Finite Group Databasebeta

← #25097893

Subgroups — #25097893

Order 11008.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583696C211yesmaximal, characteristic
2C2×#14583664C211yesmaximal, characteristic, complemented
3C2×#104×D43C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5#19143037C211yesmaximal, characteristic, complemented
6#19134925C211yesmaximal, characteristic, complemented
7#19134924C211yesmaximal, characteristic, complemented
8#19134923C211yesmaximal, characteristic, complemented
9#19134922C211yesmaximal, characteristic, complemented
10#19134921C211yesmaximal, characteristic, complemented
11#19134920C211yesmaximal, characteristic, complemented
12#19134919C211yesmaximal, characteristic, complemented
13#19134320C211yesmaximal, characteristic, complemented
14#19134287C211yesmaximal, characteristic, complemented
15C43×#1876C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#41×D43C2211yescharacteristic
18#14583696—24no—
19#14583696—24no—
20C2×#13063357C411yescharacteristic, complemented
21C2×#13063357C411yescharacteristic, complemented
22C2×#13063354C411yescharacteristic, complemented
23C2×#13063354C411yescharacteristic, complemented
24C2×#13063352C411yescharacteristic, complemented
25C2×#13063352C411yescharacteristic, complemented
26C2×#13063349C411yescharacteristic, complemented
27C2×#13063349C411yescharacteristic, complemented
28C2×#13063347C2211yescharacteristic
29C2×#13063345C2211yescharacteristic
30C2×#13063345C2211yescharacteristic
31#14583664—24no—
32#14583664—24no—
33C2×#13063333—21no—
34C2×#13063333C2211yescharacteristic, complemented
35C2×#13063332C2211yescharacteristic, complemented
36C2×#13063331—21no—
37C2×#13063331C2211yescharacteristic, complemented
38C22×#10621872—21no—
39C22×#10621872C2211yescharacteristic
40C22×#10621872C2211yescharacteristic
41C2×M16×D43—21no—
42C2×M16×D43C2211yescharacteristic
43C2×M16×D43C2211yescharacteristic
44C2×C42×D43C2211yescharacteristic
45C2×#13063253C2211yescharacteristic, complemented
46C2×#13063253C2211yescharacteristic, complemented
47C2×#13063252C2211yescharacteristic, complemented
48C2×#13063252C2211yescharacteristic, complemented
49C2×#13063251C2211yescharacteristic, complemented
50C2×#13063251C2211yescharacteristic, complemented
51#104×D43—24no—
52#104×D43—24no—
53#14582867C2211yescharacteristic, complemented
54#14582866C2211yescharacteristic, complemented
55#14582865C2211yescharacteristic, complemented
56#14582864—21no—
57#14582864—21no—
58#14582861—21no—
59#14582861—21no—
60#14582664C2211yescharacteristic, complemented
61#14582663C2211yescharacteristic, complemented
62#14582663C2211yescharacteristic, complemented
63#14582654C2211yescharacteristic, complemented
64#14582653C2211yescharacteristic, complemented
65#14582653C2211yescharacteristic, complemented
66C2×#135×C43C2211yescharacteristic
67C2×#131×C43C2211yescharacteristic, complemented
68C2×#104×C43C2211yescharacteristic, complemented
69C2×#104×C43C2211yescharacteristic, complemented
70C43×#408C2211yescharacteristic, complemented
71C43×#341C2211yescharacteristic, complemented
