Finite Group Databasebeta

← #25112046

Subgroups — #25112046

Order 11008.

1498 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×#14583555C211yesmaximal, characteristic
2C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4C22×#13063250C211yesmaximal, characteristic, complemented
5#19137526C211yesmaximal, characteristic, complemented
6#19135526C211yesmaximal, characteristic, complemented
7#19135405C211yesmaximal, characteristic, complemented
8#19135017C211yesmaximal, characteristic, complemented
9#19134913C211yesmaximal, characteristic, complemented
10#19134906C211yesmaximal, characteristic, complemented
11#19134609C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic, complemented
13#19134529C211yesmaximal, characteristic, complemented
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1893C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583555—24no—
20#14583555C418yescomplemented
21C2×#13063312C2211yescharacteristic
22C2×#13063311—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063302—21no—
25C2×#13063297—21no—
26C2×#13063290C2211yescharacteristic
27C2×D4×Dic43—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C8×C22⋊D43—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33#14582892—24no—
34C2×#13063250—24no—
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×#13063246C2211yescharacteristic
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
57C23×C8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—41no—
68C2×#10621900—41no—
69C2×#10621900C2×C414yescomplemented
70C22×Dic86—22no—
71C22×Dic86—22no—
72C22×Dic86—22no—
73C22×Dic86—21no—
74C22×Dic86—41no—
75C22×Dic86—41no—
76C22×Dic86C2×C414yes—
77C22×Dic86C2311yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×C22⋊D43—21no—
80C22×C22⋊D43D411yescharacteristic
81C23×Dic43—21no—
82C23×Dic43—21no—
83C23×Dic43—21no—
84C22×C4×D43C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C2×C8×D43—22no—
88C2×C8×D43—22no—
89C2×C8×D43—41no—
90#13063312—22no—
91#13063312C2×C414yescomplemented
92#13063311—28no—
93#13063305—22no—
94#13063305C2×C414yescomplemented
95#13063302—28no—
96#13063297—28no—
97#13063290—22no—
98#13063290C2×C414yescomplemented
99D4×Dic43—28no—
100C4×C22⋊D43C2×C414yes—
101C4×C22⋊D43D414yes—
102#13063283—22no—
103#13063283—41no—
104C2×C4⋊Dic43—21no—
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⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43D411yescharacteristic
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#13063250—22no—
126#13063250—22no—
127#13063250D414yescomplemented
128#13063248—22no—
129#13063248—22no—
130#13063248—41no—
131#13063248—41no—
132#13063246—22no—
133#13063246—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×D4×C43—21no—
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43—22no—
145C22×C8×C43—22no—
146C22×C8×C43—41no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149#121×C43—22no—
150#121×C43C2×C414yes—
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156#102×C43—22no—
157#102×C43—41no—
158#95×C43—21no—
159C24×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43C2×D411yescharacteristic
162C2×D4×C43—21no—
163C2×D4×C43—24no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43C22×C412yes—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43C22×C412yes—
179C22×C4×C43C2×D412yes—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2411yescharacteristic
182C2×C22⋊D43—22no—
183C2×C22⋊D43—22no—
184C2×C22⋊D43—24no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43C22⋊C414yes—
188C22×Dic43—24no—
189C22×Dic43—24no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—42no—
199C22×Dic43—42no—
200C22×Dic43—81no—
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204#10621900—28no—
205#10621900—44no—
206#10621900—44no—
207#10621900—44no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43C22×C412yes—
213C2×C4×D43C2×D412yes—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—21no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86—21no—
221C2×Dic86—28no—
222C2×Dic86—24no—
223C2×Dic86—21no—
224C2×Dic86—44no—
225C2×Dic86—44no—
226C2×Dic86—44no—
227C2×Dic86—42no—
228C2×Dic86—42no—
229C2×Dic86C22×C412yes—
230C2×Dic86C22×C412yes—
231C2×Dic86C2×D412yes—
232C2×Dic86#4112yes—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—44no—
