Finite Group Databasebeta

← #25117341

Subgroups — #25117341

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143815C211yesmaximal, characteristic
2C2×#14583022C211yesmaximal, characteristic, complemented
3#19143319C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5#19143043C211yesmaximal, characteristic, complemented
6#19135485C211yesmaximal, characteristic, complemented
7#19135245C211yesmaximal, characteristic, complemented
8#19135037C211yesmaximal, characteristic, complemented
9#19134925C211yesmaximal, characteristic, complemented
10#19134923C211yesmaximal, characteristic, complemented
11#19134869C211yesmaximal, characteristic, complemented
12#19134801C211yesmaximal, characteristic, complemented
13#19134436C211yesmaximal, characteristic, complemented
14#19134358C211yesmaximal, characteristic, complemented
15C43×#1938C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063331C2211yescharacteristic
21C2×#13063331C2211yescharacteristic, complemented
22C2×M16×D43C2211yescharacteristic
23#14583411C2211yescharacteristic
24C2×C42×D43C2211yescharacteristic
25#14583064C411yescharacteristic, complemented
26#14583062C411yescharacteristic, complemented
27#14583056C411yescharacteristic, complemented
28#14583051C411yescharacteristic, complemented
29#14583047C411yescharacteristic, complemented
30#14583045C411yescharacteristic, complemented
31#14583039C411yescharacteristic, complemented
32#14583034C411yescharacteristic, complemented
33#14583022—24no—
34#14582976—21no—
35#14582969—21no—
36#14582969—21no—
37#14582964—21no—
38C2×#13063261C2211yescharacteristic, complemented
39C2×#13063260C2211yescharacteristic, complemented
40C2×#13063253C2211yescharacteristic
41C2×#13063253C2211yescharacteristic, complemented
42C2×#13063252C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44C2×#13063251C2211yescharacteristic, complemented
45#104×D43—24no—
46#14582893C2211yescharacteristic
47#14582867C2211yescharacteristic, complemented
48#14582866C2211yescharacteristic
49#14582864—21no—
50#14582864—21no—
51#14582862C2211yescharacteristic
52#14582861—21no—
53C2×(C2×D43)⋊C8C2211yescharacteristic
54C2×(C2×D43)⋊C8C2211yescharacteristic
55C22⋊C8×D43—21no—
56#14582855C2211yescharacteristic, complemented
57C2×#13063236C2211yescharacteristic, complemented
58#14582663C2211yescharacteristic, complemented
59#14582658C2211yescharacteristic, complemented
60#14582653C2211yescharacteristic, complemented
61#14582653C2211yescharacteristic, complemented
62C43×#424C2211yescharacteristic, complemented
63C2×#104×C43C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C43×#408C2211yescharacteristic
66C2×#97×C43C2211yescharacteristic, complemented
67C43×#341C2211yescharacteristic, complemented
68C43×#339C2211yescharacteristic, complemented
69C2×#10621902C2×C411yescharacteristic
70C2×#10621898—21no—
71C2×#10621898C2311yescharacteristic
72C2×#10621898C2311yescharacteristic
73C2×#10621900—21no—
74C2×#10621900C2×C411yescharacteristic
75#41×D43—22no—
76#41×D43—22no—
77#41×D43—41no—
78#41×D43—41no—
79C2×Q8×D43C2×C411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43C2×C411yescharacteristic
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85#13063347—22no—
86#13063347—22no—
87#13063345—41no—
88#13063345—41no—
