Finite Group Databasebeta

← #25002071

Subgroups — #25002071

Order 11008.

1230 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063332C211yesmaximal, characteristic
2C2×#14582900C211yesmaximal, characteristic
3C2×#14582668C211yesmaximal, characteristic, complemented
4C2×#14582667C211yesmaximal, characteristic, complemented
5C2×#14582663C211yesmaximal, characteristic, complemented
6C2×#14582661C211yesmaximal, characteristic, complemented
7C2×C43×#417C211yesmaximal, characteristic
8C2×#13063332—22no—
9C2×#13063332—22no—
10C2×#13063332—22no—
11C2×#13063332—22no—
12C2×#13063332—22no—
13C2×#13063332C414yescomplemented
14C22×#10621877—21no—
15C22×#10621877C2211yescharacteristic
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8—21no—
18C23×C43⋊C8C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20#14582900—22no—
21#14582900C414yescomplemented
22C2×#13063249—21no—
23C2×#13063246—21no—
24#14582668—22no—
25#14582667—22no—
26#14582663—22no—
27#14582661—21no—
28#14582661—21no—
29C22×#41×C43C2211yescharacteristic
30C22×M16×C43C2211yescharacteristic
31C22×C4⋊C4×C43C2211yescharacteristic
32C43×#417—22no—
33C43×#417C414yescomplemented
34C2×#103×C43—21no—
35C2×#102×C43—21no—
36C23×Dic43—21no—
37#13063332—28no—
38#13063332—28no—
39#13063332—28no—
40#13063332—28no—
41C2×#10621877—24no—
42C2×#10621877—24no—
43C2×#10621877—21no—
44C2×#10621877—21no—
45C2×#10621877—21no—
46C2×#10621877—21no—
47C2×#10621877—24no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877C2×C412yes—
53C2×#10621877C2×C412yes—
54C2×#10621877D412yes—
55C2×#10621877D412yes—
56C22×C43⋊C8—24no—
57C22×C43⋊C8—24no—
58C22×C43⋊C8—21no—
59C22×C43⋊C8—21no—
60C22×C43⋊C8—21no—
61C22×C43⋊C8—21no—
62C22×C43⋊C8—21no—
63C22×C43⋊C8—24no—
64C22×C43⋊C8—21no—
65C22×C43⋊C8C2×C412yes—
66C22×C43⋊C8D411yescharacteristic
67C22×C43⋊C8D411yescharacteristic
68C22×C43⋊C8D412yes—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2×C412yes—
75#13063249—24no—
76#13063246—24no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C2×#41×C43C2×C412yes—
84C2×#41×C43C2×C412yes—
85C2×#41×C43C2×C412yes—
86C2×#41×C43D412yes—
87C2×#41×C43D412yes—
88C2×#41×C43Q812yes—
89C22×Q8×C43D411yescharacteristic
90C22×D4×C43—21no—
91C22×D4×C43D411yescharacteristic
92C23×C4×C43—21no—
93C23×C4×C43—21no—
94C23×C4×C43C2311yescharacteristic
95C2×M16×C43—21no—
96C2×M16×C43—21no—
97C2×M16×C43—21no—
98C2×M16×C43—21no—
99C2×M16×C43—21no—
100C2×M16×C43C2×C412yes—
101C22×C8×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2×C412yes—
108#103×C43—24no—
109#102×C43—24no—
110C24×C43—21no—
111C24×C43#4111yescharacteristic
112#41×C43—22no—
113#41×C43—22no—
114#41×C43—22no—
115#41×C43—22no—
116#41×C43—22no—
117#41×C43—22no—
118#41×C43—22no—
119#41×C43—22no—
120#41×C43—22no—
121#41×C43—22no—
122#41×C43—22no—
123#41×C43—22no—
124#41×C43C4214yes—
125#41×C43C22⋊C414yes—
126#41×C43C4⋊C414yes—
127#41×C43C4⋊C414yes—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C22⋊C412yes—
132C2×Q8×C43C22⋊C412yes—
