Finite Group Databasebeta

← #25113945

Subgroups — #25113945

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#19143043C211yesmaximal, characteristic
4#19135308C211yesmaximal, characteristic, complemented
5#19135246C211yesmaximal, characteristic, complemented
6#19135240C211yesmaximal, characteristic, complemented
7#19134871C211yesmaximal, characteristic, complemented
8#19134869C211yesmaximal, characteristic, complemented
9#19134693C211yesmaximal, characteristic, complemented
10#19134632C211yesmaximal, characteristic, complemented
11#19134537C211yesmaximal, characteristic
12#19134439C211yesmaximal, characteristic, complemented
13#19134438C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic, complemented
15C43×#1938C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#117×D43C2211yescharacteristic
21#14582959—21no—
22#14582959—21no—
23#14582955—21no—
24#14582951—21no—
25C2×#13063260C2211yescharacteristic, complemented
26C2×#13063260C2211yescharacteristic, complemented
27#14582926C2211yescharacteristic, complemented
28C2×#13063253C2211yescharacteristic
29C2×#13063252C2211yescharacteristic
30C2×#13063251C2211yescharacteristic
31#14582896C2211yescharacteristic
32#14582895C2211yescharacteristic
33#14582894C411yescharacteristic, complemented
34#14582894C411yescharacteristic, complemented
35#14582893C2211yescharacteristic
36#14582892C411yescharacteristic, complemented
37#14582892C411yescharacteristic, complemented
38#103×D43C411yescharacteristic, complemented
39#103×D43C411yescharacteristic, complemented
40#102×D43C411yescharacteristic, complemented
41#102×D43C411yescharacteristic, complemented
42#14582866C2211yescharacteristic
43#14582864—21no—
44#14582864—21no—
45#14582862C2211yescharacteristic
46#14582862C2211yescharacteristic
47#14582861—21no—
48C2×(C2×D43)⋊C8C2211yescharacteristic
49C22⋊C8×D43—21no—
50#14582857C2211yescharacteristic, complemented
51#14582854C2211yescharacteristic, complemented
52C2×#13063235C2211yescharacteristic, complemented
53C4×(C2×D43)⋊C4C2211yescharacteristic
54#14582664C2211yescharacteristic, complemented
55#14582660C2211yescharacteristic, complemented
56#14582659C2211yescharacteristic, complemented
57#14582658C2211yescharacteristic, complemented
58#14582654C2211yescharacteristic, complemented
59#14582653C2211yescharacteristic, complemented
60C43×#424C2211yescharacteristic, complemented
61C2×#104×C43C2211yescharacteristic
62C43×#416C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C2×#97×C43C2211yescharacteristic, complemented
65C43×#341C2211yescharacteristic, complemented
66C43×#339C2211yescharacteristic, 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#13063333—22no—
82#13063333—41no—
83#13063331—22no—
84#13063331—41no—
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621872—21no—
88C2×#10621872—21no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—21no—
92C2×C8×D43—21no—
93C2×C8×D43—41no—
94C2×C8×D43—41no—
95C2×C8×D43C2×C411yescharacteristic
96C2×C8×D43C2×C411yescharacteristic
97C2×C8×D43C2×C411yescharacteristic
98C2×C8×D43C2×C411yescharacteristic
99#13063284C2311yescharacteristic
100#13063283C2×C411yescharacteristic
101#13063283C2×C411yescharacteristic
102#13063282—21no—
103#13063281—21no—
104C4⋊C4×D43C2×C411yescharacteristic
105C4⋊C4×D43C2×C411yescharacteristic
106C2×(C2×D43)⋊C4—21no—
107C22⋊C4×D43—21no—
108C2×C4×Dic43C2311yescharacteristic
109C42×D43—21no—
110#13063260—41no—
111#13063260—41no—
112C4⋊(C43⋊C8)—21no—
113C4⋊(C43⋊C8)—21no—
114#13063253—22no—
115#13063252—41no—
116#13063251—22no—
117#13063250C2×C411yescharacteristic
118#13063250C2×C411yescharacteristic
119#13063249C2×C411yescharacteristic
120#13063249C2×C411yescharacteristic
121#13063248C2×C411yescharacteristic
122#13063248C2×C411yescharacteristic
123#13063247C2×C411yescharacteristic
124#13063247C2×C411yescharacteristic
125#13063246C2×C411yescharacteristic
126#13063246C2×C411yescharacteristic
127#13063245C2×C411yescharacteristic
128#13063245C2×C411yescharacteristic
129C22⋊(C43⋊C8)—21no—
130C22⋊(C43⋊C8)—21no—
131(C2×D43)⋊C8—21no—
132(C2×D43)⋊C8—21no—
133(C2×D43)⋊C8—21no—
134(C2×D43)⋊C8—21no—
135(C2×D43)⋊C8D411yescharacteristic
136(C2×D43)⋊C8D411yescharacteristic
137(C2×D43)⋊C8D411yescharacteristic
138(C2×D43)⋊C8D411yescharacteristic
139#13063235—21no—
140#13063235—21no—
