Finite Group Databasebeta

← #25113969

Subgroups — #25113969

Order 11008.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143112C211yesmaximal, characteristic
2#19143041C211yesmaximal, characteristic
3#19135305C211yesmaximal, characteristic, complemented
4#19135298C211yesmaximal, characteristic, complemented
5#19135243C211yesmaximal, characteristic, complemented
6#19135243C211yesmaximal, characteristic, complemented
7#19134869C211yesmaximal, characteristic, complemented
8#19134869C211yesmaximal, characteristic, complemented
9#19134694C211yesmaximal, characteristic, complemented
10#19134635C211yesmaximal, characteristic, complemented
11#19134538C211yesmaximal, characteristic
12#19134441C211yesmaximal, characteristic, complemented
13#19134434C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C43×#2924C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C2×#13063260C2211yescharacteristic, complemented
21C2×#13063260C2211yescharacteristic, complemented
22C2×#13063251C2211yescharacteristic
23C2×#13063251C2211yescharacteristic
24C2×#13063251C2211yescharacteristic
25C2×#13063251C2211yescharacteristic
26#14582907C411yescharacteristic, complemented
27#14582907C411yescharacteristic, complemented
28#14582903C411yescharacteristic, complemented
29#14582903C411yescharacteristic, complemented
30#14582898C411yescharacteristic, complemented
31#14582898C411yescharacteristic, complemented
32#14582898C411yescharacteristic, complemented
33#14582898C411yescharacteristic, complemented
34#14582893C2211yescharacteristic
35#14582893C2211yescharacteristic
36#14582893C2211yescharacteristic
37#14582893C2211yescharacteristic
38#14582865C2211yescharacteristic
39#14582865C2211yescharacteristic
40#14582864—21no—
41#14582864—21no—
42#14582863C2211yescharacteristic
43#14582861—21no—
44C22⋊C8×D43—21no—
45C2×#13063235C2211yescharacteristic, complemented
46C2×C8×Dic43C2211yescharacteristic, complemented
47C4×C22⋊Dic43C2211yescharacteristic
48#14582663C2211yescharacteristic, complemented
49#14582663C2211yescharacteristic, complemented
50#14582658C2211yescharacteristic, complemented
51#14582658C2211yescharacteristic, complemented
52#14582658C2211yescharacteristic, complemented
53#14582658C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56C2×#117×C43C2211yescharacteristic
57C43×#433—21no—
58C43×#433—21no—
59C43×#432—21no—
60C43×#431—21no—
61C43×#424C2211yescharacteristic, complemented
62C43×#424C2211yescharacteristic, complemented
63C43×#407C2211yescharacteristic
64C2×C22⋊C8×C43C2211yescharacteristic
65C43×#405C2211yescharacteristic, complemented
66C43×#405C2211yescharacteristic, complemented
67C2×#10621898—21no—
68C2×#10621898—21no—
69C2×#10621898—22no—
70C2×#10621898—22no—
71C2×#10621898—41no—
72C2×#10621898—41no—
73C2×#10621898C2×C411yescharacteristic
74C2×#10621898C2×C411yescharacteristic
75C2×#10621898C2311yescharacteristic
76C2×#10621898C2311yescharacteristic
77C22×Dic86C2×C411yescharacteristic
78C22×D172C2×C411yescharacteristic
79C22×C22⋊D43—21no—
80C22×C4×D43—21no—
81#13063331—22no—
82#13063331—22no—
83#13063331—41no—
84#13063331—41no—
85C2×#10621877—41no—
86C2×#10621877—41no—
87C2×#10621877C2×C411yescharacteristic
88C2×#10621877C2×C411yescharacteristic
89C2×#10621877C2×C411yescharacteristic
90C2×#10621877C2×C411yescharacteristic
91C2×#10621877C2311yescharacteristic
92C2×#10621877C2311yescharacteristic
93C2×#10621872—21no—
94C2×#10621872—21no—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C2×C8×D43—21no—
