Finite Group Databasebeta

← #25097885

Subgroups — #25097885

Order 11008.

1698 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583696C211yesmaximal, characteristic
2C2×#131×D43C211yesmaximal, characteristic, complemented
3C2×#14582914C211yesmaximal, characteristic, complemented
4C2×#14582914C211yesmaximal, characteristic, complemented
5#408×D43C211yesmaximal, 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#19134290C211yesmaximal, 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
31C2×#13063333—21no—
32C2×#13063333C2211yescharacteristic, complemented
33C2×#13063332C2211yescharacteristic, complemented
34C2×#13063331—21no—
35C2×#13063331C2211yescharacteristic, complemented
36#131×D43—24no—
37#131×D43—24no—
38C22×#10621872C2211yescharacteristic
39C2×M16×D43—21no—
40C2×M16×D43C2211yescharacteristic
41C2×M16×D43C2211yescharacteristic
42C22×C8×D43—21no—
43C22×C8×D43C2211yescharacteristic
44C2×#13063282C2211yescharacteristic
45#14582914—24no—
46#14582914—24no—
47C2×#13063253C2211yescharacteristic, complemented
48C2×#13063253C2211yescharacteristic, complemented
49C2×#13063252C2211yescharacteristic, complemented
50C2×#13063252C2211yescharacteristic, complemented
51C2×#13063251C2211yescharacteristic, complemented
52C2×#13063251C2211yescharacteristic, complemented
53#14582867C2211yescharacteristic, complemented
54#14582866C2211yescharacteristic, complemented
55#14582865C2211yescharacteristic, complemented
56#14582864—21no—
57#14582864—21no—
58C22⋊C8×D43—21no—
59C22⋊C8×D43—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×D43C2311yescharacteristic
100#13063357—24no—
101#13063357—24no—
102#13063354—24no—
103#13063354—24no—
104#13063352—24no—
105#13063352—24no—
106#13063349—24no—
107#13063349—24no—
108#13063347—22no—
109#13063347—22no—
110#13063345—22no—
111#13063345—22no—
112#13063345—22no—
113#13063345—22no—
114C2×Dic172C2×C411yescharacteristic
115C2×#10621885C2×C411yescharacteristic
116C2×#10621885C2×C411yescharacteristic
117C2×#10621873C2×C411yescharacteristic
118C2×#10621873C2×C411yescharacteristic
119C2×#10621883C2×C411yescharacteristic
120C2×#10621883C2×C411yescharacteristic
121C2×#10621884C2×C411yescharacteristic
122C2×#10621884C2×C411yescharacteristic
123C2×D344C2×C411yescharacteristic
124C2×#10621882C2×C411yescharacteristic
125C2×#10621882C2×C411yescharacteristic
126#13063333—28no—
127#13063333—22no—
128#13063333—22no—
129#13063332—22no—
130#13063332—22no—
131#13063331—28no—
132#13063331—22no—
133#13063331—22no—
134C2×#10621877—21no—
135C2×#10621877C2311yescharacteristic
136C2×#10621877C2311yescharacteristic
137C2×#10621872—21no—
138C2×#10621872—22no—
139C2×#10621872—22no—
140C2×#10621872—21no—
141C2×#10621872—21no—
142C2×#10621872—21no—
143C2×#10621872C2×C411yescharacteristic
144C2×#10621872C2×C411yescharacteristic
145C2×#10621872C2×C411yescharacteristic
146C2×#10621872C2×C411yescharacteristic
147M16×D43—28no—
148M16×D43—22no—
149M16×D43—22no—
150M16×D43—22no—
151M16×D43D414yes—
152C22×C43⋊C8—21no—
153C22×C43⋊C8C2311yescharacteristic
154C22×C43⋊C8C2311yescharacteristic
155C2×C8×D43—28no—
156C2×C8×D43—21no—
157C2×C8×D43—22no—
158C2×C8×D43—22no—
