—
447C23×C43—81no—
448C23×C43—81no—
449C23×C43—816no—
450C23×C43C22×D411yescharacteristic
451C23×C43C22×D411yescharacteristic
452C23×C43C22×D411yescharacteristic
453C22×D43—24no—
454C22×D43—24no—
455C22×D43—22no—
456C22×D43—216no—
457C22×D43—24no—
458C22×D43—216no—
459C22×D43—21no—
460C22×D43—42no—
461C22×D43—42no—
462C22×D43—42no—
463C22×D43—44no—
464C22×D43—84no—
465C22×D43—84no—
466C22×D43—84no—
467C22×D43—84no—
468C22×D43—82no—
469C22×D43—82no—
470C22×D43—832no—
471C22×D43C22×D412yes—
472C22×D43C22×D412yes—
473D4×C43—28no—
474D4×C43—28no—
475D4×C43—28no—
476D4×C43—24no—
477D4×C43—24no—
478D4×C43—44no—
479D4×C43—42no—
480D4×C43—82no—
481D4×C43C22×D418yes—
482C2×C4×C43—22no—
483C2×C4×C43—22no—
484C2×C4×C43—22no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—81no—
489C2×C4×C43C22×D411yescharacteristic
490C2×C4×C43C22×D411yescharacteristic
491C2×C4×C43C22×D411yescharacteristic
492C2×C4×C43C22×D414yes—
493C2×C4×C43C2511yescharacteristic
494C22⋊D43—28no—
495C22⋊D43—216no—
496C22⋊D43—216no—
497C22⋊D43—24no—
498C22⋊D43—28no—
499C22⋊D43—24no—
500C22⋊D43—216no—
501C22⋊D43—24no—
502C22⋊D43—216no—
503C22⋊D43—42no—
504C22⋊D43—42no—
505C22⋊D43—44no—
506C22⋊D43—44no—
507C22⋊D43—82no—
508C22⋊D43—82no—
509C22⋊D43—81no—
510C22⋊D43#12018yes—
511C2×Dic43—24no—
512C2×Dic43—216no—
513C2×Dic43—22no—
514C2×Dic43—24no—
515C2×Dic43—216no—
516C2×Dic43—21no—
517C2×Dic43—21no—
518C2×Dic43—21no—
519C2×Dic43—44no—
520C2×Dic43C22×D412yes—
521C2×Dic43C22×D412yes—
522D172—24no—
523D172—24no—
524D172—22no—
525D172—22no—
526D172—22no—
527D172—82no—
528D172#12014yes—
529D172C22×D414yes—
530C4×D43—28no—
531C4×D43—24no—
532C4×D43—28no—
533C4×D43—24no—
534C4×D43—24no—
535C4×D43—42no—
536C4×D43—82no—
537C4×D43C22×D418yes—
538Dic86—24no—
539Dic86—22no—
540Dic86—22no—
541Dic86—24no—
542Dic86—22no—
543Dic86#12014yes—
544Dic86C22×D414yes—
545C8×C43—22no—
546C8×C43—22no—
547C43⋊C8—24no—
548#60372—431nomaximal, Sylow
549C22×C43—21no—
550C22×C43—21no—
551C22×C43—21no—
552C22×C43—21no—
553C22×C43—21no—
554C22×C43—28no—
555C22×C43—21no—
556C22×C43—21no—
557C22×C43—44no—
558C22×C43—416no—
559C22×C43—44no—
560C22×C43—44no—
561C22×C43—42no—
562C22×C43—42no—
563C22×C43—42no—
564C22×C43—88no—
565C22×C43—88no—
566C22×C43—162no—
567C22×C43C2×#12012yes—
568C22×C43#57612yescomplemented
569C22×C43C23×D411yescharacteristic
570C2×D43—22no—
571C2×D43—22no—
572C2×D43—22no—
573C2×D43—24no—
574C2×D43—22no—
575C2×D43—22no—
576C2×D43—48no—
577C2×D43—48no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—41no—
581C2×D43—41no—
582C2×D43—41no—
583C2×D43—816no—
584C2×D43—816no—
585C2×D43—164no—
586C2×D43C2×#12014yes—
