Finite Group Databasebeta

← #25130622

Subgroups — #25130622

Order 11008.

1088 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
1C2×#14583584C211yesmaximal, characteristic
2C2×#14583205C211yesmaximal, characteristic, complemented
3C2×#14582993C211yesmaximal, characteristic, complemented
4#19139506C211yesmaximal, characteristic
5#19135800C211yesmaximal, characteristic, complemented
6#19135791C211yesmaximal, characteristic, complemented
7#19135606C211yesmaximal, characteristic, complemented
8#19135605C211yesmaximal, characteristic, complemented
9#19135558C211yesmaximal, characteristic, complemented
10#19135387C211yesmaximal, characteristic
11#19134906C211yesmaximal, characteristic, complemented
12#19134902C211yesmaximal, characteristic, complemented
13#19134791C211yesmaximal, characteristic, complemented
14#19134609C211yesmaximal, characteristic, complemented
15C43×#1852C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17#14583584—24no—
18#14583584—24no—
19C2×#13063320—21no—
20C2×#13063316C2211yescharacteristic
21C2×#13063315—21no—
22C2×#13063308—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063305C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26C2×#13063304C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×#13063290C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063284—21no—
31C2×#13063283C2211yescharacteristic
32#14583205—24no—
33#14582993—24no—
34C2×#13063256C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582833—21no—
47#14582814—21no—
48#14582792—21no—
49#14582788—21no—
50#14582764C2211yescharacteristic
51#14582756C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×C4⋊C4×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C22×C22⋊D43D411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C2×Dic172—22no—
68C2×Dic172—22no—
69C2×Dic172—22no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063320—28no—
73#13063316—22no—
74#13063316D414yes—
75#13063315—28no—
76#13063308—28no—
77#13063305—22no—
78#13063305—22no—
79#13063305—22no—
80#13063305—41no—
81#13063304—22no—
82#13063304—22no—
83#13063304—22no—
84#13063304—41no—
85#13063290—22no—
86#13063290—22no—
87#13063290—22no—
88#13063290D414yes—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91#13063284—28no—
92#13063283—22no—
93#13063283—22no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4D411yescharacteristic
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43D411yescharacteristic
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43C2311yescharacteristic
117#13063256—22no—
118Dic43⋊C8—22no—
119#13063250—22no—
120#13063250—41no—
121#13063248—22no—
122#13063248—22no—
123#13063248—22no—
124#13063248—41no—
125C22⋊(C43⋊C8)—41no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—41no—
128C8×Dic43—22no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C23×C4×C43—21no—
133C23×C4×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—22no—
138C2×C4⋊C4×C43—22no—
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144#107×C43—22no—
145#107×C43—22no—
146C22⋊C8×C43—22no—
147#95×C43—21no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C22×C4×C43—24no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—42no—
162C22×C4×C43—42no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—41no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86C2×D412yes—
192C2×Dic86#4112yes—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43#4112yes—
199C4⋊C4×C43—24no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43C2×D412yes—
207C4⋊C4×C43C2×D412yes—
208C22⋊C4×C43—42no—
209C22⋊Dic43—24no—
210C22⋊Dic43—22no—
211C22⋊Dic43—42no—
212(C2×D43)⋊C4—24no—
213(C2×D43)⋊C4—24no—
214(C2×D43)⋊C4—22no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217C4⋊Dic43—24no—
218C4⋊Dic43—21no—
219C4⋊Dic43—24no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—42no—
223C4⋊Dic43C2×D412yes—
224Dic43⋊C4—24no—
225Dic43⋊C4—24no—
226Dic43⋊C4—24no—
227Dic43⋊C4—22no—
228Dic43⋊C4—42no—
229Dic43⋊C4—42no—
