Finite Group Databasebeta

← #25112074

Subgroups — #25112074

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×#14583544C211yesmaximal, characteristic
2C2×#14582969C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137495C211yesmaximal, characteristic, complemented
6#19135525C211yesmaximal, characteristic, complemented
7#19135409C211yesmaximal, characteristic, complemented
8#19135032C211yesmaximal, characteristic, complemented
9#19135017C211yesmaximal, characteristic, complemented
10#19134911C211yesmaximal, characteristic, complemented
11#19134901C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic, complemented
15C43×#1802C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic, complemented
19C22×C8×D43C2211yescharacteristic
20#14583544—24no—
21#14583544C418yescomplemented
22C2×#13063313C2211yescharacteristic
23C2×#13063309—21no—
24C2×#13063305C2211yescharacteristic
25C2×#13063300C2211yescharacteristic
26C2×#13063299—21no—
27C2×#13063295—21no—
28C2×C4×D172C2211yescharacteristic
29C2×#13063287—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic, complemented
32C22×(C2×D43)⋊C4—21no—
33#14582969—24no—
34#14582897—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×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
48C2×#13063236C2211yescharacteristic, complemented
49#14582795—21no—
50#14582770—21no—
51#14582770—21no—
52#14582756C2211yescharacteristic
53#14582756C2211yescharacteristic, complemented
54C4×C4⋊Dic43C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#384C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—41no—
69C2×#10621900—41no—
70C2×#10621900C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×D172—21no—
73C22×D172D411yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C22⋊D43—21no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—22no—
80C2×D4×D43—41no—
81C2×D4×D43—41no—
82C2×D4×D43C2×C414yescomplemented
83C23×Dic43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C22×C4×D43C2311yescharacteristic
88C2×#10621872—22no—
89C2×#10621872—22no—
90C2×#10621872—41no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—22no—
94C2×C8×D43—22no—
95C2×C8×D43—41no—
96#13063313—22no—
97#13063313C2×C414yescomplemented
98#13063309—28no—
99#13063305—22no—
100#13063305C2×C414yescomplemented
101#13063300—22no—
102#13063300C2×C414yescomplemented
103#13063299—28no—
104#13063295—28no—
105C4×D172C2×C414yes—
106C4×D172D414yes—
107#13063287—44no—
108C2×C4⋊Dic43—21no—
109C2×C4⋊Dic43D411yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C4⋊C4×D43—22no—
115C4⋊C4×D43—22no—
116C4⋊C4×D43—41no—
117C4⋊C4×D43—41no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—28no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4D411yescharacteristic
126C2×(C2×D43)⋊C4D411yescharacteristic
127C2×C4×Dic43—21no—
128#13063250—22no—
129#13063250—41no—
130#13063248—22no—
131#13063248—41no—
132#13063247—22no—
133#13063247—41no—
134#13063246—22no—
135#13063246D414yescomplemented
136#13063245—22no—
137#13063245—41no—
138(C2×D43)⋊C8—22no—
139(C2×D43)⋊C8—22no—
140#13063236—22no—
141C43⋊#95—21no—
142C43⋊#95—21no—
143C43⋊#95—21no—
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43—21no—
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C4×D4×C43—22no—
149C4×D4×C43C2×C414yescomplemented
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43—21no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C22⋊C4×C43—21no—
156C2×C42×C43C2311yescharacteristic
157C4⋊C8×C43—22no—
158#102×C43—22no—
159#102×C43—22no—
160C24×C43—21no—
161C23×D43—21no—
162C23×D43—24no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—81no—
168C23×D43—81no—
169C23×D43C2×D411yescharacteristic
170C23×D43C2×D411yescharacteristic
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43C22×C412yes—
175C2×D4×C43C2×D412yes—
176C2×D4×C43#4112yes—
177C22×C4×C43—24no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—81no—
