Finite Group Databasebeta

← #25976476

Subgroups — #25976476

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
2C2×#14583627C211yesmaximal, characteristic, complemented
3#19147439C214yesmaximal, complemented
4#19147400C212yesmaximal, complemented
5#19147365C214yesmaximal, complemented
6#19147326C212yesmaximal, complemented
7#19147293C212yesmaximal, complemented
8#19147282C212yesmaximal, complemented
9#19144996C212yesmaximal, complemented
10#19144989C211yesmaximal, characteristic, complemented
11#19144418C212yesmaximal, complemented
12#19144411C211yesmaximal, characteristic, complemented
13#19144069C211yesmaximal, characteristic, complemented
14#19144069C212yesmaximal, complemented
15C4×#13063358C211yesmaximal, characteristic, complemented
16C4×#13063358C212yesmaximal, complemented
17Q8×M16×C43C211yesmaximal, characteristic, complemented
18C2×#13063358C2211yescharacteristic
19C2×#13063358C2212yes—
20#14583634C2211yescharacteristic
21#14583634C2212yes—
22#14583628C2211yescharacteristic
23#14583627—21no—
24#14583627—22no—
25#14583627—21no—
26#14583627C2212yes—
27#14583627C2212yes—
28#14583627C2214yes—
29#14583622C2211yescharacteristic
30#14583622C2212yes—
31#14583597—21no—
32#14583597—22no—
33#14583571C2211yescharacteristic
34#14583560—21no—
35#14583449C2211yescharacteristic
36#14583449C2212yes—
37C2×#13063325C2211yescharacteristic
38C2×#13063323—21no—
39#14583436—22no—
40#14583436—21no—
41C2×#13063317C2212yes—
42C2×#13063315—22no—
43C4×#10621902—21no—
44C4×#10621898C2211yescharacteristic
45C4×#10621898C2212yes—
46C2×C4×Dic86C2212yes—
47C2×C4×Dic86C2211yescharacteristic
48C2×#13063290—21no—
49#14583268C2214yes—
50#14583264C2214yes—
51#14583259C2214yes—
52#14583254C2214yes—
53#14583254C2214yes—
54#14583250C2212yes—
55#14583246C2212yes—
56#14583207C2214yes—
57#14583207C2214yes—
58#14583200C2214yes—
59#14583200C2214yes—
60#14583195C2212yes—
61#14583190C2212yes—
62#14583185C2212yes—
63#14583180C2212yes—
64#14583122C2214yes—
65#14583122C2214yes—
66#14583122C2214yes—
67#14583110C2212yes—
68#14583110C2214yes—
69#14583100C2212yes—
70#14583100C2214yes—
71#14583007C2214yes—
72#14583007C2212yes—
73#14583001C2214yes—
74#14583001C2212yes—
75C4×Dic172C2214yes—
76C4×Dic172C2212yes—
77C4×#10621873C2212yes—
78C4×#10621873C2214yes—
79#14582941C2212yes—
80#14582941C2211yescharacteristic
81#14582909C2211yescharacteristic
82#14582901C2212yes—
83#14582901C2212yes—
84#14582901C2211yescharacteristic
85#14582901C2212yes—
86#14582901C2212yes—
87C2×C4×Q8×C43C2211yescharacteristic
88C43×#446C2212yes—
89C43×#446C2214yes—
90C8×Q8×C43C2212yes—
91C43×#423C2211yescharacteristic
92C43×#423C2212yes—
93C4×M16×C43C2211yescharacteristic
94C4×M16×C43C2212yes—
95C2×#10621902—21no—
96C2×#10621898C2311yescharacteristic
97C2×#10621898C2312yes—
