Finite Group Databasebeta

← C2×#19144049 #25963416

Subgroups — C2×#19144049 #25963416

Order 11008.

2874 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063348C211yesmaximal, characteristic, complemented
2C22×#13063346C211yesmaximal, characteristic, complemented
3C2×#14583448C211yesmaximal, characteristic, complemented
4C2×C4×#10621902C211yesmaximal, characteristic, complemented
5#19144049C2116yesmaximal, direct product factor
6C2×#14583121C211yesmaximal, characteristic, complemented
7C2×#14583107C211yesmaximal, characteristic, complemented
8C2×#14583097C211yesmaximal, characteristic, complemented
9C2×#14583115C211yesmaximal, characteristic, complemented
10C2×#14583111C211yesmaximal, characteristic, complemented
11C2×#14583103C211yesmaximal, characteristic, complemented
12C2×#14583093C211yesmaximal, characteristic, complemented
13C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
14C2×#14582894C211yesmaximal, characteristic, complemented
15C2×#14582892C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic
19C22×#10621900C2211yescharacteristic
20C2×#13063348—28no—
21C2×#13063348C2218yescomplemented
22C2×#13063346—28no—
23C2×#13063346C2218yescomplemented
24C22×#10621885C2211yescharacteristic
25C22×#10621873C2211yescharacteristic
26C22×#10621884C2211yescharacteristic
27C22×#10621884C2211yescharacteristic
28C22×D344C2211yescharacteristic
29C22×#10621882C2211yescharacteristic
30C22×C8×D43C2211yescharacteristic
31C22×C8×D43C2211yescharacteristic
32#14583448—24no—
33#14583448C2218yescomplemented
34C2×#13063323C2211yescharacteristic
35C2×#13063321C2211yescharacteristic
36C2×#13063313C2211yescharacteristic
37C2×#13063298—21no—
38C2×#13063298—21no—
39C4×#10621902—24no—
40C4×#10621902C2218yescomplemented
41C2×Q8×Dic43C2211yescharacteristic
42C2×C4×D172—21no—
43C2×C4×D172C2211yescharacteristic
44C2×#13063287—21no—
45C2×#13063287C2211yescharacteristic
46C2×(C22⋊D43)⋊C4—21no—
47C2×(C22⋊D43)⋊C4—21no—
48C2×#13063283—21no—
49C2×#13063283C2211yescharacteristic
50C2×C42×D43—21no—
51C2×C42×D43C2211yescharacteristic
52#14583121C2218yescomplemented
53#14583115C2218yescomplemented
54#14583111C2218yescomplemented
55#14583107C2218yescomplemented
56#14583103C2218yescomplemented
57#14583097C2218yescomplemented
58#14583093C2218yescomplemented
59C2×C4⋊(C43⋊C8)C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C4⋊C8×D43C2218yescomplemented
63#14582894C2218yescomplemented
64#14582892C2218yescomplemented
65C2×#13063250C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063248C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×#13063246C2211yescharacteristic
70C2×#13063245C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic
73C2×#124×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C43×#464C2218yescomplemented
76C2×C4⋊C8×C43C2211yescharacteristic
77C2×#103×C43C2211yescharacteristic
78C2×#102×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902—24no—
83C2×#10621902—24no—
84C2×#10621902D418yescomplemented
85C2×#10621902C2314yes—
86C2×#10621902C2314yes—
87C2×#10621900—24no—
88C2×#10621900—22no—
89C2×#10621900—24no—
90C2×#10621900C2314yes—
91C22×Dic86C2311yescharacteristic
92C22×D172—21no—