587C4×C43—21no—
588C4×C43—21no—
589C4×C43—42no—
590C4×C43C2×#12012yes—
591C4×C43C23×D412yes—
592Dic43—22no—
593Dic43—24no—
594Dic43—41no—
595Dic43—41no—
596Dic43—41no—
597Dic43C2×#12014yes—
598C22×H(5,𝔽2)—431no—
599C2×#576—432no—
600#3488—431no—
601#3012—434no—
602#3012—432no—
603#3008—434no—
604#3008—432no—
605#3006—432no—
606#3006—431no—
607#3003—432no—
608#3003—431no—
609#3002—432no—
610#3002—431no—
611C2×#447—432no—
612C2×#447D4311yescharacteristic, complemented
613#2897—432no—
614#2880—431no—
615C2×C43—22no—
616C2×C43—22no—
617C2×C43—48no—
618C2×C43—41no—
619C2×C43—82no—
620C2×C43C22×#12011yescharacteristic
621C2×C43C2×#57611yescharacteristic
622C2×C43#358511yescharacteristic
623D43—24no—
624D43—42no—
625D43—44no—
626D43—81no—
627C2×H(5,𝔽2)—432no—
628C2×H(5,𝔽2)—434no—
629C2×H(5,𝔽2)—432no—
630C2×H(5,𝔽2)—431no—
631C2×H(5,𝔽2)—862no—
632C2×H(5,𝔽2)—861no—
633C2×H(5,𝔽2)—861no—
634C2×H(5,𝔽2)—8616no—
635C22×#41—431no—
636C22×#41—432no—
637C22×#41—431no—
638C22×#41—861no—
639C23×D4—432no—
640C23×D4—861no—
641C23×D4—862no—
642C23×D4C2×D4311yescharacteristic, complemented
643#576—8616no—
644C2×AGL(1,ℤ/8)—432no—
645C2×AGL(1,ℤ/8)—432no—
646C2×AGL(1,ℤ/8)—434no—
647C2×AGL(1,ℤ/8)—434no—
648C2×#135—434no—
649C2×#135—432no—
650C22×D8—434no—
651C22×D8C2×D4312yescomplemented
652C2×#131—432no—
653#550—861no—
654#548—861no—
655#546—862no—
656#546—861no—
657D42—861no—
658D42—862no—
659#537—432no—
660#537—431no—
661#535—431no—
662#535—432no—
663#525—431no—
664#525—432no—
665C2×#121—432no—
666C2×#121C2×D4311yescharacteristic, complemented
667#520—431no—
668#452—434no—
669#452—432no—
670#451—431no—
671#450—432no—
672#450—432no—
673#450—434no—
674#450—431no—
675#449—434no—
676#449—434no—
677#449—434no—
678#449—434no—
679#449—432no—
680#448—432no—
681#448—431no—
682#447—432no—
683#447—432no—
684#447—434no—
685#447—434no—
686#447—432no—
687#447—434no—
688#447—431no—
689#447C2×D4312yescomplemented
690#447C2×D4312yescomplemented
691#447C2×D4314yescomplemented
692#418—432no—
693#418—434no—
694#417—432no—
695#417—434no—
696#416—432no—
697#416—434no—
698C2×#102—434no—
699C2×#102C2×D4312yescomplemented
700#408—432no—
701#408—434no—
702#407—431no—
703#407—432no—
704C2×C22⋊C8—432no—
705C2×C22⋊C8C2×D4311yescharacteristic, complemented
706C43#6037211yescharacteristic, complemented, Sylow
707C25—21no—
708C25—862no—
709H(5,𝔽2)—4316no—
710H(5,𝔽2)—8616no—
711H(5,𝔽2)—8616no—
712H(5,𝔽2)—868no—
713H(5,𝔽2)—868no—
714H(5,𝔽2)—8616no—
715H(5,𝔽2)—8632no—
716H(5,𝔽2)—8616no—
717H(5,𝔽2)—868no—
718H(5,𝔽2)—868no—
719C2×#41—431no—
720C2×#41—432no—
721C2×#41—431no—
722C2×#41—431no—
723C2×#41—432no—
724C2×#41—431no—
