Finite Group Databasebeta

← #25064453

Subgroups — #25064453

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148438C211yesmaximal, characteristic
2#19143634C211yesmaximal, characteristic, complemented
3#19137499C211yesmaximal, characteristic, complemented
4#19133157C211yesmaximal, characteristic, complemented
5#19133153C211yesmaximal, characteristic, complemented
6#19133137C211yesmaximal, characteristic, complemented
7#19133136C211yesmaximal, characteristic, complemented
8#19133135C211yesmaximal, characteristic, complemented
9#19133100C211yesmaximal, characteristic, complemented
10#19133099C211yesmaximal, characteristic, complemented
11#19133098C211yesmaximal, characteristic, complemented
12#19133096C211yesmaximal, characteristic, complemented
13#19133092C211yesmaximal, characteristic, complemented
14#19133088C211yesmaximal, characteristic, complemented
15C43×#1513C211yesmaximal, characteristic, complemented
16#14583633—21no—
17#14583632—21no—
18#14583620C411yescharacteristic, complemented
19#14583617C411yescharacteristic, complemented
20#14583613C411yescharacteristic, complemented
21#14583612C411yescharacteristic, complemented
22#14583598—21no—
23#14583594—21no—
24#14583568C411yescharacteristic, complemented
25#14583567C411yescharacteristic, complemented
26#14583551C411yescharacteristic, complemented
27#14583548C411yescharacteristic, complemented
28#14583484—21no—
29#14583482—21no—
30#14583464—21no—
31#14583451C2211yescharacteristic
32#14583444C2211yescharacteristic
33#14583412C2211yescharacteristic
34#14583410C2211yescharacteristic
35#14583409C2211yescharacteristic
36#14583378—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38C2×(C22⋊D43)⋊C4—21no—
39#14582975—21no—
40#14582975—21no—
41#14582974—21no—
42#14582974—21no—
43#14582949C2211yescharacteristic
44#14582949C2211yescharacteristic
45#14582863C2211yescharacteristic
46#14582861C2211yescharacteristic
47#14582861C2211yescharacteristic
48#14582794—21no—
49#14582771—21no—
50#14582770—21no—
51#14582763C2211yescharacteristic
52#14582758C2211yescharacteristic
53#14582750C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55#95×D43C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582636C2211yescharacteristic
59#14582636C2211yescharacteristic
60#14582635C2211yescharacteristic
61#14582635C2211yescharacteristic
62#14582634C2211yescharacteristic
63#14582634C2211yescharacteristic
64#14582633C2211yescharacteristic
65#14582633C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#525C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C43×#380C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic, complemented
76C2×#10621898C2×C411yescharacteristic, complemented
77C2×#10621900—21no—
78C2×#10621900C2×C411yescharacteristic, complemented
79C22×C22⋊D43D411yescharacteristic
80C23×Dic43—21no—
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83C2×#10621877—21no—
84C2×#10621872—21no—
85C2×#10621872—21no—
86#13063324C2×C411yescharacteristic, complemented
87#13063324C2×C411yescharacteristic, complemented
88#13063323C2×C411yescharacteristic, complemented
89#13063321—21no—
90#13063321—21no—
91#13063321C2×C411yescharacteristic, complemented
92#13063320—21no—
93#13063319—21no—
94#13063318—21no—
95#13063318—21no—
96#13063315—21no—
97#13063313—21no—
98#13063312—21no—
99#13063311—21no—
100#13063311—21no—
101#13063311—21no—
102#13063311—21no—
103#13063311—21no—
104#13063310—21no—
105#13063310—21no—
106#13063308—21no—
107#13063308—21no—
108#13063307—21no—
109#13063307—21no—
110#13063306—21no—
111#13063305C2×C411yescharacteristic, complemented
