Finite Group Databasebeta

← #25112479

Subgroups — #25112479

Order 11008.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583696C211yesmaximal, characteristic
2C2×#14583018C211yesmaximal, characteristic, complemented
3C2×#14583014C211yesmaximal, characteristic, complemented
4#19143043C211yesmaximal, characteristic, complemented
5#19143042C211yesmaximal, characteristic, complemented
6#19135485C211yesmaximal, characteristic, complemented
7#19135482C211yesmaximal, characteristic, complemented
8#19134924C211yesmaximal, characteristic, complemented
9#19134923C211yesmaximal, characteristic, complemented
10#19134921C211yesmaximal, characteristic, complemented
11#19134636C211yesmaximal, characteristic, complemented
12#19134537C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14#19134377C211yesmaximal, 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×#13063333C2211yescharacteristic, complemented
32C2×#13063332C2211yescharacteristic, complemented
33C2×#13063331C2211yescharacteristic, complemented
34C22×#10621872C2211yescharacteristic
35#14583018—24no—
36#14583014—24no—
37C2×#13063260C2211yescharacteristic, complemented
38C2×#13063260C2211yescharacteristic, complemented
39C2×#13063253C2211yescharacteristic, complemented
40C2×#13063253C2211yescharacteristic, complemented
41C2×#13063252C2211yescharacteristic, complemented
42C2×#13063252C2211yescharacteristic, complemented
43C2×#13063251C2211yescharacteristic, complemented
44C2×#13063251C2211yescharacteristic, complemented
45#14582867—21no—
46#14582867C2211yescharacteristic, complemented
47#14582866C2211yescharacteristic, complemented
48#14582865—21no—
49#14582865C2211yescharacteristic, complemented
50#14582864—21no—
51#14582864—21no—
52#14582862—21no—
53#14582862C2211yescharacteristic
54#14582862C2211yescharacteristic
55#14582861—21no—
56C2×(C2×D43)⋊C8—21no—
57C2×(C2×D43)⋊C8C2211yescharacteristic
58C22⋊C8×D43—21no—
59C2×#13063236C2211yescharacteristic, complemented
60C2×C8×Dic43C2211yescharacteristic, complemented
61C4×(C2×D43)⋊C4C2211yescharacteristic
62#14582664C2211yescharacteristic, complemented
63#14582653C2211yescharacteristic, complemented
64C2×#135×C43C2211yescharacteristic
65C2×#131×C43C2211yescharacteristic, complemented
66C2×#104×C43C2211yescharacteristic, complemented
67C2×#104×C43C2211yescharacteristic, complemented
68C43×#408C2211yescharacteristic, complemented
69C43×#341C2211yescharacteristic, complemented
70C43×#336C2211yescharacteristic, complemented
71C2×#10621902C2×C411yescharacteristic
72C2×#10621902C2×C411yescharacteristic
73C2×#10621898—21no—
74C2×#10621898—21no—
75C2×#10621898C2311yescharacteristic
76C2×#10621898C2311yescharacteristic
77C2×#10621900—21no—
78C2×#10621900—21no—
79C2×#10621900C2×C411yescharacteristic
80C2×#10621900C2×C411yescharacteristic
81#41×D43—22no—
82#41×D43—22no—
83#41×D43—22no—
84#41×D43—22no—
85#41×D43—41no—
86#41×D43—41no—
87#41×D43—41no—
88#41×D43—41no—
89C2×Q8×D43C2×C411yescharacteristic
90C2×Q8×D43C2×C411yescharacteristic
91C2×D4×D43—21no—
92C2×D4×D43—21no—
93C2×D4×D43C2×C411yescharacteristic
94C2×D4×D43C2×C411yescharacteristic
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98#13063357—24no—