239C2×C8×C43C2×D412yes—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43C22×C412yes—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—42no—
248C22⋊Dic43—24no—
249C22⋊Dic43—24no—
250C22⋊Dic43C22⋊C414yes—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—42no—
253(C2×D43)⋊C4—81no—
254(C2×D43)⋊C4C22⋊C414yes—
255C4⋊Dic43—21no—
256C4⋊Dic43—24no—
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—
274C8×D43—44no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—22no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43C2×C22⋊C412yes—
287C23×C43#13512yes—
288C23×C43#13512yes—
289C23×C43C22×D411yescharacteristic
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—21no—
293C22×D43—21no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43C2×C22⋊C412yes—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—48no—
300D4×C43—41no—
301D4×C43—41no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
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×C43C2×C22⋊C412yes—
318C2×C4×C43C23×C411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C2×C4×C43H(5,𝔽2)11yescharacteristic
324C22⋊D43—28no—
325C22⋊D43—48no—
326C2×Dic43—22no—
327C2×Dic43—21no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—48no—
338C2×Dic43—48no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—84no—
347C2×Dic43C2×C22⋊C412yes—
348C2×Dic43C2×C22⋊C412yes—
349C2×Dic43C2×C22⋊C412yes—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—48no—
360Dic86—41no—
361Dic86—41no—
362Dic86C4×D414yes—
363C8×C43—22no—
364C8×C43—41no—
365C43⋊C8—41no—
366C43⋊C8—41no—
367#22416—431nomaximal, Sylow
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43#41614yescomplemented
382C22×C43C22×C22⋊C411yescharacteristic
383C22×C43D4211yescharacteristic
384C22×C43#54611yescharacteristic
385C22×C43C2×#13511yescharacteristic
386C22×C43C2×#13511yescharacteristic
387C22×C43#57711yescharacteristic
388C22×C43#57811yescharacteristic
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C4×C43—22no—
397C4×C43—42no—
398C4×C43—81no—
399C4×C43—81no—
400C4×C43C2×C4×D411yescharacteristic
401C4×C43#51811yescharacteristic
402C4×C43D4211yescharacteristic
403C4×C43#54611yescharacteristic
404Dic43—24no—
405Dic43—22no—
406Dic43—22no—
407Dic43—22no—
408Dic43—42no—
409Dic43—42no—
410Dic43—81no—
411C2×#548—431no—
412C2×C8×D4—431no—
413C2×#416—431no—
414C22×#103—431no—
415#2352—431no—
416#1983—431no—
417#1958—431no—
418#1893D4311yescharacteristic, complemented
419#1892—431no—
420#1874—431no—
421#1873—431no—
422#1805—431no—
423#1788—431no—
424#1787—431no—
425C4×#103—431no—
426C2×C43—24no—
427C2×C43—82no—
428C2×C43D4×C22⋊C411yescharacteristic
429C2×C43C2×#41611yescharacteristic
430C2×C43#289811yescharacteristic
431C2×C43#328211yescharacteristic
432C2×C43#328511yescharacteristic
433C2×C43#330011yescharacteristic
434C2×C43#330111yescharacteristic
435D43—42no—
436C22×#41—431no—
437C23×Q8—431no—
438C23×C8—431no—
439C23×C8C2×D4311yescharacteristic
440#548—438no—
441#548—864no—
442C2×#124—431no—
443C2×#124—861no—
444C2×C22⋊Q8—431no—
445C2×C22⋊Q8—861no—
446C2×#121—861no—
447C2×#121C2×D4311yescharacteristic
448C2×C4×Q8—431no—
449C2×C4×D4—431no—
450C2×C4×D4—861no—
451C2×#117—431no—
452C22×C4⋊C4—431no—
453C8×D4—864no—
454C2×C4⋊C8—431no—
455#416—864no—
456C2×#103—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—864no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102C2×D4311yescharacteristic
468C2×#102C2×D4311yescharacteristic
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#2241611yescharacteristic, 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—431no—
494C22×Q8—862no—
495C22×Q8—862no—
496C22×Q8—861no—
497C22×Q8—862no—
498C22×Q8—1721no—
499C22×Q8—1721no—
500C22×D4—21no—
501C22×D4—431no—
502C22×D4—861no—
503C22×D4C22×D4311yescharacteristic
504C23×C4—431no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4—861no—
508C23×C4C22×D4311yescharacteristic
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—41no—
512C22×C8—431no—
513C22×C8—431no—
514C22×C8—862no—
515C22×C8—862no—
516C22×C8—1721no—
517C22×C8C22×D4311yescharacteristic
518C22×C8C22×D4311yescharacteristic
519#124—434no—
520#124—862no—
521#124—868no—
522C22⋊Q8—434no—
523C22⋊Q8—868no—
524C22⋊Q8—862no—
525#121—22no—
526#121—868no—
527#121C4×D4314yes—
528C4×Q8—434no—
529C4×Q8—862no—
530C4×D4—434no—
531C4×D4—434no—
532C4×D4—868no—
