Finite Group Databasebeta

← #25130540

Subgroups — #25130540

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583613C211yesmaximal, characteristic
2C2×#14583193C211yesmaximal, characteristic, complemented
3C2×#14582990C211yesmaximal, characteristic, complemented
4#19139519C211yesmaximal, characteristic, complemented
5#19135775C211yesmaximal, characteristic, complemented
6#19135599C211yesmaximal, characteristic, complemented
7#19135598C211yesmaximal, characteristic, complemented
8#19135554C211yesmaximal, characteristic, complemented
9#19135387C211yesmaximal, characteristic, complemented
10#19134906C211yesmaximal, characteristic, complemented
11#19134905C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134791C211yesmaximal, characteristic, complemented
14#19134593C211yesmaximal, characteristic, complemented
15C43×#2033C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17#14583613—24no—
18#14583613—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063312—21no—
21C2×#13063311—21no—
22C2×#13063305C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063297—21no—
25C2×#13063296C2211yescharacteristic
26C2×#13063290C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×#13063281—21no—
32#14583193—24no—
33#14582990—24no—
34C2×#13063258C2211yescharacteristic
35C2×#13063256C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582823—21no—
46#14582822—21no—
47#14582799—21no—
48#14582796—21no—
49#14582768C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43D411yescharacteristic
67C23×Dic43—21no—
68C22×C4×D43C2311yescharacteristic
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063324—22no—
75#13063324D414yes—
76#13063312—28no—
77#13063311—28no—
78#13063305—22no—
79#13063305—41no—
80#13063304—22no—
81#13063304—41no—
82#13063297—28no—
83#13063296—22no—
84#13063296—22no—
85#13063290—22no—
86#13063290—22no—
87D4×Dic43—22no—
88D4×Dic43D414yes—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91#13063284—22no—
92#13063284—22no—
93#13063283—22no—
94#13063283—22no—
95#13063281—28no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4D411yescharacteristic
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43D411yescharacteristic
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4D411yescharacteristic
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43C2311yescharacteristic
119#13063258—22no—
120#13063256—22no—
121Dic43⋊C8—22no—
122#13063250—22no—
123#13063250—22no—
124#13063248—22no—
125#13063246—41no—
126C22⋊(C43⋊C8)—22no—
127(C2×D43)⋊C8—22no—
128(C2×D43)⋊C8—41no—
129C8×Dic43—22no—
130C43⋊#95—21no—
131C22×D4×C43—21no—
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136#121×C43—22no—
137#121×C43—22no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143#107×C43—22no—
144#102×C43—22no—
145#102×C43—41no—
146C22⋊C8×C43—41no—
147#95×C43—21no—
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C23×D43C2×D411yescharacteristic
151C2×D4×C43—24no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43C2×D412yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—24no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—81no—
176C2×C22⋊D43—81no—
177C22×Dic43—24no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—42no—
183C22×Dic43—42no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—24no—
199C2×Dic86—81no—
200C2×Dic86—81no—
201C2×Dic86#4112yes—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C2×D412yes—
214C22⋊C4×C43—24no—
215C22⋊C4×C43—81no—
216C22⋊Dic43—24no—
217C22⋊Dic43—24no—
218C22⋊Dic43—24no—
219C22⋊Dic43—22no—
220C22⋊Dic43—42no—
221#10621883—28no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—22no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—81no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—42no—
231C4⋊Dic43C2×D412yes—
232C4⋊Dic43C2×D412yes—
233Dic43⋊C4—24no—
234Dic43⋊C4—22no—
235Dic43⋊C4—42no—
236Dic43⋊C4—42no—
237Dic43⋊C4—42no—
238Dic43⋊C4—81no—
239C4×Dic43—24no—
240C4×Dic43—24no—
241C4×Dic43—42no—
242C4×Dic43C2×D412yes—
