Finite Group Databasebeta

← #25113944

Subgroups — #25113944

Order 11008.

894 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#19143252C211yesmaximal, characteristic, complemented
2#416×D43C211yesmaximal, characteristic
3#19143042C211yesmaximal, characteristic
4#19135307C211yesmaximal, characteristic, complemented
5#19135305C211yesmaximal, characteristic, complemented
6#19135244C211yesmaximal, characteristic, complemented
7#19135242C211yesmaximal, characteristic, complemented
8#19134872C211yesmaximal, characteristic, complemented
9#19134693C211yesmaximal, characteristic, complemented
10#19134630C211yesmaximal, characteristic, complemented
11#19134537C211yesmaximal, characteristic
12#19134440C211yesmaximal, characteristic, complemented
13#19134437C211yesmaximal, characteristic, complemented
14#19134370C211yesmaximal, characteristic, complemented
15C43×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#117×D43C2211yescharacteristic
20#14582959—21no—
21#14582959—21no—
22#14582955—21no—
23#14582951—21no—
24C2×#13063261C2211yescharacteristic, complemented
25#14582926C2211yescharacteristic, complemented
26C2×#13063253C2211yescharacteristic
27C2×#13063252C2211yescharacteristic
28C2×#13063251C2211yescharacteristic
29#14582896C2211yescharacteristic
30#14582895C2211yescharacteristic
31#14582894C411yescharacteristic, complemented
32#14582894C411yescharacteristic, complemented
33#14582893C2211yescharacteristic
34#14582892C411yescharacteristic, complemented
35#14582892C411yescharacteristic, complemented
36#103×D43C411yescharacteristic, complemented
37#103×D43C411yescharacteristic, complemented
38#102×D43C411yescharacteristic, complemented
39#102×D43C411yescharacteristic, complemented
40#14582867—21no—
41#14582867C2211yescharacteristic
42#14582865—21no—
43#14582865C2211yescharacteristic
44#14582862—21no—
45#14582862C2211yescharacteristic
46#14582862C2211yescharacteristic
47C2×(C2×D43)⋊C8—21no—
48C2×(C2×D43)⋊C8C2211yescharacteristic
49#14582857C2211yescharacteristic, complemented
50#14582854C2211yescharacteristic, complemented
51C2×#13063236C2211yescharacteristic, complemented
52C2×#13063235C2211yescharacteristic, complemented
53C4×(C2×D43)⋊C4C2211yescharacteristic
54#14582663C2211yescharacteristic, complemented
55#14582663C2211yescharacteristic, complemented
56#14582660C2211yescharacteristic, complemented
57#14582659C2211yescharacteristic, complemented
58#14582658C2211yescharacteristic, complemented
59#14582653C2211yescharacteristic, complemented
60C2×#131×C43C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic, complemented
62C43×#424C2211yescharacteristic, complemented
63C2×#104×C43C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C43×#339C2211yescharacteristic, complemented
66C43×#336C2211yescharacteristic, complemented
67C2×#10621902C2×C411yescharacteristic
68C2×#10621898—21no—
69C2×#10621898C2311yescharacteristic
70C2×#10621900—21no—
71C2×#10621900C2×C411yescharacteristic
72#41×D43—22no—
73#41×D43—22no—
74#41×D43—41no—
75#41×D43—41no—
76C2×Q8×D43C2×C411yescharacteristic
77C2×D4×D43—21no—
78C2×D4×D43C2×C411yescharacteristic
79C22×C4×D43—21no—
80C22×C4×D43C2311yescharacteristic
81#13063332—22no—
82#13063332—41no—
83C2×#10621877—21no—
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C22×C43⋊C8—21no—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C2×C8×D43—41no—
90C2×C8×D43—41no—
91C2×C8×D43C2×C411yescharacteristic
92C2×C8×D43C2×C411yescharacteristic
