Finite Group Databasebeta

← #25959948

Subgroups — #25959948

Order 11008.

1854 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142578C211yesmaximal, characteristic, complemented
2#19141624C211yesmaximal, characteristic, complemented
3#19141560C212yesmaximal, complemented
4#19140296C211yesmaximal, characteristic, complemented
5#19140288C211yesmaximal, characteristic, complemented
6#19140091C211yesmaximal, characteristic, complemented
7#19139686C212yesmaximal, complemented
8#19139678C212yesmaximal, complemented
9#19138831C212yesmaximal, complemented
10#19138828C212yesmaximal, complemented
11#19138756C212yesmaximal, complemented
12#19138753C212yesmaximal, complemented
13#19138218C212yesmaximal
14#19137722C212yesmaximal, complemented
15#19137713C212yesmaximal, complemented
16#19137682C212yesmaximal, complemented
17#19137082C211yesmaximal, characteristic
18#19137075C212yesmaximal, complemented
19C43×#2593C211yesmaximal, characteristic, complemented
20C22×#10621900C2211yescharacteristic
21C2×#13063324C2212yes—
22C2×#13063318C2212yes—
23C2×#13063318C2212yes—
24C2×#13063316C2211yescharacteristic
25C2×#13063316C2211yescharacteristic
26C2×#13063311C2212yes—
27C2×#13063302C2212yes—
28C2×#13063283C2211yescharacteristic
29C2×#13063282C2212yes—
30C2×#13063282C2212yes—
31C2×C42×D43C2211yescharacteristic
32#14582838C2211yescharacteristic
33#14582836C2211yescharacteristic
34#14582835C2212yes—
35#14582835C2212yes—
36#14582834C2211yescharacteristic
37#14582833C2212yes—
38#14582832C2212yes—
39#14582829C2211yescharacteristic
40#14582826C2211yescharacteristic
41#14582825C2211yescharacteristic
42#14582822C2212yes—
43#14582822C2212yes—
44#14582820C2212yes—
45#14582819C2212yes—
46#14582815C2212yes—
47#14582814C2212yes—
48#14582813C2212yes—
49#14582805C2211yescharacteristic
50#14582805C2212yes—
51#14582804C2211yescharacteristic
52#14582803C2212yes—
53#14582803C2212yes—
54#14582802C2211yescharacteristic
55#14582799C2212yes—
56#14582798C2212yes—
57#14582797C2212yes—
58#14582796C2212yes—
59#14582796C2212yes—
60#14582796C2212yes—
61#14582796C2212yes—
62#14582794C2212yes—
63#14582794C2212yes—
64#14582793C2212yes—
65#14582793C2212yes—
66#14582793C2212yes—
67#14582792C2212yes—
68#14582792C2212yes—
69#14582791C2212yes—
70#14582788C2212yes—
71#14582787C2212yes—
72#14582786C2212yes—
73#14582786C2212yes—
74#14582784C2212yes—
75#14582782C2212yes—
76#14582781C2212yes—
77#14582781C2212yes—
78#14582775C2212yes—
79#14582775C2212yes—
80#14582774C2212yes—
81#14582773C2212yes—
82#14582773C2212yes—
83#14582771C2212yes—
84#14582770C2212yes—
85#14582770C2212yes—
86C4⋊C4×Dic43C2212yes—
87C4⋊C4×Dic43C2212yes—
88C4×Dic43⋊C4C2212yes—
89C4×Dic43⋊C4C2212yes—
90C4×Dic43⋊C4C2212yes—
91C4×Dic43⋊C4C2212yes—
92C4×C4⋊Dic43C2212yes—
93C22⋊C4×Dic43C2212yes—
94C22⋊C4×Dic43C2212yes—
95C22⋊C4×Dic43C2212yes—
96#14582744C2211yescharacteristic
97#14582744C2211yescharacteristic
98C43×#400C2211yescharacteristic
99C43×#398C2211yescharacteristic
100C43×#394C2212yes—
101C43×#390C2211yescharacteristic
102C43×#388C2212yes—
103C43×#388C2212yes—
104C43×#388C2212yes—
105C43×#388C2212yes—
106C4×C4⋊C4×C43C2212yes—
107C2×#10621900—24no—
108C2×#10621900—42no—
109C2×#10621900—42no—
110C22×Dic86C2312yes—
111C22×Dic86C2311yescharacteristic
112C22×C22⋊D43C2312yes—
113C23×Dic43C2312yes—
