Finite Group Databasebeta

← #25063756

Subgroups — #25063756

Order 11008.

1574 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583409C211yesmaximal, characteristic
2#407×D43C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D43C211yesmaximal, characteristic, complemented
4#19133116C211yesmaximal, characteristic, complemented
5#19133114C211yesmaximal, characteristic, complemented
6#19133111C211yesmaximal, characteristic, complemented
7#19133096C214yesmaximal, complemented
8#19133083C214yesmaximal, complemented
9C43×#1507C211yesmaximal, characteristic, complemented
10C22×#10621900C411yescharacteristic, complemented
11C23×C4×D43C2211yescharacteristic
12C2×M16×D43—21no—
13#14583409—21no—
14#14583409—21no—
15#14583409—21no—
16#14583409—21no—
17#14583409C412yescomplemented
18#14583409C412yescomplemented
19#14583409C2212yes—
20#14583409C2212yes—
21C2×#13063307—21no—
22C2×#13063305C411yescharacteristic, complemented
23C2×#13063304C2211yescharacteristic
24C2×#13063296C411yescharacteristic, complemented
25C2×#13063293—21no—
26C2×D4×Dic43—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063283C411yescharacteristic, complemented
29C2×C22⋊C4×D43—21no—
30C2×C42×D43—21no—
31#14582863C2211yescharacteristic
32#14582862—21no—
33#14582861—21no—
34#14582861C2212yescomplemented
35C22⋊C8×D43—21no—
36C22⋊C8×D43C2212yescomplemented
37C22⋊C4×Dic43—21no—
38C4×(C2×D43)⋊C4—21no—
39C4×C22⋊Dic43C2211yescharacteristic
40#14582746C2212yescomplemented
41#95×D43C2212yescomplemented
42#14582637C2214yescomplemented
43#14582635C2214yescomplemented
44#14582633C2214yescomplemented
45C2×#121×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C4×C22⋊C4×C43C2211yescharacteristic
48C43×#327C2214yescomplemented
49C24×D43D411yescharacteristic
50C2×#10621900—21no—
51C2×#10621900—21no—
52C2×#10621900—44no—
53C2×#10621900C2×C412yes—
54C2×#10621900C2×C412yescomplemented
55C22×Dic86C2×C411yescharacteristic, complemented
56C22×C22⋊D43—21no—
57C22×C22⋊D43—21no—
58C23×Dic43—21no—
59C23×Dic43D411yescharacteristic
60C22×C4×D43—22no—
61C22×C4×D43—44no—
62C22×C4×D43C2×C411yescharacteristic
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43C2×C411yescharacteristic
65C22×C4×D43C2×C411yescharacteristic
66C22×C4×D43D411yescharacteristic
67C22×C4×D43D411yescharacteristic
68C22×C4×D43D411yescharacteristic
69C22×C4×D43D411yescharacteristic
70C22×C4×D43D411yescharacteristic
71C22×C4×D43D411yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C2×#10621877—21no—
75C2×#10621872—22no—
76M16×D43—44no—
77C2×C8×D43—22no—
78#13063307—22no—
79#13063307—22no—
80#13063307—22no—
81#13063307—22no—
82#13063305—21no—
83#13063305—21no—
84#13063305C2×C412yes—
85#13063305C2×C412yescomplemented
86#13063304—21no—
87#13063304—21no—
88#13063304C2×C412yescomplemented
89#13063304C2312yes—
90#13063296—21no—
91#13063296—21no—
92#13063296C2×C412yes—
93#13063296C2×C412yescomplemented
94#13063293—22no—
95#13063293—22no—
96#13063293—22no—
97#13063293—22no—
98D4×Dic43—22no—
99D4×Dic43—22no—
100D4×Dic43—22no—
101D4×Dic43—22no—
102(C22⋊D43)⋊C4—22no—
103(C22⋊D43)⋊C4—22no—
104(C22⋊D43)⋊C4—22no—
105(C22⋊D43)⋊C4—22no—
106#13063283—21no—
107#13063283—21no—
108#13063283C2×C412yes—
109#13063283C2×C412yescomplemented
110C2×C4⋊Dic43—21no—
