Finite Group Databasebeta

← #25101763

Subgroups — #25101763

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583505C211yesmaximal, characteristic
2C2×#14582959C211yesmaximal, characteristic, complemented
3#19136949C211yesmaximal, characteristic, complemented
4#19135553C211yesmaximal, characteristic, complemented
5#19135522C211yesmaximal, characteristic, complemented
6#19135521C211yesmaximal, characteristic, complemented
7#19134916C211yesmaximal, characteristic, complemented
8#19134916C211yesmaximal, characteristic, complemented
9#19134911C211yesmaximal, characteristic, complemented
10#19134911C211yesmaximal, characteristic, complemented
11#19134419C211yesmaximal, characteristic, complemented
12#19134419C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1989C211yesmaximal, characteristic, complemented
16#14583505—24no—
17#14583505C418yescomplemented
18C2×#13063322C2211yescharacteristic
19C2×#13063310—21no—
20C2×#13063310—21no—
21C2×#13063300—21no—
22C2×#13063300—21no—
23C2×#13063300C2211yescharacteristic
24C2×#13063300C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×#13063283C2211yescharacteristic
28C2×#13063282C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14582959—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×#13063235C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×Dic43⋊C4—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582750—21no—
49C4×(C2×D43)⋊C4—21no—
50#14582746—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#125×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×D172—21no—
63C22×D172—21no—
64C22×D172—21no—
65C22×D172—21no—
66C22×D172C2311yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063322—22no—
75#13063322C2×C414yescomplemented
76#13063310—28no—
77#13063310—28no—
78#13063300—22no—
79#13063300—22no—
80#13063300—28no—
81#13063300—28no—
82#13063300C2×C414yes—
83#13063300C2×C414yes—
84#13063287—22no—
85#13063287—22no—
86#13063287C2×C414yescomplemented
87#13063287C2×C414yescomplemented
88#13063283—22no—
89#13063283—22no—
90#13063282C2×C414yes—
91#13063282D414yes—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4D411yescharacteristic
96C2×Dic43⋊C4D411yescharacteristic
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×(C2×D43)⋊C4D411yescharacteristic
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111C4⋊(C43⋊C8)—22no—
112#13063247—22no—
113#13063247—22no—
114#13063247—22no—
115#13063247—22no—
116#13063245—22no—
117#13063245—22no—
118#13063245—22no—
119#13063245—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063235—22no—
123C8×Dic43—22no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129#125×C43—22no—
130#125×C43C2×C414yescomplemented
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139C4⋊C8×C43—22no—
140#95×C43—21no—
141C23×D43—21no—
142C23×D43—21no—
143C23×D43C2×D411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—24no—
159C2×D172—24no—
160C2×D172—24no—
161C2×D172—24no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—81no—
171C2×D172—81no—
172C2×D172—81no—
173C2×D172—81no—
174C2×D172—81no—
175C2×D172—81no—
176C2×D172—81no—
177C2×D172—81no—
178C2×D172C22×C412yes—
179C2×D172C22×C412yes—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—24no—
185C2×C4×D43—24no—
186C2×C4×D43—24no—
187C2×C4×D43—81no—
188C2×C4×D43—81no—
189C2×C4×D43—81no—
190C2×C4×D43—81no—
191C2×C4×D43—81no—
192C2×C4×D43—81no—
193C2×C4×D43C22×C412yes—
194C2×C4×D43C2×D412yes—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C4⋊C4×C43—24no—
202C4⋊C4×C43—24no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43C22×C412yes—
208C4⋊C4×C43C22×C412yes—
209C4⋊C4×C43#4112yes—
210C4⋊C4×C43#4112yes—
211C42×C43—81no—
212C42×C43C22×C412yes—
213C42×C43C2×D412yes—
214(C2×D43)⋊C4—24no—
215(C2×D43)⋊C4—24no—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—24no—
218(C2×D43)⋊C4—24no—
219(C2×D43)⋊C4C22⋊C414yes—
220(C2×D43)⋊C4C22⋊C414yes—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43#4112yes—
224C4⋊Dic43#4112yes—
225Dic43⋊C4—24no—
226Dic43⋊C4C22⋊C414yes—
227Dic43⋊C4C22⋊C414yes—
228C4×Dic43—24no—
229C4×Dic43—81no—
230C4×Dic43—81no—
231C4×Dic43—81no—
232C4×Dic43C22×C412yes—
