Finite Group Databasebeta

← #25113972

Subgroups — #25113972

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#19143255C211yesmaximal, characteristic, complemented
2#19143114C211yesmaximal, characteristic
3#19143044C211yesmaximal, characteristic
4#19135303C211yesmaximal, characteristic, complemented
5#19135296C211yesmaximal, characteristic, complemented
6#19135246C211yesmaximal, characteristic, complemented
7#19135246C211yesmaximal, characteristic, complemented
8#19134868C211yesmaximal, characteristic, complemented
9#19134868C211yesmaximal, characteristic, complemented
10#19134695C211yesmaximal, characteristic, complemented
11#19134635C211yesmaximal, characteristic, complemented
12#19134440C211yesmaximal, characteristic, complemented
13#19134433C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#1789C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20#14582957—21no—
21#14582957—21no—
22#14582953—21no—
23#14582949—21no—
24C2×#13063260C2211yescharacteristic, complemented
25C2×#13063260C2211yescharacteristic, complemented
26#14582927C2211yescharacteristic, complemented
27#14582927C2211yescharacteristic, complemented
28#14582908C411yescharacteristic, complemented
29#14582908C411yescharacteristic, complemented
30#14582904C411yescharacteristic, complemented
31#14582904C411yescharacteristic, complemented
32#14582900C411yescharacteristic, complemented
33#14582900C411yescharacteristic, complemented
34#14582900C411yescharacteristic, complemented
35#14582900C411yescharacteristic, complemented
36#14582895C2211yescharacteristic
37#14582895C2211yescharacteristic
38#14582895C2211yescharacteristic
39#14582895C2211yescharacteristic
40#14582866—21no—
41#14582866—21no—
42#14582866C2211yescharacteristic
43#14582866C2211yescharacteristic
44#14582863—21no—
45#14582863C2211yescharacteristic
46C2×C22⋊(C43⋊C8)—21no—
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48#14582857C2211yescharacteristic, complemented
49#14582857C2211yescharacteristic, complemented
50C2×#13063236C2211yescharacteristic, complemented
51C2×C4×C43⋊C8C2211yescharacteristic, complemented
52#14582663C2211yescharacteristic, complemented
53#14582663C2211yescharacteristic, complemented
54#14582659C2211yescharacteristic, complemented
55#14582659C2211yescharacteristic, complemented
56#14582659C2211yescharacteristic, complemented
57#14582659C2211yescharacteristic, complemented
58#14582654C2211yescharacteristic, complemented
59#14582654C2211yescharacteristic, complemented
60C22×#41×C43C2211yescharacteristic
61C2×#104×C43C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C2×#104×C43C2211yescharacteristic
65C43×#407C2211yescharacteristic
66C4×C22⋊C4×C43C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69#13063332—41no—
70#13063332—41no—
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877—41no—
74C2×#10621877—41no—
75C2×#10621877C2×C411yescharacteristic
76C2×#10621877C2×C411yescharacteristic
77C2×#10621877C2×C411yescharacteristic
78C2×#10621877C2×C411yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C22×C43⋊C8—21no—
82C22×C43⋊C8—21no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063284—21no—
88#13063284—21no—
89#13063284C2×C411yescharacteristic
90#13063284C2×C411yescharacteristic
91#13063284C2311yescharacteristic
92#13063284C2311yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×C22⋊Dic43—21no—
96C2×C4×Dic43—21no—
97#13063260—41no—
98#13063260—41no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103#13063249C2×C411yescharacteristic
104#13063249C2×C411yescharacteristic
105#13063249C2×C411yescharacteristic
106#13063249C2×C411yescharacteristic
107#13063249C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063249C2×C411yescharacteristic
110#13063249C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063246C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114#13063246C2×C411yescharacteristic
115#13063246C2×C411yescharacteristic
116#13063246C2×C411yescharacteristic
117#13063246C2×C411yescharacteristic
118#13063246C2×C411yescharacteristic
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121C22⋊(C43⋊C8)—21no—
122C22⋊(C43⋊C8)—21no—
123C22⋊(C43⋊C8)—21no—
124C22⋊(C43⋊C8)—21no—
125C22⋊(C43⋊C8)D411yescharacteristic
126C22⋊(C43⋊C8)D411yescharacteristic
127C22⋊(C43⋊C8)D411yescharacteristic
128C22⋊(C43⋊C8)D411yescharacteristic
129#13063236—41no—
130#13063235—21no—
131#13063235—21no—
132C4×C43⋊C8—41no—
133C8×Dic43—21no—
134C8×Dic43—21no—
135C2×#41×C43—21no—
136C2×#41×C43—21no—
137C2×#41×C43—22no—
138C2×#41×C43—22no—
139C2×#41×C43—41no—
140C2×#41×C43—41no—
141C2×#41×C43C2×C411yescharacteristic
142C2×#41×C43C2×C411yescharacteristic
