Finite Group Databasebeta

← #25266458

Subgroups — #25266458

Order 11008.

2926 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×#13063281C211yesmaximal, characteristic, complemented
3#19138911C212yesmaximal, complemented
4#19138902C212yesmaximal, complemented
5#19138887C214yesmaximal, complemented
6#19138879C212yesmaximal, complemented
7#19138873C211yesmaximal, characteristic, complemented
8#19138868C212yesmaximal, complemented
9#19137923C211yesmaximal, characteristic
10#19137922C211yesmaximal, characteristic
11#19137853C214yesmaximal, complemented
12#19137114C212yesmaximal, complemented
13#19137112C212yesmaximal, complemented
14#19137074C212yesmaximal, complemented
15#19136975C212yesmaximal, complemented
16#19136973C211yesmaximal, characteristic, complemented
17C43×#2483C211yesmaximal, characteristic, complemented
18C23×C22⋊D43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063309C2212yes—
22C2×#13063308C2212yes—
23C2×(C22⋊D43)⋊C4—28no—
24C2×(C22⋊D43)⋊C4C2212yes—
25C2×(C22⋊D43)⋊C4C2212yes—
26C2×(C22⋊D43)⋊C4C2212yes—
27C2×(C22⋊D43)⋊C4C2212yes—
28C2×#13063281—28no—
29C2×#13063281C2212yes—
30C2×#13063281C2212yes—
31C2×#13063281C2212yes—
32C2×#13063281C2212yescomplemented
33C2×#13063281C2212yescomplemented
34C22×Dic43⋊C4C2211yescharacteristic
35C22×Dic43⋊C4C2211yescharacteristic, complemented
36C22×Dic43⋊C4C2211yescharacteristic, complemented
37C22×C22⋊Dic43C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic, complemented
41C22×C4×Dic43C2211yescharacteristic, complemented
42#14582840C2214yescomplemented
43#14582834C2214yescomplemented
44#14582833C2214yescomplemented
45#14582828C2214yescomplemented
46#14582827C2214yescomplemented
47#14582815C2214yes—
48#14582814C2214yes—
49#14582796C2214yescomplemented
50#14582794C2214yescomplemented
51#14582789C2214yescomplemented
52#14582788C2214yescomplemented
53#14582782C2214yescomplemented
54#14582781C2214yescomplemented
55#14582778C2212yes—
56#14582776C2212yes—
57#14582774C2212yes—
58#14582772C2212yes—
59#14582771C2212yes—
60#14582771C2212yescomplemented
61#14582762C2212yes—
62#14582760C2212yes—
63#14582760C2212yescomplemented
64#14582758C2214yescomplemented
65#14582758C2214yescomplemented
66#14582757C2212yescomplemented
67#14582757C2212yescomplemented
68#14582755C2211yescharacteristic
69#14582754C2212yes—
70#14582754C2212yes—
71C4⋊C4×Dic43C2214yescomplemented
72#14582750C2214yescomplemented
73C22⋊C4×Dic43C2212yescomplemented
74C22⋊C4×Dic43C2212yescomplemented
75#14582746C2214yescomplemented
76#14582746C2214yescomplemented
77C22×C22⋊C4×C43C2211yescharacteristic
78C22×C22⋊C4×C43C2211yescharacteristic
79C43×#397C2214yescomplemented
80C43×#385C2212yes—
81C43×#385C2212yescomplemented
82C43×#381C2212yes—
83C43×#381C2212yescomplemented
84C43×#379C2211yescharacteristic
85C24×D43C2311yescharacteristic
86C22×C22⋊D43—24no—
87C22×C22⋊D43—28no—
88C22×C22⋊D43C2312yes—
89C22×C22⋊D43C2312yes—
