Finite Group Databasebeta

← #25107921

Subgroups — #25107921

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583046C211yesmaximal, characteristic
2#19137284C211yesmaximal, characteristic, complemented
3#19137188C211yesmaximal, characteristic, complemented
4#19135474C211yesmaximal, characteristic, complemented
5#19135459C211yesmaximal, characteristic, complemented
6#19135290C211yesmaximal, characteristic, complemented
7#19135269C211yesmaximal, characteristic, complemented
8#19135235C211yesmaximal, characteristic, complemented
9#19135214C211yesmaximal, characteristic, complemented
10#19134944C211yesmaximal, characteristic, complemented
11#19134930C211yesmaximal, characteristic, complemented
12#19134912C211yesmaximal, characteristic, complemented
13#19134533C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1852C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14583046C418yescomplemented
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582804C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582799—21no—
40#14582795C2211yescharacteristic
41#14582791—21no—
42#14582778—21no—
43#14582778—21no—
44#14582775—21no—
45#14582773—21no—
46#14582756—21no—
47#14582756—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C2×#10621898—22no—
61C2×#10621898—41no—
62C2×#10621898—41no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898C2×C414yescomplemented
66C22×Dic86C2311yescharacteristic
67C22×D172C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C2×#10621873—41no—
74C2×#10621873—41no—
75C2×#10621873C2×C414yescomplemented
76C2×D344—41no—
77C2×D344—41no—
78C2×D344C2×C414yescomplemented
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063299—22no—
82#13063299C2×C414yes—
83#13063287—41no—
84#13063287—41no—
85#13063284—41no—
86#13063284—41no—
87C2×C4⋊Dic43D411yescharacteristic
88C2×C4⋊Dic43D411yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43D411yescharacteristic
92C2×C22⋊Dic43D411yescharacteristic
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104#13063250C2×C414yescomplemented
105#13063248—41no—
106#13063248—41no—
107#13063247C2×C414yescomplemented
108#13063245—41no—
109#13063245—41no—
110#13063245—41no—
111#13063245—41no—
112C22⋊(C43⋊C8)—22no—
113#13063235—41no—
114C8×Dic43—41no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—41no—
127C2×C4⋊C4×C43—41no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133#107×C43—41no—
134#107×C43—41no—
135C22⋊C8×C43C2×C414yescomplemented
136#95×C43—21no—
137C24×C43C2×D411yescharacteristic
138C23×D43—21no—
139C23×D43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—42no—
149C22×C4×C43—81no—
150C22×C4×C43—81no—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4112yes—
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—24no—
156C2×C22⋊D43—24no—
157C2×C22⋊D43—42no—
158C2×C22⋊D43—42no—
159C2×C22⋊D43—81no—
160C2×C22⋊D43—81no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167#10621898—44no—
168#10621898—44no—
169#10621898—44no—
170#10621898—44no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172C22×C412yes—
182C2×D172C22×C412yes—
183C2×C4×D43—24no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—81no—
188C2×C4×D43—81no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86C22×C412yes—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43C22×C412yes—
200C2×C8×C43C22×C412yes—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—42no—
210C22⋊C4×C43—81no—
211C22⋊Dic43—41no—
212C22⋊Dic43—41no—
213(C2×D43)⋊C4—24no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—81no—
216(C2×D43)⋊C4—81no—
217(C2×D43)⋊C4—81no—
218(C2×D43)⋊C4—81no—
219(C2×D43)⋊C4—81no—
220(C2×D43)⋊C4—81no—
221C4⋊Dic43—21no—
222C4⋊Dic43—41no—
223C4⋊Dic43—41no—
224C4⋊Dic43C22×C412yes—
225Dic43⋊C4—81no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—81no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237D344—44no—
238#10621873—44no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43C4×D412yes—
