Finite Group Databasebeta

← #25113039

Subgroups — #25113039

Order 11008.

1154 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
1C2×#14583604C211yesmaximal, characteristic
2C2×#14582974C211yesmaximal, characteristic
3#19137539C211yesmaximal, characteristic
4#19135554C211yesmaximal, characteristic, complemented
5#19135541C211yesmaximal, characteristic, complemented
6#19135027C211yesmaximal, characteristic, complemented
7#19135026C211yesmaximal, characteristic, complemented
8#19134906C211yesmaximal, characteristic, complemented
9#19134905C211yesmaximal, characteristic, complemented
10#19134680C211yesmaximal, characteristic, complemented
11#19134599C211yesmaximal, characteristic, complemented
12#19134414C211yesmaximal, characteristic, complemented
13#19134314C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#1823C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18#14583604—24no—
19#14583604C418yescomplemented
20C2×#13063324C2211yescharacteristic
21C2×#13063315—21no—
22C2×#13063305C2211yescharacteristic
23C2×#13063304—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063303—21no—
26C2×#13063290C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582974—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40#14582799—21no—
41#14582793—21no—
42#14582788—21no—
43#14582768C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46#14582750—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43D411yescharacteristic
65C22×C4×D43—21no—
66C22×C4×D43C2311yescharacteristic
67C2×#10621877—22no—
68C2×#10621877—22no—
69C2×#10621877—41no—
70C2×#10621872—22no—
71C2×#10621872—22no—
72C2×#10621872—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063324—22no—
76#13063324C2×C414yes—
77#13063315—28no—
78#13063305—22no—
79#13063305C2×C414yes—
80#13063304—22no—
81#13063304—28no—
82#13063304C2×C414yes—
83#13063303—28no—
84#13063290—22no—
85#13063290C2×C414yes—
86C4×C22⋊D43—28no—
87C4×C22⋊D43C2×C414yes—
88C4×C22⋊D43D414yes—
89#13063284—22no—
90#13063284—41no—
91#13063283—22no—
92#13063283—41no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4D411yescharacteristic
104C4⋊C4×D43—22no—
105C4⋊C4×D43C2×C414yes—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43D411yescharacteristic
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×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118Dic43⋊C8—22no—
119#13063250—22no—
120#13063250—41no—
121#13063248—22no—
122#13063248—41no—
123(C2×D43)⋊C8—22no—
124C8×Dic43—22no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C23×C4×C43—21no—
128C23×C4×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C2×C4⋊C4×C43—22no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C414yes—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C22⋊C8×C43—22no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43C2×D411yescharacteristic
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—24no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—81no—
153C22×C4×C43—81no—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43C22⋊C414yes—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—24no—
173C2×C4×D43—81no—
174C2×C4×D43—81no—
175C2×C4×D43C22×C412yes—
176C2×C4×D43C2×D412yes—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—24no—
183C2×Dic86—81no—
184C2×Dic86—81no—
185C2×Dic86C22×C412yes—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C4⋊C4×C43—24no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43C22×C412yes—
200C4⋊C4×C43C22×C412yes—
201C22⋊C4×C43—81no—
202C22⋊Dic43—24no—
203C22⋊Dic43—42no—
204C22⋊Dic43C22⋊C414yes—
205(C2×D43)⋊C4—24no—
206(C2×D43)⋊C4—42no—
207(C2×D43)⋊C4—81no—
208(C2×D43)⋊C4C22⋊C414yes—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—24no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43C22×C412yes—
215C4⋊Dic43#4112yes—
216Dic43⋊C4—24no—
217Dic43⋊C4—24no—
218Dic43⋊C4—24no—
219Dic43⋊C4—24no—
220Dic43⋊C4—42no—
221Dic43⋊C4—81no—
222Dic43⋊C4C22⋊C414yes—
223C4×Dic43—24no—
224C4×Dic43—42no—
225C4×Dic43—42no—
226C4×Dic43—42no—
227C4×Dic43C22×C412yes—
228C4×Dic43C2×D412yes—
229#10621877—44no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8#4112yes—
236#10621872—44no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43C2×C22⋊C412yes—