133C2×Q8×C43C4⋊C412yes—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—22no—
138C2×D4×C43—22no—
139C2×D4×C43—22no—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43—22no—
143C2×D4×C43C22⋊C412yes—
144C2×D4×C43C22⋊C412yes—
145C2×D4×C43C4⋊C412yes—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×C4×C43—41no—
156C22×C4×C43—81no—
157C22×C4×C43—81no—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×Q811yescharacteristic
169C22×C4×C43#4111yescharacteristic
170C22×C4×C43#4111yescharacteristic
171C22×C4×C43#4111yescharacteristic
172C22×Dic43—22no—
173C22×Dic43—41no—
174C22×Dic43—41no—
175C22×Dic43—81no—
176C22×Dic43—81no—
177M16×C43—22no—
178M16×C43—22no—
179M16×C43—41no—
180M16×C43—41no—
181C2×C8×C43—22no—
182C2×C8×C43—41no—
183C2×C8×C43—41no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊Dic43—22no—
189C4⋊Dic43—22no—
190C4⋊Dic43—41no—
191C4⋊Dic43—41no—
192#10621877—216no—
193#10621877—22no—
194#10621877—22no—
195#10621877—22no—
196#10621877—22no—
197#10621877—22no—
198#10621877—41no—
199#10621877—41no—
200#10621877C22⋊C414yes—
201C2×C43⋊C8—216no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—22no—
208C2×C43⋊C8—22no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—22no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—22no—
214C2×C43⋊C8—41no—
215C2×C43⋊C8—41no—
216C2×C43⋊C8C22⋊C412yes—
217C2×C43⋊C8C22⋊C412yes—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43#11711yescharacteristic
230C23×C43C4×D411yescharacteristic
231C23×C43C4×D411yescharacteristic
232C23×C43#12111yescharacteristic
233C23×C43C22⋊Q811yescharacteristic
234C23×C43#12311yescharacteristic
235C23×C43#12311yescharacteristic
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—22no—
239Q8×C43#9514yes—
240D4×C43—24no—
241D4×C43—24no—
242D4×C43—24no—
243D4×C43—24no—
244D4×C43—22no—
245D4×C43—22no—
246D4×C43—22no—
247D4×C43#9514yes—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—24no—
252C2×C4×C43—24no—
253C2×C4×C43—24no—
254C2×C4×C43—24no—
255C2×C4×C43—42no—
256C2×C4×C43—82no—
257C2×C4×C43—81no—
258C2×C4×C43—81no—
259C2×C4×C43—82no—
260C2×C4×C43C2×C4211yescharacteristic
261C2×C4×C43C2×C22⋊C411yescharacteristic
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C2×C4⋊C411yescharacteristic
267C2×C4×C43C2×C4⋊C411yescharacteristic
268C2×C4×C43C2×C4⋊C411yescharacteristic
269C2×C4×C43#11711yescharacteristic
270C2×C4×C43C4×D411yescharacteristic
271C2×C4×C43C4×D411yescharacteristic
272C2×C4×C43C4×D411yescharacteristic
273C2×C4×C43C4×D411yescharacteristic
274C2×C4×C43C4×D411yescharacteristic
275C2×C4×C43C4×D411yescharacteristic
276C2×C4×C43#12011yescharacteristic
277C2×C4×C43#12011yescharacteristic
278C2×C4×C43#12011yescharacteristic
279C2×C4×C43#12011yescharacteristic
280C2×C4×C43#12111yescharacteristic
281C2×C4×C43#12111yescharacteristic
282C2×C4×C43#12111yescharacteristic
283C2×C4×C43C22⋊Q811yescharacteristic
284C2×C4×C43C22⋊Q811yescharacteristic
285C2×C4×C43C22⋊Q811yescharacteristic
286C2×C4×C43#12311yescharacteristic
287C2×C4×C43#12311yescharacteristic