98C22×Dic86—21no—
99C22×Dic86C2311yescharacteristic
100#13063358—28no—
101#13063358—24no—
102C2×Dic172C2314yes—
103C2×Dic172C2312yes—
104C2×#10621873C2314yes—
105C2×#10621873C2312yes—
106#13063325—21no—
107#13063325—21no—
108#13063325C2311yescharacteristic
109#13063325C2312yes—
110#13063325C2312yes—
111#13063325C2312yes—
112#13063323—22no—
113#13063323—22no—
114#13063323—24no—
115#13063322C2311yescharacteristic
116#13063322C2312yes—
117#13063320—22no—
118#13063320—22no—
119#13063320—22no—
120#13063317—22no—
121#13063317—22no—
122#13063317C2314yes—
123#13063317C2314yes—
124#13063316—21no—
125#13063316—22no—
126#13063315—24no—
127#13063315—24no—
128#13063315—24no—
129#13063315—24no—
130#13063314—21no—
131#13063314—22no—
132#13063313C2312yes—
133#13063313C2312yes—
134#13063313C2312yes—
135#13063310—22no—
136#13063310—22no—
137#13063310—22no—
138#13063301—21no—
139#13063301—22no—
140#13063300—21no—
141#13063300—22no—
142#13063299—21no—
143#13063299—22no—
144#13063299—22no—
145#13063299—21no—
146Q8×Dic43—21no—
147C4×Dic86—22no—
148C4×Dic86—22no—
149C4×Dic86—21no—
150C4×Dic86—21no—
151C4×Dic86C2312yes—
152C4×Dic86C2314yes—
153C4×Dic86C2314yes—
154C4×Dic86C2312yes—
155C4×Dic86C2311yescharacteristic
156C4×Dic86C2312yes—
157C4×Dic86C2311yescharacteristic
158C4×Dic86C2312yes—
159#13063290—22no—
160#13063290—22no—
161#13063290—24no—
162C4×D172—22no—
163C4×D172—21no—
164C4×D172—22no—
165C4×D172—21no—
166C4×D172C2311yescharacteristic
167C4×D172C2312yes—
168C4×D172C2311yescharacteristic
169C4×D172C2312yes—
170#13063287—21no—
171#13063287—22no—
172C4×C22⋊D43—21no—
173C4×C22⋊D43—22no—
174C4×C22⋊D43—22no—
175C4×C22⋊D43—21no—
176#13063284C2311yescharacteristic
177#13063283—21no—
178#13063283—22no—
179#13063282—22no—
180#13063282—21no—
181C2×C4⋊Dic43—21no—
182C2×C4⋊Dic43C2311yescharacteristic
183C2×C4⋊Dic43C2312yes—
184C2×Dic43⋊C4—22no—
185C2×Dic43⋊C4—21no—
186C2×Dic43⋊C4—22no—
187C2×Dic43⋊C4—22no—
188C2×C4×Dic43—22no—
189C2×C4×Dic43—21no—
190C42×D43—22no—
191C42×D43—21no—
192#13063259C2314yes—
193#13063259C2312yes—
194#13063257C2314yes—
195#13063257C2312yes—
196#13063250C2314yes—
197#13063250C2314yes—
198#13063250C2314yes—
199#13063250C2314yes—
200#13063250C2312yes—
201#13063250C2312yes—
202#13063250C2312yes—
203#13063247C2314yes—
204#13063247C2314yes—
205#13063247C2314yes—
206#13063247C2314yes—
207#13063247C2312yes—
208C22×Q8×C43D411yescharacteristic
209C2×M16×C43C2311yescharacteristic
210C2×M16×C43C2311yescharacteristic
211C2×M16×C43C2312yes—
212C4×Q8×C43D411yescharacteristic
213C4×Q8×C43D412yes—
214C4×Q8×C43D411yescharacteristic
215C4×Q8×C43C2311yescharacteristic
216C4×Q8×C43C2311yescharacteristic
217C4×Q8×C43C2312yes—
218C2×C4⋊C4×C43D411yescharacteristic
219C2×C4⋊C4×C43D412yes—
220C2×C42×C43C2312yes—
221C2×C42×C43C2311yescharacteristic