143C2×#41×C43C2311yescharacteristic
144C2×#41×C43C2311yescharacteristic
145C22×Q8×C43C2×C411yescharacteristic
146C22×D4×C43—21no—
147C22×D4×C43C2×C411yescharacteristic
148C23×C4×C43—21no—
149C23×C4×C43C2311yescharacteristic
150C2×M16×C43C2311yescharacteristic
151C2×M16×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153C2×C42×C43C2311yescharacteristic
154C2×C42×C43C2311yescharacteristic
155#104×C43—22no—
156#104×C43—22no—
157#104×C43—41no—
158#104×C43—41no—
159C22⋊C8×C43—21no—
160C22⋊C8×C43—21no—
161#95×C43—21no—
162C24×C43—21no—
163C24×C43#4111yescharacteristic
164#41×C43—21no—
165#41×C43—21no—
166#41×C43—22no—
167#41×C43—22no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—42no—
173#41×C43—42no—
174#41×C43—41no—
175#41×C43—41no—
176#41×C43—42no—
177#41×C43—42no—
178#41×C43#4112yes—
179#41×C43#4112yes—
180C2×Q8×C43—21no—
181C2×Q8×C43—22no—
182C2×Q8×C43—41no—
183C2×Q8×C43C22×C411yescharacteristic
184C2×Q8×C43C22×C411yescharacteristic
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—22no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—41no—
194C2×D4×C43C22×C411yescharacteristic
195C2×D4×C43C22×C411yescharacteristic
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—42no—
208C22×C4×C43—42no—
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43#4111yescharacteristic
214C22×C4×C43C2411yescharacteristic
215C22×Dic43—21no—
216C22×Dic43—21no—
217M16×C43—21no—
218M16×C43—21no—
219M16×C43—21no—
220M16×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C22⋊C4×C43—42no—
224C42×C43—21no—
225C42×C43—21no—
226C42×C43—21no—
227C42×C43—21no—
228C22⋊Dic43—21no—
229C22⋊Dic43—21no—
230C22⋊Dic43—21no—
231C22⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43C22×C411yescharacteristic
235C4⋊Dic43C22×C411yescharacteristic
236C4⋊Dic43C22×C411yescharacteristic
237C4⋊Dic43C22×C411yescharacteristic
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—21no—
242#10621877—21no—
243#10621877—21no—
244#10621877—21no—
245#10621877—21no—
246#10621877—41no—
247#10621877—41no—
248#10621877—41no—
249#10621877—41no—
250#10621877—42no—
251#10621877—42no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—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⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—42no—
263C2×C43⋊C8—42no—
264C2×C43⋊C8C22×C411yescharacteristic
265C2×C43⋊C8C22×C411yescharacteristic
266C2×C43⋊C8C22×C411yescharacteristic
267C2×C43⋊C8C22×C411yescharacteristic
268C2×C43⋊C8C2×D411yescharacteristic
269C2×C43⋊C8C2×D411yescharacteristic
270C2×C43⋊C8C2×D411yescharacteristic
271C2×C43⋊C8C2×D411yescharacteristic
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—81no—
281C23×C43C4×D411yescharacteristic
282C23×C43C4×D411yescharacteristic
283C23×C43C2×#4111yescharacteristic
284Q8×C43—21no—
285Q8×C43—21no—
286Q8×C43—21no—
287Q8×C43—42no—
288Q8×C43#11712yes—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—21no—
292D4×C43—21no—
293D4×C43—21no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43#11712yes—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43C4×D411yescharacteristic
326C2×C4×C43C4×D411yescharacteristic
327C2×C4×C43C23×C411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×Dic43—21no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—42no—
338C2×Dic43—81no—
339C8×C43—41no—
340C8×C43—41no—
341C43⋊C8—21no—
342C43⋊C8—21no—
343C43⋊C8—21no—
344C43⋊C8—21no—
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—22no—
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—84no—
369C22×C43C2×C4×D411yescharacteristic
370C22×C43#55111yescharacteristic
371C22×C43#55111yescharacteristic
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—22no—
375C4×C43—42no—
376C4×C43—41no—
377C4×C43—81no—
378C4×C43C2×#11711yescharacteristic
379C4×C43#51811yescharacteristic
380C4×C43#54611yescharacteristic
381C4×C43#54611yescharacteristic
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#1789D4311yescharacteristic
398#1765—431no—
399#1764—431no—
400#1753—431no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—41no—
404C2×C43—41no—
405C2×C43—42no—
406C2×C43—81no—
407C2×C43#234211yescharacteristic
408C2×C43#295511yescharacteristic
409C2×C43#295611yescharacteristic
410C22×#41C2×D4311yescharacteristic
411C2×#131—431no—
412C2×#131—431no—
413C22×M16—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#424—431no—
423C2×#104C2×D4311yescharacteristic
424C2×#104C2×D4311yescharacteristic
425C2×#104C2×D4311yescharacteristic
426C2×#104C2×D4311yescharacteristic
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—431no—
447C2×C22⋊C8—861no—
448#405—431no—
449#405—431no—
450C2×#97—431no—
