Finite Group Databasebeta

← #25112218

Subgroups — #25112218

Order 11008.

1466 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583559C211yesmaximal, characteristic
2C2×#14582975C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic, complemented
4C2×#14582906C211yesmaximal, characteristic, complemented
5#19137526C211yesmaximal, characteristic, complemented
6#19135524C211yesmaximal, characteristic, complemented
7#19135403C211yesmaximal, characteristic, complemented
8#19135032C211yesmaximal, characteristic, complemented
9#19134916C211yesmaximal, characteristic, complemented
10#19134903C211yesmaximal, characteristic, complemented
11#19134609C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1894C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19#14583559—24no—
20#14583559C418yescomplemented
21C2×#13063314C2211yescharacteristic
22C2×#13063311—21no—
23C2×#13063303—21no—
24C2×#13063300C2211yescharacteristic
25C2×#13063298—21no—
26C2×#13063290C2211yescharacteristic
27C2×#13063287—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31#14582975—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33#14582906—24no—
34#14582901—24no—
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×C8×Dic43C2211yescharacteristic
48#14582791—21no—
49#14582786—21no—
50#14582776—21no—
51#14582764C2211yescharacteristic
52#14582756C2211yescharacteristic
53C4⋊C4×Dic43C2211yescharacteristic
54C22⋊C4×Dic43—21no—
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898C2×C414yes—
70C22×Dic86—21no—
71C22×Dic86C2311yescharacteristic
72C2×Q8×D43—22no—
73C2×Q8×D43—22no—
74C2×Q8×D43—22no—
75C2×Q8×D43—41no—
76C2×Q8×D43—41no—
77C2×Q8×D43C2×C414yescomplemented
78C22×D172—21no—
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43D411yescharacteristic
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C2×#10621872—22no—
87C2×#10621872—22no—
88C2×#10621872—41no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91#13063314—22no—
92#13063314C2×C414yescomplemented
93#13063311—28no—
94#13063303—28no—
95#13063300—22no—
96#13063300C2×C414yescomplemented
97#13063298—28no—
98#13063290—22no—
99#13063290C2×C414yescomplemented
100#13063287—28no—
101C4×C22⋊D43C2×C414yes—
102C4×C22⋊D43D414yes—
103#13063283—22no—
104#13063283—41no—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43—41no—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4D411yescharacteristic
112C2×C22⋊Dic43D411yescharacteristic
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123Dic43⋊C8—22no—
124#13063250—22no—
125#13063250D414yescomplemented
126#13063249—22no—
127#13063249—41no—
128#13063248—22no—
129#13063248—22no—
130#13063247—22no—
131#13063247—22no—
132#13063245—41no—
133#13063245—41no—
134C22⋊(C43⋊C8)—22no—
135(C2×D43)⋊C8—22no—
136C8×Dic43—22no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×Q8×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C2×M16×C43—22no—
144C2×M16×C43—22no—
145C2×M16×C43—41no—
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22⋊Q8×C43—22no—
149C22⋊Q8×C43C2×C414yes—
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156#103×C43—22no—
157#103×C43—41no—
158#95×C43—21no—
159C24×C43C2×D411yescharacteristic
160C23×D43—21no—
161C23×D43C2×D411yescharacteristic
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C22×C412yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43C22×C412yes—
177C22×C4×C43C2×D412yes—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—24no—
181C2×C22⋊D43—41no—
182C2×C22⋊D43—41no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43C22⋊C414yes—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—81no—
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195Q8×D43—28no—
196Q8×D43—44no—
