Finite Group Databasebeta

← #25107934

Subgroups — #25107934

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583033C211yesmaximal, characteristic
2#19137284C211yesmaximal, characteristic, complemented
3#19137177C211yesmaximal, characteristic, complemented
4#19135468C211yesmaximal, characteristic, complemented
5#19135458C211yesmaximal, characteristic, complemented
6#19135289C211yesmaximal, characteristic, complemented
7#19135275C211yesmaximal, characteristic, complemented
8#19135225C211yesmaximal, characteristic, complemented
9#19135218C211yesmaximal, characteristic, complemented
10#19134940C211yesmaximal, characteristic, complemented
11#19134940C211yesmaximal, characteristic, complemented
12#19134915C211yesmaximal, characteristic, complemented
13#19134792C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063287C2211yescharacteristic, complemented
20C2×#13063284C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14583033C418yescomplemented
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063256C2211yescharacteristic, complemented
25C2×#13063247C2211yescharacteristic, complemented
26C2×#13063247C2211yescharacteristic, complemented
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063235C2211yescharacteristic, complemented
31C2×C8×Dic43C2211yescharacteristic, complemented
32#14582802—21no—
33#14582802—21no—
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582800C2211yescharacteristic, complemented
39#14582799—21no—
40#14582795C2211yescharacteristic, complemented
41#14582791—21no—
42#14582775—21no—
43#14582773—21no—
44#14582755—21no—
45#14582755—21no—
46C4⋊C4×Dic43C2211yescharacteristic, complemented
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C23×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C2×#10621882—41no—
64C2×#10621882—41no—
65C2×#10621882—41no—
66C2×#10621882—41no—
67C2×#10621882C2×C414yes—
68C2×#10621882C2×C414yes—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063299—22no—
72#13063299C2×C414yes—
73#13063287—41no—
74#13063287—41no—
75#13063284—41no—
76#13063284—41no—
77#13063284—41no—
78#13063284—41no—
79C2×C4⋊Dic43D411yescharacteristic
80C2×C4⋊Dic43D411yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43D411yescharacteristic
95C2×C22⋊Dic43D411yescharacteristic
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104#13063258—41no—
105#13063256—41no—
106#13063247—41no—
107#13063247—41no—
108#13063246C2×C414yescomplemented
109#13063246C2×C414yescomplemented
110C22⋊(C43⋊C8)C2×C414yescomplemented
111#13063235—41no—
112C8×Dic43—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C25×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—22no—
118C22×D4×C43—41no—
119C22×D4×C43—41no—
120C22×D4×C43—41no—
121C22×D4×C43—41no—
122C22×D4×C43C2×C414yescomplemented
123C22×D4×C43C2311yescharacteristic
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131#102×C43—41no—
132#102×C43—41no—
133#102×C43—41no—
134#102×C43—41no—
135C22⋊C8×C43—22no—
136#95×C43—21no—
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—24no—
140C24×C43—42no—
141C24×C43—42no—
142C24×C43—81no—
143C24×C43—81no—
144C24×C43—81no—
145C24×C43—81no—
146C24×C43C2×D411yescharacteristic
147C23×D43—21no—
148C2×D4×C43—24no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—44no—
160C2×D4×C43—44no—
161C2×D4×C43—44no—
162C2×D4×C43—44no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43C22×C412yes—
166C2×D4×C43C22×C412yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C22×C412yes—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43#4112yes—
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—24no—
178C2×C22⋊D43—81no—
179C2×C22⋊D43—81no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172C22×C412yes—
193C2×C4×D43—42no—
194C2×C4×D43—81no—
195C2×C4×D43—81no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C22⋊C4×C43—81no—
207C22⋊Dic43—41no—
208C22⋊Dic43—41no—
209C22⋊Dic43—42no—
210C22⋊Dic43—81no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213C22⋊Dic43—81no—
214C22⋊Dic43—81no—
215C22⋊Dic43—81no—
216C22⋊Dic43—81no—
217C22⋊Dic43—81no—
218#10621882—44no—
219#10621882—44no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—81no—
