Finite Group Databasebeta

← #25969645

Subgroups — #25969645

Order 11008.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147985C211yesmaximal, characteristic, complemented
2C2×#14583520C211yesmaximal, characteristic, complemented
3#19146066C214yesmaximal, complemented
4#19146056C214yesmaximal, complemented
5#19146023C214yesmaximal, complemented
6#19146008C214yesmaximal, complemented
7#19144411C212yesmaximal, complemented
8#19144402C211yesmaximal, characteristic, complemented
9#19144394C211yesmaximal, characteristic, complemented
10#19144225C212yesmaximal, complemented
11#19144214C212yesmaximal, complemented
12#19144090C212yesmaximal, complemented
13#19144069C211yesmaximal, characteristic, complemented
14#19144061C211yesmaximal, characteristic, complemented
15C43×#2905C211yesmaximal, characteristic, complemented
16C2×#13063358C2212yes—
17C2×#13063353C2212yes—
18#14583520—22no—
19#14583520—22no—
20#14583520C2214yes—
21#14583520C2214yes—
22#14583520C2212yescomplemented
23#14583520C2212yescomplemented
24#14583511C2212yescomplemented
25#14583504C2212yescomplemented
26#14583496—21no—
27#14583496—21no—
28#14583487—21no—
29#14583487—21no—
30#14583456C2211yescharacteristic
31#14583449C2211yescharacteristic
32C2×#13063325C2211yescharacteristic
33#14583427—22no—
34#14583427—22no—
35C2×#13063320—21no—
36C2×#13063313C2211yescharacteristic
37C2×#13063311—21no—
38#14583410C2212yes—
39C2×#13063307—21no—
40C2×#13063304C2211yescharacteristic
41C2×#13063303—21no—
42C2×#13063299C2211yescharacteristic
43C4×#10621898C2212yes—
44C2×C4×Dic86C2211yescharacteristic
45C2×C4×D172C2211yescharacteristic
46#14583207C2214yescomplemented
47#14583200C2214yescomplemented
48#14583195C2214yescomplemented
49#14583195C2212yescomplemented
50#14583190C2214yescomplemented
51#14583190C2212yescomplemented
52#14583185C2214yescomplemented
53#14583185C2212yescomplemented
54#14583180C2214yescomplemented
55#14583180C2212yescomplemented
56#14583157C2214yescomplemented
57#14583152C2214yes—
58#14583145C2214yes—
59#14583145C2214yescomplemented
60#14583140C2214yescomplemented
61#14583135C2214yes—
62#14583128C2214yes—
63#14583128C2214yescomplemented
64#14583122C2214yescomplemented
65#14583122C2214yescomplemented
66#14583122C2214yescomplemented
67#14583115C2214yescomplemented
68#14583115C2214yescomplemented
69#14583115C2214yescomplemented
70#14583110C2212yescomplemented
71#14583105C2212yescomplemented
72#14583100C2212yescomplemented
73#14583095C2212yescomplemented
74#14582941C2212yes—
75#14582941C2212yes—
76#14582909C2212yes—
77#14582905C2212yes—
78#14582901C2212yes—
79#14582901C2212yes—
80C22×M16×C43C2212yes—
81C2×#117×C43C2211yescharacteristic
82C43×#424C2214yescomplemented
83C43×#424C2214yescomplemented
84C43×#423C2211yescharacteristic
85C43×#423C2211yescharacteristic
86C43×#423C2212yes—
87C2×#10621898C2312yes—
88C22×Dic86—21no—
89C22×Dic86C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C4×D43—21no—
93#13063358—44no—
94#13063353—44no—
95C2×Dic172C2314yes—
96C2×#10621873C2314yes—
97C2×#10621873C2314yes—
98C2×D344C2314yes—
99#13063325—22no—