111C2×C4⋊Dic43C2×C411yescharacteristic, complemented
112C2×Dic43⋊C4—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—22no—
119C22⋊C4×D43—28no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—22no—
123C42×D43—44no—
124C22⋊(C43⋊C8)—21no—
125C22⋊(C43⋊C8)C2312yes—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128C43⋊#95—22no—
129C43⋊#95C2312yes—
130C22×D4×C43—21no—
131C22×D4×C43C2×C411yescharacteristic, complemented
132C23×C4×C43C2311yescharacteristic
133C2×M16×C43—21no—
134#121×C43—21no—
135#121×C43—21no—
136#121×C43C2×C412yescomplemented
137#121×C43C2312yes—
138C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C42×C43—21no—
142C22⋊C8×C43—21no—
143C22⋊C8×C43C2312yes—
144#95×C43C2312yes—
145C24×C43—21no—
146C24×C43C2×D411yescharacteristic
147C23×D43—24no—
148C23×D43—42no—
149C23×D43—42no—
150C23×D43C22⋊C411yescharacteristic
151C23×D43C22⋊C411yescharacteristic
152C23×D43C22⋊C411yescharacteristic
153C23×D43C22⋊C411yescharacteristic
154C23×D43C2×D411yescharacteristic
155C23×D43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C2×D4×C43—44no—
160C2×D4×C43—42no—
161C2×D4×C43C22×C412yes—
162C22×C4×C43—21no—
163C22×C4×C43—22no—
164C22×C4×C43—42no—
165C22×C4×C43C22×C411yescharacteristic
166C22×C4×C43C22×C411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—22no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—44no—
176C2×C22⋊D43—44no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—22no—
182C22×Dic43—42no—
183C22×Dic43—44no—
184C22×Dic43C22⋊C411yescharacteristic
185C22×Dic43C22⋊C411yescharacteristic
186C22×Dic43C22⋊C411yescharacteristic
187C22×Dic43C22⋊C411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190#10621900—44no—
191#10621900—44no—
192#10621900—44no—
193#10621900—44no—
194C2×C4×D43—24no—
195C2×C4×D43—24no—
196C2×C4×D43—24no—
197C2×C4×D43—28no—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43—44no—
202C2×C4×D43—44no—
203C2×C4×D43—42no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43C22⋊C411yescharacteristic
210C2×C4×D43C22⋊C411yescharacteristic
211C2×C4×D43C22⋊C411yescharacteristic
212C2×C4×D43C22⋊C411yescharacteristic
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22⋊C411yescharacteristic
217C2×C4×D43C22×C411yescharacteristic
218C2×C4×D43C22×C411yescharacteristic
219C2×C4×D43C22×C411yescharacteristic
220C2×C4×D43C22×C411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×C4×D43C2×D411yescharacteristic
225C2×Dic86—21no—
226C2×Dic86—42no—
227C2×Dic86C22×C412yes—
228M16×C43—42no—
229C2×C8×C43—22no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C22×C412yes—
232C22⋊C4×C43—24no—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—22no—
235C42×C43—42no—
236C22⋊Dic43—24no—
237C22⋊Dic43—22no—
238C22⋊Dic43—22no—
239C22⋊Dic43—22no—
240C22⋊Dic43—22no—
241(C2×D43)⋊C4—28no—
242(C2×D43)⋊C4—22no—
243(C2×D43)⋊C4—22no—
244(C2×D43)⋊C4—22no—
245(C2×D43)⋊C4—22no—
246C4⋊Dic43—21no—
247C4⋊Dic43—22no—
248C4⋊Dic43—22no—
249C4⋊Dic43C22×C412yes—
250Dic43⋊C4—22no—
251Dic43⋊C4—22no—
252C4×Dic43—22no—
253C4×Dic43—22no—
254C4×Dic43—44no—
255C4×Dic43—42no—
256#10621877—42no—
257C2×C43⋊C8—22no—
258#10621872—44no—
259C8×D43—44no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—41no—
264C23×C43—42no—
265C23×C43—42no—