89C2×Dic172C2×C411yescharacteristic, complemented
90C2×#10621885C2×C411yescharacteristic, complemented
91C2×#10621873C2×C411yescharacteristic, complemented
92C2×#10621873C2×C411yescharacteristic, complemented
93C2×#10621883C2×C411yescharacteristic, complemented
94C2×#10621884C2×C411yescharacteristic, complemented
95C2×D344C2×C411yescharacteristic, complemented
96C2×#10621882C2×C411yescharacteristic, complemented
97#13063333—22no—
98#13063333—41no—
99#13063331—22no—
100#13063331—22no—
101#13063331—41no—
102#13063331—41no—
103C2×#10621877C2311yescharacteristic
104C2×#10621877C2311yescharacteristic
105C2×#10621872—21no—
106C2×#10621872—21no—
107C2×#10621872—21no—
108C2×#10621872—21no—
109M16×D43—22no—
110M16×D43—41no—
111C22×C43⋊C8C2311yescharacteristic
112C22×C43⋊C8C2311yescharacteristic
113C2×C8×D43—21no—
114C2×C8×D43—21no—
115C2×C8×D43—21no—
116C2×C8×D43—21no—
117#13063309—21no—
118#13063305C2×C411yescharacteristic
119#13063305C2×C411yescharacteristic
120#13063300C2×C411yescharacteristic
121#13063300C2×C411yescharacteristic
122#13063295—21no—
123C4×D172—21no—
124C4×D172—21no—
125C2×C4×Dic43—21no—
126C2×C4×Dic43C2311yescharacteristic
127C42×D43—22no—
128C42×D43—41no—
129#13063261—22no—
130#13063260—41no—
131#13063253—22no—
132#13063253D414yescomplemented
133#13063252—22no—
134#13063251—22no—
135#13063251—41no—
136#13063248C2×C411yescharacteristic, complemented
137#13063248C2×C411yescharacteristic, complemented
138#13063245C2×C411yescharacteristic, complemented
139#13063245C2×C411yescharacteristic, complemented
140C22⋊(C43⋊C8)—21no—
141C22⋊(C43⋊C8)—21no—
142(C2×D43)⋊C8—21no—
143(C2×D43)⋊C8—21no—
144(C2×D43)⋊C8—21no—
145(C2×D43)⋊C8—21no—
146(C2×D43)⋊C8C2×C411yescharacteristic
147(C2×D43)⋊C8C2×C411yescharacteristic
148(C2×D43)⋊C8C2×C411yescharacteristic
149(C2×D43)⋊C8C2×C411yescharacteristic
150(C2×D43)⋊C8D411yescharacteristic
151(C2×D43)⋊C8D411yescharacteristic
152(C2×D43)⋊C8D411yescharacteristic
153(C2×D43)⋊C8D411yescharacteristic
154#13063236—21no—
155#13063236—41no—
156C4×C43⋊C8—21no—
157C2×#41×C43C2311yescharacteristic
158C2×M16×C43C2311yescharacteristic
159C2×M16×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161C22×C8×C43C2311yescharacteristic
162#117×C43C2311yescharacteristic
163C2×C42×C43C2311yescharacteristic
164C4⋊C8×C43—21no—
165C4⋊C8×C43—21no—
166#104×C43—22no—
167#103×C43C2×C411yescharacteristic, complemented
168#103×C43C2×C411yescharacteristic, complemented
169#102×C43C2×C411yescharacteristic, complemented
170#102×C43C2×C411yescharacteristic, complemented
171C22⋊C8×C43—21no—
172C22⋊C8×C43—21no—
173#97×C43—22no—
174C23×D43—21no—
175C23×D43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43#4111yescharacteristic
193#10621902—22no—
194#10621902—41no—
195Q8×D43—22no—
196Q8×D43—41no—
197#10621900—22no—
198#10621900—41no—
199#10621900—42no—
200#10621900—42no—
201D4×D43—22no—
202D4×D43—42no—
203D4×D43—42no—
204D4×D43—41no—
205#10621898—21no—
206#10621898—21no—
207#10621898—21no—
208#10621898—21no—
209#10621898—21no—
210#10621898—21no—
211#10621898—42no—
212#10621898—42no—
213#10621898C2×D412yes—
214#10621898#4112yes—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172C22×C411yescharacteristic
219C2×D172C22×C411yescharacteristic
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43C22×C411yescharacteristic
