Finite Group Databasebeta

← #25968104

Subgroups — #25968104

Order 11008.

2196 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583449C211yesmaximal, characteristic, complemented
2C2×#14583433C211yesmaximal, characteristic, complemented
3#19145634C214yesmaximal, complemented
4#19145624C212yesmaximal, complemented
5#19145615C212yesmaximal, complemented
6#19145573C214yesmaximal, complemented
7#19145562C214yesmaximal, complemented
8#19145061C212yesmaximal, complemented
9#19144996C212yesmaximal, complemented
10#19144069C212yesmaximal, complemented
11#19144061C212yesmaximal, complemented
12#19143857C212yesmaximal, complemented
13#19143849C212yesmaximal, complemented
14C43×#2920C211yesmaximal, characteristic, complemented
15C22×#10621898C2212yes—
16C2×#13063358C2214yescomplemented
17C2×#13063353C2214yescomplemented
18#14583449—21no—
19#14583449—21no—
20#14583449—21no—
21#14583449—21no—
22#14583449C2212yes—
23#14583449C2212yes—
24#14583449C2212yescomplemented
25#14583449C2212yescomplemented
26C2×#13063325C2211yescharacteristic, complemented
27C2×#13063322C2211yescharacteristic, complemented
28#14583433—21no—
29#14583433—21no—
30#14583433—21no—
31#14583433—21no—
32#14583433C2212yes—
33#14583433C2212yes—
34#14583433C2212yescomplemented
35#14583433C2212yescomplemented
36C2×#13063319—21no—
37C2×#13063317C2211yescharacteristic, complemented
38C2×#13063313C2211yescharacteristic, complemented
39C2×#13063313C2212yescomplemented
40C2×#13063308—21no—
41C2×#13063304C2211yescharacteristic
42C2×#13063299—21no—
43C2×#13063299—21no—
44C2×#13063299C2211yescharacteristic
45C2×C4×Dic86C2211yescharacteristic, complemented
46C2×C4×D172—21no—
47C2×C4×D172—21no—
48C2×C4×D172C2211yescharacteristic, complemented
49C2×C4×C22⋊D43—21no—
50C2×#13063282—21no—
51#14583293C2214yescomplemented
52#14583288C2214yescomplemented
53#14583283C2218yescomplemented
54#14583268C2214yescomplemented
55#14583264C2214yescomplemented
56#14583254C2218yescomplemented
57#14583122C2218yescomplemented
58#14583115C2218yescomplemented
59#14583110C2214yescomplemented
60#14583105C2214yescomplemented
61#14583100C2214yescomplemented
62#14583095C2214yescomplemented
63#14583063C2218yescomplemented
64#14583057C2214yescomplemented
65#14583052C2214yescomplemented
66#14583046C2218yescomplemented
67#14583040C2214yes—
68#14583035C2214yes—
69#14582901C2214yescomplemented
70#14582901C2214yescomplemented
71C22×C42×C43C2211yescharacteristic
72C43×#432C2212yescomplemented
73C43×#432C2212yescomplemented
74C43×#431C2212yescomplemented
75C43×#431C2212yescomplemented
76C43×#423C2212yescomplemented
77C43×#407C2212yes—
78C4×M16×C43C2212yescomplemented
79C2×#10621898—22no—
80C2×#10621898—22no—
81C2×#10621898—48no—
82C2×#10621898C2314yes—
83C2×#10621898C2314yes—
84C22×Dic86C2311yescharacteristic
85C22×Dic86C2312yes—
86C22×D172—21no—
87C22×D172—21no—
88C22×D172C2311yescharacteristic
89C22×D172C2312yes—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—22no—
92C22×C4×D43—21no—
93C22×C4×D43—22no—
94#13063358—48no—
95#13063353—48no—
96C2×Dic172C2318yes—
97C2×#10621873C2318yes—
98C2×#10621873C2318yes—
99C2×D344C2318yes—
100#13063325—21no—
101#13063325—21no—
102#13063325C2312yes—
103#13063325C2312yes—
104#13063322—21no—
105#13063322—21no—
106#13063322C2312yes—