98C2×C8×D43—21no—
99C2×C22⋊Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063260—41no—
103#13063260—41no—
104#13063251—22no—
105#13063251—22no—
106#13063251—41no—
107#13063251—41no—
108#13063248C2×C411yescharacteristic
109#13063248C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111#13063248C2×C411yescharacteristic
112#13063248C2×C411yescharacteristic
113#13063248C2×C411yescharacteristic
114#13063248C2×C411yescharacteristic
115#13063248C2×C411yescharacteristic
116#13063245C2×C411yescharacteristic
117#13063245C2×C411yescharacteristic
118#13063245C2×C411yescharacteristic
119#13063245C2×C411yescharacteristic
120#13063245C2×C411yescharacteristic
121#13063245C2×C411yescharacteristic
122#13063245C2×C411yescharacteristic
123#13063245C2×C411yescharacteristic
124C22⋊(C43⋊C8)—21no—
125C22⋊(C43⋊C8)—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129(C2×D43)⋊C8—21no—
130#13063235—41no—
131C8×Dic43—41no—
132C43⋊#95—21no—
133C23×C4×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138#117×C43—21no—
139#117×C43—21no—
140#117×C43C2×C411yescharacteristic
141#117×C43C2×C411yescharacteristic
142#117×C43C2311yescharacteristic
143#117×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2×C411yescharacteristic
145C2×C4⋊C4×C43C2×C411yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148C4⋊C8×C43—21no—
149C4⋊C8×C43—21no—
150C4⋊C8×C43—21no—
151C4⋊C8×C43—21no—
152C22⋊C8×C43—21no—
153C22⋊C8×C43—21no—
154C22⋊C8×C43D411yescharacteristic
155C22⋊C8×C43D411yescharacteristic
156C22⋊C8×C43D411yescharacteristic
157C22⋊C8×C43D411yescharacteristic
158#97×C43—21no—
159#97×C43—21no—
160C4×C8×C43—21no—
161C4×C8×C43—21no—
162C24×C43#4111yescharacteristic
163C23×D43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43#4111yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—21no—
177C2×C22⋊D43—21no—
178C2×C22⋊D43—21no—
179C2×C22⋊D43—21no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—42no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185#10621898—21no—
186#10621898—21no—
187#10621898—21no—
188#10621898—21no—
189#10621898—21no—
190#10621898—21no—
191#10621898—22no—
192#10621898—22no—
193#10621898—41no—
194#10621898—41no—
195#10621898—42no—
196#10621898—42no—
197#10621898—42no—
198#10621898—42no—
199#10621898#4112yes—
200#10621898#4112yes—
201C2×D172—21no—
202C2×D172—22no—
203C2×D172—41no—
204C2×D172C22×C411yescharacteristic
205C2×D172C22×C411yescharacteristic
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—42no—
211C2×C4×D43—42no—
212C2×Dic86—22no—
213C2×Dic86—21no—
214C2×Dic86—41no—
215C2×Dic86C22×C411yescharacteristic
216C2×Dic86C22×C411yescharacteristic
217M16×C43—21no—
218M16×C43—21no—
219M16×C43—21no—
220M16×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43C2×D411yescharacteristic
228C2×C8×C43C2×D411yescharacteristic
229C2×C8×C43C2×D411yescharacteristic
230C2×C8×C43C2×D411yescharacteristic
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43C22×C411yescharacteristic
234C4⋊C4×C43C22×C411yescharacteristic
235C4⋊C4×C43C22×C411yescharacteristic
236C4⋊C4×C43C22×C411yescharacteristic
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C42×C43—21no—
242C42×C43—21no—
243C42×C43—21no—
244C42×C43—21no—
245C22⋊Dic43—42no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250#10621877—21no—
251#10621877—21no—
252#10621877—21no—
253#10621877—21no—
254#10621877—41no—
255#10621877—41no—
256#10621877—41no—