234C2×C4×D43C22×C411yescharacteristic
235C2×C4×D43C2×D411yescharacteristic
236C2×C4×D43C2×D411yescharacteristic
237C2×Dic86—21no—
238C2×Dic86C22×C411yescharacteristic
239C2×Dic86C22×C411yescharacteristic
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43C22×C411yescharacteristic
251C2×C8×C43C22×C411yescharacteristic
252C2×C8×C43C2×D411yescharacteristic
253C2×C8×C43C2×D411yescharacteristic
254C4⋊C4×C43C22×C411yescharacteristic
255C4⋊C4×C43C22×C411yescharacteristic
256C22⋊C4×C43—21no—
257C42×C43—21no—
258C42×C43—21no—
259C42×C43C2×D412yes—
260#10621885—41no—
261#10621884—41no—
262#10621883—41no—
263#10621882—41no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4×Dic43—21no—
271C4×Dic43—21no—
272C4×Dic43—42no—
273#10621877—21no—
274#10621877—21no—
275#10621877—21no—
276#10621877C2×D412yes—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8C22×C411yescharacteristic
284C2×C43⋊C8C22×C411yescharacteristic
285C2×C43⋊C8C2×D411yescharacteristic
286C2×C43⋊C8C2×D411yescharacteristic
287Dic172—22no—
288D344—22no—
289#10621873—22no—
290#10621873—22no—
291#10621872—42no—
292#10621872—42no—
293#10621872—42no—
294#10621872—42no—
295C8×D43—42no—
296C8×D43—42no—
297C8×D43—42no—
298C8×D43—42no—
299C23×C43—21no—
300C23×C43C2×#4111yescharacteristic
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—22no—
305C22×D43—21no—
306C22×D43—41no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—81no—
310C22×D43C4×D411yescharacteristic
311C22×D43C4×D411yescharacteristic
312Q8×C43—21no—
313Q8×C43—21no—
314D4×C43—21no—
315D4×C43—21no—
316D4×C43—41no—
317D4×C43—41no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43C23×C411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43H(5,𝔽2)11yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C22⋊D43—22no—
333C22⋊D43—22no—
334C22⋊D43—42no—
335C22⋊D43—42no—
336C22⋊D43—41no—
337C22⋊D43—41no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—22no—
342C2×Dic43—21no—
343C2×Dic43—42no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43C4×D411yescharacteristic
347C2×Dic43C4×D411yescharacteristic
348D172—21no—
349D172—21no—
350D172—21no—
351D172—42no—
352D172—42no—
353D172—81no—
354D172C4×D412yes—
355C4×D43—21no—
356C4×D43—21no—
357C4×D43—21no—
358C4×D43—21no—
359C4×D43—21no—
360C4×D43—22no—
361C4×D43—21no—
362C4×D43—22no—
363C4×D43—21no—
364C4×D43—21no—
365C4×D43—42no—
366C4×D43—42no—
367C4×D43—48no—
368C4×D43—41no—
369C4×D43—41no—
370Dic86—21no—
371Dic86—21no—
372Dic86—21no—
373Dic86—42no—
374Dic86C4×D412yes—
375C8×C43—21no—
376C8×C43—21no—
377C8×C43—21no—
378C8×C43—21no—
379C8×C43—41no—
380C8×C43—41no—
381C43⋊C8—21no—
382C43⋊C8—21no—
383C43⋊C8—22no—
384C43⋊C8—21no—
385C43⋊C8—21no—
386C43⋊C8—41no—
387#22886—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43C2×C4×D411yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43#55111yescharacteristic
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—21no—
399C2×D43—22no—
400C2×D43—21no—
401C2×D43—21no—
402C2×D43—42no—
403C2×D43—42no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—84no—
410C2×D43#44412yescomplemented
411C4×C43—42no—
412C4×C43—41no—
413C4×C43—41no—
414C4×C43—41no—
415C4×C43C2×C4×D411yescharacteristic
416C4×C43#51811yescharacteristic
417C4×C43D4211yescharacteristic