114C22×C4×D43C2312yes—
115C22×C4×D43C2311yescharacteristic
116#13063324—28no—
117#13063318—28no—
118#13063318—28no—
119#13063316—42no—
120#13063316—42no—
121#13063311—44no—
122#13063302—44no—
123#13063283—42no—
124#13063282—28no—
125#13063282—44no—
126C2×C4⋊Dic43C2312yes—
127C2×C4⋊Dic43C2312yes—
128C2×C4⋊Dic43C2312yes—
129C2×C4⋊Dic43C2312yes—
130C2×C4⋊Dic43C2312yes—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4C2312yes—
135C2×Dic43⋊C4C2312yes—
136C2×Dic43⋊C4C2312yes—
137C2×Dic43⋊C4C2312yes—
138C2×Dic43⋊C4C2312yes—
139C2×Dic43⋊C4C2312yes—
140C2×Dic43⋊C4C2312yes—
141C2×Dic43⋊C4C2312yes—
142C2×Dic43⋊C4C2312yes—
143C2×Dic43⋊C4C2312yes—
144C2×Dic43⋊C4C2312yes—
145C2×Dic43⋊C4C2312yes—
146C2×C22⋊Dic43C2312yes—
147C2×C22⋊Dic43C2312yes—
148C2×C22⋊Dic43C2312yes—
149C2×C22⋊Dic43C2312yes—
150C2×C22⋊Dic43C2312yes—
151C2×C22⋊Dic43C2312yes—
152C2×(C2×D43)⋊C4C2312yes—
153C2×(C2×D43)⋊C4C2312yes—
154C2×(C2×D43)⋊C4C2312yes—
155C2×(C2×D43)⋊C4C2312yes—
156C2×(C2×D43)⋊C4C2311yescharacteristic
157C2×(C2×D43)⋊C4C2311yescharacteristic
158C2×C4×Dic43C2311yescharacteristic
159C2×C4×Dic43C2312yes—
160C2×C4×Dic43C2312yes—
161C2×C4×Dic43C2312yes—
162C2×C4×Dic43C2312yes—
163C2×C4×Dic43C2311yescharacteristic
164C2×C4×Dic43C2312yes—
165C2×C4×Dic43C2312yes—
166C2×C4×Dic43C2311yescharacteristic
167C2×C4×Dic43C2312yes—
168C42×D43—42no—
169C43⋊#95C2311yescharacteristic
170C43⋊#95C2312yes—
171C43⋊#95C2312yes—
172C43⋊#95C2312yes—
173C43⋊#95C2312yes—
174C43⋊#95C2312yes—
175C43⋊#95C2312yes—
176C43⋊#95C2312yes—
177C43⋊#95C2312yes—
178C43⋊#95C2311yescharacteristic
179C43⋊#95C2312yes—
180C43⋊#95C2312yes—
181C43⋊#95C2312yes—
182C43⋊#95C2312yes—
183C43⋊#95C2312yes—
184C43⋊#95C2312yes—
185C43⋊#95C2312yes—
186C43⋊#95C2312yes—
187C22×D4×C43C2311yescharacteristic
188C2×C4⋊C4×C43C2312yes—
189C2×C4⋊C4×C43C2312yes—
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C4⋊C4×C43C2311yescharacteristic
192C2×C4⋊C4×C43C2311yescharacteristic
193C2×C22⋊C4×C43C2312yes—
194C2×C22⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2312yes—
196C2×C22⋊C4×C43C2312yes—
197C2×C22⋊C4×C43C2312yes—
198C2×C22⋊C4×C43C2312yes—
199C2×C42×C43C2312yes—
200C2×C42×C43C2311yescharacteristic
201C2×C42×C43C2312yes—
202#95×C43C2312yes—
203#95×C43C2311yescharacteristic
204#95×C43C2312yes—
205#95×C43C2312yes—
206#95×C43C2312yes—
207#95×C43C2311yescharacteristic
208C24×C43C2412yes—
209C23×D43C2411yescharacteristic
210C2×D4×C43—22no—
211C2×D4×C43—41no—
212C2×D4×C43—41no—
213C22×C4×C43C2412yes—
214C22×C4×C43C2412yes—
215C22×C4×C43C2411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217C22×C4×C43C2412yes—
218C22×C4×C43C2412yes—
219C22×C4×C43C2411yescharacteristic
220C22×C4×C43C2412yes—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—42no—
224C22×Dic43—24no—
225C22×Dic43—24no—
226C22×Dic43—42no—
227C22×Dic43C2412yes—
228C22×Dic43C2411yescharacteristic
229C22×Dic43C2411yescharacteristic
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C22×Dic43C2411yescharacteristic
236#10621900—416no—
237C2×C4×D43—22no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—22no—
241C2×C4×D43—24no—
242C2×C4×D43—22no—
243C2×Dic86—24no—
244C2×Dic86—41no—
245C2×Dic86—41no—
246C2×Dic86—42no—
247C2×Dic86—42no—
248C2×Dic86#4114yes—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—41no—
252C4⋊C4×C43—41no—