451C2×C4×C8—431no—
452C4×C22⋊C4C2×D4311yescharacteristic
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—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C4×D4311yescharacteristic
469C2×#41C4×D4311yescharacteristic
470C2×#41C22×D4311yescharacteristic
471C2×#41C22×D4311yescharacteristic
472C22×Q8C4×D4311yescharacteristic
473C22×D4—21no—
474C22×D4C4×D4311yescharacteristic
475C23×C4—21no—
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—431no—
496C22×C8—431no—
497C22×C8—861no—
498C22×C8—861no—
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—22no—
519#104—22no—
520#104—41no—
521#104—41no—
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—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—861no—
551#97—861no—
552#97—1721no—
553C4×C8—861no—
554C4×C8—861no—
555C4×C8—1721no—
556#95—21no—
557C24—21no—
558C24#1062190011yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1062190012yes—
574#41#1062190012yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C2×C4×D4311yescharacteristic
579C2×Q8C2×C4×D4311yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C2×C4×D4311yescharacteristic
590C2×D4C2×C4×D4311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4C2×C4×D4311yescharacteristic
607C22×C4C2×C4×D4311yescharacteristic
608C22×C4D4×D4311yescharacteristic
609C22×C4D4×D4311yescharacteristic
610C22×C4#1062190011yescharacteristic
611C22×C4C23×D4311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—861no—
617M16—861no—
618M16—861no—
619M16—861no—
620M16—1721no—
621M16—1721no—
622M16—1721no—
623M16—1721no—
624M16—1722no—
625M16—1722no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—431no—
629C2×C8—431no—
630C2×C8—431no—
631C2×C8—431no—
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—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—1722no—
647C2×C8—1722no—
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—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23(C22⋊D43)⋊C411yescharacteristic
677C23(C22⋊D43)⋊C411yescharacteristic
678C23C2×#1062190011yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1306328112yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1306328112yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—3441no—
725C2×C4—1722no—
726C2×C4(C22⋊D43)⋊C411yescharacteristic
727C2×C4(C22⋊D43)⋊C411yescharacteristic
728C2×C4C22×C4×D4311yescharacteristic
729C2×C4C2×D4×D4311yescharacteristic
730C2×C4C2×#1062190011yescharacteristic
731C2×C4C2×#1062190011yescharacteristic
732C2×C4#1306337011yescharacteristic
733C2×C4#1306337011yescharacteristic
734C8—41no—
735C8—41no—
736C8—861no—
737C8—861no—
738C8—861no—
739C8—861no—
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—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×(C22⋊D43)⋊C411yescharacteristic
764C22#1458358011yescharacteristic
765C22#1458358011yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—81no—
772C4—1721no—
773C4—1721no—
774C4—1721no—
775C4—1721no—
776C4C2×#1306328111yescharacteristic
777C4#1458337211yescharacteristic
778C4#1458353611yescharacteristic
779C4#1458353611yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#1913744611yescharacteristic
787C2#1914349411yescharacteristic
788C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1789C2
socleC22×C43C2×C4×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#1789D43
hypocenterC43#22588
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. #19143255C2semidirect
4. #19135303C2semidirect
5. #19135296C2semidirect
6. #19135246C2semidirect
7. #19135246C2semidirect
8. #19134868C2semidirect
9. #19134868C2semidirect
10. #19134695C2semidirect
11. #19134635C2semidirect
12. #19134440C2semidirect
13. #19134433C2semidirect
14. #19134379C2semidirect
24. C2×#13063260C22semidirect
25. C2×#13063260C22semidirect
26. #14582927C22semidirect
27. #14582927C22semidirect
28. #14582908C4semidirect
29. #14582908C4semidirect
30. #14582904C4semidirect
31. #14582904C4semidirect
32. #14582900C4semidirect
33. #14582900C4semidirect
34. #14582900C4semidirect
35. #14582900C4semidirect
48. #14582857C22semidirect
49. #14582857C22semidirect
50. C2×#13063236C22semidirect
51. C2×C4×C43⋊C8C22semidirect
52. #14582663C22semidirect
53. #14582663C22semidirect
54. #14582659C22semidirect
55. #14582659C22semidirect
56. #14582659C22semidirect
57. #14582659C22semidirect
58. #14582654C22semidirect
59. #14582654C22semidirect
461. C43#22588semidirect

Maximal subgroups

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

subgroupindex
#191432552
#191431142
#191430442
#191353032
#191352962
#191352462
#191348682
#191346952
#191346352
#191344402
#191344332
#191343792
C43×#17892
#2258843