Finite Group Databasebeta

← C2×#19144285 #25963843

Subgroups — C2×#19144285 #25963843

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C22×#13063331C211yesmaximal, characteristic, complemented
3C2×#14583479C211yesmaximal, characteristic
4C2×#14583472C211yesmaximal, characteristic, complemented
5#19144285C2116yesmaximal, direct product factor
6C2×#14583155C211yesmaximal, characteristic, complemented
7C2×#14583154C211yesmaximal, characteristic, complemented
8C2×#14583147C211yesmaximal, characteristic, complemented
9C2×#14583146C211yesmaximal, characteristic, complemented
10C2×#14583139C211yesmaximal, characteristic, complemented
11C2×#14583131C211yesmaximal, characteristic, complemented
12C2×#14583128C211yesmaximal, characteristic, complemented
13C2×#14582940C211yesmaximal, characteristic, complemented
14C2×#14582894C211yesmaximal, characteristic, complemented
15C2×#103×D43C211yesmaximal, characteristic, complemented
16C2×C43×#467C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621898C2211yescharacteristic
19C22×Q8×D43C2211yescharacteristic
20C2×#13063357—28no—
21C2×#13063357C2218yescomplemented
22C22×#10621885C2211yescharacteristic
23C22×#10621873C2211yescharacteristic
24C22×#10621884C2211yescharacteristic
25C2×#13063331—28no—
26C2×#13063331C2218yescomplemented
27C22×#10621877C2211yescharacteristic
28C22×#10621872C2211yescharacteristic
29C22×#10621872C2211yescharacteristic
30C22×C8×D43C2211yescharacteristic
31C22×C8×D43C2211yescharacteristic
32#14583479—24no—
33#14583479C2218yes—
34#14583472—24no—
35#14583472C2218yescomplemented
36C2×#13063324—21no—
37C2×#13063311—21no—
38C2×#13063310—21no—
39C2×#13063307—21no—
40C2×#13063305C2211yescharacteristic
41C2×#13063304C2211yescharacteristic
42C2×#13063303—21no—
43C2×#13063301C2211yescharacteristic
44C2×#13063301C2211yescharacteristic
45C2×#13063300—21no—
46C2×#13063300C2211yescharacteristic
47C2×#13063299C2211yescharacteristic
48C2×#13063298—21no—
49C2×#13063298—21no—
50C2×#13063283C2211yescharacteristic
51C2×C4⋊C4×D43C2211yescharacteristic
52#14583155C2218yescomplemented
53#14583154C2218yescomplemented
54#14583147C2218yescomplemented
55#14583146C2218yescomplemented
56#14583139C2218yescomplemented
57#14583131C2218yescomplemented
58#14583128C2218yescomplemented
59#14582940C2218yescomplemented
60C2×#13063258C2211yescharacteristic
61C2×#13063257C2211yescharacteristic
62C2×#13063256C2211yescharacteristic
63#14582894C2218yescomplemented
64C2×#13063250C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063248C2211yescharacteristic
68#103×D43C2218yescomplemented
69C2×#13063247C2211yescharacteristic
70C2×#13063245C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C23×C8×C43C2211yescharacteristic
73C2×C22⋊Q8×C43C2211yescharacteristic
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#467C2218yescomplemented
76C2×#107×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×#103×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—24no—
81C2×#10621902—24no—
82C2×#10621902C2314yes—
83C2×#10621898—24no—
84C2×#10621898—24no—
85C2×#10621898D414yes—
