Finite Group Databasebeta

← #25112783

Subgroups — #25112783

Order 11008.

1132 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583602C211yesmaximal, characteristic
2M16×D172C211yesmaximal, characteristic, complemented
3#19143330C211yesmaximal, characteristic, complemented
4#19135589C211yesmaximal, characteristic, complemented
5#19135057C211yesmaximal, characteristic, complemented
6#19135057C211yesmaximal, characteristic, complemented
7#19135057C211yesmaximal, characteristic, complemented
8#19135057C211yesmaximal, characteristic, complemented
9#19134677C211yesmaximal, characteristic, complemented
10#19134674C211yesmaximal, characteristic, complemented
11#19134584C211yesmaximal, characteristic, complemented
12C4×#13063241C211yesmaximal, characteristic, complemented
13#19134332C211yesmaximal, characteristic, complemented
14#343×D43C211yesmaximal, characteristic, complemented
15C43×#1998C211yesmaximal, characteristic, complemented
16C2×M16×D43C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20#14583602—21no—
21#14583602—21no—
22#14583602—21no—
23#14583602—21no—
24#14583602—21no—
25#14583602—21no—
26#14583602—21no—
27#14583602—21no—
28C2×#13063320C412yes—
29C2×#13063310C412yes—
30C2×#13063300C412yes—
31C2×#13063300C2211yescharacteristic
32C2×#13063300C2211yescharacteristic
33C2×C4×D172C2211yescharacteristic
34C2×C4×D172C2211yescharacteristic
35C2×#13063287C412yes—
36C2×#13063283C2211yescharacteristic
37C2×C4⋊C4×D43C2211yescharacteristic
38#14582978—21no—
39#14582976—21no—
40#14582972—21no—
41#14582972—21no—
42#14582969—21no—
43#14582969—21no—
44C8×D172—21no—
45#14582964—21no—
46#14582923C2211yescharacteristic
47C2×#13063241C2211yescharacteristic
48C2×#13063241C2211yescharacteristic
49C2×#13063241C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51#14582862C2211yescharacteristic
52#14582862C2211yescharacteristic
53#14582862C2211yescharacteristic
54#14582862C2211yescharacteristic
55C4×#10621877C2211yescharacteristic
56#14582668C2211yescharacteristic
57#14582668C2211yescharacteristic
58#14582668C2211yescharacteristic
59#14582668C2211yescharacteristic
60#14582667C2211yescharacteristic
61#14582667C2211yescharacteristic
62#14582667C2211yescharacteristic
63#14582667C2211yescharacteristic
64C2×#125×C43C2211yescharacteristic
65C43×#423C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C43×#343C2211yescharacteristic
68C43×#343C2211yescharacteristic
69C43×#343C2211yescharacteristic
70C43×#343C2211yescharacteristic
71C22×D172C2×C412yes—
72C22×D172C2×C412yes—
73C22×D172C2×C411yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C4×D43C2×C412yes—
76C22×C4×D43C2×C412yes—
77C22×C4×D43C2311yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621872—21no—
84C2×#10621872—21no—
85C2×#10621872—21no—
86C2×#10621872—21no—
87M16×D43—22no—
88M16×D43—22no—
89M16×D43—22no—
90M16×D43—22no—
91M16×D43—41no—
92M16×D43—41no—
93M16×D43—41no—
94M16×D43—41no—
95C2×C8×D43—21no—
96C2×C8×D43—21no—
97C2×C8×D43—21no—
98C2×C8×D43—21no—
99#13063320—22no—
100#13063320—22no—