230C4×Dic43—24no—
231C4×Dic43—24no—
232C4×Dic43—42no—
233C4×Dic43C2×D412yes—
234C4×Dic43C2×D412yes—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241Dic172—28no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43#13512yes—
249C23×C43C22×D411yescharacteristic
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C2×C4×C43—22no—
258C2×C4×C43—21no—
259C2×C4×C43—22no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—48no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43C22×D411yescharacteristic
278C2×C4×C43C22×D411yescharacteristic
279C2×C4×C43C2×#4111yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43H(5,𝔽2)11yescharacteristic
282C2×C4×C432−1+411yescharacteristic
283C22⋊D43—44no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43#12012yes—
304C2×Dic43#12012yes—
305C4×D43—41no—
306C4×D43—41no—
307C4×D43—41no—
308C4×D43—41no—
309Dic86—22no—
310Dic86—22no—
311Dic86—22no—
312Dic86—22no—
313Dic86—41no—
314Dic86—41no—
315Dic86—41no—
316Dic86—41no—
317C8×C43—22no—
318C8×C43—41no—
319C43⋊C8—41no—
320C43⋊C8—41no—
321#24127—431nomaximal, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43C2×#12011yescharacteristic
330C22×C43#54611yescharacteristic
331C22×C43#54711yescharacteristic
332C22×C43C2×#13511yescharacteristic
333C22×C43#57511yescharacteristic
334C22×C43#57811yescharacteristic
335C22×C43#57811yescharacteristic
336C2×D43—41no—
337C2×D43—41no—
338C2×D43—41no—
339C2×D43—41no—
340C2×D43—41no—
341C2×D43—41no—
342C2×D43—41no—
343C4×C43—41no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43—81no—
347C4×C43—81no—
348C4×C43#52511yescharacteristic
349C4×C43#53711yescharacteristic
350C4×C43#54811yescharacteristic
351C4×C43#55011yescharacteristic
352Dic43—22no—
353Dic43—22no—
354Dic43—42no—
355Dic43—42no—
356Dic43—41no—
357Dic43—42no—
358Dic43—81no—
359C2×#552—431no—
360C2×#479—431no—
361C2×C4×Q16—431no—
362#2536—431no—
363#2036—431no—
364#2035—431no—
365#2001—431no—
366#2001—431no—
367#1991—431no—
368#1954—431no—
369#1873—431no—
370#1872—431no—
371#1854—431no—
372#1852D4311yescharacteristic, complemented
373#1805—431no—
374C2×C43—42no—
375C2×C43#240711yescharacteristic
376C2×C43#300211yescharacteristic
377C2×C43#301111yescharacteristic
378C2×C43#330011yescharacteristic
379C2×C43#332711yescharacteristic
380C2×C43#333611yescharacteristic
381C2×C43#335211yescharacteristic
382D43—81no—
383C22×Q16—431no—
384#552—864no—
385#552—864no—
386C2×#126—861no—
387C2×#125—431no—
388C2×#125—861no—
389C2×#123—861no—
390C2×C22⋊Q8—431no—
391C2×C22⋊Q8—431no—
392C2×C22⋊Q8—431no—
393C2×C22⋊Q8—431no—
394C2×C4×Q8—431no—
395C2×C4×Q8—431no—
396C2×C4×D4—431no—
397C2×#117—431no—
398C2×#117—861no—
399C22×C4⋊C4C2×D4311yescharacteristic
400#479—864no—
401C4×Q16—864no—
402C2×#107C2×D4311yescharacteristic
403C2×#107C2×D4311yescharacteristic
404C2×#106—431no—
405C2×C4⋊C8—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×C22⋊C8—431no—
413C2×C22⋊C8—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8C2×D4311yescharacteristic
416C2×C4×C8—431no—
417#398—861no—
418#394—861no—
419#388—861no—
420#388—861no—
421#382—431no—
422#380—431no—
423#380C2×D4311yescharacteristic
424#340—431no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340C2×D4311yescharacteristic
429#340C2×D4311yescharacteristic
430C43#2412711yescharacteristic, complemented, Sylow
431C22×Q8—431no—
432C22×Q8—431no—
433C22×D4—431no—
434C23×C4—21no—
435C23×C4—431no—
436C23×C4C22×D4311yescharacteristic
437C2×Q16—862no—
438C2×Q16—862no—
439C2×Q16—862no—
440C22×C8—431no—
441C22×C8—431no—
442C22×C8C22×D4311yescharacteristic
443C22×C8C22×D4311yescharacteristic
444#126—868no—
445#125—434no—
446#125—862no—
447#125—868no—
448#123—868no—
449C22⋊Q8—862no—
450C22⋊Q8—862no—
451C22⋊Q8—862no—
452C22⋊Q8—862no—
453C22⋊Q8—862no—
454C22⋊Q8—862no—
455C22⋊Q8—1721no—
456C22⋊Q8—1721no—
457C4×Q8—434no—
458C4×Q8—862no—
459C4×Q8—862no—
460C4×Q8—862no—
461C4×D4—862no—
462C4×D4—862no—
463#117—862no—
464#117—868no—
