Finite Group Databasebeta

← #25976448

Subgroups — #25976448

Order 11008.

1880 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148190C211yesmaximal, characteristic, complemented
2C2×#14583609C211yesmaximal, characteristic, complemented
3#19147424C214yesmaximal, complemented
4#19147378C212yesmaximal, complemented
5#19147350C214yesmaximal, complemented
6#19147304C212yesmaximal, complemented
7#19147257C212yesmaximal, complemented
8#19147246C212yesmaximal, complemented
9#19144996C212yesmaximal, complemented
10#19144989C211yesmaximal, characteristic, complemented
11#19144418C212yesmaximal, complemented
12#19144411C211yesmaximal, characteristic, complemented
13#19144061C212yesmaximal, complemented
14#19144061C211yesmaximal, characteristic, complemented
15C4×#13063353C211yesmaximal, characteristic, complemented
16C4×#13063353C212yesmaximal, complemented
17Q8×M16×C43C211yesmaximal, characteristic, complemented
18C2×#13063353C2211yescharacteristic
19C2×#13063353C2212yes—
20#14583634C2212yescomplemented
21#14583634C2211yescharacteristic, complemented
22#14583628C2211yescharacteristic, complemented
23#14583622C2212yescomplemented
24#14583622C2211yescharacteristic, complemented
25#14583609—21no—
26#14583609—22no—
27#14583609—21no—
28#14583609C2212yes—
29#14583609C2214yes—
30#14583609C2212yes—
31#14583597—21no—
32#14583597—22no—
33#14583571C2211yescharacteristic, complemented
34#14583560—21no—
35#14583449C2211yescharacteristic
36#14583449C2212yes—
37C2×#13063325C2211yescharacteristic
38#14583436—22no—
39#14583436—21no—
40C2×#13063317C2212yes—
41C2×#13063303—22no—
42C2×#13063301—21no—
43C4×#10621902—21no—
44C4×#10621898C2211yescharacteristic
45C4×#10621898C2212yes—
46C2×C4×D172C2212yes—
47C2×C4×D172C2211yescharacteristic
48C2×C4⋊C4×D43—21no—
49#14583268C2214yescomplemented
50#14583264C2214yescomplemented
51#14583259C2214yescomplemented
52#14583254C2214yescomplemented
53#14583254C2214yescomplemented
54#14583250C2212yescomplemented
55#14583246C2212yescomplemented
56#14583207C2214yescomplemented
57#14583207C2214yescomplemented
58#14583200C2214yescomplemented
59#14583200C2214yescomplemented
60#14583195C2212yescomplemented
61#14583190C2212yescomplemented
62#14583185C2212yescomplemented
63#14583180C2212yescomplemented
64#14583115C2214yes—
65#14583115C2214yes—
66#14583115C2214yes—
67#14583105C2214yes—
68#14583105C2212yes—
69#14583095C2214yes—
70#14583095C2212yes—
71#14583012C2214yes—
72#14583012C2212yes—
73#14583001C2214yes—
74#14583001C2212yes—
75C4×#10621873C2212yes—
76C4×#10621873C2214yes—
77C4×D344C2212yes—
78C4×D344C2214yes—
79#14582941C2212yes—
80#14582941C2211yescharacteristic
81#14582905C2211yescharacteristic
82#14582901C2212yes—
83#14582901C2212yes—
84#14582901C2211yescharacteristic
85#14582901C2212yes—
