Finite Group Databasebeta

← #25097571

Subgroups — #25097571

Order 11008.

1550 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621900C211yesmaximal, characteristic
2C2×#14582938C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic
4C2×#14582897C211yesmaximal, characteristic
5#389×D43C211yesmaximal, characteristic, complemented
6#19134864C211yesmaximal, characteristic, complemented
7#19134860C211yesmaximal, characteristic, complemented
8#19134856C211yesmaximal, characteristic, complemented
9#19134852C211yesmaximal, characteristic, complemented
10#19134848C211yesmaximal, characteristic, complemented
11#19134844C211yesmaximal, characteristic, complemented
12#19134840C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134287C211yesmaximal, characteristic, complemented
15C43×#1864C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C4×#10621900—24no—
20C4×#10621900—24no—
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24C2×C4×C22⋊D43—21no—
25C2×(C22⋊D43)⋊C4—21no—
26C2×#13063283C2211yescharacteristic
27C2×#13063281—21no—
28C2×C4⋊C4×D43—21no—
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31C22×C4×Dic43—21no—
32C2×C42×D43C2211yescharacteristic
33#14582938—24no—
34C2×#13063259C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37#14582897—24no—
38#14582897C418yescomplemented
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×#13063246C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582797C2211yescharacteristic
47#14582796—21no—
48#14582795C2211yescharacteristic
49#14582794—21no—
50#95×D43—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582654C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×#106×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#389C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900C2×C414yes—
68C2×#10621900D414yes—
69C2×#10621900Q814yes—
70C22×Dic86C2311yescharacteristic
71C22×C22⋊D43—21no—
72C23×Dic43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43D411yescharacteristic
77C22×C4×D43D411yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C2×#10621872—22no—
80C2×#10621872—22no—
81C2×#10621872—22no—
82C2×#10621872—22no—
83C2×#10621872—22no—
84C2×#10621872C2×C414yescomplemented
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C4×Dic86—22no—
88C4×Dic86—22no—
89#13063290—22no—
90#13063290—22no—
91D4×Dic43—22no—
92D4×Dic43—22no—
93C4×C22⋊D43—28no—
94(C22⋊D43)⋊C4—28no—
95#13063283—22no—
96#13063283D414yes—
97#13063281—28no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C4⋊C4×D43—22no—
109C4⋊C4×D43—22no—
110C4⋊C4×D43—22no—
111C4⋊C4×D43—44no—
112C4⋊C4×D43C2×C414yescomplemented
113C2×C22⋊Dic43—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×C4×Dic43—28no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43D411yescharacteristic
120C2×C4×Dic43D411yescharacteristic
121C2×C4×Dic43C2311yescharacteristic
122C42×D43—22no—
123C42×D43—22no—
124#13063259—22no—
125#13063258—22no—
126#13063256—22no—
127#13063250—22no—
128#13063250C2×C414yescomplemented
129#13063248—22no—
130#13063248C2×C414yescomplemented
131#13063246—22no—
132#13063246C2×C414yescomplemented
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C22×D4×C43C2311yescharacteristic
137C23×C4×C43—21no—
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C4×D4×C43—22no—
141C4×D4×C43—22no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43C2311yescharacteristic
148#106×C43—22no—
149#102×C43—22no—
150#102×C43C2×C414yescomplemented
151#95×C43—21no—
152C24×C43—21no—
153C23×D43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43C22×C412yes—
158C2×D4×C43C2×D412yes—
159C2×D4×C43C2×Q812yes—
160C22×C4×C43—24no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×C22⋊D43—24no—