222C4⋊C8×C43C2312yes—
223C4⋊C8×C43C2314yes—
224C4⋊C8×C43C2312yes—
225C4⋊C8×C43C2314yes—
226#97×C43C2312yes—
227#97×C43C2314yes—
228C4×C8×C43C2312yes—
229C4×C8×C43C2314yes—
230C2×Q8×C43—42no—
231C2×Q8×C43C2×D411yescharacteristic
232C2×Q8×C43C2×D411yescharacteristic
233C2×Q8×C43C2×D412yes—
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2×D412yes—
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2×D412yes—
238C22×C4×C43C2411yescharacteristic
239C2×C22⋊D43—21no—
240C2×C22⋊D43—22no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—22no—
244#10621902—44no—
245#10621898—22no—
246#10621898—24no—
247#10621898—22no—
248#10621898—24no—
249C2×D172—22no—
250C2×D172—21no—
251C2×D172—22no—
252C2×D172—21no—
253C2×D172C2411yescharacteristic
254C2×D172C2412yes—
255C2×C4×D43—22no—
256C2×C4×D43—21no—
257C2×C4×D43—22no—
258C2×C4×D43—21no—
259C2×C4×D43—22no—
260C2×C4×D43—21no—
261C2×Dic86—21no—
262C2×Dic86—22no—
263C2×Dic86—22no—
264C2×Dic86—22no—
265C2×Dic86—44no—
266C2×Dic86#4114yescomplemented
267C2×Dic86C2411yescharacteristic
268C2×Dic86C2412yes—
269C2×Dic86C2412yes—
270M16×C43—22no—
271M16×C43—24no—
272M16×C43—22no—
273C2×C8×C43C2412yes—
274C2×C8×C43C2412yes—
275C2×C8×C43C2414yes—
276C4⋊C4×C43C2×D411yescharacteristic
277C4⋊C4×C43C2×D412yes—
278C4⋊C4×C43C2×D411yescharacteristic
279C4⋊C4×C43C2×D412yes—
280C4⋊C4×C43C2×D412yes—
281C4⋊C4×C43C2×D412yes—
282C4⋊C4×C43C2×D412yes—
283C42×C43C2×D412yes—
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D412yes—
286C42×C43C2×D411yescharacteristic
287C42×C43C2412yes—
288C42×C43C2411yescharacteristic
289C42×C43C2411yescharacteristic
290C42×C43C2412yes—
291C22⋊Dic43—21no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—22no—
296(C2×D43)⋊C4—22no—
297(C2×D43)⋊C4—22no—
298(C2×D43)⋊C4—22no—
299(C2×D43)⋊C4—22no—
300(C2×D43)⋊C4—22no—
301(C2×D43)⋊C4—22no—
302C4⋊Dic43—22no—
303C4⋊Dic43—22no—
304C4⋊Dic43—21no—
305C4⋊Dic43—22no—
306C4⋊Dic43—22no—
307C4⋊Dic43—21no—
308C4⋊Dic43—22no—
309C4⋊Dic43—21no—
310C4⋊Dic43C2412yes—
311C4⋊Dic43C2414yes—
312C4⋊Dic43C2411yescharacteristic
313C4⋊Dic43C2411yescharacteristic
314Dic43⋊C4—24no—
315Dic43⋊C4—24no—
316Dic43⋊C4—22no—
317Dic43⋊C4—22no—
318Dic43⋊C4—24no—
319Dic43⋊C4—24no—
320Dic43⋊C4—24no—
321Dic43⋊C4—24no—
322Dic43⋊C4—21no—
323Dic43⋊C4—22no—
324Dic43⋊C4—22no—
325Dic43⋊C4—21no—
326C4×Dic43—21no—
327C4×Dic43—22no—
328C4×Dic43—21no—
329C4×Dic43—22no—
330C4×Dic43—21no—
331C4×Dic43—24no—
332C4×Dic43—24no—
333C4×Dic43—22no—
334C4×Dic43—22no—
335Dic172—28no—
336Dic172—24no—
337#10621873—28no—
338#10621873—24no—
339C23×C43C22×D411yescharacteristic
340C22×D43—22no—
341C22×D43—21no—
342Q8×C43—22no—
343Q8×C43—22no—
344Q8×C43—42no—
345C2×C4×C43—22no—
346C2×C4×C43—42no—
347C2×C4×C43—41no—
348C2×C4×C43—42no—
349C2×C4×C43C22×D412yes—
