Finite Group Databasebeta

← #25064084

Subgroups — #25064084

Order 11008.

1510 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583409C211yesmaximal, characteristic
2C2×#14582861C211yesmaximal, characteristic, complemented
3#380×D43C211yesmaximal, characteristic, complemented
4#19133168C211yesmaximal, characteristic, complemented
5#19133166C211yesmaximal, characteristic, complemented
6#19133163C211yesmaximal, characteristic, complemented
7#19133135C214yesmaximal, complemented
8#19133096C214yesmaximal, complemented
9C43×#1519C211yesmaximal, characteristic, complemented
10C22×#10621900C411yescharacteristic, complemented
11C23×C4×D43C2211yescharacteristic
12C22×#10621872—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×C4⋊C4×D43—21no—
30C2×C22⋊C4×D43—21no—
31#14582861—21no—
32#14582861—21no—
33#14582861C2212yescomplemented
34#14582861C2212yescomplemented
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×(C2×D43)⋊C8—21no—
37#14582759C2211yescharacteristic
38#14582758C2212yescomplemented
39#14582757—21no—
40#14582756—21no—
41#95×D43C2212yescomplemented
42#14582637C2214yescomplemented
43#14582635C2214yescomplemented
44#14582633C2214yescomplemented
45C2×#121×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C43×#380C2211yescharacteristic
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×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—44no—
77C22×C43⋊C8—21no—
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⋊Dic43—21no—
112C2×C4⋊Dic43C2×C411yescharacteristic, complemented
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4—22no—
115C4⋊C4×D43—44no—
116C2×C22⋊Dic43—21no—
117C2×C22⋊Dic43—21no—
118C2×C22⋊Dic43—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—22no—
122C22⋊C4×D43—44no—
123C2×C4×Dic43—21no—
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
133C22×C8×C43—21no—
134#121×C43—21no—
135#121×C43—21no—
136#121×C43C2×C412yescomplemented
137#121×C43C2312yes—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C22⋊C8×C43—21no—
143C22⋊C8×C43C2312yes—
144#95×C43C2312yes—
145C24×C43—21no—
146C24×C43C2×D411yescharacteristic
147C23×D43—22no—
148C23×D43—22no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43C22⋊C411yescharacteristic
152C23×D43C22⋊C411yescharacteristic
153C23×D43C22⋊C411yescharacteristic
154C23×D43C22⋊C411yescharacteristic
155C23×D43C2×D411yescharacteristic
156C23×D43C2×D411yescharacteristic
157C2×D4×C43—21no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43C22×C412yes—
164C22×C4×C43—21no—
165C22×C4×C43—22no—
166C22×C4×C43—42no—
167C22×C4×C43C22×C411yescharacteristic
168C22×C4×C43C22×C411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—22no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—44no—
178C2×C22⋊D43—44no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—22no—
184C22×Dic43—42no—
185C22×Dic43—44no—
186C22×Dic43C22⋊C411yescharacteristic
187C22×Dic43C22⋊C411yescharacteristic
188C22×Dic43C22⋊C411yescharacteristic
189C22×Dic43C22⋊C411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192#10621900—44no—
193#10621900—44no—
194#10621900—44no—
195#10621900—44no—
196C2×C4×D43—24no—
197C2×C4×D43—24no—
198C2×C4×D43—24no—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43—42no—
202C2×C4×D43—44no—
203C2×C4×D43—44no—
204C2×C4×D43—44no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
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×D43C22×C411yescharacteristic
222C2×C4×D43C22×C411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×C4×D43C2×D411yescharacteristic
225C2×C4×D43C2×D411yescharacteristic