266C23×C43—42no—
267C23×C43C2×C22⋊C411yescharacteristic
268C23×C43C2×C22⋊C411yescharacteristic
269C23×C43C22×D411yescharacteristic
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—416no—
288C22×D43#10414yes—
289C22×D43C2×C22⋊C411yescharacteristic
290C22×D43C2×C22⋊C411yescharacteristic
291C22×D43C2×C22⋊C411yescharacteristic
292C22×D43C2×C22⋊C411yescharacteristic
293D4×C43—42no—
294D4×C43—44no—
295D4×C43—44no—
296D4×C43—42no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—24no—
301C2×C4×C43—22no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43C2×C22⋊C411yescharacteristic
309C2×C4×C43C2×C22⋊C411yescharacteristic
310C2×C4×C43C23×C411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C22⋊D43—44no—
313C22⋊D43—44no—
314C22⋊D43—44no—
315C22⋊D43—44no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—24no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—44no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—44no—
331C2×Dic43C2×C22⋊C411yescharacteristic
332C2×Dic43C2×C22⋊C411yescharacteristic
333C2×Dic43C2×C22⋊C411yescharacteristic
334C2×Dic43C2×C22⋊C411yescharacteristic
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—41no—
345C4×D43—41no—
346C4×D43—41no—
347C4×D43—41no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—416no—
351C4×D43#9914yes—
352Dic86—42no—
353Dic86—42no—
354C8×C43—42no—
355C43⋊C8—42no—
356#17542—431nomaximal, Sylow
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—21no—
364C22×C43—44no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—84no—
369C22×C43C2×#10412yes—
370C22×C43C22×C22⋊C411yescharacteristic
371C22×C43#57512yes—
372C2×D43—28no—
373C2×D43—21no—
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—21no—
380C2×D43—21no—
381C2×D43—21no—
382C2×D43—44no—
383C2×D43—44no—
384C2×D43—44no—
385C2×D43—44no—
386C2×D43—44no—
387C2×D43C2×#9912yes—
388C2×D43C2×#10412yes—
389C2×D43C2×#10412yes—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—21no—
393C4×C43—44no—
394C4×C43—42no—
395C4×C43C2×#9912yes—
396Dic43—21no—
397Dic43—21no—
398Dic43—21no—
399Dic43—44no—
400Dic43—42no—
401Dic43—42no—
402Dic43C2×#9912yes—
403C2×#525—431no—
404C2×#407—431no—
405C2×C4×C22⋊C4—431no—
406#1508—431no—
407#1508—431no—
408#1507—431no—
409#1507D4311yescharacteristic, complemented
410#1504—434no—
411#1501—434no—
412C2×C43—22no—
413C2×C43—22no—
414C2×C43—41no—
415C2×C43—82no—
416C2×C43C22×#9911yescharacteristic
417C2×C43#289611yescharacteristic
418C2×C43C22×#10411yescharacteristic
419D43—22no—
420D43—22no—
421D43—22no—
422D43—41no—
423C22×#41—431no—
424C24×C4—431no—
425C22×M16—861no—
426#525—432no—
427#525—432no—
428#525—432no—
429#525—432no—
430#525—861no—
431#525—861no—
432#525—861no—
433#525—861no—
434C2×#123—861no—
435C2×C22⋊Q8—431no—
436C2×C22⋊Q8—431no—
437C2×#121—431no—
438C2×#121C2×D4311yescharacteristic
439C2×#120—861no—
440C2×C4×D4—861no—
441C2×C4×D4—861no—
442C2×#117—431no—
443C22×C22⋊C4—861no—
444C22×C42—861no—
445#407—431no—
446#407—432no—
447#407—861no—
448#407—861no—
449#407C2×D4311yescharacteristic
450C2×C22⋊C8—432no—
451C2×C22⋊C8—861no—
452C4×C22⋊C4—431no—
453C4×C22⋊C4—432no—
454C4×C22⋊C4—861no—
455C4×C22⋊C4—861no—
456C4×C22⋊C4C2×D4311yescharacteristic
457C2×#95—432no—
458#328—434no—
459#328—434no—
460#327—434no—
