Finite Group Databasebeta

← #25112093

Subgroups — #25112093

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×#14583548C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4#19137520C211yesmaximal, characteristic, complemented
5#19135516C211yesmaximal, characteristic, complemented
6#19135413C211yesmaximal, characteristic, complemented
7#19135028C211yesmaximal, characteristic, complemented
8#19135015C211yesmaximal, characteristic, complemented
9#19134904C211yesmaximal, characteristic, complemented
10#19134902C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134532C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C2×C43×#417C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583548—24no—
19#14583548C418yescomplemented
20C2×#13063323C2211yescharacteristic
21C2×#13063308—21no—
22C2×#13063306—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063301C2211yescharacteristic
25C2×#13063297—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C22×Dic43⋊C4—21no—
30#14582968—24no—
31C2×Dic43⋊C8C2211yescharacteristic
32#14582892—24no—
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44#14582789—21no—
45#14582780—21no—
46#14582778—21no—
47#14582764C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582756C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51C4×C22⋊Dic43—21no—
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×#41×C43C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C43×#417—24no—
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—41no—
68C2×#10621900—41no—
69C2×#10621900C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43D411yescharacteristic
73C23×Dic43—21no—
74C23×Dic43—21no—
75C22×C4×D43C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—22no—
79C2×C8×D43—22no—
80C2×C8×D43—41no—
81#13063323—22no—
82#13063323C2×C414yescomplemented
83#13063308—28no—
84#13063306—28no—
85#13063304—22no—
86#13063304C2×C414yes—
87#13063301—22no—
88#13063301C2×C414yescomplemented
89#13063297—28no—
90D4×Dic43—22no—
91D4×Dic43C2×C414yescomplemented
92C4×C22⋊D43C2×C414yes—
93C4×C22⋊D43D414yes—
94#13063283—22no—
95#13063283—41no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—28no—
104C2×Dic43⋊C4D411yescharacteristic
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43D411yescharacteristic
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116Dic43⋊C8—22no—
117#13063250—22no—
118#13063250—41no—
119#13063249—41no—
120#13063249—41no—
121#13063248—22no—
122#13063248—41no—
123#13063246—22no—
124#13063246—22no—
125C22⋊(C43⋊C8)—22no—
126(C2×D43)⋊C8—22no—
127#13063235—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—41no—
137C2×#41×C43—41no—
138C2×#41×C43C2×C414yes—
139C22×Q8×C43C2311yescharacteristic
140C22×D4×C43—21no—
141C22×D4×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43—21no—
144C23×C4×C43C2311yescharacteristic
145C2×M16×C43—22no—
146C2×M16×C43—22no—
147C2×M16×C43—41no—
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C2×C4⋊C4×C43—22no—
151C2×C4⋊C4×C43—21no—
152C2×C4⋊C4×C43—41no—
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155#103×C43—22no—
156#103×C43—22no—
157#102×C43—22no—
158#102×C43D414yescomplemented
159C24×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43C2×D411yescharacteristic
162#41×C43—28no—
163#41×C43—44no—
164#41×C43—44no—
165#41×C43—44no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43C22×C412yes—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—24no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43C22×C412yes—
179C2×D4×C43C2×D412yes—
180C2×D4×C43#4112yes—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—24no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43—42no—
193C22×C4×C43—81no—
194C22×C4×C43C22×C412yes—
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—24no—
199C2×C22⋊D43—41no—
200C2×C22⋊D43—41no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43C22⋊C414yes—
204C22×Dic43—24no—
205C22×Dic43—24no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—42no—
211C22×Dic43—42no—
212C22×Dic43—42no—
213C22×Dic43—42no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621900—28no—
218#10621900—44no—
219#10621900—44no—
220#10621900—44no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43C22×C412yes—
226C2×C4×D43C2×D412yes—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86C22×C412yes—
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—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—42no—