72C43×#336C2211yescharacteristic, complemented
73C2×#10621902C2×C411yescharacteristic
74C2×#10621902C2×C411yescharacteristic
75C2×#10621898—21no—
76C2×#10621898—21no—
77C2×#10621898C2311yescharacteristic
78C2×#10621898C2311yescharacteristic
79C2×#10621900—21no—
80C2×#10621900—21no—
81C2×#10621900C2×C411yescharacteristic
82C2×#10621900C2×C411yescharacteristic
83#41×D43—22no—
84#41×D43—22no—
85#41×D43—22no—
86#41×D43—22no—
87#41×D43—22no—
88#41×D43—22no—
89#41×D43D414yes—
90#41×D43D414yes—
91C2×Q8×D43C2×C411yescharacteristic
92C2×Q8×D43C2×C411yescharacteristic
93C2×D4×D43—21no—
94C2×D4×D43—21no—
95C2×D4×D43C2×C411yescharacteristic
96C2×D4×D43C2×C411yescharacteristic
97C22×C4×D43—21no—
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43C2311yescharacteristic
101#13063357—24no—
102#13063357—24no—
103#13063354—24no—
104#13063354—24no—
105#13063352—24no—
106#13063352—24no—
107#13063349—24no—
108#13063349—24no—
109#13063347—22no—
110#13063347—22no—
111#13063345—22no—
112#13063345—22no—
113#13063345—22no—
114#13063345—22no—
115C2×Dic172C2×C411yescharacteristic, complemented
116C2×#10621885C2×C411yescharacteristic, complemented
117C2×#10621885C2×C411yescharacteristic, complemented
118C2×#10621873C2×C411yescharacteristic, complemented
119C2×#10621873C2×C411yescharacteristic, complemented
120C2×#10621883C2×C411yescharacteristic, complemented
121C2×#10621883C2×C411yescharacteristic, complemented
122C2×#10621884C2×C411yescharacteristic, complemented
123C2×#10621884C2×C411yescharacteristic, complemented
124C2×D344C2×C411yescharacteristic, complemented
125C2×#10621882C2×C411yescharacteristic, complemented
126C2×#10621882C2×C411yescharacteristic, complemented
127#13063333—28no—
128#13063333—22no—
129#13063333—22no—
130#13063332—22no—
131#13063332—22no—
132#13063331—28no—
133#13063331—22no—
134#13063331—22no—
135C2×#10621877—21no—
136C2×#10621877C2311yescharacteristic
137C2×#10621877C2311yescharacteristic
138C2×#10621872—28no—
139C2×#10621872—21no—
140C2×#10621872—22no—
141C2×#10621872—22no—
142C2×#10621872—22no—
143C2×#10621872—22no—
144C2×#10621872—21no—
145C2×#10621872—21no—
146C2×#10621872—21no—
147C2×#10621872C2×C411yescharacteristic
148C2×#10621872C2×C411yescharacteristic
149C2×#10621872C2×C411yescharacteristic
150C2×#10621872C2×C411yescharacteristic
151C2×#10621872D411yescharacteristic
152C2×#10621872D411yescharacteristic
153C2×#10621872D411yescharacteristic
154C2×#10621872D411yescharacteristic
155M16×D43—28no—
156M16×D43—22no—
157M16×D43—22no—
158M16×D43—22no—
159M16×D43D414yes—
160C22×C43⋊C8—21no—
161C22×C43⋊C8C2311yescharacteristic
162C22×C43⋊C8C2311yescharacteristic
163C2×C8×D43—21no—
164C2×C8×D43—21no—
165C2×C8×D43—21no—
166C2×C8×D43—21no—
167C2×C4×Dic43—21no—
168C2×C4×Dic43C2311yescharacteristic
169C42×D43—22no—
170C42×D43—22no—
171#13063253—22no—
172#13063253—22no—
173#13063252—22no—
174#13063252—22no—
175#13063251—22no—
176#13063251—22no—
177C22⋊(C43⋊C8)—21no—
178C22⋊(C43⋊C8)—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182(C2×D43)⋊C8—21no—
183C2×#41×C43C2311yescharacteristic
184C2×#41×C43C2311yescharacteristic
185#135×C43—22no—
186#135×C43—22no—