90C23×Dic43—28no—
91C23×Dic43D418yes—
92C23×Dic43C2311yescharacteristic
93C23×Dic43C2311yescharacteristic
94C23×Dic43C2311yescharacteristic
95C23×Dic43C2311yescharacteristic
96C23×Dic43C2311yescharacteristic
97C23×Dic43C2311yescharacteristic
98C23×Dic43C2311yescharacteristic
99C23×Dic43C2311yescharacteristic
100C23×Dic43C2311yescharacteristic
101C22×C4×D43—24no—
102C22×C4×D43—28no—
103C22×C4×D43C2312yes—
104C22×C4×D43C2312yes—
105#13063309—28no—
106#13063308—28no—
107(C22⋊D43)⋊C4—28no—
108(C22⋊D43)⋊C4—28no—
109(C22⋊D43)⋊C4—28no—
110(C22⋊D43)⋊C4—28no—
111#13063281—28no—
112#13063281—28no—
113#13063281—28no—
114#13063281—28no—
115#13063281—28no—
116C2×C4⋊Dic43C2314yes—
117C2×Dic43⋊C4—24no—
118C2×Dic43⋊C4—24no—
119C2×Dic43⋊C4—24no—
120C2×Dic43⋊C4C2312yes—
121C2×Dic43⋊C4C2314yes—
122C2×Dic43⋊C4C2312yes—
123C2×Dic43⋊C4C2314yes—
124C2×Dic43⋊C4C2312yes—
125C2×Dic43⋊C4C2312yes—
126C2×Dic43⋊C4C2312yes—
127C2×Dic43⋊C4C2312yes—
128C2×Dic43⋊C4C2314yes—
129C2×C22⋊Dic43—24no—
130C2×C22⋊Dic43C2312yes—
131C2×C22⋊Dic43C2312yes—
132C2×C22⋊Dic43C2312yes—
133C2×C22⋊Dic43C2312yes—
134C2×C22⋊Dic43C2312yes—
135C2×(C2×D43)⋊C4—24no—
136C2×(C2×D43)⋊C4C2312yes—
137C2×(C2×D43)⋊C4C2314yes—
138C2×(C2×D43)⋊C4C2314yes—
139C2×(C2×D43)⋊C4C2312yes—
140C2×(C2×D43)⋊C4C2314yes—
141C2×(C2×D43)⋊C4C2314yes—
142C2×C4×Dic43—24no—
143C2×C4×Dic43—24no—
144C2×C4×Dic43—24no—
145C2×C4×Dic43C2312yes—
146C2×C4×Dic43C2312yes—
147C2×C4×Dic43C2312yes—
148C2×C4×Dic43C2312yes—
149C2×C4×Dic43C2312yes—
150C2×C4×Dic43C2312yes—
151C2×C4×Dic43C2314yes—
152C43⋊#95C2314yes—
153C43⋊#95C2314yes—
154C43⋊#95C2314yes—
155C43⋊#95C2314yes—
156C43⋊#95C2314yes—
157C43⋊#95C2314yes—
158C43⋊#95C2314yes—
159C25×C43C2311yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C2×C4⋊C4×C43C2314yes—
165C2×C22⋊C4×C43—24no—
166C2×C22⋊C4×C43—24no—
167C2×C22⋊C4×C43C2312yes—
168C2×C22⋊C4×C43C2312yes—
169C2×C22⋊C4×C43C2312yes—
170C2×C22⋊C4×C43C2312yes—
171C2×C22⋊C4×C43C2312yes—
172C2×C22⋊C4×C43C2312yes—
173C2×C22⋊C4×C43C2312yes—
174#95×C43C2314yes—
175#95×C43C2314yes—
176#95×C43C2314yes—
177C24×C43—24no—
178C24×C43—24no—
179C24×C43—42no—
180C24×C43C2×D414yes—
181C24×C43C2411yescharacteristic
182C24×C43C2411yescharacteristic
183C24×C43C2411yescharacteristic
184C23×D43—22no—
185C23×D43—24no—
186C23×D43—24no—
187C23×D43—42no—
188C23×D43C2412yes—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—24no—
194C22×C4×C43—24no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2414yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2412yes—
202C2×C22⋊D43—232no—
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43#4118yes—
209C22×Dic43—232no—
210C22×Dic43—24no—
211C22×Dic43—24no—
212C22×Dic43—24no—
213C22×Dic43—24no—
214C22×Dic43—24no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—24no—
219C22×Dic43—24no—
220C22×Dic43—42no—
221C22×Dic43C2×D414yes—
222C22×Dic43C2×D414yes—
223C22×Dic43C2×D414yes—