461#327C2×D4314yescomplemented
462C43#1754211yescharacteristic, complemented, Sylow
463C25—431no—
464C2×#41—432no—
465C2×#41—432no—
466C2×#41—861no—
467C2×#41—861no—
468C2×#41—1724no—
469C22×Q8—431no—
470C22×D4—21no—
471C22×D4—861no—
472C22×D4—861no—
473C22×D4C4×D4311yescharacteristic, complemented
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—862no—
488C23×C4—861no—
489C23×C4—1724no—
490C23×C4C22×D4311yescharacteristic
491C2×M16—21no—
492C2×M16—862no—
493C2×M16—861no—
494C2×M16—1724no—
495C22×C8—862no—
496#123—862no—
497#123—862no—
498#123—862no—
499#123—862no—
500C22⋊Q8—432no—
501C22⋊Q8—432no—
502C22⋊Q8—432no—
503C22⋊Q8—432no—
504C22⋊Q8—861no—
505C22⋊Q8—861no—
506C22⋊Q8—861no—
507C22⋊Q8—861no—
508#121—21no—
509#121—21no—
510#121—432no—
511#121—432no—
512#121—861no—
513#121—861no—
514#121C4×D4312yescomplemented
515#121C22×D4312yes—
516#120—862no—
517#120—862no—
518#120—862no—
519#120—862no—
520C4×D4—862no—
521C4×D4—862no—
522C4×D4—862no—
523C4×D4—862no—
524C4×D4—862no—
525C4×D4—862no—
526C4×D4—862no—
527C4×D4—862no—
528#117—432no—
529#117—432no—
530#117—861no—
531#117—861no—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4—861no—
535C2×C4⋊C4C4×D4311yescharacteristic, complemented
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—868no—
539C2×C22⋊C4—862no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C42—21no—
546C2×C42—861no—
547C2×C42—862no—
548C2×C42—861no—
549C2×C42—1724no—
550C22⋊C8—21no—
551C22⋊C8—432no—
552C22⋊C8—862no—
553C22⋊C8—862no—
554C22⋊C8—861no—
555C22⋊C8C22×D4312yes—
556#95—432no—
557#95—862no—
558#95C22×D4312yes—
559C24—21no—
560C24—431no—
561C24—431no—
562C24—431no—
563C24—431no—
564C24—431no—
565C24—431no—
566C24—864no—
567C24—1722no—
568C24—1722no—
569C24D4×D4311yescharacteristic
570#41—1724no—
571#41—1724no—
572#41—1724no—
573#41—1724no—
574C2×Q8—432no—
575C2×Q8—861no—
576C2×Q8—1722no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—44no—
582C2×D4—862no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—1724no—
587C2×D4—1724no—
588C2×D4C2×C4×D4312yes—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—42no—
592C22×C4—431no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—864no—
615C22×C4—864no—
616C22×C4—864no—
617C22×C4—868no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—862no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4—1722no—
629C22×C4—1722no—
630C22×C4—1722no—
631C22×C4—1722no—
632C22×C4—1724no—
633C22×C4—1724no—
634C22×C4—1722no—
635C22×C4—1724no—
636C22×C4C2×C4×D4311yescharacteristic
637C22×C4C2×C4×D4311yescharacteristic
638C22×C4D4×D4311yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641C22×C4C23×D4311yescharacteristic
642M16—42no—
643M16—1724no—
644M16—1722no—
645C2×C8—22no—
646C2×C8—862no—
647C2×C8—1724no—
648C4⋊C4—21no—
649C4⋊C4—432no—
650C4⋊C4—862no—
651C4⋊C4—862no—
652C4⋊C4—861no—
653C4⋊C4—862no—
654C4⋊C4—862no—
655C4⋊C4C2×C4×D4312yes—
656C22⋊C4—24no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—862no—
660C22⋊C4—862no—
661C22⋊C4—862no—
662C22⋊C4—862no—
663C22⋊C4—868no—
664C22⋊C4—862no—
665C22⋊C4—862no—
666C22⋊C4—864no—
667C22⋊C4—862no—
668C22⋊C4—862no—
669C42—42no—
670C42—862no—
671C42—862no—
672C42—1722no—
673C42—1724no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—431no—
