Finite Group Databasebeta

← #25105980

Subgroups — #25105980

Order 11008.

1250 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583470C211yesmaximal, characteristic
2C2×#14582957C211yesmaximal, characteristic, complemented
3#19137202C211yesmaximal, characteristic, complemented
4#19135526C211yesmaximal, characteristic, complemented
5#19135526C211yesmaximal, characteristic, complemented
6#19135516C211yesmaximal, characteristic, complemented
7#19135516C211yesmaximal, characteristic, complemented
8#19135413C211yesmaximal, characteristic, complemented
9#19135410C211yesmaximal, characteristic, complemented
10#19135405C211yesmaximal, characteristic, complemented
11#19135395C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic
13#19134531C211yesmaximal, characteristic, complemented
14#19134529C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17#14583470—24no—
18#14583470C418yescomplemented
19C2×#13063323C2211yescharacteristic
20C2×#13063323C2211yescharacteristic
21C2×#13063312C2211yescharacteristic
22C2×#13063312C2211yescharacteristic
23C2×#13063306—21no—
24C2×#13063306—21no—
25C2×#13063304—21no—
26C2×#13063304—21no—
27C2×#13063284C2211yescharacteristic
28#14582957—24no—
29C2×Dic43⋊C8C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×#13063235C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582793—21no—
47#14582787—21no—
48#14582784—21no—
49#14582782—21no—
50#14582768C2211yescharacteristic
51#14582764C2211yescharacteristic
52#14582759C2211yescharacteristic
53C4⋊C4×Dic43C2211yescharacteristic
54C4⋊C4×Dic43C2211yescharacteristic
55C22×#41×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86—22no—
64C22×Dic86—41no—
65C22×Dic86—41no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C22×Dic86C2×C414yes—
69C22×Dic86C2311yescharacteristic
70C22×Dic86C2311yescharacteristic
71C23×Dic43—21no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063323—22no—
75#13063323—22no—
76#13063323C2×C414yes—
77#13063323C2×C414yes—
78#13063312—22no—
79#13063312—22no—
80#13063312C2×C414yes—
81#13063312C2×C414yes—
82#13063306—28no—
83#13063306—28no—
84#13063304—28no—
85#13063304—28no—
86#13063284C2×C414yes—
87#13063284D414yes—
88C2×C4⋊Dic43D411yescharacteristic
89C2×C4⋊Dic43D411yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43D411yescharacteristic
104C2×C22⋊Dic43D411yescharacteristic
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109Dic43⋊C8—22no—
110Dic43⋊C8—22no—
111#13063250—41no—
112#13063250—41no—
113#13063250—41no—
114#13063250—41no—
115#13063249—41no—
116#13063249—41no—
117#13063248—41no—
118#13063248—41no—
119#13063248—41no—
120#13063248—41no—
121#13063246—41no—
122#13063246—41no—
123C22⋊(C43⋊C8)—22no—
124#13063235—22no—
125C8×Dic43—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C2×#41×C43—22no—
132C2×#41×C43—41no—
133C2×#41×C43—41no—
134C2×#41×C43—41no—
135C2×#41×C43—41no—
136C2×#41×C43C2×C414yes—
137C22×Q8×C43C2311yescharacteristic
138C22×D4×C43—21no—
139C22×D4×C43C2311yescharacteristic
140C23×C4×C43—21no—
141C23×C4×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#103×C43—41no—
148#103×C43—41no—
149#102×C43—41no—
150#102×C43—41no—
151C22⋊C8×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155#41×C43—44no—
156#41×C43—44no—
157#41×C43—44no—
158#41×C43—44no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43C22×C412yes—
165C2×D4×C43—21no—
166C2×D4×C43—24no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43C22×C412yes—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—24no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—42no—
183C22×C4×C43—42no—
184C22×C4×C43C22×C412yes—
185C22×C4×C43C2×D412yes—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—24no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—24no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—44no—
211C2×Dic86—44no—
212C2×Dic86—42no—
213C2×Dic86—42no—
214C2×Dic86—44no—
215C2×Dic86—44no—
216C2×Dic86C22×C412yes—
217C2×Dic86C22×C412yes—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C22⋊C4×C43—81no—
229C22⋊Dic43—24no—
230C22⋊Dic43—24no—