197Q8×D43—44no—
198Q8×D43—44no—
199#10621898—28no—
200#10621898—44no—
201#10621898—44no—
202#10621898—44no—
203C2×D172—21no—
204C2×D172—24no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—42no—
210C2×D172—42no—
211C2×D172C22×C412yes—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—24no—
217C2×C4×D43—24no—
218C2×C4×D43—42no—
219C2×C4×D43—42no—
220C2×C4×D43—42no—
221C2×C4×D43—42no—
222C2×C4×D43C22×C412yes—
223C2×C4×D43C2×D412yes—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—24no—
228C2×Dic86—42no—
229C2×Dic86—42no—
230C2×Dic86C22×C412yes—
231C2×Dic86C2×D412yes—
232C2×Dic86#4112yes—
233M16×C43—44no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43C2×D412yes—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43C22×C412yes—
247C22⋊C4×C43—24no—
248C22⋊C4×C43—42no—
249C22⋊Dic43C22⋊C414yes—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—42no—
254(C2×D43)⋊C4—81no—
255(C2×D43)⋊C4C22⋊C414yes—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—42no—
260C4⋊Dic43C2×D412yes—
261Dic43⋊C4—24no—
262Dic43⋊C4C22⋊C414yes—
263C4×Dic43—24no—
264C4×Dic43—42no—
265C4×Dic43—81no—
266C4×Dic43C22×C412yes—
267C4×Dic43C2×D412yes—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274#10621872—44no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43C2×C22⋊C412yes—
282C23×C43C22×D411yescharacteristic
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—22no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43C2×C22⋊C412yes—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—41no—
300Q8×C43—41no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43C2×C22⋊C412yes—
320C2×C4×C43C23×C411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×C4×C43H(5,𝔽2)11yescharacteristic
325C2×C4×C43H(5,𝔽2)11yescharacteristic
326C22⋊D43—44no—
327C22⋊D43—48no—
328C2×Dic43—22no—
329C2×Dic43—21no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—22no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—84no—
344C2×Dic43C2×C22⋊C412yes—
345C2×Dic43C2×C22⋊C412yes—
346C2×Dic43C2×C22⋊C412yes—
347D172—22no—
348D172—22no—
349D172—48no—
350D172—41no—
351D172—41no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—48no—
357C4×D43—48no—
358Dic86—22no—
359Dic86—22no—
360Dic86—22no—
361Dic86—48no—
362Dic86C4×D414yes—
363C8×C43—22no—
364C8×C43—41no—
365C43⋊C8—41no—
366C43⋊C8—41no—
367#22429—431nomaximal, Sylow
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43C22×C22⋊C411yescharacteristic
376C22×C43D4211yescharacteristic
377C22×C43#54611yescharacteristic
378C22×C43#57511yescharacteristic
379C22×C43#57511yescharacteristic
380C22×C43#57711yescharacteristic
381C22×C43#57811yescharacteristic
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C2×D43—41no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—81no—
393C2×D43—81no—
394C2×D43—81no—
395C2×D43—81no—
396C4×C43—22no—
397C4×C43—42no—
398C4×C43—42no—
399C4×C43—81no—
400C4×C43—81no—
401C4×C43C2×C4×D411yescharacteristic
402C4×C43#51811yescharacteristic
403C4×C43D4211yescharacteristic
404C4×C43#54611yescharacteristic
405Dic43—24no—
406Dic43—22no—
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43—81no—
411C2×#548—431no—
412C2×#436—431no—
413C2×#417—431no—
414C2×#419—431no—
415#2352—431no—
416#1983—431no—
417#1958—431no—
418#1895—431no—
419#1894D4311yescharacteristic, complemented
420#1875—431no—
421#1872—431no—
422#1805—431no—
423#1788—431no—
424#1787—431no—
425C4×#103—431no—
426C2×C43—42no—
427C2×C43D4×C22⋊C411yescharacteristic
428C2×C43#289611yescharacteristic
429C2×C43#289811yescharacteristic
430C2×C43#327511yescharacteristic
431C2×C43#327711yescharacteristic
432C2×C43#332611yescharacteristic
433C2×C43#332711yescharacteristic
434D43—42no—
435D43—82no—