93C2×C8×D43C2×C411yescharacteristic
94C2×C8×D43C2×C411yescharacteristic
95#13063284C2311yescharacteristic
96#13063283C2×C411yescharacteristic
97#13063283C2×C411yescharacteristic
98#13063282—21no—
99#13063281—21no—
100C4⋊C4×D43C2×C411yescharacteristic
101C4⋊C4×D43C2×C411yescharacteristic
102C2×(C2×D43)⋊C4—21no—
103C22⋊C4×D43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C42×D43—21no—
106#13063261—41no—
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109#13063253—41no—
110#13063252—22no—
111#13063251—41no—
112#13063250C2×C411yescharacteristic
113#13063250C2×C411yescharacteristic
114#13063249C2×C411yescharacteristic
115#13063249C2×C411yescharacteristic
116#13063248C2×C411yescharacteristic
117#13063248C2×C411yescharacteristic
118#13063247C2×C411yescharacteristic
119#13063247C2×C411yescharacteristic
120#13063246C2×C411yescharacteristic
121#13063246C2×C411yescharacteristic
122#13063245C2×C411yescharacteristic
123#13063245C2×C411yescharacteristic
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129(C2×D43)⋊C8—21no—
130(C2×D43)⋊C8—21no—
131(C2×D43)⋊C8—21no—
132(C2×D43)⋊C8D411yescharacteristic
133(C2×D43)⋊C8D411yescharacteristic
134(C2×D43)⋊C8D411yescharacteristic
135(C2×D43)⋊C8D411yescharacteristic
136#13063236—41no—
137#13063235—21no—
138#13063235—21no—
139#13063235—41no—
140C8×Dic43—21no—
141C8×Dic43—21no—
142C43⋊#95—21no—
143C2×#41×C43C2311yescharacteristic
144#131×C43—22no—
145#131×C43—41no—
146C2×M16×C43—21no—
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C22×C8×C43—21no—
150C22×C8×C43C2311yescharacteristic
151C22×C8×C43C2311yescharacteristic
152#117×C43C2311yescharacteristic
153C2×C42×C43C2311yescharacteristic
154#108×C43—41no—
155C4⋊C8×C43—21no—
156C4⋊C8×C43—21no—
157#104×C43—22no—
158#103×C43C2×C411yescharacteristic
159#103×C43C2×C411yescharacteristic
160#102×C43C2×C411yescharacteristic
161#102×C43C2×C411yescharacteristic
162C23×D43—21no—
163C23×D43#4111yescharacteristic
164#41×C43—21no—
165#41×C43—21no—
166#41×C43#4112yes—
167#41×C43#4112yes—
168C2×Q8×C43C22×C411yescharacteristic
169C2×D4×C43—21no—
170C2×D4×C43C22×C411yescharacteristic
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2411yescharacteristic
174C2×C22⋊D43—21no—
175C2×C22⋊D43—21no—
176C2×C22⋊D43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43#4111yescharacteristic
180#10621902—22no—
181#10621902—41no—
182Q8×D43—22no—
183Q8×D43—41no—
184#10621900—22no—
185#10621900—41no—
186#10621900—42no—
187#10621900—42no—
188D4×D43—22no—
189D4×D43—42no—
190D4×D43—42no—
191D4×D43—41no—
192#10621898—21no—
193#10621898—21no—
194#10621898—21no—
195#10621898—21no—
196#10621898—42no—
197#10621898—42no—
198C2×D172—21no—
199C2×D172C22×C411yescharacteristic
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43C22×C411yescharacteristic
212C2×C4×D43C22×C411yescharacteristic
213C2×C4×D43C2×D411yescharacteristic
214C2×C4×D43C2×D411yescharacteristic
215C2×Dic86—21no—
216C2×Dic86C22×C411yescharacteristic
217M16×C43—21no—
218M16×C43—21no—
219M16×C43—21no—
220M16×C43—21no—
221M16×C43—42no—
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—42no—
229C2×C8×C43C22×C411yescharacteristic
230C2×C8×C43C22×C411yescharacteristic
231C2×C8×C43C2×D411yescharacteristic
232C2×C8×C43C2×D411yescharacteristic
233C4⋊C4×C43C22×C411yescharacteristic
234C4⋊C4×C43C22×C411yescharacteristic
235C22⋊C4×C43—21no—
236C42×C43—21no—
237C42×C43—21no—
238C42×C43—21no—
239C22⋊Dic43—21no—
240(C2×D43)⋊C4—21no—
241(C2×D43)⋊C4—21no—
242(C2×D43)⋊C4—42no—