86#14582901C2212yes—
87C2×C4×Q8×C43C2211yescharacteristic
88C43×#446C2212yescomplemented
89C43×#446C2214yescomplemented
90C8×Q8×C43C2212yescomplemented
91C43×#423C2211yescharacteristic
92C43×#423C2212yes—
93C4×M16×C43C2211yescharacteristic
94C4×M16×C43C2212yes—
95C2×#10621902—21no—
96C2×#10621898C2311yescharacteristic
97C2×#10621898C2312yes—
98C22×Dic86—21no—
99C22×D172C2311yescharacteristic
100C22×C4×D43—21no—
101C22×C4×D43—22no—
102#13063353—24no—
103#13063353—28no—
104C2×#10621873C2312yes—
105C2×#10621873C2314yes—
106C2×D344C2312yes—
107C2×D344C2314yes—
108#13063325—21no—
109#13063325—21no—
110#13063325C2311yescharacteristic
111#13063325C2312yes—
112#13063325C2312yes—
113#13063325C2312yes—
114#13063322C2311yescharacteristic
115#13063322C2312yes—
116#13063320—22no—
117#13063320—22no—
118#13063320—22no—
119#13063317—22no—
120#13063317—22no—
121#13063317C2314yes—
122#13063317C2314yes—
123#13063316—21no—
124#13063316—22no—
125#13063314—21no—
126#13063314—22no—
127#13063313C2312yes—
128#13063313C2312yes—
129#13063313C2312yes—
130#13063310—22no—
131#13063310—22no—
132#13063310—22no—
133#13063303—24no—
134#13063303—24no—
135#13063303—24no—
136#13063303—24no—
137#13063301—21no—
138#13063301—22no—
139#13063301—22no—
140#13063301—22no—
141#13063301—24no—
142#13063300—21no—
143#13063300—22no—
144#13063299—21no—
145#13063299—22no—
146#13063299—21no—
147#13063299—22no—
148Q8×Dic43—21no—
149C4×Dic86C2311yescharacteristic
150C4×Dic86C2312yes—
151C4×Dic86C2311yescharacteristic
152C4×Dic86C2312yes—
153C4×D172—21no—
154C4×D172—21no—
155C4×D172—22no—
156C4×D172—22no—
157C4×D172—22no—
158C4×D172—21no—
159C4×D172—22no—
160C4×D172—21no—
161C4×D172C2311yescharacteristic
162C4×D172C2312yes—
163C4×D172C2312yes—
164C4×D172C2314yes—
165C4×D172C2314yes—
166C4×D172C2312yes—
167C4×D172C2311yescharacteristic
168C4×D172C2312yes—
169#13063287—21no—
170#13063287—22no—
171C4×C22⋊D43—21no—
172C4×C22⋊D43—22no—
173C4×C22⋊D43—21no—
174C4×C22⋊D43—22no—
175#13063284C2311yescharacteristic
176#13063283—21no—
177#13063283—22no—
178#13063282—22no—
179#13063282—21no—
180C2×C4⋊Dic43—21no—
181C2×C4⋊Dic43C2311yescharacteristic
182C2×C4⋊Dic43C2312yes—
183C2×Dic43⋊C4—22no—
184C2×Dic43⋊C4—22no—
185C4⋊C4×D43—22no—
186C4⋊C4×D43—22no—
187C4⋊C4×D43—24no—
188C2×(C2×D43)⋊C4—22no—
189C2×(C2×D43)⋊C4—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#13063247C2314yes—
202#13063247C2314yes—
203#13063247C2314yes—
204#13063247C2314yes—
205#13063247C2312yes—
206#13063247C2312yes—
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—
230C23×D43—21no—
231C2×Q8×C43—42no—
232C2×Q8×C43C2×D411yescharacteristic
233C2×Q8×C43C2×D411yescharacteristic
234C2×Q8×C43C2×D412yes—
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2×D412yes—
238C22×C4×C43C2×D412yes—