246C23×C43C22×D411yescharacteristic
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
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×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—84no—
280C2×C4×C43C4×D412yes—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43H(5,𝔽2)11yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C22⋊D43—48no—
288C22⋊D43—84no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307D172—22no—
308D172—22no—
309D172—22no—
310D172—22no—
311D172—41no—
312D172—41no—
313D172—41no—
314D172—41no—
315C4×D43—48no—
316C4×D43—84no—
317Dic86—22no—
318Dic86—22no—
319Dic86—41no—
320Dic86—41no—
321C8×C43—22no—
322C8×C43—22no—
323C43⋊C8—41no—
324C43⋊C8—41no—
325#22055—431nomaximal, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43C2×C4×D411yescharacteristic
334C22×C43#53411yescharacteristic
335C22×C43#53511yescharacteristic
336C22×C43#57611yescharacteristic
337C22×C43#57611yescharacteristic
338C22×C43#57711yescharacteristic
339C22×C43#57811yescharacteristic
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C4×C43—22no—
355C4×C43—81no—
356C4×C43—81no—
357C4×C43—81no—
358C4×C43—81no—
359C4×C43#51811yescharacteristic
360C4×C43#51811yescharacteristic
361C4×C43#53811yescharacteristic
362C4×C43#53811yescharacteristic
363Dic43—42no—
364Dic43—41no—
365Dic43—41no—
366Dic43—42no—
367Dic43—41no—
368Dic43—41no—
369C2×#449—431no—
370#2324—431no—
371#2311—431no—
372#1973—431no—
373#1970—431no—
374#1936—431no—
375#1933—431no—
376#1928—431no—
377#1925—431no—
378#1879—431no—
379#1877—431no—
380#1874—431no—
381#1852D4311yescharacteristic, complemented
382#1788—431no—
383#1750—431no—
384C2×C43—42no—
385C2×C43#232111yescharacteristic
386C2×C43#294611yescharacteristic
387C2×C43#295111yescharacteristic
388C2×C43#319811yescharacteristic
389C2×C43#320311yescharacteristic
390C2×C43#322011yescharacteristic
391C2×C43#322511yescharacteristic
392D43—82no—
393D43—82no—
394C22×#41—431no—
395C22×SD16—431no—
396C22×D8—431no—
397C2×#121—431no—
398C2×C4×D4—431no—
399C2×#117—431no—
400C22×C4⋊C4C2×D4311yescharacteristic
401#449—438no—
402C2×#107C2×D4311yescharacteristic
403C2×#107C2×D4311yescharacteristic
404C2×#103—431no—
405C2×#103—431no—
406C2×#103—431no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×C22⋊C8—431no—
413C2×C22⋊C8C2×D4311yescharacteristic
414C2×#97—431no—
415C2×C4×C8—431no—
416#391—431no—
417#391—431no—
418#390—431no—
419#390—431no—
420#390—431no—
421#390—861no—
422#389—431no—
423#388—861no—
424#386—861no—
425#386—861no—
426#386—861no—
427#385—861no—
428#380—861no—
429#380—861no—
430#380C2×D4311yescharacteristic
431C4×C4⋊C4—431no—
432#340—431no—
433#340—431no—
434#340C2×D4311yescharacteristic
435#340C2×D4311yescharacteristic
436#336—431no—
437#336—431no—
438C43#2205511yescharacteristic, complemented, Sylow
439C2×#41—434no—
440C2×#41—862no—
441C2×#41—1721no—
442C2×#41—1721no—
443C2×#41—1721no—
444C2×#41—1721no—
445C22×Q8—431no—
446C22×D4—431no—
447C22×D4—431no—
448C22×D4—861no—
449C22×D4—861no—
450C23×C4—21no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4C22×D4311yescharacteristic
454C2×SD16—434no—
455C2×SD16—1721no—
456C2×SD16—1721no—
457C2×D8—434no—
458C2×D8—1721no—
459C2×D8—1721no—
460C22×C8—431no—
461C22×C8—431no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464#121—434no—
465#121—862no—
466C4×D4—1721no—
467C4×D4—1721no—
468#117—1721no—
469#117—1721no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—431no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C42—431no—
493C2×C42—431no—
494C2×C42—861no—
495#107—41no—
496#107—41no—
497#103—434no—
498#103—1721no—
499#103—1721no—
500#102—434no—
501#102—1721no—
502#102—1721no—
503#102—1721no—
504#102—1721no—
505C22⋊C8—862no—
506C22⋊C8C4×D4314yescomplemented
507#97—1721no—
508C4×C8—1721no—
509#95—21no—
510#95—861no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—861no—
517C24—861no—
518C24D4×D4311yescharacteristic
519#41—1724no—
520#41—1724no—
521#41—1724no—
522#41—1724no—
