Finite Group Databasebeta

← #25065482

Subgroups — #25065482

Order 11008.

904 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148407C211yesmaximal, characteristic
2#19143722C211yesmaximal, characteristic
3#19143717C211yesmaximal, characteristic
4#19133331C211yesmaximal, characteristic, complemented
5#19133311C211yesmaximal, characteristic, complemented
6#19133310C211yesmaximal, characteristic, complemented
7#19133295C211yesmaximal, characteristic, complemented
8#19133294C211yesmaximal, characteristic, complemented
9#19133292C211yesmaximal, characteristic, complemented
10#19133278C211yesmaximal, characteristic, complemented
11#19133265C211yesmaximal, characteristic, complemented
12#19133258C211yesmaximal, characteristic, complemented
13C2×#14582646C211yesmaximal, characteristic, complemented
14#332×D43C211yesmaximal, characteristic, complemented
15C43×#1552C211yesmaximal, characteristic, complemented
16Q8×Dic86—21no—
17#14583627—21no—
18#14583609—21no—
19#14583607—21no—
20#14583607—21no—
21Q8×D172—21no—
22#14583562—21no—
23#14583562—21no—
24#14583529C412yes—
25#14583529C412yes—
26#14583527C412yes—
27#14583454C2211yescharacteristic
28#14583454C2211yescharacteristic
29C2×#13063325C2211yescharacteristic
30C4⋊Q8×D43C2211yescharacteristic
31C4⋊Q8×D43C2211yescharacteristic
32#14583379C412yes—
33C4×#10621898C2211yescharacteristic
34#14583028—21no—
35#14583027—21no—
36#14582972—21no—
37#14582970—21no—
38#14582969—21no—
39#14582967—21no—
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582956C2211yescharacteristic
43#14582955C2211yescharacteristic
44#14582955C2211yescharacteristic
45#14582951C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582921C2211yescharacteristic
48#14582921C2211yescharacteristic
49C2×C4⋊(C43⋊C8)C2211yescharacteristic
50C4⋊C8×D43C2211yescharacteristic
51C4⋊C8×D43C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582645C2211yescharacteristic
60#14582644C2211yescharacteristic
61#14582644C2211yescharacteristic
62#14582644C2211yescharacteristic
63#14582644C2211yescharacteristic
64C43×#533C2211yescharacteristic
65C43×#432C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C43×#332C2211yescharacteristic
68C43×#332C2211yescharacteristic
69C43×#332C2211yescharacteristic
70C43×#332C2211yescharacteristic
71C2×#10621898C2×C411yescharacteristic
72C22×Dic86—21no—
73C2×Q8×D43—21no—
74C2×Q8×D43—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80#13063325—21no—
81#13063325—21no—
82#13063325—22no—
83#13063325C2×C412yes—
84#13063325C2311yescharacteristic
85#13063325C2311yescharacteristic
86#13063324—22no—
87#13063324—22no—
88#13063324—21no—
89#13063324—21no—
90#13063324C2×C412yes—
91#13063324C2×C412yes—
92#13063323—21no—
93#13063323—21no—
94#13063317—22no—
95#13063316C2×C412yes—
96#13063316C2×C412yes—
97#13063315—22no—
98#13063315—22no—
99#13063305—21no—
100#13063305—21no—
101#13063305—22no—
102#13063305—22no—
103#13063303—22no—
104#13063303—22no—
105#13063302—22no—
106#13063302—22no—
107#13063301—21no—
108#13063301—21no—
109Q8×Dic43—21no—
110Q8×Dic43—21no—
111C4×Dic86—22no—
112C4×Dic86D411yescharacteristic
113C4×Dic86D411yescharacteristic
114#13063290—21no—
115#13063290—21no—
116C4×D172—22no—
117C4×D172D411yescharacteristic