99#13063357—24no—
100#13063354—24no—
101#13063354—24no—
102#13063352—24no—
103#13063352—24no—
104#13063349—24no—
105#13063349—24no—
106#13063347—22no—
107#13063347—22no—
108#13063345—22no—
109#13063345—22no—
110#13063345D414yes—
111#13063345D414yes—
112C2×Dic172C2×C411yescharacteristic
113C2×#10621885C2×C411yescharacteristic
114C2×#10621885C2×C411yescharacteristic
115C2×#10621873C2×C411yescharacteristic
116C2×#10621873C2×C411yescharacteristic
117C2×#10621883C2×C411yescharacteristic
118C2×#10621883C2×C411yescharacteristic
119C2×#10621884C2×C411yescharacteristic
120C2×#10621884C2×C411yescharacteristic
121C2×D344C2×C411yescharacteristic
122C2×#10621882C2×C411yescharacteristic
123C2×#10621882C2×C411yescharacteristic
124#13063333—22no—
125#13063333—41no—
126#13063332—22no—
127#13063332—41no—
128#13063331—22no—
129#13063331—41no—
130C2×#10621877—21no—
131C2×#10621877C2311yescharacteristic
132C2×#10621877C2311yescharacteristic
133C2×#10621872—22no—
134C2×#10621872—22no—
135C2×#10621872—21no—
136C2×#10621872—21no—
137C2×#10621872C2×C411yescharacteristic
138C2×#10621872C2×C411yescharacteristic
139C2×#10621872C2×C411yescharacteristic
140C2×#10621872C2×C411yescharacteristic
141C22×C43⋊C8—21no—
142C22×C43⋊C8C2311yescharacteristic
143C22×C43⋊C8C2311yescharacteristic
144C2×C8×D43—21no—
145C2×C8×D43—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×C4×Dic43C2311yescharacteristic
148#13063260—22no—
149#13063260—22no—
150#13063253—22no—
151#13063253—41no—
152#13063252—22no—
153#13063252—41no—
154#13063251—22no—
155#13063251—41no—
156C22⋊(C43⋊C8)—21no—
157C22⋊(C43⋊C8)—21no—
158(C2×D43)⋊C8—21no—
159(C2×D43)⋊C8—21no—
160(C2×D43)⋊C8—21no—
161(C2×D43)⋊C8—21no—
162(C2×D43)⋊C8—21no—
163(C2×D43)⋊C8—21no—
164(C2×D43)⋊C8—21no—
165(C2×D43)⋊C8—21no—
166(C2×D43)⋊C8D411yescharacteristic
167(C2×D43)⋊C8D411yescharacteristic
168(C2×D43)⋊C8D411yescharacteristic
169(C2×D43)⋊C8D411yescharacteristic
170#13063236—22no—
171C8×Dic43—22no—
172C43⋊#95—21no—
173C2×#41×C43C2311yescharacteristic
174C2×#41×C43C2311yescharacteristic
175#135×C43—22no—
176#135×C43—22no—
177C2×Q16×C43C2×C411yescharacteristic
178C2×SD16×C43C2×C411yescharacteristic
179C2×SD16×C43C2×C411yescharacteristic
180C2×D8×C43C2×C411yescharacteristic
181#131×C43—22no—
182#131×C43—41no—
183C2×M16×C43—21no—
184C2×M16×C43C2311yescharacteristic
185C2×M16×C43C2311yescharacteristic
186C22×C8×C43—21no—
187C22×C8×C43C2311yescharacteristic
188C22×C8×C43C2311yescharacteristic
189C2×C42×C43C2311yescharacteristic
190#104×C43—22no—
191#104×C43—41no—
192C22⋊C8×C43—21no—
193C22⋊C8×C43—21no—
194C23×D43—21no—
195C23×D43—21no—
196C23×D43#4111yescharacteristic
197#41×C43—21no—
198#41×C43—21no—
199#41×C43—21no—
200#41×C43—21no—
201#41×C43—21no—
202#41×C43—21no—
203#41×C43C2×D412yes—
204#41×C43C2×D412yes—
205C2×Q8×C43C22×C411yescharacteristic
206C2×Q8×C43C22×C411yescharacteristic
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43C22×C411yescharacteristic
210C2×D4×C43C22×C411yescharacteristic
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C2411yescharacteristic
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43#4111yescharacteristic