239C22×C4×C43C2411yescharacteristic
240C2×C22⋊D43—21no—
241C2×C22⋊D43—22no—
242C22×Dic43—21no—
243C22×Dic43—22no—
244#10621902—44no—
245#10621898—22no—
246#10621898—24no—
247#10621898—22no—
248#10621898—24no—
249C2×D172—21no—
250C2×D172—22no—
251C2×D172—22no—
252C2×D172—21no—
253C2×D172—22no—
254C2×D172—21no—
255C2×D172#4114yescomplemented
256C2×D172C2411yescharacteristic
257C2×D172C2412yes—
258C2×D172C2412yes—
259C2×C4×D43—22no—
260C2×C4×D43—21no—
261C2×C4×D43—22no—
262C2×C4×D43—21no—
263C2×C4×D43—22no—
264C2×C4×D43—22no—
265C2×C4×D43—22no—
266C2×C4×D43—21no—
267C2×C4×D43—24no—
268C2×C4×D43—24no—
269C2×C4×D43—44no—
270C2×C4×D43—84no—
271C2×Dic86—22no—
272C2×Dic86—22no—
273C2×Dic86—82no—
274C2×Dic86C2411yescharacteristic
275C2×Dic86C2412yes—
276M16×C43—22no—
277M16×C43—24no—
278M16×C43—22no—
279C2×C8×C43C2412yes—
280C2×C8×C43C2412yes—
281C2×C8×C43C2414yes—
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—
289C42×C43C2×D412yes—
290C42×C43C2×D411yescharacteristic
291C42×C43C2×D412yes—
292C42×C43C2×D411yescharacteristic
293C42×C43C2412yes—
294C42×C43C2411yescharacteristic
295C42×C43C2411yescharacteristic
296C42×C43C2412yes—
297C22⋊Dic43—21no—
298(C2×D43)⋊C4—24no—
299(C2×D43)⋊C4—24no—
300(C2×D43)⋊C4—22no—
301(C2×D43)⋊C4—22no—
302(C2×D43)⋊C4—22no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—22no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—22no—
307(C2×D43)⋊C4—22no—
308(C2×D43)⋊C4—22no—
309(C2×D43)⋊C4—22no—
310(C2×D43)⋊C4—22no—
311(C2×D43)⋊C4—22no—
312C4⋊Dic43—22no—
313C4⋊Dic43—22no—
314C4⋊Dic43—21no—
315C4⋊Dic43—22no—
316C4⋊Dic43—22no—
317C4⋊Dic43—21no—
318C4⋊Dic43—22no—
319C4⋊Dic43—21no—
320C4⋊Dic43C2412yes—
321C4⋊Dic43C2414yes—
322C4⋊Dic43C2411yescharacteristic
323C4⋊Dic43C2411yescharacteristic
324Dic43⋊C4—24no—
325Dic43⋊C4—24no—
326Dic43⋊C4—24no—
327Dic43⋊C4—24no—
328Dic43⋊C4—22no—
329Dic43⋊C4—21no—
330Dic43⋊C4—22no—
331Dic43⋊C4—21no—
332C4×Dic43—21no—
333C4×Dic43—22no—
334C4×Dic43—21no—
335C4×Dic43—22no—
336C4×Dic43—21no—
337D344—24no—
338D344—28no—
339#10621873—24no—
340#10621873—28no—
341C23×C43C22×D411yescharacteristic
342C22×D43—24no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—21no—
346C22×D43—42no—
347C22×D43—42no—
348Q8×C43—22no—
349Q8×C43—22no—
350Q8×C43—42no—
351C2×C4×C43—22no—
352C2×C4×C43—41no—
353C2×C4×C43—42no—
354C2×C4×C43—42no—
355C2×C4×C43C22×D412yes—
356C2×C4×C43C22×D412yes—
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D412yes—
359C2×C4×C43C22×D412yes—
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C2×#4112yes—
365C2×C4×C432−1+412yes—
366C2×C4×C43C2511yescharacteristic
367C22⋊D43—42no—
368C22⋊D43—44no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—22no—
372C2×Dic43—21no—
373C2×Dic43—22no—
374C2×Dic43—24no—
375C2×Dic43—44no—