100#13063325C2311yescharacteristic
101#13063325C2311yescharacteristic
102#13063325C2314yes—
103#13063325C2311yescharacteristic
104#13063322C2311yescharacteristic
105#13063320—24no—
106#13063320—24no—
107#13063320—22no—
108#13063320—22no—
109#13063318—22no—
110#13063318—22no—
111#13063317C2312yes—
112#13063315—22no—
113#13063315—22no—
114#13063313—22no—
115#13063313C2314yes—
116#13063313C2312yes—
117#13063311—24no—
118#13063311—24no—
119#13063311—22no—
120#13063311—22no—
121#13063310—22no—
122#13063310—22no—
123#13063308—22no—
124#13063307—24no—
125#13063307—24no—
126#13063307—22no—
127#13063307—22no—
128#13063304—22no—
129#13063304—21no—
130#13063304—21no—
131#13063304C2312yes—
132#13063304C2314yes—
133#13063304C2312yes—
134#13063303—24no—
135#13063303—24no—
136#13063303—22no—
137#13063303—22no—
138#13063299—22no—
139#13063299—21no—
140#13063299—21no—
141#13063299C2314yes—
142#13063299C2312yes—
143#13063299C2312yes—
144#13063298—22no—
145#13063298—22no—
146#13063294—22no—
147C4×Dic86—21no—
148C4×Dic86—21no—
149C4×Dic86—21no—
150C4×Dic86—21no—
151C4×Dic86C2312yes—
152C4×Dic86C2312yes—
153C4×Dic86C2312yes—
154C4×Dic86C2312yes—
155C4×D172—21no—
156C4×D172—21no—
157C4×D172—21no—
158C4×D172—21no—
159C4×D172C2312yes—
160C4×D172C2312yes—
161C4×D172C2312yes—
162C4×D172C2312yes—
163C4×C22⋊D43—22no—
164C4×C22⋊D43—22no—
165C4×C22⋊D43—22no—
166C4×C22⋊D43—22no—
167#13063284C2312yes—
168#13063282—22no—
169C2×C4⋊Dic43—21no—
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2311yescharacteristic
172C2×Dic43⋊C4—21no—
173C2×Dic43⋊C4—21no—
174C2×C22⋊Dic43—21no—
175C2×(C2×D43)⋊C4—21no—
176C2×(C2×D43)⋊C4—21no—
177C2×(C2×D43)⋊C4—21no—
178C2×(C2×D43)⋊C4—21no—
179C2×C4×Dic43—21no—
180C42×D43—22no—
181#13063259C2314yes—
182#13063259C2314yes—
183#13063257C2314yes—
184#13063257C2314yes—
185#13063250C2314yes—
186#13063250C2314yes—
187#13063250C2314yes—
188#13063250C2314yes—
189#13063247C2314yes—
190#13063247C2314yes—
191#13063247C2314yes—
192#13063247C2314yes—
193C23×C4×C43C2311yescharacteristic
194C2×M16×C43—44no—
195C2×M16×C43C2312yes—
196C2×M16×C43C2312yes—
197C2×M16×C43C2314yes—
198C22×C8×C43C2314yes—
199#117×C43D412yes—
200#117×C43D412yes—
201#117×C43C2312yes—
202#117×C43C2312yes—
203C2×C4⋊C4×C43D411yescharacteristic
204C2×C4⋊C4×C43D411yescharacteristic
205C2×C22⋊C4×C43D411yescharacteristic
206C2×C22⋊C4×C43D411yescharacteristic
207C2×C42×C43C2311yescharacteristic
208C2×C42×C43C2311yescharacteristic
209C4⋊C8×C43C2312yes—
210C4⋊C8×C43C2312yes—
211C4⋊C8×C43C2312yes—
212C4⋊C8×C43C2314yes—
213C4⋊C8×C43C2314yes—
214C4⋊C8×C43C2312yes—
215C24×C43C2×D411yescharacteristic
216C23×D43—21no—
217C22×C4×C43—22no—
218C22×C4×C43—22no—
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2412yes—
226C22×C4×C43C2411yescharacteristic
227C2×C22⋊D43—22no—
228C2×C22⋊D43—22no—
229C2×C22⋊D43—22no—
230C2×C22⋊D43—24no—
231C2×C22⋊D43—82no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235#10621898—24no—
236#10621898—24no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172—21no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172C2412yes—
243C2×D172C2412yes—