523C2×Q8—432no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×D4—432no—
530C2×D4—432no—
531C2×D4—864no—
532C2×D4—864no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—3441no—
544C2×D4—3441no—
545C2×D4—1722no—
546C2×D4—1722no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—864no—
565C22×C4—3441no—
566C22×C4—3441no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4C2×C4×D4312yes—
571C22×C4D4×D4311yescharacteristic
572C22×C4#1062190212yes—
573C22×C4C23×D4311yescharacteristic
574SD16—1724no—
575D8—1724no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8C2×C4×D4312yes—
587C2×C8C2×C4×D4312yes—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—432no—
598C4⋊C4—861no—
599C4⋊C4—3441no—
600C4⋊C4—1721no—
601C4⋊C4—1721no—
602C22⋊C4—81no—
603C22⋊C4—864no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—3441no—
608C22⋊C4—3441no—
609C22⋊C4—3441no—
610C22⋊C4—1722no—
611C22⋊C4—1721no—
612C22⋊C4—1721no—
613C42—861no—
614C42—861no—
615C42—861no—
616C42—861no—
617C42—3441no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—862no—
625C23—862no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23#1306328712yes—
639C23C2×D4×D4311yescharacteristic
640Q8—862no—
641Q8—862no—
642Q8—1721no—
643Q8—1721no—
644D4—862no—
645D4—862no—
646D4—862no—
647D4—862no—
648D4—3444no—
649D4—1728no—
650D4—1721no—
651D4—1721no—
652D4—1721no—
653D4—1721no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—84no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—3444no—
688C2×C4—1728no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4#1306328712yes—
694C2×C4C22×C4×D4311yescharacteristic
695C2×C4C2×#1062190211yescharacteristic
696C2×C4#1306337011yescharacteristic
697C2×C4#1306337011yescharacteristic
698C2×C4#1306337111yescharacteristic
699C2×C4#1306337111yescharacteristic
700C8—22no—
701C8—22no—
702C8—1721no—
703C8—1721no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—3441no—
712C22—3441no—
713C22—3441no—
714C22—3441no—
715C22—3441no—
716C22—3441no—
717C22—3441no—
718C22—3441no—
719C22—1722no—
720C22—1722no—
721C22—1722no—
722C22—1722no—
723C22—1722no—
724C22—1722no—
725C22C2×#1306328711yescharacteristic
726C22#1458346011yescharacteristic
727C22#1458346411yescharacteristic
728C22#1458370011yescharacteristic
729C22#1458370311yescharacteristic
730C22#1458370811yescharacteristic
731C22#1458371211yescharacteristic
732C4—22no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—1722no—
738C4—1721no—
739C4—1721no—
740C4—1722no—
741C4—1721no—
742C4—1721no—
743C4#1458337111yescharacteristic
744C4#1458337111yescharacteristic
745C4#1458348911yescharacteristic
746C4#1458348911yescharacteristic
747C2—42no—
748C2—3442no—
749C2—3442no—
750C2#1913725211yescharacteristic
751C2#1914342511yescharacteristic
752C2#1914346911yescharacteristic
753C2#1914545411yescharacteristic
754C2#1914549911yescharacteristic
755C2#1914564111yescharacteristic
756C2#1914571011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1852C2
socleC23×C43C22×D4
prime radicalC2×#14583046C2
cosocleC22×C4×C43C24
hypercenter#1852D43
hypocenterC43#22055
LCSG ▷ C2×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. #19137284C2semidirect
3. #19137188C2semidirect
4. #19135474C2semidirect
5. #19135459C2semidirect
6. #19135290C2semidirect
7. #19135269C2semidirect
8. #19135235C2semidirect
9. #19135214C2semidirect
10. #19134944C2semidirect
11. #19134930C2semidirect
12. #19134912C2semidirect
13. #19134533C2semidirect
14. #19134363C2semidirect
15. C43×#1852C2semidirect
22. #14583046C4semidirect
65. C2×#10621898C2×C4semidirect
75. C2×#10621873C2×C4semidirect
78. C2×D344C2×C4semidirect
104. #13063250C2×C4semidirect
107. #13063247C2×C4semidirect
135. C22⋊C8×C43C2×C4semidirect
381. #1852D43semidirect
438. C43#22055semidirect
506. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830462
#191372842
#191371882
#191354742
#191354592
#191352902
#191352692
#191352352
#191352142
#191349442
#191349302
#191349122
#191345332
#191343632
C43×#18522
#2205543