233C4×Dic43C2×D412yes—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C23×C43C22×D411yescharacteristic
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
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—
261C22×D43C2×C22⋊C412yes—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
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×C43C2×C22⋊C412yes—
279C2×C4×C43C2×C22⋊C412yes—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43C2×C22⋊C412yes—
299C2×Dic43C2×C22⋊C412yes—
300C2×Dic43C2×C22⋊C412yes—
301D172—22no—
302D172—22no—
303D172—22no—
304D172—22no—
305D172—41no—
306D172—41no—
307D172—41no—
308D172—41no—
309D172—84no—
310D172—84no—
311D172—84no—
312D172—84no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—84no—
318C4×D43—84no—
319C4×D43—84no—
320C8×C43—41no—
321C8×C43—41no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324#21399—431nomaximal, Sylow
325C22×C43C22×C22⋊C411yescharacteristic
326C22×C43#52511yescharacteristic
327C22×C43#52511yescharacteristic
328C22×C43#57611yescharacteristic
329C22×C43#57611yescharacteristic
330C22×C43#57711yescharacteristic
331C22×C43#57711yescharacteristic
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—22no—
335C2×D43—41no—
336C2×D43—41no—
337C2×D43—41no—
338C2×D43—41no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43C4×#4111yescharacteristic
360C4×C43C4×#4111yescharacteristic
361C4×C43#53211yescharacteristic
362C4×C43#53211yescharacteristic
363Dic43—22no—
364Dic43—22no—
365Dic43—22no—
366Dic43—42no—
367Dic43—42no—
368C2×#540—431no—
369C2×#433—431no—
370#2274—431no—
371#1989—431no—
372#1989D4311yescharacteristic, complemented
373#1982—431no—
374#1982—431no—
375#1875—431no—
376#1875—431no—
377#1874—431no—
378#1874—431no—
379#1762—431no—
380#1762—431no—
381C4×#102—431no—
382C4×#102—431no—
383C2×C43#229711yescharacteristic
384C2×C43#289711yescharacteristic
385C2×C43#289711yescharacteristic
386C2×C43#311911yescharacteristic
387C2×C43#311911yescharacteristic
388C2×C43#312211yescharacteristic
389C2×C43#312611yescharacteristic
390D43—42no—
391D43—82no—
392D43—82no—
393#540—438no—
394#540—864no—
395C2×#127—431no—
396C2×#125C2×D4311yescharacteristic
397C2×#123—861no—
398C2×#123—861no—
399C2×#121—431no—
400C2×#121—431no—
401C2×#121—861no—
402C2×#121—861no—
403C2×C4×D4—431no—
404C2×C4×D4—431no—
405C2×#117—431no—
406C2×#117—431no—
407C22×C4⋊C4—431no—
408#433—864no—
409C2×C4⋊C8—431no—
410C2×C4⋊C8C2×D4311yescharacteristic
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×C22⋊C8—431no—
420C2×C22⋊C8—431no—
421C2×#97—431no—
422C2×C4×C8—431no—
423C4×C4⋊C4—431no—
424C4×C4⋊C4—431no—
425C4×C4⋊C4—431no—
426C4×C4⋊C4—861no—
427C4×C4⋊C4—861no—
428C4×C4⋊C4C2×D4311yescharacteristic
429C4×C22⋊C4—861no—
430C4×C22⋊C4—861no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340C2×D4311yescharacteristic
436#340C2×D4311yescharacteristic
437#340C2×D4311yescharacteristic
438#340C2×D4311yescharacteristic
439C43#2139911yescharacteristic, complemented, Sylow
440C22×D4—431no—
441C22×D4—431no—
442C22×D4—861no—
443C22×D4—861no—
444C22×D4—861no—
445C22×D4—861no—
446C23×C4—431no—
447C23×C4—861no—
448C23×C4—861no—
449C23×C4—861no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8C22×D4311yescharacteristic
453C22×C8C22×D4311yescharacteristic
454#127—434no—
455#127—862no—
456#125—22no—
457#125C4×D4314yescomplemented
458#123—868no—
459#123—868no—
460#121—434no—
461#121—434no—
462#121—868no—
463#121—868no—
464#121—862no—
465#121—862no—
466C4×D4—434no—
467C4×D4—434no—
468C4×D4—862no—
469C4×D4—862no—
470#117—434no—
471#117—434no—
472#117—862no—
473#117—862no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C22⋊C4—431no—
488C2×C22⋊C4—431no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C42—21no—
495C2×C42—431no—
496C2×C42—861no—
497C2×C42—861no—
498C2×C42—861no—
499C2×C42—861no—
500C2×C42C22×D4311yescharacteristic
501C4⋊C8—22no—
502C4⋊C8—862no—
503#102—862no—
504#102—862no—
505#102—862no—
506#102—862no—
507#102—862no—
508#102—862no—
509#102—862no—
510#102—862no—
511C22⋊C8—862no—
512C22⋊C8—862no—
513#97—862no—
514C4×C8—862no—
515#95—21no—
516#95—861no—
517#95—861no—
518#95—861no—
519C24—431no—
520C24—861no—
521C24—861no—
522C2×D4—432no—
523C2×D4—432no—