226C2×C4×D43C2×D411yescharacteristic
227C2×Dic86—21no—
228C2×Dic86—42no—
229C2×Dic86C22×C412yes—
230C2×C8×C43—22no—
231C2×C8×C43—42no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—42no—
234C4⋊C4×C43C22×C412yes—
235C22⋊C4×C43—22no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—42no—
238C22⋊Dic43—22no—
239C22⋊Dic43—22no—
240C22⋊Dic43—22no—
241C22⋊Dic43—22no—
242C22⋊Dic43—42no—
243(C2×D43)⋊C4—22no—
244(C2×D43)⋊C4—22no—
245(C2×D43)⋊C4—22no—
246(C2×D43)⋊C4—22no—
247(C2×D43)⋊C4—44no—
248C4⋊Dic43—21no—
249C4⋊Dic43—22no—
250C4⋊Dic43—22no—
251C4⋊Dic43—42no—
252C4⋊Dic43C22×C412yes—
253Dic43⋊C4—22no—
254Dic43⋊C4—22no—
255Dic43⋊C4—44no—
256C4×Dic43—22no—
257C4×Dic43—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—42no—
260#10621872—44no—
261#10621872—44no—
262C23×C43—22no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—42no—
266C23×C43—42no—
267C23×C43—42no—
268C23×C43C2×C22⋊C411yescharacteristic
269C23×C43C2×C22⋊C411yescharacteristic
270C23×C43AGL(1,ℤ/8)12yes—
271C23×C43#13712yes—
272C23×C43C22×D411yescharacteristic
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—48no—
294C22×D43—48no—
295C22×D43C2×C22⋊C411yescharacteristic
296C22×D43C2×C22⋊C411yescharacteristic
297C22×D43C2×C22⋊C411yescharacteristic
298C22×D43C2×C22⋊C411yescharacteristic
299D4×C43—42no—
300D4×C43—42no—
301D4×C43—42no—
302D4×C43—44no—
303D4×C43—42no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43C2×C22⋊C411yescharacteristic
316C2×C4×C43C2×C22⋊C411yescharacteristic
317C2×C4×C43C23×C411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C22⋊D43—44no—
320C22⋊D43—44no—
321C22⋊D43—44no—
322C22⋊D43—44no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—44no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—44no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—41no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—41no—
355C4×D43—41no—
356C4×D43—41no—
357C4×D43—88no—
358C4×D43#9914yes—
359Dic86—42no—
360Dic86—42no—
361C8×C43—42no—
362C43⋊C8—42no—
363#17592—431nomaximal, Sylow
364C22×C43—21no—
365C22×C43—21no—
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—84no—
376C22×C43#41712yes—
377C22×C43#41712yes—
378C22×C43C22×C22⋊C411yescharacteristic
379C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C43C2×#13711yescharacteristic
381C2×D43—24no—
382C2×D43—24no—
383C2×D43—21no—
384C2×D43—21no—
385C2×D43—21no—
386C2×D43—21no—
387C2×D43—21no—
388C2×D43—21no—
389C2×D43—21no—
390C2×D43—21no—
391C2×D43—21no—
392C2×D43—21no—
393C2×D43—44no—
394C2×D43—44no—
395C2×D43—44no—
396C2×D43—44no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43C2×#9912yes—
400C2×D43#42112yes—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—21no—
404C4×C43—42no—
405C4×C43—82no—
406C4×C43C2×#9912yes—
407Dic43—21no—
408Dic43—21no—
409Dic43—21no—
410Dic43—42no—
411Dic43—42no—
412Dic43—82no—
413Dic43C2×#9912yes—
414C2×#525—431no—
415C2×#407—431no—
416C2×#380—431no—
417#1520—431no—
418#1520—431no—
419#1519—431no—
420#1519D4311yescharacteristic, complemented
421#1513—434no—
422#1504—434no—
423C2×C43—21no—
424C2×C43—21no—
425C2×C43—22no—
426C2×C43—22no—
427C2×C43—82no—
428C2×C43C22×#9911yescharacteristic
429C2×C43C2×#41711yescharacteristic
430C2×C43C2×#42111yescharacteristic
431D43—22no—
432D43—22no—
433D43—41no—
434D43—41no—
435C22×#41—431no—
436C24×C4—431no—
437C22×M16—861no—
438#525—432no—
439#525—432no—
440#525—432no—
441#525—432no—
442#525—861no—
443#525—861no—
444#525—861no—
445#525—861no—
446C2×#123—861no—
447C2×C22⋊Q8—431no—
448C2×C22⋊Q8—431no—
449C2×#121—431no—