288C2×Dic43—42no—
289C2×Dic43—82no—
290C2×Dic43—81no—
291C2×Dic43—81no—
292C2×Dic43—82no—
293C8×C43—42no—
294C43⋊C8—22no—
295C43⋊C8—24no—
296C43⋊C8—22no—
297C43⋊C8—42no—
298#10774—431nomaximal, Sylow
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—21no—
305C22×C43—21no—
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—21no—
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—24no—
312C22×C43—42no—
313C22×C43—42no—
314C22×C43—42no—
315C22×C43—42no—
316C22×C43—42no—
317C22×C43—42no—
318C22×C43C4×C22⋊C411yescharacteristic
319C22×C43#38011yescharacteristic
320C22×C43#38111yescharacteristic
321C22×C43#38511yescharacteristic
322C22×C43#38511yescharacteristic
323C22×C43#38611yescharacteristic
324C22×C43#38611yescharacteristic
325C22×C43#47111yescharacteristic
326C22×C43#47111yescharacteristic
327C22×C43#47211yescharacteristic
328C22×C43#47311yescharacteristic
329C4×C43—24no—
330C4×C43—82no—
331C4×C43C2×#9511yescharacteristic
332C4×C43C4×C22⋊C411yescharacteristic
333C4×C43#37911yescharacteristic
334C4×C43#38011yescharacteristic
335C4×C43#38511yescharacteristic
336C4×C43#38511yescharacteristic
337C4×C43#38611yescharacteristic
338C4×C43#38611yescharacteristic
339Dic43—82no—
340C22×#131—431no—
341C2×#417—431no—
342C2×#417D4311yescharacteristic
343C2×#343—431no—
344C2×#343—431no—
345C2×#341—431no—
346C2×#340—431no—
347C2×C43—21no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43—21no—
351C2×C43—44no—
352C2×C43C22⋊#9511yescharacteristic
353C2×C43#181511yescharacteristic
354C2×C43#181611yescharacteristic
355C2×C43#190711yescharacteristic
356C2×C43#190711yescharacteristic
357C2×C43#190811yescharacteristic
358C2×C43#190811yescharacteristic
359C22×#41C2×D4311yescharacteristic
360C2×#131—434no—
361C2×#131—862no—
362C2×#131—862no—
363C2×#131—862no—
364C2×#131—862no—
365C2×#131—862no—
366C22×M16—431no—
367C22×M16—431no—
368C22×M16—861no—
369C22×M16C2×D4311yescharacteristic
370C23×C8—431no—
371C23×C8—861no—
372C22×C4⋊C4—431no—
373C22×C4⋊C4C2×D4311yescharacteristic
374#417—22no—
375#417—434no—
376#417—862no—
377#417Dic4314yescomplemented
378C2×#103—21no—
379C2×#103—861no—
380C2×#102—21no—
381C2×#102—861no—
382#343—862no—
383#343—862no—
384#341—862no—
385#340—861no—
386#340—861no—
387C43#1077411yescharacteristic, complemented, Sylow
388C2×#41—21no—
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—21no—
392C2×#41—21no—
393C2×#41—21no—
394C2×#41Dic8612yes—
395C2×#41C4×D4312yes—
396C2×#41C4×D4312yes—
397C2×#41D17212yes—
398C2×#41C2×Dic4312yes—
399C2×#41C22⋊D4312yes—
400C22×Q8C22⋊D4311yescharacteristic
401C22×D4—21no—
402C22×D4C22⋊D4311yescharacteristic
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—861no—
406C23×C4C22×D4311yescharacteristic
407#131—868no—
408#131—868no—
409#131—868no—
410#131—868no—
411C2×M16—21no—
412C2×M16—21no—
413C2×M16—21no—
414C2×M16—21no—
415C2×M16—21no—
416C2×M16—432no—
417C2×M16—432no—
418C2×M16—432no—
419C2×M16—432no—
420C2×M16—864no—
421C2×M16—864no—
422C2×M16—864no—
423C2×M16—861no—