93C22×D172—21no—
94C22×D172C2311yescharacteristic
95C22×D172C2311yescharacteristic
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C23×Dic43—21no—
100C22×C4×D43—21no—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43—21no—
104C22×C4×D43D411yescharacteristic
105C22×C4×D43D411yescharacteristic
106C22×C4×D43C2311yescharacteristic
107#13063348—232no—
108#13063346—232no—
109C2×#10621885—24no—
110C2×#10621885C2314yes—
111C2×#10621873—24no—
112C2×#10621873C2314yes—
113C2×#10621884—24no—
114C2×#10621884—24no—
115C2×#10621884C2314yes—
116C2×#10621884C2314yes—
117C2×D344—24no—
118C2×D344C2314yes—
119C2×#10621882—24no—
120C2×#10621882C2314yes—
121C22×C43⋊C8C2311yescharacteristic
122C22×C43⋊C8C2311yescharacteristic
123C2×C8×D43—24no—
124C2×C8×D43—24no—
125C2×C8×D43C2314yes—
126C2×C8×D43C2314yes—
127#13063323—22no—
128#13063323C2314yes—
129#13063321—22no—
130#13063321C2314yes—
131#13063313—22no—
132#13063313C2314yes—
133#13063298—28no—
134#13063298—28no—
135Q8×Dic43—22no—
136Q8×Dic43C2314yes—
137C4×D172—28no—
138C4×D172—22no—
139C4×D172C2314yes—
140#13063287—28no—
141#13063287—22no—
142#13063287C2314yes—
143(C22⋊D43)⋊C4—28no—
144(C22⋊D43)⋊C4—28no—
145#13063283—22no—
146#13063283—28no—
147#13063283C2314yes—
148C2×C4⋊Dic43—21no—
149C2×C4⋊Dic43C2311yescharacteristic
150C2×Dic43⋊C4—21no—
151C2×Dic43⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×(C2×D43)⋊C4—21no—
157C2×C4×Dic43—21no—
158C2×C4×Dic43—21no—
159C2×C4×Dic43D411yescharacteristic
160C2×C4×Dic43D411yescharacteristic
161C2×C4×Dic43C2311yescharacteristic
162C42×D43—28no—
163C42×D43D414yes—
164C42×D43C2314yes—
165C4⋊(C43⋊C8)C2314yes—
166Dic43⋊C8C2314yes—
167Dic43⋊C8C2314yes—
168#13063250C2314yes—
169#13063249C2314yes—
170#13063248C2314yes—
171#13063247C2314yes—
172#13063246C2314yes—
173#13063245C2314yes—
174C22×Q8×C43C2311yescharacteristic
175C22×Q8×C43C2311yescharacteristic
176C22×D4×C43C2311yescharacteristic
177C2×Q16×C43—24no—
178C2×Q16×C43C2314yes—
179C2×SD16×C43—24no—
180C2×SD16×C43C2314yes—
181C22×C8×C43C2311yescharacteristic
182C22×C8×C43C2311yescharacteristic
183#124×C43—22no—
184#124×C43C2314yes—
185C4×Q8×C43—22no—
186C4×Q8×C43C2314yes—
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43C2311yescharacteristic
189C2×C22⋊C4×C43—21no—
190C2×C22⋊C4×C43—21no—
191C2×C42×C43—21no—
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43C2314yes—
194#103×C43C2314yes—
195#102×C43C2314yes—
196C24×C43—21no—
197C23×D43—21no—
198C23×D43—21no—
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×C43C2×D414yes—
206C2×Q8×C43C2412yes—
207C2×Q8×C43C2412yes—
208C2×D4×C43—21no—
209C2×D4×C43—22no—
210C2×D4×C43—22no—
211C2×D4×C43C2412yes—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—44no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43—44no—
224C22×Dic43—24no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—44no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231#10621902—216no—
232#10621902—28no—
233#10621902—28no—
234#10621902—28no—
235#10621902—48no—
236#10621902C2×D4116yescomplemented
237#10621900—28no—
238#10621900—28no—
239#10621900—48no—
240C2×D172—21no—
241C2×D172—22no—
242C2×D172—21no—
243C2×D172—28no—