86C2×#10621898C2314yes—
87C22×Dic86—21no—
88C22×Dic86D411yescharacteristic
89C22×Dic86C2311yescharacteristic
90C2×Q8×D43—22no—
91C2×Q8×D43—24no—
92C2×Q8×D43—24no—
93C2×Q8×D43C2314yes—
94C22×D172—21no—
95C22×D172—21no—
96C22×D172D411yescharacteristic
97C22×D172C2311yescharacteristic
98C22×C22⋊D43—21no—
99C22×C22⋊D43D411yescharacteristic
100C22×C22⋊D43D411yescharacteristic
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43—21no—
104C22×C4×D43C2311yescharacteristic
105C22×C4×D43C2311yescharacteristic
106#13063357—232no—
107C2×#10621885—24no—
108C2×#10621885C2314yes—
109C2×#10621873—24no—
110C2×#10621873C2314yes—
111C2×#10621884—24no—
112C2×#10621884C2314yes—
113#13063331—232no—
114C2×#10621877—24no—
115C2×#10621877C2314yes—
116C2×#10621872—24no—
117C2×#10621872D418yescomplemented
118C2×#10621872C2314yes—
119C2×#10621872C2314yes—
120C22×C43⋊C8C2311yescharacteristic
121C22×C43⋊C8C2311yescharacteristic
122C2×C8×D43—24no—
123C2×C8×D43—24no—
124C2×C8×D43C2314yes—
125C2×C8×D43C2314yes—
126#13063324—28no—
127#13063311—28no—
128#13063310—28no—
129#13063307—28no—
130#13063305—22no—
131#13063305C2314yes—
132#13063304—22no—
133#13063304C2314yes—
134#13063303—28no—
135#13063301—22no—
136#13063301—22no—
137#13063301C2314yes—
138#13063301C2314yes—
139#13063300—28no—
140#13063300—22no—
141#13063300C2314yes—
142#13063299—22no—
143#13063299C2314yes—
144#13063298—28no—
145#13063298—28no—
146#13063283—22no—
147#13063283C2314yes—
148C2×C4⋊Dic43—21no—
149C2×C4⋊Dic43C2311yescharacteristic
150C2×C4⋊Dic43C2311yescharacteristic
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C4⋊C4×D43—22no—
156C4⋊C4×D43C2314yes—
157C2×C22⋊Dic43—21no—
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×C4×Dic43—21no—
165#13063258C2314yes—
166#13063257C2314yes—
167#13063256C2314yes—
168#13063250C2314yes—
169#13063249C2314yes—
170#13063249C2314yes—
171#13063248C2314yes—
172#13063247C2314yes—
173#13063245C2314yes—
174C22×Q8×C43C2311yescharacteristic
175C22×Q8×C43C2311yescharacteristic
176C23×C4×C43C2311yescharacteristic
177C2×Q16×C43—24no—
178C2×Q16×C43C2314yes—
179C22×C8×C43—24no—
180C22×C8×C43C2314yes—
181C22×C8×C43C2311yescharacteristic
182C22×C8×C43C2311yescharacteristic
183C22⋊Q8×C43—22no—
184C22⋊Q8×C43—22no—
185C22⋊Q8×C43C2314yes—
186C22⋊Q8×C43C2314yes—
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43—21no—
189C2×C4⋊C4×C43C2311yescharacteristic
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C22⋊C4×C43—21no—
192C2×C22⋊C4×C43—21no—
193#107×C43C2314yes—
194#103×C43C2314yes—
195#103×C43C2314yes—
196C24×C43C2×D411yescharacteristic
197C23×D43—21no—
198C23×D43C2×D411yescharacteristic
199C23×D43C2×D411yescharacteristic
200C2×Q8×C43—21no—
201C2×Q8×C43—21no—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43—22no—
205C2×Q8×C43—22no—
206C2×Q8×C43C2412yes—
207C2×Q8×C43C2412yes—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—82no—
222C2×C22⋊D43C2×D414yes—
223C2×C22⋊D43C2×D414yes—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621902—28no—
230#10621902—28no—
231#10621902—48no—
232Q8×D43—28no—
233Q8×D43—28no—
234Q8×D43—48no—