243C4×Dic43C2×D412yes—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8#4112yes—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43C22×D411yescharacteristic
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—84no—
277C2×C4×C43—21no—
278C2×C4×C43—22no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C2×C4×C432−1+411yescharacteristic
299C22⋊D43—44no—
300C22⋊D43—84no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—48no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43#12012yes—
320C2×Dic43#12012yes—
321C2×Dic43#13512yes—
322C2×Dic43#13712yes—
323C4×D43—41no—
324C4×D43—41no—
325C4×D43—41no—
326C4×D43—41no—
327Dic86—22no—
328Dic86—22no—
329Dic86—41no—
330Dic86—41no—
331Dic86—84no—
332C8×C43—41no—
333C8×C43—41no—
334C43⋊C8—22no—
335C43⋊C8—41no—
336#24121—431nomaximal, Sylow
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—41no—
343C22×C43—42no—
344C22×C43—41no—
345C22×C43—42no—
346C22×C43—41no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43C2×#12011yescharacteristic
352C22×C43#54611yescharacteristic
353C22×C43#54711yescharacteristic
354C22×C43C2×#13511yescharacteristic
355C22×C43C2×#13711yescharacteristic
356C22×C43#57611yescharacteristic
357C22×C43#57711yescharacteristic
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—41no—
363C2×D43—41no—
364C2×D43—41no—
365C4×C43—41no—
366C4×C43—42no—
367C4×C43—81no—
368C4×C43—81no—
369C4×C43#52511yescharacteristic
370C4×C43#53711yescharacteristic
371C4×C43#54811yescharacteristic
372C4×C43#55011yescharacteristic
373Dic43—22no—
374Dic43—42no—
375Dic43—41no—
376Dic43—42no—
377Dic43—42no—
378Dic43—81no—
379Dic43#45214yes—
380C2×#555—431no—
381C2×#477—431no—
382C2×C4×SD16—431no—
383#2538—431no—
384#2033—431no—
385#2033D4311yescharacteristic, complemented
386#2000—431no—
387#2000—431no—
388#1990—431no—
389#1954—431no—
390#1873—431no—
391#1873—431no—
392#1854—431no—
393#1854—431no—
394#1802—431no—
395C2×C43—81no—
396C2×C43—82no—
397C2×C43#240711yescharacteristic
398C2×C43C2×#45211yescharacteristic
399C2×C43#301211yescharacteristic
400C2×C43#330511yescharacteristic
401C2×C43#332911yescharacteristic
402C2×C43#334011yescharacteristic
403C2×C43#335711yescharacteristic
404D43—81no—
405C22×SD16—431no—
406#555—864no—
407#555—864no—
408C2×C4⋊Q8—431no—
409C2×#124—861no—
410C2×#124—861no—
411C2×C22⋊Q8—431no—
412C2×C22⋊Q8—431no—
413C2×#121—431no—
414C2×#121—861no—
415C2×#121C2×D4311yescharacteristic
416C2×C4×Q8—431no—
417C2×C4×D4—431no—
418C2×C4×D4—431no—
419C2×#117—431no—
420C2×#117—431no—
421C2×#117—861no—
422#477—864no—
423C4×SD16—864no—
424C2×#107—431no—
425C2×#107C2×D4311yescharacteristic
426C2×#106—431no—
427C2×C4⋊C8—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#102—431no—
432C2×#102C2×D4311yescharacteristic
433C2×#102C2×D4311yescharacteristic
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×C22⋊C8C2×D4311yescharacteristic
438C2×C4×C8—431no—
439#396—861no—
440#396—861no—
441#390—861no—
442#389—861no—
443#384—431no—
444#380—431no—
445#380C2×D4311yescharacteristic
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340C2×D4311yescharacteristic
452C43#2412111yescharacteristic, complemented, Sylow
453C22×Q8—431no—
454C22×Q8—861no—
455C22×D4—21no—
456C22×D4—431no—
457C22×D4—861no—
458C22×D4C22×D4311yescharacteristic
459C23×C4—431no—
460C23×C4—861no—
461C23×C4C22×D4311yescharacteristic
462C2×SD16—862no—
463C2×SD16—862no—
464C2×SD16—862no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C4⋊Q8—434no—
470C4⋊Q8—862no—
471#124—868no—
472#124—868no—
473C22⋊Q8—862no—
474C22⋊Q8—862no—
475C22⋊Q8—1721no—
476C22⋊Q8—1721no—
477#121—22no—
478#121—22no—
479#121—862no—
480#121—868no—
481#121—862no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×D4—434no—
485C4×D4—862no—
486C4×D4—862no—
487C4×D4—862no—
488#117—868no—
489#117—862no—
490#117—862no—
491#117—862no—
492#117—862no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—431no—
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×C42—431no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42—861no—
