Finite Group Databasebeta

← #25003392

Subgroups — #25003392

Order 11008.

1278 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063358C211yesmaximal, characteristic
2C2×#14582901C211yesmaximal, characteristic
3C22×#13063250C211yesmaximal, characteristic, complemented
4C22×#13063243C211yesmaximal, characteristic, complemented
5C2×#14582865C211yesmaximal, characteristic
6C2×#14582667C211yesmaximal, characteristic, complemented
7C2×C43×#341C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C23×Dic86C2211yescharacteristic
10C2×#13063358—22no—
11C2×#13063358—22no—
12C2×#13063358—22no—
13C2×#13063358—22no—
14C2×#13063358—22no—
15C2×#13063358C414yescomplemented
16C22×Dic172—21no—
17C22×#10621873—21no—
18C22×#10621877C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20#14582901—22no—
21#14582901—22no—
22C2×#13063250—22no—
23C2×#13063250—21no—
24C2×#13063250—22no—
25C2×#13063250—22no—
26C2×#13063247—21no—
27C2×#13063243—22no—
28C2×#13063243—22no—
29C2×#13063243—22no—
30#14582865—22no—
31#14582865—22no—
32C2×(C2×D43)⋊C8—22no—
33#14582667—22no—
34C22×M16×C43C2211yescharacteristic
35C22×M16×C43C2211yescharacteristic
36C23×C8×C43C2211yescharacteristic
37C43×#341—22no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898C2×C412yes—
49C2×#10621898D412yes—
50C22×Dic86—21no—
51C22×Dic86—21no—
52C22×Dic86—21no—
53C22×Dic86—21no—
54C22×Dic86—21no—
55C22×Dic86—21no—
56C22×Dic86—21no—
57C22×Dic86—21no—
58C22×Dic86—21no—
59C22×Dic86—21no—
60C22×Dic86—21no—
61C22×Dic86C2×C412yes—
62C22×Dic86D412yes—
63C22×Dic86D411yescharacteristic
64C22×Dic86D412yes—
65C22×D172D411yescharacteristic
66C22×C22⋊D43—21no—
67C23×Dic43—21no—
68C23×Dic43—21no—
69C22×C4×D43—21no—
70#13063358—28no—
71#13063358—28no—
72#13063358—28no—
73#13063358—28no—
74C2×Dic172—24no—
75C2×Dic172—24no—
76C2×Dic172—24no—
77C2×#10621873—24no—
78C2×#10621873—24no—
79C2×#10621873—24no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C2×#10621877D412yes—
86C22×C43⋊C8—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43D412yes—
93#13063250—28no—
94#13063250—24no—
95#13063247—24no—
96#13063243—28no—
97(C2×D43)⋊C8—28no—
98C23×C4×C43C2311yescharacteristic
99C2×M16×C43—21no—
100C2×M16×C43—21no—
101C2×M16×C43—21no—
102C2×M16×C43—21no—
103C2×M16×C43—21no—
104C2×M16×C43—21no—
105C2×M16×C43—21no—
106C2×M16×C43—21no—
107C2×M16×C43C2×C412yes—
108C2×M16×C43D412yes—
109C2×M16×C43D412yes—
110C2×M16×C43D412yes—
111C22×C8×C43—21no—
112C22×C8×C43—21no—
113C22×C8×C43—21no—
114C22×C8×C43—21no—
115C22×C8×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119C22×C8×C43D412yes—
120C24×C43#4111yescharacteristic
121C23×D43—21no—
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×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43#4111yescharacteristic
134C22×C4×C43#4111yescharacteristic
135C22×C4×C43#4111yescharacteristic
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43—41no—
139C2×C22⋊D43—41no—
140C2×C22⋊D43—41no—
141C2×C22⋊D43—41no—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—41no—
148C22×Dic43—41no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152C22×Dic43—41no—
153C22×Dic43—82no—
154#10621898—22no—
