Finite Group Databasebeta

← #25131157

Subgroups — #25131157

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic
2C2×#14583184C211yesmaximal, characteristic, complemented
3C2×#14583121C211yesmaximal, characteristic, complemented
4#19135791C211yesmaximal, characteristic, complemented
5#19135784C211yesmaximal, characteristic
6#19135603C211yesmaximal, characteristic, complemented
7#19135596C211yesmaximal, characteristic
8#19135543C211yesmaximal, characteristic, complemented
9#19135527C211yesmaximal, characteristic, complemented
10#19134939C211yesmaximal, characteristic, complemented
11#19134932C211yesmaximal, characteristic, complemented
12#19134862C211yesmaximal, characteristic, complemented
13#19134855C211yesmaximal, characteristic, complemented
14#19134579C211yesmaximal, characteristic, complemented
15C43×#2323C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18#14583520—24no—
19#14583520—24no—
20C2×#13063325C2211yescharacteristic
21C2×#13063320—21no—
22C2×#13063313C2211yescharacteristic
23C2×#13063311—21no—
24C2×#13063307—21no—
25C2×#13063304C2211yescharacteristic
26C2×#13063303—21no—
27C2×#13063299C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×D172C2211yescharacteristic
30#14583184—24no—
31#14583121—24no—
32C2×#13063256C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#389—21no—
57C43×#389C2211yescharacteristic
58C43×#388—21no—
59C43×#388—21no—
60C43×#387—21no—
61C43×#380C2211yescharacteristic
62C4×C4⋊C4×C43C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C4×D43—21no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—41no—
71C2×#10621884—22no—
72C2×#10621884—22no—
73C2×#10621884—41no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063325—22no—
79#13063325D414yes—
80#13063320—28no—
81#13063313—22no—
82#13063313D414yes—
83#13063311—28no—
84#13063307—28no—
85#13063304—22no—
86#13063304—22no—
87#13063303—28no—
88#13063299—22no—
89#13063299—22no—
90C4×Dic86—22no—
91C4×Dic86—22no—
92C4×D172—22no—
93C4×D172—22no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C22⋊Dic43—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105#13063256—22no—
106#13063256—22no—
107C4⋊(C43⋊C8)—22no—
108C4⋊(C43⋊C8)—22no—
109#13063249—22no—
110#13063249—22no—
111#13063248—22no—
112#13063248—22no—
113#13063248—41no—
114#13063245—22no—
115#13063245—22no—
116#13063245—41no—
117C22⋊(C43⋊C8)—41no—
118C22⋊(C43⋊C8)—41no—
119C22×Q8×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C22⋊Q8×C43—22no—
122C22⋊Q8×C43—22no—
123C4×Q8×C43—22no—
124C4×Q8×C43—22no—
125#117×C43—22no—
126#117×C43—22no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C4⋊C4×C43D411yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C22⋊C4×C43D411yescharacteristic
139C2×C42×C43—21no—
140C2×C42×C43—21no—
141C2×C42×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143#95×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43C2×D411yescharacteristic
149C23×D43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43#4112yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2411yescharacteristic
172C2×C22⋊D43—24no—
173C2×C22⋊D43—81no—
174C2×C22⋊D43—81no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172C2×D412yes—
184C2×C4×D43—24no—
185C2×C4×D43—81no—
186C2×C4×D43—81no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—24no—
193C2×Dic86—81no—
194C2×Dic86—81no—
195C2×Dic86C2×D412yes—
196C4⋊C4×C43—24no—
197C4⋊C4×C43—22no—
198C4⋊C4×C43—22no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—42no—
205C4⋊C4×C43—81no—
206C4⋊C4×C43#4112yes—
207C22⋊C4×C43—24no—
208C22⋊C4×C43—22no—
209C22⋊C4×C43—22no—
210C22⋊C4×C43—81no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—42no—
214C42×C43—81no—
215C42×C43C2×D412yes—
216C42×C43C2×D412yes—
217C22⋊Dic43—24no—
218#10621885—44no—
219#10621884—44no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—24no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—24no—
224C4⋊Dic43—24no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43C2×D412yes—
228C4⋊Dic43C2×D412yes—
229Dic43⋊C4—24no—