235#10621898—216no—
236#10621898—28no—
237#10621898—28no—
238C2×D172—21no—
239C2×D172—24no—
240C2×D172—24no—
241C2×D172—24no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—44no—
245C2×D172—82no—
246C2×D172C2×D414yes—
247C2×D172C2412yes—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—24no—
251C2×C4×D43—24no—
252C2×C4×D43—24no—
253C2×C4×D43—44no—
254C2×C4×D43—44no—
255C2×C4×D43—82no—
256C2×C4×D43C2×D414yes—
257C2×C4×D43C2×D412yes—
258C2×C4×D43C2×D412yes—
259C2×C4×D43#4114yes—
260C2×C4×D43C2412yes—
261C2×C4×D43C2412yes—
262C2×Dic86—24no—
263C2×Dic86—22no—
264C2×Dic86—22no—
265C2×Dic86—21no—
266C2×Dic86—24no—
267C2×Dic86—44no—
268C2×Dic86C2×D414yes—
269C2×Dic86C2412yes—
270Q16×C43—28no—
271C2×C8×C43—22no—
272C2×C8×C43—28no—
273C2×C8×C43C2×D414yes—
274C2×C8×C43C2412yes—
275C2×C8×C43C2412yes—
276C4⋊C4×C43—24no—
277C4⋊C4×C43—24no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43C2412yes—
281C4⋊C4×C43C2412yes—
282C22⋊C4×C43—24no—
283C22⋊C4×C43—24no—
284C22⋊Dic43—24no—
285#10621885—28no—
286#10621884—28no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293C4⋊Dic43—21no—
294C4⋊Dic43—21no—
295C4⋊Dic43—24no—
296C4⋊Dic43C2412yes—
297C4⋊Dic43C2412yes—
298Dic43⋊C4—24no—
299Dic43⋊C4—24no—
300Dic43⋊C4—24no—
301Dic43⋊C4—24no—
302C4×Dic43—24no—
303#10621877—28no—
304C2×C43⋊C8—22no—
305C2×C43⋊C8C2×D414yes—
306C2×C43⋊C8C2412yes—
307C2×C43⋊C8C2412yes—
308#10621873—28no—
309#10621872—28no—
310#10621872C2×D4116yescomplemented
311C8×D43—28no—
312C8×D43—28no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43C22×D412yes—
317C23×C43C22×D411yescharacteristic
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43#12114yes—
328C22×D43C22×D412yes—
329C22×D43C22×D412yes—
330Q8×C43—22no—
331Q8×C43—22no—
332Q8×C43—22no—
333Q8×C43—22no—
334Q8×C43—42no—
335Q8×C43—42no—
336C2×C4×C43—22no—
337C2×C4×C43—24no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—42no—
345C2×C4×C43—42no—
346C2×C4×C43—42no—
347C2×C4×C43—42no—
348C2×C4×C43C22×D412yes—
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D412yes—
351C2×C4×C43C2×#4112yes—
352C2×C4×C43C2511yescharacteristic
353C22⋊D43—28no—
354C22⋊D43—28no—
355C22⋊D43—84no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—42no—
361C2×Dic43—42no—
362C2×Dic43—42no—
363C2×Dic43#12114yes—
364C2×Dic43C22×D412yes—
365C2×Dic43C22×D412yes—
366D172—28no—
367D172—22no—
368D172—22no—
369D172—48no—
370D172—42no—
371D172—84no—
372C4×D43—24no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—48no—
376C4×D43—48no—
377C4×D43—84no—
378C4×D43#12118yes—
379C4×D43C22×D414yes—
380C4×D43C2×#4114yes—
381Dic86—28no—
382Dic86—22no—
383Dic86—22no—
384Dic86—42no—
385Dic86—48no—
386C8×C43—22no—
387C8×C43C22×D414yes—
388C43⋊C8—22no—
389C43⋊C8C22×D414yes—
390C2×#3063—431nomaximal, Sylow
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—44no—
395C22×C43C2×#12112yes—
396C22×C43#57712yes—
397C22×C43#57812yes—
398C22×C43C23×D411yescharacteristic
399C2×D43—28no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—44no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—84no—
410C2×D43C2×#12114yes—