450C2×#121C2×D4311yescharacteristic
451C2×#120—861no—
452C2×C4×D4—861no—
453C2×C4×D4—861no—
454C2×#117—431no—
455C22×C4⋊C4—861no—
456C22×C22⋊C4—861no—
457#407—432no—
458#407—432no—
459#407—861no—
460#407—861no—
461C2×C22⋊C8—431no—
462C2×C22⋊C8—861no—
463C2×C22⋊C8C2×D4311yescharacteristic
464#380—431no—
465#380—432no—
466#380—861no—
467#380—861no—
468#380C2×D4311yescharacteristic
469C2×#95—432no—
470#328—434no—
471#328—434no—
472#327—434no—
473#327C2×D4314yescomplemented
474C43#1759211yescharacteristic, complemented, Sylow
475C25—431no—
476C2×#41—432no—
477C2×#41—432no—
478C2×#41—861no—
479C2×#41—861no—
480C2×#41—1724no—
481C22×Q8—431no—
482C22×D4—21no—
483C22×D4—861no—
484C22×D4—861no—
485C22×D4C4×D4311yescharacteristic, complemented
486C23×C4—431no—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—431no—
491C23×C4—431no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—431no—
497C23×C4—431no—
498C23×C4—431no—
499C23×C4—862no—
500C23×C4—861no—
501C23×C4—1724no—
502C23×C4C22×D4311yescharacteristic
503C2×M16—862no—
504C2×M16—862no—
505C2×M16—1724no—
506C22×C8—21no—
507C22×C8—861no—
508#123—862no—
509#123—862no—
510#123—862no—
511#123—862no—
512C22⋊Q8—432no—
513C22⋊Q8—432no—
514C22⋊Q8—432no—
515C22⋊Q8—432no—
516C22⋊Q8—861no—
517C22⋊Q8—861no—
518C22⋊Q8—861no—
519C22⋊Q8—861no—
520#121—21no—
521#121—21no—
522#121—432no—
523#121—432no—
524#121—861no—
525#121—861no—
526#121C4×D4312yescomplemented
527#121C22×D4312yes—
528#120—862no—
529#120—862no—
530#120—862no—
531#120—862no—
532C4×D4—862no—
533C4×D4—862no—
534C4×D4—862no—
535C4×D4—862no—
536C4×D4—862no—
537C4×D4—862no—
538C4×D4—862no—
539C4×D4—862no—
540#117—432no—
541#117—432no—
542#117—861no—
543#117—861no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—862no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—1724no—
551C2×C4⋊C4C4×D4311yescharacteristic, complemented
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—862no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—1724no—
561C2×C42—861no—
562C22⋊C8—21no—
563C22⋊C8—432no—
564C22⋊C8—862no—
565C22⋊C8—862no—
566C22⋊C8—861no—
567C22⋊C8C22×D4312yes—
568#95—432no—
569#95—862no—
570#95C22×D4312yes—
571C24—21no—
572C24—431no—
573C24—431no—
574C24—431no—
575C24—431no—
576C24—431no—
577C24—431no—
578C24—862no—
579C24—862no—
580C24—1722no—
581C24—1722no—
582C24D4×D4311yescharacteristic
583#41—1724no—
584#41—1724no—
585#41—1724no—
586#41—1724no—
587C2×Q8—432no—
588C2×Q8—861no—
589C2×Q8—1722no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—862no—
597C2×D4—862no—
598C2×D4—862no—
599C2×D4—862no—
600C2×D4—1724no—
601C2×D4—1724no—
602C2×D4C2×C4×D4312yes—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—42no—
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—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—864no—
629C22×C4—864no—
630C22×C4—864no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—862no—
636C22×C4—1722no—
637C22×C4—1722no—
638C22×C4—1722no—
639C22×C4—1722no—
640C22×C4—1722no—
641C22×C4—1722no—
642C22×C4—1722no—
643C22×C4—1722no—
644C22×C4—1722no—
645C22×C4—1724no—
646C22×C4—1724no—
647C22×C4—1724no—
648C22×C4—1722no—
649C22×C4—1724no—
650C22×C4C2×C4×D4311yescharacteristic
651C22×C4C2×C4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656M16—1724no—
657M16—1724no—
658C2×C8—22no—
659C2×C8—42no—
660C2×C8—862no—
661C2×C8—1722no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—432no—
665C4⋊C4—862no—
666C4⋊C4—862no—
667C4⋊C4—861no—
668C4⋊C4—862no—
669C4⋊C4—862no—
670C4⋊C4—1722no—
671C4⋊C4—1724no—
