Finite Group Databasebeta

← #36312954

Subgroups — #36312954

Order 21248.

11346 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128537C212yesmaximal, complemented
2#24921255C214yesmaximal, complemented
3#24921252C214yesmaximal, complemented
4#24921245C214yesmaximal, complemented
5#24921238C214yesmaximal, complemented
6#24921232C214yesmaximal, complemented
7#24921226C214yesmaximal, complemented
8#24921224C218yesmaximal, complemented
9#24920946C2116yesmaximal, complemented
10#24920796C211yesmaximal, characteristic, complemented
11#24920790C214yesmaximal, complemented
12C2×#19128247C212yesmaximal, complemented
13#532×D83C214yesmaximal, complemented
14C2×#19128169C211yesmaximal, characteristic, complemented
15C83×#3449C211yesmaximal, characteristic, complemented
16#19128537—232no—
17C2×#14581840C2214yescomplemented
18C2×#14581839C2214yescomplemented
19C2×#14581839C2214yescomplemented
20C2×#14581838C2214yescomplemented
21C2×#14581838C2214yescomplemented
22C2×#14581837C2218yescomplemented
23C2×#14581837C2214yescomplemented
24C22×#13050590C2211yescharacteristic
25C22×#13050590C2218yescomplemented
26C22×#13050590C2212yescomplemented
27C2×#41×D83C2218yescomplemented
28C2×#41×D83C2218yescomplemented
29#19128369C22116yescomplemented
30#19128364C22116yescomplemented
31#19128361C22116yescomplemented
32#19128357C22116yescomplemented
33#19128353C22116yescomplemented
34#19128349C22132yescomplemented
35#19128348C22116yescomplemented
36#19128343C22132yescomplemented
37#19128342C22116yescomplemented
38#19128338C22132yescomplemented
39#19128335C22116yescomplemented
40#19128333C22132yescomplemented
41#19128282C2214yescomplemented
42#19128278C22116yescomplemented
43#19128277C2214yescomplemented
44#19128276C2218yescomplemented
45#19128271C2218yescomplemented
46#19128270C2214yescomplemented
47#19128269C2218yescomplemented
48#19128264C2218yescomplemented
49#19128263C2214yescomplemented
50#19128259C22116yescomplemented
51#19128252C2214yescomplemented
52#19128251C2214yescomplemented
53#19128250C2218yescomplemented
54#19128249C2214yescomplemented
55#19128248C22116yescomplemented
56#19128247C2218yescomplemented
57#19128247C2218yescomplemented
58#19128247C2214yescomplemented
59#19128247C2214yescomplemented
60#19128247C2214yescomplemented
61#19128247C2214yescomplemented
62#19128246C22116yescomplemented
63C2×#14581790C2212yescomplemented
64C4⋊Q8×D83C2214yescomplemented
65C2×#14581788C2212yescomplemented
66#127×D83C2214yescomplemented
67C2×#14581781C2212yescomplemented
68C2×#14581779C2212yescomplemented
69#124×D83C2218yescomplemented
70#19128213C2218yescomplemented
71#19128210C22132yescomplemented
72C2×#14581764C2218yescomplemented
73#121×D83C22116yescomplemented
74#19128169C2218yescomplemented
75#19128169C2214yescomplemented
76#19128169C2214yescomplemented
77C2×#14581757C2212yescomplemented
78C2×#14581754C2212yescomplemented
79C2×C4×C22⋊D83C2218yescomplemented
80C2×(C22⋊D83)⋊C4C2214yescomplemented