418C4×C43#54611yescharacteristic
419Dic43—22no—
420Dic43—21no—
421Dic43—21no—
422Dic43—42no—
423Dic43—41no—
424#3002—431no—
425C2×#444—431no—
426#2933—431no—
427C22×#104—431no—
428#2880—431no—
429#1975—431no—
430#1938D4311yescharacteristic, complemented
431#1929—431no—
432#1896—431no—
433#1876—431no—
434#1876—431no—
435#1866—431no—
436#1855—431no—
437#1765—431no—
438#1749—431no—
439C2×C43—21no—
440C2×C43—21no—
441C2×C43—81no—
442C2×C43#235811yescharacteristic
443C2×C43C2×#44411yescharacteristic
444C2×C43#295611yescharacteristic
445D43—22no—
446D43—41no—
447D43—42no—
448D43—81no—
449C22×#41—431no—
450C2×#135—431no—
451C2×#135—431no—
452C2×#131—431no—
453C2×#131—431no—
454C2×#131—431no—
455C22×M16—431no—
456#525—431no—
457C22×C42—431no—
458#452—431no—
459#452—431no—
460#451—431no—
461#450—431no—
462#449—431no—
463#449—431no—
464#448—431no—
465#447—431no—
466#444—864no—
467#436—861no—
468#435—861no—
469#435—861no—
470C8×D4—861no—
471C2×#108—431no—
472C2×#108—431no—
473#424C2×D4311yescharacteristic, complemented
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104—431no—
478C2×#104—431no—
479C2×#104—864no—
480C2×#104C2×D4311yescharacteristic
481#416—431no—
482#416C2×D4311yescharacteristic
483#408—431no—
484#408—431no—
485#408—861no—
486#408—861no—
487#408C2×D4311yescharacteristic
488#407—431no—
489#407—861no—
490C2×C22⋊C8—431no—
491C2×C22⋊C8—431no—
492C2×C22⋊C8—861no—
493#405—431no—
494C2×#97—431no—
495C2×#97C2×D4311yescharacteristic, complemented
496#341—431no—
497#341C2×D4311yescharacteristic, complemented
498#339—431no—
499#339C2×D4311yescharacteristic, complemented
500#336—431no—
501#336—431no—
502C43#2288611yescharacteristic, complemented, Sylow
503C2×#41—431no—
504C2×#41—431no—
505C2×#41—431no—
506C2×#41—431no—
507C2×#41—861no—
508C2×#41—861no—
509C2×#41—862no—
510C2×#41—862no—
511C2×#41—1721no—
512C2×#41—1721no—
513C2×#41C22×D4311yescharacteristic
514C22×Q8—431no—
515C22×D4—431no—
516C22×D4—861no—
517C23×C4—431no—
518C23×C4—861no—
519C23×C4—861no—
520#135—862no—
521#135—862no—
522#135—1721no—
523#135—1721no—
524C2×Q16—431no—
525C2×Q16—431no—
526C2×SD16—431no—
527C2×SD16—431no—
528C2×SD16—431no—
529C2×SD16—431no—
530C2×D8—431no—
531C2×D8—431no—
532#131—862no—
533#131—862no—
534#131—862no—
535#131—1721no—
536#131—1721no—
537#131—1721no—
538C2×M16—431no—
539C2×M16—431no—
540C2×M16—861no—
541C2×M16—861no—
542C2×M16—861no—
543C2×M16—861no—
544C2×M16—862no—
545C2×M16—1721no—
546C2×M16C22×D4311yescharacteristic
547C2×M16C22×D4311yescharacteristic
548C22×C8—431no—
549C22×C8—431no—
550C22×C8—861no—
551C22×C8—861no—
552C22×C8—861no—
553C22×C8—861no—
554C22×C8C22×D4311yescharacteristic
555C22×C8C22×D4311yescharacteristic
556#123—861no—
557C22⋊Q8—431no—
558C22⋊Q8—431no—
559#121—431no—
560#121—431no—
561#120—861no—
562C4×D4—861no—
563C4×D4—861no—
564#117C22×D4311yescharacteristic
565C2×C42—431no—
566C2×C42—862no—
567C2×C42—861no—
568C2×C42—1721no—
569C2×C42C22×D4311yescharacteristic
570#108—862no—
571#108—1721no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—22no—
575#104—434no—
576#104—862no—
577#104—862no—
578#104—862no—
579#104—1721no—
580#103—431no—
581#103—431no—
582#103C4×D4311yescharacteristic, complemented
583#103C4×D4311yescharacteristic, complemented
584#102—431no—