170C2×C22⋊D43—24no—
171C2×C22⋊D43—24no—
172C22×Dic43—24no—
173C22×Dic43—24no—
174C22×Dic43—24no—
175C22×Dic43—24no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—42no—
181C22×Dic43—42no—
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185#10621900—28no—
186#10621900—28no—
187#10621900—28no—
188#10621900C4⋊C4116yescomplemented
189C2×C4×D43—22no—
190C2×C4×D43—22no—
191C2×C4×D43—24no—
192C2×C4×D43—22no—
193C2×C4×D43—22no—
194C2×C4×D43—41no—
195C2×C4×D43—41no—
196C2×C4×D43—42no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43C22×C412yes—
202C2×C4×D43C2×D412yes—
203C2×C4×D43C2×D412yes—
204C2×C4×D43C2×Q812yes—
205C2×C4×D43#4112yes—
206C2×C4×D43#4112yes—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86C22×C412yes—
211C2×Dic86C2×D412yes—
212C2×Dic86C2×Q812yes—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43C22×C412yes—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—42no—
224C4⋊C4×C43C22×C412yes—
225C4⋊C4×C43C2×D412yes—
226C22⋊C4×C43—24no—
227C42×C43—21no—
228C42×C43—21no—
229C22⋊Dic43—24no—
230(C2×D43)⋊C4—24no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—42no—
236C4⋊Dic43C22×C412yes—
237C4⋊Dic43C2×D412yes—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—42no—
242Dic43⋊C4—42no—
243Dic43⋊C4—42no—
244C4×Dic43—24no—
245C4×Dic43—24no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248C4×Dic43—22no—
249C4×Dic43—22no—
250C4×Dic43—24no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8C22×C412yes—
257#10621872—28no—
258#10621872—44no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43C22×D411yescharacteristic
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43C4×D412yes—
272C22×D43#12012yes—
273C22×D43C22⋊Q812yes—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—22no—
277D4×C43C2×C4⋊C414yescomplemented
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—48no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43#13712yes—
294C2×C4×C43C23×C411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C22×Q811yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C22⋊D43—216no—
301C2×Dic43—22no—
302C2×Dic43—21no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—216no—
307C2×Dic43—22no—
308C2×Dic43—21no—
309C2×Dic43—22no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—48no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43C4×D412yes—
321C2×Dic43#12012yes—
322C2×Dic43C22⋊Q812yes—
323C2×Dic43AGL(1,ℤ/8)12yes—
324C4×D43—44no—
325C4×D43—44no—
326C4×D43—48no—
327C4×D43—84no—
328C4×D43C2×C4⋊C414yes—
329C4×D43C4×D414yes—
330C4×D43C22⋊Q814yes—
331C4×D43#12314yes—
332Dic86—22no—
333Dic86—22no—
334Dic86—22no—
335Dic86C2×C4⋊C414yescomplemented
336C8×C43—22no—
337C8×C43—41no—
338C43⋊C8—22no—
339C43⋊C8—41no—
340#20875—431nomaximal, Sylow
341C22×C43—24no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43C2×C4×D411yescharacteristic
349C22×C43C2×#12011yescharacteristic
350C22×C43C2×C22⋊Q811yescharacteristic
351C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C43C2×#13711yescharacteristic
353C22×C43#57511yescharacteristic
354C22×C43#57511yescharacteristic
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43#38514yes—
362C4×C43—22no—
363C4×C43—42no—
364C4×C43—41no—
365C4×C43—42no—
366C4×C43—81no—
367C4×C43C22×C4⋊C411yescharacteristic
368C4×C43C2×C4×D411yescharacteristic
369C4×C43C2×C22⋊Q811yescharacteristic
370C4×C43C2×#12311yescharacteristic
371Dic43—22no—
372Dic43—24no—
373Dic43—42no—
374Dic43—42no—
375Dic43—41no—
376Dic43—81no—
377Dic43#38514yes—
378C2×C4×#41—431no—
379C2×#428—431no—
380C2×#417—431no—
381C2×#417—431no—
382C2×#389—431no—
383#1865—431no—
384#1865—431no—
385#1864—431no—
386#1864D4311yescharacteristic, complemented