224C22×Dic43C2×D414yes—
225C22×Dic43C2×D414yes—
226C22×Dic43C2×D414yes—
227C22×Dic43#4118yes—
228C22×Dic43C2414yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2411yescharacteristic
232C22×Dic43C2411yescharacteristic
233C22×Dic43C2412yes—
234C22×Dic43C2411yescharacteristic
235C22×Dic43C2411yescharacteristic
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—28no—
239C2×C4×D43—28no—
240C2×C4×D43—416no—
241C4⋊C4×C43—44no—
242C22⋊C4×C43—24no—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—24no—
248C22⋊C4×C43—42no—
249C22⋊Dic43—24no—
250C22⋊Dic43—24no—
251C22⋊Dic43—24no—
252C22⋊Dic43—24no—
253C22⋊Dic43—42no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—28no—
257(C2×D43)⋊C4—28no—
258(C2×D43)⋊C4—44no—
259(C2×D43)⋊C4—44no—
260C4⋊Dic43—28no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—28no—
268Dic43⋊C4—28no—
269Dic43⋊C4—44no—
270C4×Dic43—24no—
271C4×Dic43—24no—
272C4×Dic43—24no—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43—24no—
276C4×Dic43—28no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—28no—
282C23×C43—28no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—44no—
287C23×C43—416no—
288C23×C43C22×D412yes—
289C23×C43C22×D412yes—
290C23×C43C22×D412yes—
291C23×C43C2×#4114yes—
292C23×C43C2×#4114yes—
293C23×C43C2511yescharacteristic
294C22×D43—28no—
295C22×D43—22no—
296C22×D43—24no—
297C22×D43—22no—
298C22×D43—24no—
299C22×D43—416no—
300C22×D43—44no—
301C22×D43—44no—
302C22×D43C2×#4114yes—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—24no—
308C2×C4×C43—24no—
309C2×C4×C43—24no—
310C2×C4×C43—24no—
311C2×C4×C43—24no—
312C2×C4×C43—24no—
313C2×C4×C43—24no—
314C2×C4×C43—44no—
315C2×C4×C43—44no—
316C2×C4×C43—44no—
317C2×C4×C43—44no—
318C22⋊D43—216no—
319C22⋊D43—216no—
320C2×Dic43—28no—
321C2×Dic43—28no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—28no—
327C2×Dic43—28no—
328C2×Dic43—28no—
329C2×Dic43—28no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—24no—
333C2×Dic43—24no—
334C2×Dic43—24no—
335C2×Dic43—24no—
336C2×Dic43—24no—
337C2×Dic43—44no—
338C2×Dic43—44no—
339C2×Dic43#123116yescomplemented
340C2×Dic43C22×D412yes—
341C2×Dic43C22×D412yes—
342C2×Dic43C22×D412yes—
343C2×Dic43C22×D412yes—
344C2×Dic43C2×#4114yes—
345C2×Dic43C2×#4114yes—
346C2×Dic43C2×#4114yes—
347C4×D43—48no—
348C4×D43—48no—
349#34809—431nomaximal, Sylow
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—28no—
355C22×C43—28no—
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—416no—
360C22×C43—44no—
361C22×C43C2×#12314yes—
362C22×C43#52514yes—
363C22×C43C23×D411yescharacteristic
364C22×C43C22×#4112yes—
365C22×C43C22×#4112yes—
366C22×C43#58512yes—
367C2×D43—24no—
368C2×D43—28no—
369C2×D43—416no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—44no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43—44no—
378Dic43—22no—
379Dic43—22no—
380Dic43—24no—
381Dic43—42no—
382Dic43—42no—
383Dic43—44no—