225#10621902—22no—
226#10621902—22no—
227#10621902—41no—
228#10621902—41no—
229Q8×D43—22no—
230Q8×D43—22no—
231Q8×D43—41no—
232Q8×D43—41no—
233#10621900—22no—
234#10621900—22no—
235#10621900—41no—
236#10621900—41no—
237#10621900—42no—
238#10621900—42no—
239#10621900—42no—
240#10621900—42no—
241D4×D43—22no—
242D4×D43—22no—
243D4×D43—42no—
244D4×D43—42no—
245D4×D43—42no—
246D4×D43—42no—
247D4×D43—41no—
248D4×D43—41no—
249#10621898—21no—
250#10621898—21no—
251#10621898—21no—
252#10621898—21no—
253#10621898—21no—
254#10621898—21no—
255#10621898—42no—
256#10621898—42no—
257#10621898—42no—
258#10621898—42no—
259#10621898C2×D412yes—
260#10621898C2×D412yes—
261C2×D172—21no—
262C2×D172—21no—
263C2×D172C22×C411yescharacteristic
264C2×D172C22×C411yescharacteristic
265C2×C4×D43—21no—
266C2×C4×D43—21no—
267C2×C4×D43—21no—
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×C4×D43—21no—
272C2×C4×D43—21no—
273C2×C4×D43—21no—
274C2×C4×D43—21no—
275C2×C4×D43—42no—
276C2×C4×D43—42no—
277C2×C4×D43—42no—
278C2×C4×D43—42no—
279C2×C4×D43C22×C411yescharacteristic
280C2×C4×D43C22×C411yescharacteristic
281C2×C4×D43C2×D411yescharacteristic
282C2×C4×D43C2×D411yescharacteristic
283C2×Dic86—21no—
284C2×Dic86—21no—
285C2×Dic86C22×C411yescharacteristic
286C2×Dic86C22×C411yescharacteristic
287Q16×C43—22no—
288SD16×C43—22no—
289SD16×C43—22no—
290D8×C43—22no—
291M16×C43—21no—
292M16×C43—21no—
293M16×C43—21no—
294M16×C43—21no—
295M16×C43—42no—
296C2×C8×C43—21no—
297C2×C8×C43—21no—
298C2×C8×C43—21no—
299C2×C8×C43—21no—
300C2×C8×C43—21no—
301C2×C8×C43—21no—
302C2×C8×C43—42no—
303C2×C8×C43C22×C411yescharacteristic
304C2×C8×C43C22×C411yescharacteristic
305C2×C8×C43C2×D411yescharacteristic
306C2×C8×C43C2×D411yescharacteristic
307C42×C43—21no—
308C42×C43—21no—
309#10621885—22no—
310#10621885C22⋊C414yescomplemented
311#10621884—22no—
312#10621884C22⋊C414yescomplemented
313#10621883—22no—
314#10621883C22⋊C414yescomplemented
315#10621882—22no—
316#10621882C22⋊C414yescomplemented
317(C2×D43)⋊C4—42no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320#10621877—21no—
321#10621877—21no—
322#10621877—21no—
323#10621877—21no—
324#10621877—42no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—42no—
330C2×C43⋊C8C22×C411yescharacteristic
331C2×C43⋊C8C22×C411yescharacteristic
332C2×C43⋊C8C2×D411yescharacteristic
333C2×C43⋊C8C2×D411yescharacteristic
334C2×C43⋊C8C2×D412yes—
335C2×C43⋊C8C2×D412yes—
336Dic172—22no—
337D344—22no—
338#10621873—22no—
339#10621873—22no—
340#10621872—22no—
341#10621872—22no—
342#10621872—22no—
343#10621872—22no—
344#10621872—42no—
345#10621872—42no—
346C8×D43—42no—
347C8×D43—42no—
348C23×C43—21no—
349C23×C43—21no—
350C23×C43C2×#4111yescharacteristic
351C22×D43—21no—
352C22×D43—21no—
353C22×D43—21no—
354C22×D43—21no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—42no—
358C22×D43—42no—
359C22×D43—42no—
360C22×D43—42no—
361C22×D43—81no—
362C22×D43—81no—
363C22×D43C4×D411yescharacteristic
364C22×D43C4×D411yescharacteristic
365Q8×C43—21no—
366Q8×C43—21no—
367Q8×C43—21no—
368Q8×C43C2×C22⋊C412yes—
369D4×C43—22no—
370D4×C43—22no—
371D4×C43—21no—
372D4×C43—21no—
373D4×C43—21no—