187C2×Q16×C43C2×C411yescharacteristic, complemented
188C2×SD16×C43C2×C411yescharacteristic, complemented
189C2×SD16×C43C2×C411yescharacteristic, complemented
190C2×D8×C43C2×C411yescharacteristic, complemented
191#131×C43—22no—
192#131×C43—22no—
193C2×M16×C43—21no—
194C2×M16×C43C2311yescharacteristic
195C2×M16×C43C2311yescharacteristic
196C22×C8×C43—21no—
197C22×C8×C43C2311yescharacteristic
198C22×C8×C43C2311yescharacteristic
199C2×C42×C43C2311yescharacteristic
200#104×C43—22no—
201#104×C43—22no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43—21no—
204C23×D43—21no—
205C23×D43—21no—
206C23×D43#4111yescharacteristic
207#41×C43—21no—
208#41×C43—21no—
209#41×C43—21no—
210#41×C43—21no—
211#41×C43—21no—
212#41×C43—21no—
213#41×C43C2×D412yes—
214#41×C43C2×D412yes—
215C2×Q8×C43C22×C411yescharacteristic
216C2×Q8×C43C22×C411yescharacteristic
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43C22×C411yescharacteristic
220C2×D4×C43C22×C411yescharacteristic
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43#4111yescharacteristic
235#10621902—22no—
236#10621902—22no—
237#10621902—22no—
238#10621902C22⋊C414yes—
239Q8×D43—22no—
240Q8×D43—22no—
241Q8×D43—22no—
242Q8×D43C22⋊C414yes—
243#10621900—24no—
244#10621900—24no—
245#10621900—22no—
246#10621900—22no—
247#10621900—22no—
248#10621900—42no—
249#10621900—42no—
250#10621900C22⋊C414yes—
251D4×D43—22no—
252D4×D43—24no—
253D4×D43—24no—
254D4×D43—22no—
255D4×D43—22no—
256D4×D43—42no—
257D4×D43—42no—
258D4×D43C22⋊C414yes—
259#10621898—21no—
260#10621898—21no—
261#10621898—24no—
262#10621898—24no—
263#10621898—21no—
264#10621898—21no—
265#10621898—21no—
266#10621898—21no—
267#10621898—42no—
268#10621898—42no—
269#10621898C2×D412yes—
270#10621898C2×D412yes—
271C2×D172—21no—
272C2×D172—21no—
273C2×D172C22×C411yescharacteristic
274C2×D172C22×C411yescharacteristic
275C2×C4×D43—21no—
276C2×C4×D43—21no—
277C2×C4×D43—24no—
278C2×C4×D43—24no—
279C2×C4×D43—21no—
280C2×C4×D43—21no—
281C2×C4×D43—21no—
282C2×C4×D43—21no—
283C2×C4×D43—42no—
284C2×C4×D43—42no—
285C2×C4×D43—42no—
286C2×C4×D43—42no—
287C2×C4×D43—42no—
288C2×C4×D43C22×C411yescharacteristic
289C2×C4×D43C22×C411yescharacteristic
290C2×C4×D43C2×D411yescharacteristic
291C2×C4×D43C2×D411yescharacteristic
292C2×C4×D43C2×D412yes—
293C2×C4×D43C2×D412yes—
294C2×C4×D43C2×D412yes—
295C2×C4×D43#4112yes—
296C2×Dic86—21no—
297C2×Dic86—21no—
298C2×Dic86C22×C411yescharacteristic
299C2×Dic86C22×C411yescharacteristic
300Q16×C43—22no—
301SD16×C43—22no—
302SD16×C43—22no—
303D8×C43—22no—
304M16×C43—24no—
305M16×C43—21no—
306M16×C43—21no—
307M16×C43—21no—
308M16×C43C2×D412yes—
309C2×C8×C43—24no—
310C2×C8×C43—21no—
311C2×C8×C43—21no—
312C2×C8×C43—21no—
313C2×C8×C43—21no—
314C2×C8×C43—21no—
315C2×C8×C43—21no—
316C2×C8×C43C22×C411yescharacteristic
317C2×C8×C43C22×C411yescharacteristic
318C2×C8×C43C2×D411yescharacteristic
319C2×C8×C43C2×D411yescharacteristic
320C42×C43—21no—
321C42×C43—21no—
322#10621885—22no—
323#10621885—22no—
324#10621884—22no—
325#10621884—22no—
326#10621883—22no—
327#10621883—22no—
328#10621882—22no—
329#10621882—22no—
330C4×Dic43—21no—