424C2×M16—861no—
425C2×M16—861no—
426C2×M16—861no—
427C2×M16—861no—
428C2×M16—861no—
429C2×M16—861no—
430C2×M16—861no—
431C2×M16C2×Dic4312yes—
432C22×C8—21no—
433C22×C8—432no—
434C22×C8—431no—
435C22×C8—431no—
436C22×C8—432no—
437C22×C8—864no—
438C22×C8—864no—
439C22×C8—864no—
440C22×C8—861no—
441C22×C8—861no—
442C22×C8—861no—
443C22×C8—861no—
444C22×C8—861no—
445C22×C8—861no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—432no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4C2×Dic4312yes—
458#103—24no—
459#103—864no—
460#102—24no—
461#102—864no—
462C24—21no—
463C24#1062190011yescharacteristic
464#41—22no—
465#41—22no—
466#41—22no—
467#41—22no—
468#41—22no—
469#41—22no—
470#41—22no—
471#41—22no—
472#41—22no—
473#41—22no—
474#41—22no—
475#41—22no—
476#41C4×Dic4314yes—
477#41Dic43⋊C414yes—
478#41C4⋊Dic4314yes—
479#41(C2×D43)⋊C414yes—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8Dic43⋊C412yes—
484C2×Q8(C2×D43)⋊C412yes—
485C2×Q8C22⋊Dic4312yes—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4Dic43⋊C412yes—
496C2×D4(C2×D43)⋊C412yes—
497C2×D4C22⋊Dic4312yes—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—862no—
511C22×C4—3441no—
512C22×C4—3441no—
513C22×C4—1721no—
514C22×C4—1721no—
515C22×C4C2×Dic8611yescharacteristic
516C22×C4C2×C4×D4311yescharacteristic
517C22×C4C2×C4×D4311yescharacteristic
518C22×C4C2×D17211yescharacteristic
519C22×C4D4×D4311yescharacteristic
520C22×C4D4×D4311yescharacteristic
521C22×C4D4×D4311yescharacteristic
522C22×C4D4×D4311yescharacteristic
523C22×C4#1062190011yescharacteristic
524C22×C4#1062190011yescharacteristic
525C22×C4#1062190011yescharacteristic
526C22×C4C22×Dic4311yescharacteristic
527C22×C4C2×C22⋊D4311yescharacteristic
528C22×C4C2×C22⋊D4311yescharacteristic
529M16—22no—
530M16—22no—
531M16—41no—
532M16—41no—
533M16—434no—
534M16—8616no—
535M16—862no—
536M16—862no—
537M16—862no—
538M16—862no—
539M16—862no—
540M16—1721no—
541M16—1721no—
542C2×C8—22no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—432no—
546C2×C8—432no—
547C2×C8—8616no—
548C2×C8—862no—
549C2×C8—862no—
550C2×C8—862no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—862no—
554C2×C8—862no—
555C2×C8—861no—
556C2×C8—861no—
557C2×C8—862no—
558C2×C8—862no—
559C2×C8—862no—
560C2×C8—1721no—
561C2×C8—1721no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—862no—
567C4⋊C4—862no—
568C4⋊C4—1721no—
569C4⋊C4—1721no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23#1306328111yescharacteristic
582C23(C22⋊D43)⋊C411yescharacteristic
583C23D4×Dic4311yescharacteristic
584C23#1306329711yescharacteristic
585C23#1306330211yescharacteristic
586C23#1306330611yescharacteristic
587C23#1306330911yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—22no—
591Q8C43⋊#9514yes—
592D4—24no—
593D4—24no—
594D4—24no—
595D4—24no—
596D4—22no—
597D4—22no—
598D4—22no—
599D4C43⋊#9514yes—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—42no—
608C2×C4—82no—
609C2×C4—81no—
610C2×C4—81no—
611C2×C4—82no—
612C2×C4—3442no—
613C2×C4—3441no—