350C2×C4×C43C22×D412yes—
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D412yes—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C2×#4112yes—
359C2×C4×C432−1+412yes—
360C2×C4×C43C2511yescharacteristic
361C22⋊D43—42no—
362C22⋊D43—44no—
363C2×Dic43—24no—
364C2×Dic43—22no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367C2×Dic43—22no—
368C2×Dic43—24no—
369C2×Dic43—22no—
370C2×Dic43—21no—
371C2×Dic43—44no—
372C2×Dic43—42no—
373D172—21no—
374D172—22no—
375D172—21no—
376D172—22no—
377D172—44no—
378D172—42no—
379D172—82no—
380D172—81no—
381C4×D43—44no—
382C4×D43—44no—
383C4×D43—42no—
384C4×D43—42no—
385C4×D43—82no—
386C4×D43—81no—
387Dic86—24no—
388Dic86—22no—
389Dic86—21no—
390Dic86—22no—
391Dic86—21no—
392Dic86—22no—
393Dic86—44no—
394Dic86—44no—
395Dic86C2×#4114yes—
396C8×C43—22no—
397C8×C43—24no—
398C8×C43—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—21no—
415C4×C43—22no—
416C4×C43—22no—
417C4×C43#54812yes—
418C4×C43#57512yes—
419C4×C43C22×#4111yescharacteristic
420C4×C43C2×2−1+411yescharacteristic
421Dic43—24no—
422Dic43—41no—
423Dic43—42no—
424Dic43—41no—
425Dic43—42no—
426Dic43—44no—
427Dic43—41no—
428#3480—431no—
429C2×#557—431no—
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×M16D4311yescharacteristic, complemented
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—432no—
456#557—432no—
457#557—434no—
458#557—431no—
459#557—861no—
460#557—861no—
461#557—862no—
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—431no—
471C2×C4⋊Q8—861no—
472#529—862no—
473#529—861no—
474C2×#125—432no—
475C2×#125—862no—
476C4×#41—431no—
477C4×#41—432no—
478C4×#41—861no—
479C2×C4×Q8—432no—
480C2×C4×Q8—431no—
481C2×C4×Q8—861no—
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#446C2×D4312yes—
506#446C2×D4314yes—
507C8×Q8C2×D4312yes—
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#423C2×D4311yescharacteristic
519#423C2×D4312yes—
520#419—431no—
521#417—432no—
522#417—432no—
523#417—432no—
524#417—432no—
525#417—431no—
526C4×M16C2×D4311yescharacteristic
527C4×M16C2×D4312yes—
528C43#6132011yescharacteristic, complemented, Sylow
529C2×#41—431no—
530C2×#41—432no—
531C2×#41—861no—
532C22×Q8—431no—
533C22×Q8—861no—
534C22×Q8D17211yescharacteristic
535#137—864no—
536#137—868no—
537C2×Q16—434no—
538C2×Q16—432no—
539C2×SD16—432no—
540C2×SD16—434no—
541C2×M16C22×D4311yescharacteristic
542C2×M16C22×D4312yes—
543C2×M16C22×D4311yescharacteristic
544C4⋊Q8—432no—
545C4⋊Q8—432no—
546C4⋊Q8—431no—
547C4⋊Q8—432no—
548C4⋊Q8—862no—
549C4⋊Q8—862no—
550C4⋊Q8—864no—
551C4⋊Q8—861no—
552C4⋊Q8—861no—
553#127—431no—
554#127—432no—
555#126—862no—
556#126—862no—
557#126—862no—
558#125—434no—
559#125—434no—
560#125—864no—
561#125—864no—
562#125—864no—
563#125—864no—
564#125—861no—
565#125—862no—
566#125—862no—
567#125—862no—