118C4×D172D411yescharacteristic
119C4×C22⋊D43D411yescharacteristic
120C4×C22⋊D43D411yescharacteristic
121C4×C22⋊D43D411yescharacteristic
122C4×C22⋊D43D411yescharacteristic
123(C22⋊D43)⋊C4—22no—
124(C22⋊D43)⋊C4—22no—
125#13063284C2×C411yescharacteristic
126#13063283C2×C412yes—
127#13063283C2×C412yes—
128#13063282C2×C411yescharacteristic
129#13063282C2×C411yescharacteristic
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43C2×C412yes—
132C4⋊C4×D43—21no—
133C4⋊C4×D43—21no—
134C4⋊C4×D43C2×C412yes—
135C4⋊C4×D43C2×C412yes—
136C42×D43C2311yescharacteristic
137C42×D43C2311yescharacteristic
138C4⋊(C43⋊C8)—21no—
139C4⋊(C43⋊C8)C2311yescharacteristic
140C4⋊(C43⋊C8)C2311yescharacteristic
141C4⋊(C43⋊C8)C2311yescharacteristic
142C4⋊(C43⋊C8)C2311yescharacteristic
143Dic43⋊C8—21no—
144Dic43⋊C8—21no—
145Dic43⋊C8—21no—
146Dic43⋊C8—21no—
147C22⋊(C43⋊C8)—21no—
148(C2×D43)⋊C8—21no—
149(C2×D43)⋊C8—21no—
150(C2×D43)⋊C8—21no—
151(C2×D43)⋊C8—21no—
152#13063236—21no—
153#13063235—21no—
154#13063235—21no—
155C8×Dic43—21no—
156C8×Dic43—21no—
157C22×C8×C43—21no—
158C4⋊Q8×C43C2311yescharacteristic
159C4⋊Q8×C43C2311yescharacteristic
160#125×C43C2×C412yes—
161C22⋊Q8×C43—21no—
162C22⋊Q8×C43—21no—
163C4×Q8×C43—21no—
164C4×Q8×C43—21no—
165#117×C43C2×C412yes—
166C2×C42×C43C2311yescharacteristic
167C4⋊C8×C43—21no—
168C4⋊C8×C43C2311yescharacteristic
169C4⋊C8×C43C2311yescharacteristic
170C4⋊C8×C43C2311yescharacteristic
171C4⋊C8×C43C2311yescharacteristic
172C22⋊C8×C43—21no—
173#97×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C22×C4×C43C22×C411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C2×C22⋊D43C22⋊C411yescharacteristic
180C2×C22⋊D43C22⋊C411yescharacteristic
181C22×Dic43—22no—
182Q8×D43—81no—
183Q8×D43—81no—
184Q8×D43—81no—
185Q8×D43—81no—
186#10621898—24no—
187C2×D172C22⋊C411yescharacteristic
188C2×C4×D43—22no—
189C2×C4×D43—22no—
190C2×C4×D43C22×C411yescharacteristic
191C2×C4×D43C22×C411yescharacteristic
192C2×C4×D43C2×D411yescharacteristic
193C2×C4×D43C2×D411yescharacteristic
194C2×C4×D43C2×D411yescharacteristic
195C2×C4×D43C2×D411yescharacteristic
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—22no—
199C2×Dic86—22no—
200C2×Dic86—22no—
201C2×Dic86—81no—
202C2×Dic86—81no—
203C2×Dic86C22⋊C411yescharacteristic
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—81no—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—22no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C22×C412yes—
214C4⋊C4×C43C22×C412yes—
215C22⋊C4×C43—22no—
216C42×C43—22no—
217C42×C43C22×C411yescharacteristic
218C42×C43C2×D411yescharacteristic
219C42×C43C2×D411yescharacteristic
220C42×C43C2411yescharacteristic
221C22⋊Dic43C22⋊C411yescharacteristic
222C22⋊Dic43C22⋊C411yescharacteristic
223(C2×D43)⋊C4—22no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4C22⋊C411yescharacteristic
226(C2×D43)⋊C4C22⋊C411yescharacteristic
227(C2×D43)⋊C4C22⋊C411yescharacteristic
228(C2×D43)⋊C4C22⋊C411yescharacteristic
229C4⋊Dic43—22no—
230C4⋊Dic43—22no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—22no—
234C4⋊Dic43—22no—
235C4⋊Dic43C22⋊C411yescharacteristic
236C4⋊Dic43C22⋊C411yescharacteristic
237C4⋊Dic43C22×C412yes—
238C4⋊Dic43C22×C412yes—
239Dic43⋊C4—22no—