682C23—431no—
683C23—431no—
684C23—434no—
685C23—431no—
686C23—862no—
687C23—862no—
688C23—862no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—1721no—
697C23—1721no—
698C23—1721no—
699C23—1721no—
700C23—1721no—
701C23—1721no—
702C23—1721no—
703C23—17216no—
704C23C22⋊C4×D4311yescharacteristic
705C23C22⋊C4×D4311yescharacteristic
706C23C2×D4×D4311yescharacteristic
707Q8—1722no—
708Q8—1722no—
709D4—42no—
710D4—44no—
711D4—44no—
712D4—42no—
713D4—1724no—
714D4—1724no—
715D4—1724no—
716D4—1724no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—431no—
729C2×C4—434no—
730C2×C4—431no—
731C2×C4—431no—
732C2×C4—431no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—864no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—17216no—
755C2×C4—1724no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4—1724no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4C22⋊C4×D4311yescharacteristic
765C2×C4C22⋊C4×D4311yescharacteristic
766C2×C4C22×C4×D4311yescharacteristic
767C2×C4C2×D4×D4311yescharacteristic
768C8—42no—
769C8—1722no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—432no—
783C22—432no—
784C22—432no—
785C22—868no—
786C22—861no—
787C22—861no—
788C22—861no—
789C22—861no—
790C22—861no—
791C22—861no—
792C22—861no—
793C22—861no—
794C22—861no—
795C22—1724no—
796C22—1724no—
797C22—1724no—
798C22—1724no—
799C22—1724no—
800C22#104×D4312yes—
801C22C2×C22⋊C4×D4311yescharacteristic
802C22#1458369512yes—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—44no—
807C4—42no—
808C4—432no—
809C4—861no—
810C4—861no—
811C4—861no—
812C4—1724no—
813C4—1722no—
814C4—1722no—
815C4#99×D4312yes—
816C2—22no—
817C2—22no—
818C2—41no—
819C2—82no—
820C2—862no—
821C2—862no—
822C2—862no—
823C2—1721no—
824C2C2×#99×D4311yescharacteristic
825C2#1914310911yescharacteristic
826C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1507C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583409C2
cosocleC22×C4×C43C24
hypercenter#1507D43
hypocenterC43#17542
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #407×D43C2semidirect
3. C4×C22⋊C4×D43C2semidirect
4. #19133116C2semidirect
5. #19133114C2semidirect
6. #19133111C2semidirect
7. #19133096C2semidirect
8. #19133083C2semidirect
9. C43×#1507C2semidirect
10. C22×#10621900C4semidirect
17. #14583409C4semidirect
18. #14583409C4semidirect
22. C2×#13063305C4semidirect
24. C2×#13063296C4semidirect
28. C2×#13063283C4semidirect
34. #14582861C22semidirect
36. C22⋊C8×D43C22semidirect
40. #14582746C22semidirect
41. #95×D43C22semidirect
42. #14582637C22semidirect
43. #14582635C22semidirect
44. #14582633C22semidirect
48. C43×#327C22semidirect
54. C2×#10621900C2×C4semidirect
55. C22×Dic86C2×C4semidirect
85. #13063305C2×C4semidirect
88. #13063304C2×C4semidirect
93. #13063296C2×C4semidirect
109. #13063283C2×C4semidirect
111. C2×C4⋊Dic43C2×C4semidirect
131. C22×D4×C43C2×C4semidirect
136. #121×C43C2×C4semidirect
138. C2×C4⋊C4×C43C2×C4semidirect
409. #1507D43semidirect
461. #327C2×D43semidirect
462. C43#17542semidirect
473. C22×D4C4×D43semidirect
514. #121C4×D43semidirect
535. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834092
#407×D432
C4×C22⋊C4×D432
#191331162
#191331142
#191331112
#191330962
#191330832
C43×#15072
#1754243