Finite Group Databasebeta

← #25124107

Subgroups — #25124107

Order 11008.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14582939C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4C2×#14582898C211yesmaximal, characteristic, complemented
5C2×#14582863C211yesmaximal, characteristic, complemented
6#19135798C212yesmaximal, complemented
7#19135791C212yesmaximal, complemented
8#19135784C212yesmaximal, complemented
9#19135777C212yesmaximal, complemented
10#19134314C211yesmaximal, characteristic, complemented
11C2×C43×#380C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C22×#10621877C2211yescharacteristic
15#14583410—24no—
16#14583410—24no—
17C2×#13063308—21no—
18C2×#13063304C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×#13063294—21no—
23C2×C4×C22⋊D43—21no—
24C2×C4×C22⋊D43—21no—
25C2×#13063284C2211yescharacteristic
26#14582939—24no—
27C2×#13063258C2212yescomplemented
28C2×#13063256C2212yescomplemented
29#14582898—24no—
30#14582898—24no—
31C2×#13063248C2212yescomplemented
32C2×#13063248C2212yescomplemented
33C2×#13063245C2212yescomplemented
34C2×#13063245C2212yescomplemented
35#14582863—24no—
36C2×C22⋊(C43⋊C8)C2212yes—
37C2×C22⋊(C43⋊C8)C2212yes—
38#14582661C2212yescomplemented
39#14582661C2212yescomplemented
40C24×C4×C43C2211yescharacteristic
41C22×C4⋊C4×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C22×C22⋊C4×C43—21no—
44C43×#380—21no—
45C43×#380—21no—
46C43×#380C2212yes—
47C43×#380C2212yes—
48C2×#95×C43—21no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898—22no—
53C2×#10621898—22no—
54C2×#10621898D414yes—
55C22×Dic86C2311yescharacteristic
56C22×D172C2311yescharacteristic
57C22×C22⋊D43—21no—
58C22×C22⋊D43—21no—
59C22×C22⋊D43—21no—
60C22×C4×D43—21no—
61C2×#10621877—22no—
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C2×#10621877—22no—
66C2×#10621877D414yescomplemented
67C22×C43⋊C8C2312yes—
68C22×C43⋊C8C2312yes—
69#13063308—28no—
70#13063304—22no—
71#13063304—22no—
72#13063304—22no—
73#13063304—22no—
74#13063299—22no—
75#13063299—22no—
76#13063299—22no—
77#13063299—22no—
78#13063294—28no—
79C4×C22⋊D43—28no—
80C4×C22⋊D43—28no—
81#13063284—22no—
82#13063284D414yes—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×C4×Dic43—21no—
93#13063258—24no—
94#13063256—24no—
95#13063248—24no—
96#13063248—24no—
97#13063245—24no—
98#13063245—24no—
99C22⋊(C43⋊C8)—24no—
100C22⋊(C43⋊C8)—24no—
101C25×C43D411yescharacteristic
102C23×C4×C43—22no—
103C23×C4×C43—22no—
104C23×C4×C43—22no—
105C23×C4×C43—22no—
106C23×C4×C43—22no—
107C23×C4×C43—22no—
108C23×C4×C43—21no—
109C23×C4×C43—21no—
110C23×C4×C43D411yescharacteristic
111C23×C4×C43D411yescharacteristic
112C23×C4×C43D411yescharacteristic
113C23×C4×C43C2311yescharacteristic
114C23×C4×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43—22no—
118C2×C4⋊C4×C43—22no—
119C2×C4⋊C4×C43—22no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2312yes—
123C2×C4⋊C4×C43C2312yes—
124C2×C22⋊C4×C43—22no—
125C2×C22⋊C4×C43—22no—
126C2×C22⋊C4×C43—44no—
127#95×C43—22no—
128#95×C43—22no—
129C24×C43—22no—
130C24×C43—22no—
131C24×C43—22no—
132C24×C43—22no—
133C24×C43—22no—
134C24×C43—41no—
135C24×C43—41no—
136C24×C43C2×D411yescharacteristic
137C24×C43C2×D411yescharacteristic
138C24×C43C2×D411yescharacteristic
139C23×D43—21no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—42no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43—44no—
168C22×C4×C43—44no—
169C22×C4×C43—44no—
170C22×C4×C43—44no—
171C22×C4×C43—42no—
172C22×C4×C43—42no—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D412yes—
175C22×C4×C43C2×D412yes—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43#4112yes—
180C22×C4×C43#4112yes—
181C22×C4×C43#4112yes—
182C22×C4×C43C2411yescharacteristic
183C2×C22⋊D43—24no—
184C2×C22⋊D43—24no—
185C2×C22⋊D43—24no—
186C2×C22⋊D43—42no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C2×C22⋊D43—42no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195#10621898—28no—
196#10621898—28no—
197#10621898—44no—
198#10621898—44no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172C2×D412yes—
205C2×C4×D43—24no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86C2×D412yes—
214C4⋊C4×C43—22no—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—42no—
219C4⋊C4×C43—42no—
220C22⋊C4×C43—44no—
221C22⋊C4×C43—44no—
222C22⋊Dic43—24no—
223C22⋊Dic43—24no—
224C22⋊Dic43—24no—