257#10621877—41no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8C22×C411yescharacteristic
265C2×C43⋊C8C22×C411yescharacteristic
266C2×C43⋊C8C22×C411yescharacteristic
267C2×C43⋊C8C22×C411yescharacteristic
268#10621872—42no—
269#10621872—42no—
270C8×D43—42no—
271C8×D43—42no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43C4×D411yescharacteristic
277C23×C43C4×D411yescharacteristic
278C23×C43C2×#4111yescharacteristic
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—81no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—42no—
299C2×C4×C43—81no—
300C2×C4×C43C4×D411yescharacteristic
301C2×C4×C43C4×D411yescharacteristic
302C2×C4×C43C23×C411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C22⋊D43—22no—
309C22⋊D43—22no—
310C22⋊D43—42no—
311C22⋊D43—42no—
312C22⋊D43—41no—
313C22⋊D43—41no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—21no—
317C2×Dic43—42no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323D172—21no—
324D172—21no—
325D172—21no—
326D172—42no—
327D172#11712yes—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—42no—
331C4×D43—42no—
332C4×D43—41no—
333C4×D43—41no—
334Dic86—21no—
335Dic86—21no—
336Dic86—21no—
337Dic86—42no—
338Dic86#11712yes—
339C8×C43—21no—
340C8×C43—21no—
341C8×C43—21no—
342C8×C43—21no—
343C8×C43—41no—
344C8×C43—41no—
345C43⋊C8—21no—
346C43⋊C8—21no—
347C43⋊C8—21no—
348C43⋊C8—21no—
349C43⋊C8—41no—
350C43⋊C8—41no—
351#22588—431nomaximal, Sylow
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—21no—
355C22×C43—21no—
356C22×C43—21no—
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—21no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43C2×C4×D411yescharacteristic
363C22×C43#55111yescharacteristic
364C22×C43#55111yescharacteristic
365C2×D43—22no—
366C2×D43—41no—
367C2×D43—41no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—84no—
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—41no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43C2×#11711yescharacteristic
379C4×C43#51811yescharacteristic
380C4×C43#54611yescharacteristic
381C4×C43#54611yescharacteristic
382Dic43—22no—
383Dic43—42no—
384Dic43—41no—
385Dic43—81no—
386#2924D4311yescharacteristic, complemented
387#2896—431no—
388#2880—431no—
389#1938—431no—
390#1937—431no—
391#1929—431no—
392#1929—431no—
393#1866—431no—
394#1866—431no—
395#1826—431no—
396#1811—431no—
397#1789—431no—
398#1765—431no—
399#1764—431no—
400#1753—431no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—41no—
404C2×C43—41no—
405C2×C43#234211yescharacteristic
406C2×C43#295511yescharacteristic
407C2×C43#295611yescharacteristic
408D43—42no—
409D43—81no—
410C22×#41—431no—
411C2×#131—431no—
412C2×#131—431no—
413C22×M16—431no—
414C2×#117C2×D4311yescharacteristic
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108—431no—
420C2×#108—431no—
421#424C2×D4311yescharacteristic, complemented
422#424C2×D4311yescharacteristic, complemented
423C2×#104—431no—
424C2×#104—431no—
425C2×#104—431no—
426C2×#104—431no—
427#419—431no—
428#419—431no—
429#418—431no—
430#418—431no—
431#417—431no—
432#417—431no—
433#417—431no—
434#417—431no—
435#416—431no—
436#416—431no—
437#416—431no—
438#416—431no—
439#408—431no—
440#408—431no—
441#408—861no—
442#408—861no—
443#407—431no—
444#407—861no—
445#407C2×D4311yescharacteristic
446C2×C22⋊C8—861no—
447C2×C22⋊C8C2×D4311yescharacteristic
448#405C2×D4311yescharacteristic, complemented
449#405C2×D4311yescharacteristic, complemented
450C2×#97—431no—
451C2×C4×C8—431no—