141#13063235—41no—
142C8×Dic43—21no—
143C8×Dic43—21no—
144C43⋊#95—21no—
145C2×#41×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150#117×C43C2311yescharacteristic
151C2×C42×C43C2311yescharacteristic
152C4⋊C8×C43—21no—
153C4⋊C8×C43—21no—
154#104×C43—41no—
155#103×C43C2×C411yescharacteristic
156#103×C43C2×C411yescharacteristic
157#102×C43C2×C411yescharacteristic
158#102×C43C2×C411yescharacteristic
159C22⋊C8×C43—21no—
160C22⋊C8×C43—21no—
161#97×C43—41no—
162C23×D43—21no—
163C23×D43#4111yescharacteristic
164#41×C43—21no—
165#41×C43—21no—
166#41×C43—21no—
167#41×C43—21no—
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—42no—
195#10621898—42no—
196#10621898#4112yes—
197#10621898#4112yes—
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—
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×C43C22×C411yescharacteristic
228C2×C8×C43C22×C411yescharacteristic
229C2×C8×C43C2×D411yescharacteristic
230C2×C8×C43C2×D411yescharacteristic
231C4⋊C4×C43C22×C411yescharacteristic
232C4⋊C4×C43C22×C411yescharacteristic
233C22⋊C4×C43—21no—
234C42×C43—21no—
235C42×C43—21no—
236C42×C43—21no—
237C22⋊Dic43—21no—
238(C2×D43)⋊C4—21no—
239(C2×D43)⋊C4—21no—
240(C2×D43)⋊C4—42no—
241C4⋊Dic43C22×C411yescharacteristic
242C4⋊Dic43C22×C411yescharacteristic
243Dic43⋊C4—21no—
244Dic43⋊C4—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250#10621877—21no—
251#10621877—21no—
252#10621877—21no—
253#10621877—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8C22×C411yescharacteristic
261C2×C43⋊C8C22×C411yescharacteristic
262C2×C43⋊C8C2×D411yescharacteristic
263C2×C43⋊C8C2×D411yescharacteristic
264#10621872—42no—
265#10621872—42no—
266C8×D43—41no—
267C8×D43—41no—
268C8×D43—41no—
269C8×D43—41no—
270C8×D43—42no—
271C8×D43—42no—
272C23×C43—21no—
273C23×C43C2×#4111yescharacteristic
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—22no—
278C22×D43—41no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—81no—
282C22×D43C4×D411yescharacteristic
283C22×D43C4×D411yescharacteristic
284Q8×C43—21no—
285Q8×C43—21no—
286D4×C43—21no—
287D4×C43—21no—
288D4×C43—41no—
289D4×C43—41no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
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—22no—
305C22⋊D43—22no—
306C22⋊D43—42no—
307C22⋊D43—42no—
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—42no—
321D172#11712yes—
322C4×D43—21no—
323C4×D43—21no—
324C4×D43—21no—
325C4×D43—21no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—21no—
329C4×D43—21no—
330C4×D43—21no—
331C4×D43—21no—
332C4×D43—42no—
333C4×D43—42no—
334C4×D43—42no—
335C4×D43—81no—
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#22586—431nomaximal, Sylow
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—41no—
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—22no—
364C2×D43—21no—
365C2×D43—21no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—84no—
371C2×D43#44412yes—
372C4×C43—41no—
373C4×C43—41no—
374C4×C43—41no—
375C4×C43—81no—
376C4×C43C2×#11711yescharacteristic
377C4×C43#51811yescharacteristic
378C4×C43#54611yescharacteristic
379C4×C43#54611yescharacteristic
380Dic43—22no—
381Dic43—21no—
382Dic43—21no—
383Dic43—41no—
384Dic43—41no—
385Dic43—81no—
386#2924—431no—
387C2×#416—431no—
388#2880—431no—
389#1938—431no—
390#1938D4311yescharacteristic, complemented
391#1929—431no—
392#1929—431no—
393#1866—431no—
394#1866—431no—
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—81no—
404C2×C43#234211yescharacteristic
405C2×C43C2×#44411yescharacteristic
406C2×C43#295711yescharacteristic
407D43—22no—
408D43—41no—
409D43—42no—
410C22×#41—431no—
411C2×#131—431no—
412C2×#131—431no—
413C23×C8—431no—
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#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—861no—
441#408—861no—
442#408C2×D4311yescharacteristic
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×#97C2×D4311yescharacteristic, complemented
452C4×C22⋊C4—431no—
453#341—431no—
454#341C2×D4311yescharacteristic, complemented
455#339—431no—
456#339—431no—
457#339—431no—
458#339C2×D4311yescharacteristic, complemented
459#336—431no—
460#336—431no—
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—862no—
478#131—862no—
479#131—1721no—
480#131—1721no—
481C2×M16—431no—
482C2×M16—431no—
483C2×M16—861no—
484C2×M16—861no—