244C2×D172—24no—
245C2×D172—24no—
246C2×D172—22no—
247C2×D172—22no—
248C2×D172—44no—
249C2×D172C2×D414yes—
250C2×D172C2412yes—
251C2×D172C2412yes—
252C2×C4×D43—28no—
253C2×C4×D43—24no—
254C2×C4×D43—24no—
255C2×C4×D43—24no—
256C2×C4×D43—24no—
257C2×C4×D43—24no—
258C2×C4×D43—42no—
259C2×C4×D43—44no—
260C2×C4×D43—44no—
261C2×C4×D43—44no—
262C2×C4×D43C2×D414yes—
263C2×C4×D43C2×D414yes—
264C2×C4×D43C2×D414yes—
265C2×C4×D43C2×D412yes—
266C2×C4×D43#4114yes—
267C2×C4×D43C2412yes—
268C2×Dic86—22no—
269C2×Dic86—22no—
270C2×Dic86—21no—
271C2×Dic86C2412yes—
272Q16×C43—28no—
273SD16×C43—28no—
274C2×C8×C43—22no—
275C2×C8×C43—22no—
276C2×C8×C43C2412yes—
277C2×C8×C43C2412yes—
278C4⋊C4×C43—24no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43C2412yes—
281C22⋊C4×C43—24no—
282C22⋊C4×C43—24no—
283C42×C43—24no—
284C42×C43C2×D412yes—
285C42×C43C2412yes—
286#10621885—28no—
287#10621884—28no—
288#10621884—28no—
289#10621882—28no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293(C2×D43)⋊C4—24no—
294(C2×D43)⋊C4—24no—
295C4⋊Dic43—21no—
296C4⋊Dic43—24no—
297C4⋊Dic43C2412yes—
298Dic43⋊C4—24no—
299Dic43⋊C4—24no—
300C4×Dic43—24no—
301C4×Dic43—24no—
302C4×Dic43C2×D414yes—
303C4×Dic43C2×D412yes—
304C4×Dic43C2×D414yes—
305C4×Dic43C2412yes—
306C2×C43⋊C8—22no—
307C2×C43⋊C8—22no—
308C2×C43⋊C8C2412yes—
309C2×C43⋊C8C2412yes—
310D344—28no—
311#10621873—28no—
312C8×D43—28no—
313C8×D43—28no—
314C23×C43—22no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43C22×D411yescharacteristic
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—24no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43#12114yes—
330C22×D43C22×D412yes—
331Q8×C43—24no—
332Q8×C43—22no—
333Q8×C43—22no—
334Q8×C43—22no—
335Q8×C43—42no—
336Q8×C43C22×D414yes—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—42no—
340C2×C4×C43—24no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—42no—
347C2×C4×C43—42no—
348C2×C4×C43C22×D412yes—
349C2×C4×C43C22×D412yes—
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D412yes—
352C2×C4×C43C2×#4112yes—
353C2×C4×C43C2511yescharacteristic
354C22⋊D43—48no—
355C22⋊D43—48no—
356C22⋊D43—48no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—42no—
361C2×Dic43—42no—
362C2×Dic43—48no—
363C2×Dic43#12114yes—
364C2×Dic43#13514yescomplemented
365C2×Dic43C22×D412yes—
366C2×Dic43C22×D412yes—
367C2×Dic43C22×D412yes—
368D172—216no—
369D172—24no—
370D172—22no—
371D172—22no—
372D172—22no—
373D172—48no—
374D172—42no—
375D172C22×D414yes—
376C4×D43—216no—
377C4×D43—28no—
378C4×D43—44no—
379C4×D43—48no—
380C4×D43—48no—
381C4×D43—48no—
382C4×D43#12118yes—
383C4×D43C22×D414yes—
384C4×D43C2×#4114yes—
385Dic86—22no—
386Dic86—22no—
387Dic86—42no—
388C8×C43—22no—
389C8×C43—22no—
390C43⋊C8—22no—
391C43⋊C8—22no—
392C2×#3035—431nomaximal, Sylow
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—84no—
397C22×C43C2×#12112yes—
398C22×C43C2×#13512yes—
399C22×C43#57512yes—
400C22×C43C23×D411yescharacteristic
401C2×D43—28no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—24no—
405C2×D43—48no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—84no—
412C2×D43C2×#12114yes—
413C4×C43—24no—
414C4×C43—22no—
415C4×C43—22no—
416C4×C43—42no—