244C23×C43C22×D411yescharacteristic
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43C2×C22⋊C412yes—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
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—84no—
271C2×C4×C43C2×C22⋊C412yes—
272C2×C4×C43C23×C411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43H(5,𝔽2)11yescharacteristic
277C2×C4×C432−1+411yescharacteristic
278C22⋊D43—28no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43C2×C22⋊C412yes—
296C2×Dic43C2×C22⋊C412yes—
297C2×Dic43C2×C22⋊C412yes—
298C2×Dic43#13712yes—
299C2×Dic43#13712yes—
300C4×D43—22no—
301C4×D43—22no—
302C4×D43—22no—
303C4×D43—22no—
304C4×D43—84no—
305Dic86—22no—
306Dic86—22no—
307Dic86—41no—
308Dic86—41no—
309Dic86—84no—
310C8×C43—41no—
311C8×C43—41no—
312C43⋊C8—22no—
313C43⋊C8—41no—
314#22502—431nomaximal, Sylow
315C22×C43—22no—
316C22×C43—22no—
317C22×C43—22no—
318C22×C43—41no—
319C22×C43—41no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43C22×C22⋊C411yescharacteristic
323C22×C43#54611yescharacteristic
324C22×C43#54711yescharacteristic
325C22×C43C2×#13711yescharacteristic
326C22×C43C2×#13711yescharacteristic
327C22×C43#57611yescharacteristic
328C22×C43#57711yescharacteristic
329C2×D43—22no—
330C2×D43—22no—
331C2×D43—22no—
332C2×D43—41no—
333C2×D43—41no—
334C2×D43—41no—
335C2×D43—41no—
336C4×C43—22no—
337C4×C43—42no—
338C4×C43—42no—
339C4×C43—81no—
340C4×C43—81no—
341C4×C43C4×#4111yescharacteristic
342C4×C43#52011yescharacteristic
343C4×C43#54611yescharacteristic
344C4×C43#54711yescharacteristic
345Dic43—22no—
346Dic43—22no—
347Dic43—42no—
348Dic43—42no—
349Dic43—42no—
350Dic43—81no—
351Dic43#41914yes—
352C2×#554—431no—
353C2×#436—431no—
354#2354—431no—
355#1990—431no—
356#1987—431no—
357#1894—431no—
358#1894—431no—
359#1873—431no—
360#1873—431no—
361#1823—431no—
362#1823D4311yescharacteristic, complemented
363#1803—431no—
364C4×#103—431no—
365#1736—431no—
366#1736—431no—
367C2×C43—42no—
368C2×C43#233911yescharacteristic
369C2×C43C2×#41911yescharacteristic
370C2×C43#289711yescharacteristic
371C2×C43#333111yescharacteristic
372C2×C43#333311yescharacteristic
373C2×C43#335611yescharacteristic
374C2×C43#335711yescharacteristic
375D43—42no—
376C22×M16—431no—
377C22×M16—431no—
378#554—438no—
379#554—864no—
380C2×C4⋊Q8—431no—
381C2×#125—861no—
382C2×C22⋊Q8—431no—
383C2×C22⋊Q8—431no—
384C2×C22⋊Q8—861no—
385C2×C22⋊Q8—861no—
386C2×C4×Q8—431no—
387C2×C4×D4—431no—
388C2×C4×D4—861no—
389C2×#117—431no—
390C2×#117—431no—
391C22×C4⋊C4—431no—
392C22×C4⋊C4C2×D4311yescharacteristic
393#436—864no—
394C2×C4⋊C8—431no—
395C2×#103—431no—
396C2×#103—431no—
397C2×#103—431no—
398C2×#103—431no—
399C2×C22⋊C8—431no—
400C2×C22⋊C8C2×D4311yescharacteristic
401C2×C4×C8—431no—
402#390—861no—
403#388—861no—
404#388—861no—
405#384—431no—
406#380—431no—
407#380C2×D4311yescharacteristic
408C4×C4⋊C4—431no—
409C4×C4⋊C4—861no—
410#340—431no—
411#340—431no—
412#340—431no—
413#340—431no—
414#340—431no—
415#340—431no—
416#340—431no—
417#340—431no—
418#340C2×D4311yescharacteristic
419#340C2×D4311yescharacteristic
420#340C2×D4311yescharacteristic
421#340C2×D4311yescharacteristic
422C43#2250211yescharacteristic, complemented, Sylow
423C22×Q8—431no—
424C22×Q8—861no—
425C22×D4—431no—
426C23×C4—21no—
427C23×C4—431no—
428C23×C4—861no—
429C23×C4C22×D4311yescharacteristic
430C2×M16—862no—
431C2×M16—862no—
432C2×M16—862no—
433C2×M16—862no—
434C2×M16—1721no—
435C2×M16—1721no—
436C22×C8—431no—
437C22×C8—431no—
438C22×C8C22×D4311yescharacteristic
439C22×C8C22×D4311yescharacteristic
440C4⋊Q8—434no—
441C4⋊Q8—862no—
442#125—868no—
443C22⋊Q8—434no—
444C22⋊Q8—434no—
445C22⋊Q8—868no—
446C22⋊Q8—868no—
447C22⋊Q8—862no—
448C22⋊Q8—862no—
449C4×Q8—434no—
450C4×Q8—862no—
451C4×D4—434no—
452C4×D4—434no—
453C4×D4—868no—
454#117—862no—
455#117—862no—
456#117—1721no—
457#117—1721no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—434no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—862no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4C4×D4314yes—
474C2×C4⋊C4C22×D4311yescharacteristic
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—431no—
480C2×C22⋊C4—431no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C42—431no—
487C2×C42—861no—
488C2×C42—861no—
489C2×C42—861no—