182C22×C4×C43—81no—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—24no—
187C2×C22⋊D43—24no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C2×C22⋊D43—42no—
192C22×Dic43—24no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200#10621900—28no—
201#10621900—44no—
202#10621900—44no—
203#10621900—44no—
204D4×D43—28no—
205D4×D43—44no—
206D4×D43—44no—
207D4×D43—44no—
208C2×D172—21no—
209C2×D172—24no—
210C2×D172—22no—
211C2×D172—22no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—81no—
217C2×D172—81no—
218C2×D172C22⋊C414yes—
219C2×D172C22×C412yes—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—81no—
233C2×C4×D43—81no—
234C2×C4×D43C22×C412yes—
235C2×C4×D43C22×C412yes—
236C2×C4×D43C2×D412yes—
237C2×C4×D43C2×D412yes—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86C22×C412yes—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—42no—
256C4⋊C4×C43—81no—
257C4⋊C4×C43C22×C412yes—
258C22⋊C4×C43—24no—
259C42×C43C22×C412yes—
260C42×C43C2×D412yes—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—42no—
266(C2×D43)⋊C4—42no—
267(C2×D43)⋊C4C22⋊C414yes—
268(C2×D43)⋊C4C22⋊C414yes—
269C4⋊Dic43—21no—
270C4⋊Dic43—24no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43C22⋊C414yes—
274C4⋊Dic43C2×D412yes—
275Dic43⋊C4—42no—
276Dic43⋊C4—42no—
277C4×Dic43—42no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8C2×D412yes—
284#10621872—44no—
285C8×D43—44no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43C22×D411yescharacteristic
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—22no—
305C22×D43—48no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—48no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43—84no—
317C22×D43—84no—
318C22×D43C2×C22⋊C412yes—
319C22×D43C2×C22⋊C412yes—
320C22×D43AGL(1,ℤ/8)12yes—
321C22×D43#13712yes—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—22no—
325D4×C43C4×D414yescomplemented
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—22no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—84no—
340C2×C4×C43C2×C22⋊C412yes—
341C2×C4×C43C2×C22⋊C412yes—
342C2×C4×C43C23×C411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C22⋊D43—48no—
349C22⋊D43—48no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—48no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43C2×C22⋊C412yes—
365C2×Dic43C2×C22⋊C412yes—
366D172—28no—
367D172—22no—
368D172—22no—
369D172—41no—
370D172—41no—
371D172—84no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—84no—
381C4×D43—84no—
382Dic86—22no—
383Dic86—22no—
384Dic86—41no—
385Dic86—41no—
386C8×C43—41no—
387C8×C43—41no—
388C43⋊C8—22no—
389C43⋊C8—41no—
390#22419—431nomaximal, Sylow
391C22×C43—24no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43C22×C22⋊C411yescharacteristic
399C22×C43D4211yescharacteristic
400C22×C43#54611yescharacteristic
401C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C43C2×#13711yescharacteristic
403C22×C43#57611yescharacteristic
404C22×C43#57711yescharacteristic
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—41no—
415C2×D43—41no—
416C2×D43—41no—
417C2×D43—41no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—816no—
422C2×D43—81no—
423C2×D43—81no—
424C2×D43—81no—
425C2×D43—81no—
426C2×D43#41714yescomplemented
427C4×C43—22no—
428C4×C43—22no—
429C4×C43—42no—
430C4×C43—81no—
431C4×C43—81no—
432C4×C43C2×C4×D411yescharacteristic
433C4×C43#51811yescharacteristic
434C4×C43D4211yescharacteristic
435C4×C43#54611yescharacteristic
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#1895—431no—
449#1892—431no—
450#1874—431no—
451#1872—431no—
452#1802D4311yescharacteristic, complemented
453#1788—431no—
454#1786—431no—
455#1762—431no—
456C2×C43—44no—
457C2×C43D4×C22⋊C411yescharacteristic
458C2×C43C2×#41711yescharacteristic
459C2×C43#289711yescharacteristic
460C2×C43#326411yescharacteristic
461C2×C43#326611yescharacteristic