107#13063322C2312yes—
108#13063319—22no—
109#13063319—22no—
110#13063319—22no—
111#13063319—22no—
112#13063317—21no—
113#13063317—21no—
114#13063317C2312yes—
115#13063317C2312yes—
116#13063313—21no—
117#13063313—21no—
118#13063313—22no—
119#13063313—22no—
120#13063313C2314yes—
121#13063313C2312yes—
122#13063313C2312yes—
123#13063313C2314yes—
124#13063308—22no—
125#13063308—22no—
126#13063308—22no—
127#13063308—22no—
128#13063304—21no—
129#13063304—21no—
130#13063304C2312yes—
131#13063304C2312yes—
132#13063299—22no—
133#13063299—22no—
134#13063299—22no—
135#13063299—22no—
136#13063299—22no—
137#13063299—22no—
138#13063299—22no—
139#13063299—22no—
140#13063299—21no—
141#13063299—21no—
142#13063299C2312yes—
143#13063299C2312yes—
144C4×Dic86—21no—
145C4×Dic86—21no—
146C4×Dic86C2312yes—
147C4×Dic86C2312yes—
148C4×D172—22no—
149C4×D172—22no—
150C4×D172—22no—
151C4×D172—22no—
152C4×D172—22no—
153C4×D172—22no—
154C4×D172—22no—
155C4×D172—22no—
156C4×D172—21no—
157C4×D172—21no—
158C4×D172C2312yes—
159C4×D172C2312yes—
160C4×C22⋊D43—22no—
161C4×C22⋊D43—22no—
162C4×C22⋊D43—22no—
163C4×C22⋊D43—22no—
164#13063282—22no—
165#13063282—22no—
166#13063282—22no—
167#13063282—22no—
168C2×C4⋊Dic43—21no—
169C2×C4⋊Dic43—21no—
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2311yescharacteristic
172C2×Dic43⋊C4—21no—
173C2×Dic43⋊C4—21no—
174C2×Dic43⋊C4—21no—
175C2×Dic43⋊C4—21no—
176C2×C22⋊Dic43—21no—
177C2×(C2×D43)⋊C4—21no—
178C2×(C2×D43)⋊C4—21no—
179C2×(C2×D43)⋊C4—21no—
180C2×(C2×D43)⋊C4—22no—
181C2×(C2×D43)⋊C4—22no—
182C2×(C2×D43)⋊C4—21no—
183C2×C4×Dic43—21no—
184#13063250C2318yes—
185#13063250C2318yes—
186#13063247C2318yes—
187#13063247C2318yes—
188C23×C4×C43D411yescharacteristic
189C23×C4×C43D411yescharacteristic
190C23×C4×C43C2311yescharacteristic
191C2×M16×C43C2314yes—
192C2×C42×C43D411yescharacteristic
193C2×C42×C43D411yescharacteristic
194C2×C42×C43D411yescharacteristic
195C2×C42×C43D411yescharacteristic
196C2×C42×C43D411yescharacteristic
197C2×C42×C43D411yescharacteristic
198C2×C42×C43C2311yescharacteristic
199C2×C42×C43C2311yescharacteristic
200C2×C42×C43C2311yescharacteristic
201C2×C42×C43C2311yescharacteristic
202C2×C42×C43C2311yescharacteristic
203C2×C42×C43C2311yescharacteristic
204C4⋊C8×C43C2314yes—
205C4⋊C8×C43C2314yes—
206C22⋊C8×C43C2314yes—
207C22⋊C8×C43C2314yes—
208#97×C43C2314yes—
209C4×C8×C43C2314yes—
210C24×C43C2×D411yescharacteristic
211C23×D43—21no—
212C23×D43—22no—
213C22×C4×C43—24no—
214C22×C4×C43—42no—
215C22×C4×C43—42no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C2×C22⋊D43—22no—
235C2×C22⋊D43—22no—
236C2×C22⋊D43—24no—
237C2×C22⋊D43—24no—
238C2×C22⋊D43—44no—
239C2×C22⋊D43—48no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—22no—
243C22×Dic43—21no—
244#10621898—28no—
245#10621898—28no—
246#10621898—44no—
247#10621898—44no—
248#10621898—48no—
249#10621898—48no—
250C2×D172—21no—
251C2×D172—22no—
252C2×D172—22no—
253C2×D172—22no—
254C2×D172—22no—
255C2×D172—22no—
256C2×D172—24no—
257C2×D172—44no—
258C2×D172—44no—
259C2×D172—44no—
260C2×D172C2414yes—
261C2×D172C2412yes—
262C2×C4×D43—22no—
263C2×C4×D43—22no—
264C2×C4×D43—24no—
265C2×C4×D43—24no—
266C2×C4×D43—44no—
267C2×C4×D43—48no—
268C2×Dic86—24no—
269C2×Dic86—21no—
270C2×Dic86—22no—
271C2×Dic86—44no—
