Finite Group Databasebeta

← #25112089

Subgroups — #25112089

Order 11008.

1478 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×#14583553C211yesmaximal, characteristic
2C2×#14582969C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic, complemented
4C2×#14582892C211yesmaximal, characteristic, complemented
5#19137521C211yesmaximal, characteristic, complemented
6#19135517C211yesmaximal, characteristic, complemented
7#19135414C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic, complemented
9#19135017C211yesmaximal, characteristic, complemented
10#19134906C211yesmaximal, characteristic, complemented
11#19134901C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic, complemented
13#19134532C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic, complemented
15C43×#1804C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621900C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583553—24no—
21#14583553C418yescomplemented
22C2×#13063325C2211yescharacteristic
23C2×#13063309—21no—
24C2×#13063309—21no—
25C2×#13063305C2211yescharacteristic
26C2×#13063305C2211yescharacteristic
27C2×#13063299—21no—
28C2×C4×D172C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C22×C4⋊Dic43—21no—
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582969—24no—
33#14582897—24no—
34#14582892—24no—
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×#13063246C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×#13063236C2211yescharacteristic
48#14582788—21no—
49#14582782—21no—
50#14582777—21no—
51#14582756C2211yescharacteristic
52#14582756C2211yescharacteristic
53C4×C4⋊Dic43C2211yescharacteristic
54#14582746—21no—
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#382C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900—22no—
70C2×#10621900—41no—
71C2×#10621900—41no—
72C2×#10621900—41no—
73C2×#10621900—41no—
74C2×#10621900C2×C414yes—
75C2×#10621900C2×C414yescomplemented
76C22×Dic86C2311yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×D172D411yescharacteristic
79C22×C22⋊D43—21no—
80C22×C22⋊D43—21no—
81C23×Dic43—21no—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C2×#10621872—22no—
87C2×#10621872—22no—
88C2×#10621872—41no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—22no—
92C2×C8×D43—22no—
93C2×C8×D43—41no—
94#13063325—22no—
95#13063325C2×C414yescomplemented
96#13063309—28no—
97#13063309—28no—
98#13063305—22no—
99#13063305—22no—
100#13063305C2×C414yes—
101#13063305C2×C414yescomplemented
102#13063299—28no—
103C4×D172C2×C414yes—
104C4×D172D414yes—
105#13063283—22no—
106#13063283—41no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43—21no—
109C2×C4⋊Dic43—21no—
110C2×C4⋊Dic43—21no—
111C2×C4⋊Dic43—28no—
112C2×C4⋊Dic43D411yescharacteristic
113C2×C4⋊Dic43C2311yescharacteristic
114C2×C4⋊Dic43C2311yescharacteristic
115C2×Dic43⋊C4—21no—
116C4⋊C4×D43—22no—
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—21no—
123C2×(C2×D43)⋊C4D411yescharacteristic
124C2×(C2×D43)⋊C4D411yescharacteristic
125C2×C4×Dic43—21no—
126C2×C4×Dic43—21no—
127#13063250—22no—
128#13063250—22no—
129#13063250—41no—
130#13063250—41no—
131#13063248—22no—
132#13063248—22no—
133#13063248—41no—
134#13063248—41no—
135#13063246—22no—
136#13063246D414yescomplemented
137(C2×D43)⋊C8—22no—
138(C2×D43)⋊C8—22no—
139#13063236—22no—
140C43⋊#95—21no—
141C43⋊#95—21no—
142C43⋊#95—21no—
143C22×D4×C43C2311yescharacteristic
144C23×C4×C43—21no—
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C4×D4×C43—22no—
148C4×D4×C43C2×C414yescomplemented
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153C2×C42×C43C2311yescharacteristic
154C4⋊C8×C43—22no—
155#102×C43—22no—
156#102×C43—22no—
157#95×C43—21no—
158#95×C43—21no—