240Dic43⋊C4—22no—
241Dic43⋊C4—22no—
242Dic43⋊C4—22no—
243Dic43⋊C4—22no—
244Dic43⋊C4—22no—
245Dic43⋊C4C22⋊C411yescharacteristic
246Dic43⋊C4C22⋊C411yescharacteristic
247Dic43⋊C4C22⋊C411yescharacteristic
248Dic43⋊C4C22⋊C411yescharacteristic
249C4×Dic43—22no—
250C4×Dic43—22no—
251C4×Dic43C22×C411yescharacteristic
252C4×Dic43C22×C411yescharacteristic
253C4×Dic43C2×D411yescharacteristic
254C4×Dic43C2×D411yescharacteristic
255C4×Dic43C2×D411yescharacteristic
256C4×Dic43C2×D411yescharacteristic
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—81no—
262#10621872—81no—
263#10621872—81no—
264C8×D43—81no—
265C8×D43—81no—
266C23×C43C2×C22⋊C411yescharacteristic
267C22×D43C2×C22⋊C411yescharacteristic
268C22×D43C2×C22⋊C411yescharacteristic
269Q8×C43—41no—
270Q8×C43—41no—
271Q8×C43—41no—
272Q8×C43—41no—
273C2×C4×C43—22no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43C2×C22⋊C411yescharacteristic
281C2×C4×C43C2×C22⋊C411yescharacteristic
282C2×C4×C43C2×C22⋊C411yescharacteristic
283C2×C4×C43C23×C411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C22×D411yescharacteristic
286C22⋊D43—22no—
287C22⋊D43#10114yes—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—82no—
291C2×Dic43C2×C22⋊C411yescharacteristic
292C2×Dic43C2×C22⋊C411yescharacteristic
293C2×Dic43C2×C22⋊C411yescharacteristic
294C2×Dic43C2×C22⋊C411yescharacteristic
295C2×Dic43C2×C22⋊C411yescharacteristic
296C2×Dic43C2×C22⋊C411yescharacteristic
297D172—22no—
298C4×D43—22no—
299C4×D43—21no—
300C4×D43—21no—
301C4×D43—21no—
302C4×D43—21no—
303C4×D43—21no—
304C4×D43—21no—
305C4×D43—21no—
306C4×D43—21no—
307C4×D43—22no—
308C4×D43—82no—
309C4×D43—82no—
310Dic86—22no—
311Dic86—41no—
312Dic86—41no—
313Dic86—41no—
314Dic86—41no—
315Dic86—82no—
316Dic86—82no—
317Dic86—82no—
318C8×C43—41no—
319C8×C43—41no—
320C8×C43—41no—
321C8×C43—41no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324C43⋊C8—41no—
325C43⋊C8—41no—
326#17774—431nomaximal, Sylow
327C22×C43—21no—
328C22×C43—21no—
329C22×C43C2×#10112yes—
330C22×C43C22×C22⋊C411yescharacteristic
331C2×D43—21no—
332C2×D43—21no—
333C2×D43—21no—
334C2×D43—21no—
335C2×D43—21no—
336C2×D43C2×#10112yes—
337C4×C43—21no—
338C4×C43—21no—
339C4×C43—21no—
340C4×C43—21no—
341C4×C43—42no—
342C4×C43—42no—
343C4×C43#57611yescharacteristic
344C4×C43#57711yescharacteristic
345C4×C43#57711yescharacteristic
346C4×C43#57811yescharacteristic
347Dic43—21no—
348Dic43—21no—
349Dic43—21no—
350Dic43—21no—
351Dic43—21no—
352Dic43—42no—
353Dic43—42no—
354Dic43C2×#10112yes—
355#3503—431no—
356#2990—431no—
357#2990—431no—
358#1561—431no—
359#1556—431no—
360#1556—431no—
361#1552—431no—
362#1552—431no—
363#1552—431no—
364#1552D4311yescharacteristic, complemented
365#1549—431no—
366#1546—431no—
367#1544—431no—
368C2×#332—431no—
369C2×#332—431no—
370C2×C43—22no—
371C2×C43C22×#10111yescharacteristic
372C2×C43#289711yescharacteristic
373C2×C43#289811yescharacteristic
374D43—22no—
375D43—41no—
376Q82—861no—
377#557—861no—
378#554—861no—
379#554—861no—
380#554—861no—
381D4×Q8—861no—
382D4×Q8—861no—
383D4×Q8—861no—
384#544—432no—
385#544—432no—
386#544—432no—
387#533—431no—
388#533—431no—
389#533C2×D4311yescharacteristic
390C2×C4⋊Q8—431no—
391C2×C4⋊Q8—431no—
392C2×C4⋊Q8—431no—