272C2×Dic86C2414yes—
273C2×Dic86C2412yes—
274M16×C43—28no—
275C2×C8×C43C2418yes—
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2×D411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2×D411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C42×C43C2×D411yescharacteristic
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D411yescharacteristic
286C42×C43C2×D411yescharacteristic
287C42×C43C2×D411yescharacteristic
288C42×C43C2411yescharacteristic
289C42×C43C2411yescharacteristic
290C42×C43C2411yescharacteristic
291C42×C43C2411yescharacteristic
292C22⋊Dic43—22no—
293C22⋊Dic43—22no—
294(C2×D43)⋊C4—22no—
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—24no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—22no—
305(C2×D43)⋊C4—22no—
306C4⋊Dic43—22no—
307C4⋊Dic43—22no—
308C4⋊Dic43—22no—
309C4⋊Dic43—22no—
310C4⋊Dic43—21no—
311C4⋊Dic43—21no—
312C4⋊Dic43C2412yes—
313C4⋊Dic43C2412yes—
314Dic43⋊C4—22no—
315Dic43⋊C4—22no—
316Dic43⋊C4—22no—
317Dic43⋊C4—22no—
318Dic43⋊C4—22no—
319Dic43⋊C4—22no—
320Dic43⋊C4—22no—
321Dic43⋊C4—22no—
322C4×Dic43—22no—
323C4×Dic43—22no—
324Dic172—48no—
325D344—48no—
326#10621873—48no—
327#10621873—48no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—41no—
331C23×C43C22×D411yescharacteristic
332C23×C43C22×D411yescharacteristic
333C23×C43C22×D411yescharacteristic
334C22×D43—22no—
335C22×D43—24no—
336C22×D43—44no—
337C22×D43—42no—
338C22×D43—44no—
339C22×D43—42no—
340C22×D43—42no—
341C22×D43—44no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43H(5,𝔽2)14yes—
371C2×C4×C43C2511yescharacteristic
372C22⋊D43—48no—
373C22⋊D43—44no—
374C22⋊D43—48no—
375C22⋊D43—44no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—24no—
380C2×Dic43—44no—
381C2×Dic43—42no—
382C2×Dic43—42no—
383C2×Dic43—42no—
384D172—24no—
385D172—24no—
386D172—24no—
387D172—44no—
388D172—44no—
389D172—44no—
390D172—44no—
391D172—42no—
392D172—44no—
393C4×D43—44no—
394C4×D43—48no—
395C4×D43—48no—
396C4×D43—44no—
397Dic86—24no—
398Dic86—24no—
399Dic86—24no—
400Dic86—44no—
401Dic86—42no—
402C8×C43—28no—
403#60805—431nomaximal, Sylow
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—44no—
412C22×C43#53512yes—
413C22×C43#57512yes—
414C22×C43C23×D411yescharacteristic
415C2×D43—44no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—44no—
419C2×D43—44no—
420C2×D43—42no—
421C2×D43—88no—
422C2×D43—84no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—21no—
432C4×C43#53512yes—
433C4×C43#57512yes—
434C4×C43C2×H(5,𝔽2)12yes—
435Dic43—44no—
436Dic43—42no—
437Dic43—42no—
438Dic43—42no—
439C2×#532—431no—
440C2×#529—431no—
441#3219—434no—
442#3218—432no—
443#3217—432no—
444#3212—434no—
445#3211—434no—
446#3153—432no—
447#3142—432no—
448#3037—432no—
449#3036—432no—
450#3007—432no—
451#3006—432no—
452#2920D4311yescharacteristic, complemented
453C2×C43—22no—
454C2×C43—22no—
455C2×C43—41no—
456C2×C43C2×#53511yescharacteristic
457C2×C43C2×#57511yescharacteristic
458C2×C43C2×#57511yescharacteristic
459D43—84no—
460D43—82no—
461C22×#41—432no—
462C2×#137—434no—
463C2×AGL(1,ℤ/8)—434no—
464#532—432no—
465#532—432no—
466#532—432no—
467#532—432no—
468#532—861no—
469#532—861no—
470#532—861no—
471#532—861no—
472C2×C4⋊Q8—431no—
473C2×#127—431no—
474#529—432no—
475#529—432no—
476#529—432no—
