Finite Group Databasebeta

← #25113961

Subgroups — #25113961

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#19143253C211yesmaximal, characteristic, complemented
2#19143112C211yesmaximal, characteristic
3#19143045C211yesmaximal, characteristic
4#19135307C211yesmaximal, characteristic, complemented
5#19135300C211yesmaximal, characteristic, complemented
6#19135241C211yesmaximal, characteristic, complemented
7#19135241C211yesmaximal, characteristic, complemented
8#19134871C211yesmaximal, characteristic, complemented
9#19134871C211yesmaximal, characteristic, complemented
10#19134635C211yesmaximal, characteristic, complemented
11#19134540C211yesmaximal, characteristic
12#19134436C211yesmaximal, characteristic, complemented
13#19134429C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#1826C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063333C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20#14582960—21no—
21#14582960—21no—
22#14582956—21no—
23#14582952—21no—
24C2×#13063260C2211yescharacteristic, complemented
25C2×#13063260C2211yescharacteristic, complemented
26#14582926C2211yescharacteristic, complemented
27#14582926C2211yescharacteristic, complemented
28C2×#13063253C2211yescharacteristic
29C2×#13063253C2211yescharacteristic
30C2×#13063253C2211yescharacteristic
31C2×#13063253C2211yescharacteristic
32#14582907C411yescharacteristic, complemented
33#14582907C411yescharacteristic, complemented
34#14582903C411yescharacteristic, complemented
35#14582903C411yescharacteristic, complemented
36#14582898C411yescharacteristic, complemented
37#14582898C411yescharacteristic, complemented
38#14582898C411yescharacteristic, complemented
39#14582898C411yescharacteristic, complemented
40#14582893C2211yescharacteristic
41#14582893C2211yescharacteristic
42#14582893C2211yescharacteristic
43#14582893C2211yescharacteristic
44#14582867C2211yescharacteristic
45#14582867C2211yescharacteristic
46#14582864—21no—
47#14582864—21no—
48#14582863C2211yescharacteristic
49#14582861—21no—
50C2×C22⋊(C43⋊C8)C2211yescharacteristic
51C22⋊C8×D43—21no—
52#14582855C2211yescharacteristic, complemented
53#14582855C2211yescharacteristic, complemented
54C2×#13063236C2211yescharacteristic, complemented
55C2×C4×C43⋊C8C2211yescharacteristic, complemented
56#14582663C2211yescharacteristic, complemented
57#14582663C2211yescharacteristic, complemented
58#14582654C2211yescharacteristic, complemented
59#14582654C2211yescharacteristic, complemented
60C2×#117×C43C2211yescharacteristic
61C43×#407C2211yescharacteristic
62C4×C22⋊C4×C43C2211yescharacteristic
63C43×#339C2211yescharacteristic, complemented
64C43×#339C2211yescharacteristic, complemented
65C43×#339C2211yescharacteristic, complemented
66C43×#339C2211yescharacteristic, 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#13063333—22no—
82#13063333—22no—
83#13063333—41no—
84#13063333—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
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C2×C8×D43—21no—
100C2×C8×D43—21no—
101#13063260—41no—
102#13063260—41no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)—21no—
107#13063253—22no—
108#13063253—22no—
109#13063253—41no—
110#13063253—41no—
111#13063248C2×C411yescharacteristic
112#13063248C2×C411yescharacteristic
113#13063248C2×C411yescharacteristic
114#13063248C2×C411yescharacteristic
115#13063248C2×C411yescharacteristic
116#13063248C2×C411yescharacteristic
117#13063248C2×C411yescharacteristic
118#13063248C2×C411yescharacteristic
119#13063245C2×C411yescharacteristic
120#13063245C2×C411yescharacteristic
121#13063245C2×C411yescharacteristic
122#13063245C2×C411yescharacteristic
123#13063245C2×C411yescharacteristic
124#13063245C2×C411yescharacteristic
125#13063245C2×C411yescharacteristic
126#13063245C2×C411yescharacteristic
127C22⋊(C43⋊C8)—21no—
128C22⋊(C43⋊C8)—21no—
129C22⋊(C43⋊C8)D411yescharacteristic
130C22⋊(C43⋊C8)D411yescharacteristic
131C22⋊(C43⋊C8)D411yescharacteristic
132C22⋊(C43⋊C8)D411yescharacteristic
133(C2×D43)⋊C8—21no—
134(C2×D43)⋊C8—21no—
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137#13063236—21no—
138#13063236—21no—
139#13063236—41no—
140C4×C43⋊C8—21no—
141C4×C43⋊C8—21no—
142C4×C43⋊C8—41no—
143C23×C4×C43C2311yescharacteristic
144C2×M16×C43C2311yescharacteristic
145C2×M16×C43C2311yescharacteristic
146#117×C43—21no—
147#117×C43—21no—
148#117×C43C2×C411yescharacteristic
149#117×C43C2×C411yescharacteristic
150#117×C43C2311yescharacteristic
151#117×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2×C411yescharacteristic
153C2×C4⋊C4×C43C2×C411yescharacteristic
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156C2×C42×C43—21no—
157C2×C42×C43C2311yescharacteristic
158C2×C42×C43C2311yescharacteristic
159C22⋊C8×C43—21no—
160C22⋊C8×C43—21no—
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×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43C22×C411yescharacteristic
173C22×C4×C43C22×C411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43#4111yescharacteristic
177C22×C4×C43C2411yescharacteristic
178C2×C22⋊D43—21no—
179C2×C22⋊D43—21no—
180C2×C22⋊D43—21no—
181C2×C22⋊D43—21no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—42no—
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—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43C22×C411yescharacteristic
226C4⋊C4×C43C22×C411yescharacteristic
227C4⋊C4×C43C22×C411yescharacteristic
228C4⋊C4×C43C22×C411yescharacteristic
229C22⋊C4×C43—21no—
230C22⋊C4×C43—21no—
231C22⋊C4×C43—21no—
232C22⋊C4×C43—21no—