223(C2×D43)⋊C4—81no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—41no—
230C4⋊Dic43—41no—
231C4⋊Dic43C22×C412yes—
232Dic43⋊C4—81no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—42no—
238C4×Dic43—81no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8C22×C412yes—
244C2×C43⋊C8C22×C412yes—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—48no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—84no—
267C23×C43—84no—
268C23×C43—84no—
269C23×C43—84no—
270C23×C43—84no—
271C23×C43—84no—
272C23×C43C4×D412yes—
273C23×C43C22×D411yescharacteristic
274C22×D43—22no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—48no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—41no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43C4×D412yes—
303C2×C4×C43C23×C411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C22⋊D43—84no—
310C2×Dic43—22no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331D172—22no—
332D172—22no—
333D172—41no—
334D172—41no—
335C4×D43—84no—
336C8×C43—41no—
337C8×C43—41no—
338C43⋊C8—22no—
339C43⋊C8—22no—
340#22056—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—816no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43C2×C4×D411yescharacteristic
364C22×C43#53411yescharacteristic
365C22×C43#53511yescharacteristic
366C22×C43#57611yescharacteristic
367C22×C43#57611yescharacteristic
368C22×C43#57611yescharacteristic
369C22×C43#57711yescharacteristic
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C2×D43—81no—
377C4×C43—22no—
378C4×C43—81no—
379C4×C43—81no—
380C4×C43#51811yescharacteristic
381C4×C43#51811yescharacteristic
382C4×C43#53811yescharacteristic
383C4×C43#53811yescharacteristic
384Dic43—41no—
385Dic43—41no—
386Dic43—41no—
387Dic43—41no—
388Dic43—42no—
389Dic43—81no—
390Dic43—81no—
391C2×#447—431no—
392#2324—431no—
393#2309—431no—
394#1972—431no—
395#1970—431no—
396#1936—431no—
397#1934—431no—
398#1926—431no—
399#1925—431no—
400#1879—431no—
401#1879—431no—
402#1875—431no—
403#1854—431no—
404#1786D4311yescharacteristic, complemented
405#1750—431no—
406C2×C43—42no—
407C2×C43—82no—
408C2×C43—82no—
409C2×C43#232111yescharacteristic
410C2×C43#294611yescharacteristic
411C2×C43#294811yescharacteristic
412C2×C43#319811yescharacteristic
413C2×C43#319911yescharacteristic
414C2×C43#322011yescharacteristic
415C2×C43#322411yescharacteristic
416D43—82no—
417C23×D4C2×D4311yescharacteristic
418C22×D8—431no—
419C22×D8—431no—
420C2×#121—431no—
421C2×C4×D4—431no—
422C2×#117—431no—
423C2×#117—431no—
424#447—438no—
425C2×#107—431no—
426C2×#106—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102C2×D4311yescharacteristic
432C2×#102C2×D4311yescharacteristic
433C2×#102C2×D4311yescharacteristic
434C2×#102C2×D4311yescharacteristic
435C2×C22⋊C8—431no—
436C2×C22⋊C8C2×D4311yescharacteristic
437C2×#97—431no—
438C2×C4×C8—431no—
439#390—431no—
440#390—431no—
441#390—431no—
442#390—431no—
443#390—431no—
444#390—861no—
445#390—861no—
446#390—861no—
447#389—431no—
448#388—861no—
449#386—861no—
450#385—861no—
451#380C2×D4311yescharacteristic
452#379—861no—
453#379—861no—
454C4×C4⋊C4—431no—
455#340—431no—
456#340—431no—
457#340—431no—
458#340—431no—
459#336—431no—
460#336—431no—
461C43#2205611yescharacteristic, complemented, Sylow
462C25—21no—
463C22×D4—21no—
464C22×D4—22no—
465C22×D4—41no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—431no—
470C22×D4—861no—
471C22×D4C4×D4314yescomplemented
472C22×D4C22×D4311yescharacteristic
473C22×D4C22×D4311yescharacteristic
474C23×C4—861no—
475C23×C4C22×D4311yescharacteristic
476C2×D8—434no—
477C2×D8—434no—
478C2×D8—1721no—
479C2×D8—1721no—
480C2×D8—1721no—
481C2×D8—1721no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486#121—434no—
487#121—862no—
488C4×D4—1721no—
489C4×D4—1721no—
490#117—1721no—
491#117—1721no—
492#117—1721no—
493#117—1721no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—861no—
521C2×C42—861no—
522#107—1721no—
523#106—1721no—
524#102—41no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102—434no—
529#102—434no—
530#102—1721no—
531#102—1721no—
532C22⋊C8—22no—
533C22⋊C8—434no—
534#97—1721no—
535C4×C8—1721no—