725C2×#41—434no—
726C2×#41—432no—
727C2×#41—434no—
728C2×#41—432no—
729C2×#41—431no—
730C2×#41—432no—
731C2×#41—868no—
732C2×#41—868no—
733C2×#41—862no—
734C2×#41—862no—
735C2×#41—862no—
736C2×#41—864no—
737C2×#41—862no—
738C2×#41—861no—
739C2×#41—8616no—
740C2×#41—8616no—
741C2×#41—861no—
742C2×#41—861no—
743C22×Q8—431no—
744C22×Q8—431no—
745C22×D4—28no—
746C22×D4—21no—
747C22×D4—21no—
748C22×D4—21no—
749C22×D4—21no—
750C22×D4—434no—
751C22×D4—432no—
752C22×D4—432no—
753C22×D4—434no—
754C22×D4—431no—
755C22×D4—431no—
756C22×D4—862no—
757C22×D4—862no—
758C22×D4—862no—
759C22×D4—8616no—
760C22×D4—862no—
761C22×D4—864no—
762C22×D4—862no—
763C22×D4—861no—
764C22×D4—8616no—
765C22×D4—862no—
766C22×D4—864no—
767C22×D4—864no—
768C22×D4—864no—
769C22×D4—864no—
770C22×D4—862no—
771C22×D4—862no—
772C22×D4—8632no—
773C22×D4—861no—
774C22×D4C22×D4312yes—
775C22×D4C22×D4312yes—
776C22×D4C22×D4312yes—
777C22×D4C22×D4311yescharacteristic, complemented
778C23×C4—432no—
779C23×C4—862no—
780C23×C4—861no—
781C23×C4C22×D4311yescharacteristic
782AGL(1,ℤ/8)—8616no—
783AGL(1,ℤ/8)—8616no—
784AGL(1,ℤ/8)—868no—
785AGL(1,ℤ/8)—868no—
786#135—868no—
787#135—8616no—
788C2×Q16—432no—
789C2×SD16—434no—
790C2×SD16—434no—
791C2×SD16—432no—
792C2×SD16—432no—
793C2×D8—28no—
794C2×D8—434no—
795C2×D8—434no—
796C2×D8—432no—
797C2×D8—8616no—
798C2×D8C22×D4314yescomplemented
799C2×D8C22×D4314yescomplemented
800#131—868no—
801C2×M16—432no—
802C2×M16—434no—
803C22×C8—434no—
804C22×C8C22×D4312yescomplemented
805#127—862no—
806#127—861no—
807#124—862no—
808#124—861no—
809#123—862no—
810#123—861no—
811C22⋊Q8—431no—
812C22⋊Q8—431no—
813C22⋊Q8—432no—
814C22⋊Q8—862no—
815C22⋊Q8—861no—
816#121—21no—
817#121—21no—
818#121—432no—
819#121—432no—
820#121—431no—
821#121—431no—
822#121—432no—
823#121—862no—
824#121—862no—
825#121—861no—
826#121—862no—
827#121—862no—
828#121—862no—
829#121—862no—
830#121C22×D4312yes—
831#121C22×D4312yescomplemented
832#120—862no—
833#120—862no—
834#120—862no—
835#120—862no—
836#120—861no—
837C4×Q8—861no—
838C4×D4—862no—
839C4×D4—861no—
840C4×D4—862no—
841C4×D4—862no—
842C4×D4—861no—
843C4×D4—861no—
844#117—431no—
845#117—432no—
846C2×C4⋊C4—432no—
847C2×C4⋊C4C22×D4311yescharacteristic, complemented
848C2×C22⋊C4—21no—
849C2×C22⋊C4—862no—
850#103—432no—
851#103—432no—
852#103—434no—
853#102—434no—
854#102—434no—
855#102—432no—
856#102—432no—
857#102—434no—
858#102C22×D4314yescomplemented
859#102C22×D4314yescomplemented
860C22⋊C8—432no—
861C22⋊C8—432no—
862C22⋊C8—434no—
863C22⋊C8—434no—
864C22⋊C8C22×D4311yescharacteristic
865C22⋊C8C22×D4311yescharacteristic
866C22⋊C8C22×D4312yescomplemented
