Finite Group Databasebeta

← #25001869

Subgroups — #25001869

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D43C211yesmaximal, characteristic
2C2×#14582862C211yesmaximal, characteristic
3#19136974C211yesmaximal, characteristic
4C2×#14582671C211yesmaximal, characteristic, complemented
5C2×#14582670C211yesmaximal, characteristic, complemented
6C2×#14582669C211yesmaximal, characteristic, complemented
7C2×C43×#344C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×#10621872C412yescomplemented
12C2×M16×D43—22no—
13C2×M16×D43—22no—
14C2×M16×D43—22no—
15C2×M16×D43—22no—
16C2×M16×D43—22no—
17C2×M16×D43—22no—
18C22×C8×D43C412yescomplemented
19C2×#13063284C2211yescharacteristic
20#14582862—22no—
21#14582862C412yescomplemented
22#14582862C412yescomplemented
23C2×(C2×D43)⋊C8—22no—
24#14582760C412yes—
25#14582756—22no—
26#14582754C412yes—
27C4×(C2×D43)⋊C4—22no—
28#14582671—22no—
29#14582670—22no—
30#14582669—22no—
31C22×M16×C43C2211yescharacteristic
32C22×M16×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C43×#344—22no—
35C24×D43C2×C411yescharacteristic
36C23×Dic43C2×C411yescharacteristic
37C22×C4×D43—21no—
38C22×C4×D43—21no—
39C22×C4×D43—21no—
40C22×C4×D43—21no—
41C22×C4×D43—21no—
42C22×C4×D43—21no—
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43C2×C411yescharacteristic
46C22×C4×D43C2×C411yescharacteristic
47C22×C4×D43C2×C411yescharacteristic
48C22×C4×D43C2×C411yescharacteristic
49C22×C4×D43D412yes—
50C22×C4×D43D412yes—
51C22×C4×D43D412yes—
52C22×C4×D43Q812yes—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877—21no—
62C2×#10621877C2×C412yes—
63C2×#10621877D412yes—
64C2×#10621877D412yes—
65C2×#10621872—24no—
66C2×#10621872—24no—
67C2×#10621872—24no—
68M16×D43—28no—
69M16×D43—28no—
70M16×D43—28no—
71M16×D43—28no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8C2×C412yes—
74C2×C8×D43—24no—
75C2×C8×D43—24no—
76C2×C8×D43—24no—
77#13063284—21no—
78#13063284—21no—
79#13063284—21no—
80#13063284—21no—
81C2×C4⋊Dic43—21no—
82C2×C22⋊Dic43C2×C412yes—
83C2×(C2×D43)⋊C4—24no—
84C2×C4×Dic43—21no—
85(C2×D43)⋊C8—24no—
86(C2×D43)⋊C8—24no—
87C43⋊#95—24no—
88C23×C4×C43C2311yescharacteristic
89C2×M16×C43—21no—
90C2×M16×C43—21no—
91C2×M16×C43—21no—
92C2×M16×C43—21no—
93C2×M16×C43—21no—
94C2×M16×C43—21no—
95C2×M16×C43—21no—
96C2×M16×C43—21no—
97C2×M16×C43—21no—
98C2×M16×C43C2×C412yes—
99C2×M16×C43D412yes—
100C2×M16×C43D412yes—
101C22×C8×C43—21no—
102C22×C8×C43C2×C412yes—
103#117×C43—21no—
104#117×C43—21no—
105#117×C43—21no—
106#117×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C22⋊C4×C43C2×C412yes—
109C2×C42×C43—21no—
110C24×C43C22×C411yescharacteristic
111C23×D43—21no—
112C23×D43—21no—
113C23×D43—21no—
114C23×D43—21no—
115C23×D43—44no—
116C23×D43C4211yescharacteristic
117C23×D43C4211yescharacteristic
118C23×D43C22⋊C412yes—
119C23×D43C4⋊C412yes—
120C22×C4×C43—22no—
121C22×C4×C43C22×C411yescharacteristic
122C22×C4×C43C22×C411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×Q811yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C22×C4×C43#4111yescharacteristic
