Finite Group Databasebeta

← #25112072

Subgroups — #25112072

Order 11008.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583546C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137491C211yesmaximal, characteristic, complemented
6#19135526C211yesmaximal, characteristic, complemented
7#19135410C211yesmaximal, characteristic, complemented
8#19135017C211yesmaximal, characteristic, complemented
9#19134913C211yesmaximal, characteristic, complemented
10#19134901C211yesmaximal, characteristic, complemented
11#19134594C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134419C211yesmaximal, characteristic, complemented
15C43×#1895C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583546—24no—
20#14583546C418yescomplemented
21C2×#13063312C2211yescharacteristic
22C2×#13063307—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063296—21no—
25C2×#13063293—21no—
26C2×#13063287C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×(C22⋊D43)⋊C4—21no—
29C22×C4⋊Dic43C2211yescharacteristic, complemented
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C22⋊C4×D43—21no—
32#14582968—24no—
33C2×Dic43⋊C8C2211yescharacteristic, complemented
34#14582901—24no—
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063250C2211yescharacteristic, complemented
37C2×#13063248C2211yescharacteristic, complemented
38C2×#13063248C2211yescharacteristic, complemented
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45#102×D43—24no—
46C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×#13063235C2211yescharacteristic, complemented
49#14582796—21no—
50#14582773—21no—
51#14582771—21no—
52#14582768C2211yescharacteristic, complemented
53#14582756C2211yescharacteristic
54C4⋊C4×Dic43C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C22×M16×C43C2211yescharacteristic, complemented
58C2×#121×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—41no—
69C2×#10621898—41no—
70C2×#10621898C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C22⋊D43D411yescharacteristic
76C2×D4×D43—22no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—41no—
80C2×D4×D43—41no—
81C2×D4×D43C2×C414yescomplemented
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C2×C8×D43—22no—
90C2×C8×D43—22no—
91C2×C8×D43—41no—
92#13063312—22no—
93#13063312C2×C414yescomplemented
94#13063307—28no—
95#13063305—22no—
96#13063305C2×C414yescomplemented
97#13063296—28no—
98#13063293—28no—
99#13063287—22no—
100#13063287C2×C414yescomplemented
101C4×C22⋊D43C2×C414yes—
102C4×C22⋊D43D414yes—
103(C22⋊D43)⋊C4—44no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43—41no—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4D411yescharacteristic
114C4⋊C4×D43—22no—
115C4⋊C4×D43—41no—
116C2×C22⋊Dic43—21no—
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43D411yescharacteristic
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4D411yescharacteristic
123C22⋊C4×D43—28no—
124C2×C4×Dic43—21no—
125C2×C4×Dic43C2311yescharacteristic
126Dic43⋊C8—22no—
127#13063250—22no—
128#13063250—22no—
129#13063248—41no—
130#13063248—41no—
131#13063247—22no—
132#13063247D414yescomplemented
133#13063246—22no—
134#13063246—41no—
135#13063245—22no—
136#13063245—22no—
137C22⋊(C43⋊C8)—22no—
138(C2×D43)⋊C8—22no—
139#13063235—22no—
140C43⋊#95—21no—
141C43⋊#95—21no—
142C22×D4×C43—21no—
143C22×D4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C2×M16×C43—22no—
146C2×M16×C43—22no—
147C2×M16×C43—41no—
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150#121×C43—22no—
151#121×C43C2×C414yescomplemented
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C22⋊C4×C43—21no—
156C2×C22⋊C4×C43—21no—
157#102×C43—22no—
158#102×C43—41no—
159#95×C43—21no—
160C24×C43—21no—
161C24×C43C2×D411yescharacteristic
162C23×D43—21no—
163C23×D43—24no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—42no—
168C23×D43—81no—
169C23×D43—81no—
170C23×D43C2×D411yescharacteristic
171C2×D4×C43—21no—
172C2×D4×C43—24no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—81no—
178C2×D4×C43—81no—
179C2×D4×C43C22×C412yes—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43C22×C412yes—