376C2×Dic43—42no—
377D172—24no—
378D172—21no—
379D172—22no—
380D172—22no—
381D172—21no—
382D172—22no—
383D172—44no—
384D172—42no—
385D172—81no—
386D172—82no—
387D172C2×#4114yes—
388C4×D43—44no—
389C4×D43—44no—
390C4×D43—44no—
391C4×D43—42no—
392C4×D43—44no—
393C4×D43—42no—
394C4×D43—81no—
395C4×D43—82no—
396C4×D43—84no—
397C4×D43—84no—
398Dic86—21no—
399Dic86—22no—
400Dic86—21no—
401Dic86—22no—
402Dic86—82no—
403Dic86—82no—
404C8×C43—22no—
405C8×C43—24no—
406C8×C43—22no—
407#61318—431nomaximal, Sylow
408C22×C43—21no—
409C22×C43—21no—
410C22×C43#54812yes—
411C22×C43C23×D411yescharacteristic
412C2×D43—24no—
413C2×D43—48no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—41no—
417C2×D43—42no—
418C2×D43—42no—
419C2×D43—41no—
420C2×D43—42no—
421C2×D43—41no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—22no—
425C4×C43—22no—
426C4×C43—21no—
427C4×C43—22no—
428C4×C43—22no—
429C4×C43#54812yes—
430C4×C43#57512yes—
431C4×C43C22×#4111yescharacteristic
432C4×C43C2×2−1+411yescharacteristic
433Dic43—44no—
434Dic43—41no—
435Dic43—41no—
436Dic43—42no—
437Dic43—41no—
438Dic43—42no—
439#3480—431no—
440C2×#554—431no—
441#3376—434no—
442#3372—432no—
443#3370—434no—
444#3366—432no—
445#3361—432no—
446#3360—432no—
447#3142—432no—
448#3141—431no—
449#3080—432no—
450#3079—431no—
451#3036—431no—
452#3036—432no—
453Q8×M16D4311yescharacteristic, complemented
454C4×AGL(1,ℤ/8)—431no—
455C4×AGL(1,ℤ/8)—432no—
456C2×C43—22no—
457C2×C43C2×#54811yescharacteristic
458C2×C43C2×#57511yescharacteristic
459C2×C43#358511yescharacteristic
460D43—44no—
461D43—82no—
462D43—81no—
463C2×AGL(1,ℤ/8)—431no—
464C2×AGL(1,ℤ/8)—432no—
465#559—431no—
466#559—432no—
467#557—431no—
468#556—431no—
469#556—432no—
470#554—432no—
471#554—432no—
472#554—434no—
473#554—861no—
474#554—861no—
475#554—862no—
476#553—861no—
477#553—862no—
478#550—431no—
479#548—861no—
480#532—431no—
481#532—432no—
482C2×C4⋊Q8—431no—
483#529—862no—
484#529—861no—
485C2×#125—432no—
486C2×C22⋊Q8—861no—
487C2×C22⋊Q8—862no—
488C4×#41—431no—
489C4×#41—432no—
490C4×#41—861no—
491C2×C4×Q8C2×D4311yescharacteristic
492C2×C4×D4—432no—
493C2×C4×D4—431no—
494C22×C4⋊C4—861no—
495#491—434no—
496#490—434no—
497#489—434no—
498#488—434no—
499#488—434no—
500#487—432no—
501#486—432no—
502#479—434no—
503#479—434no—
504#478—434no—
505#478—434no—
506#477—432no—
507#476—432no—
508#475—432no—
509#474—432no—
510#463—434no—
511#463—434no—
512#463—434no—
513#461—432no—
514#461—434no—
515#459—432no—
516#459—434no—
517#446C2×D4312yescomplemented
518#446C2×D4314yescomplemented
519C8×Q8C2×D4312yescomplemented
520#442—434no—
521#442—432no—
522#440—434no—
523#440—432no—
524C4×SD16—434no—
525C4×SD16—432no—
526C4×D8—432no—
527C4×D8—434no—
528#428—432no—
529#428—431no—
530#423C2×D4311yescharacteristic