452C4×C22⋊C4—431no—
453#341—431no—
454#341—431no—
455#339—431no—
456#339—431no—
457#339—431no—
458#339—431no—
459#336—431no—
460#336—431no—
461C43#2258811yescharacteristic, complemented, Sylow
462C2×#41—431no—
463C2×#41—431no—
464C2×#41—431no—
465C2×#41—431no—
466C2×#41—862no—
467C2×#41—862no—
468C2×#41—861no—
469C2×#41—861no—
470C2×#41—1721no—
471C2×#41—1721no—
472C22×Q8—431no—
473C22×D4—431no—
474C22×D4—861no—
475C23×C4—861no—
476C23×C4C22×D4311yescharacteristic
477#131—862no—
478#131—862no—
479#131—1721no—
480#131—1721no—
481C2×M16—431no—
482C2×M16—431no—
483C2×M16—431no—
484C2×M16—431no—
485C2×M16—431no—
486C2×M16—431no—
487C2×M16—861no—
488C2×M16—861no—
489C2×M16—1721no—
490C2×M16—1721no—
491C2×M16C22×D4311yescharacteristic
492C2×M16C22×D4311yescharacteristic
493C22×C8—431no—
494C22×C8—431no—
495C22×C8—861no—
496C22×C8—861no—
497C22×C8C22×D4311yescharacteristic
498C22×C8C22×D4311yescharacteristic
499#117—21no—
500#117—21no—
501#117C4×D4311yescharacteristic
502#117C4×D4311yescharacteristic
503#117C22×D4311yescharacteristic
504#117C22×D4311yescharacteristic
505C2×C4⋊C4C4×D4311yescharacteristic
506C2×C4⋊C4C4×D4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—861no—
509C2×C42—21no—
510C2×C42—431no—
511C2×C42—431no—
512#108—1721no—
513#108—1721no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—862no—
519#104—862no—
520#104—1721no—
521#104—1721no—
522#103—431no—
523#103—431no—
524#103—431no—
525#103—431no—
526#103—431no—
527#103—431no—
528#103—431no—
529#103—431no—
530#102—431no—
531#102—431no—
532#102—431no—
533#102—431no—
534#102—431no—
535#102—431no—
536#102—431no—
537#102—431no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—861no—
541C22⋊C8—861no—
542C22⋊C8—861no—
543C22⋊C8—861no—
544C22⋊C8—861no—
545C22⋊C8—861no—
546C22⋊C8C22⋊D4311yescharacteristic
547C22⋊C8C22⋊D4311yescharacteristic
548C22⋊C8C22⋊D4311yescharacteristic
549C22⋊C8C22⋊D4311yescharacteristic
550#97—21no—
551#97—21no—
552#97—1721no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—1721no—
556#95—861no—
557C24—861no—
558C24#1062189811yescharacteristic
559#41—432no—
560#41—432no—
561#41—862no—
562#41—862no—
563#41—861no—
564#41—861no—
565#41—861no—
566#41—861no—
567#41—861no—
568#41—861no—
569#41—1722no—
570#41—1722no—
571#41—1721no—
572#41—1721no—
573#41—1722no—
574#41—1722no—
575C2×Q8—431no—
576C2×Q8—431no—
577C2×Q8—862no—
578C2×Q8—861no—
579C2×Q8—1721no—
580C2×D4—431no—
581C2×D4—431no—
582C2×D4—862no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—1721no—
589C2×D4—1722no—
590C2×D4—1722no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4C2×C4×D4311yescharacteristic
607C22×C4C2×C4×D4311yescharacteristic
608C22×C4#1062189811yescharacteristic
609C22×C4C2×C22⋊D4311yescharacteristic
610C22×C4C2×C22⋊D4311yescharacteristic
611C22×C4C23×D4311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—861no—
617M16—861no—
618M16—861no—
619M16—861no—
620M16—1722no—
621M16—1722no—
622M16—1721no—
623M16—1721no—
624M16—1721no—
625M16—1721no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—431no—
633C2×C8—431no—
634C2×C8—431no—
635C2×C8—431no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—1722no—
643C2×C8—1722no—
644C2×C8C2×C22⋊D4311yescharacteristic
645C2×C8C2×C22⋊D4311yescharacteristic
646C2×C8C2×C22⋊D4311yescharacteristic
647C2×C8C2×C22⋊D4311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C2×C4×D4311yescharacteristic
651C4⋊C4C2×C4×D4311yescharacteristic