81C4×D4×D83C22116yescomplemented
82C2×#14581749C2212yescomplemented
83C22×C4×Dic83C2211yescharacteristic, complemented
84C2×C42×D83C2212yescomplemented
85C22×#41×C83C2212yescomplemented
86#537×C83C2214yescomplemented
87#536×C83C2214yescomplemented
88#535×C83C2214yescomplemented
89#534×C83C2214yescomplemented
90#532×C83C2214yescomplemented
91#525×C83C2218yescomplemented
92C2×#117×C83C2211yescharacteristic, complemented
93#14581840—232no—
94#14581839—232no—
95#14581839—232no—
96#14581838—232no—
97#14581838—232no—
98#14581837—232no—
99#14581837—264no—
100C2×#13050591C2318yes—
101C2×#13050591C2318yes—
102C2×#13050590—264no—
103C2×#13050590—216no—
104C2×#13050590D4116yescomplemented
105C2×#13050590C23116yes—
106C2×#13050590C2318yes—
107C2×#13050590C2318yes—
108C2×#13050590C23116yes—
109C2×#13050590C2314yes—
110C2×#13050590C2314yes—
111C2×#13050590C2314yes—
112C2×#13050590C2314yes—
113C2×#13050590C2314yes—
114C2×#13050590C2314yes—
115C2×#13050589C23116yes—
116C2×#13050589C2318yes—
117C2×#13050589C23116yes—
118C2×#13050589C2318yes—
119#41×D83—264no—
120#41×D83—264no—
121C22×Dic166C2318yes—
122C22×Dic166C2312yes—
123C22×Dic166C2311yescharacteristic
124C2×Q8×D83C2318yes—
125C2×Q8×D83C2318yes—
126C22×D332C2318yes—
127C22×D332C2312yes—
128C22×D332C2311yescharacteristic
129C22×C22⋊D83C23116yes—
130C22×C22⋊D83C2314yes—
131C22×C22⋊D83C2318yes—
132C22×C22⋊D83C2312yes—
133C2×D4×D83C23116yes—
134C2×D4×D83C2318yes—
135C2×D4×D83C23116yes—
136C2×D4×D83C2318yes—
137C2×D4×D83C23116yes—
138C23×Dic83C2312yes—
139C22×C4×D83C23116yes—
140C22×C4×D83C2314yes—
141C22×C4×D83C2314yes—
142C22×C4×D83C2312yes—
143#14581792C2314yes—
144#14581791C23116yes—
145#14581790C2318yes—
146#14581790C2314yes—
147#14581790C2314yes—
148#14581789C2314yes—
149#14581788C23116yes—
150#14581788C2318yes—
151#14581788C2314yes—
152#14581788C2314yes—
153#14581781C2318yes—
154#14581781C2314yes—
155#14581781C2314yes—
156#14581780C2318yes—
157#14581779C2318yes—
158#14581779C2314yes—
159#14581779C2314yes—
160#14581778C23132yes—
161#14581777C23132yes—
162#14581776C23116yes—
163#14581774C23132yes—
164#14581772C23116yes—
165#14581770C23132yes—
166#14581769C23132yes—
167#14581767C23116yes—
168#14581767C23116yes—
169#14581766C23116yes—
170#14581765C23132yes—
171#14581765C23132yes—
172#14581764C23116yes—
173#14581764C23132yes—
174#14581764C23116yes—
175#14581764C23116yes—
176#14581764C23116yes—
177#14581763C23116yes—
178#14581762C23116yes—
179#14581762C23132yes—
180#14581760C23132yes—
181#14581757C2318yes—
182#14581757C2318yes—
183C4×D332C23116yes—
184D4×Dic83C23116yes—
185#14581754C2318yes—
186#14581754C2318yes—
187#14581754C23116yes—
188C4×C22⋊D83C23116yes—
189C4×C22⋊D83C23116yes—
190C4×C22⋊D83C23116yes—
191C4×C22⋊D83C23116yes—
192(C22⋊D83)⋊C4C23116yes—
193(C22⋊D83)⋊C4C23132yes—
194(C22⋊D83)⋊C4C23116yes—
195#14581749C2318yes—
196#14581749C2318yes—
197C2×Dic83⋊C4C2318yes—
198C2×Dic83⋊C4C2314yes—
199C4⋊C4×D83C23116yes—