477#529—432no—
478#529—861no—
479#529—861no—
480#529—861no—
481#529—861no—
482C2×#126—861no—
483C2×#125—431no—
484C2×#124—431no—
485C2×#124—432no—
486C2×#123—861no—
487C2×C22⋊Q8—431no—
488C2×#121—431no—
489C2×#121—861no—
490C2×#121—861no—
491C2×C4×Q8—431no—
492C2×C4×D4—431no—
493C2×C4×D4—861no—
494C2×C4×D4—861no—
495C2×C4×D4—861no—
496C2×#117—861no—
497C22×C42C2×D4311yescharacteristic
498#497—434no—
499#496—434no—
500#495—438no—
501#491—434no—
502#490—434no—
503#488—438no—
504#464—438no—
505#463—438no—
506#462—434no—
507#461—434no—
508#460—434no—
509#459—434no—
510#452—438no—
511#451—434no—
512#450—434no—
513#449—438no—
514#448—434no—
515#447—434no—
516#432C2×D4312yescomplemented
517#432C2×D4312yescomplemented
518#431C2×D4312yescomplemented
519#431C2×D4312yescomplemented
520#423C2×D4312yescomplemented
521#417—434no—
522#417—434no—
523#407C2×D4312yes—
524C4×M16C2×D4312yescomplemented
525C43#6080511yescharacteristic, complemented, Sylow
526C2×#41—434no—
527C2×#41—434no—
528C2×#41—862no—
529C2×#41—862no—
530C2×#41—1728no—
531C22×Q8—431no—
532C22×Q8—432no—
533C22×D4—431no—
534C22×D4—432no—
535C22×D4—861no—
536C22×D4—862no—
537C22×D4—861no—
538C22×D4—861no—
539C23×C4—861no—
540C23×C4—862no—
541C23×C4D17211yescharacteristic
542C23×C4D17211yescharacteristic
543C23×C4C22×D4311yescharacteristic
544#137—1728no—
545AGL(1,ℤ/8)—1728no—
546C2×Q16—438no—
547C2×SD16—438no—
548C2×SD16—438no—
549C2×D8—438no—
550C2×M16C22×D4314yes—
551C4⋊Q8—432no—
552C4⋊Q8—432no—
553C4⋊Q8—861no—
554C4⋊Q8—861no—
555#127—432no—
556#127—432no—
557#127—861no—
558#127—861no—
559#126—862no—
560#126—862no—
561#126—862no—
562#126—862no—
563#125—432no—
564#125—432no—
565#125—861no—
566#125—861no—
567#124—432no—
568#124—432no—
569#124—434no—
570#124—434no—
571#124—861no—
572#124—861no—
573#124—862no—
574#124—862no—
575#123—862no—
576#123—862no—
577#123—862no—
578#123—862no—
579C22⋊Q8—432no—
580C22⋊Q8—432no—
581C22⋊Q8—861no—
582C22⋊Q8—861no—
583#121—432no—
584#121—432no—
585#121—861no—
586#121—861no—
587#121—862no—
588#121—862no—
589#121—862no—
590#121—862no—
591#121—862no—
592#121—862no—
593#121—862no—
594#121—862no—
595C4×Q8—432no—
596C4×Q8—432no—
597C4×Q8—861no—
598C4×Q8—861no—
599C4×D4—432no—
600C4×D4—432no—
601C4×D4—862no—
602C4×D4—862no—
603C4×D4—862no—
604C4×D4—862no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—862no—
608C4×D4—862no—
609C4×D4—862no—
610C4×D4—862no—
611C4×D4—862no—
612C4×D4—862no—
613C4×D4—862no—
614C4×D4—862no—
615#117—862no—
616#117—862no—
617#117—862no—
618#117—862no—
619C2×C4⋊C4—431no—
620C2×C4⋊C4—431no—
621C2×C4⋊C4—861no—
622C2×C4⋊C4—861no—
623C2×C4⋊C4—861no—
624C2×C4⋊C4—861no—
625C2×C4⋊C4—861no—
626C2×C4⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4—861no—
629C2×C22⋊C4—861no—
630C2×C22⋊C4—861no—
631C2×C22⋊C4—862no—
632C2×C22⋊C4—862no—
633C2×C22⋊C4—861no—
634C2×C42—861no—
635C2×C42D17211yescharacteristic
636C2×C42D17211yescharacteristic
637C2×C42D17211yescharacteristic
638C2×C42D17211yescharacteristic
639C2×C42D17211yescharacteristic
640C2×C42D17211yescharacteristic
641C2×C42C22×D4311yescharacteristic
642C2×C42C22×D4311yescharacteristic
643C2×C42C22×D4311yescharacteristic
644C2×C42C22×D4311yescharacteristic
645C2×C42C22×D4311yescharacteristic
646C2×C42C22×D4311yescharacteristic