159C2×C8×D43—21no—
160C2×C8×D43—21no—
161C2×C8×D43—21no—
162C2×C8×D43D411yescharacteristic
163C2×C8×D43D411yescharacteristic
164C2×C8×D43D411yescharacteristic
165C2×C8×D43D411yescharacteristic
166#13063282—22no—
167#13063282—22no—
168C2×Dic43⋊C4—21no—
169C2×(C2×D43)⋊C4—21no—
170C2×C4×Dic43C2311yescharacteristic
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
188C2×SD16×C43C2×C411yescharacteristic
189C2×SD16×C43C2×C411yescharacteristic
190C2×D8×C43C2×C411yescharacteristic
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×D43C22×C411yescharacteristic
286C2×C4×D43C22×C411yescharacteristic
287C2×C4×D43C2×D411yescharacteristic
288C2×C4×D43C2×D411yescharacteristic
289C2×C4×D43C2×D412yes—
290C2×C4×D43C2×D412yes—
291C2×C4×D43C2×D412yes—
292C2×C4×D43#4112yes—
293C2×Dic86—21no—
294C2×Dic86—21no—
295C2×Dic86C22×C411yescharacteristic
296C2×Dic86C22×C411yescharacteristic
297Q16×C43—22no—
298SD16×C43—22no—
299SD16×C43—22no—
300D8×C43—22no—
301M16×C43—24no—
302M16×C43—21no—
303M16×C43—21no—
304M16×C43—21no—
305M16×C43C2×D412yes—
306C2×C8×C43—24no—
307C2×C8×C43—21no—
308C2×C8×C43—21no—
309C2×C8×C43—21no—
310C2×C8×C43—21no—
311C2×C8×C43—21no—
312C2×C8×C43—21no—
313C2×C8×C43C22×C411yescharacteristic
314C2×C8×C43C22×C411yescharacteristic
315C2×C8×C43C2×D411yescharacteristic
316C2×C8×C43C2×D411yescharacteristic
317C42×C43—21no—
318C42×C43—21no—
319#10621885—22no—
320#10621885—22no—
321#10621884—22no—
322#10621884—22no—
323#10621883—22no—
324#10621883—22no—
325#10621882—22no—
326#10621882—22no—
327(C2×D43)⋊C4—42no—
328Dic43⋊C4—42no—
329C4×Dic43—21no—
330C4×Dic43—21no—
331#10621877—24no—
332#10621877—21no—
333#10621877—21no—
334#10621877—21no—
335#10621877C2×D412yes—
336C2×C43⋊C8—24no—
337C2×C43⋊C8—21no—
338C2×C43⋊C8—21no—
339C2×C43⋊C8—21no—
340C2×C43⋊C8—21no—
341C2×C43⋊C8—21no—
342C2×C43⋊C8—21no—
343C2×C43⋊C8C22×C411yescharacteristic
344C2×C43⋊C8C22×C411yescharacteristic
345C2×C43⋊C8C2×D411yescharacteristic
346C2×C43⋊C8C2×D411yescharacteristic
347Dic172—22no—
348D344—22no—
349#10621873—22no—
350#10621873—22no—
351#10621872—24no—
352#10621872—24no—
353#10621872—22no—
354#10621872—22no—
355#10621872—22no—
356#10621872—22no—
357#10621872—24no—
358#10621872—42no—
359C8×D43—24no—
360C8×D43—24no—
361C8×D43—22no—
362C8×D43—24no—
363C8×D43—22no—
364C8×D43—22no—
365C8×D43—22no—
366C8×D43—42no—
367C23×C43—21no—
368C23×C43—21no—
369C23×C43C2×#4111yescharacteristic
370C22×D43—21no—
371C22×D43—24no—
372C22×D43—21no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—42no—
376C22×D43—42no—
377C22×D43—42no—
378C22×D43—42no—
379C22×D43—42no—
380C22×D43C4×D411yescharacteristic
381C22×D43C4×D411yescharacteristic
382C22×D43#12112yes—
383C22×D43#12312yes—
384Q8×C43—21no—
385Q8×C43—21no—
386Q8×C43—21no—
387Q8×C43C2×C22⋊C412yes—
388D4×C43—22no—
389D4×C43—22no—
390D4×C43—21no—
391D4×C43—21no—
392D4×C43—21no—
393D4×C43—41no—
394D4×C43—41no—
395D4×C43C2×C22⋊C412yes—
396C2×C4×C43—21no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—21no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43C23×C411yescharacteristic
406C2×C4×C43C22×D411yescharacteristic
407C2×C4×C43C22×D411yescharacteristic