243C4⋊Dic43C22×C411yescharacteristic
244C4⋊Dic43C22×C411yescharacteristic
245Dic43⋊C4—21no—
246Dic43⋊C4—21no—
247C4×Dic43—21no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43—21no—
251C4×Dic43—21no—
252#10621877—21no—
253#10621877—21no—
254#10621877—21no—
255#10621877—21no—
256#10621877—42no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—42no—
264C2×C43⋊C8C22×C411yescharacteristic
265C2×C43⋊C8C22×C411yescharacteristic
266C2×C43⋊C8C2×D411yescharacteristic
267C2×C43⋊C8C2×D411yescharacteristic
268C8×D43—41no—
269C8×D43—41no—
270C8×D43—41no—
271C8×D43—41no—
272C23×C43—21no—
273C23×C43C2×#4111yescharacteristic
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—22no—
277C22×D43—21no—
278C22×D43—41no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—81no—
282C22×D43C4×D411yescharacteristic
283C22×D43C4×D411yescharacteristic
284Q8×C43—21no—
285Q8×C43#11712yes—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—21no—
289D4×C43#11712yes—
290C2×C4×C43—21no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43C23×C411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C22⋊D43—42no—
305C22⋊D43—42no—
306C22⋊D43—41no—
307C22⋊D43—41no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—42no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43C4×D411yescharacteristic
318C2×Dic43C4×D411yescharacteristic
319D172—21no—
320D172—21no—
321D172—42no—
322C4×D43—21no—
323C4×D43—21no—
324C4×D43—21no—
325C4×D43—21no—
326C4×D43—21no—
327C4×D43—21no—
328C4×D43—21no—
329C4×D43—21no—
330C4×D43—42no—
331C4×D43—42no—
332C4×D43—42no—
333C4×D43—41no—
334C4×D43—41no—
335C4×D43—81no—
336Dic86—21no—
337Dic86—21no—
338Dic86—42no—
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#22586—431nomaximal, Sylow
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—22no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43C2×C4×D411yescharacteristic
358C22×C43#55111yescharacteristic
359C22×C43#55111yescharacteristic
360C2×D43—21no—
361C2×D43—21no—
362C2×D43—21no—
363C2×D43—21no—
364C2×D43—21no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—41no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—84no—
371C2×D43#44412yes—
372C4×C43—22no—
373C4×C43—41no—
374C4×C43—41no—
375C4×C43—81no—
376C4×C43C2×#11711yescharacteristic
377C4×C43#51811yescharacteristic
378C4×C43#54611yescharacteristic
379C4×C43#54611yescharacteristic
380Dic43—21no—
381Dic43—21no—
382Dic43—41no—
383Dic43—41no—
384Dic43—41no—
385Dic43—81no—
386#2924—431no—
387C2×#416—431no—
388#2880—431no—
389#1938—431no—
390#1938—431no—
391#1929—431no—
392#1929—431no—
393#1866—431no—
394#1866D4311yescharacteristic, complemented
395#1826—431no—
396#1810—431no—
397#1789—431no—
398#1765—431no—
399#1765—431no—
400#1752—431no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—42no—
404C2×C43#234211yescharacteristic
405C2×C43C2×#44411yescharacteristic
406C2×C43#295711yescharacteristic
407D43—22no—
408D43—41no—
409D43—81no—
410C22×#41—431no—
411C2×#131—431no—
412C2×#131C2×D4311yescharacteristic
413C23×C8—431no—
414C2×#117—431no—
415#433—861no—
416#433—861no—
417#432—861no—
418#431—861no—
419C2×#108—431no—
420C2×#108C2×D4311yescharacteristic, complemented
421#424—431no—
422#424C2×D4311yescharacteristic, complemented
423C2×#104—431no—
424C2×#104—431no—
425C2×#104—431no—
426C2×#104C2×D4311yescharacteristic
427#416—431no—
428#416—431no—
429#416—431no—
430#416—431no—
431#416—431no—
432#416—431no—
433#416—431no—
434#416C2×D4311yescharacteristic