231C22⋊Dic43—24no—
232C22⋊Dic43—24no—
233C22⋊Dic43—81no—
234C22⋊Dic43C22⋊C414yes—
235C22⋊Dic43C22⋊C414yes—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43C22⋊C414yes—
241C4⋊Dic43C22⋊C414yes—
242Dic43⋊C4—24no—
243Dic43⋊C4—24no—
244Dic43⋊C4—24no—
245Dic43⋊C4—24no—
246Dic43⋊C4—81no—
247Dic43⋊C4—81no—
248C4×Dic43—81no—
249C4×Dic43—81no—
250C4×Dic43C22×C412yes—
251C4×Dic43C22×C412yes—
252C4×Dic43C2×D412yes—
253C4×Dic43C2×D412yes—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—22no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43C2×C22⋊C412yes—
274C23×C43C22×D411yescharacteristic
275Q8×C43—22no—
276Q8×C43—22no—
277Q8×C43—41no—
278Q8×C43—41no—
279D4×C43—22no—
280D4×C43—22no—
281D4×C43—48no—
282D4×C43—41no—
283D4×C43—41no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—48no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43C2×C22⋊C412yes—
301C2×C4×C43C23×C411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—48no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43C2×C22⋊C412yes—
329C2×Dic43C2×C22⋊C412yes—
330C2×Dic43C2×C22⋊C412yes—
331C2×Dic43C2×C22⋊C412yes—
332Dic86—22no—
333Dic86—22no—
334Dic86—22no—
335Dic86—22no—
336Dic86—48no—
337Dic86—41no—
338Dic86—41no—
339Dic86—41no—
340Dic86—41no—
341C8×C43—41no—
342C8×C43—41no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345#21814—431nomaximal, Sylow
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43C22×C22⋊C411yescharacteristic
361C22×C43#53511yescharacteristic
362C22×C43#53511yescharacteristic
363C22×C43#57711yescharacteristic
364C22×C43#57711yescharacteristic
365C22×C43#57811yescharacteristic
366C22×C43#57811yescharacteristic
367C4×C43—22no—
368C4×C43—42no—
369C4×C43—81no—
370C4×C43—81no—
371C4×C43#51811yescharacteristic
372C4×C43#51811yescharacteristic
373C4×C43#53511yescharacteristic
374C4×C43#53511yescharacteristic
375Dic43—22no—
376Dic43—22no—
377Dic43—22no—
378Dic43—22no—
379Dic43—42no—
380Dic43—42no—
381Dic43—81no—
382Dic43—81no—
383C2×#536—431no—
384C2×#433—431no—
385#2314—431no—
386#1983—431no—
387#1983—431no—
388#1981—431no—
389#1981—431no—
390#1960—431no—
391#1959—431no—
392#1958—431no—
393#1956—431no—
394#1788—431no—
395#1788D4311yescharacteristic
396#1787—431no—
397#1787—431no—
398C2×C43—42no—
399C2×C43—82no—
400C2×C43#230911yescharacteristic
401C2×C43#289811yescharacteristic
402C2×C43#289811yescharacteristic
403C2×C43#322111yescharacteristic
404C2×C43#322311yescharacteristic
405C2×C43#322511yescharacteristic
406C2×C43#322511yescharacteristic
407C22×#41C2×D4311yescharacteristic
408C23×Q8—431no—
409#536—438no—
410#536—864no—
411C2×C4⋊Q8—431no—
412C2×C4⋊Q8—431no—
413C2×#124—431no—
414C2×#124—431no—
415C2×#123—861no—
416C2×#123—861no—
417C2×C22⋊Q8—861no—
418C2×C22⋊Q8—861no—
419C2×#117—431no—
420#433—864no—
421C2×C4⋊C8—431no—
422C2×C4⋊C8—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103C2×D4311yescharacteristic
434C2×#103C2×D4311yescharacteristic
435C2×#102—431no—
436C2×#102—431no—
437C2×#102C2×D4311yescharacteristic
438C2×#102C2×D4311yescharacteristic
439C2×C22⋊C8—431no—
440C2×C22⋊C8C2×D4311yescharacteristic
441C2×#97—431no—
442C2×C4×C8—431no—
443#388—861no—
444#388—861no—
445#387—861no—
446#387—861no—
447#384—431no—
448#382—431no—
449#380—431no—
450#380C2×D4311yescharacteristic
451C4×C4⋊C4—431no—
452C4×C4⋊C4—431no—
453C43#2181411yescharacteristic, complemented, Sylow
454C2×#41—22no—
455C2×#41—41no—
456C2×#41—41no—
457C2×#41—41no—
458C2×#41—41no—
459C2×#41C4×D4314yes—
460C22×Q8—434no—
461C22×Q8—431no—
462C22×Q8—431no—
463C22×Q8—861no—
464C22×Q8—862no—
465C22×Q8—1721no—
466C22×Q8—1721no—
467C22×Q8—1721no—
468C22×Q8—1721no—
469C22×Q8C22×D4311yescharacteristic
470C22×D4—21no—
471C22×D4C22×D4311yescharacteristic
472C23×C4—21no—
473C23×C4—861no—
474C23×C4C22×D4311yescharacteristic
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C4⋊Q8—434no—
480C4⋊Q8—434no—
481C4⋊Q8—862no—
482C4⋊Q8—862no—
483#124—434no—
484#124—434no—
485#124—862no—
486#124—862no—
487#123—868no—
488#123—868no—
489C22⋊Q8—868no—
490C22⋊Q8—868no—
491#117—434no—