411C4×C43—22no—
412C4×C43—42no—
413C4×C43—42no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43C2×#12112yes—
417C4×C43C23×D411yescharacteristic
418C4×C43C22×#4111yescharacteristic
419Dic43—22no—
420Dic43—42no—
421Dic43—42no—
422Dic43—42no—
423Dic43C2×#12114yes—
424C22×#137—431no—
425C22×#131—431no—
426C2×#537—431no—
427C2×#536—431no—
428#3063—4316no—
429C2×#470—431no—
430C2×#470—431no—
431C2×#468—431no—
432C2×#468—431no—
433C2×#467—431no—
434C2×#467D4311yescharacteristic, complemented
435C2×#465—431no—
436C2×#465—431no—
437C2×#428—431no—
438C2×#416—431no—
439C22×#103—431no—
440C2×C43—42no—
441C2×C43#306314yescomplemented
442C2×C43C22×#12111yescharacteristic
443C2×C43C2×#57711yescharacteristic
444C2×C43C2×#57811yescharacteristic
445D43—24no—
446D43—42no—
447D43—82no—
448C22×#41—431no—
449C22×#41—431no—
450C23×Q8—431no—
451C2×#137—438no—
452C2×#137—868no—
453C22×Q16—431no—
454C22×Q16C2×D4311yescharacteristic
455C22×SD16—431no—
456C22×SD16—431no—
457C2×#131—438no—
458C2×#131—868no—
459C22×M16—431no—
460C22×M16—431no—
461C22×M16—431no—
462C23×C8—431no—
463C23×C8—431no—
464C23×C8C2×D4311yescharacteristic
465#537—438no—
466#537—864no—
467#536—438no—
468#536—864no—
469C2×C4⋊Q8—861no—
470C2×#124—861no—
471C2×#123—861no—
472C2×#123—861no—
473C2×C22⋊Q8—431no—
474C2×C22⋊Q8—431no—
475C2×C22⋊Q8—431no—
476C2×C22⋊Q8—431no—
477C2×C22⋊Q8—861no—
478C2×C22⋊Q8C2×D4311yescharacteristic
479C2×C22⋊Q8C2×D4311yescharacteristic
480C2×#121—431no—
481C2×#121—431no—
482C2×#121—861no—
483C2×#121—861no—
484C2×#121—861no—
485C2×#117—431no—
486C22×C4⋊C4—431no—
487#470—438no—
488#470—438no—
489#468—438no—
490#468—438no—
491#467—438no—
492#467C2×D4318yescomplemented
493#465—438no—
494#465—438no—
495#428—438no—
496C2×#107—431no—
497C2×#107C2×D4311yescharacteristic
498C2×#106—431no—
499C2×#106—431no—
500#416—438no—
501C2×#103—431no—
502C2×#103—431no—
503C2×#103—431no—
504C2×#103—431no—
505C2×#103—438no—
506C2×#103C2×D4311yescharacteristic
507C2×#103C2×D4311yescharacteristic
508C2×#102—431no—
509C2×#102—431no—
510C43C2×#306311yescharacteristic, complemented, Sylow
511C2×#41—434no—
512C2×#41—434no—
513C2×#41—434no—
514C2×#41—864no—
515C2×#41—864no—
516C2×#41—862no—
517C2×#41—864no—
518C2×#41—864no—
519C22×Q8—431no—
520C22×Q8—434no—
521C22×Q8—431no—
522C22×Q8—861no—
523C22×Q8—862no—
524C22×Q8—864no—
525C22×Q8—864no—
526C22×Q8C22×D4311yescharacteristic
527C22×Q8C22×D4311yescharacteristic
528C22×D4—431no—
529C22×D4—431no—
530C22×D4—431no—
531C22×D4—431no—
532C22×D4—861no—
533C22×D4—861no—
534C22×D4—861no—
535C23×C4—431no—
536C23×C4—431no—
537C23×C4—861no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4C22×D4311yescharacteristic
541#137—8632no—
542C2×Q16—24no—
543C2×Q16—434no—
544C2×Q16—864no—
545C2×Q16C22×D4314yes—
546C2×SD16—434no—
547C2×SD16—434no—
548C2×SD16—864no—
549C2×SD16—864no—
550#131—8632no—
551C2×M16—434no—
552C2×M16—438no—
553C2×M16—434no—
554C2×M16—434no—
555C2×M16—864no—
556C2×M16—864no—
557C22×C8—24no—
558C22×C8—431no—
559C22×C8—431no—
560C22×C8—434no—
561C22×C8—434no—
562C22×C8—864no—
563C22×C8—864no—
564C22×C8C22×D4311yescharacteristic