387#1863—431no—
388#1863—431no—
389#1862—431no—
390#1862—431no—
391#1736—431no—
392#1728—431no—
393C2×C43—44no—
394C2×C43C2×#38511yescharacteristic
395C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
396C2×C43C4×#13711yescharacteristic
397C2×C43#300611yescharacteristic
398C2×C43#300711yescharacteristic
399C2×C43#307911yescharacteristic
400C2×C43#308011yescharacteristic
401D43—24no—
402C22×#41—431no—
403C22×M16—431no—
404C22×M16—431no—
405C4×#41—864no—
406C4×#41—864no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×D4—431no—
410C2×C4×D4—861no—
411C2×C4×D4—861no—
412C2×C4×D4C2×D4311yescharacteristic
413C2×#117—431no—
414C2×#117—861no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—861no—
418C22×C42—431no—
419C22×C42—861no—
420#428—864no—
421C2×#107—431no—
422C2×#107—431no—
423C2×#106—431no—
424C2×#106C2×D4311yescharacteristic
425#417—438no—
426#417—864no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102C2×D4311yescharacteristic
434C2×#102C2×D4311yescharacteristic
435#389—431no—
436#389—431no—
437#389—431no—
438#389—861no—
439#389—861no—
440#389C2×D4311yescharacteristic
441C2×#95—861no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340C2×D4311yescharacteristic
446#336—431no—
447#336—431no—
448#336—431no—
449#336C2×D4311yescharacteristic
450C43#2087511yescharacteristic, complemented, Sylow
451C2×#41—434no—
452C2×#41—434no—
453C2×#41—434no—
454C2×#41—862no—
455C2×#41—862no—
456C2×#41—862no—
457C22×Q8—431no—
458C22×D4—861no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—431no—
462C23×C4—431no—
463C23×C4—431no—
464C23×C4—861no—
465C23×C4—861no—
466C23×C4—861no—
467C23×C4—861no—
468C2×M16—434no—
469C2×M16—862no—
470C2×M16—862no—
471C2×M16—862no—
472C2×M16—862no—
473C2×M16—862no—
474C22×C8—431no—
475C22×C8—431no—
476C22×C8C22×D4311yescharacteristic
477C22×C8C22×D4311yescharacteristic
478C4×Q8—862no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—868no—
485C4×D4—862no—
486C4×D4—868no—
487C4×D4—862no—
488#117—434no—
489#117—868no—
490#117—862no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—434no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—862no—
497C2×C4⋊C4—862no—
498C2×C4⋊C4—862no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—1724no—
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C42—431no—
514C2×C42—431no—
515C2×C42—431no—
516C2×C42—862no—
517C2×C42—862no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42—868no—
521C2×C42—861no—
522C2×C42C22×D4311yescharacteristic
523#107—862no—
524#107—862no—
525#106—22no—
526#106—862no—
527#103—434no—
528#103—434no—
529#103—862no—
530#103—862no—
531#102—22no—
532#102—434no—
533#102—862no—
534#102C4×D4314yescomplemented
535#95—21no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—431no—
541#41—4316no—
542#41—868no—
543#41—868no—
544#41—868no—
545C2×Q8—432no—
546C2×Q8—432no—
547C2×Q8—432no—
548C2×Q8—861no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—864no—
555C2×D4—864no—
556C2×D4—864no—
557C2×D4C2×C4×D4312yes—
558C2×D4D4×D4312yes—
559C2×D4Q8×D4312yes—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—431no—
567C22×C4—432no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—432no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—864no—
579C22×C4—864no—
580C22×C4—864no—
581C22×C4—864no—
582C22×C4—861no—
583C22×C4—864no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—862no—
587C22×C4—861no—
588C22×C4—1721no—
589C22×C4—1721no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4—1722no—
593C22×C4—1722no—
594C22×C4—1722no—
595C22×C4—1722no—
596C22×C4—1722no—
597C22×C4D4×D4311yescharacteristic
598C22×C4D4×D4311yescharacteristic
599C22×C4C23×D4311yescharacteristic
600M16—868no—