230Dic43⋊C4—24no—
231C4×Dic43—24no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43C22×D411yescharacteristic
252C22×D43—22no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259Q8×C43—22no—
260Q8×C43—22no—
261Q8×C43—41no—
262Q8×C43—41no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
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#12012yes—
293C2×C4×C43#12012yes—
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×C4×C432−1+411yescharacteristic
300C22⋊D43—84no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310D172—22no—
311D172—22no—
312D172—41no—
313D172—41no—
314C4×D43—84no—
315Dic86—22no—
316Dic86—22no—
317Dic86—41no—
318Dic86—41no—
319Dic86—84no—
320C43⋊C8—41no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324#24169—431nomaximal, Sylow
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43C2×#12011yescharacteristic
333C22×C43#52511yescharacteristic
334C22×C43#53711yescharacteristic
335C22×C43#57711yescharacteristic
336C22×C43#57711yescharacteristic
337C22×C43#57711yescharacteristic
338C22×C43#57811yescharacteristic
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—81no—
343C2×D43—81no—
344C2×D43—81no—
345C2×D43—81no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—41no—
350C4×C43—42no—
351C4×C43—41no—
352C4×C43—41no—
353C4×C43—81no—
354C4×C43—81no—
355C4×C43#54611yescharacteristic
356C4×C43#54711yescharacteristic
357C4×C43#54811yescharacteristic
358C4×C43#55011yescharacteristic
359Dic43—42no—
360Dic43—42no—
361Dic43—42no—
362C2×#542—431no—
363C2×#475—431no—
364C2×#464—431no—
365#2323D4311yescharacteristic, complemented
366#2035—431no—
367#2034—431no—
368#2001—431no—
369#2000—431no—
370#1987—431no—
371#1983—431no—
372#1878—431no—
373#1877—431no—
374#1865—431no—
375#1864—431no—
376#1798—431no—
377C2×C43—81no—
378C2×C43#240711yescharacteristic
379C2×C43#300911yescharacteristic
380C2×C43#301311yescharacteristic
381C2×C43#312111yescharacteristic
382C2×C43#312511yescharacteristic
383C2×C43#325811yescharacteristic
384C2×C43#326311yescharacteristic
385D43—82no—
386C22×Q16—431no—
387C22×SD16—431no—
388#542—864no—
389#542—864no—
390C2×C4⋊Q8—431no—
391C2×#126—861no—
392C2×#124—431no—
393C2×#124—861no—
394C2×#123—861no—
395C2×C22⋊Q8—431no—
396C2×C22⋊Q8—861no—
397C2×C22⋊Q8C2×D4311yescharacteristic
398C2×#121—431no—
399C2×C4×Q8—431no—
400C2×C4×Q8C2×D4311yescharacteristic
401C2×C4×D4—431no—
402C2×#117C2×D4311yescharacteristic
403#475—864no—
404#464—864no—
405C2×#106—431no—
406C2×#106—431no—
407C2×C4⋊C8—431no—
408C2×C4⋊C8—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#103—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×C22⋊C8—431no—
418C2×C22⋊C8—431no—
419#391C2×D4311yescharacteristic
420#389—21no—
421#389C2×D4311yescharacteristic
422#388—21no—
423#388—21no—
424#387—21no—
425#380C2×D4311yescharacteristic
426C4×C4⋊C4C2×D4311yescharacteristic
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#336—431no—
432#336—431no—
433C43#2416911yescharacteristic, complemented, Sylow
434C22×Q8—431no—
435C22×Q8—861no—
436C22×Q8C22×D4311yescharacteristic
437C22×D4—431no—
438C22×D4—861no—
439C23×C4—861no—
440C23×C4C22×D4311yescharacteristic
441C2×Q16—862no—
442C2×Q16—862no—
443C2×Q16—1721no—
444C2×SD16—862no—
445C2×SD16—862no—
446C2×SD16—1721no—
447C22×C8—431no—
448C22×C8—431no—
449C22×C8—431no—
450C22×C8—431no—
451C4⋊Q8—434no—
452C4⋊Q8—862no—
453#126—868no—
454#124—434no—
455#124—868no—
456#124—862no—
457#123—868no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—868no—
461C22⋊Q8—862no—
462C22⋊Q8—862no—
463#121—862no—
464#121—862no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—862no—
468C4×Q8—862no—
469C4×D4—862no—
470C4×D4—862no—
471#117—22no—
472#117—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4C22⋊D4311yescharacteristic
482C2×C4⋊C4C22⋊D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4C22⋊D4311yescharacteristic
494C2×C22⋊C4C22⋊D4311yescharacteristic
495C2×C42—21no—
496C2×C42—21no—
497C2×C42—861no—
498C2×C42C22×D4311yescharacteristic