531#423C2×D4312yes—
532#418—431no—
533#417—432no—
534#417—432no—
535#417—432no—
536#417—432no—
537#417—431no—
538C4×M16C2×D4311yescharacteristic
539C4×M16C2×D4312yes—
540C43#6131811yescharacteristic, complemented, Sylow
541C2×#41—431no—
542C2×#41—432no—
543C2×#41—861no—
544C22×Q8—861no—
545C22×Q8D17211yescharacteristic
546C22×D4—431no—
547C23×C4—862no—
548C23×C4—861no—
549AGL(1,ℤ/8)—864no—
550AGL(1,ℤ/8)—868no—
551C2×SD16—434no—
552C2×SD16—432no—
553C2×D8—432no—
554C2×D8—434no—
555C2×M16C22×D4311yescharacteristic
556C2×M16C22×D4312yes—
557C2×M16C22×D4311yescharacteristic
558C4⋊Q8—432no—
559C4⋊Q8—432no—
560C4⋊Q8—431no—
561C4⋊Q8—432no—
562C4⋊Q8—861no—
563C4⋊Q8—861no—
564#127—431no—
565#127—432no—
566#126—862no—
567#126—862no—
568#126—862no—
569#125—434no—
570#125—434no—
571#125—861no—
572#125—862no—
573#125—862no—
574#125—862no—
575#124—432no—
576#124—432no—
577#124—432no—
578#124—861no—
579#124—862no—
580#123—862no—
581#123—862no—
582#123—862no—
583C22⋊Q8—862no—
584C22⋊Q8—862no—
585C22⋊Q8—864no—
586C22⋊Q8—861no—
587C22⋊Q8—862no—
588C22⋊Q8—864no—
589C22⋊Q8—864no—
590C22⋊Q8—864no—
591C22⋊Q8—864no—
592#121—861no—
593#121—862no—
594#121—861no—
595#121—862no—
596#121—861no—
597#121—862no—
598C4×Q8—432no—
599C4×Q8—431no—
600C4×Q8—431no—
601C4×Q8—432no—
602C4×Q8—861no—
603C4×Q8D17211yescharacteristic
604C4×Q8D17212yes—
605C4×Q8D17211yescharacteristic
606C4×Q8C22×D4311yescharacteristic
607C4×Q8C22×D4311yescharacteristic
608C4×Q8C22×D4312yes—
609C4×D4—432no—
610C4×D4—434no—
611C4×D4—434no—
612C4×D4—432no—
613C4×D4—431no—
614C4×D4—432no—
615C4×D4—432no—
616C4×D4—431no—
617C4×D4—861no—
618C4×D4—862no—
619C4×D4—861no—
620C4×D4—862no—
621C4×D4—861no—
622C4×D4—862no—
623C4×D4—862no—
624C4×D4—861no—
625C4×D4—862no—
626C4×D4—861no—
627C4×D4—862no—
628C4×D4—861no—
629C4×D4—862no—
630C4×D4—861no—
631#117—431no—
632#117—861no—
633#117—862no—
634#117—862no—
635#117—861no—
636C2×C4⋊C4—431no—
637C2×C4⋊C4—432no—
638C2×C4⋊C4—862no—
639C2×C4⋊C4—861no—
640C2×C4⋊C4—862no—
641C2×C4⋊C4—862no—
642C2×C4⋊C4—862no—
643C2×C4⋊C4—864no—
644C2×C4⋊C4D17211yescharacteristic
645C2×C4⋊C4D17212yes—
646C2×C22⋊C4—861no—
647C2×C22⋊C4—862no—
648C2×C42—862no—
649C2×C42—861no—
650C2×C42C22×D4312yes—
651C2×C42C22×D4311yescharacteristic
652#107—434no—
653#107—432no—
654#106—434no—
655#106—432no—
656C4⋊C8C22×D4312yes—
657C4⋊C8C22×D4314yes—
658C4⋊C8C22×D4314yes—
659C4⋊C8C22×D4312yes—
660#103—434no—
661#103—432no—
662#103—434no—
663#103—434no—
664#103—434no—
665#102—434no—
666#102—432no—
667#102—434no—
668#102—434no—
669#102—434no—
670#102—432no—
671#102—432no—
672#97C22×D4312yes—
673#97C22×D4314yes—
674C4×C8C22×D4312yes—
675C4×C8C22×D4314yes—
676C24—861no—
677#41—862no—
678#41—864no—
679#41—862no—
680#41—864no—
681#41—1724no—