331C4×Dic43—21no—
332C4×Dic43—42no—
333#10621877—24no—
334#10621877—21no—
335#10621877—21no—
336#10621877—21no—
337#10621877C2×D412yes—
338C2×C43⋊C8—24no—
339C2×C43⋊C8—21no—
340C2×C43⋊C8—21no—
341C2×C43⋊C8—21no—
342C2×C43⋊C8—21no—
343C2×C43⋊C8—21no—
344C2×C43⋊C8—21no—
345C2×C43⋊C8C22×C411yescharacteristic
346C2×C43⋊C8C22×C411yescharacteristic
347C2×C43⋊C8C2×D411yescharacteristic
348C2×C43⋊C8C2×D411yescharacteristic
349Dic172—22no—
350D344—22no—
351#10621873—22no—
352#10621873—22no—
353#10621872—24no—
354#10621872—24no—
355#10621872—22no—
356#10621872—22no—
357#10621872—22no—
358#10621872—22no—
359#10621872—22no—
360#10621872—24no—
361#10621872—22no—
362#10621872—22no—
363#10621872—22no—
364#10621872—42no—
365C8×D43—24no—
366C8×D43—24no—
367C8×D43—24no—
368C8×D43—42no—
369C23×C43—21no—
370C23×C43—21no—
371C23×C43C2×#4111yescharacteristic
372C22×D43—21no—
373C22×D43—24no—
374C22×D43—21no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—42no—
378C22×D43—81no—
379C22×D43—81no—
380C22×D43—81no—
381C22×D43—81no—
382C22×D43C4×D411yescharacteristic
383C22×D43C4×D411yescharacteristic
384C22×D43#12112yes—
385C22×D43#12312yes—
386Q8×C43—21no—
387Q8×C43—21no—
388Q8×C43—21no—
389Q8×C43C2×C22⋊C412yes—
390D4×C43—22no—
391D4×C43—22no—
392D4×C43—21no—
393D4×C43—21no—
394D4×C43—21no—
395D4×C43—41no—
396D4×C43—41no—
397D4×C43C2×C22⋊C412yes—
398C2×C4×C43—21no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—21no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43C23×C411yescharacteristic
408C2×C4×C43C22×D411yescharacteristic
409C2×C4×C43C22×D411yescharacteristic
410C2×C4×C43C22×D411yescharacteristic
411C2×C4×C43C22×D411yescharacteristic
412C2×C4×C43C2×#4111yescharacteristic
413C22⋊D43—22no—
414C22⋊D43—22no—
415C22⋊D43—24no—
416C22⋊D43—24no—
417C22⋊D43—41no—
418C22⋊D43—41no—
419C22⋊D43—42no—
420C22⋊D43—42no—
421C2×Dic43—21no—
422C2×Dic43—24no—
423C2×Dic43—22no—
424C2×Dic43—21no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43—42no—
428C2×Dic43C4×D411yescharacteristic
429C2×Dic43C4×D411yescharacteristic
430C2×Dic43#12112yes—
431C2×Dic43#12312yes—
432D172—24no—
433D172—21no—
434D172—21no—
435D172—21no—
436D172—42no—
437D172C2×C22⋊C412yes—
438C4×D43—24no—
439C4×D43—22no—
440C4×D43—22no—
441C4×D43—24no—
442C4×D43—48no—
443C4×D43—42no—
444C4×D43—41no—
445C4×D43—41no—
446C4×D43—42no—
447C4×D43C2×C22⋊C412yes—
448C4×D43C2×C22⋊C412yes—
449C4×D43C4×D412yes—
450C4×D43C4×D412yes—
451C4×D43#12012yes—
452C4×D43#12012yes—
453C4×D43#12112yes—
454C4×D43#12112yes—
455Dic86—21no—
456Dic86—24no—
457Dic86—21no—
458Dic86—21no—
459Dic86—42no—
460Dic86C2×C22⋊C412yes—
461C8×C43—21no—
462C8×C43—21no—
463C8×C43—22no—
464C8×C43—21no—
465C8×C43—21no—
466C8×C43—41no—
467C43⋊C8—21no—
468C43⋊C8—21no—
469C43⋊C8—22no—
470C43⋊C8—21no—
471C43⋊C8—21no—
472C43⋊C8—41no—
473#20918—431nomaximal, Sylow
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—22no—
477C22×C43—41no—
478C22×C43—41no—
479C22×C43—41no—
480C22×C43—41no—
481C22×C43—41no—
482C22×C43C2×C4×D411yescharacteristic
483C22×C43C2×#12111yescharacteristic
484C22×C43C2×#12311yescharacteristic
485C2×D43—21no—