521#107—22no—
522#107—862no—
523#106—862no—
524C4⋊C8—862no—
525#103—862no—
526#103—862no—
527#103—862no—
528#102—22no—
529#102—41no—
530#102—1721no—
531C22⋊C8—41no—
532C22⋊C8—862no—
533C22⋊C8—862no—
534C22⋊C8—1721no—
535C4×C8—862no—
536#95—21no—
537#95—861no—
538C24—21no—
539C24—431no—
540C24D4×D4311yescharacteristic
541C2×Q8—432no—
542C2×Q8—864no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×Q8—3441no—
549C2×Q8—3441no—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—862no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—864no—
562C2×D4—3441no—
563C2×D4—3441no—
564C2×D4D4×D4312yes—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—431no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—864no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—1722no—
589C22×C4—1722no—
590C22×C4D4×D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592SD16—868no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—432no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—862no—
613C4⋊C4—864no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—3441no—
619C4⋊C4—1722no—
620C4⋊C4—1722no—
621C4⋊C4—1722no—
622C4⋊C4—1722no—
623C4⋊C4D4×D4312yes—
624C22⋊C4—24no—
625C22⋊C4—81no—
626C22⋊C4—862no—
627C22⋊C4—864no—
628C22⋊C4—862no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C22⋊C4—3441no—
633C22⋊C4—1722no—
634C22⋊C4—1722no—
635C42—432no—
636C42—432no—
637C42—864no—
638C42—864no—
639C42—1722no—
640C23—22no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23—861no—
658C23—861no—
659C23—861no—
660C23—861no—
661C23C2×D4×D4311yescharacteristic
662Q8—862no—
663Q8—862no—
664Q8—3444no—
665Q8—1721no—
666Q8—1721no—
667D4—22no—
668D4—22no—
669D4—41no—
670D4—41no—
671D4—84no—
672D4—3444no—
673D4—1724no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—432no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—862no—
697C2×C4—861no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—1728no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4#41×D4311yescharacteristic
719C2×C4#41×D4311yescharacteristic
720C2×C4#1306337011yescharacteristic
721C2×C4#1306337211yescharacteristic
722C8—41no—
723C8—41no—
724C8—862no—
725C8—1721no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—1721no—
741C22—1721no—
742C22—1721no—
743C22—1721no—
744C22—1721no—
745C22—1721no—
746C22—1721no—
747C22#120×D4311yescharacteristic
748C22#1458353811yescharacteristic
749C22#1458354711yescharacteristic
750C22#135×D4311yescharacteristic
751C22#137×D4311yescharacteristic
752C22#1458370011yescharacteristic
753C22#1458370911yescharacteristic
754C4—41no—
755C4—42no—
756C4—81no—
757C4—81no—
758C4—434no—
759C4—862no—
760C4—3441no—
761C4—1722no—
762C4—1721no—
763C4—1722no—
764C4—1722no—
765C4#1458340711yescharacteristic
766C4#1458347611yescharacteristic
767C4#1458355711yescharacteristic
768C4#1458356711yescharacteristic
769C2—81no—
770C2—82no—
771C2—3441no—
772C2#1913793511yescharacteristic
773C2#452×D4311yescharacteristic
774C2#1914389411yescharacteristic
775C2#1914654011yescharacteristic
776C2#1914688411yescharacteristic
777C2#1914700611yescharacteristic
778C2#1914721411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2033C2
socleC23×C43C22×D4
prime radicalC2×#14583613C2
hypercenter#2033D43
hypocenterC43#24121
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#14583193C2semidirect
3. C2×#14582990C2semidirect
4. #19139519C2semidirect
5. #19135775C2semidirect
6. #19135599C2semidirect
7. #19135598C2semidirect
8. #19135554C2semidirect
9. #19135387C2semidirect
10. #19134906C2semidirect
11. #19134905C2semidirect
12. #19134792C2semidirect
13. #19134791C2semidirect
14. #19134593C2semidirect
15. C43×#2033C2semidirect
385. #2033D43semidirect
452. C43#24121semidirect

Maximal subgroups

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

subgroupindex
C2×#145836132
C2×#145831932
C2×#145829902
#191395192
#191357752
#191355992
#191355982
#191355542
#191353872
#191349062
#191349052
#191347922
#191347912
#191345932
C43×#20332
#2412143