524C2×D4—864no—
525C2×D4—864no—
526C2×D4—864no—
527C2×D4—864no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—861no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—3441no—
539C2×D4—3441no—
540C2×D4—3441no—
541C2×D4—3441no—
542C2×D4—3441no—
543C2×D4—3441no—
544C2×D4—3441no—
545C2×D4—3441no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—431no—
551C22×C4—431no—
552C22×C4—431no—
553C22×C4—432no—
554C22×C4—432no—
555C22×C4—864no—
556C22×C4—864no—
557C22×C4—864no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—3441no—
565C22×C4—3441no—
566C22×C4—3441no—
567C22×C4—3441no—
568C22×C4—3441no—
569C22×C4—3441no—
570C22×C4D4×D4311yescharacteristic
571C22×C4D4×D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—434no—
592C4⋊C4—434no—
593C4⋊C4—432no—
594C4⋊C4—432no—
595C4⋊C4—864no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4C2×C4×D4312yes—
599C4⋊C4C2×C4×D4312yes—
600C4⋊C4#1062190212yes—
601C4⋊C4#1062190212yes—
602C22⋊C4—434no—
603C22⋊C4—434no—
604C22⋊C4—864no—
605C22⋊C4—864no—
606C22⋊C4—864no—
607C22⋊C4—864no—
608C22⋊C4—864no—
609C42—81no—
610C42—432no—
611C42—432no—
612C42—864no—
613C42—3441no—
614C42—3441no—
615C42—3441no—
616C42C2×C4×D4312yes—
617C42D4×D4312yes—
618C23—432no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—862no—
626C23—862no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23C2×D4×D4311yescharacteristic
640D4—862no—
641D4—862no—
642D4—862no—
643D4—862no—
644D4—3444no—
645D4—3444no—
646D4—3444no—
647D4—3444no—
648D4—1721no—
649D4—1721no—
650D4—1721no—
651D4—1721no—
652C2×C4—21no—
653C2×C4—21no—
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—432no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—3444no—
684C2×C4—3444no—
685C2×C4—3444no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4C22⋊C4×D4312yes—
691C2×C4C22⋊C4×D4312yes—
692C2×C4C22×C4×D4311yescharacteristic
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4#41×D4311yescharacteristic
695C2×C4#41×D4311yescharacteristic
696C2×C4C2×#1062190211yescharacteristic
697C2×C4C2×#1062190211yescharacteristic
698C8—41no—
699C8—41no—
700C8—1721no—
701C8—1721no—
702C22—862no—
703C22—862no—
704C22—862no—
705C22—3441no—
706C22—3441no—
707C22—3441no—
708C22—3441no—
709C22—3441no—
710C22—3441no—
711C22—3441no—
712C22—3441no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22—1722no—
718C22—1722no—
719C22—1721no—
720C22—1721no—
721C22—1721no—
722C22—1721no—
723C22C2×C22⋊C4×D4311yescharacteristic
724C22#1458341211yescharacteristic
725C22#1458341211yescharacteristic
726C22#1458370111yescharacteristic
727C22#1458370311yescharacteristic
728C22#1458370611yescharacteristic
729C22#1458370811yescharacteristic
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—862no—
737C4—862no—
738C4—862no—
739C4—1722no—
740C4—1722no—
741C4C4×#1062190211yescharacteristic
742C4C4×#1062190211yescharacteristic
743C4#1458344811yescharacteristic
744C4#1458345011yescharacteristic
745C2—3442no—
746C2—3442no—
747C2—1722no—
748C2#1913708411yescharacteristic
749C2#1914311711yescharacteristic
750C2#1914311911yescharacteristic
751C2#1914479911yescharacteristic
752C2#1914480111yescharacteristic
753C2#1914484011yescharacteristic
754C2#1914488811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1989C2
socleC23×C43C22×D4
prime radicalC2×#14583505C2
cosocleC22×C4×C43C24
hypercenter#1989D43
hypocenterC43#21399
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
2. C2×#14582959C2semidirect
3. #19136949C2semidirect
4. #19135553C2semidirect
5. #19135522C2semidirect
6. #19135521C2semidirect
7. #19134916C2semidirect
8. #19134916C2semidirect
9. #19134911C2semidirect
10. #19134911C2semidirect
11. #19134419C2semidirect
12. #19134419C2semidirect
13. #19134409C2semidirect
14. #19134409C2semidirect
15. C43×#1989C2semidirect
17. #14583505C4semidirect
75. #13063322C2×C4semidirect
86. #13063287C2×C4semidirect
87. #13063287C2×C4semidirect
130. #125×C43C2×C4semidirect
372. #1989D43semidirect
439. C43#21399semidirect
457. #125C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835052
C2×#145829592
#191369492
#191355532
#191355222
#191355212
#191349162
#191349112
#191344192
#191344092
C43×#19892
#2139943