682C2×Q8—42no—
683C2×Q8—432no—
684C2×Q8—431no—
685C2×Q8—862no—
686C2×Q8—862no—
687C2×Q8—3442no—
688C2×Q8C2×D17211yescharacteristic
689C2×Q8C2×D17211yescharacteristic
690C2×Q8C2×D17212yes—
691C2×D4—434no—
692C2×D4—432no—
693C2×D4—432no—
694C2×D4—431no—
695C2×D4—861no—
696C2×D4—862no—
697C2×D4—861no—
698C2×D4—861no—
699C2×D4—862no—
700C2×D4—862no—
701C2×D4—861no—
702C2×D4—862no—
703C22×C4—861no—
704C22×C4—862no—
705C22×C4—861no—
706C22×C4—862no—
707C22×C4—864no—
708C22×C4—864no—
709C22×C4—862no—
710C22×C4—861no—
711C22×C4—862no—
712C22×C4—861no—
713C22×C4—862no—
714C22×C4—862no—
715C22×C4—3444no—
716C22×C4—1724no—
717C22×C4C2×D17211yescharacteristic
718C22×C4C2×D17212yes—
719C22×C4C2×D17211yescharacteristic
720C22×C4C2×D17212yes—
721C22×C4C23×D4311yescharacteristic
722SD16—868no—
723SD16—864no—
724D8—864no—
725D8—868no—
726M16—22no—
727M16—24no—
728M16—22no—
729C2×C8C23×D4312yes—
730C2×C8C23×D4312yes—
731C2×C8C23×D4314yes—
732C4⋊C4—432no—
733C4⋊C4—434no—
734C4⋊C4—431no—
735C4⋊C4—431no—
736C4⋊C4—861no—
737C4⋊C4—862no—
738C4⋊C4—864no—
739C4⋊C4—864no—
740C4⋊C4—862no—
741C4⋊C4—862no—
742C4⋊C4—864no—
743C4⋊C4—864no—
744C4⋊C4—862no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4—862no—
748C4⋊C4—862no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C4⋊C4—862no—
752C4⋊C4C2×D17211yescharacteristic
753C4⋊C4C2×D17211yescharacteristic
754C4⋊C4C2×D17212yes—
755C4⋊C4C2×D17212yes—
756C4⋊C4C2×D17212yes—
757C4⋊C4C2×D17212yes—
758C4⋊C4C2×D17212yes—
759C22⋊C4—861no—
760C22⋊C4—862no—
761C22⋊C4—862no—
762C22⋊C4—864no—
763C22⋊C4—864no—
764C22⋊C4—861no—
765C22⋊C4—862no—
766C22⋊C4—862no—
767C22⋊C4—861no—
768C22⋊C4—862no—
769C22⋊C4—862no—
770C22⋊C4—862no—
771C22⋊C4—862no—
772C22⋊C4—862no—
773C22⋊C4—862no—
774C42—861no—
775C42—861no—
776C42—862no—
777C42—862no—
778C42—861no—
779C42C2×D17212yes—
780C42C2×D17211yescharacteristic
781C42C2×D17212yes—
782C42C2×D17211yescharacteristic
783C42C23×D4312yes—
784C42C23×D4311yescharacteristic
785C42C23×D4311yescharacteristic
786C42C23×D4312yes—
787C23—864no—
788C23—862no—
789C23—862no—
790C23—861no—
791C23—1722no—
792C23—1722no—
793C23C22×D17211yescharacteristic
794Q8—22no—
795Q8—22no—
796Q8—42no—
797Q8—862no—
798Q8—861no—
799Q8—862no—
800Q8—861no—
801Q8—3442no—
802Q8—3442no—
803D4—434no—
804D4—864no—
805D4—862no—
806D4—861no—
807D4—862no—
808D4—862no—
809D4—861no—
810D4—3442no—
811D4—3441no—
812D4—1724no—
813D4—1722no—
814D4—1724no—
815D4—1722no—
816C2×C4—22no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—861no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—864no—
826C2×C4—3444no—
827C2×C4—3444no—
828C2×C4—3442no—
829C2×C4—3441no—
830C2×C4—1724no—
831C2×C4—1724no—
832C2×C4—1724no—
833C2×C4—1722no—
834C2×C4—1724no—
835C2×C4—1722no—
836C2×C4—1724no—
837C2×C4—1722no—