485C2×M16C22×D4311yescharacteristic
486C2×M16C22×D4311yescharacteristic
487C22×C8—431no—
488C22×C8—431no—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8—431no—
492C22×C8—431no—
493C22×C8—861no—
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—1721no—
513#108—1721no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—861no—
517C4⋊C8—861no—
518#104—41no—
519#104—862no—
520#104—862no—
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—21no—
539C22⋊C8—21no—
540C22⋊C8—431no—
541C22⋊C8—431no—
542C22⋊C8—431no—
543C22⋊C8—431no—
544C22⋊C8—861no—
545C22⋊C8—861no—
546C22⋊C8—861no—
547C22⋊C8—861no—
548C22⋊C8—861no—
549C22⋊C8—861no—
550#97—41no—
551#97—861no—
552#97—861no—
553#97—1721no—
554C4×C8—861no—
555C4×C8—861no—
556#95—861no—
557C24—431no—
558C24—861no—
559#41—21no—
560#41—21no—
561#41—21no—
562#41—21no—
563#41—432no—
564#41—432no—
565#41—861no—
566#41—861no—
567#41—862no—
568#41—862no—
569#41—1722no—
570#41—1722no—
571#41—1721no—
572#41—1722no—
573#41—1722no—
574#41—1721no—
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—861no—
617M16—861no—
618M16—861no—
619M16—861no—
620M16—1722no—
621M16—1722no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—431no—
629C2×C8—431no—
630C2×C8—431no—
631C2×C8—431no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—1721no—
639C2×C8—1721no—
640C2×C8—1721no—
641C2×C8—1721no—
642C2×C8—1722no—
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—21no—
681Q8—432no—
682Q8—861no—
683Q8—1722no—
684D4—21no—
685D4—21no—
686D4—41no—
687D4—41no—
688D4—432no—
689D4—862no—
690D4—862no—
691D4—861no—
692D4—1722no—
693D4—1722no—
694D4—1722no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
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—862no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—862no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—3441no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4C22×C4×D4311yescharacteristic
729C2×C4C2×D4×D4311yescharacteristic
730C2×C4#41×D4311yescharacteristic
731C2×C4#41×D4311yescharacteristic
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—41no—
749C22—41no—
750C22—41no—
751C22—432no—
752C22—861no—
753C22—861no—
754C22—861no—
755C22—861no—
756C22—861no—
757C22—862no—
758C22—3444no—
759C22—1722no—
760C22—1722no—
761C22—1721no—
762C22—1721no—
763C22C4×D4×D4311yescharacteristic
764C22#1458357411yescharacteristic
765C22#1458357711yescharacteristic
766C4—41no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—861no—
771C4—861no—
772C4—862no—
773C4—3441no—
774C4—1721no—
775C4—1721no—
776C4#117×D4311yescharacteristic
777C4#1458337111yescharacteristic
778C4#1458353811yescharacteristic
779C4#1458354211yescharacteristic
780C2—21no—
781C2—21no—
782C2—81no—
783C2—862no—
784C2—1721no—
785C2—1722no—
786C2#1913744311yescharacteristic
787C2#444×D4311yescharacteristic
788C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1938C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1938D43
hypocenterC43#22586
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
1. #19143252C2semidirect
4. #19135308C2semidirect
5. #19135246C2semidirect
6. #19135240C2semidirect
7. #19134871C2semidirect
8. #19134869C2semidirect
9. #19134693C2semidirect
10. #19134632C2semidirect
12. #19134439C2semidirect
13. #19134438C2semidirect
14. #19134372C2semidirect
15. C43×#1938C2semidirect
25. C2×#13063260C22semidirect
26. C2×#13063260C22semidirect
27. #14582926C22semidirect
33. #14582894C4semidirect
34. #14582894C4semidirect
36. #14582892C4semidirect
37. #14582892C4semidirect
38. #103×D43C4semidirect
39. #103×D43C4semidirect
40. #102×D43C4semidirect
41. #102×D43C4semidirect
50. #14582857C22semidirect
51. #14582854C22semidirect
52. C2×#13063235C22semidirect
54. #14582664C22semidirect
55. #14582660C22semidirect
56. #14582659C22semidirect
57. #14582658C22semidirect
58. #14582654C22semidirect
59. #14582653C22semidirect
60. C43×#424C22semidirect
64. C2×#97×C43C22semidirect
65. C43×#341C22semidirect
66. C43×#339C22semidirect
390. #1938D43semidirect
422. #424C2×D43semidirect
451. C2×#97C2×D43semidirect
454. #341C2×D43semidirect
458. #339C2×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
#191430432
#191353082
#191352462
#191352402
#191348712
#191348692
#191346932
#191346322
#191345372
#191344392
#191344382
#191343722
C43×#19382
#2258643