155#10621898—22no—
156#10621898—22no—
157#10621898—22no—
158#10621898—22no—
159#10621898—22no—
160#10621898—22no—
161#10621898—22no—
162#10621898—41no—
163#10621898—41no—
164#10621898—41no—
165#10621898—41no—
166#10621898—41no—
167#10621898—41no—
168#10621898—41no—
169#10621898—41no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C22⋊C412yes—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43—41no—
179C2×C4×D43—41no—
180C2×C4×D43—41no—
181C2×C4×D43—41no—
182C2×Dic86—22no—
183C2×Dic86—22no—
184C2×Dic86—22no—
185C2×Dic86—22no—
186C2×Dic86—22no—
187C2×Dic86—21no—
188C2×Dic86—22no—
189C2×Dic86—22no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—22no—
193C2×Dic86—22no—
194C2×Dic86—22no—
195C2×Dic86—22no—
196C2×Dic86—22no—
197C2×Dic86—21no—
198C2×Dic86—22no—
199C2×Dic86—22no—
200C2×Dic86—22no—
201C2×Dic86—21no—
202C2×Dic86—41no—
203C2×Dic86—41no—
204C2×Dic86—41no—
205C2×Dic86—41no—
206C2×Dic86—41no—
207C2×Dic86—41no—
208C2×Dic86—41no—
209C2×Dic86—41no—
210C2×Dic86—41no—
211C2×Dic86—41no—
212C2×Dic86—41no—
213C2×Dic86—41no—
214C2×Dic86C22⋊C412yes—
215C2×Dic86C22⋊C414yes—
216M16×C43—22no—
217M16×C43—22no—
218M16×C43—22no—
219M16×C43—22no—
220M16×C43—22no—
221M16×C43—41no—
222M16×C43—41no—
223M16×C43C22⋊C414yes—
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C2×C8×C43—22no—
227C2×C8×C43—22no—
228C2×C8×C43—22no—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43—41no—
232C2×C8×C43—41no—
233C2×C8×C43—41no—
234C2×C8×C43—41no—
235C2×C8×C43—41no—
236C2×C8×C43—41no—
237C4⋊Dic43—22no—
238C4⋊Dic43—22no—
239C4⋊Dic43—41no—
240C4⋊Dic43—41no—
241#10621877—22no—
242#10621877—22no—
243#10621877—41no—
244#10621877—41no—
245C2×C43⋊C8—22no—
246C2×C43⋊C8—41no—
247C2×C43⋊C8—41no—
248Dic172—216no—
249#10621873—216no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43C4×D411yescharacteristic
253C23×C43#12111yescharacteristic
254C23×C43#12111yescharacteristic
255C23×C43#12111yescharacteristic
256C23×C43#12311yescharacteristic
257C23×C43#12311yescharacteristic
258C23×C43#12411yescharacteristic
259C22×D43—22no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—42no—
263C22×D43—42no—
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C2×C22⋊C411yescharacteristic
267C2×C4×C43C4×D411yescharacteristic
268C2×C4×C43C4×D411yescharacteristic
269C2×C4×C43C4×D411yescharacteristic
270C2×C4×C43#12011yescharacteristic
271C2×C4×C43#12011yescharacteristic
272C2×C4×C43#12011yescharacteristic
273C2×C4×C43#12011yescharacteristic
274C2×C4×C43#12011yescharacteristic
275C2×C4×C43#12011yescharacteristic
276C2×C4×C43#12011yescharacteristic
277C2×C4×C43#12011yescharacteristic
278C2×C4×C43#12111yescharacteristic
279C2×C4×C43#12111yescharacteristic
280C2×C4×C43#12111yescharacteristic
281C2×C4×C43#12111yescharacteristic
282C2×C4×C43#12111yescharacteristic
283C2×C4×C43#12111yescharacteristic
284C2×C4×C43#12111yescharacteristic
285C2×C4×C43#12111yescharacteristic
286C2×C4×C43#12111yescharacteristic
287C2×C4×C43#12311yescharacteristic
288C2×C4×C43#12311yescharacteristic
289C2×C4×C43#12411yescharacteristic
290C2×C4×C43#12711yescharacteristic
291C2×C4×C43#12711yescharacteristic
292C22⋊D43—42no—