200C2×C22⋊Dic83C2318yes—
201C2×(C2×D83)⋊C4C2318yes—
202C2×(C2×D83)⋊C4C2314yes—
203C22⋊C4×D83C23132yes—
204C2×C4×Dic83C2311yescharacteristic
205C2×C4×Dic83C2314yes—
206C2×C4×Dic83C2311yescharacteristic
207C2×C4×Dic83C2314yes—
208C2×C4×Dic83C2312yes—
209C2×C4×Dic83C2312yes—
210C2×C4×Dic83C2312yes—
211C42×D83C2318yes—
212C42×D83C2314yes—
213C42×D83C2314yes—
214C2×#41×C83—216no—
215C2×#41×C83C2314yes—
216C2×#41×C83C2314yes—
217C2×#41×C83C2314yes—
218C2×#41×C83C2314yes—
219C22×Q8×C83C2312yes—
220C22×D4×C83C2314yes—
221C22×D4×C83C2312yes—
222C23×C4×C83C2314yes—
223C23×C4×C83C2311yescharacteristic
224C4⋊Q8×C83C2314yes—
225#127×C83C2314yes—
226#124×C83C2318yes—
227#123×C83C23116yes—
228C22⋊Q8×C83C23116yes—
229#121×C83C23116yes—
230#121×C83C23116yes—
231#120×C83C23116yes—
232C4×D4×C83C23116yes—
233#117×C83C2314yes—
234#117×C83C2314yes—
235C2×C4⋊C4×C83C2312yes—
236C2×C22⋊C4×C83C2312yes—
237C2×C42×C83C2312yes—
238C23×D83C24116yes—
239C23×D83C2414yes—
240C23×D83C2412yes—
241#13050591—232no—
242#13050591—232no—
243#13050590—216no—
244#13050590—216no—
245#13050590—216no—
246#13050590—216no—
247#13050590—264no—
248#13050590—232no—
249#13050590—264no—
250#13050590—232no—
251#13050590C2×D4132yescomplemented
252#13050590C2×D4132yescomplemented
253#13050589—264no—
254#13050589—264no—
255#13050589—232no—
256#13050589—232no—
257C2×Dic166—28no—
258C2×Dic166—232no—
259C2×Dic166C2×D418yescomplemented
260C2×Dic166C24116yes—
261C2×Dic166C2414yes—
262C2×Dic166C2414yes—
263C2×Dic166C2414yes—
264Q8×D83—232no—
265Q8×D83—232no—
266C2×D332—28no—
267C2×D332—232no—
268C2×D332C2×D418yescomplemented
269C2×D332C24116yes—
270C2×D332C2414yes—
271C2×D332C2414yes—
272C2×D332C24116yes—
273C2×D332C2414yes—
274C2×C22⋊D83—216no—
275C2×C22⋊D83—264no—
276C2×C22⋊D83—416no—
277C2×C22⋊D83C2×D4116yescomplemented
278C2×C22⋊D83C24116yes—
279C2×C22⋊D83C2418yes—
280C2×C22⋊D83C2418yes—
281C2×C22⋊D83C24116yes—
282C2×C22⋊D83C24116yes—
283C2×C22⋊D83C24116yes—
284C2×C22⋊D83C2418yes—
285D4×D83—264no—
286D4×D83—264no—
287D4×D83—232no—
288D4×D83—232no—
289D4×D83—432no—
290C22×Dic83—44no—
291C22×Dic83C2412yes—
292C22×Dic83C2414yes—
293C22×Dic83C24116yes—
294C22×Dic83C2414yes—
295C22×Dic83C2412yes—
296C22×Dic83C2414yes—
297C22×Dic83C2412yes—
298C2×C4×D83—216no—
299C2×C4×D83—264no—
300C2×C4×D83—48no—
301C2×C4×D83C2×D4116yescomplemented
302C2×C4×D83C2418yes—
303C2×C4×D83C24116yes—
304C2×C4×D83C2418yes—
305C2×C4×D83C24116yes—
306C2×C4×D83C2418yes—
307C2×C4×D83C2418yes—
308C2×C4×D83C2414yes—
309C2×C4×D83C2414yes—
310C4⋊Dic83C24116yes—
311Dic83⋊C4C24116yes—
312Dic83⋊C4C24116yes—
313Dic83⋊C4C24116yes—
314C22⋊Dic83C24116yes—
315C22⋊Dic83C24116yes—
316(C2×D83)⋊C4C24116yes—
317(C2×D83)⋊C4C24132yes—
318(C2×D83)⋊C4C24116yes—
319(C2×D83)⋊C4C24116yes—
320C4×Dic83C2418yes—
321C4×Dic83C2411yescharacteristic
322C4×Dic83C2412yes—
323C4×Dic83C2414yes—
324C4×Dic83C2411yescharacteristic
325C4×Dic83C2414yes—
326C4×Dic83C2418yes—
327C4×Dic83C2412yes—
328C4×Dic83C2412yes—