417C4×C43—42no—
418C4×C43C2×#12112yes—
419C4×C43C23×D411yescharacteristic
420C4×C43C22×#4111yescharacteristic
421Dic43—22no—
422Dic43—42no—
423Dic43—42no—
424Dic43C2×#12114yes—
425Dic43C2×#13514yescomplemented
426C22×#135—431no—
427C22×#135—431no—
428C2×#532—431no—
429C2×C4×#41—431no—
430#3035—4316no—
431C2×#464—431no—
432C2×#464D4311yescharacteristic, complemented
433C2×#462—431no—
434C2×#460—431no—
435C2×#463—431no—
436C2×#463—431no—
437C2×#461—431no—
438C2×#459—431no—
439C22×C4⋊C8—431no—
440C2×#416—431no—
441C2×#416—431no—
442C2×C43—82no—
443C2×C43#303514yescomplemented
444C2×C43C22×#12111yescharacteristic
445C2×C43C22×#13511yescharacteristic
446C2×C43C2×#57511yescharacteristic
447D43—24no—
448D43—44no—
449D43—82no—
450C22×#41—431no—
451C22×#41—431no—
452C22×#41—431no—
453C2×#135—438no—
454C2×#135—438no—
455C2×#135—868no—
456C2×#135—868no—
457C22×Q16—431no—
458C22×Q16C2×D4311yescharacteristic
459C22×SD16—431no—
460C22×SD16—431no—
461C22×SD16—431no—
462C22×SD16C2×D4311yescharacteristic
463C22×D8—431no—
464C22×D8—431no—
465C23×C8—431no—
466C23×C8—431no—
467#532—438no—
468#532—864no—
469C2×C4⋊Q8—431no—
470C2×#127—431no—
471C2×#124—431no—
472C2×#124C2×D4311yescharacteristic
473C2×#121—861no—
474C2×#121—861no—
475C4×#41—438no—
476C4×#41—864no—
477C2×C4×Q8—431no—
478C2×C4×Q8C2×D4311yescharacteristic
479C2×C4×D4—431no—
480C2×C4×D4—431no—
481C2×C4×D4—861no—
482C2×C4×D4—861no—
483C2×C4×D4—861no—
484C2×C4×D4—861no—
485C2×#117—431no—
486C2×#117—861no—
487C22×C42—431no—
488C22×C42—861no—
489#464—438no—
490#464C2×D4318yescomplemented
491#463—438no—
492#463—438no—
493#462—438no—
494#461—438no—
495#460—438no—
496#459—438no—
497C2×C4⋊C8—431no—
498C2×C4⋊C8—431no—
499C2×C4⋊C8—431no—
500C2×C4⋊C8—438no—
501C2×C4⋊C8C2×D4311yescharacteristic
502#416—438no—
503#416—438no—
504C2×#103—431no—
505C2×#103—431no—
506C2×#103—431no—
507C2×#103C2×D4311yescharacteristic
508C2×#102—431no—
509C2×#102—431no—
510C2×#102—431no—
511C2×#102C2×D4311yescharacteristic
512C43C2×#303511yescharacteristic, complemented, Sylow
513C2×#41—438no—
514C2×#41—434no—
515C2×#41—434no—
516C2×#41—434no—
517C2×#41—862no—
518C2×#41—862no—
519C2×#41—864no—
520C2×#41—862no—
521C2×#41—864no—
522C2×#41—864no—
523C2×#41—864no—
524C2×#41—864no—
525C22×Q8—431no—
526C22×Q8C22×D4311yescharacteristic
527C22×Q8C22×D4311yescharacteristic
528C22×D4—431no—
529C22×D4—431no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4—861no—
534C22×D4—861no—
535C22×D4C22×D4311yescharacteristic
536C23×C4—431no—
537C23×C4—431no—
538C23×C4—431no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4—861no—
542C23×C4—861no—
543C23×C4—861no—
544#135—8632no—
545#135—8632no—
546C2×Q16—24no—
547C2×Q16—434no—
548C2×Q16—864no—
549C2×Q16C22×D4314yes—
550C2×SD16—24no—
551C2×SD16—434no—
552C2×SD16—434no—
553C2×SD16—434no—
554C2×SD16—864no—
555C2×SD16—864no—
556C2×SD16—864no—
557C2×SD16C22×D4314yes—
558C2×D8—434no—
559C2×D8—434no—
560C2×D8—864no—
561C2×D8—864no—
562C22×C8—431no—
563C22×C8—431no—
564C22×C8—434no—
565C22×C8—434no—
566C22×C8—864no—
567C22×C8—864no—
568C22×C8C22×D4311yescharacteristic
569C22×C8C22×D4311yescharacteristic
570C4⋊Q8—434no—
571C4⋊Q8—862no—
572#127—434no—