133C22×C4×C43#4111yescharacteristic
134C22×C4×C43#4111yescharacteristic
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43C4211yescharacteristic
141C22×Dic43C4211yescharacteristic
142C22×Dic43C22⋊C412yes—
143C22×Dic43C4⋊C412yes—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43C22⋊C412yes—
177C2×C4×D43C22⋊C412yes—
178C2×C4×D43C22⋊C412yes—
179C2×C4×D43C22⋊C412yes—
180C2×C4×D43C4⋊C412yes—
181C2×C4×D43C4⋊C412yes—
182C2×C4×D43C4⋊C412yes—
183C2×C4×D43C4⋊C412yes—
184M16×C43—22no—
185M16×C43—22no—
186M16×C43—22no—
187M16×C43—22no—
188M16×C43—22no—
189M16×C43—22no—
190M16×C43—41no—
191M16×C43—41no—
192C2×C8×C43—22no—
193C2×C8×C43—22no—
194C2×C8×C43—22no—
195C2×C8×C43—41no—
196C2×C8×C43—41no—
197C2×C8×C43C22⋊C414yescomplemented
198C4⋊C4×C43—41no—
199C4⋊C4×C43—41no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C42×C43—41no—
203C42×C43—41no—
204C22⋊Dic43—22no—
205C22⋊Dic43—22no—
206(C2×D43)⋊C4—48no—
207C4⋊Dic43—41no—
208C4⋊Dic43—41no—
209C4×Dic43—41no—
210C4×Dic43—41no—
211#10621877—22no—
212#10621877—22no—
213#10621877—22no—
214#10621877—22no—
215#10621877—22no—
216#10621877—22no—
217#10621877—41no—
218#10621877—41no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8—41no—
223C2×C43⋊C8—41no—
224C2×C43⋊C8C22⋊C414yescomplemented
225#10621872—216no—
226C8×D43—216no—
227C23×C43—42no—
228C23×C43C2×C4211yescharacteristic
229C23×C43C2×C22⋊C411yescharacteristic
230C23×C43C2×C4⋊C411yescharacteristic
231C23×C43C4×D411yescharacteristic
232C23×C43C4×D411yescharacteristic
233C23×C43C4×D411yescharacteristic
234C23×C43C4×D411yescharacteristic
235C22×D43—21no—
236C22×D43—21no—
237C22×D43—24no—
238C22×D43—21no—
239C22×D43—21no—
240C22×D43—22no—
241C22×D43—22no—
242C22×D43—22no—
243C22×D43—22no—
244C22×D43—24no—
245C22×D43—24no—
246C22×D43—42no—
247C22×D43—42no—
248C22×D43—42no—
249C22×D43—44no—
250C22×D43—44no—
251C22×D43—44no—
252C22×D43—44no—
253C22×D43#9512yes—
254C22×D43#9512yes—
255C2×C4×C43—44no—
256C2×C4×C43—42no—
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C2×C22⋊C411yescharacteristic
261C2×C4×C43C2×C4⋊C411yescharacteristic
262C2×C4×C43C2×C4⋊C411yescharacteristic
263C2×C4×C43#11711yescharacteristic
264C2×C4×C43#11711yescharacteristic
265C2×C4×C43C4×D411yescharacteristic
266C2×C4×C43C4×D411yescharacteristic
267C2×C4×C43C4×D411yescharacteristic
268C2×C4×C43C4×D411yescharacteristic
269C2×C4×C43#12011yescharacteristic
270C2×C4×C43#12011yescharacteristic
271C2×C4×C43#12011yescharacteristic
272C2×C4×C43#12011yescharacteristic
273C2×C4×C43#12111yescharacteristic
274C2×C4×C43#12111yescharacteristic
275C2×C4×C43#12111yescharacteristic
276C2×C4×C43#12111yescharacteristic
277C2×C4×C43C22⋊Q811yescharacteristic
278C2×C4×C43C22⋊Q811yescharacteristic
279C2×C4×C43C22⋊Q811yescharacteristic
280C2×C4×C43C22⋊Q811yescharacteristic
281C2×C4×C43#12311yescharacteristic
282C2×C4×C43#12311yescharacteristic
283C2×C4×C43#12311yescharacteristic