435C2×#103—431no—
436C2×#103—431no—
437C2×#102—431no—
438C2×#102—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—431no—
447C2×C22⋊C8—861no—
448#405—431no—
449#405—431no—
450C2×#97—431no—
451C2×#97—431no—
452C4×C22⋊C4—431no—
453#341—431no—
454#341—431no—
455#339—431no—
456#339—431no—
457#339—431no—
458#339C2×D4311yescharacteristic, complemented
459#336—431no—
460#336C2×D4311yescharacteristic, complemented
461C43#2258611yescharacteristic, complemented, Sylow
462C2×#41—431no—
463C2×#41—431no—
464C2×#41—431no—
465C2×#41—861no—
466C2×#41—861no—
467C2×#41—862no—
468C2×#41—862no—
469C2×#41—1721no—
470C2×#41—1721no—
471C2×#41C22×D4311yescharacteristic
472C22×Q8—431no—
473C22×D4—431no—
474C22×D4—861no—
475C23×C4—431no—
476C23×C4—861no—
477#131—22no—
478#131—41no—
479#131—862no—
480#131—1721no—
481C2×M16—21no—
482C2×M16—431no—
483C2×M16—431no—
484C2×M16—861no—
485C2×M16C22×D4311yescharacteristic
486C2×M16C22×D4311yescharacteristic
487C22×C8—21no—
488C22×C8—431no—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8—431no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—861no—
495C22×C8—1721no—
496C22×C8—1721no—
497C22×C8C22×D4311yescharacteristic
498C22×C8C22×D4311yescharacteristic
499#117—431no—
500#117—431no—
501#117—431no—
502#117—861no—
503#117—861no—
504#117C22×D4311yescharacteristic
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C42—431no—
510C2×C42—861no—
511C2×C42C22×D4311yescharacteristic
512#108—41no—
513#108—1721no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—861no—
517C4⋊C8—861no—
518#104—22no—
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#103C4×D4311yescharacteristic
529#103C4×D4311yescharacteristic
530#102—431no—
531#102—431no—
532#102—431no—
533#102—431no—
534#102—431no—
535#102—431no—
536#102C4×D4311yescharacteristic
537#102C4×D4311yescharacteristic
538C22⋊C8—431no—
539C22⋊C8—431no—
540C22⋊C8—431no—
541C22⋊C8—431no—
542C22⋊C8—861no—
543C22⋊C8—861no—
544C22⋊C8—861no—
545C22⋊C8—861no—
546C22⋊C8—861no—
547C22⋊C8—861no—
548C22⋊C8—861no—
549C22⋊C8—861no—
550#97—861no—
551#97—861no—
552#97—1721no—
553#97—1721no—
554C4×C8—861no—
555C4×C8—861no—
556#95—861no—
557C24—431no—
558C24—861no—
559#41—21no—
560#41—21no—
561#41—862no—
562#41—862no—
563#41—861no—
564#41—861no—
565#41—861no—
566#41—861no—
567#41—1722no—
568#41—1722no—
569#41—1721no—
570#41—1722no—
571#41—1722no—
572#41—1721no—
573#41#1062190012yes—
574#41#1062190212yes—
575C2×Q8—431no—
576C2×Q8—861no—
577C2×Q8—862no—
578C2×Q8—1721no—
579C2×Q8C2×C4×D4311yescharacteristic
580C2×D4—21no—
581C2×D4—431no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—862no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—1721no—
588C2×D4—1722no—
589C2×D4—1722no—
590C2×D4C2×C4×D4311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—1722no—
610C22×C4—1722no—
611C22×C4C23×D4311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—42no—
617M16—861no—
618M16—861no—
619M16—861no—
620M16—861no—
621M16—1722no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8—431no—
630C2×C8—431no—
631C2×C8—431no—
632C2×C8—431no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—1721no—
640C2×C8—1721no—
641C2×C8—1721no—
642C2×C8—1721no—
643C2×C8—1722no—
644C2×C8C2×C4×D4311yescharacteristic
645C2×C8C2×C4×D4311yescharacteristic
646C2×C8D4×D4311yescharacteristic
647C2×C8D4×D4311yescharacteristic
648C4⋊C4—431no—
649C4⋊C4—431no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4C2×C4×D4311yescharacteristic