374D4×C43—41no—
375D4×C43—41no—
376D4×C43C2×C22⋊C412yes—
377C2×C4×C43—21no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—21no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43C23×C411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C2×C4×C43H(5,𝔽2)11yescharacteristic
391C2×C4×C43H(5,𝔽2)11yescharacteristic
392C22⋊D43—22no—
393C22⋊D43—22no—
394C22⋊D43—42no—
395C22⋊D43—42no—
396C22⋊D43—42no—
397C22⋊D43—42no—
398C22⋊D43—41no—
399C22⋊D43—41no—
400C2×Dic43—21no—
401C2×Dic43—21no—
402C2×Dic43—21no—
403C2×Dic43—22no—
404C2×Dic43—21no—
405C2×Dic43—42no—
406C2×Dic43—42no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43C4×D411yescharacteristic
410C2×Dic43C4×D411yescharacteristic
411D172—21no—
412D172—21no—
413D172—21no—
414D172—42no—
415D172—42no—
416D172C2×C22⋊C412yes—
417C4×D43—21no—
418C4×D43—21no—
419C4×D43—21no—
420C4×D43—21no—
421C4×D43—22no—
422C4×D43—22no—
423C4×D43—21no—
424C4×D43—21no—
425C4×D43—21no—
426C4×D43—21no—
427C4×D43—42no—
428C4×D43—42no—
429C4×D43—42no—
430C4×D43—42no—
431C4×D43—41no—
432C4×D43—41no—
433Dic86—21no—
434Dic86—21no—
435Dic86—21no—
436Dic86—42no—
437Dic86—42no—
438Dic86C2×C22⋊C412yes—
439C8×C43—21no—
440C8×C43—21no—
441C8×C43—21no—
442C8×C43—21no—
443C8×C43—41no—
444C8×C43—41no—
445C43⋊C8—21no—
446C43⋊C8—21no—
447C43⋊C8—41no—
448C43⋊C8—41no—
449C43⋊C8C2×C22⋊C412yes—
450C43⋊C8C2×C22⋊C412yes—
451#22453—431nomaximal, Sylow
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—22no—
455C22×C43—41no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43—41no—
460C22×C43C2×C4×D411yescharacteristic
461C22×C43#54611yescharacteristic
462C22×C43#54611yescharacteristic
463C2×D43—21no—
464C2×D43—21no—
465C2×D43—22no—
466C2×D43—21no—
467C2×D43—21no—
468C2×D43—21no—
469C2×D43—21no—
470C2×D43—41no—
471C2×D43—41no—
472C2×D43—41no—
473C2×D43—41no—
474C2×D43—41no—
475C2×D43—81no—
476C2×D43—81no—
477C2×D43—84no—
478C2×D43—84no—
479C4×C43—22no—
480C4×C43—41no—
481C4×C43—81no—
482C4×C43C22×C22⋊C411yescharacteristic
483C4×C43#51811yescharacteristic
484C4×C43D4211yescharacteristic
485C4×C43D4211yescharacteristic
486Dic43—22no—
487Dic43—21no—
488Dic43—21no—
489Dic43—42no—
490Dic43—41no—
491C2×#575—431no—
492C2×#444—431no—
493C2×#443—431no—
494#2880—431no—
495#2880—431no—
496#1975—431no—
497#1974—431no—
498#1876—431no—
499#1876—431no—
500#1876—431no—
501#1876D4311yescharacteristic, complemented
502#1811—431no—
503#1789—431no—
504#1789—431no—
505#1753—431no—
506C2×C43—21no—
507C2×C43—21no—
508C2×C43—42no—
509C2×C43—81no—
510C2×C43D4×C22⋊C411yescharacteristic
511C2×C43#295511yescharacteristic
512C2×C43#295611yescharacteristic
513D43—41no—
514D43—41no—
515D43—42no—
516D43—81no—
517C22×#41—431no—
518C22×#41—431no—
519#575—864no—
520#575—864no—
521C2×#137—431no—
522C2×#137—431no—
523C2×#137—431no—
524C2×#137—431no—
525C2×AGL(1,ℤ/8)—431no—
526C2×AGL(1,ℤ/8)—431no—
527C2×AGL(1,ℤ/8)—431no—
528C2×AGL(1,ℤ/8)—431no—
529C2×#135—431no—
530C2×#135—431no—
531C2×#135—431no—
532C2×#135C2×D4311yescharacteristic
533C2×#131—431no—
534C2×#131—431no—
535C2×#131—431no—
536C2×#131C2×D4311yescharacteristic, complemented
537C22×M16—431no—
538#444—864no—
539#443—864no—