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—432no—
585C4×Q8—434no—
586C4×Q8—434no—
587C4×Q8—432no—
588C4×Q8—432no—
589C4×Q8—431no—
590C4×Q8—431no—
591C4×Q8—432no—
592C4×Q8—861no—
593C4×Q8—862no—
594C4×Q8—862no—
595C4×Q8—864no—
596C4×Q8—862no—
597C4×Q8—862no—
598C4×Q8—861no—
599C4×Q8—861no—
600C4×Q8D17211yescharacteristic
601C4×Q8D17212yes—
602C4×Q8D17211yescharacteristic
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—431no—
626C2×C4⋊C4—432no—
627C2×C4⋊C4—861no—
628C2×C4⋊C4—862no—
629C2×C4⋊C4—862no—
630C2×C4⋊C4—862no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4D17211yescharacteristic
633C2×C4⋊C4D17212yes—
634C2×C42—862no—
635C2×C42—861no—
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⋊C8C22×D4312yes—
645C4⋊C8C22×D4314yes—
646C4⋊C8C22×D4314yes—
647C4⋊C8C22×D4312yes—
648#103—434no—
649#103—432no—
650#103—434no—
651#103—434no—
652#103—434no—
653#103—432no—
654#103—432no—
655#102—434no—
656#102—432no—
657#102—434no—
658#102—434no—
659#102—434no—
660#97C22×D4312yes—
661#97C22×D4314yes—
662C4×C8C22×D4312yes—
663C4×C8C22×D4314yes—
664#41—862no—
665#41—864no—
666#41—862no—
667#41—864no—
668#41—1724no—
669C2×Q8—42no—
670C2×Q8—434no—
671C2×Q8—432no—
672C2×Q8—432no—
673C2×Q8—431no—
674C2×Q8—861no—
675C2×Q8—862no—
676C2×Q8—862no—
677C2×Q8—862no—
678C2×Q8—1724no—
679C2×Q8C2×D17211yescharacteristic
680C2×Q8C2×D17211yescharacteristic
681C2×Q8C2×D17212yes—
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—861no—
691C22×C4—861no—
692C22×C4—862no—
693C22×C4—862no—
694C22×C4—861no—
695C22×C4—862no—
696C22×C4—861no—
697C22×C4—862no—
698C22×C4—861no—
699C22×C4C2×D17211yescharacteristic
700C22×C4C2×D17212yes—
701C22×C4C2×D17211yescharacteristic
702C22×C4C2×D17212yes—
703C22×C4C23×D4311yescharacteristic
704Q16—868no—
705Q16—864no—
706SD16—864no—
707SD16—868no—
708M16—22no—
709M16—24no—
710M16—22no—
711C2×C8C23×D4312yes—
712C2×C8C23×D4312yes—
713C2×C8C23×D4314yes—
714C4⋊C4—432no—
715C4⋊C4—434no—
716C4⋊C4—431no—
717C4⋊C4—431no—
718C4⋊C4—861no—
719C4⋊C4—862no—
720C4⋊C4—862no—
721C4⋊C4—862no—
722C4⋊C4—864no—
723C4⋊C4—864no—
724C4⋊C4—864no—
725C4⋊C4—864no—
726C4⋊C4—864no—
727C4⋊C4—864no—
728C4⋊C4—862no—
729C4⋊C4—862no—
730C4⋊C4—861no—
731C4⋊C4—862no—
732C4⋊C4—862no—
733C4⋊C4—861no—
734C4⋊C4—862no—
735C4⋊C4—861no—
736C4⋊C4—862no—
737C4⋊C4—861no—
738C4⋊C4C2×D17211yescharacteristic
739C4⋊C4C2×D17212yes—
740C4⋊C4C2×D17211yescharacteristic
741C4⋊C4C2×D17212yes—
742C4⋊C4C2×D17212yes—
743C4⋊C4C2×D17212yes—
744C4⋊C4C2×D17212yes—
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—861no—
757C42—862no—
758C42—861no—
759C42—862no—
760C42—861no—
761C42—864no—
762C42—864no—
763C42—862no—
764C42—862no—
765C42C2×D17212yes—
766C42C2×D17211yescharacteristic
767C42C2×D17212yes—
768C42C2×D17211yescharacteristic