244C2×C4×D43—22no—
245C2×C4×D43—22no—
246C2×C4×D43—22no—
247C2×C4×D43—22no—
248C2×C4×D43—22no—
249C2×C4×D43—82no—
250C2×Dic86—22no—
251C2×Dic86—22no—
252C2×Dic86—21no—
253C2×Dic86—21no—
254C2×Dic86—21no—
255C2×Dic86—24no—
256C2×Dic86—82no—
257C2×Dic86C2412yes—
258C2×Dic86C2412yes—
259M16×C43—24no—
260M16×C43—24no—
261M16×C43—44no—
262C2×C8×C43—44no—
263C2×C8×C43C2414yes—
264C2×C8×C43C2414yes—
265C4⋊C4×C43C2×D412yes—
266C4⋊C4×C43C2×D412yes—
267C4⋊C4×C43C2×D412yes—
268C4⋊C4×C43C2×D412yes—
269C22⋊C4×C43C2×D412yes—
270C22⋊C4×C43C2×D412yes—
271C22⋊C4×C43C2×D412yes—
272C22⋊C4×C43C2×D412yes—
273C42×C43C2×D412yes—
274C42×C43C2×D411yescharacteristic
275C42×C43C2×D411yescharacteristic
276C42×C43C2411yescharacteristic
277C42×C43C2412yes—
278C42×C43C2411yescharacteristic
279C22⋊Dic43—24no—
280C22⋊Dic43—22no—
281C22⋊Dic43—22no—
282C22⋊Dic43—22no—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—22no—
294C4⋊Dic43—24no—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43C2412yes—
302C4⋊Dic43C2412yes—
303C4⋊Dic43C2412yes—
304C4⋊Dic43C2412yes—
305Dic43⋊C4—22no—
306Dic43⋊C4—22no—
307Dic43⋊C4—24no—
308Dic43⋊C4—22no—
309Dic43⋊C4—22no—
310Dic43⋊C4—22no—
311Dic43⋊C4—22no—
312Dic43⋊C4—22no—
313Dic43⋊C4—22no—
314C4×Dic43—22no—
315C4×Dic43—22no—
316C4×Dic43—22no—
317C4×Dic43—22no—
318C4×Dic43—22no—
319Dic172—44no—
320D344—44no—
321#10621873—44no—
322#10621873—44no—
323C23×C43—22no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43C22×D412yes—
327C23×C43C22×D411yescharacteristic
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—42no—
331C22×D43—42no—
332C22×D43—42no—
333C2×C4×C43—22no—
334C2×C4×C43—24no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D412yes—
344C2×C4×C43C22×D412yes—
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D412yes—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43H(5,𝔽2)12yes—
350C2×C4×C432−1+412yes—
351C2×C4×C43C2511yescharacteristic
352C22⋊D43—44no—
353C22⋊D43—82no—
354C22⋊D43—82no—
355C22⋊D43—84no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—42no—
363C2×Dic43—42no—
364C2×Dic43—42no—
365D172—22no—
366D172—22no—
367D172—22no—
368D172—22no—
369D172—42no—
370D172—81no—
371D172—81no—
372C4×D43—44no—
373C4×D43—82no—
374C4×D43—82no—
375C4×D43—82no—
376C4×D43—82no—
377Dic86—22no—
378Dic86—22no—
379Dic86—22no—
380Dic86—22no—
381Dic86—42no—
382Dic86—81no—
383Dic86—81no—
384Dic86—84no—
385C8×C43—24no—
386C8×C43—24no—
387#60919—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—22no—
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—82no—
394C22×C43#53712yes—
395C22×C43C23×D411yescharacteristic
396C2×D43—42no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—84no—
403C4×C43—22no—
404C4×C43—21no—
405C4×C43—21no—
406C4×C43—21no—
407C4×C43—22no—
408C4×C43—21no—
409C4×C43—22no—
410C4×C43#53712yes—
411C4×C43C2×H(5,𝔽2)11yescharacteristic
412C4×C43C2×2−1+411yescharacteristic
413Dic43—42no—
414Dic43—42no—
415Dic43—42no—
416Dic43—42no—
417Dic43—42no—
418Dic43—42no—
419#3455—431no—
420C2×#542—431no—
421#3263—434no—
422#3262—434no—
423#3258—434no—
424#3257—434no—
425#3079—432no—
426#3078—431no—