329C24×C83C2414yes—
330C24×C83C2411yescharacteristic
331#41×C83—216no—
332#41×C83—216no—
333#41×C83—216no—
334#41×C83—216no—
335C2×Q8×C83—28no—
336C2×Q8×C83C2414yes—
337C2×Q8×C83C2414yes—
338C2×D4×C83—216no—
339C2×D4×C83—28no—
340C2×D4×C83C2418yes—
341C2×D4×C83C2418yes—
342C2×D4×C83C2414yes—
343C2×D4×C83C2414yes—
344C2×D4×C83C24116yes—
345C22×C4×C83—216no—
346C22×C4×C83C2×D418yescomplemented
347C22×C4×C83C2418yes—
348C22×C4×C83C2418yes—
349C22×C4×C83C2414yes—
350C22×C4×C83C2414yes—
351C22×C4×C83C2411yescharacteristic
352C22×C4×C83C2412yes—
353C22×C4×C83C2411yescharacteristic
354C22×C4×C83C2412yes—
355C4⋊C4×C83C2418yes—
356C4⋊C4×C83C24116yes—
357C22⋊C4×C83C2418yes—
358C22⋊C4×C83C24132yes—
359C42×C83C2414yes—
360C42×C83C2414yes—
361C23×C83—28no—
362C23×C83—42no—
363C23×C83—48no—
364C23×C83C22×D414yes—
365C23×C83C2518yes—
366C23×C83C2512yes—
367C23×C83C2511yescharacteristic
368C22×D83—28no—
369C22×D83—232no—
370C22×D83—44no—
371C22×D83—432no—
372C22×D83—48no—
373C22×D83C22×D418yes—
374C22×D83C2518yes—
375C22×D83C2514yes—
376Q8×C83—28no—
377Q8×C83—28no—
378D4×C83—216no—
379D4×C83—216no—
380D4×C83—28no—
381D4×C83—28no—
382D4×C83—416no—
383C2×C4×C83—28no—
384C2×C4×C83—216no—
385C2×C4×C83—216no—
386C2×C4×C83—44no—
387C2×C4×C83C22×D418yes—
388C2×C4×C83C22×D418yes—
389C2×C4×C83C22×D414yes—
390C2×C4×C83C22×D414yes—
391C2×C4×C83C2518yes—
392C2×C4×C83C2518yes—
393C2×C4×C83C2511yescharacteristic
394C2×C4×C83C2512yes—
395C2×C4×C83C2511yescharacteristic
396C22⋊D83—216no—
397C22⋊D83—216no—
398C22⋊D83—232no—
399C22⋊D83—232no—
400C22⋊D83—232no—
401C22⋊D83—416no—
402C22⋊D83C22×D4132yes—
403C2×Dic83—28no—
404C2×Dic83—232no—
405C2×Dic83—24no—
406C2×Dic83—28no—
407C2×Dic83—44no—
408C2×Dic83—42no—
409C2×Dic83C22×D418yes—
410C2×Dic83C2512yes—
411C2×Dic83C2514yes—
412C2×Dic83C2518yes—
413C2×Dic83C2514yes—
414C2×Dic83C2512yes—
415D332—232no—
416D332—28no—
417D332—28no—
418D332—416no—
419D332C22×D4116yes—
420C4×D83—232no—
421C4×D83—216no—
422C4×D83—216no—
423C4×D83—232no—
424C4×D83—216no—
425C4×D83—48no—
426C4×D83C22×D4116yes—
427C4×D83C22×D4116yes—
428Dic166—28no—
429Dic166—28no—
430Dic166—232no—
431Dic166C22×D4116yes—
432C22×C83—22no—
433C22×C83—24no—
434C22×C83—28no—
435C22×C83—216no—
436C22×C83—44no—
437C22×C83—88no—
438C22×C83C23×D414yes—
439C22×C83C23×D412yes—
440C22×C83C2611yescharacteristic
441C2×D83—28no—
442C2×D83—28no—
443C2×D83—216no—
444C2×D83—48no—
445C2×D83—832no—
446C2×D83—88no—
447C2×D83C23×D418yes—
448C4×C83—28no—
449C4×C83—28no—
450C4×C83C23×D412yes—
451C4×C83C23×D414yes—
452C4×C83C23×D412yes—
453Dic83—28no—
454Dic83—22no—
455Dic83—24no—
456Dic83C23×D418yes—
457Dic83#58514yescomplemented
458#62812—831nomaximal, Sylow
459C2×C83—22no—
460C2×C83—24no—
461C2×C83—48no—
462C2×C83C24×D411yescharacteristic
463C2×C83C2×#58512yes—
464D83—28no—
465D83—48no—
466C2×#585—832no—
467#3500—834no—
468#3500—834no—
469#3499—834no—
470#3498—834no—
471#3497—834no—
472#3496—834no—
473#3496—838no—