585#102—431no—
586#102C4×D4311yescharacteristic, complemented
587#102C4×D4311yescharacteristic, complemented
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—431no—
591C22⋊C8—431no—
592C22⋊C8—431no—
593C22⋊C8—431no—
594C22⋊C8—431no—
595C22⋊C8—431no—
596C22⋊C8—431no—
597C22⋊C8—431no—
598C22⋊C8—861no—
599C22⋊C8—861no—
600C22⋊C8—861no—
601C22⋊C8—861no—
602C22⋊C8—861no—
603C22⋊C8—861no—
604#97—22no—
605#97—861no—
606#97—1721no—
607C4×C8—861no—
608C24—431no—
609C24—861no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—432no—
615#41—432no—
616#41—861no—
617#41—861no—
618#41—862no—
619#41—862no—
620#41—861no—
621#41—861no—
622#41—861no—
623#41—861no—
624#41—1722no—
625#41—1722no—
626#41—1721no—
627#41—1722no—
628#41—1722no—
629#41—1721no—
630C2×Q8—431no—
631C2×Q8—431no—
632C2×Q8—861no—
633C2×Q8—862no—
634C2×Q8—1721no—
635C2×Q8C2×C4×D4311yescharacteristic
636C2×D4—21no—
637C2×D4—431no—
638C2×D4—431no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—862no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—1721no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4C2×C4×D4311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—1722no—
669C22×C4—1722no—
670C22×C4—1722no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4C23×D4311yescharacteristic
674Q16—862no—
675Q16—1721no—
676SD16—862no—
677SD16—862no—
678SD16—1721no—
679SD16—1721no—
680D8—862no—
681D8—1721no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—432no—
687M16—861no—
688M16—861no—
689M16—861no—
690M16—1722no—
691M16—1722no—
692M16—1722no—
693M16—1722no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—431no—
701C2×C8—431no—
702C2×C8—431no—
703C2×C8—431no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—1722no—
711C2×C8—1722no—
712C2×C8—1722no—
713C2×C8—1722no—
714C2×C8C2×C4×D4311yescharacteristic
715C2×C8C2×C4×D4311yescharacteristic
716C2×C8D4×D4311yescharacteristic
717C2×C8D4×D4311yescharacteristic
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4C2×C4×D4311yescharacteristic
721C4⋊C4C2×C4×D4311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C42—21no—
728C42—21no—
729C42—861no—
730C42—861no—
731C42—1722no—
732C42D4×D4312yes—
733C23—21no—
734C23—431no—
735C23—431no—
736C23—862no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—3441no—
742C23—1721no—
743C23—1722no—
744C23—1722no—
745C23#41×D4311yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—432no—
749Q8—861no—
750Q8—861no—
751Q8—861no—
752Q8—1722no—
753D4—21no—
754D4—21no—
755D4—41no—
756D4—41no—
757D4—432no—
758D4—862no—
759D4—862no—
760D4—861no—
761D4—861no—
762D4—861no—
763D4—3441no—
764D4—1722no—
765D4—1722no—
766D4—1722no—
767D4—1722no—
768D4—1721no—
769D4—1721no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—431no—
779C2×C4—431no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—862no—
789C2×C4—861no—
790C2×C4—862no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—862no—
794C2×C4—861no—
795C2×C4—1722no—
796C2×C4—1722no—
797C2×C4—1728no—
798C2×C4—1722no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4C22×C4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C2×D4×D4311yescharacteristic
806C2×C4#41×D4311yescharacteristic
807C2×C4#1306337111yescharacteristic
808C2×C4#1306337111yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—41no—