436C22×#41—431no—
437C23×Q8—431no—
438C22×M16—431no—
439C22×M16C2×D4311yescharacteristic
440#548—438no—
441#548—864no—
442C2×#124—431no—
443C2×#124—861no—
444C2×C22⋊Q8—861no—
445C2×C22⋊Q8C2×D4311yescharacteristic
446C2×#121—431no—
447C2×#121—861no—
448C2×C4×Q8—431no—
449C2×C4×D4—431no—
450C2×C4×D4—861no—
451C2×#117—431no—
452C22×C4⋊C4—431no—
453#436—864no—
454C2×C4⋊C8—431no—
455#419—864no—
456#417—864no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103C2×D4311yescharacteristic
464C2×#103C2×D4311yescharacteristic
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×C22⋊C8—431no—
470C2×C22⋊C8—431no—
471C2×C4×C8—431no—
472#388—861no—
473#387—861no—
474#386—861no—
475#382—431no—
476#380—431no—
477#380C2×D4311yescharacteristic
478C4×C4⋊C4—431no—
479C4×C22⋊C4—861no—
480#340—431no—
481#340—431no—
482#340C2×D4311yescharacteristic
483#340C2×D4311yescharacteristic
484C43#2242911yescharacteristic, complemented, Sylow
485C2×#41—434no—
486C2×#41—862no—
487C2×#41—862no—
488C2×#41—862no—
489C2×#41—1721no—
490C2×#41—1721no—
491C22×Q8—434no—
492C22×Q8—431no—
493C22×Q8—861no—
494C22×Q8—862no—
495C22×Q8—862no—
496C22×Q8—862no—
497C22×Q8—1721no—
498C22×Q8—1721no—
499C22×Q8C22×D4311yescharacteristic
500C22×D4—431no—
501C22×D4—431no—
502C22×D4—861no—
503C22×D4—861no—
504C23×C4—431no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4—861no—
508C23×C4C22×D4311yescharacteristic
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—41no—
512C2×M16—862no—
513C2×M16—862no—
514C2×M16—1721no—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8C22×D4311yescharacteristic
518C22×C8C22×D4311yescharacteristic
519#124—434no—
520#124—862no—
521#124—868no—
522C22⋊Q8—22no—
523C22⋊Q8—868no—
524C22⋊Q8C4×D4314yes—
525#121—434no—
526#121—868no—
527#121—862no—
528C4×Q8—434no—
529C4×Q8—862no—
530C4×D4—434no—
531C4×D4—434no—
532C4×D4—868no—
533#117—862no—
534#117—1721no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—862no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—1721no—
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C4⋊C4C22×D4311yescharacteristic
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—431no—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C42—431no—
556C2×C42—861no—
557C2×C42—861no—
558C2×C42—861no—
559C4⋊C8—862no—
560#103—22no—
561#103—41no—
562#103—434no—
563#103—862no—
564#103—862no—
565#103—862no—
566#103—862no—
567#103—1721no—
568#102—862no—
569#102—862no—
570#102—1721no—
571#102—1721no—
572C22⋊C8—862no—
573C22⋊C8—862no—
574C4×C8—862no—
575#95—21no—
576#95—861no—
577#95—861no—
578#95—861no—
579#95—861no—
580C24—431no—
581C24—861no—
582C24D4×D4311yescharacteristic
583#41—868no—
584#41—1724no—
585#41—1724no—
586#41—1724no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—432no—
593C2×Q8—432no—
594C2×Q8—432no—
595C2×Q8—864no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—868no—
600C2×Q8—1722no—
601C2×Q8—1722no—
602C2×Q8—1724no—
603C2×Q8—1724no—
604C2×Q8—1724no—
605C2×Q8C2×C4×D4312yes—
606C2×D4—434no—
607C2×D4—432no—
608C2×D4—864no—
609C2×D4—864no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—1722no—
616C2×D4—1722no—
617C2×D4—1721no—
618C2×D4—1721no—
619C2×D4—1722no—
620C2×D4—1722no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—432no—
633C22×C4—432no—
634C22×C4—864no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—864no—
642C22×C4—861no—
643C22×C4—3441no—
644C22×C4—1722no—
645C22×C4—1722no—
646C22×C4—1722no—
647C22×C4—1722no—
648C22×C4—1722no—
649C22×C4—1722no—
650C22×C4C2×C4×D4312yes—
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4312yes—
653C22×C4C23×D4311yescharacteristic
654M16—44no—