490C2×C42—861no—
491C4⋊C8—862no—
492#103—862no—
493#103—862no—
494#103—1721no—
495#103—1721no—
496C22⋊C8—22no—
497C22⋊C8—862no—
498C4×C8—862no—
499#95—21no—
500#95—861no—
501#95—861no—
502C24—431no—
503C24D4×D4311yescharacteristic
504C2×Q8—432no—
505C2×Q8—864no—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—3441no—
512C2×Q8—3441no—
513C2×D4—434no—
514C2×D4—862no—
515C2×D4—862no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—431no—
528C22×C4—431no—
529C22×C4—431no—
530C22×C4—432no—
531C22×C4—432no—
532C22×C4—864no—
533C22×C4—861no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—861no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4—3441no—
542C22×C4—3441no—
543C22×C4C2×C4×D4312yes—
544C22×C4D4×D4311yescharacteristic
545C22×C4D4×D4312yes—
546C22×C4C23×D4311yescharacteristic
547M16—1724no—
548M16—1724no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—432no—
556C2×C8—861no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C4⋊C4—24no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—434no—
569C4⋊C4—432no—
570C4⋊C4—432no—
571C4⋊C4—864no—
572C4⋊C4—864no—
573C4⋊C4—864no—
574C4⋊C4—864no—
575C4⋊C4—864no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—3441no—
581C4⋊C4—1722no—
582C4⋊C4C2×C4×D4312yes—
583C4⋊C4C2×C4×D4312yes—
584C22⋊C4—81no—
585C22⋊C4—434no—
586C22⋊C4—434no—
587C22⋊C4—864no—
588C22⋊C4—864no—
589C22⋊C4—3441no—
590C22⋊C4—1722no—
591C22⋊C4—1722no—
592C42—432no—
593C42—432no—
594C42—864no—
595C42—1722no—
596C42—1722no—
597C42—1722no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—432no—
605C23—861no—
606C23—861no—
607C23—861no—
608C23—861no—
609C23—861no—
610C23—861no—
611C23C22⋊C4×D4312yes—
612C23C2×D4×D4311yescharacteristic
613Q8—862no—
614Q8—862no—
615Q8—3444no—
616Q8—1721no—
617Q8—1721no—
618D4—868no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—432no—
639C2×C4—432no—
640C2×C4—432no—
641C2×C4—432no—
642C2×C4—432no—
643C2×C4—861no—
644C2×C4—861no—
645C2×C4—861no—
646C2×C4—861no—
647C2×C4—862no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—3444no—
655C2×C4—1721no—
656C2×C4—1721no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4C22⋊C4×D4312yes—
665C2×C4C22×C4×D4311yescharacteristic
666C2×C4C2×D4×D4311yescharacteristic
667C2×C4#41×D4311yescharacteristic
668C2×C4#41×D4311yescharacteristic
669C2×C4#1306337111yescharacteristic
670C2×C4#1306337211yescharacteristic
671C8—41no—
672C8—41no—
673C8—862no—
674C8—1721no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—862no—
683C22—862no—
684C22—862no—
685C22—1721no—
686C22—1721no—
687C22—1721no—
688C22—1721no—
689C22C2×C22⋊C4×D4311yescharacteristic
690C22#1458354111yescharacteristic
691C22#1458354711yescharacteristic
692C22#137×D4311yescharacteristic
693C22#137×D4311yescharacteristic
694C22#1458370011yescharacteristic
695C22#1458370511yescharacteristic
696C4—22no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—434no—
702C4—862no—
703C4—862no—
704C4—3441no—
705C4—1722no—
706C4—1722no—
707C4—1722no—
708C4#1458336711yescharacteristic
709C4#1458337911yescharacteristic
710C4#1458354111yescharacteristic
711C4#1458354711yescharacteristic
712C2—42no—
713C2—1722no—
714C2#1913741911yescharacteristic
715C2#419×D4311yescharacteristic
716C2#1914311611yescharacteristic
717C2#1914690911yescharacteristic
718C2#1914693111yescharacteristic
719C2#1914720311yescharacteristic
720C2#1914721411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1823C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1823D43
hypocenterC43#22502
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #19135554C2semidirect
5. #19135541C2semidirect
6. #19135027C2semidirect
7. #19135026C2semidirect
8. #19134906C2semidirect
9. #19134905C2semidirect
10. #19134680C2semidirect
11. #19134599C2semidirect
12. #19134414C2semidirect
13. #19134314C2semidirect
14. #19134313C2semidirect
15. C43×#1823C2semidirect
19. #14583604C4semidirect
362. #1823D43semidirect
422. C43#22502semidirect

Maximal subgroups

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

subgroupindex
C2×#145836042
C2×#145829742
#191375392
#191355542
#191355412
#191350272
#191350262
#191349062
#191349052
#191346802
#191345992
#191344142
#191343142
#191343132
C43×#18232
#2250243