614C2×C4—3441no—
615C2×C4—3442no—
616C2×C4—1722no—
617C2×C4C2×C4×Dic4311yescharacteristic
618C2×C4C22⋊C4×D4311yescharacteristic
619C2×C4C22⋊C4×D4311yescharacteristic
620C2×C4C2×(C2×D43)⋊C411yescharacteristic
621C2×C4C2×(C2×D43)⋊C411yescharacteristic
622C2×C4C2×C22⋊Dic4311yescharacteristic
623C2×C4C2×Dic43⋊C411yescharacteristic
624C2×C4C2×Dic43⋊C411yescharacteristic
625C2×C4C2×C4⋊Dic4311yescharacteristic
626C2×C4#1306328111yescharacteristic
627C2×C4(C22⋊D43)⋊C411yescharacteristic
628C2×C4(C22⋊D43)⋊C411yescharacteristic
629C2×C4(C22⋊D43)⋊C411yescharacteristic
630C2×C4D4×Dic4311yescharacteristic
631C2×C4D4×Dic4311yescharacteristic
632C2×C4D4×Dic4311yescharacteristic
633C2×C4#1306329311yescharacteristic
634C2×C4#1306329311yescharacteristic
635C2×C4#1306329511yescharacteristic
636C2×C4#1306329511yescharacteristic
637C2×C4#1306329711yescharacteristic
638C2×C4#1306329711yescharacteristic
639C2×C4#1306329711yescharacteristic
640C2×C4#1306330211yescharacteristic
641C2×C4#1306330211yescharacteristic
642C2×C4#1306330211yescharacteristic
643C2×C4#1306330611yescharacteristic
644C2×C4#1306330911yescharacteristic
645C8—42no—
646C8—862no—
647C8—862no—
648C8—864no—
649C8—1722no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—24no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22C22⋊C4×Dic4311yescharacteristic
670C22#1458275711yescharacteristic
671C22#1458276011yescharacteristic
672C22#1458277111yescharacteristic
673C22#1458277411yescharacteristic
674C22#1458277611yescharacteristic
675C22#1458277911yescharacteristic
676C22#1458316011yescharacteristic
677C22#1458316411yescharacteristic
678C22#1458316711yescharacteristic
679C22#1458317211yescharacteristic
680C4—24no—
681C4—82no—
682C4—3442no—
683C4C2×C43⋊#9511yescharacteristic
684C4C22⋊C4×Dic4311yescharacteristic
685C4#1458275411yescharacteristic
686C4#1458275711yescharacteristic
687C4#1458277111yescharacteristic
688C4#1458277411yescharacteristic
689C4#1458277611yescharacteristic
690C4#1458277911yescharacteristic
691C2—21no—
692C2—21no—
693C2—21no—
694C2—21no—
695C2—44no—
696C2#1913281711yescharacteristic
697C2#1913465211yescharacteristic
698C2#1913465711yescharacteristic
699C2#1913510111yescharacteristic
700C2#1913510511yescharacteristic
701C2#1913510811yescharacteristic
702C2#1913511211yescharacteristic
subgroupG/H
centerC23#13063297
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×#417C2
socleC23×C43#121
prime radicalC22×#41×C43C22
cosocleC23×C4×C43C23
hypercenterC2×#417D43
hypocenterC43#10774
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
3. C2×#14582668C2semidirect
4. C2×#14582667C2semidirect
5. C2×#14582663C2semidirect
6. C2×#14582661C2semidirect
13. C2×#13063332C4semidirect
21. #14582900C4semidirect
33. C43×#417C4semidirect
377. #417Dic43semidirect
387. C43#10774semidirect

Maximal subgroups

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

subgroupindex
C22×#130633322
C2×#145829002
C2×#145826682
C2×#145826672
C2×#145826632
C2×#145826612
C2×C43×#4172
#1077443