284C2×C4×C43#12311yescharacteristic
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—44no—
294C2×Dic43—42no—
295C2×Dic43#9512yes—
296C2×Dic43#9512yes—
297C4×D43—22no—
298C4×D43—22no—
299C4×D43—22no—
300C4×D43—22no—
301C4×D43—22no—
302C4×D43—22no—
303C4×D43—22no—
304C4×D43—22no—
305C4×D43—22no—
306C4×D43—22no—
307C4×D43—22no—
308C4×D43—22no—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C8×C43—24no—
314C8×C43—42no—
315C43⋊C8—24no—
316C43⋊C8—42no—
317#10729—431nomaximal, Sylow
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43C2×#9511yescharacteristic
326C22×C43C4×C22⋊C411yescharacteristic
327C22×C43C4×C22⋊C411yescharacteristic
328C22×C43#38511yescharacteristic
329C22×C43#38511yescharacteristic
330C22×C43#38611yescharacteristic
331C22×C43#38611yescharacteristic
332C2×D43—24no—
333C2×D43—24no—
334C2×D43—22no—
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—44no—
340C2×D43—44no—
341C2×D43—44no—
342C2×D43—44no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43#34414yescomplemented
346C4×C43—82no—
347C4×C43#37911yescharacteristic
348C4×C43#38011yescharacteristic
349C4×C43#38011yescharacteristic
350C4×C43#38111yescharacteristic
351C4×C43#38511yescharacteristic
352C4×C43#38511yescharacteristic
353C4×C43#38611yescharacteristic
354C4×C43#38611yescharacteristic
355Dic43—22no—
356Dic43—22no—
357Dic43—82no—
358C23×M16—431no—
359C2×#407—431no—
360#2280—431no—
361C2×#344—431no—
362C2×#344—431no—
363C2×#344—431no—
364C2×#344D4311yescharacteristic, complemented
365C2×C43—21no—
366C2×C43—21no—
367C2×C43—21no—
368C2×C43—21no—
369C2×C43—21no—
370C2×C43—21no—
371C2×C43C22⋊#9511yescharacteristic
372C2×C43C2×#34412yes—
373D43—24no—
374D43—42no—
375C24×C4—431no—
376C22×M16—431no—
377C22×M16—432no—
378C22×M16—431no—
379C22×M16—862no—
380C22×M16—862no—
381C22×M16—862no—
382C22×M16—862no—
383C22×M16—862no—
384C22×M16—862no—
385C22×M16C2×D4311yescharacteristic
386C22×M16C2×D4311yescharacteristic
387C23×C8—432no—
388C2×#117—431no—
389C2×#117C2×D4311yescharacteristic
390#407—432no—
391#407—432no—
392#407—862no—
393C2×C22⋊C8—862no—
394#381—432no—
395#380—862no—
396#379—432no—
397C4×C22⋊C4—862no—
398#344—22no—
399#344—862no—
400#344—862no—
401#344—862no—
402C43#1072911yescharacteristic, complemented, Sylow
403C25—431no—
404C23×C4—431no—
405C23×C4—431no—
406C23×C4—431no—
407C23×C4—431no—
408C23×C4—431no—
409C23×C4—432no—
410C23×C4—432no—
411C23×C4—432no—
412C23×C4—432no—
413C23×C4—861no—
414C23×C4—861no—
415C23×C4—861no—
416C23×C4—861no—
417C23×C4—861no—
418C23×C4—861no—
419C23×C4—861no—
420C23×C4—861no—
421C23×C4C22×D4311yescharacteristic
422C2×M16—21no—
423C2×M16—21no—
424C2×M16—21no—
425C2×M16—21no—
426C2×M16—21no—
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16—21no—
431C2×M16—432no—
432C2×M16—432no—
433C2×M16—432no—
434C2×M16—864no—
435C2×M16—864no—
436C2×M16—868no—
437C2×M16—868no—
438C2×M16—868no—
439C2×M16—868no—
440C2×M16—861no—
441C2×M16—861no—
442C2×M16—861no—
443C2×M16—861no—