384Dic43C2×#12314yes—
385Dic43C2×#12314yes—
386C22×C4×D4—431no—
387C22×#117—431no—
388#2487—432no—
389#2486—432no—
390#2485—434no—
391#2484—432no—
392#2483—431no—
393#2483D4311yescharacteristic, complemented
394#2482—432no—
395#2405—431no—
396#2405—431no—
397#2395—434no—
398C4×#123—432no—
399C4×#123—432no—
400#2296—432no—
401#2280—432no—
402#2280—431no—
403C2×C43—24no—
404C2×C43—24no—
405C2×C43—42no—
406C2×C43C22×#12311yescharacteristic
407C2×C43C2×#52511yescharacteristic
408C2×C43#344911yescharacteristic
409C2×C43#347514yes—
410D43—44no—
411C23×D4—431no—
412C24×C4—431no—
413C24×C4—431no—
414C2×#123—432no—
415C2×#123—432no—
416C2×C4×D4—432no—
417C2×C4×D4—432no—
418C2×C4×D4—432no—
419C2×C4×D4—432no—
420C2×C4×D4—868no—
421C2×#117—432no—
422C2×#117—432no—
423C2×#117—432no—
424C2×#117—432no—
425C2×#117—432no—
426C2×#117—868no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4—431no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4C2×D4311yescharacteristic
433C22×C22⋊C4C2×D4311yescharacteristic
434C22×C42—431no—
435C22×C42—431no—
436C22×C42—431no—
437#400—434no—
438#399—434no—
439#398—434no—
440#397—434no—
441#397—434no—
442#397C2×D4314yescomplemented
443#394—434no—
444#394—434no—
445#389—434no—
446#389—434no—
447#388—434no—
448#388—434no—
449#387—434no—
450#387—434no—
451#386—432no—
452#386—432no—
453#385—432no—
454#385—432no—
455#385—432no—
456#385—432no—
457#385C2×D4312yes—
458#385C2×D4312yescomplemented
459#381—432no—
460#381—432no—
461#381—432no—
462#381C2×D4312yes—
463#381C2×D4312yescomplemented
464#380—432no—
465#380—432no—
466#380—434no—
467#380—434no—
468#379—431no—
469#379—432no—
470#379—432no—
471#379C2×D4311yescharacteristic
472C4×C4⋊C4—434no—
473C4×C4⋊C4—434no—
474C4×C22⋊C4—432no—
475C4×C22⋊C4—432no—
476C4×C22⋊C4—434no—
477C4×C22⋊C4—434no—
478C43#3480911yescharacteristic, complemented, Sylow
479C25—431no—
480C25C22×D4311yescharacteristic
481C22×D4—432no—
482C22×D4—432no—
483C22×D4—868no—
484C22×D4—864no—
485C23×C4—431no—
486C23×C4—438no—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—431no—
491C23×C4—431no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—432no—
496C23×C4—432no—
497C23×C4—864no—
498C23×C4—868no—
499C23×C4—868no—
500C23×C4C22×D4311yescharacteristic
501C23×C4C22×D4311yescharacteristic
502C23×C4C22×D4311yescharacteristic
503C23×C4C22×D4311yescharacteristic
504#123—868no—
505#123—868no—
506C4×D4—868no—
507C4×D4—868no—
508C4×D4—868no—
509C4×D4—868no—
510#117—868no—
511#117—868no—
512#117—868no—
513#117—868no—
514#117—868no—
515C2×C4⋊C4—432no—
516C2×C4⋊C4—432no—
517C2×C4⋊C4—432no—
518C2×C4⋊C4—432no—
519C2×C4⋊C4—432no—
520C2×C4⋊C4—432no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—864no—
526C2×C4⋊C4—864no—
527C2×C4⋊C4—864no—
528C2×C4⋊C4C22×D4314yes—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—432no—
532C2×C22⋊C4—432no—
533C2×C22⋊C4—432no—
534C2×C22⋊C4—432no—