427#3077—431no—
428#3056—432no—
429#3055—432no—
430#3040—432no—
431#3037—431no—
432#3036—431no—
433#2905D4311yescharacteristic, complemented
434C2×C43—22no—
435C2×C43—42no—
436C2×C43C2×#53711yescharacteristic
437C2×C43#358511yescharacteristic
438C2×C43#358611yescharacteristic
439D43—82no—
440D43—82no—
441C2×#137—432no—
442C2×AGL(1,ℤ/8)—432no—
443C22×M16C2×D4312yes—
444#542—434no—
445#542—434no—
446#542—432no—
447#542—432no—
448#542—862no—
449#542—862no—
450#541—432no—
451#540—432no—
452#539—861no—
453#539—861no—
454#538—861no—
455#538—861no—
456#533—431no—
457#532—431no—
458C2×C4⋊Q8—431no—
459#529—862no—
460#529—862no—
461C2×#126—861no—
462C2×#124—431no—
463C2×#124—861no—
464#525—432no—
465C2×#123—861no—
466C2×C22⋊Q8—431no—
467C2×C22⋊Q8—861no—
468C2×#121—431no—
469C4×#41—432no—
470C2×C4×Q8—431no—
471C2×C4×D4—431no—
472C2×#117C2×D4311yescharacteristic
473#479—434no—
474#478—434no—
475#477—432no—
476#477—434no—
477#476—432no—
478#476—434no—
479#475—432no—
480#475—434no—
481#474—432no—
482#474—434no—
483#470—434no—
484#469—434no—
485#468—434no—
486#468—434no—
487#467—434no—
488#466—434no—
489#465—434no—
490#465—434no—
491#464—434no—
492#464—434no—
493#464—434no—
494#463—434no—
495#463—434no—
496#463—434no—
497#462—432no—
498#461—432no—
499#460—432no—
500#459—432no—
501#428—432no—
502#428—432no—
503#424C2×D4314yescomplemented
504#424C2×D4314yescomplemented
505#423C2×D4311yescharacteristic
506#423C2×D4311yescharacteristic
507#423C2×D4312yes—
508#419—432no—
509#418—432no—
510#417—432no—
511#417—432no—
512C43#6091911yescharacteristic, complemented, Sylow
513C2×#41—432no—
514C22×Q8—431no—
515C22×Q8—861no—
516C22×D4—431no—
517C22×D4—861no—
518C23×C4—861no—
519C23×C4C22×D4311yescharacteristic
520#137—1724no—
521AGL(1,ℤ/8)—1724no—
522C2×Q16—434no—
523C2×SD16—434no—
524C2×SD16—434no—
525C2×D8—434no—
526C2×M16—44no—
527C2×M16C22×D4312yes—
528C2×M16C22×D4312yes—
529C2×M16C22×D4314yes—
530C22×C8C22×D4314yes—
531C4⋊Q8—434no—
532C4⋊Q8—431no—
533C4⋊Q8—431no—
534C4⋊Q8—431no—
535C4⋊Q8—862no—
536#127—431no—
537#126—864no—
538#126—864no—
539#126—862no—
540#126—862no—
541#126—862no—
542#126—862no—
543#125—432no—
544#125—862no—
545#125—862no—
546#124—434no—
547#124—432no—
548#124—864no—
549#124—864no—
550#124—862no—
551#124—862no—
552#124—862no—
553#123—862no—
554#123—862no—
555#123—862no—
556#123—864no—
557#123—864no—
558#123—862no—
559#123—862no—
560C22⋊Q8—434no—
561C22⋊Q8—432no—
562C22⋊Q8—432no—
563C22⋊Q8—862no—
564C22⋊Q8—861no—
565C22⋊Q8—861no—
566C22⋊Q8—864no—
567C22⋊Q8—864no—
568C22⋊Q8—862no—
569C22⋊Q8—862no—
570#121—434no—
571#121—432no—
572#121—432no—
573#121—862no—
574#121—861no—
575#121—861no—
576#121—862no—
577#121—862no—
578#120—862no—
579C4×Q8—432no—
580C4×Q8—432no—
581C4×Q8—432no—
582C4×Q8—432no—
583C4×Q8—861no—
584C4×Q8—861no—
585C4×Q8—861no—
586C4×Q8—861no—
587C4×D4—432no—
588C4×D4—432no—
589C4×D4—432no—
590C4×D4—432no—
591C4×D4—862no—
592C4×D4—862no—
593C4×D4—862no—
594C4×D4—862no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599#117—432no—
600#117—862no—
601#117D17212yes—
602#117D17212yes—
603#117C22×D4312yes—