867C24—28no—
868C24—22no—
869C24—22no—
870C24—22no—
871C24—21no—
872C24—82no—
873C24—82no—
874C24—432no—
875C24—864no—
876C24—864no—
877C24—862no—
878C24—8616no—
879C24—861no—
880C24—3444no—
881C24—3444no—
882C24D4×D4311yescharacteristic
883#41—438no—
884#41—4316no—
885#41—438no—
886#41—868no—
887#41—868no—
888#41—864no—
889#41—864no—
890#41—864no—
891#41—864no—
892#41—868no—
893#41—868no—
894#41—868no—
895#41—868no—
896#41—868no—
897#41—8616no—
898#41—8616no—
899#41—8616no—
900#41—8632no—
901#41—8616no—
902#41—868no—
903#41—864no—
904#41—864no—
905#41—864no—
906#41—1724no—
907C2×Q8—431no—
908C2×Q8—432no—
909C2×Q8—431no—
910C2×Q8—432no—
911C2×Q8—431no—
912C2×Q8—864no—
913C2×Q8—864no—
914C2×Q8—861no—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—28no—
918C2×D4—28no—
919C2×D4—28no—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—22no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—24no—
926C2×D4—24no—
927C2×D4—21no—
928C2×D4—82no—
929C2×D4—432no—
930C2×D4—4316no—
931C2×D4—432no—
932C2×D4—432no—
933C2×D4—432no—
934C2×D4—431no—
935C2×D4—432no—
936C2×D4—431no—
937C2×D4—432no—
938C2×D4—431no—
939C2×D4—864no—
940C2×D4—864no—
941C2×D4—862no—
942C2×D4—868no—
943C2×D4—868no—
944C2×D4—864no—
945C2×D4—864no—
946C2×D4—862no—
947C2×D4—868no—
948C2×D4—8616no—
949C2×D4—8616no—
950C2×D4—8616no—
951C2×D4—8632no—
952C2×D4—8616no—
953C2×D4—868no—
954C2×D4—8632no—
955C2×D4—864no—
956C2×D4—864no—
957C2×D4—8616no—
958C2×D4—8616no—
959C2×D4—868no—
960C2×D4—8632no—
961C2×D4—8632no—
962C2×D4—8632no—
963C2×D4—862no—
964C2×D4—862no—
965C2×D4—868no—
966C2×D4—862no—
967C2×D4—862no—
968C2×D4—861no—
969C2×D4—862no—
970C2×D4—861no—
971C2×D4—861no—
972C2×D4—861no—
973C2×D4—3444no—
974C2×D4—1724no—
975C2×D4—1728no—
976C2×D4D4×D4318yescomplemented
977C2×D4C23×D4312yes—
978C2×D4C23×D4314yes—
979C22×C4—24no—
980C22×C4—21no—
981C22×C4—432no—
982C22×C4—432no—
983C22×C4—432no—
984C22×C4—432no—
985C22×C4—432no—
986C22×C4—868no—
987C22×C4—868no—
988C22×C4—862no—
989C22×C4—864no—
990C22×C4—864no—
991C22×C4—862no—
992C22×C4—8616no—
993C22×C4—861no—
994C22×C4—862no—
995C22×C4—862no—
996C22×C4—861no—
997C22×C4D4×D4311yescharacteristic
998C22×C4D4×D4311yescharacteristic
999C22×C4D4×D4311yescharacteristic
1000C22×C4C23×D4311yescharacteristic
1001C22×C4C23×D4311yescharacteristic
1002C22×C4C23×D4311yescharacteristic
1003Q16—864no—
1004SD16—864no—
1005SD16—864no—
1006SD16—868no—
1007SD16—868no—
1008D8—28no—
1009D8—28no—
1010D8—864no—
1011D8—868no—
1012D8—868no—
1013M16—868no—
1014M16—864no—
1015C2×C8—24no—
1016C2×C8—434no—
1017C2×C8—868no—
1018C2×C8C23×D4312yes—
1019C2×C8C23×D4312yes—
1020C4⋊C4—21no—