672C4⋊C4C2×C4×D4312yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—862no—
677C22⋊C4—862no—
678C22⋊C4—862no—
679C22⋊C4—862no—
680C22⋊C4—862no—
681C22⋊C4—862no—
682C22⋊C4—862no—
683C22⋊C4—862no—
684C22⋊C4—1724no—
685C22⋊C4—1722no—
686C42—862no—
687C42—862no—
688C23—22no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—431no—
695C23—431no—
696C23—431no—
697C23—431no—
698C23—862no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—862no—
703C23—862no—
704C23—861no—
705C23—861no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—861no—
711C23—861no—
712C23—1721no—
713C23—1721no—
714C23—1721no—
715C23—1721no—
716C23—1721no—
717C23—1721no—
718C23—1728no—
719C23—1728no—
720C23C22⋊C4×D4311yescharacteristic
721C23C22⋊C4×D4311yescharacteristic
722C23#1306334912yes—
723C23#1306335412yes—
724C23C2×D4×D4311yescharacteristic
725Q8—1722no—
726Q8—1722no—
727D4—42no—
728D4—44no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—1724no—
733D4—1724no—
734D4—1724no—
735D4—1724no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—431no—
748C2×C4—434no—
749C2×C4—431no—
750C2×C4—431no—
751C2×C4—431no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—3448no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1724no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4—1724no—
778C2×C4—1722no—
779C2×C4—1722no—
780C2×C4—1722no—
781C2×C4—1722no—
782C2×C4—1722no—
783C2×C4C22⋊C4×D4311yescharacteristic
784C2×C4C22⋊C4×D4311yescharacteristic
785C2×C4C22×C4×D4311yescharacteristic
786C2×C4C2×D4×D4311yescharacteristic
787C8—42no—
788C8—1722no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—432no—
802C22—432no—
803C22—864no—
804C22—864no—
805C22—861no—
806C22—861no—
807C22—861no—
808C22—861no—
809C22—861no—
810C22—861no—
811C22—861no—
812C22—861no—
813C22—861no—
814C22—861no—
815C22—1724no—
816C22—1724no—
817C22—1724no—
818C22—1724no—
819C22—1722no—
820C22—1722no—
821C22#1458289712yes—
822C22#1458289712yes—
823C22C2×C22⋊C4×D4311yescharacteristic
824C22C2×#1306334911yescharacteristic
825C22C2×#1306335411yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—42no—
830C4—82no—
831C4—432no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—3442no—
836C4—1722no—
837C4—1722no—
838C4#99×D4312yes—
839C2—21no—
840C2—22no—
841C2—21no—
842C2—22no—
843C2—82no—
844C2—862no—
845C2—862no—
846C2—1721no—
847C2—1721no—
848C2C2×#99×D4311yescharacteristic
849C2C2×#1458289711yescharacteristic
850C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1519C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583409C2
cosocleC22×C4×C43C24
hypercenter#1519D43
hypocenterC43#17592
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. C2×#14582861C2semidirect
3. #380×D43C2semidirect
4. #19133168C2semidirect
5. #19133166C2semidirect
6. #19133163C2semidirect
7. #19133135C2semidirect
8. #19133096C2semidirect
9. C43×#1519C2semidirect
10. C22×#10621900C4semidirect
17. #14583409C4semidirect
18. #14583409C4semidirect
22. C2×#13063305C4semidirect
24. C2×#13063296C4semidirect
28. C2×#13063283C4semidirect
33. #14582861C22semidirect
34. #14582861C22semidirect
38. #14582758C22semidirect
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
112. C2×C4⋊Dic43C2×C4semidirect
131. C22×D4×C43C2×C4semidirect
136. #121×C43C2×C4semidirect
139. C2×C4⋊C4×C43C2×C4semidirect
420. #1519D43semidirect
473. #327C2×D43semidirect
474. C43#17592semidirect
485. C22×D4C4×D43semidirect
526. #121C4×D43semidirect
551. 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
C2×#145828612
#380×D432
#191331682
#191331662
#191331632
#191331352
#191330962
C43×#15192
#1759243