393#520—432no—
394C4×#41—431no—
395#446—861no—
396#446—861no—
397#435—861no—
398#435—861no—
399#435—861no—
400#435—861no—
401C8×D4—861no—
402C8×D4—861no—
403#432—431no—
404#432—431no—
405#432—431no—
406#432C2×D4311yescharacteristic
407#431—431no—
408#431—431no—
409#423—431no—
410#423—431no—
411C2×C4⋊C8—431no—
412C2×C4⋊C8—431no—
413C2×C4⋊C8—431no—
414C2×C4⋊C8C2×D4311yescharacteristic
415#332—431no—
416#332—431no—
417#332—431no—
418#332—431no—
419#332—431no—
420#332—431no—
421#332—431no—
422#332—431no—
423#332—431no—
424#332—431no—
425#332—431no—
426#332—431no—
427#332C2×D4311yescharacteristic
428#332C2×D4311yescharacteristic
429#332C2×D4311yescharacteristic
430#332C2×D4311yescharacteristic
431C43#1777411yescharacteristic, complemented, Sylow
432C2×#41—431no—
433C22×Q8—861no—
434C22×Q8—861no—
435C22×Q8—861no—
436C2×M16—861no—
437C2×M16—861no—
438C22×C8—21no—
439C22×C8—861no—
440C22×C8—861no—
441C22×C8—861no—
442C4⋊Q8—432no—
443C4⋊Q8—432no—
444C4⋊Q8—432no—
445C4⋊Q8—431no—
446C4⋊Q8—431no—
447C4⋊Q8—862no—
448C4⋊Q8—861no—
449C4⋊Q8—861no—
450C4⋊Q8—861no—
451C4⋊Q8—861no—
452C4⋊Q8—862no—
453C4⋊Q8—862no—
454C4⋊Q8—861no—
455C4⋊Q8—861no—
456C4⋊Q8C22×D4311yescharacteristic
457C4⋊Q8C22×D4311yescharacteristic
458#125—432no—
459#125—432no—
460#125—862no—
461#125—862no—
462#125—862no—
463#125C4×D4312yes—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—862no—
467C22⋊Q8—862no—
468C22⋊Q8—862no—
469C22⋊Q8—862no—
470C22⋊Q8—862no—
471C22⋊Q8—862no—
472C22⋊Q8—861no—
473C22⋊Q8—861no—
474C22⋊Q8—861no—
475C22⋊Q8—861no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—431no—
479C4×Q8—431no—
480C4×Q8—862no—
481C4×Q8—861no—
482C4×Q8—861no—
483C4×Q8—861no—
484C4×Q8—861no—
485C4×D4—431no—
486C4×D4—431no—
487C4×D4—431no—
488C4×D4—431no—
489C4×D4—431no—
490C4×D4—431no—
491C4×D4—862no—
492C4×D4—862no—
493C4×D4—862no—
494#117—431no—
495#117—431no—
496#117—431no—
497#117—432no—
498#117—432no—
499#117C4×D4312yes—
500C2×C4⋊C4—432no—
501C2×C4⋊C4—432no—
502C2×C4⋊C4—432no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C42—431no—
507C2×C42—431no—
508C2×C42C22×D4311yescharacteristic
509C4⋊C8—21no—
510C4⋊C8—431no—
511C4⋊C8—431no—
512C4⋊C8—431no—
513C4⋊C8—431no—
514C4⋊C8—861no—
515C4⋊C8—861no—
516C4⋊C8—861no—
517C4⋊C8—861no—
518C4⋊C8—861no—
519C4⋊C8C22×D4311yescharacteristic
520C4⋊C8C22×D4311yescharacteristic
521C4⋊C8C22×D4311yescharacteristic
522C4⋊C8C22×D4311yescharacteristic
523C22⋊C8—21no—
524C22⋊C8—861no—
525C22⋊C8—861no—
526C22⋊C8—861no—
527C22⋊C8—861no—
528C22⋊C8—861no—
529#97—21no—
530#97—861no—
531#97—861no—
532#97—861no—
533C4×C8—861no—
534C4×C8—861no—
535#41—864no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—431no—
539C2×Q8—862no—
540C2×Q8—862no—
541C2×Q8—862no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×Q8—3441no—
545C2×Q8—3441no—
546C2×Q8—3441no—
547C2×Q8—3441no—
548C2×Q8—3441no—
549C2×Q8—3441no—
550C2×D4—431no—
551C2×D4—431no—
552C2×D4—431no—
553C22×C4—431no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4C2×C4×D4311yescharacteristic
563C22×C4D4×D4311yescharacteristic
564C22×C4D4×D4311yescharacteristic
565M16—3441no—
566M16—3441no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—81no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—3441no—