604#117C22×D4312yes—
605C2×C4⋊C4—431no—
606C2×C4⋊C4—431no—
607C2×C4⋊C4—861no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4D17211yescharacteristic
611C2×C4⋊C4D17211yescharacteristic
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C22⋊C4D17211yescharacteristic
618C2×C22⋊C4D17211yescharacteristic
619C2×C42—861no—
620C2×C42—862no—
621C2×C42C22×D4311yescharacteristic
622C2×C42C22×D4311yescharacteristic
623#107—434no—
624#107—434no—
625#106—434no—
626#106—434no—
627C4⋊C8C22×D4312yes—
628C4⋊C8C22×D4312yes—
629C4⋊C8C22×D4312yes—
630C4⋊C8C22×D4314yes—
631C4⋊C8C22×D4314yes—
632C4⋊C8C22×D4312yes—
633#103—434no—
634#103—434no—
635#103—434no—
636#103—434no—
637#102—434no—
638#102—434no—
639#102—434no—
640#102—434no—
641C24—861no—
642C24C2×D17211yescharacteristic
643#41—864no—
644#41—864no—
645C2×Q8—432no—
646C2×Q8—432no—
647C2×Q8—861no—
648C2×Q8—861no—
649C2×Q8—864no—
650C2×Q8—861no—
651C2×Q8—862no—
652C2×Q8—862no—
653C2×Q8—3442no—
654C2×D4—432no—
655C2×D4—432no—
656C2×D4—862no—
657C2×D4—862no—
658C2×D4—864no—
659C2×D4—862no—
660C2×D4—861no—
661C2×D4—861no—
662C2×D4—861no—
663C2×D4—862no—
664C2×D4—862no—
665C2×D4—3442no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—862no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4—3442no—
677C22×C4C2×D17211yescharacteristic
678C22×C4C2×D17212yes—
679C22×C4C2×D17211yescharacteristic
680C22×C4C2×D17211yescharacteristic
681C22×C4C2×D17211yescharacteristic
682C22×C4C2×D17211yescharacteristic
683C22×C4C23×D4312yes—
684C22×C4C23×D4311yescharacteristic
685Q16—1724no—
686SD16—1724no—
687SD16—1724no—
688D8—1724no—
689M16—24no—
690M16—24no—
691M16—44no—
692C2×C8—44no—
693C2×C8C23×D4314yes—
694C2×C8C23×D4314yes—
695C4⋊C4—432no—
696C4⋊C4—432no—
697C4⋊C4—432no—
698C4⋊C4—432no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—862no—
702C4⋊C4—862no—
703C4⋊C4—864no—
704C4⋊C4—864no—
705C4⋊C4—862no—
706C4⋊C4—862no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—862no—
710C4⋊C4—862no—
711C4⋊C4—862no—
712C4⋊C4—862no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4C2×D17212yes—
716C4⋊C4C2×D17212yes—
717C4⋊C4C2×D17212yes—
718C4⋊C4C2×D17212yes—
719C22⋊C4—864no—
720C22⋊C4—862no—
721C22⋊C4—862no—
722C22⋊C4—862no—
723C22⋊C4—862no—
724C22⋊C4—862no—
725C22⋊C4—864no—
726C22⋊C4—864no—
727C22⋊C4—864no—
728C22⋊C4—862no—
729C22⋊C4—862no—
730C22⋊C4—862no—
731C22⋊C4—862no—
732C22⋊C4—862no—
733C22⋊C4—862no—
734C22⋊C4C2×D17212yes—
735C22⋊C4C2×D17212yes—
736C22⋊C4C2×D17212yes—
737C22⋊C4C2×D17212yes—
738C42—862no—
739C42—862no—
740C42—862no—
741C42—862no—
742C42—862no—
743C42C2×D17212yes—
744C42C2×D17211yescharacteristic
745C42C2×D17211yescharacteristic
746C42C23×D4311yescharacteristic
747C42C23×D4312yes—
748C42C23×D4311yescharacteristic
749C23—22no—
750C23—41no—
751C23—41no—
752C23—862no—
753C23—862no—
754C23—1722no—
755C23—1722no—
756C23—1722no—
757C23C22×D17212yes—
758C23C22×D17211yescharacteristic
759Q8—862no—
760Q8—862no—
761Q8—862no—
762Q8—862no—
763Q8—3444no—
764Q8—3441no—
765Q8—3441no—
766Q8—1722no—
767D4—862no—
768D4—862no—
769D4—862no—
770D4—862no—
771D4—3441no—
772D4—3441no—
773D4—3444no—