408C2×C4×C43C22×D411yescharacteristic
409C2×C4×C43C22×D411yescharacteristic
410C2×C4×C43C2×#4111yescharacteristic
411C22⋊D43—22no—
412C22⋊D43—22no—
413C22⋊D43—24no—
414C22⋊D43—24no—
415C22⋊D43—41no—
416C22⋊D43—41no—
417C22⋊D43—42no—
418C22⋊D43—42no—
419C2×Dic43—21no—
420C2×Dic43—24no—
421C2×Dic43—21no—
422C2×Dic43—42no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43C4×D411yescharacteristic
427C2×Dic43C4×D411yescharacteristic
428C2×Dic43#12112yes—
429C2×Dic43#12312yes—
430D172—24no—
431D172—21no—
432D172—21no—
433D172—21no—
434D172—42no—
435D172C2×C22⋊C412yes—
436C4×D43—24no—
437C4×D43—22no—
438C4×D43—22no—
439C4×D43—24no—
440C4×D43—42no—
441C4×D43—41no—
442C4×D43—41no—
443C4×D43—42no—
444C4×D43C2×C22⋊C412yes—
445C4×D43C2×C22⋊C412yes—
446C4×D43C4×D412yes—
447C4×D43C4×D412yes—
448C4×D43#12012yes—
449C4×D43#12012yes—
450C4×D43#12112yes—
451C4×D43#12112yes—
452Dic86—21no—
453Dic86—24no—
454Dic86—21no—
455Dic86—21no—
456Dic86—42no—
457Dic86C2×C22⋊C412yes—
458C8×C43—21no—
459C8×C43—21no—
460C8×C43—21no—
461C8×C43—22no—
462C8×C43—21no—
463C8×C43—41no—
464C43⋊C8—21no—
465C43⋊C8—21no—
466C43⋊C8—21no—
467C43⋊C8—22no—
468C43⋊C8—21no—
469C43⋊C8—41no—
470#20917—431nomaximal, Sylow
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—22no—
474C22×C43—41no—
475C22×C43—41no—
476C22×C43—41no—
477C22×C43—41no—
478C22×C43—41no—
479C22×C43C2×C4×D411yescharacteristic
480C22×C43C2×#12111yescharacteristic
481C22×C43C2×#12311yescharacteristic
482C2×D43—21no—
483C2×D43—21no—
484C2×D43—21no—
485C2×D43—21no—
486C2×D43—22no—
487C2×D43—42no—
488C2×D43—42no—
489C2×D43—48no—
490C2×D43—41no—
491C2×D43—41no—
492C2×D43—41no—
493C2×D43—41no—
494C2×D43—41no—
495C2×D43—84no—
496C2×D43#38612yes—
497C2×D43#38612yes—
498C4×C43—22no—
499C4×C43—41no—
500C4×C43—81no—
501C4×C43C22×C22⋊C411yescharacteristic
502C4×C43C2×C4×D411yescharacteristic
503C4×C43C2×#12011yescharacteristic
504C4×C43C2×#12111yescharacteristic
505Dic43—22no—
506Dic43—41no—
507Dic43—81no—
508Dic43#38612yes—
509Dic43#38612yes—
510C2×#575—431no—
511C22×#131—431no—
512C2×#421—431no—
513C2×#421—431no—
514C2×#408—431no—
515#1876—431no—
516#1876—431no—
517#1876—431no—
518#1876—431no—
519#1876—431no—
520#1876—431no—
521#1876—431no—
522#1876D4311yescharacteristic, complemented
523#1738—431no—
524#1729—431no—
525C2×C43—21no—
526C2×C43—21no—
527C2×C43—42no—
528C2×C43—81no—
529C2×C43C2×#38611yescharacteristic
530C2×C43#295511yescharacteristic
531C2×C43#295511yescharacteristic
532D43—22no—
533D43—22no—
534D43—42no—
535D43—81no—
536C22×#41—431no—
537C22×#41—431no—
538#575—864no—
539#575—864no—
540C2×#137—431no—
541C2×#137—431no—
542C2×#137—431no—
543C2×#137—431no—
544C2×AGL(1,ℤ/8)—431no—
545C2×AGL(1,ℤ/8)—431no—
546C2×AGL(1,ℤ/8)—431no—
547C2×AGL(1,ℤ/8)—431no—
548C2×#135—431no—
549C2×#135—431no—
550C2×#135—431no—
551C2×#135C2×D4311yescharacteristic
552C2×#131—431no—
553C2×#131—431no—
554C2×#131—431no—
555C2×#131—861no—
556C2×#131—861no—
557C2×#131—864no—
558C2×#131—864no—
559C2×#131C2×D4311yescharacteristic, complemented
560C22×M16—431no—
561C22×M16—431no—
562C22×M16—431no—
563C22×M16—861no—
564C23×C8—431no—
565C23×C8—861no—
