Finite Group Databasebeta

← #25128776

Subgroups — #25128776

Order 11008.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic, complemented
2C2×#14583044C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic, complemented
4#19135746C211yesmaximal, characteristic, complemented
5#19135741C211yesmaximal, characteristic, complemented
6#19135596C211yesmaximal, characteristic, complemented
7#19135591C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic, complemented
11#19134913C211yesmaximal, characteristic, complemented
12#19134903C211yesmaximal, characteristic, complemented
13#19134888C211yesmaximal, characteristic, complemented
14#19134687C211yesmaximal, characteristic, complemented
15C43×#2407C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19#14583595—24no—
20#14583595—24no—
21C2×#13063320—21no—
22C2×#13063317C2211yescharacteristic
23C2×#13063307—21no—
24C2×#13063299C2211yescharacteristic
25C2×#13063299C2211yescharacteristic
26C2×#13063297—21no—
27C2×C4×D172C2211yescharacteristic
28C2×(C22⋊D43)⋊C4—21no—
29C2×#13063284C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31#14583044—24no—
32#14582895—24no—
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×#121×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#394—21no—
57C43×#392—21no—
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#386—21no—
61C43×#385—21no—
62C43×#380C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884—41no—
71C2×#10621882—22no—
72C2×#10621882—22no—
73C2×#10621882—41no—
74C22×C43⋊C8—22no—
75C22×C43⋊C8—41no—
76C22×C43⋊C8—41no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063320—28no—
82#13063317—22no—
83#13063317—22no—
84#13063307—28no—
85#13063299—22no—
86#13063299—22no—
87#13063299—22no—
88#13063299D414yescomplemented
89#13063297—28no—
90C4×D172—22no—
91C4×D172—22no—
92(C22⋊D43)⋊C4—28no—
93#13063284—22no—
94#13063284D414yescomplemented
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—22no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×C22⋊Dic43—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×C4×Dic43—21no—
108#13063249—22no—
109#13063249—22no—
110#13063249—22no—
111#13063246—22no—
112#13063246—22no—
113#13063246—22no—
114#13063245—41no—
115#13063245—41no—
116C22⋊(C43⋊C8)—22no—
117C22⋊(C43⋊C8)—41no—
118C22⋊(C43⋊C8)—41no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—41no—
124C2×#41×C43—41no—
125C22×Q8×C43C2311yescharacteristic
126C22×D4×C43—21no—
127C22×D4×C43—21no—
128C22×D4×C43D411yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C22⋊Q8×C43—22no—
134C22⋊Q8×C43—41no—
135#121×C43—22no—
136#121×C43—41no—
137C4×D4×C43—22no—
138C4×D4×C43—22no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43D411yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43D411yescharacteristic
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C42×C43C2311yescharacteristic
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157C23×D43—21no—
158#41×C43—28no—
159#41×C43—44no—
160#41×C43—44no—
161#41×C43—44no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43#4112yes—
168C2×D4×C43—21no—
169C2×D4×C43—22no—
170C2×D4×C43—22no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—41no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43—81no—
182C2×D4×C43#4112yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—42no—
197C22×C4×C43—42no—
198C22×C4×C43—42no—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—42no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43—81no—
212C22×Dic43—24no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—81no—
217C22×Dic43—81no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172C2×D412yes—
224C2×C4×D43—24no—
225C2×C4×D43—81no—
226C2×C4×D43—81no—
227C4⋊C4×C43—22no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—42no—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—81no—
239C22⋊C4×C43—81no—
240C42×C43—21no—
241C42×C43—21no—
242C22⋊Dic43—24no—
243#10621884—44no—
244#10621882—44no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43C2×D412yes—
253C4⋊Dic43C2×D412yes—
254C4⋊Dic43C2×D412yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257C4×Dic43—24no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—44no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—22no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43#12012yes—