233C22⋊C4×C43—42no—
234C42×C43—21no—
235C42×C43—21no—
236C42×C43—21no—
237C42×C43—21no—
238C42×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—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—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
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⋊C8C22×C411yescharacteristic
261C2×C43⋊C8C22×C411yescharacteristic
262C2×C43⋊C8C22×C411yescharacteristic
263C2×C43⋊C8C22×C411yescharacteristic
264C2×C43⋊C8C2×D411yescharacteristic
265C2×C43⋊C8C2×D411yescharacteristic
266C2×C43⋊C8C2×D411yescharacteristic
267C2×C43⋊C8C2×D411yescharacteristic
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—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—81no—
306C2×C4×C43C4×D411yescharacteristic
307C2×C4×C43C4×D411yescharacteristic
308C2×C4×C43C23×C411yescharacteristic
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C22⋊D43—22no—
315C22⋊D43—22no—
316C22⋊D43—42no—
317C22⋊D43—42no—
318C22⋊D43—41no—
319C22⋊D43—41no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—42no—
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—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—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—41no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43—81no—
380C4×C43C2×#11711yescharacteristic
381C4×C43#51811yescharacteristic
382C4×C43#54611yescharacteristic
383C4×C43#54611yescharacteristic
384Dic43—22no—
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#1826D4311yescharacteristic, complemented
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—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—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#339C2×D4311yescharacteristic, complemented
456#339C2×D4311yescharacteristic, complemented
457#339C2×D4311yescharacteristic, complemented
458#339C2×D4311yescharacteristic, complemented
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—431no—
496C22×C8—431no—
497C22×C8—861no—
498C22×C8—861no—
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—21no—
509C2×C42—21no—
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—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—861no—
558C24#1062190011yescharacteristic
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—21no—
598C22×C4—21no—
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×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—1722no—
621M16—1722no—
622M16—1721no—
623M16—1721no—
624M16—1721no—
625M16—1721no—
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—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—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—861no—
672C23—861no—
673C23—3441no—
674C23—1722no—
675C23—1722no—
676C23(C22⋊D43)⋊C411yescharacteristic
677C23(C22⋊D43)⋊C411yescharacteristic
678C23C2×#1062190011yescharacteristic
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—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—81no—
717C2×C4—861no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—861no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4(C22⋊D43)⋊C411yescharacteristic
727C2×C4(C22⋊D43)⋊C411yescharacteristic
728C2×C4C22×C4×D4311yescharacteristic
729C2×C4C2×D4×D4311yescharacteristic
730C2×C4#41×D4311yescharacteristic
731C2×C4#41×D4311yescharacteristic
732C2×C4#1306337111yescharacteristic
733C2×C4#1306337111yescharacteristic
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—81no—
755C22—81no—
756C22—862no—
757C22—3444no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22C2×(C22⋊D43)⋊C411yescharacteristic
764C22#1458357211yescharacteristic
765C22#1458357211yescharacteristic
766C4—21no—
767C4—21no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—862no—
775C4—1721no—
776C4#117×D4311yescharacteristic
777C4#1458337311yescharacteristic
778C4#1458354111yescharacteristic
779C4#1458354111yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—3441no—
785C2—1722no—
786C2#1913743711yescharacteristic
787C2#1914349411yescharacteristic
788C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C2×C4×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#22588
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
1. #19143253C2semidirect
4. #19135307C2semidirect
5. #19135300C2semidirect
6. #19135241C2semidirect
7. #19135241C2semidirect
8. #19134871C2semidirect
9. #19134871C2semidirect
10. #19134635C2semidirect
12. #19134436C2semidirect
13. #19134429C2semidirect
14. #19134379C2semidirect
15. C43×#1826C2semidirect
24. C2×#13063260C22semidirect
25. C2×#13063260C22semidirect
26. #14582926C22semidirect
27. #14582926C22semidirect
32. #14582907C4semidirect
33. #14582907C4semidirect
34. #14582903C4semidirect
35. #14582903C4semidirect
36. #14582898C4semidirect
37. #14582898C4semidirect
38. #14582898C4semidirect
39. #14582898C4semidirect
52. #14582855C22semidirect
53. #14582855C22semidirect
54. C2×#13063236C22semidirect
55. C2×C4×C43⋊C8C22semidirect
56. #14582663C22semidirect
57. #14582663C22semidirect
58. #14582654C22semidirect
59. #14582654C22semidirect
63. C43×#339C22semidirect
64. C43×#339C22semidirect
65. C43×#339C22semidirect
66. C43×#339C22semidirect
395. #1826D43semidirect
455. #339C2×D43semidirect
456. #339C2×D43semidirect
457. #339C2×D43semidirect
458. #339C2×D43semidirect
461. C43#22588semidirect

Maximal subgroups

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

subgroupindex
#191432532
#191431122
#191430452
#191353072
#191353002
#191352412
#191348712
#191346352
#191345402
#191344362
#191344292
#191343792
C43×#18262
#2258843