474D4×#41—8316no—
475#3449—834no—
476#3449—831no—
477#3449D8311yescharacteristic, complemented
478C2×#532—832no—
479C2×#532—834no—
480C2×C4×#41—831no—
481C83#6281211yescharacteristic, complemented, Sylow
482#585—16632no—
483C2×2−1+4—834no—
484C2×2−1+4—834no—
485C2×2−1+4—834no—
486C2×H(5,𝔽2)—834no—
487C2×H(5,𝔽2)—834no—
488C2×H(5,𝔽2)—838no—
489C2×H(5,𝔽2)—834no—
490C22×#41—838no—
491C22×#41—838no—
492C22×#41—831no—
493C22×#41—832no—
494C22×#41—838no—
495C22×#41C2×D8312yescomplemented
496#550—8316no—
497D4×Q8—8316no—
498#548—8316no—
499#548—8316no—
500#547—8332no—
501#547—8316no—
502#546—8332no—
503#546—8316no—
504#546—8316no—
505#546—8332no—
506D42—8316no—
507D42—8332no—
508#537—8316no—
509#537—834no—
510#537C2×D8314yescomplemented
511#536—838no—
512#536—838no—
513#536—834no—
514#536C2×D8314yescomplemented
515#535—838no—
516#535—838no—
517#535—834no—
518#535C2×D8314yescomplemented
519#534—8316no—
520#534—834no—
521#534C2×D8314yescomplemented
522#532—834no—
523#532—834no—
524#532—838no—
525#532—838no—
526#532—834no—
527#532—834no—
528#532—834no—
529#532—834no—
530#532—838no—
531#532—8316no—
532#532—8316no—
533#532—834no—
534#532C2×D8314yescomplemented
535C2×C4⋊Q8—832no—
536C2×C4⋊Q8—834no—
537C2×#127—832no—
538C2×#127—834no—
539C2×#124—832no—
540C2×#124—832no—
541C2×#124—838no—
542#525—8332no—
543#525—838no—
544#525C2×D8318yescomplemented
545C2×#121—838no—
546C2×#121—8316no—
547C4×#41—838no—
548C4×#41—834no—
549C4×#41—834no—
550C2×C4×Q8—832no—
551C2×C4×D4—838no—
552C2×C4×D4—8316no—
553C2×C4×D4—832no—
554C2×C4×D4—834no—
555C2×#117—832no—
556C2×#117C2×D8311yescharacteristic, complemented
557C22×C42—831no—
558C22×C42—832no—
5592−1+4—16632no—
5602−1+4—16632no—
5612−1+4—16632no—
562H(5,𝔽2)—16664no—
563H(5,𝔽2)—16632no—
564H(5,𝔽2)—16632no—
565H(5,𝔽2)—16632no—
566C2×#41—216no—
567C2×#41—838no—
568C2×#41—838no—
569C2×#41—838no—
570C2×#41—8316no—
571C2×#41—8316no—
572C2×#41—838no—
573C2×#41—8316no—
574C2×#41—834no—
575C2×#41—834no—
576C2×#41—8316no—
577C2×#41—834no—
578C2×#41—834no—
579C2×#41—834no—
580C2×#41—834no—
581C2×#41—838no—
582C2×#41—8316no—
583C2×#41—838no—
584C2×#41—16664no—
585C2×#41—16664no—
586C2×#41—16664no—
587C2×#41—16616no—
588C2×#41C22×D8314yes—
589C2×#41C22×D8314yes—
590C2×#41C22×D8314yes—
591C2×#41C22×D8314yes—
592C22×Q8—838no—
593C22×Q8—838no—
594C22×Q8—831no—
595C22×Q8—832no—
596C22×Q8—838no—
597C22×Q8C22×D8312yes—
598C22×D4—838no—
599C22×D4—8316no—
600C22×D4—832no—
601C22×D4—834no—
602C22×D4—8316no—
603C22×D4—8316no—
604C22×D4—838no—
605C22×D4—8316no—
606C22×D4—838no—
607C22×D4—831no—
608C22×D4—832no—
609C22×D4—838no—
610C22×D4C22×D8314yes—
611C22×D4C22×D8312yes—
612C23×C4—832no—
613C23×C4—834no—
614C23×C4—832no—
615C23×C4—8316no—
616C23×C4—834no—
617C23×C4C22×D8314yes—
618C23×C4C22×D8311yescharacteristic
619C4⋊Q8—834no—
620C4⋊Q8—834no—
621C4⋊Q8—838no—
622C4⋊Q8—8316no—
623C4⋊Q8—834no—
624C4⋊Q8C22×D8314yes—
625#127—834no—
626#127—834no—
627#127—838no—
628#127—8316no—