566C2×#117—431no—
567#421—864no—
568#421—864no—
569C2×#104—431no—
570C2×#104—431no—
571C2×#104—431no—
572C2×#104—431no—
573C2×#104—431no—
574C2×#104—431no—
575C2×#104C2×D4311yescharacteristic, complemented
576C2×#104C2×D4311yescharacteristic, complemented
577#408—431no—
578#408—431no—
579#408—431no—
580#408—861no—
581#408—861no—
582#408C2×D4311yescharacteristic, complemented
583C2×C22⋊C8—861no—
584C2×C22⋊C8—861no—
585#341—431no—
586#341—431no—
587#341—431no—
588#341C2×D4311yescharacteristic, complemented
589#336—431no—
590#336—431no—
591#336—431no—
592#336C2×D4311yescharacteristic, complemented
593C43#2091711yescharacteristic, complemented, Sylow
594C2×#41—434no—
595C2×#41—434no—
596C2×#41—431no—
597C2×#41—431no—
598C2×#41—431no—
599C2×#41—431no—
600C2×#41—431no—
601C2×#41—431no—
602C2×#41—861no—
603C2×#41—861no—
604C2×#41—861no—
605C2×#41—861no—
606C2×#41—862no—
607C2×#41—862no—
608C2×#41—862no—
609C2×#41—862no—
610C2×#41—862no—
611C2×#41—862no—
612C2×#41C22×D4311yescharacteristic
613C2×#41C22×D4311yescharacteristic
614C22×Q8—431no—
615C22×Q8—431no—
616C22×D4—431no—
617C22×D4—431no—
618C22×D4—861no—
619C22×D4—861no—
620C23×C4—431no—
621C23×C4—861no—
622C23×C4—861no—
623#137—864no—
624#137—864no—
625#137—864no—
626#137—864no—
627AGL(1,ℤ/8)—864no—
628AGL(1,ℤ/8)—864no—
629AGL(1,ℤ/8)—864no—
630AGL(1,ℤ/8)—864no—
631#135—22no—
632#135—22no—
633#135—862no—
634#135—862no—
635#135—862no—
636#135—862no—
637#135—862no—
638#135—862no—
639C2×Q16—431no—
640C2×Q16—431no—
641C2×Q16—431no—
642C2×Q16C4×D4311yescharacteristic
643C2×SD16—431no—
644C2×SD16—431no—
645C2×SD16—431no—
646C2×SD16—431no—
647C2×SD16—431no—
648C2×SD16—431no—
649C2×SD16C4×D4311yescharacteristic
650C2×SD16C4×D4311yescharacteristic
651C2×D8—431no—
652C2×D8—431no—
653C2×D8—431no—
654C2×D8C4×D4311yescharacteristic
655#131—22no—
656#131—22no—
657#131—862no—
658#131—862no—
659#131—868no—
660#131—862no—
661#131—868no—
662#131—862no—
663#131—862no—
664#131—862no—
665C2×M16—21no—
666C2×M16—431no—
667C2×M16—431no—
668C2×M16—431no—
669C2×M16—431no—
670C2×M16—431no—
671C2×M16—434no—
672C2×M16—431no—
673C2×M16—861no—
674C2×M16—861no—
675C2×M16—862no—
676C2×M16—862no—
677C2×M16—861no—
678C2×M16—861no—
679C2×M16—862no—
680C2×M16—868no—
681C2×M16—861no—
682C2×M16—862no—
683C2×M16—862no—
684C2×M16C22×D4311yescharacteristic
685C2×M16C22×D4311yescharacteristic
686C22×C8—21no—
687C22×C8—431no—
688C22×C8—431no—
689C22×C8—431no—
690C22×C8—431no—
691C22×C8—431no—
692C22×C8—431no—
693C22×C8—861no—
694C22×C8—862no—
695C22×C8—862no—
696C22×C8—861no—
697C22×C8—868no—
698C22×C8—861no—
699C22×C8—861no—
700C22×C8—861no—
701C22×C8C22×D4311yescharacteristic
702C22×C8C22×D4311yescharacteristic
703#117—862no—
704#117—862no—
705C2×C4⋊C4—861no—
706C2×C22⋊C4—861no—
707C2×C42—431no—
708C2×C42C22×D4311yescharacteristic
709#104—22no—
710#104—22no—
711#104—862no—
712#104—862no—
713#104—862no—
714#104—862no—
715#104—862no—
716#104—862no—
717C22⋊C8—21no—
718C22⋊C8—21no—
719C22⋊C8—861no—
720C22⋊C8—861no—
721C22⋊C8—861no—
722C22⋊C8—861no—
723C22⋊C8—861no—
724C22⋊C8—861no—
725C24—431no—
726C24—861no—
727C24—861no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—434no—