647C4⋊C8C22×D4314yes—
648C4⋊C8C22×D4314yes—
649#103—438no—
650#103—438no—
651#102—438no—
652#102—438no—
653C22⋊C8C22×D4314yes—
654C22⋊C8C22×D4314yes—
655#97C22×D4314yes—
656C4×C8C22×D4314yes—
657C24—861no—
658C24—862no—
659C24C2×D17211yescharacteristic
660#41—868no—
661#41—868no—
662#41—1724no—
663#41—1724no—
664#41—1728no—
665#41—1728no—
666C2×Q8—434no—
667C2×Q8—432no—
668C2×Q8—861no—
669C2×Q8—862no—
670C2×Q8—864no—
671C2×Q8—1724no—
672C2×D4—434no—
673C2×D4—432no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—864no—
677C2×D4—864no—
678C2×D4—861no—
679C2×D4—862no—
680C2×D4—862no—
681C2×D4—862no—
682C2×D4—862no—
683C2×D4—862no—
684C2×D4—864no—
685C2×D4—1724no—
686C2×D4—1724no—
687C2×D4—1724no—
688C2×D4—1728no—
689C2×D4—1724no—
690C22×C4—24no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—862no—
697C22×C4—862no—
698C22×C4—862no—
699C22×C4—864no—
700C22×C4—864no—
701C22×C4—1728no—
702C22×C4—1724no—
703C22×C4C2×D17211yescharacteristic
704C22×C4C2×D17211yescharacteristic
705C22×C4C2×D17211yescharacteristic
706C22×C4C2×D17211yescharacteristic
707C22×C4C2×D17211yescharacteristic
708C22×C4C2×D17211yescharacteristic
709C22×C4C2×D17211yescharacteristic
710C22×C4C2×D17211yescharacteristic
711C22×C4C2×D17211yescharacteristic
712C22×C4C2×D17211yescharacteristic
713C22×C4C2×D17211yescharacteristic
714C22×C4C2×D17211yescharacteristic
715C22×C4C2×D17211yescharacteristic
716C22×C4C2×D17211yescharacteristic
717C22×C4C2×D17211yescharacteristic
718C22×C4C23×D4311yescharacteristic
719C22×C4C23×D4311yescharacteristic
720C22×C4C23×D4311yescharacteristic
721Q16—1728no—
722SD16—1728no—
723SD16—1728no—
724D8—1728no—
725M16—28no—
726C2×C8C23×D4318yes—
727C4⋊C4—432no—
728C4⋊C4—432no—
729C4⋊C4—861no—
730C4⋊C4—861no—
731C4⋊C4—862no—
732C4⋊C4—862no—
733C4⋊C4—862no—
734C4⋊C4—862no—
735C4⋊C4—862no—
736C4⋊C4—862no—
737C4⋊C4—862no—
738C4⋊C4—862no—
739C4⋊C4—862no—
740C4⋊C4—862no—
741C4⋊C4—862no—
742C4⋊C4—862no—
743C22⋊C4—862no—
744C22⋊C4—862no—
745C22⋊C4—862no—
746C22⋊C4—862no—
747C22⋊C4—862no—
748C22⋊C4—862no—
749C22⋊C4—862no—
750C22⋊C4—862no—
751C22⋊C4—864no—
752C22⋊C4—864no—
753C22⋊C4—864no—
754C22⋊C4—864no—
755C22⋊C4—862no—
756C22⋊C4—862no—
757C42—862no—
758C42—862no—
759C42C2×D17211yescharacteristic
760C42C2×D17211yescharacteristic
761C42C2×D17211yescharacteristic
762C42C2×D17211yescharacteristic
763C42C2×D17211yescharacteristic
764C42C2×D17211yescharacteristic
765C42C2×D17211yescharacteristic
766C42C2×D17211yescharacteristic
767C42C2×D17211yescharacteristic
768C42C2×D17211yescharacteristic
769C42C2×D17211yescharacteristic
770C42C2×D17211yescharacteristic
771C42C23×D4311yescharacteristic
772C42C23×D4311yescharacteristic
773C42C23×D4311yescharacteristic
774C42C23×D4311yescharacteristic
775C23—22no—
776C23—22no—
777C23—41no—
778C23—862no—
779C23—864no—
780C23—1724no—
781C23—1722no—
782C23—1724no—
783C23—1722no—
784C23—1724no—
785C23—1722no—
786C23C22×D17211yescharacteristic
787C23C22×D17211yescharacteristic
788C23C22×D17211yescharacteristic
789Q8—864no—
790Q8—864no—
791Q8—864no—
792Q8—1724no—
793Q8—1722no—
794D4—864no—
795D4—864no—
796D4—864no—
797D4—1724no—
798D4—1724no—
799D4—1724no—
800D4—1724no—
801D4—1728no—
802D4—1724no—
803D4—1724no—
804D4—1728no—
805D4—1724no—