769C42C23×D4312yes—
770C42C23×D4311yescharacteristic
771C42C23×D4311yescharacteristic
772C42C23×D4312yes—
773C23—862no—
774C23—861no—
775C23C22×D17211yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—42no—
779Q8—434no—
780Q8—864no—
781Q8—862no—
782Q8—862no—
783Q8—861no—
784Q8—862no—
785Q8—861no—
786Q8—1724no—
787Q8—1724no—
788D4—862no—
789D4—861no—
790D4—862no—
791D4—861no—
792D4—3442no—
793D4—3441no—
794D4—1724no—
795D4—1722no—
796D4—1724no—
797D4—1722no—
798C2×C4—22no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—864no—
803C2×C4—862no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—862no—
807C2×C4—861no—
808C2×C4—862no—
809C2×C4—864no—
810C2×C4—3442no—
811C2×C4—3441no—
812C2×C4—1724no—
813C2×C4—1724no—
814C2×C4—1722no—
815C2×C4—1724no—
816C2×C4—1722no—
817C2×C4—1722no—
818C2×C4C22×D17212yes—
819C2×C4C22×D17211yescharacteristic
820C2×C4C22×D17212yes—
821C2×C4C22×D17211yescharacteristic
822C2×C4C22×D17212yes—
823C2×C4C22×D17212yes—
824C2×C4C22×D17211yescharacteristic
825C2×C4C22×D17211yescharacteristic
826C2×C4C22×D17211yescharacteristic
827C2×C4#41×D4312yes—
828C2×C4#1306337312yes—
829C2×C4C24×D4311yescharacteristic
830C8—22no—
831C8—24no—
832C8—22no—
833C22—21no—
834C22—21no—
835C22—1722no—
836C22—1721no—
837C22—1722no—
838C22—1721no—
839C22—1722no—
840C22—1721no—
841C22#1458356112yes—
842C22C23×D17211yescharacteristic
843C4—21no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—21no—
848C4—22no—
849C4—21no—
850C4—864no—
851C4—1721no—
852C4—1724no—
853C4—1722no—
854C4—1721no—
855C4—1721no—
856C4—1722no—
857C4#1458356112yes—
858C4#1458369912yes—
859C4C2×#41×D4311yescharacteristic
860C4C2×#1306337311yescharacteristic
861C2—22no—
862C2—3442no—
863C2—3441no—
864C2C2×#1458356111yescharacteristic
865C2C2×#1458369911yescharacteristic
866C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingQ8×M16×C43C2
socleC22×C43C23×D4
prime radical#19148190C2
hypercenterQ8×M16D43
hypocenterC43#61320
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
2. C2×#14583627C2semidirect
3. #19147439C2semidirect
4. #19147400C2semidirect
5. #19147365C2semidirect
6. #19147326C2semidirect
7. #19147293C2semidirect
8. #19147282C2semidirect
9. #19144996C2semidirect
10. #19144989C2semidirect
11. #19144418C2semidirect
12. #19144411C2semidirect
13. #19144069C2semidirect
14. #19144069C2semidirect
15. C4×#13063358C2semidirect
16. C4×#13063358C2semidirect
17. Q8×M16×C43C2semidirect
266. C2×Dic86#41semidirect
442. Q8×M16D43semidirect
528. C43#61320semidirect

Maximal subgroups

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

subgroupindex
#191481902
C2×#145836272
#191474392
#191474002
#191473652
#191473262
#191472932
#191472822
#191449962
#191449892
#191444182
#191444112
#191440692
C4×#130633582
Q8×M16×C432
#6132043