293C22⋊D43—42no—
294C22⋊D43—42no—
295C22⋊D43—42no—
296C2×Dic43—24no—
297C2×Dic43—22no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—42no—
301C2×Dic43—41no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305C2×Dic43—41no—
306C2×Dic43—42no—
307C2×Dic43—82no—
308C2×Dic43—82no—
309C2×Dic43—82no—
310D172—22no—
311D172—22no—
312D172—41no—
313D172—41no—
314C4×D43—42no—
315C4×D43—42no—
316C4×D43—42no—
317C4×D43—42no—
318Dic86—24no—
319Dic86—22no—
320Dic86—24no—
321Dic86—22no—
322Dic86—42no—
323Dic86—42no—
324Dic86—42no—
325Dic86—42no—
326Dic86—42no—
327Dic86—41no—
328Dic86—42no—
329Dic86—41no—
330C8×C43—24no—
331C8×C43—42no—
332C8×C43—42no—
333C43⋊C8—42no—
334#11021—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—21no—
343C22×C43#38611yescharacteristic
344C22×C43#38611yescharacteristic
345C22×C43#39011yescharacteristic
346C22×C43#39211yescharacteristic
347C22×C43#39411yescharacteristic
348C22×C43#39411yescharacteristic
349C22×C43#39411yescharacteristic
350C22×C43#47112yes—
351C22×C43#47312yes—
352C2×D43—44no—
353C2×D43—42no—
354C2×D43—82no—
355C2×D43—81no—
356C2×D43—81no—
357C4×C43#37911yescharacteristic
358C4×C43#38611yescharacteristic
359C4×C43#38611yescharacteristic
360C4×C43#39011yescharacteristic
361C4×C43#39211yescharacteristic
362C4×C43#39211yescharacteristic
363C4×C43#39211yescharacteristic
364C4×C43#39411yescharacteristic
365Dic43—44no—
366Dic43—42no—
367Dic43—82no—
368C22×#137—431no—
369C2×#417—431no—
370C22×#103—431no—
371C22×#101—431no—
372C2×#408—431no—
373C2×#343—431no—
374C2×#341D4311yescharacteristic, complemented
375C2×C43—21no—
376C2×C43—21no—
377C2×C43—21no—
378C2×C43—21no—
379C2×C43#143811yescharacteristic
380C2×C43#190812yes—
381C2×C43#201911yescharacteristic
382C2×C43#202011yescharacteristic
383C2×C43#205212yes—
384D43—82no—
385C22×#41—431no—
386C23×Q8—431no—
387C2×#137—434no—
388C2×#137—862no—
389C2×#137—862no—
390C2×#137—862no—
391C2×#137—862no—
392C2×#137—862no—
393C22×Q16—861no—
394C22×SD16—861no—
395C22×M16—431no—
396C22×M16C2×D4311yescharacteristic
397C22×M16C2×D4311yescharacteristic
398C23×C8C2×D4311yescharacteristic
399C22×C4⋊C4—431no—
400#417—862no—
401#417—862no—
402C2×#103—862no—
403C2×#103—862no—
404C2×#103—861no—
405C2×#103—862no—
406C2×#102—861no—
407C2×#101—862no—
408C2×#101—862no—
409C2×#101—862no—
410#408—862no—
411#408—862no—
412C2×C22⋊C8—862no—
413#343—862no—
414#341—22no—
415C43#1102111yescharacteristic, complemented, Sylow
416C2×#41—432no—
417C2×#41—432no—
418C2×#41—861no—
419C2×#41—861no—
420C2×#41—861no—
421C2×#41—861no—
422C2×#41—861no—
423C2×#41—861no—
424C2×#41—861no—
425C2×#41—861no—
426C2×#41—861no—
427C2×#41—861no—
428C22×Q8—432no—
429C22×Q8—431no—
430C22×Q8—432no—
431C22×Q8—432no—
432C22×Q8—861no—
433C22×Q8—861no—
434C22×Q8—861no—
435C22×Q8—861no—
436C22×Q8—861no—
437C22×Q8—861no—
438C22×Q8—861no—
439C22×Q8—861no—
440C22×Q8—861no—
441C22×Q8—861no—
442C22×Q8—861no—
443C22×D4—431no—
444C22×D4—861no—
445C23×C4—861no—
446C23×C4—861no—
447C23×C4—861no—
448C23×C4C22×D4311yescharacteristic
449#137—868no—
450#137—868no—
451#137—868no—
452#137—868no—
453C2×Q16—864no—
454C2×Q16—864no—
455C2×Q16—864no—