735#41—434no—
736#41—432no—
737#41—432no—
738#41—864no—
739#41—864no—
740#41—864no—
741#41—864no—
742#41—862no—
743#41—862no—
744#41—862no—
745#41—862no—
746#41—862no—
747#41—862no—
748#41—861no—
749#41—861no—
750#41—861no—
751#41—861no—
752#41—861no—
753#41—861no—
754#41—1722no—
755#41—1722no—
756#41—1722no—
757#41—1722no—
758#41D4×D4312yes—
759#41D4×D4312yes—
760C2×Q8—434no—
761C2×Q8—431no—
762C2×Q8—431no—
763C2×Q8—861no—
764C2×Q8—861no—
765C2×Q8—862no—
766C2×Q8—862no—
767C2×Q8—862no—
768C2×Q8C2×C4×D4311yescharacteristic
769C2×Q8C2×C4×D4311yescharacteristic
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—434no—
773C2×D4—431no—
774C2×D4—431no—
775C2×D4—861no—
776C2×D4—861no—
777C2×D4—862no—
778C2×D4—862no—
779C2×D4—862no—
780C2×D4—861no—
781C2×D4—861no—
782C2×D4—864no—
783C2×D4—864no—
784C2×D4—861no—
785C2×D4—861no—
786C2×D4—861no—
787C2×D4—861no—
788C2×D4—1722no—
789C2×D4—1722no—
790C2×D4C2×C4×D4311yescharacteristic
791C2×D4C2×C4×D4311yescharacteristic
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—431no—
796C22×C4—431no—
797C22×C4—431no—
798C22×C4—432no—
799C22×C4—432no—
800C22×C4—432no—
801C22×C4—431no—
802C22×C4—431no—
803C22×C4—432no—
804C22×C4—864no—
805C22×C4—861no—
806C22×C4—864no—
807C22×C4—861no—
808C22×C4—861no—
809C22×C4—861no—
810C22×C4—861no—
811C22×C4—861no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—1722no—
816C22×C4—1722no—
817C22×C4C23×D4311yescharacteristic
818Q16—22no—
819Q16—862no—
820Q16—862no—
821Q16—862no—
822SD16—22no—
823SD16—22no—
824SD16—862no—
825SD16—862no—
826SD16—862no—
827SD16—862no—
828SD16—862no—
829SD16—862no—
830D8—22no—
831D8—862no—
832D8—862no—
833D8—862no—
834M16—24no—
835M16—21no—
836M16—21no—
837M16—21no—
838M16—432no—
839M16—864no—
840M16—862no—
841M16—862no—
842M16—862no—
843M16—862no—
844M16—864no—
845M16—864no—
846M16—864no—
847M16—861no—
848M16—861no—
849M16—861no—
850M16—1722no—
851M16D4×D4312yes—
852C2×C8—24no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—431no—
860C2×C8—431no—
861C2×C8—431no—
862C2×C8—431no—
863C2×C8—862no—
864C2×C8—862no—
865C2×C8—862no—
866C2×C8—862no—
867C2×C8—864no—
868C2×C8—864no—
869C2×C8—864no—
870C2×C8—864no—
871C2×C8—861no—
872C2×C8—861no—
873C2×C8—861no—
874C2×C8—861no—
875C2×C8—861no—
876C2×C8—861no—
877C2×C8—1722no—
878C2×C8C2×C4×D4311yescharacteristic
879C2×C8C2×C4×D4311yescharacteristic
880C2×C8D4×D4311yescharacteristic
881C2×C8D4×D4311yescharacteristic
882C4⋊C4—1722no—
883C22⋊C4—1722no—
884C42—21no—
885C42—21no—
886C42—861no—
887C42—861no—
888C23—21no—
889C23—21no—
890C23—431no—
891C23—431no—
892C23—432no—
893C23—432no—
894C23—864no—
895C23—861no—
896C23—861no—
897C23—1721no—
898C23—1721no—
899C23—1722no—
900C23—1722no—
901C23—1722no—
902C23—1722no—
903C23—1722no—
904C23#41×D4311yescharacteristic
905Q8—21no—
906Q8—21no—
907Q8—21no—
908Q8—432no—
909Q8—864no—
910Q8—861no—
911Q8—861no—
912Q8—861no—
913Q8—1722no—
914Q8C22⋊C4×D4312yes—
915D4—22no—
916D4—22no—
917D4—21no—
918D4—21no—
919D4—21no—
920D4—41no—
921D4—41no—
922D4—432no—
923D4—864no—
924D4—864no—
925D4—864no—
926D4—862no—
927D4—862no—
928D4—861no—
929D4—861no—
930D4—861no—