462C2×C43#330611yescharacteristic
463C2×C43#331411yescharacteristic
464D43—24no—
465D43—42no—
466D43—82no—
467C22×#41—431no—
468C23×D4—431no—
469C22×M16—431no—
470C23×C8—431no—
471#546—438no—
472#546—864no—
473C2×#124—431no—
474C2×#123—861no—
475C2×C22⋊Q8—431no—
476C2×#121—431no—
477C2×#121—861no—
478C2×#120—861no—
479C2×C4×D4—431no—
480C2×C4×D4—861no—
481C2×C4×D4C2×D4311yescharacteristic
482C22×C4⋊C4—431no—
483C22×C4⋊C4—431no—
484C22×C22⋊C4—861no—
485#435—864no—
486C2×C4⋊C8C2×D4311yescharacteristic, complemented
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#384C2×D4311yescharacteristic, complemented
508#380—431no—
509#380—431no—
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—434no—
525C22×D4—431no—
526C22×D4—431no—
527C22×D4—861no—
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—21no—
537C23×C4—431no—
538C23×C4—431no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4—861no—
542C2×M16—862no—
543C2×M16—862no—
544C2×M16—1721no—
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—434no—
558#121—868no—
559#121—862no—
560#120—868no—
561C4×D4—22no—
562C4×D4—434no—
563C4×D4—434no—
564C4×D4—1724no—
565C4×D4C4×D4314yescomplemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—862no—
572C2×C4⋊C4—862no—
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—431no—
583C2×C22⋊C4—431no—
584C2×C22⋊C4—868no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C42—861no—
592C2×C42C22×D4311yescharacteristic
593C4⋊C8—22no—
594#103—862no—
595#103—862no—
596#103—1721no—
597#103—1721no—
598#102—22no—
599#102—22no—
600#102—434no—
601#102—862no—
602#102—862no—
603#102—862no—
604#102—1721no—
605#102—1721no—
606C22⋊C8—862no—
607C22⋊C8—862no—
608#97—862no—
609#95—861no—
610#95—861no—
611#95—861no—
612C24—21no—
613C24—431no—
614C24—431no—
615C24—864no—
616C24—861no—
617C24—3441no—
618C24—3441no—
619C24—1722no—
620C24—1722no—
621C24—1722no—
622C24—1722no—
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—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—434no—
637C2×D4—432no—
638C2×D4—862no—
639C2×D4—862no—
640C2×D4—864no—
641C2×D4—864no—
642C2×D4—868no—
643C2×D4—864no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—3441no—
650C2×D4—3441no—
651C2×D4—1724no—
652C2×D4—1724no—
653C2×D4—1724no—
654C2×D4—1722no—
655C2×D4—1722no—
656C2×D4—1722no—
657C2×D4—1722no—
658C2×D4C2×C4×D4312yes—
659C2×D4D4×D4312yes—
660C2×D4#1062190212yes—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—81no—
666C22×C4—81no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—432no—
670C22×C4—432no—
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—861no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—3441no—
686C22×C4—3441no—
687C22×C4—1722no—
688C22×C4—1722no—
689C22×C4—1722no—
690C22×C4—1722no—
691C22×C4—1722no—
692C22×C4—1722no—
693C22×C4D4×D4311yescharacteristic
694C22×C4D4×D4311yescharacteristic
695C22×C4C23×D4311yescharacteristic
696M16—1724no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—432no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—1724no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—42no—
716C4⋊C4—81no—
717C4⋊C4—434no—
718C4⋊C4—432no—
719C4⋊C4—864no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—1722no—
724C4⋊C4—1722no—
725C4⋊C4C2×C4×D4312yes—
726C22⋊C4—24no—
727C22⋊C4—434no—
728C22⋊C4—434no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—1722no—
734C22⋊C4—1722no—
735C42—1722no—
736C42C2×C4×D4312yes—
737C42D4×D4312yes—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—432no—
746C23—432no—
747C23—432no—
748C23—432no—
749C23—861no—
750C23—861no—
751C23—861no—
752C23—861no—
753C23—861no—
754C23—861no—
755C23—861no—
756C23—861no—
757C23—861no—
758C23—861no—
759C23—862no—
760C23—3444no—
761C23—3444no—
762C23—3444no—
763C23—3444no—
764C23—3444no—
765C23—1728no—
766C23—1728no—
767C23—1721no—
768C23—1721no—
769C23—1721no—
770C23—1721no—