565C22×C8C22×D4314yes—
566C22×C8C22×D4311yescharacteristic
567C4⋊Q8—868no—
568#124—868no—
569#123—868no—
570#123—868no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—434no—
574C22⋊Q8—434no—
575C22⋊Q8—434no—
576C22⋊Q8—434no—
577C22⋊Q8—862no—
578C22⋊Q8—868no—
579C22⋊Q8—862no—
580C22⋊Q8—862no—
581C22⋊Q8—862no—
582C22⋊Q8C22×D4314yes—
583C22⋊Q8C22×D4314yes—
584#121—434no—
585#121—434no—
586#121—868no—
587#121—868no—
588#121—862no—
589#121—868no—
590#121—862no—
591#117—434no—
592#117—862no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—431no—
596C2×C4⋊C4—431no—
597C2×C4⋊C4—434no—
598C2×C4⋊C4—862no—
599C2×C4⋊C4—861no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—861no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4C22×D4311yescharacteristic
605C2×C4⋊C4C22×D4311yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C42—861no—
616#107—434no—
617#107C22×D4314yes—
618#106—434no—
619#106—434no—
620#103—434no—
621#103—434no—
622#103—434no—
623#103—434no—
624#103C22×D4314yes—
625#103C22×D4314yes—
626#102—434no—
627#102—434no—
628C24—431no—
629C24—431no—
630C24—861no—
631C24D4×D4311yescharacteristic
632#41—868no—
633#41—8616no—
634#41—868no—
635#41—868no—
636#41—868no—
637#41—1728no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8—22no—
644C2×Q8—434no—
645C2×Q8—432no—
646C2×Q8—864no—
647C2×Q8—864no—
648C2×Q8—868no—
649C2×Q8—868no—
650C2×Q8—861no—
651C2×Q8—862no—
652C2×Q8—862no—
653C2×Q8—1724no—
654C2×Q8—1728no—
655C2×Q8C23×D4312yes—
656C2×Q8C23×D4312yes—
657C2×D4—434no—
658C2×D4—434no—
659C2×D4—434no—
660C2×D4—432no—
661C2×D4—864no—
662C2×D4—864no—
663C2×D4—864no—
664C2×D4—864no—
665C2×D4—864no—
666C2×D4—864no—
667C2×D4—862no—
668C2×D4—861no—
669C2×D4—862no—
670C2×D4—3442no—
671C2×D4—3442no—
672C2×D4—1724no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—431no—
680C22×C4—432no—
681C22×C4—434no—
682C22×C4—434no—
683C22×C4—432no—
684C22×C4—431no—
685C22×C4—432no—
686C22×C4—432no—
687C22×C4—864no—
688C22×C4—864no—
689C22×C4—864no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—3442no—
696C22×C4—1724no—
697C22×C4—1724no—
698C22×C4D4×D4312yes—
699C22×C4D4×D4311yescharacteristic
700C22×C4C23×D4312yes—
701C22×C4C23×D4311yescharacteristic
702Q16—28no—
703Q16—868no—
704SD16—868no—
705SD16—868no—
706M16—4316no—
707M16—868no—
708M16—868no—
709C2×C8—22no—
710C2×C8—28no—
711C2×C8—434no—
712C2×C8—432no—
713C2×C8—432no—
714C2×C8—868no—
715C2×C8—868no—
716C2×C8—862no—
717C2×C8D4×D4314yes—
718C2×C8C23×D4312yes—
719C2×C8C23×D4312yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—432no—
725C4⋊C4—432no—
726C4⋊C4—864no—
727C4⋊C4—864no—
728C4⋊C4—864no—
729C4⋊C4—864no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—864no—
733C4⋊C4C23×D4312yes—
734C4⋊C4C23×D4312yes—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—864no—
738C22⋊C4—864no—
739C22⋊C4—864no—
740C22⋊C4—864no—
741C22⋊C4—864no—
742C22⋊C4—864no—
743C22⋊C4—864no—
744C42—864no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—434no—
749C23—432no—
750C23—432no—
751C23—862no—
752C23—862no—
753C23—862no—
754C23—862no—