101#13063320—22no—
102#13063320—22no—
103#13063310—22no—
104#13063310—22no—
105#13063310—22no—
106#13063310—22no—
107#13063300—22no—
108#13063300—22no—
109#13063300—22no—
110#13063300—22no—
111#13063300—21no—
112#13063300—21no—
113#13063300—21no—
114#13063300—21no—
115#13063300—21no—
116#13063300—21no—
117#13063300—21no—
118#13063300—21no—
119C4×D172—21no—
120C4×D172—21no—
121C4×D172—21no—
122C4×D172—21no—
123C4×D172D411yescharacteristic
124C4×D172D411yescharacteristic
125C4×D172D411yescharacteristic
126C4×D172D411yescharacteristic
127C4×D172D411yescharacteristic
128C4×D172D411yescharacteristic
129C4×D172D411yescharacteristic
130C4×D172D411yescharacteristic
131#13063287—22no—
132#13063287—22no—
133#13063287—22no—
134#13063287—22no—
135#13063283—21no—
136#13063283—21no—
137#13063283—21no—
138#13063283—21no—
139C2×C4⋊Dic43C2×C411yescharacteristic
140C2×C4⋊Dic43C2311yescharacteristic
141C2×Dic43⋊C4C2×C412yes—
142C4⋊C4×D43—21no—
143C4⋊C4×D43—21no—
144C4⋊C4×D43—21no—
145C4⋊C4×D43—21no—
146C2×(C2×D43)⋊C4C2×C412yes—
147C2×(C2×D43)⋊C4C2×C412yes—
148C2×(C2×D43)⋊C4C2×C412yes—
149C2×(C2×D43)⋊C4C2×C412yes—
150C2×(C2×D43)⋊C4C2×C411yescharacteristic
151C2×(C2×D43)⋊C4C2×C411yescharacteristic
152C2×C4×Dic43C2×C412yes—
153C4⋊(C43⋊C8)—21no—
154C4⋊(C43⋊C8)—21no—
155#13063241—22no—
156#13063241—22no—
157#13063241—41no—
158#13063241—41no—
159(C2×D43)⋊C8—21no—
160(C2×D43)⋊C8—21no—
161(C2×D43)⋊C8—21no—
162(C2×D43)⋊C8—21no—
163(C2×D43)⋊C8—21no—
164(C2×D43)⋊C8—21no—
165(C2×D43)⋊C8—21no—
166(C2×D43)⋊C8—21no—
167#13063236—21no—
168C4×C43⋊C8—21no—
169C2×M16×C43C2311yescharacteristic
170C2×M16×C43C2311yescharacteristic
171C2×M16×C43C2311yescharacteristic
172C2×M16×C43C2311yescharacteristic
173#125×C43—21no—
174#125×C43—21no—
175#125×C43—21no—
176#125×C43—21no—
177C2×C4⋊C4×C43C2×C412yes—
178C2×C4⋊C4×C43C2×C412yes—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C42×C43C2311yescharacteristic
182C4⋊C8×C43—21no—
183C4⋊C8×C43—21no—
184#97×C43—21no—
185C4×C8×C43—21no—
186C23×D43C22×C411yescharacteristic
187C23×D43C22×C412yes—
188C23×D43C22×C411yescharacteristic
189C22×C4×C43C22×C412yes—
190C22×C4×C43C22×C412yes—
191C22×C4×C43C22×C411yescharacteristic
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C22×Dic43C22×C411yescharacteristic
195C22×Dic43C22×C411yescharacteristic
196C22×Dic43C22×C412yes—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—22no—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172—22no—
207C2×D172—42no—
208C2×D172—44no—
209C2×D172—82no—
210C2×D172C22⋊C411yescharacteristic
211C2×D172C22⋊C411yescharacteristic
212C2×D172C22⋊C411yescharacteristic
213C2×D172C22⋊C411yescharacteristic
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—82no—
227C2×C4×D43—82no—
228C2×C4×D43C2×D411yescharacteristic
229C2×C4×D43C2×D411yescharacteristic
230C2×C4×D43C2×D411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×C4×D43C2×D411yescharacteristic
233C2×C4×D43C2×D411yescharacteristic
234C2×C4×D43C2×D411yescharacteristic
235C2×C4×D43C2×D411yescharacteristic