188C22×C4×C43C2×D412yes—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C2×C22⋊D43—24no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—22no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—42no—
199C2×C22⋊D43C22⋊C414yes—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—42no—
204C22×Dic43—42no—
205C22×Dic43—81no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209D4×D43—28no—
210D4×D43—44no—
211D4×D43—44no—
212D4×D43—44no—
213#10621898—28no—
214#10621898—44no—
215#10621898—44no—
216#10621898—44no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172C22×C412yes—
221C2×D172C2×D412yes—
222C2×D172#4112yes—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—81no—
234C2×C4×D43—81no—
235C2×C4×D43—81no—
236C2×C4×D43C22×C412yes—
237C2×C4×D43C2×D412yes—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86C22×C412yes—
244M16×C43—44no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43C2×D412yes—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C22×C412yes—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—42no—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261C22⋊Dic43C22⋊C414yes—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—42no—
265(C2×D43)⋊C4C22⋊C414yes—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—42no—
271C4⋊Dic43C2×D412yes—
272Dic43⋊C4—42no—
273Dic43⋊C4—42no—
274Dic43⋊C4—81no—
275Dic43⋊C4C22⋊C414yes—
276C4×Dic43—42no—
277C4×Dic43C22×C412yes—
278C4×Dic43C2×D412yes—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C8×D43—44no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—22no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43C2×C22⋊C412yes—
300C23×C43C22×D411yescharacteristic
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—48no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—48no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43—84no—
317C22×D43—84no—
318C22×D43—84no—
319C22×D43C2×C22⋊C412yes—
320C22×D43AGL(1,ℤ/8)12yes—
321C22×D43#13712yes—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—41no—
325D4×C43—41no—
326D4×C43—84no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43C2×C22⋊C412yes—
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C22⋊D43—28no—
350C22⋊D43—48no—
351C22⋊D43—48no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—84no—
368C2×Dic43C2×C22⋊C412yes—
369C2×Dic43C2×C22⋊C412yes—
370C2×Dic43C2×C22⋊C412yes—
371D172—22no—
372D172—22no—
373D172—22no—
374D172C4×D414yescomplemented
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—48no—
380C4×D43—84no—
381C4×D43—84no—
382Dic86—22no—
383Dic86—22no—
384Dic86—41no—
385Dic86—41no—
386C8×C43—22no—
387C8×C43—41no—
388C43⋊C8—41no—
389C43⋊C8—41no—
390#22419—431nomaximal, Sylow
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43C22×C22⋊C411yescharacteristic
406C22×C43D4211yescharacteristic
407C22×C43#54611yescharacteristic
408C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C43C2×#13711yescharacteristic
410C22×C43#57611yescharacteristic
411C22×C43#57711yescharacteristic
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—24no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—42no—
424C2×D43—42no—
425C2×D43—816no—
426C2×D43#41714yescomplemented
427C4×C43—22no—
428C4×C43—42no—
429C4×C43—81no—
430C4×C43—81no—
431C4×C43C2×C4×D411yescharacteristic
432C4×C43#51811yescharacteristic
433C4×C43D4211yescharacteristic
434C4×C43#54611yescharacteristic
435Dic43—22no—
436Dic43—22no—
437Dic43—22no—
438Dic43—42no—
439Dic43—42no—
440Dic43—81no—
441C2×#546—431no—
442C2×#435—431no—
443C2×#417—431no—
444C22×#102—431no—
445D4×C4⋊C4—431no—
446#1983—431no—
447#1959—431no—
448#1895D4311yescharacteristic, complemented
449#1892—431no—
450#1874—431no—
451#1872—431no—
452#1802—431no—
453#1788—431no—
454#1786—431no—
455#1762—431no—
456C2×C43—42no—
457C2×C43—82no—
458C2×C43D4×C22⋊C411yescharacteristic
459C2×C43C2×#41711yescharacteristic
460C2×C43#289711yescharacteristic
461C2×C43#326411yescharacteristic
462C2×C43#326611yescharacteristic
463C2×C43#330611yescharacteristic
464C2×C43#331411yescharacteristic
465D43—24no—
466D43—44no—
467C22×#41—431no—