486C2×D43—21no—
487C2×D43—21no—
488C2×D43—21no—
489C2×D43—22no—
490C2×D43—42no—
491C2×D43—42no—
492C2×D43—41no—
493C2×D43—41no—
494C2×D43—41no—
495C2×D43—41no—
496C2×D43—41no—
497C2×D43—84no—
498C2×D43—84no—
499C2×D43#38612yes—
500C2×D43#38612yes—
501C4×C43—22no—
502C4×C43—42no—
503C4×C43—41no—
504C4×C43C22×C22⋊C411yescharacteristic
505C4×C43C2×C4×D411yescharacteristic
506C4×C43C2×#12011yescharacteristic
507C4×C43C2×#12111yescharacteristic
508Dic43—22no—
509Dic43—42no—
510Dic43—41no—
511Dic43#38612yes—
512Dic43#38612yes—
513C2×#575—431no—
514C2×#568—431no—
515C22×#104—431no—
516C22×#104—431no—
517#2879—431no—
518#1876—431no—
519#1876—431no—
520#1876—431no—
521#1876—431no—
522#1876—431no—
523#1876—431no—
524#1876—431no—
525#1876D4311yescharacteristic, complemented
526#1738—431no—
527#1728—431no—
528C2×C43—21no—
529C2×C43—21no—
530C2×C43—42no—
531C2×C43—81no—
532C2×C43C2×#38611yescharacteristic
533C2×C43#295611yescharacteristic
534C2×C43#295611yescharacteristic
535D43—22no—
536D43—22no—
537D43—42no—
538D43—81no—
539C22×#41—431no—
540C22×#41—431no—
541#575—864no—
542#575—864no—
543C2×#137—431no—
544C2×#137—431no—
545C2×#137—431no—
546C2×#137—431no—
547C2×AGL(1,ℤ/8)—431no—
548C2×AGL(1,ℤ/8)—431no—
549C2×AGL(1,ℤ/8)—431no—
550C2×AGL(1,ℤ/8)—431no—
551C2×#135—431no—
552C2×#135—431no—
553C2×#135—431no—
554C2×#135C2×D4311yescharacteristic
555#568—864no—
556#568—864no—
557C2×#131—431no—
558C2×#131—431no—
559C2×#131—431no—
560C2×#131—861no—
561C2×#131—861no—
562C2×#131C2×D4311yescharacteristic, complemented
563C22×M16—431no—
564C22×M16—431no—
565C22×M16—431no—
566C22×M16—431no—
567C22×M16—861no—
568C22×M16—861no—
569C22×C42—431no—
570C2×#104—431no—
571C2×#104—431no—
572C2×#104—431no—
573C2×#104—431no—
574C2×#104—431no—
575C2×#104—431no—
576C2×#104—864no—
577C2×#104—864no—
578C2×#104C2×D4311yescharacteristic, complemented
579C2×#104C2×D4311yescharacteristic, complemented
580#408—431no—
581#408—431no—
582#408—431no—
583#408—861no—
584#408—861no—
585#408C2×D4311yescharacteristic, complemented
586#407—861no—
587#407—861no—
588#341—431no—
589#341—431no—
590#341—431no—
591#341C2×D4311yescharacteristic, complemented
592#336—431no—
593#336—431no—
594#336—431no—
595#336C2×D4311yescharacteristic, complemented
596C43#2091811yescharacteristic, complemented, Sylow
597C2×#41—434no—
598C2×#41—434no—
599C2×#41—431no—
600C2×#41—431no—
601C2×#41—431no—
602C2×#41—431no—
603C2×#41—431no—
604C2×#41—431no—
605C2×#41—861no—
606C2×#41—861no—
607C2×#41—861no—
608C2×#41—861no—
609C2×#41—862no—
610C2×#41—862no—
611C2×#41—862no—
612C2×#41—862no—
613C2×#41—862no—
614C2×#41—862no—
615C2×#41C22×D4311yescharacteristic
616C2×#41C22×D4311yescharacteristic
617C22×Q8—431no—
618C22×Q8—431no—
619C22×D4—431no—
620C22×D4—431no—
621C22×D4—861no—
622C22×D4—861no—
623C23×C4—431no—
624C23×C4—861no—
625C23×C4—861no—
626C23×C4—861no—
627#137—864no—
628#137—864no—
629#137—864no—
630#137—864no—
631AGL(1,ℤ/8)—864no—
632AGL(1,ℤ/8)—864no—
633AGL(1,ℤ/8)—864no—
634AGL(1,ℤ/8)—864no—
635#135—22no—
636#135—22no—
637#135—862no—
638#135—862no—
639#135—862no—
640#135—862no—
641#135—862no—
642#135—862no—
