Finite Group Databasebeta

← #25130618

Subgroups — #25130618

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×#14583591C211yesmaximal, characteristic
2C2×#14583209C211yesmaximal, characteristic, complemented
3C2×#14582991C211yesmaximal, characteristic, complemented
4#19139506C211yesmaximal, characteristic
5#19135796C211yesmaximal, characteristic, complemented
6#19135604C211yesmaximal, characteristic, complemented
7#19135603C211yesmaximal, characteristic, complemented
8#19135558C211yesmaximal, characteristic, complemented
9#19135387C211yesmaximal, characteristic
10#19134906C211yesmaximal, characteristic, complemented
11#19134900C211yesmaximal, characteristic, complemented
12#19134793C211yesmaximal, characteristic, complemented
13#19134782C211yesmaximal, characteristic, complemented
14#19134608C211yesmaximal, characteristic, complemented
15C43×#2035C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17#14583591—24no—
18#14583591—24no—
19C2×#13063320—21no—
20C2×#13063316—21no—
21C2×#13063316C2211yescharacteristic
22C2×#13063309—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×#13063301C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C2×#13063281—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32#14583209—24no—
33#14582991—24no—
34C2×#13063258C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582833—21no—
46#14582814—21no—
47#14582792—21no—
48#14582788—21no—
49#14582764C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43D411yescharacteristic
65C23×Dic43—21no—
66C22×C4×D43C2311yescharacteristic
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063320—28no—
73#13063316—28no—
74#13063316—22no—
75#13063316D414yes—
76#13063309—28no—
77#13063305—22no—
78#13063305—41no—
79#13063304—22no—
80#13063304—41no—
81#13063301—22no—
82#13063301—22no—
83Q8×Dic43—22no—
84Q8×Dic43D414yes—
85#13063290—22no—
86#13063290—22no—
87C4×C22⋊D43—22no—
88C4×C22⋊D43—22no—
89#13063283—22no—
90#13063283—22no—
91#13063281—28no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—22no—
96C2×C4⋊Dic43—22no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4D411yescharacteristic
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#13063258—22no—
118#13063258—22no—
119Dic43⋊C8—22no—
120#13063250—22no—
121#13063250—22no—
122#13063249—41no—
123#13063248—22no—
124C22⋊(C43⋊C8)—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—41no—
127C8×Dic43—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×Q8×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22⋊Q8×C43—22no—
136C22⋊Q8×C43—22no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143#106×C43—22no—
144#103×C43—22no—
145#103×C43—41no—
146C22⋊C8×C43—41no—
147#95×C43—21no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43C2×D412yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—41no—
171C22×Dic43—24no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
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—21no—
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×C43C2×D412yes—
206C22⋊C4×C43—24no—
207C22⋊C4×C43—42no—
208C22⋊Dic43—22no—
209C22⋊Dic43—42no—
210#10621885—28no—
211(C2×D43)⋊C4—24no—
212(C2×D43)⋊C4—24no—
213(C2×D43)⋊C4—22no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216C4⋊Dic43—24no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—24no—
220C4⋊Dic43—24no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—42no—
224C4⋊Dic43C2×D412yes—
225C4⋊Dic43C2×D412yes—
226Dic43⋊C4—24no—
227Dic43⋊C4—24no—
228Dic43⋊C4—22no—
229Dic43⋊C4—42no—
230Dic43⋊C4—42no—
231C4×Dic43—24no—
232C4×Dic43—24no—
233C4×Dic43—42no—
234C4×Dic43C2×D412yes—
235C4×Dic43C2×D412yes—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8#4112yes—
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—
257Q8×C43—22no—
258Q8×C43—22no—
259Q8×C43—41no—
260Q8×C43—41no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
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×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43C22×D411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C432−1+411yescharacteristic
286C22⋊D43—44no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—48no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43#12012yes—
308C2×Dic43#12012yes—
309C4×D43—41no—
310C4×D43—41no—
311C4×D43—41no—
312C4×D43—41no—
313Dic86—22no—
314Dic86—22no—
315Dic86—41no—
316Dic86—41no—
317C8×C43—41no—
318C8×C43—41no—
319C43⋊C8—22no—
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—41no—
356Dic43—42no—
357Dic43—42no—
358Dic43—81no—
359C2×#552—431no—
360C2×#479—431no—
361C2×C4×Q16—431no—
362#2536—431no—
363#2036—431no—
364#2035D4311yescharacteristic, complemented
365#2001—431no—
366#2001—431no—
367#1991—431no—
368#1954—431no—