601M16—1724no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—432no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8C2×C4×D4312yes—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—432no—
620C4⋊C4—432no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—1722no—
629C4⋊C4—1722no—
630C4⋊C4—1722no—
631C4⋊C4—1722no—
632C4⋊C4C2×C4×D4312yes—
633C4⋊C4D4×D4312yes—
634C22⋊C4—24no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C42—21no—
638C42—21no—
639C42—862no—
640C42—862no—
641C42—864no—
642C42—864no—
643C42—864no—
644C42—861no—
645C42—861no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—432no—
654C23—432no—
655C23—432no—
656C23—861no—
657C23—861no—
658C23—861no—
659C23—861no—
660C23C2×D4×D4311yescharacteristic
661Q8—434no—
662Q8—862no—
663Q8—862no—
664Q8—862no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—8616no—
669D4C4⋊C4×D4314yescomplemented
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—432no—
686C2×C4—432no—
687C2×C4—432no—
688C2×C4—434no—
689C2×C4—434no—
690C2×C4—434no—
691C2×C4—434no—
692C2×C4—432no—
693C2×C4—8616no—
694C2×C4—862no—
695C2×C4—861no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—861no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—3444no—
705C2×C4—1724no—
706C2×C4—1724no—
707C2×C4—1728no—
708C2×C4—1728no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4#1306335412yes—
717C2×C4C22×C4×D4311yescharacteristic
718C2×C4C2×D4×D4311yescharacteristic
719C2×C4C2×D4×D4311yescharacteristic
720C2×C4C2×Q8×D4311yescharacteristic
721C2×C4#41×D4311yescharacteristic
722C2×C4#41×D4311yescharacteristic
723C8—22no—
724C8—41no—
725C8—862no—
726C8—1721no—
727C22—24no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—434no—
735C22—862no—
736C22—862no—
737C22—862no—
738C22—862no—
739C22—862no—
740C22—862no—
741C22C4×D4×D4311yescharacteristic
742C22#120×D4311yescharacteristic
743C22C22⋊Q8×D4311yescharacteristic
744C22AGL(1,ℤ/8)×D4311yescharacteristic
745C22C2×#1306335411yescharacteristic
746C22#1458369511yescharacteristic
747C22#1458369611yescharacteristic
748C4—22no—
749C4—41no—
750C4—42no—
751C4—42no—
752C4—81no—
753C4—434no—
754C4—862no—
755C4—864no—
756C4—3441no—
757C4—1722no—
758C4—1721no—
759C4—1722no—
760C4C2×C4⋊C4×D4311yescharacteristic
761C4C4×D4×D4311yescharacteristic
762C4C22⋊Q8×D4311yescharacteristic
763C4#123×D4311yescharacteristic
764C2—44no—
765C2—864no—
766C2#385×D4311yescharacteristic
767C2#1914340611yescharacteristic
768C2C4×#1306335411yescharacteristic
769C2#1914384411yescharacteristic
770C2#1914385011yescharacteristic
771C2#1914440711yescharacteristic
772C2#1914441211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1864C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1864D43
hypocenterC43#20875
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#14582938C2semidirect
5. #389×D43C2semidirect
6. #19134864C2semidirect
7. #19134860C2semidirect
8. #19134856C2semidirect
9. #19134852C2semidirect
10. #19134848C2semidirect
11. #19134844C2semidirect
12. #19134840C2semidirect
13. #19134313C2semidirect
14. #19134287C2semidirect
15. C43×#1864C2semidirect
38. #14582897C4semidirect
84. C2×#10621872C2×C4semidirect
112. C4⋊C4×D43C2×C4semidirect
128. #13063250C2×C4semidirect
130. #13063248C2×C4semidirect
132. #13063246C2×C4semidirect
150. #102×C43C2×C4semidirect
188. #10621900C4⋊C4semidirect
277. D4×C43C2×C4⋊C4semidirect
335. Dic86C2×C4⋊C4semidirect
386. #1864D43semidirect
450. C43#20875semidirect
534. #102C4×D43semidirect
669. D4C4⋊C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
C2×#145829382
C2×#145828972
#389×D432
#191348642
#191348602
#191348562
#191348522
#191348482
#191348442
#191348402
#191343132
#191342872
C43×#18642
#2087543