655M16—1724no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8D4×D4312yes—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—434no—
675C4⋊C4—432no—
676C4⋊C4—864no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—1722no—
681C4⋊C4C2×C4×D4312yes—
682C22⋊C4—24no—
683C22⋊C4—42no—
684C22⋊C4—434no—
685C22⋊C4—434no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—3441no—
690C22⋊C4—1722no—
691C42—432no—
692C42—432no—
693C42—864no—
694C42—3441no—
695C42—1722no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—432no—
703C23—861no—
704C23—861no—
705C23—861no—
706C23—861no—
707C23—861no—
708C23—861no—
709C23—862no—
710C23—1721no—
711C23—1721no—
712C23—1721no—
713C23—1721no—
714C23—1721no—
715C23—1721no—
716C23C22⋊C4×D4312yes—
717C23C2×D4×D4311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—41no—
721Q8—41no—
722Q8—434no—
723Q8—862no—
724Q8—862no—
725Q8—862no—
726Q8—1728no—
727D4—862no—
728D4—862no—
729D4—1728no—
730D4—1724no—
731D4—1728no—
732D4—1721no—
733D4—1721no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—432no—
753C2×C4—432no—
754C2×C4—432no—
755C2×C4—862no—
756C2×C4—861no—
757C2×C4—861no—
758C2×C4—861no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—862no—
762C2×C4—861no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—3444no—
770C2×C4—1728no—
771C2×C4—1728no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4C22⋊C4×D4312yes—
778C2×C4C22×C4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C2×D4×D4311yescharacteristic
781C2×C4#41×D4311yescharacteristic
782C2×C4#1306337011yescharacteristic
783C2×C4#1306337111yescharacteristic
784C8—22no—
785C8—41no—
786C8—1721no—
787C8—1721no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—862no—
796C22—862no—
797C22—862no—
798C22—3441no—
799C22—3441no—
800C22—3441no—
801C22—3441no—
802C22—1722no—
803C22—1722no—
804C22—1722no—
805C22—1721no—
806C22—1721no—
807C22—1721no—
808C22—1721no—
809C22C2×C22⋊C4×D4311yescharacteristic
810C22#1458353311yescharacteristic
811C22#1458353811yescharacteristic
812C22#1458369511yescharacteristic
813C22#1458369811yescharacteristic
814C22#1458370811yescharacteristic
815C22#1458371511yescharacteristic
816C4—22no—
817C4—42no—
818C4—42no—
819C4—81no—
820C4—81no—
821C4—862no—
822C4—864no—
823C4—862no—
824C4—862no—
825C4—3441no—
826C4—1722no—
827C4C4×D4×D4311yescharacteristic
828C4#1458337111yescharacteristic
829C4#1458353111yescharacteristic
830C4#1458354111yescharacteristic
831C2—42no—
832C2—3442no—
833C2—1722no—
834C2#1913741311yescharacteristic
835C2#1914311111yescharacteristic
836C2#1914312711yescharacteristic
837C2#1914622311yescharacteristic
838C2#1914624911yescharacteristic
839C2#1914684311yescharacteristic
840C2#1914685811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC2×#14583559C2
cosocleC22×C4×C43C24
hypercenter#1894D43
hypocenterC43#22429
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
2. C2×#14582975C2semidirect
3. C2×#14582901C2semidirect
4. C2×#14582906C2semidirect
5. #19137526C2semidirect
6. #19135524C2semidirect
7. #19135403C2semidirect
8. #19135032C2semidirect
9. #19134916C2semidirect
10. #19134903C2semidirect
11. #19134609C2semidirect
12. #19134533C2semidirect
13. #19134528C2semidirect
14. #19134414C2semidirect
15. C43×#1894C2semidirect
20. #14583559C4semidirect
77. C2×Q8×D43C2×C4semidirect
92. #13063314C2×C4semidirect
96. #13063300C2×C4semidirect
99. #13063290C2×C4semidirect
125. #13063250D4semidirect
419. #1894D43semidirect
484. C43#22429semidirect

Maximal subgroups

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

subgroupindex
C2×#145835592
C2×#145829752
C2×#145829012
C2×#145829062
#191375262
#191355242
#191354032
#191350322
#191349162
#191349032
#191346092
#191345332
#191345282
#191344142
C43×#18942
#2242943