774D4—3442no—
775D4—3442no—
776D4—1724no—
777D4—1722no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—862no—
790C2×C4—862no—
791C2×C4—862no—
792C2×C4—3442no—
793C2×C4—3442no—
794C2×C4—3442no—
795C2×C4—3442no—
796C2×C4—1722no—
797C2×C4—1722no—
798C2×C4—1722no—
799C2×C4—1724no—
800C2×C4C22×D17211yescharacteristic
801C2×C4C22×D17211yescharacteristic
802C2×C4C22×D17212yes—
803C2×C4C22×D17212yes—
804C2×C4C22×D17211yescharacteristic
805C2×C4C22×D17211yescharacteristic
806C2×C4C22×D17212yes—
807C2×C4C22×D17211yescharacteristic
808C2×C4#1306337012yes—
809C2×C4#1306337312yes—
810C2×C4C24×D4311yescharacteristic
811C8—24no—
812C8—24no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—82no—
819C22—3444no—
820C22—1722no—
821C22—1722no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22—1722no—
826C22#1458348012yes—
827C22C23×D17211yescharacteristic
828C4—21no—
829C4—21no—
830C4—22no—
831C4—22no—
832C4—21no—
833C4—21no—
834C4—22no—
835C4—1722no—
836C4—1722no—
837C4—1722no—
838C4—1722no—
839C4—1722no—
840C4—1722no—
841C4#1458348012yes—
842C4C2×#1306337011yescharacteristic
843C4C2×#1306337311yescharacteristic
844C2—22no—
845C2—42no—
846C2—3442no—
847C2—3442no—
848C2C2×#1458348011yescharacteristic
849C2#1914937611yescharacteristic
850C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2905C2
socleC22×C43C23×D4
hypercenter#2905D43
hypocenterC43#60919
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2905

Complements

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

NH ≅ G/Ntype
1. #19147985C2semidirect
2. C2×#14583520C2semidirect
3. #19146066C2semidirect
4. #19146056C2semidirect
5. #19146023C2semidirect
6. #19146008C2semidirect
7. #19144411C2semidirect
8. #19144402C2semidirect
9. #19144394C2semidirect
10. #19144225C2semidirect
11. #19144214C2semidirect
12. #19144090C2semidirect
13. #19144069C2semidirect
14. #19144061C2semidirect
15. C43×#2905C2semidirect
22. #14583520C22semidirect
23. #14583520C22semidirect
24. #14583511C22semidirect
25. #14583504C22semidirect
46. #14583207C22semidirect
47. #14583200C22semidirect
48. #14583195C22semidirect
49. #14583195C22semidirect
50. #14583190C22semidirect
51. #14583190C22semidirect
52. #14583185C22semidirect
53. #14583185C22semidirect
54. #14583180C22semidirect
55. #14583180C22semidirect
56. #14583157C22semidirect
59. #14583145C22semidirect
60. #14583140C22semidirect
63. #14583128C22semidirect
64. #14583122C22semidirect
65. #14583122C22semidirect
66. #14583122C22semidirect
67. #14583115C22semidirect
68. #14583115C22semidirect
69. #14583115C22semidirect
70. #14583110C22semidirect
71. #14583105C22semidirect
72. #14583100C22semidirect
73. #14583095C22semidirect
82. C43×#424C22semidirect
83. C43×#424C22semidirect
433. #2905D43semidirect
503. #424C2×D43semidirect
504. #424C2×D43semidirect
512. C43#60919semidirect

Maximal subgroups

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

subgroupindex
#191479852
C2×#145835202
#191460662
#191460562
#191460232
#191460082
#191444112
#191444022
#191443942
#191442252
#191442142
#191440902
#191440692
#191440612
C43×#29052
#6091943