291C23×C43#13512yes—
292C23×C43C22×D411yescharacteristic
293C22×D43—22no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—41no—
300Q8×C43—22no—
301Q8×C43—22no—
302Q8×C43—41no—
303Q8×C43—41no—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—44no—
307D4×C43—48no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—84no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—48no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43#12012yes—
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C22⋊D43—48no—
348C22⋊D43—84no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—84no—
359D172—22no—
360D172—22no—
361D172—41no—
362D172—41no—
363C4×D43—84no—
364C43⋊C8—41no—
365C43⋊C8—41no—
366C43⋊C8—41no—
367C43⋊C8—41no—
368#23962—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43C2×#12011yescharacteristic
391C22×C43#54611yescharacteristic
392C22×C43#54611yescharacteristic
393C22×C43C2×#13511yescharacteristic
394C22×C43#57511yescharacteristic
395C22×C43#57611yescharacteristic
396C22×C43#57711yescharacteristic
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—81no—
401C2×D43—81no—
402C2×D43—81no—
403C2×D43—81no—
404C4×C43—22no—
405C4×C43—41no—
406C4×C43—42no—
407C4×C43—41no—
408C4×C43—41no—
409C4×C43—81no—
410C4×C43—81no—
411C4×C43#52511yescharacteristic
412C4×C43#53511yescharacteristic
413C4×C43#54611yescharacteristic
414C4×C43#54611yescharacteristic
415Dic43—42no—
416Dic43—42no—
417Dic43—42no—
418C2×#553—431no—
419C2×#449—431no—
420C2×#416—431no—
421#2407D4311yescharacteristic, complemented
422#2026—431no—
423#2025—431no—
424#2000—431no—
425#1999—431no—
426#1893—431no—
427#1879—431no—
428#1877—431no—
429#1874—431no—
430#1872—431no—
431#1869—431no—
432#1825—431no—
433C2×C43—42no—
434C2×C43—42no—
435C2×C43—82no—
436C2×C43#240411yescharacteristic
437C2×C43#300211yescharacteristic
438C2×C43#301211yescharacteristic
439C2×C43#329711yescharacteristic
440C2×C43#330111yescharacteristic
441C2×C43#330711yescharacteristic
442C2×C43#330911yescharacteristic
443D43—82no—
444C22×#41C2×D4311yescharacteristic
445C22×SD16—431no—
446C22×D8—431no—
447C23×C8—431no—
448#553—864no—
449#553—864no—
450C2×#126—861no—
451C2×#125—431no—
452C2×#123—861no—
453C2×C22⋊Q8C2×D4311yescharacteristic
454C2×#121—431no—
455C2×#121—431no—
456C2×#121—861no—
457C2×#121C2×D4311yescharacteristic
458C2×C4×D4—431no—
459C2×C4×D4—861no—
460C2×C4×D4C2×D4311yescharacteristic
461C2×#117—431no—
462C22×C4⋊C4—431no—
463#449—864no—
464#416—864no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102—431no—
472C2×#102—431no—
473C2×C22⋊C8—431no—
474C2×C22⋊C8—431no—
475C2×C22⋊C8—431no—
476#394—21no—
477#392—21no—
478#391C2×D4311yescharacteristic
479#390C2×D4311yescharacteristic
480#386—21no—
481#385—21no—
482#380C2×D4311yescharacteristic
483#340—431no—
484#340—431no—
485#340—431no—
486#340—431no—
487#340—431no—
488#340—431no—
489#336—431no—
490#336—431no—
491C43#2396211yescharacteristic, complemented, Sylow
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C22×D4311yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—431no—
502C22×D4—861no—
503C22×D4—861no—
504C22×D4C22⋊D4311yescharacteristic
505C22×D4C22×D4311yescharacteristic
506C23×C4—21no—
507C23×C4—861no—
508C23×C4—861no—
509C23×C4C22×D4311yescharacteristic
510C23×C4C22×D4311yescharacteristic
511C2×SD16—862no—
512C2×SD16—862no—
513C2×SD16—1721no—
514C2×D8—862no—
515C2×D8—862no—
516C2×D8—1721no—
517C22×C8—431no—
518C22×C8—431no—
519C22×C8—431no—
520C22×C8—431no—
521C22×C8—862no—
522C22×C8—1721no—
523C22×C8—1721no—
524#126—868no—
525#125—862no—
526#125—862no—
527#123—868no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—22no—
531#121—41no—
532#121—434no—
533#121—862no—
534#121—862no—
535#121—868no—
536#121—862no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—862no—
540C4×D4—862no—
541C4×D4—868no—
542#117—434no—
543#117—862no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4—862no—
549C2×C4⋊C4—862no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4C22⋊D4311yescharacteristic
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C4⋊C4C22×D4311yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4C22⋊D4311yescharacteristic