629#127—834no—
630#127C22×D8314yes—
631#124—834no—
632#124—834no—
633#124—838no—
634#124—834no—
635#124—834no—
636#124—838no—
637#124—8332no—
638#124—838no—
639#124C22×D8318yes—
640#123—8332no—
641#123—8332no—
642#123—8316no—
643#123C22×D83116yes—
644C22⋊Q8—8332no—
645C22⋊Q8—8316no—
646C22⋊Q8—8332no—
647C22⋊Q8C22×D83116yes—
648#121—8316no—
649#121—8316no—
650#121—8316no—
651#121—8316no—
652#121—8316no—
653#121—8332no—
654#121—8316no—
655#121—8316no—
656#121—8316no—
657#121—8332no—
658#121—8332no—
659#121C22×D83116yes—
660#121C22×D83116yes—
661#120—8332no—
662#120—8332no—
663#120—8316no—
664#120C22×D83116yes—
665C4×Q8—838no—
666C4×Q8—838no—
667C4×D4—8316no—
668C4×D4—8316no—
669C4×D4—8316no—
670C4×D4—8316no—
671C4×D4—8316no—
672C4×D4—838no—
673C4×D4—838no—
674C4×D4—8316no—
675C4×D4—8316no—
676C4×D4—8316no—
677C4×D4—8332no—
678C4×D4—8316no—
679C4×D4C22×D83116yes—
680#117—838no—
681#117—838no—
682#117C22×D8314yes—
683#117C22×D8314yes—
684C2×C4⋊C4—834no—
685C2×C4⋊C4—838no—
686C2×C4⋊C4—8316no—
687C2×C4⋊C4C22×D8312yes—
688C2×C22⋊C4—838no—
689C2×C22⋊C4—834no—
690C2×C22⋊C4—838no—
691C2×C22⋊C4—8332no—
692C2×C22⋊C4C22×D8312yes—
693C2×C42—831no—
694C2×C42—834no—
695C2×C42—832no—
696C2×C42—834no—
697C2×C42—832no—
698C2×C42—832no—
699C2×C42—831no—
700C2×C42—838no—
701C2×C42—834no—
702C2×C42—834no—
703C2×C42C22×D8312yes—
704C24—832no—
705C24—8316no—
706C24—834no—
707C24C23×D8314yes—
708C24C23×D8311yescharacteristic
709#41—216no—
710#41—216no—
711#41—216no—
712#41—216no—
713#41—8332no—
714#41—8332no—
715#41—16664no—
716#41—16664no—
717#41—16632no—
718#41—16632no—
719#41—16664no—
720#41—16632no—
721#41—16632no—
722#41—16664no—
723#41—16632no—
724#41—16632no—
725#41—16616no—
726#41—16616no—
727#41—16616no—
728#41—16616no—
729C2×Q8—28no—
730C2×Q8—838no—
731C2×Q8—834no—
732C2×Q8—8316no—
733C2×Q8—834no—
734C2×Q8—834no—
735C2×Q8—16632no—
736C2×Q8—16632no—
737C2×Q8—16632no—
738C2×Q8—1668no—
739C2×Q8C23×D8314yes—
740C2×Q8C23×D8314yes—
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—33232no—
744C2×D4—33216no—
745C2×D4—8316no—
746C2×D4—8316no—
747C2×D4—838no—
748C2×D4—8316no—
749C2×D4—8316no—
750C2×D4—838no—
751C2×D4—838no—
752C2×D4—8316no—
753C2×D4—838no—
754C2×D4—8316no—
755C2×D4—834no—
756C2×D4—8316no—
757C2×D4—834no—
758C2×D4—834no—
759C2×D4—16632no—
760C2×D4—16632no—
761C2×D4—16664no—
762C2×D4—16632no—
763C2×D4—16664no—
764C2×D4—16664no—
765C2×D4—16616no—
766C2×D4—1668no—
767C2×D4C23×D8318yes—
768C2×D4C23×D8318yes—
769C2×D4C23×D8314yes—
770C2×D4C23×D8314yes—
771C2×D4C23×D83116yes—
772C22×C4—216no—
773C22×C4—3328no—
774C22×C4—3324no—
775C22×C4—834no—
776C22×C4—832no—
777C22×C4—838no—
778C22×C4—832no—
779C22×C4—8316no—
780C22×C4—834no—
781C22×C4—834no—
782C22×C4—832no—
783C22×C4—834no—
784C22×C4—834no—
785C22×C4—8316no—
786C22×C4—838no—
787C22×C4—8316no—
788C22×C4—8316no—
789C22×C4—838no—
790C22×C4—838no—
791C22×C4—16664no—
792C22×C4—16616no—
793C22×C4D4×D8318yescomplemented