456C2×SD16—864no—
457C2×SD16—864no—
458C2×SD16—864no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—432no—
468C2×M16—861no—
469C2×M16—861no—
470C2×M16—861no—
471C2×M16—861no—
472C2×M16—861no—
473C2×M16C4×D4312yes—
474C2×M16D17212yes—
475C2×M16D17212yes—
476C2×M16C22⋊D4312yes—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—861no—
486C22×C8D17212yes—
487C2×C4⋊C4—432no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493#103—868no—
494#103—864no—
495#102—864no—
496#101—868no—
497C22⋊C8—868no—
498C24—861no—
499C24#1062190211yescharacteristic
500#41—862no—
501#41—862no—
502#41—862no—
503#41—862no—
504#41—862no—
505#41—862no—
506#41—862no—
507#41—862no—
508#41—1721no—
509#41—1721no—
510#41—1721no—
511#41—1721no—
512#41—1721no—
513#41—1721no—
514#41—1721no—
515#41—1721no—
516C2×Q8—432no—
517C2×Q8—434no—
518C2×Q8—862no—
519C2×Q8—862no—
520C2×Q8—862no—
521C2×Q8—861no—
522C2×Q8—862no—
523C2×Q8—862no—
524C2×Q8—862no—
525C2×Q8—862no—
526C2×Q8—862no—
527C2×Q8—861no—
528C2×Q8—862no—
529C2×Q8—862no—
530C2×Q8—861no—
531C2×Q8—862no—
532C2×Q8—861no—
533C2×Q8—862no—
534C2×Q8—862no—
535C2×Q8—862no—
536C2×Q8—862no—
537C2×Q8—861no—
538C2×Q8—1721no—
539C2×Q8—1721no—
540C2×Q8—1721no—
541C2×Q8—1721no—
542C2×Q8—1721no—
543C2×Q8—1721no—
544C2×Q8—1721no—
545C2×Q8—1721no—
546C2×Q8—1721no—
547C2×Q8—1721no—
548C2×Q8—1721no—
549C2×Q8—1721no—
550C2×D4—432no—
551C2×D4—862no—
552C2×D4—862no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—1721no—
559C2×D4—1721no—
560C2×D4—1721no—
561C2×D4—1721no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—861no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—3442no—
570C22×C4—1721no—
571C22×C4—1721no—
572C22×C4—1721no—
573C22×C4—1721no—
574C22×C4—1721no—
575C22×C4—1721no—
576C22×C4—1721no—
577C22×C4—1721no—
578C22×C4—1721no—
579C22×C4—1721no—
580C22×C4C2×C4×D4311yescharacteristic
581C22×C4C2×D17211yescharacteristic
582C22×C4C2×D17211yescharacteristic
583C22×C4C2×D17211yescharacteristic
584C22×C4#1062189811yescharacteristic
585C22×C4#1062189811yescharacteristic
586C22×C4D4×D4311yescharacteristic
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4D4×D4311yescharacteristic
590C22×C4D4×D4311yescharacteristic
591C22×C4D4×D4311yescharacteristic
592C22×C4#1062190211yescharacteristic
593C22×C4C2×C22⋊D4311yescharacteristic
594Q16—8616no—
595SD16—8616no—
596M16—22no—
597M16—22no—
598M16—22no—
599M16—22no—
600M16—22no—
601M16—41no—
602M16—41no—
603M16—862no—
604M16—862no—
605M16—1721no—
606M16—1721no—
607M16(C2×D43)⋊C414yes—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—862no—
622C2×C8—1721no—
623C2×C8—1721no—
624C4⋊C4—862no—
625C4⋊C4—862no—
626C4⋊C4—1721no—
627C4⋊C4—1721no—
628C23—22no—
629C23—22no—
630C23—862no—
631C23—1721no—
632C23—1721no—
633C23—1722no—
634C23—1722no—
635C23#1306328711yescharacteristic
636C23#1306330011yescharacteristic
637C23#1306330011yescharacteristic
638C23#1306330011yescharacteristic
639C23#1306331011yescharacteristic
640C23#1306331011yescharacteristic
641C23#1306331411yescharacteristic
642Q8—864no—
643Q8—862no—
644Q8—864no—
645Q8—862no—
646Q8—1722no—
647Q8—1722no—
648Q8—1722no—
649Q8—1721no—
650Q8—1722no—