253C4⋊C4×C43—41no—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—24no—
256C22⋊C4×C43—24no—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43—42no—
260C42×C43—24no—
261C42×C43—41no—
262C42×C43—42no—
263C22⋊Dic43—24no—
264C22⋊Dic43—24no—
265C22⋊Dic43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43—42no—
268C22⋊Dic43—42no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—41no—
274(C2×D43)⋊C4—41no—
275C4⋊Dic43—24no—
276C4⋊Dic43—24no—
277C4⋊Dic43—24no—
278C4⋊Dic43—24no—
279C4⋊Dic43—41no—
280C4⋊Dic43—42no—
281C4⋊Dic43—41no—
282C4⋊Dic43—41no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289Dic43⋊C4—24no—
290Dic43⋊C4—42no—
291Dic43⋊C4—42no—
292Dic43⋊C4—42no—
293Dic43⋊C4—42no—
294Dic43⋊C4#4118yescomplemented
295C4×Dic43—24no—
296C4×Dic43—24no—
297C4×Dic43—24no—
298C4×Dic43—24no—
299C4×Dic43—22no—
300C4×Dic43—22no—
301C4×Dic43—41no—
302C4×Dic43—42no—
303C4×Dic43—42no—
304C4×Dic43—42no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43C2511yescharacteristic
313C22×D43—22no—
314C22×D43—21no—
315C22×D43—21no—
316C22×D43—22no—
317C22×D43H(5,𝔽2)12yes—
318D4×C43—44no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43C2×#4114yes—
339C2×C4×C43C2×#4112yes—
340C2×C4×C432−1+414yes—
341C22⋊D43—48no—
342C2×Dic43—22no—
343C2×Dic43—21no—
344C2×Dic43—22no—
345C2×Dic43—21no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—48no—
364C2×Dic43C2×#4114yes—
365C2×Dic43C2×#4114yes—
366C2×Dic43C2×#4114yes—
367C2×Dic43H(5,𝔽2)12yes—
368C4×D43—216no—
369C4×D43—28no—
370Dic86—44no—
371Dic86—84no—
372#60047—431nomaximal, Sylow
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43C22×#4111yescharacteristic
381C22×C43C22×#4112yes—
382C22×C43C2×H(5,𝔽2)11yescharacteristic
383C22×C43C2×H(5,𝔽2)11yescharacteristic
384C22×C43C2×2−1+412yes—
385C2×D43—22no—
386C2×D43—24no—
387C2×D43—42no—
388C2×D43—41no—
389C2×D43—41no—
390C4×C43—24no—
391C4×C43—22no—
392C4×C43—24no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43—41no—
397C4×C43—41no—
398Dic43—24no—
399Dic43—24no—
400Dic43—22no—
401Dic43—24no—
402Dic43—42no—
403Dic43—41no—
404Dic43—41no—
405Dic43—42no—
406Dic43—42no—
407#2809—431no—
408#2734—431no—
409#2727—432no—
410#2611—431no—
411#2611—431no—
412#2593—431no—
413#2593D4311yescharacteristic, complemented
414#2556—432no—
415#2556—432no—
416#2479—432no—
417#2479—432no—
418#2474—432no—
419#2474—432no—
420#2432—432no—
421#2373—432no—
422#2373—432no—
423#2369—432no—
424#2297—431no—
425#2296—432no—
426C2×C43—82no—
427C2×C43#348212yes—
428C2×C43#348311yescharacteristic
429C2×C43#349011yescharacteristic
430C2×C43#349212yes—
431C2×C43#355011yescharacteristic
432D43—42no—
433C22×#41—431no—
434C2×C4⋊Q8—432no—
435C2×#126—432no—
436C2×#126—432no—
437C2×#125—431no—
438C2×#125—431no—
439C2×#124—432no—
440C2×C22⋊Q8—432no—
441C2×#117—431no—
442C2×#117—432no—
443C2×#117—432no—
444C22×C42—431no—
445#400—431no—
446#400C2×D4311yescharacteristic
447#399—431no—
448#399—432no—
449#399—432no—
450#399—431no—
451#398—431no—
452#398—432no—
453#398—432no—
454#398C2×D4311yescharacteristic
455#397—431no—
456#397—431no—
457#396—432no—
458#396—432no—
459#395—432no—
460#395—432no—
461#394—432no—
462#394—432no—
463#394—432no—
464#394C2×D4312yes—
465#391—431no—
466#391—431no—
467#391—432no—
468#391—432no—
469#391—432no—
470#390—431no—
471#390—432no—