236M16×C43—21no—
237M16×C43—21no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43#4112yes—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C4⋊C4×C43—22no—
249C4⋊C4×C43—22no—
250C4⋊C4×C43—22no—
251C4⋊C4×C43—22no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C42×C43C2×D411yescharacteristic
257C42×C43C2×D411yescharacteristic
258C42×C43C2×D411yescharacteristic
259C42×C43C2×D411yescharacteristic
260(C2×D43)⋊C4—22no—
261(C2×D43)⋊C4—22no—
262(C2×D43)⋊C4—22no—
263(C2×D43)⋊C4—22no—
264(C2×D43)⋊C4—22no—
265(C2×D43)⋊C4—22no—
266(C2×D43)⋊C4—22no—
267(C2×D43)⋊C4—22no—
268(C2×D43)⋊C4C22⋊C411yescharacteristic
269(C2×D43)⋊C4C22⋊C411yescharacteristic
270(C2×D43)⋊C4C22⋊C411yescharacteristic
271(C2×D43)⋊C4C22⋊C411yescharacteristic
272(C2×D43)⋊C4C22⋊C411yescharacteristic
273(C2×D43)⋊C4C22⋊C411yescharacteristic
274(C2×D43)⋊C4C22⋊C411yescharacteristic
275(C2×D43)⋊C4C22⋊C411yescharacteristic
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43C22⋊C411yescharacteristic
279C4⋊Dic43C22⋊C411yescharacteristic
280C4⋊Dic43C22⋊C411yescharacteristic
281C4⋊Dic43C22⋊C411yescharacteristic
282Dic43⋊C4—22no—
283Dic43⋊C4—22no—
284C4×Dic43—22no—
285C4×Dic43—22no—
286#10621877—21no—
287#10621877—21no—
288#10621877—21no—
289#10621877—21no—
290#10621877—21no—
291#10621877—21no—
292#10621877—21no—
293#10621877#4112yes—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298#10621872—42no—
299#10621872—42no—
300#10621872—42no—
301#10621872—42no—
302C8×D43—42no—
303C8×D43—42no—
304C8×D43—42no—
305C8×D43—42no—
306C23×C43C23×C411yescharacteristic
307C22×D43—21no—
308C22×D43—21no—
309C22×D43—21no—
310C22×D43—21no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43C2×C22⋊C411yescharacteristic
321C22×D43C2×C22⋊C411yescharacteristic
322C22×D43C2×C22⋊C411yescharacteristic
323C22×D43C2×C22⋊C411yescharacteristic
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43C2×C22⋊C411yescharacteristic
331C2×C4×C43C2×C22⋊C411yescharacteristic
332C2×C4×C43C2×C22⋊C411yescharacteristic
333C2×C4×C43C2×C22⋊C411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C2×C4×C432−1+411yescharacteristic
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—22no—
345C2×Dic43—42no—
346C2×Dic43C2×C22⋊C411yescharacteristic
347C2×Dic43C2×C22⋊C411yescharacteristic
348C2×Dic43C2×C22⋊C411yescharacteristic
349C2×Dic43C2×C22⋊C411yescharacteristic
350D172—22no—
351D172—22no—
352D172—41no—
353D172—41no—
354D172—44no—
355D172—44no—
356D172—41no—
357D172—41no—
358D172—41no—
359D172—41no—
360D172—82no—
361D172—82no—
362C4×D43—21no—
363C4×D43—21no—
364C4×D43—21no—
365C4×D43—21no—
366C4×D43—21no—
367C4×D43—21no—
368C4×D43—21no—
369C4×D43—21no—
370C4×D43—21no—
371C4×D43—21no—
372C4×D43—21no—
373C4×D43—21no—
374C4×D43—21no—
375C4×D43—21no—
376C4×D43—21no—
377C4×D43—21no—
378C4×D43—82no—
379C4×D43—82no—
380C4×D43—82no—
381C4×D43—82no—
382C8×C43—22no—
383C8×C43—41no—
384C8×C43—41no—
385C8×C43—41no—
386C43⋊C8—22no—
387C43⋊C8—41no—
388C43⋊C8—41no—
389C43⋊C8—41no—
390#22482—431nomaximal, Sylow
391C22×C43—21no—
392C22×C43—21no—