535C2×C22⋊C4—432no—
536C2×C22⋊C4—432no—
537C2×C22⋊C4—434no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—432no—
540C2×C22⋊C4—434no—
541C2×C22⋊C4—434no—
542C2×C22⋊C4—864no—
543C2×C22⋊C4—864no—
544C2×C22⋊C4C22×D4312yes—
545C2×C22⋊C4C22×D4312yes—
546C2×C22⋊C4C22×D4312yes—
547C2×C22⋊C4C22×D4312yes—
548C2×C22⋊C4C22×D4312yes—
549C2×C22⋊C4C22×D4312yes—
550C2×C22⋊C4C22×D4312yes—
551C2×C42—432no—
552C2×C42—432no—
553C2×C42—432no—
554C2×C42—432no—
555C2×C42—434no—
556C2×C42—432no—
557C2×C42—432no—
558C2×C42—864no—
559C2×C42—864no—
560C2×C42—864no—
561#95—434no—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95C22×D4314yes—
569#95C22×D4314yes—
570#95C22×D4314yes—
571C24—24no—
572C24—24no—
573C24—42no—
574C24—432no—
575C24—864no—
576C24—862no—
577C24—864no—
578C24—1722no—
579C24D4×D4314yes—
580C24C23×D4311yescharacteristic
581C24C23×D4311yescharacteristic
582C24C23×D4311yescharacteristic
583C2×D4—438no—
584C2×D4—864no—
585C2×D4—864no—
586C2×D4—8632no—
587C2×D4—864no—
588C2×D4—864no—
589C2×D4—864no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—434no—
599C22×C4—438no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—434no—
603C22×C4—434no—
604C22×C4—434no—
605C22×C4—434no—
606C22×C4—434no—
607C22×C4—431no—
608C22×C4—432no—
609C22×C4—431no—
610C22×C4—434no—
611C22×C4—432no—
612C22×C4—432no—
613C22×C4—864no—
614C22×C4—864no—
615C22×C4—868no—
616C22×C4—868no—
617C22×C4—8632no—
618C22×C4—864no—
619C22×C4—864no—
620C22×C4—864no—
621C22×C4—864no—
622C22×C4—864no—
623C22×C4—862no—
624C22×C4—864no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—864no—
628C22×C4—17216no—
629C22×C4—1722no—
630C22×C4C23×D4312yes—
631C22×C4C23×D4314yes—
632C22×C4C23×D4312yes—
633C22×C4C23×D4312yes—
634C22×C4C23×D4312yes—
635C4⋊C4—44no—
636C4⋊C4—864no—
637C4⋊C4—864no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—864no—
641C4⋊C4—864no—
642C4⋊C4—868no—
643C4⋊C4—868no—
644C4⋊C4—868no—
645C4⋊C4—1724no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—42no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—868no—
656C22⋊C4—868no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—1724no—
662C22⋊C4—1724no—
663C22⋊C4—1722no—
664C42—864no—
665C42—864no—
666C42—864no—
667C42—864no—
668C42—864no—
669C42—864no—
670C42—868no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—28no—
676C23—28no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—44no—
681C23—416no—
682C23—434no—
683C23—868no—
684C23—862no—
685C23—864no—
686C23—862no—
687C23—864no—
688C23—17216no—
689C23—1724no—
690C23—1724no—
691C23C2×D4×D4312yes—
692C23C2×D4×D4312yes—
693C23C2×D4×D4312yes—
694C23#41×D4314yes—
695C23#41×D4314yes—
696C23C24×D4311yescharacteristic
697D4—8616no—
698D4—8616no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—4316no—
715C2×C4—432no—
716C2×C4—432no—
717C2×C4—434no—
718C2×C4—434no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—434no—