577C2×C8—3441no—
578C2×C8—3441no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—431no—
584C4⋊C4—431no—
585C4⋊C4—431no—
586C4⋊C4—431no—
587C4⋊C4—431no—
588C4⋊C4—431no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—862no—
592C4⋊C4—862no—
593C4⋊C4—862no—
594C4⋊C4—862no—
595C4⋊C4—862no—
596C4⋊C4—862no—
597C4⋊C4—862no—
598C4⋊C4—862no—
599C4⋊C4—862no—
600C4⋊C4—862no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4C2×C4×D4312yes—
604C4⋊C4C2×C4×D4312yes—
605C22⋊C4—22no—
606C22⋊C4—431no—
607C22⋊C4—431no—
608C22⋊C4—431no—
609C22⋊C4—431no—
610C22⋊C4—431no—
611C22⋊C4—431no—
612C22⋊C4—862no—
613C22⋊C4—862no—
614C42—22no—
615C42—431no—
616C42—431no—
617C42—431no—
618C42—431no—
619C42—431no—
620C42—431no—
621C42—862no—
622C42—862no—
623C42C2×C4×D4311yescharacteristic
624C42D4×D4311yescharacteristic
625C42D4×D4311yescharacteristic
626C42C23×D4311yescharacteristic
627C23—431no—
628C23—431no—
629C23C22⋊C4×D4311yescharacteristic
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—862no—
635Q8—3442no—
636Q8—3442no—
637Q8—3442no—
638Q8—1721no—
639Q8—1721no—
640Q8—1721no—
641Q8—1721no—
642D4—434no—
643D4—862no—
644D4—862no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—431no—
653C2×C4—431no—
654C2×C4—431no—
655C2×C4—431no—
656C2×C4—431no—
657C2×C4—431no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—3442no—
671C2×C4—3442no—
672C2×C4—3442no—
673C2×C4C22⋊C4×D4311yescharacteristic
674C2×C4C22⋊C4×D4311yescharacteristic
675C2×C4C22⋊C4×D4311yescharacteristic
676C2×C4C22×C4×D4311yescharacteristic
677C2×C4C2×D4×D4311yescharacteristic
678C2×C4C2×D4×D4311yescharacteristic
679C8—41no—
680C8—41no—
681C8—41no—
682C8—41no—
683C8—1721no—
684C8—1721no—
685C8—1721no—
686C8—1721no—
687C22—21no—
688C22—21no—
689C22—432no—
690C22—861no—
691C22—861no—
692C22—861no—
693C22—861no—
694C22—861no—
695C22#101×D4312yes—
696C22C2×C22⋊C4×D4311yescharacteristic
697C4—21no—
698C4—21no—
699C4—21no—
700C4—21no—
701C4—42no—
702C4—42no—
703C4—432no—
704C4—861no—
705C4—861no—
706C4—861no—
707C4—861no—
708C4—861no—
709C4—1722no—
710C4—1722no—
711C4#1458370311yescharacteristic
712C4#1458370611yescharacteristic
713C4#1458370811yescharacteristic
714C4#1458371311yescharacteristic
715C2—22no—
716C2—862no—
717C2—1721no—
718C2C2×#101×D4311yescharacteristic
719C2#1914311911yescharacteristic
720C2#1914312411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1552C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#10621898C2×C4
cosocleC42×C43C24
hypercenter#1552D43
hypocenterC43#17774
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
4. #19133331C2semidirect
5. #19133311C2semidirect
6. #19133310C2semidirect
7. #19133295C2semidirect
8. #19133294C2semidirect
9. #19133292C2semidirect
10. #19133278C2semidirect
11. #19133265C2semidirect
12. #19133258C2semidirect
13. C2×#14582646C2semidirect
14. #332×D43C2semidirect
15. C43×#1552C2semidirect
364. #1552D43semidirect
431. C43#17774semidirect

Maximal subgroups

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

subgroupindex
#191484072
#191437222
#191437172
#191333312
#191333112
#191333102
#191332952
#191332942
#191332922
#191332782
#191332652
#191332582
C2×#145826462
#332×D432
C43×#15522
#1777443