499C2×C42C22×D4311yescharacteristic
500#106—862no—
501#106—862no—
502C4⋊C8—862no—
503C4⋊C8—862no—
504#103—862no—
505#103—862no—
506#103—862no—
507#103—862no—
508#103—1721no—
509#102—862no—
510#102—862no—
511#102—1721no—
512C22⋊C8—1721no—
513C22⋊C8—1721no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519C24—861no—
520C24C2×C22⋊D4311yescharacteristic
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—432no—
527C2×Q8—864no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—3441no—
534C2×Q8—3441no—
535C2×Q8#1062189812yes—
536C2×D4—432no—
537C2×D4—864no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—3441no—
544C2×D4—3441no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—864no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—3441no—
560C22×C4—3441no—
561C22×C4C2×C22⋊D4311yescharacteristic
562C22×C4C2×C22⋊D4311yescharacteristic
563C22×C4C2×C22⋊D4311yescharacteristic
564C22×C4C2×C22⋊D4311yescharacteristic
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C23×D4311yescharacteristic
567Q16—1724no—
568SD16—1724no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—81no—
591C4⋊C4—432no—
592C4⋊C4—432no—
593C4⋊C4—864no—
594C4⋊C4—864no—
595C4⋊C4—864no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4#1062189812yes—
599C22⋊C4—24no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—81no—
603C22⋊C4—864no—
604C22⋊C4—864no—
605C22⋊C4—864no—
606C22⋊C4—864no—
607C22⋊C4—864no—
608C42—21no—
609C42—21no—
610C42—42no—
611C42—81no—
612C42—864no—
613C42D4×D4312yes—
614C42D4×D4312yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—862no—
623C23—1721no—
624C23—1721no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23C22×C22⋊D4311yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—862no—
635Q8—862no—
636Q8—3444no—
637Q8—1721no—
638Q8—1721no—
639D4—862no—
640D4—862no—
641D4—3444no—
642D4—1721no—
643D4—1721no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—3444no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4#1306329312yes—
684C2×C4#1306329312yes—
685C2×C4C2×D4×D4311yescharacteristic
686C2×C4C2×D4×D4311yescharacteristic
687C2×C4C2×#1062189811yescharacteristic
688C2×C4C2×#1062189811yescharacteristic
689C2×C4#1306337111yescharacteristic
690C2×C4#1306337211yescharacteristic
691C8—1721no—
692C8—1721no—
693C8—1721no—
694C8—1721no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—3441no—
703C22—3441no—
704C22—3441no—
705C22—3441no—
706C22—1722no—
707C22—1722no—
708C22—1722no—
709C22C2×#1306329311yescharacteristic
710C22#1458341011yescharacteristic
711C22#1458347711yescharacteristic
712C22#1458370711yescharacteristic
713C22#1458370711yescharacteristic
714C22#1458371011yescharacteristic
715C22#1458371411yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—42no—
720C4—42no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—1722no—
726C4—1722no—
727C4—1722no—
728C4#1458354511yescharacteristic
729C4#1458355411yescharacteristic
730C4#1458355811yescharacteristic
731C4#1458357011yescharacteristic
732C2—81no—
733C2—3442no—
734C2#1913794011yescharacteristic
735C2#1914387011yescharacteristic
736C2#1914390711yescharacteristic
737C2#1914482411yescharacteristic
738C2#1914487211yescharacteristic
739C2#1914601511yescharacteristic
740C2#1914606011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2323C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#2323D43
hypocenterC43#24169
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×#14583184C2semidirect
3. C2×#14583121C2semidirect
4. #19135791C2semidirect
6. #19135603C2semidirect
8. #19135543C2semidirect
9. #19135527C2semidirect
10. #19134939C2semidirect
11. #19134932C2semidirect
12. #19134862C2semidirect
13. #19134855C2semidirect
14. #19134579C2semidirect
15. C43×#2323C2semidirect
365. #2323D43semidirect
433. C43#24169semidirect

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145831842
C2×#145831212
#191357912
#191357842
#191356032
#191355962
#191355432
#191355272
#191349392
#191349322
#191348622
#191348552
#191345792
C43×#23232
#2416943