794C22×C4C23×D8314yes—
795C22×C4C23×D8318yes—
796C22×C4C23×D8318yes—
797C22×C4C23×D8314yes—
798C22×C4C23×D8311yescharacteristic
799C22×C4C23×D8312yes—
800C22×C4C23×D8311yescharacteristic
801C22×C4C23×D8312yes—
802C4⋊C4—8316no—
803C4⋊C4—8316no—
804C4⋊C4—8316no—
805C4⋊C4—8316no—
806C4⋊C4C23×D83116yes—
807C4⋊C4C23×D8318yes—
808C22⋊C4—8316no—
809C22⋊C4—8316no—
810C22⋊C4—8316no—
811C22⋊C4—8316no—
812C22⋊C4—8316no—
813C22⋊C4—8332no—
814C22⋊C4C23×D83132yes—
815C22⋊C4C23×D8318yes—
816C42—831no—
817C42—831no—
818C42—832no—
819C42—838no—
820C42—834no—
821C42—838no—
822C42—834no—
823C42—832no—
824C42—832no—
825C42C23×D8314yes—
826C42C23×D8314yes—
827C23—28no—
828C23—42no—
829C23—48no—
830C23—3324no—
831C23—3328no—
832C23—33232no—
833C23—838no—
834C23—834no—
835C23—838no—
836C23—16632no—
837C23—1668no—
838C23C2×D4×D8314yes—
839C23C24×D8318yes—
840C23C24×D8312yes—
841C23C24×D8311yescharacteristic
842Q8—28no—
843Q8—28no—
844Q8—8316no—
845Q8—16632no—
846Q8—1668no—
847Q8—1668no—
848D4—216no—
849D4—216no—
850D4—28no—
851D4—28no—
852D4—416no—
853D4—33216no—
854D4—33216no—
855D4—8332no—
856D4—8316no—
857D4—16632no—
858D4—16632no—
859D4—16632no—
860D4—16632no—
861D4—16616no—
862D4—16616no—
863D4—1668no—
864D4—1668no—
865C2×C4—28no—
866C2×C4—216no—
867C2×C4—216no—
868C2×C4—44no—
869C2×C4—3328no—
870C2×C4—3324no—
871C2×C4—3322no—
872C2×C4—838no—
873C2×C4—832no—
874C2×C4—834no—
875C2×C4—8316no—
876C2×C4—8316no—
877C2×C4—832no—
878C2×C4—834no—
879C2×C4—838no—
880C2×C4—16616no—
881C2×C4—16632no—
882C2×C4—16632no—
883C2×C4—1664no—
884C2×C4—1668no—
885C2×C4—16632no—
886C2×C4—1668no—
887C2×C4—16616no—
888C2×C4—16616no—
889C2×C4C2×D4×D8318yes—
890C2×C4C2×D4×D8314yes—
891C2×C4C2×D4×D8318yes—
892C2×C4C2×D4×D8314yes—
893C2×C4C24×D8318yes—
894C2×C4C24×D8318yes—
895C2×C4C24×D8311yescharacteristic
896C2×C4C24×D8312yes—
897C2×C4C24×D8311yescharacteristic
898C22—22no—
899C22—24no—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—88no—
904C22—3328no—
905C22—838no—
906C22—6648no—
907C22—66432no—
908C22—1668no—
909C22—16616no—
910C22—1668no—
911C22C22×D4×D8314yes—
912C22C22×D4×D8312yes—
913C22C25×D8311yescharacteristic
914C4—28no—
915C4—28no—
916C4—838no—
917C4—834no—
918C4—1668no—
919C4—1662no—
920C4—1664no—
921C4C22×D4×D8312yes—
922C4C22×D4×D8314yes—
923C4C22×D4×D8312yes—
924C2—24no—
925C2—22no—
926C2—48no—
927C2—3328no—
928C2—1668no—
929C2C23×D4×D8311yescharacteristic
930C2#585×D8312yes—
subgroupG/H
centerC2×C4C24×D83
commutator, socle, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC83×#3449C2
hypercenter#3449D83
hypocenterC83#62812
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#19128537C2semidirect
2. #24921255C2semidirect
3. #24921252C2semidirect
4. #24921245C2semidirect
5. #24921238C2semidirect
6. #24921232C2semidirect
7. #24921226C2semidirect
8. #24921224C2semidirect
9. #24920946C2semidirect
10. #24920796C2semidirect
11. #24920790C2semidirect
12. C2×#19128247C2semidirect
13. #532×D83C2semidirect