533#117—862no—
534#117—1721no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—862no—
539C2×C4⋊C4—861no—
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—434no—
561#103—862no—
562#103—862no—
563#103—862no—
564#103—862no—
565#103—862no—
566#103—1721no—
567#103—1721no—
568#102—22no—
569#102—41no—
570#102—862no—
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—21no—
581C24—431no—
582C24D4×D4311yescharacteristic
583#41—868no—
584#41—1724no—
585#41—1724no—
586#41—1724no—
587C2×Q8—432no—
588C2×Q8—432no—
589C2×Q8—432no—
590C2×Q8—432no—
591C2×Q8—868no—
592C2×Q8—864no—
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—1722no—
602C2×Q8—1722no—
603C2×Q8—1724no—
604C2×Q8—1724no—
605C2×Q8—1724no—
606C2×D4—24no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—434no—
615C2×D4—862no—
616C2×D4—862no—
617C2×D4—864no—
618C2×D4—1722no—
619C2×D4—1722no—
620C2×D4C2×C4×D4312yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—432no—
632C22×C4—432no—
633C22×C4—864no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—864no—
640C22×C4—861no—
641C22×C4—861no—
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
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—44no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—1724no—
667C2×C8D4×D4312yes—
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—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—22no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—432no—
708C23—861no—
709C23—861no—
710C23—861no—
711C23—861no—
712C23—861no—
713C23—861no—
714C23C22⋊C4×D4312yes—
715C23#1306334412yes—
716C23#1306334612yes—
717C23C2×D4×D4311yescharacteristic
718Q8—434no—
719Q8—862no—
720Q8—862no—
721Q8—862no—
722Q8—862no—
723Q8—862no—
724Q8—1728no—
725Q8—1721no—
726Q8—1721no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—868no—
733D4—1728no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—862no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—861no—
756C2×C4—861no—
757C2×C4—861no—
758C2×C4—862no—
759C2×C4—861no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—3444no—
768C2×C4—1728no—
769C2×C4—1728no—
770C2×C4—1721no—
771C2×C4—1721no—
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—22no—
792C22—22no—
793C22—22no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—862no—
802C22—862no—
803C22—862no—
804C22—1721no—
805C22—1721no—
806C22—1721no—
807C22—1721no—
808C22#1458289214yescomplemented
809C22C2×C22⋊C4×D4311yescharacteristic
810C22#1458353311yescharacteristic
811C22#1458353811yescharacteristic
812C22C2×#1306334411yescharacteristic
813C22C2×#1306334611yescharacteristic
814C22#1458370611yescharacteristic
815C22#1458371311yescharacteristic
816C4—22no—
817C4—42no—
818C4—81no—
819C4—81no—
820C4—862no—
821C4—864no—
822C4—862no—
823C4—862no—
824C4—3441no—
825C4—1722no—
826C4—1722no—
827C4C4×D4×D4311yescharacteristic
828C4#1458337111yescharacteristic
829C4#1458353111yescharacteristic
830C4#1458354111yescharacteristic
831C2—24no—
832C2—82no—
833C2—1722no—
834C2#1913741311yescharacteristic
835C2C2×#1458289211yescharacteristic
836C2#1914312411yescharacteristic
837C2#1914629911yescharacteristic
838C2#1914633311yescharacteristic
839C2#1914648811yescharacteristic
840C2#1914650311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#14583555C2
cosocleC22×C4×C43C24
hypercenter#1893D43
hypocenterC43#22416
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D43C2semidirect
3. C2×#14582892C2semidirect
4. C22×#13063250C2semidirect
5. #19137526C2semidirect
6. #19135526C2semidirect
7. #19135405C2semidirect
8. #19135017C2semidirect
9. #19134913C2semidirect
10. #19134906C2semidirect
11. #19134609C2semidirect
12. #19134532C2semidirect
13. #19134529C2semidirect
14. #19134414C2semidirect
15. C43×#1893C2semidirect
20. #14583555C4semidirect
69. C2×#10621900C2×C4semidirect
91. #13063312C2×C4semidirect
94. #13063305C2×C4semidirect
98. #13063290C2×C4semidirect
127. #13063250D4semidirect
381. C22×C43#416semidirect
418. #1893D43semidirect
484. C43#22416semidirect
808. C22#14582892semidirect

Maximal subgroups

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

subgroupindex
C2×#145835552
C2×C8×C22⋊D432
C2×#145828922
C22×#130632502
#191375262
#191355262
#191354052
#191350172
#191349132
#191349062
#191346092
#191345322
#191345292
#191344142
C43×#18932
#2241643