771C23—1721no—
772C23—1721no—
773C23C2×D4×D4311yescharacteristic
774Q8—862no—
775Q8—862no—
776Q8—1721no—
777Q8—1721no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—868no—
782D4—862no—
783D4—862no—
784D4—3444no—
785D4—1728no—
786D4—1728no—
787D4—1721no—
788D4—1721no—
789D4#1306328714yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—84no—
804C2×C4—432no—
805C2×C4—432no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—861no—
809C2×C4—861no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—862no—
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—1728no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4C22⋊C4×D4312yes—
831C2×C4C22⋊C4×D4312yes—
832C2×C4C22×C4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4C2×#1062190211yescharacteristic
836C2×C4#1306337111yescharacteristic
837C2×C4#1306337111yescharacteristic
838C8—41no—
839C8—41no—
840C8—862no—
841C8—1721no—
842C22—24no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—434no—
850C22—862no—
851C22—862no—
852C22—862no—
853C22—862no—
854C22—862no—
855C22—862no—
856C22—862no—
857C22—862no—
858C22—862no—
859C22—34416no—
860C22—3441no—
861C22—3441no—
862C22—3441no—
863C22—3441no—
864C22—1722no—
865C22—1722no—
866C22—1722no—
867C22—1721no—
868C22—1721no—
869C22—1721no—
870C22—1721no—
871C22C2×C22⋊C4×D4311yescharacteristic
872C22#1458353311yescharacteristic
873C22#1458354011yescharacteristic
874C22AGL(1,ℤ/8)×D4311yescharacteristic
875C22#137×D4311yescharacteristic
876C22#1458370011yescharacteristic
877C22#1458370511yescharacteristic
878C4—22no—
879C4—22no—
880C4—42no—
881C4—81no—
882C4—81no—
883C4—862no—
884C4—862no—
885C4—3441no—
886C4—1722no—
887C4—1722no—
888C4C2×#1306328711yescharacteristic
889C4#1458337311yescharacteristic
890C4#1458353311yescharacteristic
891C4#1458354011yescharacteristic
892C2—44no—
893C2—864no—
894C2—3442no—
895C2—1722no—
896C2#1913741511yescharacteristic
897C2#417×D4311yescharacteristic
898C2#1914311611yescharacteristic
899C2#1914607011yescharacteristic
900C2#1914611111yescharacteristic
901C2#1914655311yescharacteristic
902C2#1914667311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1802C2
socleC23×C43C22×D4
prime radicalC2×#14583544C2
cosocleC22×C4×C43C24
hypercenter#1802D43
hypocenterC43#22419
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#14582969C2semidirect
3. C2×#14582897C2semidirect
4. C2×#102×D43C2semidirect
5. #19137495C2semidirect
6. #19135525C2semidirect
7. #19135409C2semidirect
8. #19135032C2semidirect
9. #19135017C2semidirect
10. #19134911C2semidirect
11. #19134901C2semidirect
12. #19134532C2semidirect
13. #19134524C2semidirect
14. #19134420C2semidirect
15. C43×#1802C2semidirect
18. C22×#10621872C22semidirect
21. #14583544C4semidirect
31. C2×C4⋊C4×D43C22semidirect
35. C2×#13063250C22semidirect
36. C2×#13063250C22semidirect
37. C2×#13063248C22semidirect
38. C2×#13063248C22semidirect
47. C2×(C2×D43)⋊C8C22semidirect
48. C2×#13063236C22semidirect
53. #14582756C22semidirect
54. C4×C4⋊Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×C4⋊C8×C43C22semidirect
61. C43×#384C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
70. C2×#10621900C2×C4semidirect
82. C2×D4×D43C2×C4semidirect
97. #13063313C2×C4semidirect
100. #13063305C2×C4semidirect
102. #13063300C2×C4semidirect
135. #13063246D4semidirect
149. C4×D4×C43C2×C4semidirect
325. D4×C43C4×D4semidirect
426. C2×D43#417semidirect
452. #1802D43semidirect
486. C2×C4⋊C8C2×D43semidirect
507. #384C2×D43semidirect
513. #340C2×D43semidirect
514. #340C2×D43semidirect
515. C43#22419semidirect
565. C4×D4C4×D43semidirect
789. D4#13063287semidirect

Maximal subgroups

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

subgroupindex
C2×#145835442
C2×#145829692
C2×#145828972
C2×#102×D432
#191374952
#191355252
#191354092
#191350322
#191350172
#191349112
#191349012
#191345322
#191345242
#191344202
C43×#18022
#2241943