1021C4⋊C4—431no—
1022C4⋊C4—431no—
1023C4⋊C4—862no—
1024C4⋊C4—862no—
1025C4⋊C4—861no—
1026C4⋊C4—861no—
1027C4⋊C4C23×D4312yes—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—862no—
1031C22⋊C4—862no—
1032C22⋊C4—862no—
1033C22⋊C4—862no—
1034C22⋊C4—862no—
1035C22⋊C4—861no—
1036C22⋊C4—861no—
1037C22⋊C4—861no—
1038C22⋊C4—861no—
1039C22⋊C4—861no—
1040C42—862no—
1041C42—861no—
1042C23—28no—
1043C23—28no—
1044C23—22no—
1045C23—22no—
1046C23—24no—
1047C23—28no—
1048C23—22no—
1049C23—41no—
1050C23—44no—
1051C23—44no—
1052C23—42no—
1053C23—82no—
1054C23—82no—
1055C23—82no—
1056C23—82no—
1057C23—81no—
1058C23—81no—
1059C23—816no—
1060C23—432no—
1061C23—432no—
1062C23—8616no—
1063C23—864no—
1064C23—8616no—
1065C23—864no—
1066C23—864no—
1067C23—862no—
1068C23—861no—
1069C23—3444no—
1070C23—3444no—
1071C23—3444no—
1072C23—3444no—
1073C23—3442no—
1074C23—3442no—
1075C23—34432no—
1076C23—1722no—
1077C23—1722no—
1078C23—1724no—
1079C23—1722no—
1080C23C2×D4×D4311yescharacteristic
1081C23C2×D4×D4311yescharacteristic
1082C23C2×D4×D4311yescharacteristic
1083Q8—434no—
1084Q8—434no—
1085Q8—864no—
1086Q8—864no—
1087Q8—862no—
1088Q8—862no—
1089Q8—862no—
1090D4—28no—
1091D4—28no—
1092D4—28no—
1093D4—24no—
1094D4—24no—
1095D4—44no—
1096D4—42no—
1097D4—82no—
1098D4—438no—
1099D4—434no—
1100D4—434no—
1101D4—864no—
1102D4—864no—
1103D4—864no—
1104D4—8616no—
1105D4—864no—
1106D4—8616no—
1107D4—8616no—
1108D4—868no—
1109D4—8616no—
1110D4—864no—
1111D4—868no—
1112D4—862no—
1113D4—862no—
1114D4—862no—
1115D4—3442no—
1116D4—3441no—
1117D4—3442no—
1118D4—3442no—
1119D4—1724no—
1120D4—1724no—
1121D4—1722no—
1122D4—1722no—
1123D4C2×D4×D4318yes—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—81no—
1131C2×C4—432no—
1132C2×C4—438no—
1133C2×C4—432no—
1134C2×C4—864no—
1135C2×C4—864no—
1136C2×C4—868no—
1137C2×C4—864no—
1138C2×C4—8616no—
1139C2×C4—864no—
1140C2×C4—8616no—
1141C2×C4—862no—
1142C2×C4—868no—
1143C2×C4—864no—
1144C2×C4—861no—
1145C2×C4—861no—
1146C2×C4—861no—
1147C2×C4—3442no—
1148C2×C4—1724no—
1149C2×C4—1722no—
1150C2×C4C2×D4×D4311yescharacteristic
1151C2×C4C2×D4×D4311yescharacteristic
1152C2×C4C2×D4×D4311yescharacteristic
1153C2×C4C2×D4×D4314yes—
1154C2×C4C24×D4311yescharacteristic
1155C8—22no—
1156C8—22no—
1157C8—864no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—28no—
1165C22—21no—
1166C22—44no—
1167C22—416no—
1168C22—44no—
1169C22—44no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—88no—
1174C22—88no—
1175C22—162no—
1176C22—434no—
1177C22—862no—
1178C22—862no—
1179C22—862no—
1180C22—864no—
1181C22—862no—
1182C22—862no—
1183C22—34416no—
1184C22—34416no—
1185C22—1728no—