540C2×#108—431no—
541C2×#108—431no—
542C2×#104—431no—
543C2×#104—431no—
544C2×#104—431no—
545C2×#104—431no—
546C2×#104—431no—
547C2×#104—431no—
548C2×#104C2×D4311yescharacteristic, complemented
549C2×#104C2×D4311yescharacteristic, complemented
550#408—431no—
551#408—431no—
552#408—431no—
553#408—861no—
554#408—861no—
555#408—861no—
556#408—861no—
557#408C2×D4311yescharacteristic, complemented
558#407—431no—
559#407—431no—
560#407—861no—
561#407—861no—
562C2×C22⋊C8—431no—
563C2×C22⋊C8—861no—
564C2×C22⋊C8—861no—
565C2×#97—431no—
566C2×C4×C8—431no—
567C4×C22⋊C4—431no—
568#341—431no—
569#341C2×D4311yescharacteristic, complemented
570#336—431no—
571#336C2×D4311yescharacteristic, complemented
572C43#2245311yescharacteristic, complemented, Sylow
573C2×#41—431no—
574C2×#41—431no—
575C2×#41—431no—
576C2×#41—431no—
577C2×#41—431no—
578C2×#41—431no—
579C2×#41—861no—
580C2×#41—861no—
581C2×#41—861no—
582C2×#41—861no—
583C2×#41—862no—
584C2×#41—862no—
585C2×#41—862no—
586C2×#41—862no—
587C2×#41—1721no—
588C2×#41—1721no—
589C2×#41—1721no—
590C2×#41—1721no—
591C2×#41C22×D4311yescharacteristic
592C2×#41C22×D4311yescharacteristic
593C22×Q8—431no—
594C22×Q8—431no—
595C22×D4—431no—
596C22×D4—431no—
597C22×D4—861no—
598C22×D4—861no—
599C23×C4—431no—
600C23×C4—861no—
601C23×C4—861no—
602#137—864no—
603#137—864no—
604#137—864no—
605#137—864no—
606AGL(1,ℤ/8)—864no—
607AGL(1,ℤ/8)—864no—
608AGL(1,ℤ/8)—864no—
609AGL(1,ℤ/8)—864no—
610#135—22no—
611#135—22no—
612#135—434no—
613#135—434no—
614#135—862no—
615#135—862no—
616#135—862no—
617#135—862no—
618C2×Q16—431no—
619C2×Q16—431no—
620C2×Q16—431no—
621C2×Q16C4×D4311yescharacteristic
622C2×SD16—431no—
623C2×SD16—431no—
624C2×SD16—431no—
625C2×SD16—431no—
626C2×SD16—431no—
627C2×SD16—431no—
628C2×SD16C4×D4311yescharacteristic
629C2×SD16C4×D4311yescharacteristic
630C2×D8—431no—
631C2×D8—431no—
632C2×D8—431no—
633C2×D8C4×D4311yescharacteristic
634#131—22no—
635#131—41no—
636#131—862no—
637#131—862no—
638#131—862no—
639#131—1721no—
640#131—1721no—
641#131—1721no—
642C2×M16—21no—
643C2×M16—431no—
644C2×M16—431no—
645C2×M16—431no—
646C2×M16—431no—
647C2×M16—431no—
648C2×M16—431no—
649C2×M16—862no—
650C2×M16—862no—
651C2×M16—861no—
652C2×M16—861no—
653C2×M16—861no—
654C2×M16C22×D4311yescharacteristic
655C2×M16C22×D4311yescharacteristic
656C22×C8—21no—
657C22×C8—431no—
658C22×C8—431no—
659C22×C8—861no—
660C22×C8—861no—
661C22×C8—861no—
662C22×C8C22×D4311yescharacteristic
663C22×C8C22×D4311yescharacteristic
664C2×C22⋊C4—861no—
665C2×C42—431no—
666C2×C42C22×D4311yescharacteristic
667#108—862no—
668#108—862no—
669#104—22no—
670#104—41no—
671#104—862no—
672#104—862no—
673#104—862no—
674#104—1721no—
675#104—1721no—
676#104—1721no—
677C22⋊C8—21no—
678C22⋊C8—21no—
679C22⋊C8—431no—
680C22⋊C8—431no—
681C22⋊C8—431no—
682C22⋊C8—431no—
683C22⋊C8—861no—
684C22⋊C8—861no—
685C22⋊C8—861no—
686C22⋊C8—861no—
687C22⋊C8—861no—
688C22⋊C8—861no—
689C22⋊C8—861no—
690C22⋊C8—861no—
691C22⋊C8—861no—
692C22⋊C8—861no—
693#97—862no—
694C4×C8—862no—
695#95—861no—
696C24—431no—
697C24—861no—
698C24—861no—
699#41—21no—
700#41—21no—
701#41—21no—
702#41—21no—
703#41—21no—
704#41—21no—
705#41—432no—