573#127—862no—
574#124—22no—
575#124—434no—
576#124—862no—
577#124C22×D4314yes—
578#121—868no—
579#121—868no—
580C4×Q8—22no—
581C4×Q8—434no—
582C4×Q8—862no—
583C4×Q8C22×D4314yes—
584C4×D4—434no—
585C4×D4—434no—
586C4×D4—868no—
587C4×D4—868no—
588C4×D4—868no—
589C4×D4—862no—
590C4×D4—868no—
591C4×D4—862no—
592#117—434no—
593#117—868no—
594#117—862no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—431no—
597C2×C4⋊C4—861no—
598C2×C4⋊C4—861no—
599C2×C4⋊C4—861no—
600C2×C4⋊C4C22×D4311yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C22⋊C4—861no—
608C2×C42—21no—
609C2×C42—431no—
610C2×C42—431no—
611C2×C42—431no—
612C2×C42—434no—
613C2×C42—434no—
614C2×C42—868no—
615C2×C42—861no—
616C2×C42—861no—
617C2×C42C22×D4311yescharacteristic
618C4⋊C8—434no—
619C4⋊C8—434no—
620C4⋊C8—434no—
621C4⋊C8C22×D4314yes—
622#103—434no—
623#103—434no—
624#103—434no—
625#103C22×D4314yes—
626#102—434no—
627#102—434no—
628#102—434no—
629#102C22×D4314yes—
630C24—21no—
631C24—431no—
632C24—861no—
633C24—861no—
634#41—4316no—
635#41—8616no—
636#41—868no—
637#41—868no—
638#41—868no—
639#41—868no—
640#41—868no—
641#41—1728no—
642#41—1728no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—432no—
649C2×Q8—861no—
650C2×Q8—862no—
651C2×Q8—862no—
652C2×Q8D4×D4314yes—
653C2×Q8C23×D4312yes—
654C2×Q8C23×D4312yes—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—434no—
659C2×D4—432no—
660C2×D4—432no—
661C2×D4—864no—
662C2×D4—868no—
663C2×D4—864no—
664C2×D4—864no—
665C2×D4—864no—
666C2×D4—864no—
667C2×D4—861no—
668C2×D4—862no—
669C2×D4—861no—
670C2×D4—862no—
671C2×D4—862no—
672C2×D4—1724no—
673C2×D4—1724no—
674C2×D4—1724no—
675C2×D4—1724no—
676C2×D4C23×D4312yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—431no—
681C22×C4—431no—
682C22×C4—432no—
683C22×C4—434no—
684C22×C4—434no—
685C22×C4—432no—
686C22×C4—431no—
687C22×C4—434no—
688C22×C4—434no—
689C22×C4—864no—
690C22×C4—864no—
691C22×C4—868no—
692C22×C4—864no—
693C22×C4—864no—
694C22×C4—864no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—864no—
698C22×C4—1722no—
699C22×C4—1724no—
700C22×C4—1724no—
701C22×C4—1724no—
702C22×C4—1724no—
703C22×C4D4×D4311yescharacteristic
704C22×C4D4×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706Q16—28no—
707Q16—868no—
708SD16—28no—
709SD16—868no—
710SD16—868no—
711SD16—868no—
712D8—868no—
713D8—868no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—432no—
717C2×C8—432no—
718C2×C8—868no—
719C2×C8—868no—
720C2×C8—862no—
721C2×C8—862no—
722C2×C8C23×D4312yes—
723C2×C8C23×D4312yes—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—432no—
727C4⋊C4—864no—
728C4⋊C4—864no—
729C4⋊C4—864no—
730C4⋊C4—861no—
731C4⋊C4C23×D4312yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C22⋊C4—864no—
738C22⋊C4—864no—
739C42—24no—
740C42—434no—
741C42—434no—
742C42—432no—
743C42—432no—
744C42—864no—
745C42—864no—
746C42D4×D4312yes—
747C42C23×D4312yes—
748C23—22no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—434no—
753C23—432no—
754C23—862no—
755C23—862no—
756C23—864no—
757C23—862no—
758C23—862no—
759C23—1722no—
760C23—1722no—
761C23—1722no—
762C23—1722no—
763C23—1722no—
764C23C2×D4×D4311yescharacteristic
765Q8—24no—