1186C22—1728no—
1187C22—1721no—
1188C22—1721no—
1189C22—1721no—
1190C22—1722no—
1191C22—1722no—
1192C22—6884no—
1193C22#120×D4312yes—
1194C22#1458370012yescomplemented
1195C22C22×D4×D4311yescharacteristic
1196C4—21no—
1197C4—21no—
1198C4—42no—
1199C4—434no—
1200C4—862no—
1201C4—864no—
1202C4—1721no—
1203C4—1721no—
1204C4—1721no—
1205C4#120×D4312yes—
1206C4C22×D4×D4312yes—
1207C2—22no—
1208C2—22no—
1209C2—41no—
1210C2—48no—
1211C2—82no—
1212C2—864no—
1213C2—3441no—
1214C2—1722no—
1215C2—1724no—
1216C2C2×#120×D4311yescharacteristic
1217C2C2×#1458370011yescharacteristic
1218C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#447C2
socleC22×C43C23×D4
hypercenterC2×#447D43
hypocenterC43#60372
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C22×#13063370C2semidirect
2. C2×#14583700C2semidirect
3. #19148260C2semidirect
4. #19143904C2semidirect
5. #19143894C2semidirect
6. #19143859C2semidirect
7. #19143858C2semidirect
8. #19143845C2semidirect
9. #19143842C2semidirect
10. #19143822C2semidirect
11. #19143819C2semidirect
12. #19143817C2semidirect
13. #19143808C2semidirect
14. #447×D43C2semidirect
15. #19143116C2semidirect
16. #19143041C2semidirect
17. C2×C43×#447C2semidirect
23. C2×#13063370C22semidirect
24. C2×#13063370C22semidirect
25. C2×#13063370C22semidirect
27. C22×#10621898C22semidirect
29. C22×#10621900C22semidirect
32. C22×D4×D43C22semidirect
34. C2×#13063351C22semidirect
35. C2×#13063351C22semidirect
36. C2×#13063349C22semidirect
37. C2×#13063349C22semidirect
38. C2×#13063347C22semidirect
39. C2×#13063344C22semidirect
40. C2×D8×D43C22semidirect
41. C2×#13063331C22semidirect
48. #14583480C22semidirect
49. #14583478C22semidirect
50. #14583466C22semidirect
51. #14583465C22semidirect
52. #14583410C22semidirect
53. #14583409C22semidirect
54. #121×D43C22semidirect
55. #14583380C22semidirect
56. #14583063C22semidirect
57. #14583062C22semidirect
58. #14583057C22semidirect
59. #14583052C22semidirect
60. #14583051C22semidirect
61. #14583050C22semidirect
62. #14583050C22semidirect
63. #14583046C22semidirect
64. #14583045C22semidirect
65. #14583042C22semidirect
66. #14583041C22semidirect
67. #14583041C22semidirect
68. #14583040C22semidirect
69. #14583037C22semidirect
70. #14583035C22semidirect
71. #14583034C22semidirect
72. #14583033C22semidirect
73. #14583033C22semidirect
74. #14583032C22semidirect
75. #14583031C22semidirect
76. #14583031C22semidirect
77. #14582904C22semidirect
78. #14582902C22semidirect
79. #14582898C22semidirect
80. #14582897C22semidirect
81. #14582896C22semidirect
82. #14582892C22semidirect
83. #102×D43C22semidirect
84. #14582865C22semidirect