472#390C2×D4311yescharacteristic
473#389—432no—
474#389—432no—
475#389—432no—
476#389—432no—
477#389—432no—
478#389—432no—
479#389—432no—
480#389—432no—
481#388—432no—
482#388—432no—
483#388—432no—
484#388—432no—
485#388—432no—
486#388—432no—
487#388—432no—
488#388—432no—
489#388C2×D4312yes—
490#388C2×D4312yes—
491#388C2×D4312yes—
492#388C2×D4312yes—
493#387—432no—
494#387—432no—
495#387—432no—
496#387—432no—
497#387—432no—
498#387—432no—
499#386—432no—
500#386—432no—
501#385—432no—
502#385—432no—
503#385—432no—
504#385—432no—
505#385—432no—
506#385—432no—
507C4×C4⋊C4—432no—
508C4×C4⋊C4—432no—
509C4×C4⋊C4—432no—
510C4×C4⋊C4—432no—
511C4×C4⋊C4—432no—
512C4×C4⋊C4—432no—
513C4×C4⋊C4—432no—
514C4×C4⋊C4C2×D4312yes—
515C4×C22⋊C4—432no—
516C4×C22⋊C4—432no—
517C4×C22⋊C4—432no—
518#376—431no—
519#376—431no—
520C43#6004711yescharacteristic, complemented, Sylow
521C2×#41—864no—
522C2×#41—1722no—
523C2×#41—1722no—
524C22×Q8—431no—
525C22×Q8—432no—
526C22×D4—432no—
527C22×D4C22×D4311yescharacteristic
528C23×C4—432no—
529C23×C4—432no—
530C23×C4—431no—
531C4⋊Q8—868no—
532#126—868no—
533#126—868no—
534#125—1722no—
535#125—1722no—
536#124—1724no—
537C22⋊Q8—1724no—
538#117—868no—
539#117—1724no—
540#117—1722no—
541C2×C4⋊C4—432no—
542C2×C4⋊C4—432no—
543C2×C4⋊C4—432no—
544C2×C4⋊C4—432no—
545C2×C4⋊C4—432no—
546C2×C4⋊C4—432no—
547C2×C4⋊C4—432no—
548C2×C4⋊C4—432no—
549C2×C4⋊C4—432no—
550C2×C4⋊C4—432no—
551C2×C4⋊C4—432no—
552C2×C4⋊C4—432no—
553C2×C4⋊C4—432no—
554C2×C4⋊C4—432no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—432no—
557C2×C4⋊C4—432no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—432no—
561C2×C4⋊C4C22×D4312yes—
562C2×C4⋊C4C22×D4312yes—
563C2×C4⋊C4C22×D4311yescharacteristic
564C2×C4⋊C4C22×D4311yescharacteristic
565C2×C4⋊C4C22×D4311yescharacteristic
566C2×C22⋊C4—432no—
567C2×C22⋊C4—432no—
568C2×C22⋊C4—432no—
569C2×C22⋊C4—432no—
570C2×C22⋊C4—432no—
571C2×C22⋊C4—432no—
572C2×C22⋊C4—432no—
573C2×C22⋊C4—432no—
574C2×C22⋊C4—432no—
575C2×C22⋊C4—432no—
576C2×C22⋊C4—431no—
577C2×C22⋊C4—431no—
578C2×C22⋊C4C22×D4312yes—
579C2×C22⋊C4C22×D4312yes—
580C2×C22⋊C4C22×D4312yes—
581C2×C22⋊C4C22×D4312yes—
582C2×C22⋊C4C22×D4312yes—
583C2×C22⋊C4C22×D4312yes—
584C2×C42—431no—
585C2×C42—431no—
586C2×C42—432no—
587C2×C42—432no—
588C2×C42—432no—
589C2×C42—432no—
590C2×C42—432no—
591C2×C42—432no—
592C2×C42—432no—
593C2×C42—431no—
594C2×C42—1722no—
595C2×C42C22×D4312yes—
596C2×C42C22×D4312yes—
597C2×C42C22×D4311yescharacteristic
598#95—432no—
599#95—432no—
600#95—431no—
601#95—431no—
602#95—432no—
603#95—432no—
604#95—432no—
605#95—432no—
606#95—432no—
607#95—432no—
608#95—432no—
609#95—432no—
610#95—432no—
611#95—432no—
612#95—432no—
613#95—432no—
614#95—432no—
615#95—432no—
616#95C22×D4311yescharacteristic
617#95C22×D4311yescharacteristic
618#95C22×D4312yes—
619#95C22×D4312yes—
620#95C22×D4312yes—
621#95C22×D4312yes—
622C24—431no—
623C24C23×D4312yes—
624#41—17216no—
625C2×Q8—434no—
626C2×Q8—864no—
627C2×Q8—1722no—
628C2×Q8—1722no—
629C2×Q8—1721no—
630C2×Q8—1721no—
631C2×D4—22no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—1722no—
637C22×C4—432no—
638C22×C4—431no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—864no—
647C22×C4—862no—
648C22×C4—864no—
649C22×C4—862no—
650C22×C4—864no—
651C22×C4—864no—
652C22×C4—862no—