225(C2×D43)⋊C4—24no—
226(C2×D43)⋊C4—24no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43C2×D412yes—
230C4⋊Dic43C2×D412yes—
231Dic43⋊C4—24no—
232Dic43⋊C4—24no—
233C4×Dic43—24no—
234#10621877—28no—
235#10621877—44no—
236C2×C43⋊C8—22no—
237C2×C43⋊C8—22no—
238C2×C43⋊C8—22no—
239C2×C43⋊C8—22no—
240C2×C43⋊C8—22no—
241C2×C43⋊C8C2×D414yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—28no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—44no—
260C23×C43—44no—
261C23×C43—44no—
262C23×C43—44no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43#12012yes—
266C23×C43#12112yes—
267C23×C43#12312yes—
268C23×C43AGL(1,ℤ/8)12yes—
269C23×C43#13712yes—
270C23×C43C22×D411yescharacteristic
271C22×D43—22no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—44no—
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×C43—44no—
294C2×C4×C43—44no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—84no—
302C2×C4×C43—84no—
303C2×C4×C43#12012yes—
304C2×C4×C43#12112yes—
305C2×C4×C43#12114yes—
306C2×C4×C43#12114yes—
307C2×C4×C43#12314yes—
308C2×C4×C43#12312yes—
309C2×C4×C43#12414yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C22⋊D43—48no—
317C22⋊D43—48no—
318C22⋊D43—48no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328D172—22no—
329D172—22no—
330D172—41no—
331D172—41no—
332C4×D43—48no—
333Dic86—22no—
334Dic86—22no—
335Dic86—41no—
336Dic86—41no—
337C43⋊C8—24no—
338C43⋊C8—42no—
339#23482—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—416no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43#39414yes—
362C22×C43C2×#12011yescharacteristic
363C22×C43C2×#12111yescharacteristic
364C22×C43C2×#12311yescharacteristic
365C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C43C2×#13711yescharacteristic
367C22×C43#57511yescharacteristic
368C22×C43#57511yescharacteristic
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—81no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—82no—
379C4×C43—82no—
380C4×C43#39414yes—
381C4×C43C2×#12111yescharacteristic
382C4×C43C2×#12111yescharacteristic
383C4×C43C2×#12311yescharacteristic
384C4×C43C2×#12411yescharacteristic
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388C2×#525—431no—
389C2×#428—431no—
390C2×#417—431no—
391C2×#417—431no—
392C2×#407—431no—
393C2×#380D4311yescharacteristic, complemented
394#2036—432no—
395#2035—432no—
396#2034—432no—
397#2033—432no—
398#1736—431no—
399C2×C43—24no—
400C2×C43—42no—
401C2×C43—42no—
402C2×C43C2×#39411yescharacteristic
403C2×C43#300611yescharacteristic
404C2×C43#300711yescharacteristic
405C2×C43#305511yescharacteristic
406C2×C43#305611yescharacteristic
407C2×C43#309211yescharacteristic
408C2×C43#309311yescharacteristic
409D43—82no—
410C22×#41—431no—
411C24×C4C2×D4311yescharacteristic
412C22×M16—431no—
413C22×M16—431no—
414#525—864no—
415#525—864no—
416C2×#123—861no—
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8—431no—
419C2×#121—431no—
420C2×#121—431no—
421C2×#120—861no—
422C2×C4×D4—861no—
423C2×C4×D4—861no—
424C2×#117—431no—
425C22×C4⋊C4C2×D4311yescharacteristic
426C22×C4⋊C4C2×D4311yescharacteristic
427C22×C22⋊C4—21no—
428#428—864no—
429C2×#107—432no—
430C2×#106—432no—
431#417—864no—
432#417—864no—
433C2×#103—432no—
434C2×#103—432no—
435C2×#102—432no—
436C2×#102—432no—
437#407—864no—
438C2×C22⋊C8—432no—
439C2×C22⋊C8—432no—
440#380—21no—
441#380—21no—
442#380C2×D4312yes—
443#380C2×D4312yes—
444C2×#95—21no—
445#340—432no—
446#340—432no—
447C43#2348211yescharacteristic, complemented, Sylow
448C25C22⋊D4311yescharacteristic
449C2×#41—434no—
450C2×#41—862no—
451C2×#41—862no—
452C2×#41—862no—
453C2×#41—862no—
454C2×#41—862no—
455C22×Q8—431no—
456C22×D4—431no—
457C22×D4—861no—
458C22×D4—861no—
459C22×D4—861no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—861no—
469C23×C4C22⋊D4311yescharacteristic
470C23×C4C22⋊D4311yescharacteristic
471C23×C4C22⋊D4311yescharacteristic
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C23×C4C22×D4311yescharacteristic
475C2×M16—434no—
476C2×M16—862no—
477C2×M16—862no—
478C2×M16—862no—
479C2×M16—862no—
480C2×M16—862no—
481C22×C8—432no—
482C22×C8—432no—
483#123—868no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488#121—862no—
489#121—862no—
490#121—862no—
491#121—862no—
492#120—868no—
493C4×D4—868no—
494C4×D4—868no—
495#117—434no—
496#117—862no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4C22×D4312yes—