159C24×C43—21no—
160C23×D43C2×D411yescharacteristic
161C23×D43C2×D411yescharacteristic
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43C22×C412yes—
166C2×D4×C43C2×D412yes—
167C2×D4×C43#4112yes—
168C22×C4×C43—24no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—42no—
173C22×C4×C43—42no—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—24no—
178C2×C22⋊D43—24no—
179C2×C22⋊D43—42no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C22×Dic43—24no—
184C22×Dic43—24no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195#10621900—28no—
196#10621900—28no—
197#10621900—44no—
198#10621900—44no—
199#10621900—44no—
200#10621900—44no—
201#10621900—44no—
202#10621900—44no—
203C2×D172—41no—
204C2×D172—41no—
205C2×D172C22⋊C414yes—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—21no—
213C2×C4×D43—21no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×C4×D43—81no—
217C2×C4×D43C22×C412yes—
218C2×C4×D43C22×C412yes—
219C2×C4×D43C2×D412yes—
220C2×C4×D43C2×D412yes—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86C22×C412yes—
232C2×Dic86C22×C412yes—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43C22×C412yes—
245C22⋊C4×C43—24no—
246C42×C43C22×C412yes—
247C42×C43C2×D412yes—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—42no—
251(C2×D43)⋊C4—42no—
252(C2×D43)⋊C4—81no—
253(C2×D43)⋊C4C22⋊C414yes—
254(C2×D43)⋊C4C22⋊C414yes—
255C4⋊Dic43—24no—
256C4⋊Dic43—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43—24no—
259C4⋊Dic43—24no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C22⋊C414yes—
263C4⋊Dic43C2×D412yes—
264Dic43⋊C4—42no—
265C4×Dic43—42no—
266C4×Dic43—81no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8C2×D412yes—
273#10621872—44no—
274C8×D43—44no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43C22×D411yescharacteristic
283C22×D43—21no—
284C22×D43—21no—
285C22×D43—21no—
286C22×D43—21no—
287C22×D43—21no—
288C22×D43—21no—
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—21no—
293C22×D43—21no—
294C22×D43—21no—
295C22×D43C2×C22⋊C412yes—
296C22×D43C2×C22⋊C412yes—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43C4×D414yes—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—22no—
306C2×C4×C43—48no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
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×C43C2×C22⋊C412yes—
316C2×C4×C43C2×C22⋊C412yes—
317C2×C4×C43C23×C411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C22⋊D43—48no—
324C22⋊D43—48no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—48no—
333C2×Dic43—48no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43C2×C22⋊C412yes—
344C2×Dic43C2×C22⋊C412yes—
345D172—44no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—84no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—41no—
360Dic86—41no—
361Dic86—41no—
362Dic86—41no—
363C8×C43—41no—
364C8×C43—41no—
365C43⋊C8—22no—
366C43⋊C8—41no—
367#22420—431nomaximal, Sylow
368C22×C43—24no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
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—22no—
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—41no—
389C2×D43—41no—
390C2×D43—41no—
391C2×D43—41no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—42no—
399C4×C43—81no—
400C4×C43—81no—
401C4×C43C2×C4×D411yescharacteristic
402C4×C43#51811yescharacteristic
403C4×C43D4211yescharacteristic
404C4×C43#54611yescharacteristic
405Dic43—22no—
406Dic43—22no—
407Dic43—42no—
408Dic43—42no—
409Dic43—42no—
410Dic43—81no—
411C2×#547—431no—
412C2×#435—431no—
413C2×#417—431no—
414C2×#416—431no—
415#2352—431no—
416#1981—431no—
417#1960—431no—
418#1894—431no—
419#1892—431no—
420#1873—431no—
421#1872—431no—
422#1804D4311yescharacteristic, complemented