393C22×C43C22×C22⋊C411yescharacteristic
394C22×C43C4×#4111yescharacteristic
395C22×C43#52011yescharacteristic
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—21no—
399C2×D43—21no—
400C2×D43—21no—
401C2×D43—21no—
402C2×D43—21no—
403C2×D43—21no—
404C2×D43—21no—
405C2×D43—21no—
406C2×D43—21no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—81no—
413C2×D43—81no—
414C2×D43—82no—
415C2×D43—82no—
416C2×D43#41312yes—
417C4×C43—21no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—42no—
422C4×C43—42no—
423C4×C43#54611yescharacteristic
424C4×C43#54611yescharacteristic
425C4×C43#54711yescharacteristic
426C4×C43#54711yescharacteristic
427Dic43—21no—
428Dic43—21no—
429Dic43—21no—
430Dic43—21no—
431Dic43—42no—
432C2×#553—431no—
433D4×M16—431no—
434D4×M16—431no—
435#1998—431no—
436#1998D4311yescharacteristic, complemented
437#1900—431no—
438#1900—431no—
439#1900—431no—
440#1900—431no—
441#1822—431no—
442#1821—431no—
443#1800—431no—
444C4×#100—431no—
445#1742—431no—
446C2×#343—431no—
447C2×C43—21no—
448C2×C43—21no—
449C2×C43#233911yescharacteristic
450C2×C43C2×#41311yescharacteristic
451C2×C43#288811yescharacteristic
452D43—22no—
453D43—41no—
454D43—41no—
455D43—41no—
456D43—82no—
457C22×M16—431no—
458C22×M16—431no—
459C22×M16—431no—
460C22×M16—431no—
461#553—861no—
462#553—861no—
463#553—861no—
464#553—861no—
465#553—861no—
466#553—861no—
467#553—861no—
468#553—861no—
469C2×#126—432no—
470C2×#125C2×D4311yescharacteristic
471C2×#123—432no—
472C2×#121—431no—
473C2×#121—431no—
474C2×#121—432no—
475C2×C4×D4—432no—
476C2×C4×D4—431no—
477C2×C4×D4—431no—
478C2×#117—431no—
479C22×C4⋊C4—431no—
480#436—861no—
481#436—861no—
482#435—861no—
483#435—861no—
484#435—861no—
485#435—861no—
486C8×D4—861no—
487C8×D4—861no—
488#423—431no—
489#423C2×D4311yescharacteristic
490C2×#100—431no—
491C2×#100—431no—
492C2×#100—431no—
493C2×#100—431no—
494#407—431no—
495#407—431no—
496#407—431no—
497#407—431no—
498C4×M16—431no—
499C4×M16C2×D4311yescharacteristic
500#343—431no—
501#343—431no—
502#343—431no—
503#343—431no—
504#343—431no—
505#343—431no—
506#343—431no—
507#343—431no—
508#343C2×D4311yescharacteristic
509#343C2×D4311yescharacteristic
510#343C2×D4311yescharacteristic
511#343C2×D4311yescharacteristic
512C43#2248211yescharacteristic, complemented, Sylow
513C22×D4—431no—
514C22×D4—432no—
515C22×D4—432no—
516C22×D4—431no—
517C23×C4—431no—
518C23×C4—431no—
519C23×C4—432no—
520C23×C4—432no—
521C2×M16—431no—
522C2×M16—431no—
523C2×M16—431no—
524C2×M16—431no—
525C2×M16—861no—
526C2×M16—861no—
527C2×M16—861no—
528C2×M16—861no—
529C2×M16—862no—
530C2×M16—862no—
531C2×M16—862no—
532C2×M16—862no—
533C2×M16—1721no—
534C2×M16—1721no—
535C2×M16—1721no—
536C2×M16—1721no—
537C2×M16C22×D4311yescharacteristic
538C2×M16C22×D4311yescharacteristic
539C2×M16C22×D4311yescharacteristic
540C2×M16C22×D4311yescharacteristic
541C22×C8—861no—
542C22×C8—861no—
543C22×C8—861no—
544C22×C8—861no—
545#126—862no—
546#126—862no—
547#126—862no—
548#126—862no—
549#125—21no—
550#125—21no—
551#125—21no—