643C2×Q16—431no—
644C2×Q16—431no—
645C2×Q16—431no—
646C2×Q16C4×D4311yescharacteristic, complemented
647C2×SD16—431no—
648C2×SD16—431no—
649C2×SD16—431no—
650C2×SD16—431no—
651C2×SD16—431no—
652C2×SD16—431no—
653C2×SD16C4×D4311yescharacteristic, complemented
654C2×SD16C4×D4311yescharacteristic, complemented
655C2×D8—431no—
656C2×D8—431no—
657C2×D8—431no—
658C2×D8C4×D4311yescharacteristic, complemented
659#131—22no—
660#131—22no—
661#131—862no—
662#131—862no—
663#131—868no—
664#131—862no—
665#131—868no—
666#131—862no—
667#131—862no—
668#131—862no—
669C2×M16—21no—
670C2×M16—431no—
671C2×M16—431no—
672C2×M16—431no—
673C2×M16—431no—
674C2×M16—431no—
675C2×M16—431no—
676C2×M16—431no—
677C2×M16—431no—
678C2×M16—431no—
679C2×M16—434no—
680C2×M16—431no—
681C2×M16—861no—
682C2×M16—861no—
683C2×M16—862no—
684C2×M16—862no—
685C2×M16—862no—
686C2×M16—862no—
687C2×M16—868no—
688C2×M16—861no—
689C2×M16—861no—
690C2×M16—862no—
691C2×M16—868no—
692C2×M16—861no—
693C2×M16—862no—
694C2×M16—862no—
695C2×M16C22×D4311yescharacteristic
696C2×M16C22×D4311yescharacteristic
697C22×C8—21no—
698C22×C8—431no—
699C22×C8—431no—
700C22×C8—861no—
701C22×C8—861no—
702C22×C8—861no—
703C22×C8—861no—
704C22×C8—861no—
705C22×C8C22×D4311yescharacteristic
706C22×C8C22×D4311yescharacteristic
707C2×C42—431no—
708C2×C42—862no—
709C2×C42—862no—
710C2×C42—861no—
711C2×C42C22×D4311yescharacteristic
712#104—22no—
713#104—22no—
714#104—862no—
715#104—862no—
716#104—862no—
717#104—862no—
718#104—862no—
719#104—862no—
720C22⋊C8—21no—
721C22⋊C8—21no—
722C22⋊C8—861no—
723C22⋊C8—861no—
724C22⋊C8—861no—
725C22⋊C8—861no—
726C22⋊C8—861no—
727C22⋊C8—861no—
728C24—431no—
729C24—861no—
730C24—861no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—434no—
738#41—434no—
739#41—432no—
740#41—432no—
741#41—864no—
742#41—864no—
743#41—864no—
744#41—864no—
745#41—862no—
746#41—862no—
747#41—862no—
748#41—862no—
749#41—862no—
750#41—862no—
751#41—861no—
752#41—861no—
753#41—861no—
754#41—861no—
755#41—861no—
756#41—861no—
757#41—1722no—
758#41—1722no—
759#41—1722no—
760#41—1722no—
761#41D4×D4312yes—
762#41D4×D4312yes—
763C2×Q8—434no—
764C2×Q8—431no—
765C2×Q8—431no—
766C2×Q8—861no—
767C2×Q8—861no—
768C2×Q8—862no—
769C2×Q8—862no—
770C2×Q8—862no—
771C2×Q8C2×C4×D4311yescharacteristic
772C2×Q8C2×C4×D4311yescharacteristic
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—434no—
776C2×D4—431no—
777C2×D4—431no—
778C2×D4—861no—
779C2×D4—861no—
780C2×D4—862no—
781C2×D4—862no—
782C2×D4—862no—
783C2×D4—861no—
784C2×D4—861no—
785C2×D4—864no—
786C2×D4—864no—
787C2×D4—861no—
788C2×D4—861no—
789C2×D4—861no—
790C2×D4—861no—
791C2×D4—1722no—
792C2×D4—1722no—
793C2×D4C2×C4×D4311yescharacteristic
794C2×D4C2×C4×D4311yescharacteristic
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—431no—
799C22×C4—431no—
800C22×C4—431no—
801C22×C4—432no—
802C22×C4—432no—
803C22×C4—432no—
804C22×C4—431no—
805C22×C4—431no—
806C22×C4—432no—
807C22×C4—864no—
808C22×C4—861no—
809C22×C4—864no—
810C22×C4—861no—
811C22×C4—861no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—861no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—1722no—