423#1788—431no—
424#1788—431no—
425#1762—431no—
426C2×C43—44no—
427C2×C43D4×C22⋊C411yescharacteristic
428C2×C43#289611yescharacteristic
429C2×C43#289811yescharacteristic
430C2×C43#326711yescharacteristic
431C2×C43#326911yescharacteristic
432C2×C43#330711yescharacteristic
433C2×C43#331511yescharacteristic
434D43—42no—
435D43—42no—
436C22×#41—431no—
437C22×#41—431no—
438C22×M16—431no—
439C23×C8—431no—
440#547—438no—
441#547—864no—
442C2×C4⋊Q8—431no—
443C2×#123—861no—
444C2×#123—861no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—431no—
447C2×#121—861no—
448C2×C4×D4—431no—
449C2×C4×D4C2×D4311yescharacteristic
450C2×#117—431no—
451C22×C4⋊C4—431no—
452C22×C4⋊C4—861no—
453#435—864no—
454C2×C4⋊C8C2×D4311yescharacteristic
455#417—864no—
456#416—864no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102C2×D4311yescharacteristic
468C2×#102C2×D4311yescharacteristic
469C2×C22⋊C8—431no—
470C2×C22⋊C8—431no—
471C2×#97—431no—
472#388—861no—
473#387—861no—
474#386—861no—
475#382C2×D4311yescharacteristic
476#380—431no—
477#380—431no—
478C4×C4⋊C4—431no—
479C4×C22⋊C4—861no—
480#340—431no—
481#340—431no—
482#340C2×D4311yescharacteristic
483#340C2×D4311yescharacteristic
484C43#2242011yescharacteristic, complemented, Sylow
485C2×#41—434no—
486C2×#41—434no—
487C2×#41—862no—
488C2×#41—862no—
489C2×#41—862no—
490C2×#41—862no—
491C2×#41—862no—
492C2×#41—862no—
493C2×#41—1721no—
494C2×#41—1721no—
495C2×#41—1721no—
496C2×#41—1721no—
497C22×Q8—431no—
498C22×Q8—431no—
499C22×D4—431no—
500C22×D4—861no—
501C22×D4—861no—
502C22×D4C22×D4311yescharacteristic
503C23×C4—21no—
504C23×C4—431no—
505C23×C4—431no—
506C23×C4—861no—
507C23×C4—861no—
508C23×C4—861no—
509C2×M16—862no—
510C2×M16—862no—
511C2×M16—1721no—
512C22×C8—431no—
513C22×C8—431no—
514C22×C8—862no—
515C22×C8—862no—
516C22×C8—1721no—
517C22×C8C22×D4311yescharacteristic
518C22×C8C22×D4311yescharacteristic
519C4⋊Q8—434no—
520C4⋊Q8—862no—
521#123—868no—
522#123—868no—
523C22⋊Q8—434no—
524C22⋊Q8—434no—
525C22⋊Q8—862no—
526C22⋊Q8—862no—
527#121—868no—
528C4×D4—22no—
529C4×D4—434no—
530C4×D4—434no—
531C4×D4C4×D4314yescomplemented
532#117—862no—
533#117—1721no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—862no—
538C2×C4⋊C4—868no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—1721no—
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C42—861no—
557C2×C42—861no—
558C2×C42C22×D4311yescharacteristic
559C4⋊C8—22no—
560#103—862no—
561#103—862no—
562#103—862no—
563#103—862no—
564#103—1721no—
565#103—1721no—
566#103—1721no—
567#103—1721no—
568#102—22no—
569#102—22no—
570#102—434no—
571#102—862no—
572C22⋊C8—862no—
573C22⋊C8—862no—
574#97—862no—
575#95—21no—
576#95—21no—
577#95—861no—
578#95—861no—
579#95—861no—
580C24—21no—
581C24—431no—
582C24—431no—
583#41—868no—
584#41—868no—
585#41—1724no—
586#41—1724no—
587#41—1724no—
588#41—1724no—
589#41—1724no—
590#41—1724no—
591C2×Q8—432no—
592C2×Q8—432no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—861no—
600C2×Q8—861no—
601C2×Q8—861no—
602C2×Q8—861no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—434no—
607C2×D4—864no—
608C2×D4—864no—
609C2×D4—1721no—
610C2×D4—1721no—
611C2×D4—1722no—
612C2×D4—1722no—
613C2×D4—1722no—
614C2×D4—1722no—
615C2×D4C2×C4×D4312yes—
616C2×D4D4×D4312yes—
617C2×D4#1062190212yes—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—432no—
627C22×C4—432no—
628C22×C4—432no—
629C22×C4—432no—
630C22×C4—864no—
631C22×C4—864no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—3441no—
645C22×C4—1722no—
646C22×C4—1722no—
647C22×C4—1722no—
648C22×C4—1722no—
649C22×C4—1722no—
650C22×C4—1722no—
651C22×C4D4×D4311yescharacteristic
652C22×C4D4×D4311yescharacteristic
653C22×C4C23×D4311yescharacteristic