552#125—21no—
553#123—862no—
554#123—862no—
555#123—862no—
556#123—862no—
557#121—861no—
558#121—861no—
559#121—861no—
560#121—861no—
561#121—861no—
562#121—861no—
563#121—861no—
564#121—861no—
565#121—862no—
566#121—862no—
567#121—862no—
568#121—862no—
569C4×D4—431no—
570C4×D4—431no—
571C4×D4—431no—
572C4×D4—431no—
573C4×D4—431no—
574C4×D4—431no—
575C4×D4—431no—
576C4×D4—431no—
577C4×D4—862no—
578C4×D4—862no—
579C4×D4—862no—
580C4×D4—862no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4—861no—
585#117—861no—
586#117—861no—
587#117—861no—
588#117—861no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—432no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4—861no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4—861no—
596C2×C4⋊C4C4×D4312yes—
597C2×C4⋊C4C4×D4312yes—
598C2×C4⋊C4C22×D4311yescharacteristic
599C2×C4⋊C4C22×D4311yescharacteristic
600C2×C22⋊C4—431no—
601C2×C22⋊C4—431no—
602C2×C22⋊C4—432no—
603C2×C22⋊C4—432no—
604C2×C22⋊C4—432no—
605C2×C22⋊C4—432no—
606C2×C42—432no—
607C2×C42C22×D4311yescharacteristic
608C4⋊C8—21no—
609C4⋊C8—21no—
610C4⋊C8—861no—
611C4⋊C8—861no—
612#100—862no—
613#100—862no—
614#100—1721no—
615#100—1721no—
616C22⋊C8—861no—
617C22⋊C8—861no—
618C22⋊C8—861no—
619C22⋊C8—861no—
620C22⋊C8—861no—
621C22⋊C8—861no—
622C22⋊C8—861no—
623C22⋊C8—861no—
624#97—21no—
625#97—861no—
626C4×C8—21no—
627C4×C8—861no—
628C24—431no—
629C24—431no—
630C24—432no—
631C2×D4—431no—
632C2×D4—431no—
633C2×D4—431no—
634C2×D4—431no—
635C2×D4—862no—
636C2×D4—862no—
637C2×D4—862no—
638C2×D4—862no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—3442no—
646C2×D4—1722no—
647C2×D4—1724no—
648C22×C4—431no—
649C22×C4—431no—
650C22×C4—431no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—432no—
659C22×C4—862no—
660C22×C4—862no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—862no—
670C22×C4—862no—
671C22×C4—3442no—
672C22×C4—3442no—
673C22×C4C2×C4×D4312yes—
674C22×C4C2×C4×D4312yes—
675C22×C4C2×C4×D4311yescharacteristic
676C22×C4C2×C4×D4311yescharacteristic
677C22×C4C23×D4311yescharacteristic
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—432no—
686M16—861no—
687M16—861no—
688M16—861no—
689M16—861no—
690M16—861no—
691M16—861no—
692M16—861no—
693M16—1722no—
694M16—1722no—
695M16—1722no—
696M16—1722no—
697M16#1062190212yes—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—1722no—
707C2×C8—1722no—
708C2×C8—1722no—
709C2×C8—1722no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—431no—
719C4⋊C4—431no—
720C4⋊C4—431no—
721C4⋊C4—431no—
722C4⋊C4—862no—
723C4⋊C4—862no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C22⋊C4—431no—
727C22⋊C4—431no—
728C22⋊C4—431no—
729C22⋊C4—431no—
730C22⋊C4—431no—
731C22⋊C4—431no—
732C22⋊C4—431no—
733C22⋊C4—431no—
734C22⋊C4—862no—
735C22⋊C4—862no—
736C22⋊C4—862no—
737C22⋊C4—862no—
738C22⋊C4—862no—
739C22⋊C4—862no—
740C22⋊C4—862no—
741C22⋊C4—862no—
742C42—862no—
743C42—862no—
744C42D4×D4311yescharacteristic
745C42D4×D4311yescharacteristic
746C42D4×D4311yescharacteristic
747C42D4×D4311yescharacteristic