806D4—1722no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—864no—
828C2×C4—1728no—
829C2×C4—1724no—
830C2×C4—1724no—
831C2×C4—1722no—
832C2×C4—1722no—
833C2×C4—1722no—
834C2×C4—1724no—
835C2×C4—1728no—
836C2×C4C22×D17211yescharacteristic
837C2×C4C22×D17211yescharacteristic
838C2×C4C22×D17211yescharacteristic
839C2×C4C22×D17211yescharacteristic
840C2×C4C22×D17211yescharacteristic
841C2×C4C22×D17211yescharacteristic
842C2×C4C22×D17211yescharacteristic
843C2×C4C22×D17211yescharacteristic
844C2×C4C22×D17211yescharacteristic
845C2×C4C22×D17211yescharacteristic
846C2×C4C22×D17211yescharacteristic
847C2×C4#1306337114yes—
848C2×C4C24×D4311yescharacteristic
849C8—28no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—44no—
858C22—3448no—
859C22—3444no—
860C22—1722no—
861C22—1724no—
862C22—1722no—
863C22—1724no—
864C22—1724no—
865C22—1722no—
866C22#1458346812yes—
867C22#1458369912yes—
868C22C23×D17211yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—1722no—
879C4—1722no—
880C4—1724no—
881C4—1722no—
882C4#1458346812yes—
883C4#1458369912yes—
884C4C2×#1306337112yes—
885C2—22no—
886C2—22no—
887C2—41no—
888C2—3442no—
889C2—3444no—
890C2C2×#1458346811yescharacteristic
891C2C2×#1458369911yescharacteristic
892C2C2×#1458369911yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2920C2
socleC22×C43C23×D4
hypercenter#2920D43
hypocenterC43#60805
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#14583449C2semidirect
2. C2×#14583433C2semidirect
3. #19145634C2semidirect
4. #19145624C2semidirect
5. #19145615C2semidirect
6. #19145573C2semidirect
7. #19145562C2semidirect
8. #19145061C2semidirect
9. #19144996C2semidirect
10. #19144069C2semidirect
11. #19144061C2semidirect
12. #19143857C2semidirect
13. #19143849C2semidirect
14. C43×#2920C2semidirect
16. C2×#13063358C22semidirect
17. C2×#13063353C22semidirect
24. #14583449C22semidirect
25. #14583449C22semidirect
26. C2×#13063325C22semidirect
27. C2×#13063322C22semidirect
34. #14583433C22semidirect
35. #14583433C22semidirect
37. C2×#13063317C22semidirect
38. C2×#13063313C22semidirect
39. C2×#13063313C22semidirect
45. C2×C4×Dic86C22semidirect
48. C2×C4×D172C22semidirect
51. #14583293C22semidirect
52. #14583288C22semidirect
53. #14583283C22semidirect
54. #14583268C22semidirect
55. #14583264C22semidirect
56. #14583254C22semidirect
57. #14583122C22semidirect
58. #14583115C22semidirect
59. #14583110C22semidirect
60. #14583105C22semidirect
61. #14583100C22semidirect
62. #14583095C22semidirect
63. #14583063C22semidirect
64. #14583057C22semidirect
65. #14583052C22semidirect
66. #14583046C22semidirect
69. #14582901C22semidirect
70. #14582901C22semidirect
72. C43×#432C22semidirect
73. C43×#432C22semidirect
74. C43×#431C22semidirect
75. C43×#431C22semidirect
76. C43×#423C22semidirect
78. C4×M16×C43C22semidirect
452. #2920D43semidirect
516. #432C2×D43semidirect
517. #432C2×D43semidirect
518. #431C2×D43semidirect
519. #431C2×D43semidirect
520. #423C2×D43semidirect
524. C4×M16C2×D43semidirect
525. C43#60805semidirect

Maximal subgroups

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

subgroupindex
C2×#145834492
C2×#145834332
#191456342
#191456242
#191456152
#191455732
#191455622
#191450612
#191449962
#191440692
#191440612
#191438572
#191438492
C43×#29202
#6080543