653C4⋊C4C2×C4×D4311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—861no—
656C22⋊C4—861no—
657C22⋊C4—861no—
658C22⋊C4—1722no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—861no—
663C42—861no—
664C42—861no—
665C42—861no—
666C42—861no—
667C23—21no—
668C23—431no—
669C23—431no—
670C23—862no—
671C23—861no—
672C23—861no—
673C23—861no—
674C23—3441no—
675C23—1721no—
676C23—1722no—
677C23—1722no—
678C23#41×D4311yescharacteristic
679Q8—21no—
680Q8—861no—
681Q8—861no—
682Q8—1722no—
683Q8#1306328312yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—861no—
688D4—861no—
689D4—1722no—
690D4—1722no—
691D4—1722no—
692D4—1721no—
693D4—1721no—
694D4#1306328312yes—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—431no—
704C2×C4—431no—
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—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—3441no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4C22×C4×D4311yescharacteristic
729C2×C4C2×D4×D4311yescharacteristic
730C2×C4C2×#1062190011yescharacteristic
731C2×C4C2×#1062190211yescharacteristic
732C2×C4#1306337011yescharacteristic
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—22no—
749C22—41no—
750C22—41no—
751C22—432no—
752C22—861no—
753C22—861no—
754C22—861no—
755C22—861no—
756C22—861no—
757C22—3444no—
758C22—1722no—
759C22—1722no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22C4×D4×D4311yescharacteristic
764C22#1458357211yescharacteristic
765C22#1458357611yescharacteristic
766C4—22no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—861no—
771C4—861no—
772C4—3441no—
773C4—1721no—
774C4—1721no—
775C4—1721no—
776C4C2×#1306328311yescharacteristic
777C4#1458337111yescharacteristic
778C4#1458353611yescharacteristic
779C4#1458354011yescharacteristic
780C2—21no—
781C2—21no—
782C2—42no—
783C2—862no—
784C2—3441no—
785C2—1721no—
786C2#1913744211yescharacteristic
787C2#444×D4311yescharacteristic
788C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1866C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1866D43
hypocenterC43#22586
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
1. #19143252C2semidirect
4. #19135307C2semidirect
5. #19135305C2semidirect
6. #19135244C2semidirect
7. #19135242C2semidirect
8. #19134872C2semidirect
9. #19134693C2semidirect
10. #19134630C2semidirect
12. #19134440C2semidirect
13. #19134437C2semidirect
14. #19134370C2semidirect
15. C43×#1866C2semidirect
24. C2×#13063261C22semidirect
25. #14582926C22semidirect
31. #14582894C4semidirect
32. #14582894C4semidirect
34. #14582892C4semidirect
35. #14582892C4semidirect
36. #103×D43C4semidirect
37. #103×D43C4semidirect
38. #102×D43C4semidirect
39. #102×D43C4semidirect
49. #14582857C22semidirect
50. #14582854C22semidirect
51. C2×#13063236C22semidirect
52. C2×#13063235C22semidirect
54. #14582663C22semidirect
55. #14582663C22semidirect
56. #14582660C22semidirect
57. #14582659C22semidirect
58. #14582658C22semidirect
59. #14582653C22semidirect
61. C2×#108×C43C22semidirect
62. C43×#424C22semidirect
65. C43×#339C22semidirect
66. C43×#336C22semidirect
394. #1866D43semidirect
420. C2×#108C2×D43semidirect
422. #424C2×D43semidirect
458. #339C2×D43semidirect
460. #336C2×D43semidirect
461. C43#22586semidirect

Maximal subgroups

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

subgroupindex
#191432522
#416×D432
#191430422
#191353072
#191353052
#191352442
#191352422
#191348722
#191346932
#191346302
#191345372
#191344402
#191344372
#191343702
C43×#18662
#2258643