651Q8—1722no—
652Q8—1721no—
653Q8—1722no—
654D4—862no—
655D4—862no—
656D4—1722no—
657D4—1722no—
658D4—1722no—
659D4—1722no—
660D4—1721no—
661D4—1721no—
662C2×C4—862no—
663C2×C4—864no—
664C2×C4—3442no—
665C2×C4—3442no—
666C2×C4—3442no—
667C2×C4—1722no—
668C2×C4—1722no—
669C2×C4—1721no—
670C2×C4—1722no—
671C2×C4—1721no—
672C2×C4—1722no—
673C2×C4—1722no—
674C2×C4—1722no—
675C2×C4—1722no—
676C2×C4—1722no—
677C2×C4—1722no—
678C2×C4—1722no—
679C2×C4—1722no—
680C2×C4C22⋊C4×D4311yescharacteristic
681C2×C4C22⋊C4×D4311yescharacteristic
682C2×C4C2×(C2×D43)⋊C411yescharacteristic
683C2×C4#1306328711yescharacteristic
684C2×C4C4×D17211yescharacteristic
685C2×C4C4×D17211yescharacteristic
686C2×C4#1306329311yescharacteristic
687C2×C4#1306329311yescharacteristic
688C2×C4#1306329511yescharacteristic
689C2×C4#1306329511yescharacteristic
690C2×C4#1306329511yescharacteristic
691C2×C4#1306329511yescharacteristic
692C2×C4#1306329511yescharacteristic
693C2×C4#1306329511yescharacteristic
694C2×C4#1306329811yescharacteristic
695C2×C4#1306329811yescharacteristic
696C2×C4#1306329811yescharacteristic
697C2×C4#1306329811yescharacteristic
698C2×C4#1306329911yescharacteristic
699C2×C4#1306329911yescharacteristic
700C2×C4#1306330011yescharacteristic
701C2×C4#1306330011yescharacteristic
702C2×C4#1306330011yescharacteristic
703C2×C4#1306331011yescharacteristic
704C2×C4#1306331011yescharacteristic
705C2×C4#1306331311yescharacteristic
706C2×C4#1306332111yescharacteristic
707C2×C4#1306332211yescharacteristic
708C8—24no—
709C8—42no—
710C8—42no—
711C8—1722no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—3442no—
721C22—3441no—
722C22—3441no—
723C22—1724no—
724C22—1722no—
725C22#1458277711yescharacteristic
726C22#1458277711yescharacteristic
727C22#1458280011yescharacteristic
728C22#1458280911yescharacteristic
729C22#1458281611yescharacteristic
730C22#1458281611yescharacteristic
731C22#1458281711yescharacteristic
732C22#1458316312yes—
733C22#1458317512yes—
734C4—3442no—
735C4—1722no—
736C4—1724no—
737C4#1458275411yescharacteristic
738C4#1458277711yescharacteristic
739C4#1458277711yescharacteristic
740C4#1458280111yescharacteristic
741C4#1458280811yescharacteristic
742C4#1458280811yescharacteristic
743C4#1458280911yescharacteristic
744C4#1458281711yescharacteristic
745C2—21no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—3442no—
750C2#1913283511yescharacteristic
751C2#1913510912yes—
752C2#1913571211yescharacteristic
753C2#1913571711yescharacteristic
754C2#1913589612yes—
subgroupG/H
centerC23#13063300
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#341C2
socleC23×C43#121
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#341D43
hypocenterC43#11021
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
3. C22×#13063250C2semidirect
4. C22×#13063243C2semidirect
6. C2×#14582667C2semidirect
7. C2×C43×#341C2semidirect
15. C2×#13063358C4semidirect
374. C2×#341D43semidirect
415. C43#11021semidirect

Maximal subgroups

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

subgroupindex
C22×#130633582
C2×#145829012
C22×#130632502
C22×#130632432
C2×#145828652
C2×#145826672
C2×C43×#3412
#1102143