369#1873—431no—
370#1872—431no—
371#1854—431no—
372#1852—431no—
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⋊Q8C2×D4311yescharacteristic
394C2×C4×Q8—431no—
395C2×C4×Q8—431no—
396C2×C4×D4—431no—
397C2×#117—431no—
398C2×#117—861no—
399C22×C4⋊C4—431no—
400#479—864no—
401C4×Q16—864no—
402C2×#107—431no—
403C2×#107—431no—
404C2×#106C2×D4311yescharacteristic
405C2×C4⋊C8—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#103C2×D4311yescharacteristic
411C2×#103C2×D4311yescharacteristic
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#340—431no—
429#340C2×D4311yescharacteristic
430C43#2412711yescharacteristic, complemented, Sylow
431C22×Q8—431no—
432C22×Q8C22×D4311yescharacteristic
433C22×D4—431no—
434C23×C4—431no—
435C23×C4—861no—
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—22no—
450C22⋊Q8—22no—
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—868no—
464#117—862no—
465#117—862no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—862no—
472C2×C4⋊C4—862no—
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⋊C4—861no—
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—431no—
487C2×C22⋊C4—431no—
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—862no—
498#107—862no—
499#106—22no—
500C4⋊C8—862no—
501#103—22no—
502#103—41no—
503#103—862no—
504#103—862no—
505#103—862no—
506#103—1721no—
507C22⋊C8—41no—
508C22⋊C8—862no—
509C22⋊C8—862no—
510C22⋊C8—1721no—
511C4×C8—862no—
512#95—21no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—431no—
517C24D4×D4311yescharacteristic
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—432no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8D4×D4312yes—
530C2×D4—862no—
531C2×D4—862no—
532C2×D4—1721no—
533C22×C4—21no—
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—431no—
544C22×C4—431no—
545C22×C4—431no—
546C22×C4—864no—
547C22×C4—861no—
548C22×C4—861no—
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—1722no—
558C22×C4—1722no—
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—21no—
568C2×C8—432no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—432no—
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—861no—
592C4⋊C4—1722no—
593C4⋊C4—1722no—
594C4⋊C4—1722no—
595C4⋊C4D4×D4312yes—
596C22⋊C4—24no—
597C22⋊C4—42no—
598C22⋊C4—862no—
599C22⋊C4—864no—
600C22⋊C4—864no—
601C22⋊C4—862no—
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#1306334612yes—
624C23C2×D4×D4311yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—862no—
630Q8—862no—
631Q8—1721no—
632Q8—1721no—
633D4—1724no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—41no—
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—432no—
654C2×C4—432no—
655C2×C4—861no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—862no—
660C2×C4—861no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—1721no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1728no—
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×C4#41×D4311yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337211yescharacteristic
685C8—41no—
686C8—41no—
687C8—862no—
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#1458353811yescharacteristic
705C22#1458354711yescharacteristic
706C22C2×#1306334611yescharacteristic
707C22#1458369811yescharacteristic
708C22#1458371311yescharacteristic
709C22#1458371511yescharacteristic
710C4—41no—
711C4—42no—
712C4—42no—
713C4—81no—
714C4—81no—
715C4—862no—
716C4—862no—
717C4—3441no—
718C4—1722no—
719C4—1722no—
720C4—1721no—
721C4—1722no—
722C4#1458340711yescharacteristic
723C4#1458347611yescharacteristic
724C4#1458355711yescharacteristic
725C4#1458356711yescharacteristic
726C2—42no—
727C2—3441no—
728C2#1913793511yescharacteristic
729C2#1914381211yescharacteristic
730C2#1914388711yescharacteristic
731C2#1914648811yescharacteristic
732C2#1914685811yescharacteristic
733C2#1914696111yescharacteristic
734C2#1914716311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2035C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#2035D43
hypocenterC43#24127
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#14583209C2semidirect
3. C2×#14582991C2semidirect
5. #19135796C2semidirect
6. #19135604C2semidirect
7. #19135603C2semidirect
8. #19135558C2semidirect
10. #19134906C2semidirect
11. #19134900C2semidirect
12. #19134793C2semidirect
13. #19134782C2semidirect
14. #19134608C2semidirect
15. C43×#2035C2semidirect
364. #2035D43semidirect
430. C43#24127semidirect

Maximal subgroups

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

subgroupindex
C2×#145835912
C2×#145832092
C2×#145829912
#191395062
#191357962
#191356042
#191356032
#191355582
#191353872
#191349062
#191349002
#191347932
#191347822
#191346082
C43×#20352
#2412743