654M16—1724no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—432no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—1724no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—434no—
674C4⋊C4—432no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—1722no—
683C4⋊C4C2×C4×D4312yes—
684C22⋊C4—24no—
685C22⋊C4—434no—
686C22⋊C4—434no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—3441no—
690C22⋊C4—1722no—
691C22⋊C4—1722no—
692C42—3441no—
693C42—1722no—
694C42C2×C4×D4312yes—
695C42D4×D4312yes—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—432no—
704C23—432no—
705C23—861no—
706C23—861no—
707C23—861no—
708C23—861no—
709C23—861no—
710C23—861no—
711C23—861no—
712C23—861no—
713C23—861no—
714C23—861no—
715C23—861no—
716C23—861no—
717C23C2×D4×D4311yescharacteristic
718Q8—862no—
719Q8—862no—
720Q8—862no—
721Q8—862no—
722Q8—1721no—
723Q8—1721no—
724Q8—1721no—
725Q8—1721no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—1724no—
730D4—1728no—
731D4—1728no—
732D4#1306328714yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—432no—
748C2×C4—432no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
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—3444no—
765C2×C4—1728no—
766C2×C4—1728no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4C22⋊C4×D4312yes—
777C2×C4C22⋊C4×D4312yes—
778C2×C4C22×C4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C2×D4×D4311yescharacteristic
781C2×C4C2×#1062190211yescharacteristic
782C2×C4#1306337111yescharacteristic
783C2×C4#1306337111yescharacteristic
784C8—41no—
785C8—41no—
786C8—862no—
787C8—1721no—
788C22—24no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—862no—
796C22—862no—
797C22—862no—
798C22—862no—
799C22—862no—
800C22—862no—
801C22—1721no—
802C22—1721no—
803C22—1721no—
804C22—1721no—
805C22—1721no—
806C22—1721no—
807C22—1721no—
808C22—1721no—
809C22C2×C22⋊C4×D4311yescharacteristic
810C22#1458353311yescharacteristic
811C22#1458354011yescharacteristic
812C22#1458369511yescharacteristic
813C22#1458369511yescharacteristic
814C22#1458370611yescharacteristic
815C22#1458371311yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—81no—
820C4—81no—
821C4—862no—
822C4—862no—
823C4—3441no—
824C4—1722no—
825C4—1722no—
826C4—1722no—
827C4C2×#1306328711yescharacteristic
828C4#1458337311yescharacteristic
829C4#1458353311yescharacteristic
830C4#1458354011yescharacteristic
831C2—44no—
832C2—1722no—
833C2—1722no—
834C2#1913741511yescharacteristic
835C2#1914310911yescharacteristic
836C2#1914312411yescharacteristic
837C2#1914611511yescharacteristic
838C2#1914615611yescharacteristic
839C2#1914656811yescharacteristic
840C2#1914668811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1804C2
socleC23×C43C22×D4
prime radicalC2×#14583553C2
cosocleC22×C4×C43C24
hypercenter#1804D43
hypocenterC43#22420
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#14582969C2semidirect
3. C2×#14582897C2semidirect
4. C2×#14582892C2semidirect
5. #19137521C2semidirect
6. #19135517C2semidirect
7. #19135414C2semidirect
8. #19135027C2semidirect
9. #19135017C2semidirect
10. #19134906C2semidirect
11. #19134901C2semidirect
12. #19134532C2semidirect
13. #19134532C2semidirect
14. #19134420C2semidirect
15. C43×#1804C2semidirect
21. #14583553C4semidirect
75. C2×#10621900C2×C4semidirect
95. #13063325C2×C4semidirect
101. #13063305C2×C4semidirect
136. #13063246D4semidirect
148. C4×D4×C43C2×C4semidirect
422. #1804D43semidirect
484. C43#22420semidirect
531. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835532
C2×#145829692
C2×#145828972
C2×#145828922
#191375212
#191355172
#191354142
#191350272
#191350172
#191349062
#191349012
#191345322
#191344202
C43×#18042
#2242043