465#117—862no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—431no—
486C2×C22⋊C4—431no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C42—431no—
494C2×C42—861no—
495C2×C42—861no—
496C2×C42—861no—
497#107—22no—
498#107—22no—
499#106—862no—
500C4⋊C8—862no—
501#103—862no—
502#103—862no—
503#103—862no—
504#103—862no—
505#103—1721no—
506#103—1721no—
507C22⋊C8—22no—
508C22⋊C8—862no—
509C22⋊C8—1721no—
510C22⋊C8—1721no—
511C4×C8—862no—
512#95—21no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—431no—
517C24D4×D4311yescharacteristic
518C2×Q8—432no—
519C2×Q8—432no—
520C2×Q8—861no—
521C2×Q8—861no—
522C2×Q8—861no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×D4—862no—
531C2×D4—862no—
532C2×D4—1721no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—431no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4D4×D4311yescharacteristic
560C22×C4C23×D4311yescharacteristic
561Q16—868no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8#1062189812yes—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—432no—
582C4⋊C4—862no—
583C4⋊C4—864no—
584C4⋊C4—864no—
585C4⋊C4—864no—
586C4⋊C4—864no—
587C4⋊C4—864no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—1722no—
592C4⋊C4—1722no—
593C4⋊C4—1722no—
594C4⋊C4D4×D4312yes—
595C4⋊C4D4×D4312yes—
596C22⋊C4—42no—
597C22⋊C4—862no—
598C22⋊C4—864no—
599C22⋊C4—864no—
600C22⋊C4—862no—
601C22⋊C4—864no—
602C22⋊C4—1722no—
603C22⋊C4—1722no—
604C22⋊C4—1722no—
605C42—432no—
606C42—432no—
607C42—864no—
608C42—864no—
609C42—1722no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—861no—
617C23—861no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23#1306334412yes—
624C23C2×D4×D4311yescharacteristic
625Q8—862no—
626Q8—862no—
627Q8—862no—
628Q8—862no—
629Q8—1721no—
630Q8—1721no—
631Q8—1721no—
632Q8—1721no—
633D4—1724no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—432no—
655C2×C4—432no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4C2×D4×D4311yescharacteristic
680C2×C4C2×D4×D4311yescharacteristic
681C2×C4#41×D4311yescharacteristic
682C2×C4C2×#1062189811yescharacteristic
683C2×C4#1306337111yescharacteristic
684C2×C4#1306337311yescharacteristic
685C8—22no—
686C8—41no—
687C8—1721no—
688C8—1721no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—1721no—
697C22—1721no—
698C22—1721no—
699C22—1721no—
700C22—1721no—
701C22—1721no—
702C22—1721no—
703C22#120×D4311yescharacteristic
704C22#1458354111yescharacteristic
705C22#1458355011yescharacteristic
706C22C2×#1306334411yescharacteristic
707C22#1458369511yescharacteristic
708C22#1458371211yescharacteristic
709C22#1458371511yescharacteristic
710C4—42no—
711C4—42no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4—862no—
716C4—862no—
717C4—3441no—
718C4—1721no—
719C4—1722no—
720C4—1722no—
721C4—1722no—
722C4#1458340811yescharacteristic
723C4#1458347911yescharacteristic
724C4#1458355911yescharacteristic
725C4#1458357011yescharacteristic
726C2—42no—
727C2—3441no—
728C2#1913793911yescharacteristic
729C2#1914380811yescharacteristic
730C2#1914388511yescharacteristic
731C2#1914648011yescharacteristic
732C2#1914686611yescharacteristic
733C2#1914695911yescharacteristic
734C2#1914716611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1852C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#1852D43
hypocenterC43#24127
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#14583205C2semidirect
3. C2×#14582993C2semidirect
5. #19135800C2semidirect
6. #19135791C2semidirect
7. #19135606C2semidirect
8. #19135605C2semidirect
9. #19135558C2semidirect
11. #19134906C2semidirect
12. #19134902C2semidirect
13. #19134791C2semidirect
14. #19134609C2semidirect
15. C43×#1852C2semidirect
372. #1852D43semidirect
430. C43#24127semidirect

Maximal subgroups

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

subgroupindex
C2×#145835842
C2×#145832052
C2×#145829932
#191395062
#191358002
#191357912
#191356062
#191356052
#191355582
#191353872
#191349062
#191349022
#191347912
#191346092
C43×#18522
#2412743