819C22×C4—1722no—
820C22×C4—1722no—
821C22×C4—1722no—
822C22×C4—1722no—
823C22×C4C23×D4311yescharacteristic
824Q16—22no—
825Q16—862no—
826Q16—862no—
827Q16—862no—
828SD16—22no—
829SD16—22no—
830SD16—862no—
831SD16—862no—
832SD16—862no—
833SD16—862no—
834SD16—862no—
835SD16—862no—
836D8—22no—
837D8—862no—
838D8—862no—
839D8—862no—
840M16—24no—
841M16—21no—
842M16—21no—
843M16—21no—
844M16—432no—
845M16—862no—
846M16—864no—
847M16—862no—
848M16—862no—
849M16—862no—
850M16—862no—
851M16—862no—
852M16—862no—
853M16—862no—
854M16—864no—
855M16—864no—
856M16—864no—
857M16—861no—
858M16—861no—
859M16—861no—
860M16—1722no—
861M16D4×D4312yes—
862C2×C8—24no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—431no—
870C2×C8—431no—
871C2×C8—431no—
872C2×C8—431no—
873C2×C8—864no—
874C2×C8—864no—
875C2×C8—864no—
876C2×C8—864no—
877C2×C8—861no—
878C2×C8—861no—
879C2×C8—861no—
880C2×C8—861no—
881C2×C8—861no—
882C2×C8—861no—
883C2×C8—1722no—
884C2×C8C2×C4×D4311yescharacteristic
885C2×C8C2×C4×D4311yescharacteristic
886C2×C8D4×D4311yescharacteristic
887C2×C8D4×D4311yescharacteristic
888C42—21no—
889C42—21no—
890C42—861no—
891C42—861no—
892C42—1722no—
893C23—21no—
894C23—21no—
895C23—431no—
896C23—431no—
897C23—432no—
898C23—432no—
899C23—864no—
900C23—861no—
901C23—861no—
902C23—3441no—
903C23—3441no—
904C23—3441no—
905C23—3441no—
906C23—1721no—
907C23—1721no—
908C23—1722no—
909C23#41×D4311yescharacteristic
910Q8—21no—
911Q8—21no—
912Q8—21no—
913Q8—432no—
914Q8—864no—
915Q8—861no—
916Q8—861no—
917Q8—861no—
918Q8—1722no—
919Q8C22⋊C4×D4312yes—
920D4—22no—
921D4—22no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—41no—
926D4—41no—
927D4—432no—
928D4—864no—
929D4—864no—
930D4—864no—
931D4—862no—
932D4—862no—
933D4—861no—
934D4—861no—
935D4—861no—
936D4—1722no—
937D4—1722no—
938D4—1722no—
939D4—1721no—
940D4—1721no—
941D4C22⋊C4×D4312yes—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—431no—
952C2×C4—431no—
953C2×C4—432no—
954C2×C4—432no—
955C2×C4—432no—
956C2×C4—432no—
957C2×C4—432no—
958C2×C4—432no—
959C2×C4—432no—
960C2×C4—432no—
961C2×C4—432no—
962C2×C4—432no—
963C2×C4—864no—
964C2×C4—864no—
965C2×C4—864no—
966C2×C4—861no—
967C2×C4—862no—
968C2×C4—862no—
969C2×C4—862no—
970C2×C4—861no—
971C2×C4—1722no—
972C2×C4—1722no—
973C2×C4—1728no—
974C2×C4—1722no—
975C2×C4—1721no—
976C2×C4—1721no—
977C2×C4—1721no—
978C2×C4—1721no—
979C2×C4C22×C4×D4311yescharacteristic
980C2×C4C2×D4×D4311yescharacteristic
981C2×C4C2×D4×D4311yescharacteristic
982C2×C4C2×D4×D4311yescharacteristic
983C2×C4C2×D4×D4311yescharacteristic
984C2×C4#41×D4311yescharacteristic
985C8—21no—
986C8—21no—
987C8—21no—
988C8—22no—
989C8—21no—
990C8—41no—
991C8—861no—
992C8—861no—
993C8—861no—
994C8—861no—
995C8—862no—
996C8—1721no—
997C22—21no—
998C22—21no—
999C22—22no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—41no—
1005C22—432no—
1006C22—432no—
1007C22—861no—
1008C22—861no—
1009C22—861no—
1010C22—861no—
1011C22—862no—
1012C22—3444no—
1013C22—3444no—
1014C22—1722no—
1015C22—1722no—
1016C22—1721no—
1017C22—1721no—
1018C22—1721no—
1019C22—1721no—
1020C22—1721no—