653C22×C4—864no—
654C22×C4—1722no—
655C22×C4C23×D4311yescharacteristic
656C22×C4C23×D4311yescharacteristic
657C22×C4C23×D4312yes—
658C22×C4C23×D4312yes—
659C22×C4C23×D4312yes—
660C22×C4C23×D4312yes—
661C22×C4C23×D4311yescharacteristic
662C22×C4C23×D4312yes—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C4⋊C4—438no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—864no—
672C4⋊C4—864no—
673C4⋊C4—864no—
674C4⋊C4—864no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—864no—
679C4⋊C4—864no—
680C4⋊C4—1722no—
681C4⋊C4—1722no—
682C4⋊C4—1721no—
683C4⋊C4—1722no—
684C4⋊C4—1722no—
685C4⋊C4—1721no—
686C4⋊C4—1721no—
687C4⋊C4—1722no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—864no—
695C22⋊C4—864no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—1721no—
703C22⋊C4—1721no—
704C22⋊C4—1722no—
705C22⋊C4—1722no—
706C42—24no—
707C42—41no—
708C42—42no—
709C42—864no—
710C42—862no—
711C42—862no—
712C42—864no—
713C42—864no—
714C42—864no—
715C42—1722no—
716C42—1721no—
717C42—1722no—
718C42—1722no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—432no—
727C23—862no—
728C23—861no—
729C23—861no—
730C23—862no—
731C23C24×D4311yescharacteristic
732Q8—3444no—
733Q8—1724no—
734D4—44no—
735D4—1728no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—434no—
756C2×C4—434no—
757C2×C4—434no—
758C2×C4—432no—
759C2×C4—868no—
760C2×C4—8616no—
761C2×C4—862no—
762C2×C4—861no—
763C2×C4—862no—
764C2×C4—861no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—1728no—
783C2×C4#41×D4314yes—
784C2×C4#41×D4312yes—
785C2×C4#1306337214yes—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—864no—
794C22—862no—
795C22—1722no—
796C22—1721no—
797C22—1721no—
798C22C2×#41×D4312yes—
799C22C2×#41×D4311yescharacteristic
800C22H(5,𝔽2)×D4311yescharacteristic
801C22H(5,𝔽2)×D4311yescharacteristic
802C22C2×#1306337212yes—
803C4—24no—
804C4—24no—
805C4—22no—
806C4—42no—
807C4—42no—
808C4—41no—
809C4—41no—
810C4—42no—
811C4—864no—
812C4—864no—
813C4—862no—
814C4—864no—
815C4—1722no—
816C4—1721no—
817C4—1721no—
818C4—1722no—
819C4—1722no—
820C2—82no—
821C2—1722no—
822C2#1914820812yes—
823C2#1914822011yescharacteristic
824C2#1914828111yescharacteristic
825C2#1914829912yes—
826C2#1914900711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2593C2
prime radicalC22×#10621900C22
hypercenter#2593D43
hypocenterC43#60047
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2593

Complements

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

NH ≅ G/Ntype
1. #19142578C2semidirect
2. #19141624C2semidirect
3. #19141560C2semidirect
4. #19140296C2semidirect
5. #19140288C2semidirect
6. #19140091C2semidirect
7. #19139686C2semidirect
8. #19139678C2semidirect
9. #19138831C2semidirect
10. #19138828C2semidirect
11. #19138756C2semidirect
12. #19138753C2semidirect
14. #19137722C2semidirect
15. #19137713C2semidirect
16. #19137682C2semidirect
18. #19137075C2semidirect
19. C43×#2593C2semidirect
294. Dic43⋊C4#41semidirect
413. #2593D43semidirect
520. C43#60047semidirect

Maximal subgroups

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

subgroupindex
#191425782
#191416242
#191415602
#191402962
#191402882
#191400912
#191396862
#191396782
#191388312
#191388282
#191387562
#191387532
#191382182
#191377222
#191377132
#191376822
#191370822
#191370752
C43×#25932
#6004743