Finite Group Databasebeta

← #25113973

Subgroups — #25113973

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#19143249C211yesmaximal, characteristic, complemented
2#19143115C211yesmaximal, characteristic
3#19143041C211yesmaximal, characteristic
4#19135306C211yesmaximal, characteristic, complemented
5#19135299C211yesmaximal, characteristic, complemented
6#19135244C211yesmaximal, characteristic, complemented
7#19135244C211yesmaximal, characteristic, complemented
8#19134873C211yesmaximal, characteristic, complemented
9#19134873C211yesmaximal, characteristic, complemented
10#19134695C211yesmaximal, characteristic, complemented
11#19134637C211yesmaximal, characteristic, complemented
12#19134540C211yesmaximal, characteristic
13#19134439C211yesmaximal, characteristic, complemented
14#19134432C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20#14582957—21no—
21#14582957—21no—
22#14582953—21no—
23#14582949—21no—
24C2×#13063261C2211yescharacteristic, complemented
25C2×#13063261C2211yescharacteristic, complemented
26#14582925C2211yescharacteristic, complemented
27#14582925C2211yescharacteristic, complemented
28C2×#13063253C2211yescharacteristic
29C2×#13063253C2211yescharacteristic
30C2×#13063253C2211yescharacteristic
31C2×#13063253C2211yescharacteristic
32#14582909C411yescharacteristic, complemented
33#14582909C411yescharacteristic, complemented
34#14582905C411yescharacteristic, complemented
35#14582905C411yescharacteristic, complemented
36#14582901C411yescharacteristic, complemented
37#14582901C411yescharacteristic, complemented
38#14582901C411yescharacteristic, complemented
39#14582901C411yescharacteristic, complemented
40#14582896C2211yescharacteristic
41#14582896C2211yescharacteristic
42#14582896C2211yescharacteristic
43#14582896C2211yescharacteristic
44#14582865C2211yescharacteristic
45#14582865C2211yescharacteristic
46#14582864—21no—
47#14582864—21no—
48#14582863C2211yescharacteristic
49#14582863C2211yescharacteristic
50#14582861—21no—
51C22⋊C8×D43—21no—
52#14582854C2211yescharacteristic, complemented
53#14582854C2211yescharacteristic, complemented
54#14582664C2211yescharacteristic, complemented
55#14582664C2211yescharacteristic, complemented
56#14582659C2211yescharacteristic, complemented
57#14582659C2211yescharacteristic, complemented
58#14582659C2211yescharacteristic, complemented
59#14582659C2211yescharacteristic, complemented
60C22×M16×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic, complemented
63C2×C4×C8×C43C2211yescharacteristic, complemented
64C4×C22⋊C4×C43C2211yescharacteristic
65C43×#336C2211yescharacteristic, complemented
66C43×#336C2211yescharacteristic, 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×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621872—21no—
90C2×#10621872—21no—
91C2×C8×D43—21no—
92C2×C8×D43—21no—
93#13063284—21no—
94#13063284—21no—
95#13063284C2×C411yescharacteristic
96#13063284C2×C411yescharacteristic
97#13063284C2311yescharacteristic
98#13063284C2311yescharacteristic
99C2×C4⋊Dic43C2×C411yescharacteristic
100C2×C4⋊Dic43C2×C411yescharacteristic
101C2×C22⋊Dic43—21no—
102C2×C4×Dic43—21no—
103#13063261—41no—
104#13063261—41no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063253—22no—
110#13063253—22no—
111#13063253—41no—
112#13063253—41no—
113#13063250C2×C411yescharacteristic
114#13063250C2×C411yescharacteristic
115#13063250C2×C411yescharacteristic
116#13063250C2×C411yescharacteristic
117#13063250C2×C411yescharacteristic
118#13063250C2×C411yescharacteristic
119#13063250C2×C411yescharacteristic
120#13063250C2×C411yescharacteristic
121#13063247C2×C411yescharacteristic
122#13063247C2×C411yescharacteristic
123#13063247C2×C411yescharacteristic
124#13063247C2×C411yescharacteristic
125#13063247C2×C411yescharacteristic
126#13063247C2×C411yescharacteristic
127#13063247C2×C411yescharacteristic
128#13063247C2×C411yescharacteristic
129C22⋊(C43⋊C8)—21no—
130C22⋊(C43⋊C8)—21no—
131C22⋊(C43⋊C8)—21no—
132C22⋊(C43⋊C8)—21no—
133(C2×D43)⋊C8—21no—
134(C2×D43)⋊C8—21no—
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137#13063235—21no—
138#13063235—21no—