468C23×D4—431no—
469C22×M16C2×D4311yescharacteristic, complemented
470C23×C8—431no—
471#546—438no—
472#546—864no—
473C2×#124—431no—
474C2×#123—861no—
475C2×C22⋊Q8—431no—
476C2×#121—861no—
477C2×#121C2×D4311yescharacteristic
478C2×#120—861no—
479C2×C4×D4—431no—
480C2×C4×D4—431no—
481C2×C4×D4—861no—
482C22×C4⋊C4—431no—
483C22×C4⋊C4—431no—
484C22×C22⋊C4—861no—
485#435—864no—
486C2×C4⋊C8—431no—
487#417—864no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103—431no—
491C2×#103—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102—431no—
496C2×#102—431no—
497C2×#102—431no—
498C2×#102—864no—
499C2×#102C2×D4311yescharacteristic
500C2×#102C2×D4311yescharacteristic
501C2×C22⋊C8—431no—
502C2×C22⋊C8—431no—
503C2×#97—431no—
504#389—861no—
505#385—861no—
506#385—861no—
507#384—431no—
508#380—431no—
509#380C2×D4311yescharacteristic, complemented
510C4×C4⋊C4—431no—
511#340—431no—
512#340—431no—
513#340C2×D4311yescharacteristic, complemented
514#340C2×D4311yescharacteristic, complemented
515C43#2241911yescharacteristic, complemented, Sylow
516C25—861no—
517C2×#41—434no—
518C2×#41—862no—
519C2×#41—862no—
520C2×#41—862no—
521C2×#41—1721no—
522C2×#41—1721no—
523C22×Q8—431no—
524C22×D4—21no—
525C22×D4—431no—
526C22×D4—434no—
527C22×D4—431no—
528C22×D4—862no—
529C22×D4—861no—
530C22×D4—862no—
531C22×D4—862no—
532C22×D4—861no—
533C22×D4—1721no—
534C22×D4—1721no—
535C22×D4C22×D4311yescharacteristic
536C23×C4—431no—
537C23×C4—861no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4C22×D4311yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—862no—
548C22×C8—862no—
549C22×C8—1721no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#124—434no—
553#124—862no—
554#123—868no—
555C22⋊Q8—434no—
556C22⋊Q8—862no—
557#121—22no—
558#121—868no—
559#121C4×D4314yescomplemented
560#120—868no—
561C4×D4—434no—
562C4×D4—434no—
563C4×D4—434no—
564C4×D4—862no—
565C4×D4—1724no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—862no—
570C2×C4⋊C4—862no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—1721no—
577C2×C4⋊C4—1721no—
578C2×C4⋊C4C22×D4311yescharacteristic
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—431no—
584C2×C22⋊C4—431no—
585C2×C22⋊C4—868no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C42—431no—
592C2×C42—861no—
593C4⋊C8—862no—
594#103—862no—
595#103—862no—
596#103—1721no—
597#103—1721no—
598#102—22no—
599#102—41no—
600#102—434no—
601#102—862no—
602#102—862no—
603#102—862no—
604#102—862no—
605#102—1721no—
606C22⋊C8—862no—
607C22⋊C8—862no—
608#97—862no—
609#95—21no—
610#95—861no—
611#95—861no—
612C24—21no—
613C24—431no—
614C24—864no—
615C24—861no—
616C24—3441no—
617C24—3441no—
618C24—1722no—
619C24—1722no—
620C24—1722no—
621C24—1722no—
622C24D4×D4311yescharacteristic
623#41—868no—
624#41—1724no—
625#41—1724no—
626#41—1724no—
627C2×Q8—432no—
628C2×Q8—861no—
629C2×Q8—861no—
630C2×Q8—861no—
631C2×Q8—861no—
632C2×Q8—861no—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—434no—
642C2×D4—432no—
643C2×D4—432no—
644C2×D4—432no—
645C2×D4—864no—
646C2×D4—868no—
647C2×D4—862no—
648C2×D4—862no—
649C2×D4—864no—
650C2×D4—861no—
651C2×D4—861no—
652C2×D4—861no—
653C2×D4—1724no—
654C2×D4—1724no—
655C2×D4—1724no—
656C2×D4—1722no—
657C2×D4—1722no—
658C2×D4—1722no—
659C2×D4—1722no—
660C2×D4C2×C4×D4312yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—432no—
672C22×C4—432no—
673C22×C4—864no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—864no—
681C22×C4—861no—
682C22×C4—3441no—
683C22×C4—3441no—
684C22×C4—3441no—
685C22×C4—3441no—
686C22×C4—1722no—
687C22×C4—1722no—
688C22×C4—1722no—
689C22×C4—1722no—
690C22×C4—1722no—
691C22×C4—1722no—
692C22×C4C2×C4×D4312yes—
693C22×C4D4×D4311yescharacteristic
694C22×C4D4×D4312yes—
695C22×C4C23×D4311yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—1724no—
709C2×C8D4×D4312yes—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—434no—
716C4⋊C4—432no—
717C4⋊C4—864no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—3441no—
722C4⋊C4—1722no—
723C4⋊C4—1722no—
724C4⋊C4—1722no—
725C4⋊C4C2×C4×D4312yes—
726C22⋊C4—24no—
727C22⋊C4—42no—