838C2×C4C22×D17211yescharacteristic
839C2×C4C22×D17212yes—
840C2×C4C22×D17212yes—
841C2×C4C22×D17212yes—
842C2×C4C22×D17211yescharacteristic
843C2×C4C22×D17211yescharacteristic
844C2×C4C22×D17212yes—
845C2×C4C22×D17211yescharacteristic
846C2×C4C22×D17211yescharacteristic
847C2×C4#41×D4312yes—
848C2×C4#1306337312yes—
849C2×C4C24×D4311yescharacteristic
850C8—22no—
851C8—24no—
852C8—22no—
853C22—21no—
854C22—21no—
855C22—864no—
856C22—1728no—
857C22—1722no—
858C22—1721no—
859C22—1722no—
860C22—1721no—
861C22—1722no—
862C22—1721no—
863C22—1722no—
864C22—1722no—
865C22#1458356112yes—
866C22C23×D17211yescharacteristic
867C4—21no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—21no—
873C4—21no—
874C4—1721no—
875C4—1722no—
876C4—1721no—
877C4—1722no—
878C4—1721no—
879C4—1724no—
880C4#1458356112yes—
881C4#1458369912yes—
882C4C2×#41×D4311yescharacteristic
883C4C2×#1306337311yescharacteristic
884C2—22no—
885C2—3442no—
886C2—3441no—
887C2—1724no—
888C2C2×#1458356111yescharacteristic
889C2C2×#1458369911yescharacteristic
890C2#1914937611yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingQ8×M16×C43C2
socleC22×C43C23×D4
hypercenterQ8×M16D43
hypocenterC43#61318
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
1. #19148190C2semidirect
2. C2×#14583609C2semidirect
3. #19147424C2semidirect
4. #19147378C2semidirect
5. #19147350C2semidirect
6. #19147304C2semidirect
7. #19147257C2semidirect
8. #19147246C2semidirect
9. #19144996C2semidirect
10. #19144989C2semidirect
11. #19144418C2semidirect
12. #19144411C2semidirect
13. #19144061C2semidirect
14. #19144061C2semidirect
15. C4×#13063353C2semidirect
16. C4×#13063353C2semidirect
17. Q8×M16×C43C2semidirect
20. #14583634C22semidirect
21. #14583634C22semidirect
22. #14583628C22semidirect
23. #14583622C22semidirect
24. #14583622C22semidirect
33. #14583571C22semidirect
49. #14583268C22semidirect
50. #14583264C22semidirect
51. #14583259C22semidirect
52. #14583254C22semidirect
53. #14583254C22semidirect
54. #14583250C22semidirect
55. #14583246C22semidirect
56. #14583207C22semidirect
57. #14583207C22semidirect
58. #14583200C22semidirect
59. #14583200C22semidirect
60. #14583195C22semidirect
61. #14583190C22semidirect
62. #14583185C22semidirect
63. #14583180C22semidirect
88. C43×#446C22semidirect
89. C43×#446C22semidirect
90. C8×Q8×C43C22semidirect
255. C2×D172#41semidirect
453. Q8×M16D43semidirect
517. #446C2×D43semidirect
518. #446C2×D43semidirect
519. C8×Q8C2×D43semidirect
540. C43#61318semidirect

Maximal subgroups

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

subgroupindex
#191481902
C2×#145836092
#191474242
#191473782
#191473502
#191473042
#191472572
#191472462
#191449962
#191449892
#191444182
#191444112
#191440612
C4×#130633532
Q8×M16×C432
#6131843