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—42no—
770Q8—862no—
771Q8—862no—
772Q8—1722no—
773Q8C2×D4×D4314yes—
774D4—22no—
775D4—22no—
776D4—42no—
777D4—434no—
778D4—8616no—
779D4—864no—
780D4—862no—
781D4—862no—
782D4—862no—
783D4—1728no—
784D4—1728no—
785D4—1728no—
786D4—1728no—
787D4—1722no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—434no—
797C2×C4—434no—
798C2×C4—432no—
799C2×C4—432no—
800C2×C4—438no—
801C2×C4—434no—
802C2×C4—434no—
803C2×C4—432no—
804C2×C4—868no—
805C2×C4—8616no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—1724no—
810C2×C4—1728no—
811C2×C4—1728no—
812C2×C4—1728no—
813C2×C4—1728no—
814C2×C4—1722no—
815C2×C4—1722no—
816C2×C4C2×D4×D4312yes—
817C2×C4C2×D4×D4312yes—
818C2×C4C2×D4×D4311yescharacteristic
819C2×C4C2×D4×D4312yes—
820C2×C4#41×D4312yes—
821C2×C4C24×D4311yescharacteristic
822C8—22no—
823C8—22no—
824C8—862no—
825C8—862no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—84no—
830C22—434no—
831C22—862no—
832C22—862no—
833C22—868no—
834C22—864no—
835C22—3444no—
836C22—1722no—
837C22—1722no—
838C22—1722no—
839C22—1722no—
840C22—1722no—
841C22—1728no—
842C22#121×D4312yes—
843C22#135×D4312yes—
844C22#1458369812yes—
845C22C22×D4×D4311yescharacteristic
846C4—22no—
847C4—22no—
848C4—24no—
849C4—42no—
850C4—42no—
851C4—434no—
852C4—434no—
853C4—862no—
854C4—1722no—
855C4—1722no—
856C4#121×D4312yes—
857C4C22×D4×D4311yescharacteristic
858C4C2×#41×D4311yescharacteristic
859C2—82no—
860C2—864no—
861C2—3442no—
862C2—1724no—
863C2#1914404914yesdirect product factor
864C2C2×#121×D4311yescharacteristic
865C2C2×#135×D4311yescharacteristic
866C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
hypercenterC2×#464D43
hypocenterC43C2×#3035
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#13063348C2semidirect
2. C22×#13063346C2semidirect
3. C2×#14583448C2semidirect
4. C2×C4×#10621902C2semidirect
5. #19144049C2direct (N × H)
6. C2×#14583121C2semidirect
7. C2×#14583107C2semidirect
8. C2×#14583097C2semidirect
9. C2×#14583115C2semidirect
10. C2×#14583111C2semidirect
11. C2×#14583103C2semidirect
12. C2×#14583093C2semidirect
13. C2×C4⋊C8×D43C2semidirect
14. C2×#14582894C2semidirect
15. C2×#14582892C2semidirect
16. C2×C43×#464C2semidirect
21. C2×#13063348C22semidirect
23. C2×#13063346C22semidirect
33. #14583448C22semidirect
40. C4×#10621902C22semidirect
52. #14583121C22semidirect
53. #14583115C22semidirect
54. #14583111C22semidirect
55. #14583107C22semidirect
56. #14583103C22semidirect
57. #14583097C22semidirect
58. #14583093C22semidirect
62. C4⋊C8×D43C22semidirect
63. #14582894C22semidirect
64. #14582892C22semidirect
75. C43×#464C22semidirect
84. C2×#10621902D4semidirect
236. #10621902C2×D4semidirect
364. C2×Dic43#135semidirect
425. Dic43C2×#135semidirect
432. C2×#464D43semidirect
443. C2×C43#3035semidirect
490. #464C2×D43semidirect
512. C43C2×#3035semidirect
863. C2#19144049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633482
C22×#130633462
C2×#145834482
C2×C4×#106219022
#191440492
C2×#145831212
C2×#145831072
C2×#145830972
C2×#145831152
C2×#145831112
C2×#145831032
C2×#145830932
C2×C4⋊C8×D432
C2×#145828942
C2×#145828922
C2×C43×#4642
C2×#303543