244C4⋊C4×C43C2×D412yes—
245C22⋊Dic43—24no—
246C22⋊Dic43—24no—
247C22⋊Dic43—42no—
248C22⋊Dic43C22⋊C414yes—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—42no—
251(C2×D43)⋊C4—81no—
252(C2×D43)⋊C4C22⋊C414yes—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43C22×C412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4C22⋊C414yes—
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—22no—
276C23×C43—22no—
277C23×C43—21no—
278C23×C43—22no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43C2×C22⋊C412yes—
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—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—41no—
300Q8×C43—41no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—48no—
305D4×C43C4×D414yes—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—48no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—84no—
323C2×C4×C43C2×C22⋊C412yes—
324C2×C4×C43C23×C411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C22⋊D43—44no—
331C22⋊D43—48no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—48no—
341C2×Dic43—48no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43C2×C22⋊C412yes—
353C2×Dic43C2×C22⋊C412yes—
354C2×Dic43C2×C22⋊C412yes—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359Dic86—22no—
360Dic86—22no—
361Dic86—41no—
362Dic86—41no—
363C8×C43—22no—
364C8×C43—41no—
365C43⋊C8—41no—
366C43⋊C8—41no—
367#22420—431nomaximal, Sylow
368C22×C43—24no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—41no—
377C22×C43—42no—
378C22×C43—41no—
379C22×C43—42no—
380C22×C43—41no—
381C22×C43—42no—
382C22×C43C22×C22⋊C411yescharacteristic
383C22×C43D4211yescharacteristic
384C22×C43#54611yescharacteristic
385C22×C43#57511yescharacteristic
386C22×C43#57511yescharacteristic
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—42no—
399C4×C43—81no—
400C4×C43C2×C4×D411yescharacteristic
401C4×C43#51811yescharacteristic
402C4×C43D4211yescharacteristic
403C4×C43#54611yescharacteristic
404Dic43—22no—
405Dic43—22no—
406Dic43—22no—
407Dic43—42no—
408Dic43—42no—
409Dic43—81no—
410Dic43—81no—
411C2×#547—431no—
412C2×#435—431no—
413C2×#417D4311yescharacteristic, complemented
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#1804—431no—
423#1788—431no—
424#1788—431no—
425#1762—431no—
426C2×C43—42no—
427C2×C43—44no—
428C2×C43D4×C22⋊C411yescharacteristic
429C2×C43#289611yescharacteristic
430C2×C43#289811yescharacteristic
431C2×C43#326711yescharacteristic
432C2×C43#326911yescharacteristic
433C2×C43#330711yescharacteristic
434C2×C43#331511yescharacteristic
435D43—42no—
436C22×#41—431no—
437C22×#41C2×D4311yescharacteristic
438C22×M16C2×D4311yescharacteristic
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×D4—431no—
450C2×#117—431no—
451C22×C4⋊C4—861no—
452C22×C4⋊C4C2×D4311yescharacteristic
453#435—864no—
454C2×C4⋊C8—431no—
455#417—24no—
456#416—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×#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#382—431no—
476#380—431no—
477#380—431no—
478C4×C4⋊C4—431no—
479C4×C22⋊C4—861no—
480#340—431no—
481#340—431no—
482#340—431no—
483#340—431no—
484C43#2242011yescharacteristic, complemented, Sylow
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—434no—
491C2×#41—862no—
492C2×#41—862no—
493C2×#41—862no—
494C2×#41—1721no—
495C2×#41—1721no—
496C2×#41C4×D4314yes—
497C22×Q8—431no—
498C22×Q8C22×D4311yescharacteristic
499C22×D4—21no—
500C22×D4—431no—
501C22×D4—861no—
502C22×D4C22×D4311yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—431no—
506C23×C4—861no—
507C23×C4—861no—
508C23×C4C22×D4311yescharacteristic
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—41no—
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—434no—
529C4×D4—434no—
530C4×D4—434no—
531C4×D4—862no—
532#117—862no—
533#117—1721no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—868no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
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×C22⋊C4—861no—
556C2×C42—431no—
557C2×C42—861no—
558C2×C42—861no—
559C4⋊C8—862no—
560#103—22no—
561#103—22no—
562#103—862no—
563#103—862no—
564#103—1721no—
565#103—1721no—
566#103—1721no—
567#103—1721no—
568#102—22no—
569#102—862no—
570#102—862no—
571#102C22⋊D4314yescomplemented
572C22⋊C8—862no—
573C22⋊C8—862no—
574#97—862no—
575#95—861no—
576#95—861no—
577#95—861no—
578#95—861no—
579#95—861no—
580C24—21no—
581C24—431no—