728C22⋊C4—434no—
729C22⋊C4—434no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—1722no—
735C42—432no—
736C42—432no—
737C42—1722no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—432no—
752C23—432no—
753C23—432no—
754C23—861no—
755C23—861no—
756C23—861no—
757C23—861no—
758C23—862no—
759C23—862no—
760C23—862no—
761C23—3444no—
762C23—3444no—
763C23—3444no—
764C23—3444no—
765C23—3444no—
766C23—1728no—
767C23—1728no—
768C23—1721no—
769C23—1721no—
770C23—1721no—
771C23—1721no—
772C23C22⋊C4×D4312yes—
773C23C2×D4×D4311yescharacteristic
774Q8—862no—
775Q8—862no—
776Q8—1721no—
777Q8—1721no—
778D4—22no—
779D4—22no—
780D4—41no—
781D4—41no—
782D4—84no—
783D4—434no—
784D4—868no—
785D4—862no—
786D4—862no—
787D4—862no—
788D4—1728no—
789D4—1728no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—432no—
806C2×C4—432no—
807C2×C4—432no—
808C2×C4—861no—
809C2×C4—861no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—862no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—3444no—
821C2×C4—3444no—
822C2×C4—3444no—
823C2×C4—1728no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4C22⋊C4×D4312yes—
832C2×C4C22×C4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4#1306337011yescharacteristic
837C2×C4#1306337111yescharacteristic
838C8—22no—
839C8—41no—
840C8—1721no—
841C8—1721no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—434no—
857C22—862no—
858C22—862no—
859C22—862no—
860C22—862no—
861C22—862no—
862C22—862no—
863C22—864no—
864C22—34416no—
865C22—1722no—
866C22—1722no—
867C22—1722no—
868C22—1722no—
869C22—1722no—
870C22—1722no—
871C22C2×C22⋊C4×D4311yescharacteristic
872C22#1458353311yescharacteristic
873C22#1458353811yescharacteristic
874C22AGL(1,ℤ/8)×D4311yescharacteristic
875C22#137×D4311yescharacteristic
876C22#1458370311yescharacteristic
877C22#1458370911yescharacteristic
878C4—22no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—862no—
883C4—862no—
884C4—862no—
885C4—3441no—
886C4—1722no—
887C4—1722no—
888C4C4×D4×D4311yescharacteristic
889C4#1458337111yescharacteristic
890C4#1458353111yescharacteristic
891C4#1458354111yescharacteristic
892C2—42no—
893C2—82no—
894C2—864no—
895C2—1724no—
896C2#1913741311yescharacteristic
897C2#417×D4311yescharacteristic
898C2#1914312011yescharacteristic
899C2#1914608211yescharacteristic
900C2#1914611211yescharacteristic
901C2#1914655111yescharacteristic
902C2#1914667111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1895C2
socleC23×C43C22×D4
prime radicalC2×#14583546C2
cosocleC22×C4×C43C24
hypercenter#1895D43
hypocenterC43#22419
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#14582968C2semidirect
3. C2×#14582901C2semidirect
4. C2×#102×D43C2semidirect
5. #19137491C2semidirect
6. #19135526C2semidirect
7. #19135410C2semidirect
8. #19135017C2semidirect
9. #19134913C2semidirect
10. #19134901C2semidirect
11. #19134594C2semidirect
12. #19134533C2semidirect
13. #19134524C2semidirect
14. #19134419C2semidirect
15. C43×#1895C2semidirect
20. #14583546C4semidirect
29. C22×C4⋊Dic43C22semidirect
33. C2×Dic43⋊C8C22semidirect
35. C2×#13063250C22semidirect
36. C2×#13063250C22semidirect
37. C2×#13063248C22semidirect
38. C2×#13063248C22semidirect
46. C2×C22⋊(C43⋊C8)C22semidirect
48. C2×#13063235C22semidirect
52. #14582768C22semidirect
54. C4⋊C4×Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
57. C22×M16×C43C22semidirect
61. C43×#380C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
70. C2×#10621898C2×C4semidirect
81. C2×D4×D43C2×C4semidirect
93. #13063312C2×C4semidirect
96. #13063305C2×C4semidirect
100. #13063287C2×C4semidirect
132. #13063247D4semidirect
151. #121×C43C2×C4semidirect
374. D172C4×D4semidirect
426. C2×D43#417semidirect
448. #1895D43semidirect
469. C22×M16C2×D43semidirect
509. #380C2×D43semidirect
513. #340C2×D43semidirect
514. #340C2×D43semidirect
515. C43#22419semidirect
559. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835462
C2×#145829682
C2×#145829012
C2×#102×D432
#191374912
#191355262
#191354102
#191350172
#191349132
#191349012
#191345942
#191345332
#191345242
#191344192
C43×#18952
#2241943