1021C22C4×D4×D4311yescharacteristic
1022C22#121×D4311yescharacteristic
1023C22#123×D4311yescharacteristic
1024C4—22no—
1025C4—42no—
1026C4—41no—
1027C4—432no—
1028C4—432no—
1029C4—862no—
1030C4—1722no—
1031C4—1721no—
1032C4C2×C22⋊C4×D4311yescharacteristic
1033C4C4×D4×D4311yescharacteristic
1034C4#120×D4311yescharacteristic
1035C4#121×D4311yescharacteristic
1036C2—21no—
1037C2—21no—
1038C2—42no—
1039C2—81no—
1040C2—862no—
1041C2—862no—
1042C2—3441no—
1043C2—1722no—
1044C2#386×D4311yescharacteristic
1045C2#1914350011yescharacteristic
1046C2#1914350311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1876C2
socleC22×C43C2×C4×D4
prime radicalC2×#14583696C2
cosocleC22×C4×C43C24
hypercenter#1876D43
hypocenterC43#20918
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. C2×#14583664C2semidirect
3. C2×#104×D43C2semidirect
4. C2×#104×D43C2semidirect
5. #19143037C2semidirect
6. #19134925C2semidirect
7. #19134924C2semidirect
8. #19134923C2semidirect
9. #19134922C2semidirect
10. #19134921C2semidirect
11. #19134920C2semidirect
12. #19134919C2semidirect
13. #19134320C2semidirect
14. #19134287C2semidirect
15. C43×#1876C2semidirect
20. C2×#13063357C4semidirect
21. C2×#13063357C4semidirect
22. C2×#13063354C4semidirect
23. C2×#13063354C4semidirect
24. C2×#13063352C4semidirect
25. C2×#13063352C4semidirect
26. C2×#13063349C4semidirect
27. C2×#13063349C4semidirect
34. C2×#13063333C22semidirect
35. C2×#13063332C22semidirect
37. C2×#13063331C22semidirect
45. C2×#13063253C22semidirect
46. C2×#13063253C22semidirect
47. C2×#13063252C22semidirect
48. C2×#13063252C22semidirect
49. C2×#13063251C22semidirect
50. C2×#13063251C22semidirect
53. #14582867C22semidirect
54. #14582866C22semidirect
55. #14582865C22semidirect
60. #14582664C22semidirect
61. #14582663C22semidirect
62. #14582663C22semidirect
63. #14582654C22semidirect
64. #14582653C22semidirect
65. #14582653C22semidirect
67. C2×#131×C43C22semidirect
68. C2×#104×C43C22semidirect
69. C2×#104×C43C22semidirect
70. C43×#408C22semidirect
71. C43×#341C22semidirect
72. C43×#336C22semidirect
115. C2×Dic172C2×C4semidirect
116. C2×#10621885C2×C4semidirect
117. C2×#10621885C2×C4semidirect
118. C2×#10621873C2×C4semidirect
119. C2×#10621873C2×C4semidirect
120. C2×#10621883C2×C4semidirect
121. C2×#10621883C2×C4semidirect
122. C2×#10621884C2×C4semidirect
123. C2×#10621884C2×C4semidirect
124. C2×D344C2×C4semidirect
125. C2×#10621882C2×C4semidirect
126. C2×#10621882C2×C4semidirect
187. C2×Q16×C43C2×C4semidirect
188. C2×SD16×C43C2×C4semidirect
189. C2×SD16×C43C2×C4semidirect
190. C2×D8×C43C2×C4semidirect
525. #1876D43semidirect
562. C2×#131C2×D43semidirect
578. C2×#104C2×D43semidirect
579. C2×#104C2×D43semidirect
585. #408C2×D43semidirect
591. #341C2×D43semidirect
595. #336C2×D43semidirect
596. C43#20918semidirect
646. C2×Q16C4×D43semidirect
653. C2×SD16C4×D43semidirect
654. C2×SD16C4×D43semidirect
658. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836962
C2×#145836642
C2×#104×D432
#191430372
#191349252
#191349242
#191349232
#191349222
#191349212
#191349202
#191349192
#191343202
#191342872
C43×#18762
#2091843