748C23—431no—
749C23—431no—
750C23—431no—
751C23—431no—
752C23—862no—
753C23—861no—
754C23—861no—
755C23—861no—
756C23—861no—
757C23—862no—
758C23—862no—
759C23—862no—
760C23—1721no—
761C23—1721no—
762C23—1721no—
763C23—1722no—
764C23—1722no—
765C23C22×C4×D4311yescharacteristic
766D4—862no—
767D4—862no—
768D4—3442no—
769D4—3442no—
770D4—1721no—
771D4—1721no—
772D4—1724no—
773D4—1724no—
774D4—1721no—
775D4—1721no—
776D4—1721no—
777D4—1721no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—431no—
785C2×C4—431no—
786C2×C4—431no—
787C2×C4—431no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—861no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—862no—
809C2×C4—3442no—
810C2×C4—3442no—
811C2×C4—3442no—
812C2×C4—3442no—
813C2×C4—1722no—
814C2×C4C22⋊C4×D4311yescharacteristic
815C2×C4C22⋊C4×D4311yescharacteristic
816C2×C4C22⋊C4×D4311yescharacteristic
817C2×C4C22⋊C4×D4311yescharacteristic
818C2×C4C2×D4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4#41×D4311yescharacteristic
821C2×C4C2×#1062190211yescharacteristic
822C2×C4#1306337111yescharacteristic
823C2×C4#1306337311yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C8—862no—
829C8—1721no—
830C8—1721no—
831C8—1721no—
832C22—21no—
833C22—21no—
834C22—432no—
835C22—861no—
836C22—861no—
837C22—861no—
838C22—861no—
839C22—861no—
840C22—861no—
841C22—861no—
842C22—861no—
843C22—861no—
844C22—861no—
845C22—861no—
846C22—3442no—
847C22—3442no—
848C22—3441no—
849C22—3441no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22C2×C22⋊C4×D4311yescharacteristic
856C22C4×#1062190211yescharacteristic
857C22#1458338111yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—42no—
863C4—42no—
864C4—861no—
865C4—861no—
866C4—861no—
867C4—861no—
868C4—1722no—
869C4#1458354011yescharacteristic
870C4#1458354211yescharacteristic
871C4#1458355111yescharacteristic
872C4#1458355211yescharacteristic
873C2—21no—
874C2—21no—
875C2—862no—
876C2—3442no—
877C2—1721no—
878C2—1721no—
879C2—1721no—
880C2#1913742411yescharacteristic
881C2#413×D4311yescharacteristic
882C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1998C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583602C2
cosocleC22×C4×C43C24
hypercenter#1998D43
hypocenterC43#22482
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1998

Complements

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

NH ≅ G/Ntype
2. M16×D172C2semidirect
3. #19143330C2semidirect
4. #19135589C2semidirect
5. #19135057C2semidirect
6. #19135057C2semidirect
7. #19135057C2semidirect
8. #19135057C2semidirect
9. #19134677C2semidirect
10. #19134674C2semidirect
11. #19134584C2semidirect
12. C4×#13063241C2semidirect
13. #19134332C2semidirect
14. #343×D43C2semidirect
15. C43×#1998C2semidirect
436. #1998D43semidirect
512. C43#22482semidirect

Maximal subgroups

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

subgroupindex
C2×#145836022
M16×D1722
#191433302
#191355892
#191350572
#191346772
#191346742
#191345842
C4×#130632412
#191343322
#343×D432
C43×#19982
#2248243