85. #14582864C22semidirect
86. #14582863C22semidirect
87. #14582861C22semidirect
88. C22⋊C8×D43C22semidirect
89. C23×D4×C43C22semidirect
90. C22×D8×C43C22semidirect
91. C2×#121×C43C22semidirect
92. C43×#447C22semidirect
93. C43×#447C22semidirect
94. C43×#447C22semidirect
95. C2×#102×C43C22semidirect
96. C2×C22⋊C8×C43C22semidirect
107. #13063370D4semidirect
120. C2×#10621898C23semidirect
131. C2×#10621900C23semidirect
157. C2×D4×D43C23semidirect
167. C2×Dic172C23semidirect
168. C2×#10621873C23semidirect
169. C2×#10621873C23semidirect
170. C2×#10621883C23semidirect
171. C2×#10621883C23semidirect
172. C2×D344C23semidirect
173. C2×#10621882C23semidirect
174. C2×#10621882C23semidirect
177. C2×#10621877C23semidirect
178. C2×#10621872C23semidirect
179. C2×C8×D43C23semidirect
187. #13063305C23semidirect
189. #13063304C23semidirect
192. #13063300C23semidirect
195. #13063299C23semidirect
201. #13063296C23semidirect
202. #13063296C23semidirect
215. #13063284C23semidirect
216. #13063283C23semidirect
217. C4⋊C4×D43C23semidirect
219. #13063250C23semidirect
220. #13063250C23semidirect
221. #13063248C23semidirect
222. #13063247C23semidirect
223. #13063247C23semidirect
224. #13063246C23semidirect
225. #13063246C23semidirect
226. #13063245C23semidirect
228. C22⋊(C43⋊C8)C23semidirect
229. (C2×D43)⋊C8C23semidirect
230. (C2×D43)⋊C8C23semidirect
240. C22×D4×C43C23semidirect
243. C2×D8×C43C23semidirect
244. C2×D8×C43C23semidirect
245. C22×C8×C43C23semidirect
249. #121×C43C23semidirect
250. C2×C4⋊C4×C43C23semidirect
252. #102×C43C23semidirect
253. #102×C43C23semidirect
256. C22⋊C8×C43C23semidirect
287. C2×D4×C43C2×D4semidirect
340. #10621900C2×D4semidirect
352. D4×D43C2×D4semidirect
365. #10621898C2×D4semidirect
568. C22×C43#576semidirect
612. C2×#447D43semidirect
642. C23×D4C2×D43semidirect
651. C22×D8C2×D43semidirect
666. C2×#121C2×D43semidirect
689. #447C2×D43semidirect
690. #447C2×D43semidirect
691. #447C2×D43semidirect
699. C2×#102C2×D43semidirect
705. C2×C22⋊C8C2×D43semidirect
706. C43#60372semidirect
777. C22×D4C22×D43semidirect
798. C2×D8C22×D43semidirect
799. C2×D8C22×D43semidirect
804. C22×C8C22×D43semidirect
831. #121C22×D43semidirect
847. C2×C4⋊C4C22×D43semidirect
858. #102C22×D43semidirect
859. #102C22×D43semidirect
866. C22⋊C8C22×D43semidirect
976. C2×D4D4×D43semidirect
1194. C22#14583700semidirect

Maximal subgroups

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

subgroupindex
C22×#130633702
C2×#145837002
#191482602
#191439042
#191438942
#191438592
#191438582
#191438452
#191438422
#191438222
#191438192
#191438172
#191438082
#447×D432
#191431162
#191430412
C2×C43×#4472
#6037243