722C2×C4—868no—
723C2×C4—868no—
724C2×C4—868no—
725C2×C4—868no—
726C2×C4—868no—
727C2×C4—868no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—864no—
735C2×C4—864no—
736C2×C4—864no—
737C2×C4—864no—
738C2×C4—864no—
739C2×C4—1728no—
740C2×C4—1728no—
741C2×C4—1724no—
742C2×C4—1724no—
743C22—22no—
744C22—22no—
745C22—28no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—416no—
753C22—44no—
754C22—864no—
755C22—868no—
756C22—17216no—
757C22—1722no—
758C22—1724no—
759C22—1722no—
760C22#123×D4314yes—
761C22#1458340714yes—
762C22C22×D4×D4311yescharacteristic
763C22C2×#41×D4312yes—
764C22C2×#41×D4312yes—
765C22#1458373412yes—
766C4—42no—
767C4—42no—
768C4—44no—
769C4—42no—
770C4—42no—
771C4—434no—
772C4—434no—
773C4—862no—
774C4—862no—
775C4—864no—
776C4—1722no—
777C4—1724no—
778C4—1722no—
779C2—24no—
780C2—24no—
781C2—42no—
782C2—1724no—
783C2C2×#123×D4311yescharacteristic
784C2C2×#1458340711yescharacteristic
785C2#1914792111yescharacteristic
786C2#1914815014yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2483C2
prime radicalC23×C22⋊D43C22
hypercenter#2483D43
hypocenterC43#34809
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2483

Complements

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

NH ≅ G/Ntype
2. C22×#13063281C2semidirect
3. #19138911C2semidirect
4. #19138902C2semidirect
5. #19138887C2semidirect
6. #19138879C2semidirect
7. #19138873C2semidirect
8. #19138868C2semidirect
11. #19137853C2semidirect
12. #19137114C2semidirect
13. #19137112C2semidirect
14. #19137074C2semidirect
15. #19136975C2semidirect
16. #19136973C2semidirect
17. C43×#2483C2semidirect
32. C2×#13063281C22semidirect
33. C2×#13063281C22semidirect
35. C22×Dic43⋊C4C22semidirect
36. C22×Dic43⋊C4C22semidirect
40. C22×C4×Dic43C22semidirect
41. C22×C4×Dic43C22semidirect
42. #14582840C22semidirect
43. #14582834C22semidirect
44. #14582833C22semidirect
45. #14582828C22semidirect
46. #14582827C22semidirect
49. #14582796C22semidirect
50. #14582794C22semidirect
51. #14582789C22semidirect
52. #14582788C22semidirect
53. #14582782C22semidirect
54. #14582781C22semidirect
60. #14582771C22semidirect
63. #14582760C22semidirect
64. #14582758C22semidirect
65. #14582758C22semidirect
66. #14582757C22semidirect
67. #14582757C22semidirect
71. C4⋊C4×Dic43C22semidirect
72. #14582750C22semidirect
73. C22⋊C4×Dic43C22semidirect
74. C22⋊C4×Dic43C22semidirect
75. #14582746C22semidirect
76. #14582746C22semidirect
79. C43×#397C22semidirect
81. C43×#385C22semidirect
83. C43×#381C22semidirect
339. C2×Dic43#123semidirect
393. #2483D43semidirect
442. #397C2×D43semidirect
458. #385C2×D43semidirect
463. #381C2×D43semidirect
478. C43#34809semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C22×#130632812
#191389112
#191389022
#191388872
#191388792
#191388732
#191388682
#191379232
#191379222
#191378532
#191371142
#191371122
#191370742
#191369752
#191369732
C43×#24832
#3480943