444C2×M16—861no—
445C2×M16—864no—
446C2×M16—861no—
447C2×M16—861no—
448C2×M16—861no—
449C2×M16—861no—
450C2×M16C4×D4312yes—
451C2×M16D17212yes—
452C2×M16C22⋊D4312yes—
453C22×C8—21no—
454C22×C8—432no—
455C22×C8—864no—
456C22×C8—864no—
457C22×C8—864no—
458C22×C8—861no—
459C22×C8C4×D4312yes—
460#117—21no—
461#117—21no—
462#117—21no—
463#117—21no—
464#117—861no—
465#117—861no—
466#117—861no—
467#117—861no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—861no—
470C2×C22⋊C4—432no—
471C2×C22⋊C4—864no—
472C2×C22⋊C4C4×D4312yes—
473C2×C42—21no—
474C2×C42—861no—
475C22⋊C8—864no—
476C22⋊C8—864no—
477#95—864no—
478C24—431no—
479C24—432no—
480C24—432no—
481C24—431no—
482C24—861no—
483C24—861no—
484C24—861no—
485C24—861no—
486C24—1724no—
487C24C2×C4×D4311yescharacteristic
488C22×C4—22no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—432no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—432no—
497C22×C4—432no—
498C22×C4—432no—
499C22×C4—432no—
500C22×C4—432no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—862no—
530C22×C4—862no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4C2×C4×D4311yescharacteristic
539C22×C4C2×C4×D4311yescharacteristic
540C22×C4C2×D17211yescharacteristic
541C22×C4#1062189811yescharacteristic
542C22×C4#1062189811yescharacteristic
543C22×C4D4×D4311yescharacteristic
544C22×C4D4×D4311yescharacteristic
545C22×C4D4×D4311yescharacteristic
546C22×C4D4×D4311yescharacteristic
547C22×C4D4×D4311yescharacteristic
548C22×C4#1062190011yescharacteristic
549C22×C4Q8×D4311yescharacteristic
550C22×C4#1062190211yescharacteristic
551C22×C4C2×C22⋊D4311yescharacteristic
552M16—22no—
553M16—22no—
554M16—22no—
555M16—22no—
556M16—22no—
557M16—22no—
558M16—41no—
559M16—41no—
560M16—8616no—
561M16—862no—
562M16—862no—
563M16—862no—
564M16—862no—
565M16—862no—
566M16—862no—
567M16—1721no—
568M16—1721no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—434no—
575C2×C8—8616no—
576C2×C8—862no—
577C2×C8—862no—
578C2×C8—862no—
579C2×C8—1721no—
580C2×C8—1721no—
581C2×C8(C2×D43)⋊C414yescomplemented
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—1721no—
585C4⋊C4—1721no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—862no—
589C22⋊C4—862no—
590C22⋊C4—1728no—
591C42—41no—
592C42—41no—
593C42—1721no—
594C42—1721no—
595C23—42no—
596C23—432no—
597C23—432no—
598C23—864no—
599C23—864no—
600C23—864no—
601C23—861no—
602C23—861no—
603C23—861no—
604C23—861no—
605C23—862no—
606C23—862no—
607C23—862no—
608C23—862no—
609C23—1722no—
610C23—1722no—
611C23—1722no—
612C23—1724no—
613C23—1724no—
614C23—1724no—
615C23—1724no—
616C23C42×D4311yescharacteristic
617C23C22⋊C4×D4311yescharacteristic
618C23C4⋊C4×D4311yescharacteristic
619C23(C22⋊D43)⋊C411yescharacteristic
620C23C4×C22⋊D4311yescharacteristic
621C23#1306328711yescharacteristic
622C23C4×D17211yescharacteristic
623C2×C4—44no—
624C2×C4—42no—
625C2×C4—432no—
626C2×C4—432no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—862no—