14. C2×#19128169C2semidirect
15. C83×#3449C2semidirect
17. C2×#14581840C22semidirect
18. C2×#14581839C22semidirect
19. C2×#14581839C22semidirect
20. C2×#14581838C22semidirect
21. C2×#14581838C22semidirect
22. C2×#14581837C22semidirect
23. C2×#14581837C22semidirect
25. C22×#13050590C22semidirect
26. C22×#13050590C22semidirect
27. C2×#41×D83C22semidirect
28. C2×#41×D83C22semidirect
29. #19128369C22semidirect
30. #19128364C22semidirect
31. #19128361C22semidirect
32. #19128357C22semidirect
33. #19128353C22semidirect
34. #19128349C22semidirect
35. #19128348C22semidirect
36. #19128343C22semidirect
37. #19128342C22semidirect
38. #19128338C22semidirect
39. #19128335C22semidirect
40. #19128333C22semidirect
41. #19128282C22semidirect
42. #19128278C22semidirect
43. #19128277C22semidirect
44. #19128276C22semidirect
45. #19128271C22semidirect
46. #19128270C22semidirect
47. #19128269C22semidirect
48. #19128264C22semidirect
49. #19128263C22semidirect
50. #19128259C22semidirect
51. #19128252C22semidirect
52. #19128251C22semidirect
53. #19128250C22semidirect
54. #19128249C22semidirect
55. #19128248C22semidirect
56. #19128247C22semidirect
57. #19128247C22semidirect
58. #19128247C22semidirect
59. #19128247C22semidirect
60. #19128247C22semidirect
61. #19128247C22semidirect
62. #19128246C22semidirect
63. C2×#14581790C22semidirect
64. C4⋊Q8×D83C22semidirect
65. C2×#14581788C22semidirect
66. #127×D83C22semidirect
67. C2×#14581781C22semidirect
68. C2×#14581779C22semidirect
69. #124×D83C22semidirect
70. #19128213C22semidirect
71. #19128210C22semidirect
72. C2×#14581764C22semidirect
73. #121×D83C22semidirect
74. #19128169C22semidirect
75. #19128169C22semidirect
76. #19128169C22semidirect
77. C2×#14581757C22semidirect
78. C2×#14581754C22semidirect
79. C2×C4×C22⋊D83C22semidirect
80. C2×(C22⋊D83)⋊C4C22semidirect
81. C4×D4×D83C22semidirect
82. C2×#14581749C22semidirect
83. C22×C4×Dic83C22semidirect
84. C2×C42×D83C22semidirect
85. C22×#41×C83C22semidirect
86. #537×C83C22semidirect
87. #536×C83C22semidirect
88. #535×C83C22semidirect
89. #534×C83C22semidirect
90. #532×C83C22semidirect
91. #525×C83C22semidirect
92. C2×#117×C83C22semidirect
104. C2×#13050590D4semidirect
251. #13050590C2×D4semidirect
252. #13050590C2×D4semidirect
259. C2×Dic166C2×D4semidirect
268. C2×D332C2×D4semidirect
277. C2×C22⋊D83C2×D4semidirect
301. C2×C4×D83C2×D4semidirect
346. C22×C4×C83C2×D4semidirect
457. Dic83#585semidirect
477. #3449D83semidirect
481. C83#62812semidirect
495. C22×#41C2×D83semidirect
510. #537C2×D83semidirect
514. #536C2×D83semidirect
518. #535C2×D83semidirect
521. #534C2×D83semidirect
534. #532C2×D83semidirect
544. #525C2×D83semidirect
556. C2×#117C2×D83semidirect
793. C22×C4D4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191285372
#249212552
#249212522
#249212452
#249212382
#249212322
#249212262
#249212242
#249209462
#249207962
#249207902
C2×#191282472
#532×D832
C2×#191281692
C83×#34492
#6281283