582C24D4×D4311yescharacteristic
583#41—28no—
584#41—44no—
585#41—44no—
586#41—44no—
587#41—868no—
588#41—1724no—
589#41—1724no—
590#41—1724no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—432no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—861no—
600C2×Q8—861no—
601C2×Q8—861no—
602C2×Q8C2×C4×D4312yes—
603C2×D4—24no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—434no—
610C2×D4—864no—
611C2×D4—1721no—
612C2×D4—1721no—
613C2×D4—1722no—
614C2×D4—1722no—
615C2×D4C2×C4×D4312yes—
616C2×D4#1062189812yes—
617C2×D4C2×C22⋊D4312yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—24no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—81no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—864no—
637C22×C4—864no—
638C22×C4—861no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
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—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—1724no—
667C2×C8C2×C22⋊D4312yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—42no—
672C4⋊C4—434no—
673C4⋊C4—432no—
674C4⋊C4—864no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—861no—
683C4⋊C4C2×C22⋊D4312yes—
684C22⋊C4—434no—
685C22⋊C4—434no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—3441no—
690C22⋊C4—1722no—
691C22⋊C4—1722no—
692C42—432no—
693C42—432no—
694C42—3441no—
695C42—1722no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—21no—
704C23—22no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—432no—
710C23—861no—
711C23—861no—
712C23—861no—
713C23—861no—
714C23—861no—
715C23—861no—
716C23C22⋊C4×D4312yes—
717C23C2×D4×D4311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—41no—
721Q8—41no—
722Q8—862no—
723Q8—862no—
724Q8—1721no—
725Q8—1721no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—1724no—
731D4—1728no—
732D4C4×C22⋊D4314yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—84no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—432no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—861no—
756C2×C4—861no—
757C2×C4—861no—
758C2×C4—861no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
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×C4—1721no—
777C2×C4C22⋊C4×D4312yes—
778C2×C4C22×C4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C22×C22⋊D4311yescharacteristic
781C2×C4C2×#1062189811yescharacteristic
782C2×C4#1306337011yescharacteristic
783C2×C4#1306337011yescharacteristic
784C8—22no—
785C8—41no—
786C8—1721no—
787C8—1721no—
788C22—22no—
789C22—24no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—1721no—
806C22—1721no—
807C22—1721no—
808C22—1721no—
809C22C2×C22⋊C4×D4311yescharacteristic
810C22D4×C22⋊D4311yescharacteristic
811C22#1458353911yescharacteristic
812C22#1458369511yescharacteristic
813C22#1458369811yescharacteristic
814C22#1458370911yescharacteristic
815C22#1458371511yescharacteristic
816C4—22no—
817C4—42no—
818C4—42no—
819C4—81no—
820C4—862no—
821C4—862no—
822C4—862no—
823C4—3441no—
824C4—3441no—
825C4—1722no—
826C4—1722no—
827C4C2×C4×C22⋊D4311yescharacteristic
828C4#1458337211yescharacteristic
829C4D4×C22⋊D4311yescharacteristic
830C4#1458353911yescharacteristic
831C2—42no—
832C2—44no—
833C2—1722no—
834C2C22⋊C4×C22⋊D4311yescharacteristic
835C2#1914311111yescharacteristic
836C2#1914312611yescharacteristic
837C2#1914611411yescharacteristic
838C2#1914614411yescharacteristic
839C2#1914657211yescharacteristic
840C2#1914669211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583548C2
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43#22420
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582968C2semidirect
3. C2×#14582892C2semidirect
4. #19137520C2semidirect
5. #19135516C2semidirect
6. #19135413C2semidirect
7. #19135028C2semidirect
8. #19135015C2semidirect
9. #19134904C2semidirect
10. #19134902C2semidirect
11. #19134603C2semidirect
12. #19134535C2semidirect
13. #19134532C2semidirect
14. #19134422C2semidirect
15. C2×C43×#417C2semidirect
19. #14583548C4semidirect
69. C2×#10621900C2×C4semidirect
82. #13063323C2×C4semidirect
88. #13063301C2×C4semidirect
91. D4×Dic43C2×C4semidirect
158. #102×C43D4semidirect
413. C2×#417D43semidirect
484. C43#22420semidirect
571. #102C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835482
C2×#145829682
C2×#145828922
#191375202
#191355162
#191354132
#191350282
#191350152
#191349042
#191349022
#191346032
#191345352
#191345322
#191344222
C2×C43×#4172
#2242043