536#95—21no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—861no—
549C24D4×D4311yescharacteristic
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—432no—
568C2×D4—864no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—861no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—3441no—
575C2×D4—3441no—
576C2×D4C2×C4×D4312yes—
577C2×D4C2×C4×D4312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—431no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—3441no—
592C22×C4—3441no—
593C22×C4—1722no—
594C22×C4C2×C4×D4312yes—
595C22×C4D4×D4311yescharacteristic
596C22×C4#1062190012yes—
597C22×C4C23×D4311yescharacteristic
598D8—1724no—
599D8—1724no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—432no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—3441no—
623C4⋊C4—1721no—
624C4⋊C4—1721no—
625C22⋊C4—81no—
626C22⋊C4—864no—
627C22⋊C4—3441no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—3441no—
632C22⋊C4—3441no—
633C22⋊C4—3441no—
634C22⋊C4—3441no—
635C22⋊C4—3441no—
636C22⋊C4—3441no—
637C22⋊C4—1722no—
638C22⋊C4—1721no—
639C22⋊C4—1721no—
640C22⋊C4—1722no—
641C42—861no—
642C42—861no—
643C42—861no—
644C42—861no—
645C42—3441no—
646C42—1722no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—862no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23(C22⋊D43)⋊C412yes—
682C23C2×D4×D4311yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—862no—
693D4—862no—
694D4—3444no—
695D4—1721no—
696D4—1721no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—862no—
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—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—3444no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4(C22⋊D43)⋊C412yes—
732C2×C4C22×C4×D4311yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337011yescharacteristic
737C2×C4#1306337011yescharacteristic
738C8—41no—
739C8—41no—
740C8—862no—
741C8—862no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—816no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—3441no—
765C22—3441no—
766C22—3441no—
767C22—3441no—
768C22—1722no—
769C22—1722no—
770C22—1722no—
771C22C2×(C22⋊D43)⋊C411yescharacteristic
772C22#1458345911yescharacteristic
773C22#1458346411yescharacteristic
774C22#1458370011yescharacteristic
775C22#1458370311yescharacteristic
776C22#1458370311yescharacteristic
777C22#1458370511yescharacteristic
778C4—22no—
779C4—81no—
780C4—81no—
781C4—3441no—
782C4—3441no—
783C4—1722no—
784C4—1721no—
785C4—1721no—
786C4—1721no—
787C4—1721no—
788C4#1458337211yescharacteristic
789C4#1458337211yescharacteristic
790C4#1458348411yescharacteristic
791C4#1458348411yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—3442no—
796C2#1913725011yescharacteristic
797C2#1914342111yescharacteristic
798C2#1914344311yescharacteristic
799C2#1914545111yescharacteristic
800C2#1914545811yescharacteristic
801C2#1914564111yescharacteristic
802C2#1914569311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
cosocleC22×C4×C43C24
hypercenter#1786D43
hypocenterC43#22056
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. #19137284C2semidirect
3. #19137177C2semidirect
4. #19135468C2semidirect
5. #19135458C2semidirect
6. #19135289C2semidirect
7. #19135275C2semidirect
8. #19135225C2semidirect
9. #19135218C2semidirect
10. #19134940C2semidirect
11. #19134940C2semidirect
12. #19134915C2semidirect
13. #19134792C2semidirect
14. #19134363C2semidirect
15. C43×#1786C2semidirect
19. C2×#13063287C22semidirect
22. #14583033C4semidirect
23. C2×#13063258C22semidirect
24. C2×#13063256C22semidirect
25. C2×#13063247C22semidirect
26. C2×#13063247C22semidirect
30. C2×#13063235C22semidirect
31. C2×C8×Dic43C22semidirect
38. #14582800C22semidirect
40. #14582795C22semidirect
46. C4⋊C4×Dic43C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
108. #13063246C2×C4semidirect
109. #13063246C2×C4semidirect
110. C22⋊(C43⋊C8)C2×C4semidirect
122. C22×D4×C43C2×C4semidirect
404. #1786D43semidirect
461. C43#22056semidirect
471. C22×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830332
#191372842
#191371772
#191354682
#191354582
#191352892
#191352752
#191352252
#191352182
#191349402
#191349152
#191347922
#191343632
C43×#17862
#2205643