814C8—41no—
815C8—861no—
816C8—861no—
817C8—862no—
818C8—861no—
819C8—861no—
820C8—1721no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—432no—
827C22—861no—
828C22—861no—
829C22—861no—
830C22—862no—
831C22—861no—
832C22—861no—
833C22—3444no—
834C22—1722no—
835C22—1722no—
836C22—1721no—
837C22—1721no—
838C22—1721no—
839C22—1721no—
840C22—1721no—
841C22C4×D4×D4311yescharacteristic
842C22#1458354111yescharacteristic
843C22#1458357411yescharacteristic
844C4—42no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—861no—
849C4—861no—
850C4—862no—
851C4—1722no—
852C4—1721no—
853C4C4×D4×D4311yescharacteristic
854C4#1458337311yescharacteristic
855C4#1458353311yescharacteristic
856C4#1458354211yescharacteristic
857C2—21no—
858C2—21no—
859C2—81no—
860C2—862no—
861C2—3441no—
862C2—1721no—
863C2—1722no—
864C2#1913757311yescharacteristic
865C2#444×D4311yescharacteristic
866C2#1914350311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1938C2
socleC22×C43C2×C4×D4
prime radical#19143815C2
cosocleC22×C4×C43C24
hypercenter#1938D43
hypocenterC43#22886
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1938

Complements

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

NH ≅ G/Ntype
2. C2×#14583022C2semidirect
3. #19143319C2semidirect
4. C2×#104×D43C2semidirect
5. #19143043C2semidirect
6. #19135485C2semidirect
7. #19135245C2semidirect
8. #19135037C2semidirect
9. #19134925C2semidirect
10. #19134923C2semidirect
11. #19134869C2semidirect
12. #19134801C2semidirect
13. #19134436C2semidirect
14. #19134358C2semidirect
15. C43×#1938C2semidirect
21. C2×#13063331C22semidirect
25. #14583064C4semidirect
26. #14583062C4semidirect
27. #14583056C4semidirect
28. #14583051C4semidirect
29. #14583047C4semidirect
30. #14583045C4semidirect
31. #14583039C4semidirect
32. #14583034C4semidirect
38. C2×#13063261C22semidirect
39. C2×#13063260C22semidirect
41. C2×#13063253C22semidirect
44. C2×#13063251C22semidirect
47. #14582867C22semidirect
56. #14582855C22semidirect
57. C2×#13063236C22semidirect
58. #14582663C22semidirect
59. #14582658C22semidirect
60. #14582653C22semidirect
61. #14582653C22semidirect
62. C43×#424C22semidirect
66. C2×#97×C43C22semidirect
67. C43×#341C22semidirect
68. C43×#339C22semidirect
89. C2×Dic172C2×C4semidirect
90. C2×#10621885C2×C4semidirect
91. C2×#10621873C2×C4semidirect
92. C2×#10621873C2×C4semidirect
93. C2×#10621883C2×C4semidirect
94. C2×#10621884C2×C4semidirect
95. C2×D344C2×C4semidirect
96. C2×#10621882C2×C4semidirect
132. #13063253D4semidirect
136. #13063248C2×C4semidirect
137. #13063248C2×C4semidirect
138. #13063245C2×C4semidirect
139. #13063245C2×C4semidirect
167. #103×C43C2×C4semidirect
168. #103×C43C2×C4semidirect
169. #102×C43C2×C4semidirect
170. #102×C43C2×C4semidirect
410. C2×D43#444semidirect
430. #1938D43semidirect
473. #424C2×D43semidirect
495. C2×#97C2×D43semidirect
497. #341C2×D43semidirect
499. #339C2×D43semidirect
502. C43#22886semidirect
582. #103C4×D43semidirect
583. #103C4×D43semidirect
586. #102C4×D43semidirect
587. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191438152
C2×#145830222
#191433192
C2×#104×D432
#191430432
#191354852
#191352452
#191350372
#191349252
#191349232
#191348692
#191348012
#191344362
#191343582
C43×#19382
#2288643