643C2×C4—862no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—862no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—1724no—
652C2×C4—1722no—
653C2×C4C22⋊C4×D4311yescharacteristic
654C2×C4C22⋊C4×D4311yescharacteristic
655C2×C4C22⋊C4×D4311yescharacteristic
656C2×C4C2×(C2×D43)⋊C411yescharacteristic
657C2×C4C4⋊C4×D4311yescharacteristic
658C2×C4C4⋊C4×D4311yescharacteristic
659C2×C4#1306328211yescharacteristic
660C2×C4#1306328311yescharacteristic
661C2×C4(C22⋊D43)⋊C411yescharacteristic
662C2×C4C4×C22⋊D4311yescharacteristic
663C2×C4#1306328711yescharacteristic
664C2×C4C4×D17211yescharacteristic
665C2×C4#1306329311yescharacteristic
666C2×C4#1306329311yescharacteristic
667C2×C4#1306329511yescharacteristic
668C2×C4#1306329511yescharacteristic
669C2×C4#1306329611yescharacteristic
670C2×C4#1306329811yescharacteristic
671C2×C4#1306329811yescharacteristic
672C2×C4#1306330011yescharacteristic
673C2×C4#1306330111yescharacteristic
674C2×C4#1306330311yescharacteristic
675C2×C4#1306330311yescharacteristic
676C2×C4#1306330511yescharacteristic
677C2×C4#1306330711yescharacteristic
678C2×C4#1306330711yescharacteristic
679C2×C4#1306331011yescharacteristic
680C2×C4#1306331011yescharacteristic
681C8—24no—
682C8—42no—
683C8—864no—
684C8—1722no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—434no—
693C22—864no—
694C22—864no—
695C22—862no—
696C22—862no—
697C22—862no—
698C22—862no—
699C22—862no—
700C22—1724no—
701C22—1724no—
702C22—1724no—
703C22—1724no—
704C22—1722no—
705C22—1722no—
706C22#95×D4311yescharacteristic
707C22#1458274611yescharacteristic
708C22C4×(C2×D43)⋊C411yescharacteristic
709C22#1458277011yescharacteristic
710C22#1458277311yescharacteristic
711C22#1458277511yescharacteristic
712C22#1458277711yescharacteristic
713C4—82no—
714C4—862no—
715C4—862no—
716C4—3442no—
717C4#1458275411yescharacteristic
718C4#1458275611yescharacteristic
719C4#1458275811yescharacteristic
720C4#1458276111yescharacteristic
721C4#1458277011yescharacteristic
722C4#1458277311yescharacteristic
723C4#1458277511yescharacteristic
724C4#1458277711yescharacteristic
725C2—21no—
726C2—21no—
727C2—21no—
728C2—21no—
729C2—21no—
730C2—21no—
731C2—864no—
732C2—1722no—
733C2(C2×D43)⋊#9511yescharacteristic
734C2#344×D4312yes—
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×#344C2
socleC22×C43C2×#95
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenterC2×#344D43
hypocenterC43#10729
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#14582671C2semidirect
5. C2×#14582670C2semidirect
6. C2×#14582669C2semidirect
7. C2×C43×#344C2semidirect
11. C22×#10621872C4semidirect
18. C22×C8×D43C4semidirect
21. #14582862C4semidirect
22. #14582862C4semidirect
197. C2×C8×C43C22⋊C4semidirect
224. C2×C43⋊C8C22⋊C4semidirect
345. C2×D43#344semidirect
364. C2×#344D43semidirect
402. C43#10729semidirect
581. C2×C8(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D432
C2×#145828622
#191369742
C2×#145826712
C2×#145826702
C2×#145826692
C2×C43×#3442
#1072943