706#41—432no—
707#41—861no—
708#41—861no—
709#41—862no—
710#41—862no—
711#41—862no—
712#41—862no—
713#41—861no—
714#41—861no—
715#41—861no—
716#41—861no—
717#41—1722no—
718#41—1722no—
719#41—1722no—
720#41—1722no—
721#41—1721no—
722#41—1721no—
723#41—1722no—
724#41—1722no—
725#41—1722no—
726#41—1722no—
727#41—1721no—
728#41—1721no—
729#41D4×D4312yes—
730#41D4×D4312yes—
731C2×Q8—431no—
732C2×Q8—431no—
733C2×Q8—861no—
734C2×Q8—861no—
735C2×Q8—862no—
736C2×Q8—862no—
737C2×Q8—1721no—
738C2×Q8—1721no—
739C2×Q8C2×C4×D4311yescharacteristic
740C2×Q8C2×C4×D4311yescharacteristic
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—431no—
744C2×D4—431no—
745C2×D4—861no—
746C2×D4—861no—
747C2×D4—861no—
748C2×D4—861no—
749C2×D4—862no—
750C2×D4—861no—
751C2×D4—862no—
752C2×D4—861no—
753C2×D4—861no—
754C2×D4—861no—
755C2×D4—1721no—
756C2×D4—1721no—
757C2×D4—1722no—
758C2×D4—1722no—
759C2×D4—1722no—
760C2×D4—1722no—
761C2×D4C2×C4×D4311yescharacteristic
762C2×D4C2×C4×D4311yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—1722no—
785C22×C4—1722no—
786C22×C4—1722no—
787C22×C4—1722no—
788C22×C4C23×D4311yescharacteristic
789Q16—22no—
790Q16—434no—
791Q16—862no—
792Q16—862no—
793SD16—22no—
794SD16—22no—
795SD16—434no—
796SD16—434no—
797SD16—862no—
798SD16—862no—
799SD16—862no—
800SD16—862no—
801D8—22no—
802D8—434no—
803D8—862no—
804D8—862no—
805M16—21no—
806M16—21no—
807M16—21no—
808M16—21no—
809M16—42no—
810M16—862no—
811M16—862no—
812M16—862no—
813M16—862no—
814M16—861no—
815M16—861no—
816M16—861no—
817M16—861no—
818M16—1722no—
819M16—1722no—
820M16—1722no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—42no—
828C2×C8—431no—
829C2×C8—431no—
830C2×C8—432no—
831C2×C8—432no—
832C2×C8—431no—
833C2×C8—431no—
834C2×C8—861no—
835C2×C8—861no—
836C2×C8—861no—
837C2×C8—861no—
838C2×C8—1722no—
839C2×C8—1722no—
840C2×C8—1722no—
841C2×C8C2×C4×D4311yescharacteristic
842C2×C8C2×C4×D4311yescharacteristic
843C2×C8D4×D4311yescharacteristic
844C2×C8D4×D4311yescharacteristic
845C22⋊C4—1722no—
846C42—21no—
847C42—21no—
848C42—861no—
849C42—861no—
850C23—21no—
851C23—21no—
852C23—431no—
853C23—431no—
854C23—861no—
855C23—861no—
856C23—861no—
857C23—861no—
858C23—3441no—
859C23—3441no—
860C23—1721no—
861C23—1721no—
862C23—1722no—
863C23—1722no—
864C23—1722no—
865C23—1722no—
866C23#41×D4311yescharacteristic
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—432no—
871Q8—861no—
872Q8—861no—
873Q8—861no—
874Q8—1722no—
875Q8—1722no—
876Q8C22⋊C4×D4312yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—41no—
883D4—41no—
884D4—432no—
885D4—862no—
886D4—862no—
887D4—861no—
888D4—861no—
889D4—861no—
890D4—1722no—
891D4—1722no—
892D4—1722no—
893D4—1722no—
894D4—1722no—
895D4—1722no—
896D4—1721no—
897D4—1721no—
898D4C22⋊C4×D4312yes—
899C2×C4—21no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—21no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—431no—
909C2×C4—431no—
910C2×C4—861no—
911C2×C4—861no—
912C2×C4—861no—
913C2×C4—861no—
914C2×C4—861no—
915C2×C4—861no—
916C2×C4—861no—
917C2×C4—862no—
918C2×C4—861no—
919C2×C4—861no—
920C2×C4—862no—
921C2×C4—861no—
922C2×C4—861no—
923C2×C4—862no—