566C2×C22⋊C4C22⋊D4311yescharacteristic
567C2×C42—861no—
568C2×C42C22×D4311yescharacteristic
569#103—862no—
570#103—862no—
571#103—862no—
572#102—862no—
573#102—862no—
574#102—862no—
575#102—1721no—
576#102—1721no—
577C22⋊C8—862no—
578C22⋊C8—1721no—
579C22⋊C8—1721no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—861no—
585C24C2×C22⋊D4311yescharacteristic
586C24C2×C22⋊D4311yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#1062190012yes—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—81no—
611C2×D4—432no—
612C2×D4—864no—
613C2×D4—864no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—3441no—
620C2×D4—3441no—
621C2×D4—1722no—
622C2×D4—1722no—
623C2×D4#1062190012yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—864no—
641C22×C4—864no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—3441no—
646C22×C4—3441no—
647C22×C4—3441no—
648C22×C4—3441no—
649C22×C4D4×D4312yes—
650C22×C4D4×D4312yes—
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C2×C22⋊D4311yescharacteristic
654C22×C4C2×C22⋊D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656SD16—1724no—
657D8—1724no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—861no—
670C2×C8—1724no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—42no—
677C4⋊C4—432no—
678C4⋊C4—432no—
679C4⋊C4—432no—
680C4⋊C4—864no—
681C4⋊C4—864no—
682C4⋊C4—864no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C22⋊C4—864no—
694C22⋊C4—864no—
695C22⋊C4—864no—
696C22⋊C4—864no—
697C42—21no—
698C42—21no—
699C42—864no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—862no—
720C23—1721no—
721C23—1721no—
722C23—1721no—
723C23—1721no—
724C23—1721no—
725C23—1721no—
726C23#1306329312yes—
727C23#1306334512yes—
728C23C22×C22⋊D4311yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—44no—
736D4—48no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—862no—
741D4—862no—
742D4—3444no—
743D4—1728no—
744D4—1721no—
745D4—1721no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—48no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—3444no—
779C2×C4—3444no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4#1306329312yes—
787C2×C4C2×D4×D4311yescharacteristic
788C2×C4C2×D4×D4311yescharacteristic
789C2×C4C2×#1062190011yescharacteristic
790C2×C4C2×#1062190011yescharacteristic
791C2×C4#1306337011yescharacteristic
792C2×C4#1306337011yescharacteristic
793C8—1721no—
794C8—1721no—
795C8—1721no—
796C8—1721no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—3441no—
819C22—3441no—
820C22—3441no—
821C22—3441no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22C2×#1306329311yescharacteristic
826C22#1458354311yescharacteristic
827C22#1458354311yescharacteristic
828C22C2×#1306334511yescharacteristic
829C22#1458369711yescharacteristic
830C22#1458370211yescharacteristic
831C22#1458370711yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—1722no—
840C4—1722no—
841C4—1722no—
842C4#1458340511yescharacteristic
843C4#1458346411yescharacteristic
844C4#1458353611yescharacteristic
845C4#1458353611yescharacteristic
846C2—42no—
847C2—42no—
848C2—82no—
849C2—3442no—
850C2#1913791111yescharacteristic
851C2#1914381111yescharacteristic
852C2#1914389611yescharacteristic
853C2#1914644511yescharacteristic
854C2#1914649711yescharacteristic
855C2#1914657111yescharacteristic
856C2#1914660111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2407C2
socleC23×C43C22×D4
hypercenter#2407D43
hypocenterC43#23962
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#14583595C2semidirect
2. C2×#14583044C2semidirect
3. C2×#14582895C2semidirect
4. #19135746C2semidirect
5. #19135741C2semidirect
6. #19135596C2semidirect
7. #19135591C2semidirect
8. #19135021C2semidirect
9. #19134946C2semidirect
10. #19134932C2semidirect
11. #19134913C2semidirect
12. #19134903C2semidirect
13. #19134888C2semidirect
14. #19134687C2semidirect
15. C43×#2407C2semidirect
88. #13063299D4semidirect
94. #13063284D4semidirect
421. #2407D43semidirect
491. C43#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×#145830442
C2×#145828952
#191357462
#191357412
#191355962
#191355912
#191350212
#191349462
#191349322
#191349132
#191349032
#191348882
#191346872
C43×#24072
#2396243