139C8×Dic43—21no—
140C8×Dic43—21no—
141C23×C4×C43C2311yescharacteristic
142C2×M16×C43—41no—
143C2×M16×C43—41no—
144C2×M16×C43C2×C411yescharacteristic
145C2×M16×C43C2×C411yescharacteristic
146C2×M16×C43C2×C411yescharacteristic
147C2×M16×C43C2×C411yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C22×C8×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153C2×C42×C43C2311yescharacteristic
154C2×C42×C43C2311yescharacteristic
155C22⋊C8×C43D411yescharacteristic
156C22⋊C8×C43D411yescharacteristic
157C22⋊C8×C43D411yescharacteristic
158C22⋊C8×C43D411yescharacteristic
159#97×C43—41no—
160C4×C8×C43—41no—
161#95×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—41no—
218M16×C43—41no—
219M16×C43—41no—
220M16×C43—41no—
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×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43C22×C411yescharacteristic
230C2×C8×C43C22×C411yescharacteristic
231C2×C8×C43C22×C411yescharacteristic
232C2×C8×C43C22×C411yescharacteristic
233C2×C8×C43C2×D411yescharacteristic
234C2×C8×C43C2×D411yescharacteristic
235C2×C8×C43C2×D411yescharacteristic
236C2×C8×C43C2×D411yescharacteristic
237C22⋊C4×C43—42no—
238C42×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—21no—
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43C22×C411yescharacteristic
249C4⋊Dic43C22×C411yescharacteristic
250C4⋊Dic43C22×C411yescharacteristic
251C4⋊Dic43C22×C411yescharacteristic
252C4×Dic43—21no—
253C4×Dic43—21no—
254C4×Dic43—21no—
255C4×Dic43—21no—
256#10621877—21no—
257#10621877—21no—
258#10621877—21no—
259#10621877—21no—
260#10621877—21no—
261#10621877—21no—
262#10621877—21no—
263#10621877—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
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—22no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
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—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—81no—
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—21no—
344C8×C43—21no—
345C8×C43—21no—
346C8×C43—21no—
347C43⋊C8—41no—
348C43⋊C8—41no—
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—42no—
375C4×C43—81no—
376C4×C43C2×#11711yescharacteristic
377C4×C43#51811yescharacteristic
378C4×C43#54611yescharacteristic
379C4×C43#54611yescharacteristic
380Dic43—22no—
381Dic43—41no—
382Dic43—41no—
383Dic43—41no—
384Dic43—41no—
385Dic43—41no—
386#2924—431no—
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#1753D4311yescharacteristic, complemented
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×M16C2×D4311yescharacteristic
414C2×#117—431no—
415#433—861no—
416#433—861no—
417#432—861no—
418#431—861no—
419C2×#108—431no—
420C2×#108—431no—
421#424—431no—
422#424—431no—
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—431no—
445#407—861no—
446C2×C22⋊C8—861no—
447C2×C22⋊C8C2×D4311yescharacteristic
448#405—431no—
449#405—431no—
450C2×#97C2×D4311yescharacteristic, complemented
451C2×C4×C8C2×D4311yescharacteristic, complemented
452C4×C22⋊C4C2×D4311yescharacteristic
453#341—431no—
454#341—431no—
455#339—431no—
456#339—431no—
457#339—431no—
458#339—431no—
459#336C2×D4311yescharacteristic, complemented
460#336C2×D4311yescharacteristic, complemented
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—41no—
482C2×M16—41no—
483C2×M16—431no—
484C2×M16—431no—
485C2×M16—431no—
486C2×M16—431no—
487C2×M16—861no—
488C2×M16—861no—
489C2×M16C4×D4311yescharacteristic
490C2×M16C4×D4311yescharacteristic
491C2×M16C4×D4311yescharacteristic
492C2×M16C4×D4311yescharacteristic
493C22×C8—861no—
494C22×C8—861no—
495C22×C8C22×D4311yescharacteristic
496C22×C8C22×D4311yescharacteristic
497C22×C8C22×D4311yescharacteristic
498C22×C8C22×D4311yescharacteristic
499#117—431no—
500#117—431no—
501#117—431no—
502#117—431no—
503#117—861no—
504#117—861no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—861no—
509C2×C42—861no—
510C2×C42C22×D4311yescharacteristic
511C2×C42C22×D4311yescharacteristic
512#108—1721no—
513#108—1721no—
514C4⋊C8—861no—
515C4⋊C8—861no—
516C4⋊C8—861no—
517C4⋊C8—861no—
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—861no—
539C22⋊C8—861no—