924C2×C4—861no—
925C2×C4—1722no—
926C2×C4—1722no—
927C2×C4—1722no—
928C2×C4—1722no—
929C2×C4—1722no—
930C2×C4—1722no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4C22×C4×D4311yescharacteristic
936C2×C4C2×D4×D4311yescharacteristic
937C2×C4C2×D4×D4311yescharacteristic
938C2×C4C2×D4×D4311yescharacteristic
939C2×C4#1306337011yescharacteristic
940C2×C4#1306337111yescharacteristic
941C8—21no—
942C8—21no—
943C8—21no—
944C8—21no—
945C8—41no—
946C8—41no—
947C8—432no—
948C8—432no—
949C8—861no—
950C8—861no—
951C8—1721no—
952C8—1721no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—861no—
962C22—861no—
963C22—861no—
964C22—861no—
965C22—861no—
966C22—861no—
967C22—862no—
968C22—3441no—
969C22—3441no—
970C22—3444no—
971C22—3444no—
972C22—1721no—
973C22—1721no—
974C22—1721no—
975C22—1721no—
976C22—1721no—
977C22C4×D4×D4311yescharacteristic
978C22#1458353811yescharacteristic
979C22#1458354111yescharacteristic
980C4—22no—
981C4—41no—
982C4—81no—
983C4—861no—
984C4—861no—
985C4—862no—
986C4—1722no—
987C4—1721no—
988C4C2×C22⋊C4×D4311yescharacteristic
989C4#1458337111yescharacteristic
990C4#1458353111yescharacteristic
991C4#1458353311yescharacteristic
992C2—21no—
993C2—21no—
994C2—42no—
995C2—81no—
996C2—3441no—
997C2—1721no—
998C2—1721no—
999C2—1722no—
1000C2#1913741311yescharacteristic
1001C2#1914349311yescharacteristic
1002C2#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#22453
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×#14583018C2semidirect
3. C2×#14583014C2semidirect
4. #19143043C2semidirect
5. #19143042C2semidirect
6. #19135485C2semidirect
7. #19135482C2semidirect
8. #19134924C2semidirect
9. #19134923C2semidirect
10. #19134921C2semidirect
11. #19134636C2semidirect
12. #19134537C2semidirect
13. #19134537C2semidirect
14. #19134377C2semidirect
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
31. C2×#13063333C22semidirect
32. C2×#13063332C22semidirect
33. C2×#13063331C22semidirect
37. C2×#13063260C22semidirect
38. C2×#13063260C22semidirect
39. C2×#13063253C22semidirect
40. C2×#13063253C22semidirect
41. C2×#13063252C22semidirect
42. C2×#13063252C22semidirect
43. C2×#13063251C22semidirect
44. C2×#13063251C22semidirect
46. #14582867C22semidirect
47. #14582866C22semidirect
49. #14582865C22semidirect
59. C2×#13063236C22semidirect
60. C2×C8×Dic43C22semidirect
62. #14582664C22semidirect
63. #14582653C22semidirect
65. C2×#131×C43C22semidirect
66. C2×#104×C43C22semidirect
67. C2×#104×C43C22semidirect
68. C43×#408C22semidirect
69. C43×#341C22semidirect
70. C43×#336C22semidirect
310. #10621885C22⋊C4semidirect
312. #10621884C22⋊C4semidirect
314. #10621883C22⋊C4semidirect
316. #10621882C22⋊C4semidirect
501. #1876D43semidirect
536. C2×#131C2×D43semidirect
548. C2×#104C2×D43semidirect
549. C2×#104C2×D43semidirect
557. #408C2×D43semidirect
569. #341C2×D43semidirect
571. #336C2×D43semidirect
572. C43#22453semidirect

Maximal subgroups

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

subgroupindex
C2×#145836962
C2×#145830182
C2×#145830142
#191430432
#191430422
#191354852
#191354822
#191349242
#191349232
#191349212
#191346362
#191345372
#191343772
C43×#18762
#2245343