492#117—434no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C42—431no—
514C2×C42—431no—
515C2×C42—861no—
516C2×C42—861no—
517C4⋊C8—862no—
518C4⋊C8—862no—
519#103—41no—
520#103—41no—
521#103—1721no—
522#103—1721no—
523#103—1721no—
524#103—1721no—
525#103—1721no—
526#103—1721no—
527#103—1721no—
528#103—1721no—
529#103—1721no—
530#103—1721no—
531#102—41no—
532#102—41no—
533#102—1721no—
534#102—1721no—
535C22⋊C8—22no—
536C22⋊C8—862no—
537#97—862no—
538C4×C8—862no—
539#95—21no—
540#95—861no—
541#95—861no—
542#95—861no—
543#95—861no—
544#95—861no—
545C24—21no—
546C24D4×D4311yescharacteristic
547#41—44no—
548#41—44no—
549#41—44no—
550#41—44no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—432no—
557C2×Q8—432no—
558C2×Q8—864no—
559C2×Q8—861no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8—861no—
568C2×Q8—861no—
569C2×Q8—1724no—
570C2×Q8—1724no—
571C2×Q8—1722no—
572C2×Q8—1722no—
573C2×Q8—1724no—
574C2×Q8—1724no—
575C2×Q8C2×C4×D4312yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4C2×C4×D4312yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—864no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4C2×C4×D4312yes—
607C22×C4D4×D4311yescharacteristic
608C22×C4D4×D4312yes—
609C22×C4C23×D4311yescharacteristic
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—434no—
627C4⋊C4—434no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—3441no—
637C4⋊C4—3441no—
638C22⋊C4—81no—
639C22⋊C4—434no—
640C22⋊C4—434no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C22⋊C4—864no—
644C22⋊C4—864no—
645C22⋊C4—3441no—
646C42—432no—
647C42—432no—
648C42—432no—
649C42—432no—
650C42—3441no—
651C42—3441no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23C22⋊C4×D4312yes—
666C23C2×D4×D4311yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—41no—
670Q8—41no—
671Q8—862no—
672Q8—862no—
673Q8—862no—
674Q8—862no—
675Q8—1728no—
676Q8—1721no—
677Q8—1721no—
678Q8—1721no—
679Q8—1721no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—48no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—432no—
702C2×C4—432no—
703C2×C4—432no—
704C2×C4—432no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1728no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4C22⋊C4×D4312yes—
727C2×C4C22×C4×D4311yescharacteristic
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4#1306337011yescharacteristic
730C2×C4#1306337011yescharacteristic
731C2×C4#1306337011yescharacteristic
732C2×C4#1306337011yescharacteristic
733C8—41no—
734C8—41no—
735C8—1721no—
736C8—1721no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×C22⋊C4×D4311yescharacteristic
752C22#1458346411yescharacteristic
753C22#1458346411yescharacteristic
754C22#1458370611yescharacteristic
755C22#1458370911yescharacteristic
756C22#1458371311yescharacteristic
757C22#1458371511yescharacteristic
758C4—22no—
759C4—42no—
760C4—81no—
761C4—81no—
762C4—862no—
763C4—862no—
764C4—862no—
765C4—862no—
766C4—3441no—
767C4—3441no—
768C4—1722no—
769C4—1722no—
770C4#1458337211yescharacteristic
771C4#1458337211yescharacteristic
772C4#1458346411yescharacteristic
773C4#1458346411yescharacteristic
774C2—42no—
775C2—82no—
776C2#1913717611yescharacteristic
777C2#1914312411yescharacteristic
778C2#1914312611yescharacteristic
779C2#1914565411yescharacteristic
780C2#1914567611yescharacteristic
781C2#1914570011yescharacteristic
782C2#1914570811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#21814
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14582957C2semidirect
3. #19137202C2semidirect
4. #19135526C2semidirect
5. #19135526C2semidirect
6. #19135516C2semidirect
7. #19135516C2semidirect
8. #19135413C2semidirect
9. #19135410C2semidirect
10. #19135405C2semidirect
11. #19135395C2semidirect
13. #19134531C2semidirect
14. #19134529C2semidirect
18. #14583470C4semidirect
453. C43#21814semidirect

Maximal subgroups

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

subgroupindex
C2×#145834702
C2×#145829572
#191372022
#191355262
#191355162
#191354132
#191354102
#191354052
#191353952
#191345352
#191345312
#191345292
C43×#17882
#2181443