540C22⋊C8—861no—
541C22⋊C8—861no—
542C22⋊C8—861no—
543C22⋊C8—861no—
544C22⋊C8—861no—
545C22⋊C8—861no—
546C22⋊C8D17211yescharacteristic
547C22⋊C8D17211yescharacteristic
548C22⋊C8D17211yescharacteristic
549C22⋊C8D17211yescharacteristic
550#97—41no—
551#97—861no—
552#97—861no—
553C4×C8—41no—
554C4×C8—861no—
555C4×C8—861no—
556#95—21no—
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×C4C2×D17211yescharacteristic
609C22×C4C2×D17211yescharacteristic
610C22×C4#1062189811yescharacteristic
611C22×C4C23×D4311yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—861no—
617M16—861no—
618M16—861no—
619M16—861no—
620M16—861no—
621M16—861no—
622M16—861no—
623M16—861no—
624M16—1722no—
625M16—1722no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—1722no—
639C2×C8—1722no—
640C2×C8C2×C4×D4311yescharacteristic
641C2×C8C2×C4×D4311yescharacteristic
642C2×C8C2×C4×D4311yescharacteristic
643C2×C8C2×C4×D4311yescharacteristic
644C2×C8C2×D17211yescharacteristic
645C2×C8C2×D17211yescharacteristic
646C2×C8C2×D17211yescharacteristic
647C2×C8C2×D17211yescharacteristic
648C4⋊C4—431no—
649C4⋊C4—431no—
650C4⋊C4—431no—
651C4⋊C4—431no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C22⋊C4—42no—
655C22⋊C4—861no—
656C22⋊C4—861no—
657C22⋊C4—861no—
658C22⋊C4—861no—
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×D17211yescharacteristic
677C23C4×D17211yescharacteristic
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—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—861no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—3441no—
720C2×C4—1722no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4C4×D17211yescharacteristic
727C2×C4C4×D17211yescharacteristic
728C2×C4C22×C4×D4311yescharacteristic
729C2×C4C22×D17211yescharacteristic
730C2×C4#41×D4311yescharacteristic
731C2×C4#41×D4311yescharacteristic
732C2×C4#1306337011yescharacteristic
733C2×C4#1306337011yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—1721no—
743C8—1721no—
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×D17211yescharacteristic
764C22#1458357811yescharacteristic
765C22#1458357811yescharacteristic
766C4—21no—
767C4—21no—
768C4—42no—
769C4—81no—
770C4—862no—
771C4—1721no—
772C4—1721no—
773C4—1721no—
774C4—1721no—
775C4—1721no—
776C4#117×D4311yescharacteristic
777C4#1458337211yescharacteristic
778C4#1458354411yescharacteristic
779C4#1458354411yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—3441no—
785C2—1722no—
786C2#1913744711yescharacteristic
787C2#1914349911yescharacteristic
788C2#1914350611yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1753C2
socleC22×C43C2×C4×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1753D43
hypocenterC43#22588
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. #19143249C2semidirect
4. #19135306C2semidirect
5. #19135299C2semidirect
6. #19135244C2semidirect
7. #19135244C2semidirect
8. #19134873C2semidirect
9. #19134873C2semidirect
10. #19134695C2semidirect
11. #19134637C2semidirect
13. #19134439C2semidirect
14. #19134432C2semidirect
15. C43×#1753C2semidirect
24. C2×#13063261C22semidirect
25. C2×#13063261C22semidirect
26. #14582925C22semidirect
27. #14582925C22semidirect
32. #14582909C4semidirect
33. #14582909C4semidirect
34. #14582905C4semidirect
35. #14582905C4semidirect
36. #14582901C4semidirect
37. #14582901C4semidirect
38. #14582901C4semidirect
39. #14582901C4semidirect
52. #14582854C22semidirect
53. #14582854C22semidirect
54. #14582664C22semidirect
55. #14582664C22semidirect
56. #14582659C22semidirect
57. #14582659C22semidirect
58. #14582659C22semidirect
59. #14582659C22semidirect
62. C2×#97×C43C22semidirect
63. C2×C4×C8×C43C22semidirect
65. C43×#336C22semidirect
66. C43×#336C22semidirect
400. #1753D43semidirect
450. C2×#97C2×D43semidirect
451. C2×C4×C8C2×D43semidirect
459. #336C2×D43semidirect
460. #336C2×D43semidirect
461. C43#22588semidirect

Maximal subgroups

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

subgroupindex
#191432492
#191431152
#191430412
#191353062
#191352992
#191352442
#191348732
#191346952
#191346372
#191345402
#191344392
#191344322
C43×#17532
#2258843