508C2×C4⋊C4C22×D4312yes—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—44no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C42—861no—
518#107—864no—
519#106—864no—
520#103—864no—
521#103—864no—
522#102—864no—
523#102—864no—
524C22⋊C8—864no—
525C22⋊C8—864no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—41no—
534C24—41no—
535C24—861no—
536C24C2×C22⋊D4311yescharacteristic
537C24C2×C22⋊D4311yescharacteristic
538C24C2×C22⋊D4311yescharacteristic
539#41—868no—
540#41—868no—
541#41—1724no—
542#41—1724no—
543C2×Q8—432no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×D4—432no—
550C2×D4—864no—
551C2×D4—864no—
552C2×D4—864no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—1722no—
559C2×D4—1722no—
560C2×D4—1722no—
561C2×D4—1722no—
562C2×D4—1722no—
563C2×D4—1722no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—864no—
601C22×C4—1722no—
602C22×C4—1722no—
603C22×C4#1062189812yes—
604C22×C4#1062189812yes—
605C22×C4D4×D4312yes—
606C22×C4D4×D4312yes—
607C22×C4D4×D4312yes—
608C22×C4#1062190012yes—
609C22×C4C2×C22⋊D4311yescharacteristic
610C22×C4C2×C22⋊D4311yescharacteristic
611C22×C4C2×C22⋊D4311yescharacteristic
612C22×C4C23×D4311yescharacteristic
613M16—868no—
614M16—1724no—
615C2×C8—434no—
616C2×C8—862no—
617C2×C8—862no—
618C2×C8—862no—
619C2×C8—862no—
620C2×C8—862no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—432no—
628C4⋊C4—432no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C42—864no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—862no—
665C23—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23#1306329312yes—
672C23#1306329712yes—
673C23#1306330812yes—
674C23#1306335112yes—
675C23#1306335612yes—
676C23C22×C22⋊D4311yescharacteristic
677Q8—862no—
678Q8—862no—
679Q8—1721no—
680Q8—1721no—
681D4—862no—
682D4—862no—
683D4—1728no—
684D4—1728no—
685D4—1728no—
686D4—1721no—
687D4—1721no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—84no—
712C2×C4—84no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1728no—
723C2×C4#1306329312yes—
724C2×C4#1306329712yes—
725C2×C4#1306329814yes—
726C2×C4#1306329814yes—
727C2×C4#1306330714yes—
728C2×C4#1306330812yes—
729C2×C4#1306331114yes—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C2×D4×D4311yescharacteristic
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4C2×#1062189811yescharacteristic
735C2×C4C2×#1062189811yescharacteristic
736C8—864no—
737C8—1722no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—3441no—
760C22—3441no—
761C22—3441no—
762C22—3441no—
763C22—1722no—
764C22—1722no—
765C22—1722no—
766C22#1458281414yes—
767C22C2×#1306329311yescharacteristic
768C22C2×#1306329711yescharacteristic
769C22C2×#1306330811yescharacteristic
770C22C2×#1306335111yescharacteristic
771C22C2×#1306335611yescharacteristic
772C22#1458369711yescharacteristic
773C22#1458369711yescharacteristic
774C4—41no—
775C4—41no—
776C4—82no—
777C4—82no—
778C4—1722no—
779C4—1722no—
780C4—1722no—
781C4#1458281414yes—
782C4C2×#1306329811yescharacteristic
783C4C2×#1306329811yescharacteristic
784C4C2×#1306330711yescharacteristic
785C4C2×#1306331111yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—3442no—
790C2C2×#1458281411yescharacteristic
791C2#1914384511yescharacteristic
792C2#1914385311yescharacteristic
793C2#1914421011yescharacteristic
794C2#1914422111yescharacteristic
795C2#1914451811yescharacteristic
796C2#1914452611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#380C2
socleC23×C43C22×D4
prime radicalC2×#14583410C2
hypercenterC2×#380D43
hypocenterC43#23482
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#14582939C2semidirect
3. C2×#14582898C2semidirect
4. C2×#14582898C2semidirect
5. C2×#14582863C2semidirect
6. #19135798C2semidirect
7. #19135791C2semidirect
8. #19135784C2semidirect
9. #19135777C2semidirect
10. #19134314C2semidirect
11. C2×C43×#380C2semidirect
27. C2×#13063258C22semidirect
28. C2×#13063256C22semidirect
31. C2×#13063248C22semidirect
32. C2×#13063248C22semidirect
33. C2×#13063245C22semidirect
34. C2×#13063245C22semidirect
38. #14582661C22semidirect
39. #14582661C22semidirect
66. C2×#10621877D4semidirect
393. C2×#380D43semidirect
447. C43#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145829392
C2×#145828982
C2×#145828632
#191357982
#191357912
#191357842
#191357772
#191343142
C2×C43×#3802
#2348243