652C4⋊C4C2×C4×D4311yescharacteristic
653C4⋊C4C2×C4×D4311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—1722no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—861no—
664C42—861no—
665C42—861no—
666C42—861no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—861no—
672C23—861no—
673C23—3441no—
674C23—1722no—
675C23—1722no—
676C23C4×C22⋊D4311yescharacteristic
677C23C4×C22⋊D4311yescharacteristic
678C23C2×#1062189811yescharacteristic
679Q8—432no—
680Q8—861no—
681Q8—861no—
682Q8—861no—
683Q8—1722no—
684D4—432no—
685D4—862no—
686D4—862no—
687D4—861no—
688D4—861no—
689D4—861no—
690D4—1722no—
691D4—1722no—
692D4—1722no—
693D4—1721no—
694D4—1721no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—81no—
711C2×C4—861no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—861no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4C4×C22⋊D4311yescharacteristic
727C2×C4C4×C22⋊D4311yescharacteristic
728C2×C4C22×C4×D4311yescharacteristic
729C2×C4C22×C22⋊D4311yescharacteristic
730C2×C4#41×D4311yescharacteristic
731C2×C4#41×D4311yescharacteristic
732C2×C4#1306337111yescharacteristic
733C2×C4#1306337111yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—861no—
741C8—861no—
742C8—861no—
743C8—861no—
744C8—1721no—
745C8—1721no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—81no—
755C22—81no—
756C22—862no—
757C22—3444no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22C2×C4×C22⋊D4311yescharacteristic
764C22#1458357311yescharacteristic
765C22#1458357311yescharacteristic
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—862no—
773C4—3441no—
774C4—1722no—
775C4—1721no—
776C4#117×D4311yescharacteristic
777C4#1458337311yescharacteristic
778C4#1458353711yescharacteristic
779C4#1458353711yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—3441no—
785C2—1722no—
786C2#1913744511yescharacteristic
787C2#1914349611yescharacteristic
788C2#1914350211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2924C2
socleC22×C43C2×C4×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#2924D43
hypocenterC43#22588
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #19135305C2semidirect
4. #19135298C2semidirect
5. #19135243C2semidirect
6. #19135243C2semidirect
7. #19134869C2semidirect
8. #19134869C2semidirect
9. #19134694C2semidirect
10. #19134635C2semidirect
12. #19134441C2semidirect
13. #19134434C2semidirect
14. #19134381C2semidirect
15. C43×#2924C2semidirect
20. C2×#13063260C22semidirect
21. C2×#13063260C22semidirect
26. #14582907C4semidirect
27. #14582907C4semidirect
28. #14582903C4semidirect
29. #14582903C4semidirect
30. #14582898C4semidirect
31. #14582898C4semidirect
32. #14582898C4semidirect
33. #14582898C4semidirect
45. C2×#13063235C22semidirect
46. C2×C8×Dic43C22semidirect
48. #14582663C22semidirect
49. #14582663C22semidirect
50. #14582658C22semidirect
51. #14582658C22semidirect
52. #14582658C22semidirect
53. #14582658C22semidirect
54. #14582653C22semidirect
55. #14582653C22semidirect
61. C43×#424C22semidirect
62. C43×#424C22semidirect
65. C43×#405C22semidirect
66. C43×#405C22semidirect
386. #2924D43semidirect
421. #424C2×D43semidirect
422. #424C2×D43semidirect
448. #405C2×D43semidirect
449. #405C2×D43semidirect
461. C43#22588semidirect

Maximal subgroups

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

subgroupindex
#191431122
#191430412
#191353052
#191352982
#191352432
#191348692
#191346942
#191346352
#191345382
#191344412
#191344342
#191343812
C43×#29242
#2258843