931D4—1722no—
932D4—1722no—
933D4—1722no—
934D4—1721no—
935D4—1721no—
936D4C22⋊C4×D4312yes—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—431no—
947C2×C4—431no—
948C2×C4—432no—
949C2×C4—432no—
950C2×C4—432no—
951C2×C4—432no—
952C2×C4—432no—
953C2×C4—432no—
954C2×C4—432no—
955C2×C4—432no—
956C2×C4—432no—
957C2×C4—432no—
958C2×C4—864no—
959C2×C4—864no—
960C2×C4—864no—
961C2×C4—861no—
962C2×C4—862no—
963C2×C4—862no—
964C2×C4—861no—
965C2×C4—1722no—
966C2×C4—1722no—
967C2×C4—1722no—
968C2×C4—1721no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4—1721no—
973C2×C4C22×C4×D4311yescharacteristic
974C2×C4C2×D4×D4311yescharacteristic
975C2×C4C2×D4×D4311yescharacteristic
976C2×C4C2×D4×D4311yescharacteristic
977C2×C4C2×D4×D4311yescharacteristic
978C2×C4#41×D4311yescharacteristic
979C8—21no—
980C8—21no—
981C8—21no—
982C8—22no—
983C8—21no—
984C8—41no—
985C8—861no—
986C8—861no—
987C8—861no—
988C8—861no—
989C8—862no—
990C8—1721no—
991C22—21no—
992C22—21no—
993C22—22no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—432no—
1000C22—432no—
1001C22—861no—
1002C22—861no—
1003C22—861no—
1004C22—861no—
1005C22—862no—
1006C22—3444no—
1007C22—1722no—
1008C22—1722no—
1009C22—1728no—
1010C22—1721no—
1011C22—1721no—
1012C22—1721no—
1013C22—1721no—
1014C22—1721no—
1015C22C4×D4×D4311yescharacteristic
1016C22#121×D4311yescharacteristic
1017C22#123×D4311yescharacteristic
1018C4—22no—
1019C4—41no—
1020C4—81no—
1021C4—432no—
1022C4—432no—
1023C4—862no—
1024C4—3441no—
1025C4—1721no—
1026C4C2×C22⋊C4×D4311yescharacteristic
1027C4C4×D4×D4311yescharacteristic
1028C4#120×D4311yescharacteristic
1029C4#121×D4311yescharacteristic
1030C2—21no—
1031C2—21no—
1032C2—42no—
1033C2—81no—
1034C2—862no—
1035C2—862no—
1036C2—3441no—
1037C2—1722no—
1038C2#386×D4311yescharacteristic
1039C2#1914349311yescharacteristic
1040C2#1914349511yescharacteristic
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#20917
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×#131×D43C2semidirect
3. C2×#14582914C2semidirect
4. C2×#14582914C2semidirect
5. #408×D43C2semidirect
6. #19134925C2semidirect
7. #19134924C2semidirect
8. #19134923C2semidirect
9. #19134922C2semidirect
10. #19134921C2semidirect
11. #19134920C2semidirect
12. #19134919C2semidirect
13. #19134320C2semidirect
14. #19134290C2semidirect
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
32. C2×#13063333C22semidirect
33. C2×#13063332C22semidirect
35. C2×#13063331C22semidirect
47. C2×#13063253C22semidirect
48. C2×#13063253C22semidirect
49. C2×#13063252C22semidirect
50. C2×#13063252C22semidirect
51. C2×#13063251C22semidirect
52. 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
522. #1876D43semidirect
559. C2×#131C2×D43semidirect
575. C2×#104C2×D43semidirect
576. C2×#104C2×D43semidirect
582. #408C2×D43semidirect
588. #341C2×D43semidirect
592. #336C2×D43semidirect
593. C43#20917semidirect

Maximal subgroups

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

subgroupindex
C2×#145836962
C2×#131×D432
C2×#145829142
#408×D432
#191349252
#191349242
#191349232
#191349222
#191349212
#191349202
#191349192
#191343202
#191342902
C43×#18762
#2091743