755C23—862no—
756C23—862no—
757C23—1722no—
758C23—1722no—
759C23—1722no—
760C23C2×D4×D4312yes—
761C23C2×D4×D4311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—42no—
767Q8—42no—
768Q8—868no—
769Q8—862no—
770Q8—862no—
771Q8—1728no—
772Q8—1722no—
773D4—868no—
774D4—868no—
775D4—868no—
776D4—862no—
777D4—862no—
778D4—3444no—
779D4—3444no—
780D4—1728no—
781D4—1722no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—434no—
795C2×C4—432no—
796C2×C4—438no—
797C2×C4—434no—
798C2×C4—434no—
799C2×C4—432no—
800C2×C4—862no—
801C2×C4—864no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—3444no—
808C2×C4—1728no—
809C2×C4—1728no—
810C2×C4—1722no—
811C2×C4—1722no—
812C2×C4—1722no—
813C2×C4C2×D4×D4312yes—
814C2×C4C2×D4×D4311yescharacteristic
815C2×C4C2×D4×D4312yes—
816C2×C4#41×D4312yes—
817C2×C4C24×D4311yescharacteristic
818C8—22no—
819C8—434no—
820C8—862no—
821C8C2×D4×D4314yes—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—44no—
826C22—434no—
827C22—862no—
828C22—862no—
829C22—868no—
830C22—862no—
831C22—862no—
832C22—862no—
833C22—3444no—
834C22—1722no—
835C22—1722no—
836C22—1722no—
837C22—1724no—
838C22#121×D4312yes—
839C22#1458370612yes—
840C22#1458371212yes—
841C22C22×D4×D4311yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—434no—
848C4—862no—
849C4—1722no—
850C4—1722no—
851C4—1722no—
852C4#121×D4312yes—
853C4C22×D4×D4311yescharacteristic
854C4C2×#41×D4311yescharacteristic
855C2—42no—
856C2—864no—
857C2—3442no—
858C2—1722no—
859C2#1914428514yesdirect product factor
860C2C2×#121×D4311yescharacteristic
861C2C2×#1458370611yescharacteristic
862C2C2×#1458371211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#467C2
socleC23×C43C22×D4
prime radicalC2×#14583479C2
hypercenterC2×#467D43
hypocenterC43C2×#3063
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#13063357C2semidirect
2. C22×#13063331C2semidirect
4. C2×#14583472C2semidirect
5. #19144285C2direct (N × H)
6. C2×#14583155C2semidirect
7. C2×#14583154C2semidirect
8. C2×#14583147C2semidirect
9. C2×#14583146C2semidirect
10. C2×#14583139C2semidirect
11. C2×#14583131C2semidirect
12. C2×#14583128C2semidirect
13. C2×#14582940C2semidirect
14. C2×#14582894C2semidirect
15. C2×#103×D43C2semidirect
16. C2×C43×#467C2semidirect
21. C2×#13063357C22semidirect
26. C2×#13063331C22semidirect
35. #14583472C22semidirect
52. #14583155C22semidirect
53. #14583154C22semidirect
54. #14583147C22semidirect
55. #14583146C22semidirect
56. #14583139C22semidirect
57. #14583131C22semidirect
58. #14583128C22semidirect
59. #14582940C22semidirect
63. #14582894C22semidirect
68. #103×D43C22semidirect
75. C43×#467C22semidirect
117. C2×#10621872D4semidirect
310. #10621872C2×D4semidirect
434. C2×#467D43semidirect
441. C2×C43#3063semidirect
492. #467C2×D43semidirect
510. C43C2×#3063semidirect
859. C2#19144285direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633572
C22×#130633312
C2×#145834792
C2×#145834722
#191442852
C2×#145831552
C2×#145831542
C2×#145831472
C2×#145831462
C2×#145831392
C2×#145831312
C2×#145831282
C2×#145829402
C2×#145828942
C2×#103×D432
C2×C43×#4672
C2×#306343