112#13063304C2×C411yescharacteristic, complemented
113#13063304C2311yescharacteristic
114#13063302—21no—
115#13063301C2×C411yescharacteristic, complemented
116#13063300C2×C411yescharacteristic, complemented
117#13063299—21no—
118#13063299C2×C411yescharacteristic, complemented
119#13063299C2311yescharacteristic
120#13063298—21no—
121#13063298—21no—
122#13063298—21no—
123#13063297—21no—
124#13063297—21no—
125#13063297—21no—
126#13063297—21no—
127#13063296—21no—
128#13063296C2×C411yescharacteristic, complemented
129#13063295—21no—
130#13063294—21no—
131#13063293—21no—
132Q8×Dic43C2×C411yescharacteristic, complemented
133C4×Dic86—21no—
134#13063290—21no—
135#13063290—21no—
136#13063290C2×C411yescharacteristic, complemented
137D4×Dic43—21no—
138D4×Dic43C2×C411yescharacteristic, complemented
139#13063287—21no—
140#13063287C2×C411yescharacteristic, complemented
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43C2×C411yescharacteristic
147C4×C22⋊D43C2×C411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150C4×C22⋊D43D411yescharacteristic
151C4×C22⋊D43D411yescharacteristic
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155(C22⋊D43)⋊C4—21no—
156(C22⋊D43)⋊C4—44no—
157#13063284C2×C411yescharacteristic, complemented
158#13063283C2×C411yescharacteristic, complemented
159#13063283C2×C411yescharacteristic, complemented
160#13063282—21no—
161#13063281—21no—
162#13063281—21no—
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4—21no—
165C2×Dic43⋊C4—21no—
166C2×Dic43⋊C4—21no—
167C2×Dic43⋊C4D411yescharacteristic
168C4⋊C4×D43—21no—
169C2×C22⋊Dic43D411yescharacteristic
170C2×(C2×D43)⋊C4—21no—
171C2×(C2×D43)⋊C4D411yescharacteristic
172C2×C4×Dic43—21no—
173C2×C4×Dic43C2311yescharacteristic
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181C8×Dic43—21no—
182C8×Dic43—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188C2×#41×C43C2×C411yescharacteristic, complemented
189C23×C4×C43C2311yescharacteristic
190C2×M16×C43—21no—
191#123×C43—21no—
192C22⋊Q8×C43C2×C411yescharacteristic, complemented
193C22⋊Q8×C43C2311yescharacteristic
194#121×C43C2×C411yescharacteristic, complemented
195#121×C43C2311yescharacteristic
196#120×C43—21no—
197C4×D4×C43—21no—
198C4×D4×C43—21no—
199#117×C43C2×C411yescharacteristic, complemented
200C2×C4⋊C4×C43—21no—
201C2×C22⋊C4×C43—21no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206#95×C43C2311yescharacteristic
207C24×C43C2×D411yescharacteristic
208C23×D43C2×D411yescharacteristic
209#41×C43—81no—
210C2×Q8×C43C22×C411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43C22×C411yescharacteristic
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—81no—
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—22no—
228C2×C22⋊D43—22no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43C22⋊C411yescharacteristic
235C2×C22⋊D43C22⋊C411yescharacteristic
236C2×C22⋊D43C22⋊C411yescharacteristic
237C2×C22⋊D43C22⋊C411yescharacteristic
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—42no—
243C22×Dic43—42no—
244C22×Dic43—81no—
245C22×Dic43C2×D411yescharacteristic
246C22×Dic43C2×D411yescharacteristic
247C22×Dic43C2×D411yescharacteristic
248#10621902—81no—
249#10621900—42no—
250#10621900—42no—
251#10621900—81no—
252#10621898—81no—
253C2×D172—21no—
254C2×D172—21no—
255C2×D172C22×C411yescharacteristic
256C2×C4×D43—21no—
257C2×C4×D43—21no—
258C2×C4×D43—21no—
259C2×C4×D43—42no—
260C2×C4×D43—42no—
261C2×C4×D43—81no—
262C2×C4×D43—81no—
263C2×C4×D43C22×C411yescharacteristic
264C2×C4×D43C22×C411yescharacteristic
265C2×C4×D43C2×D411yescharacteristic
266C2×C4×D43C2×D411yescharacteristic
267C2×Dic86—21no—
268C2×Dic86—21no—
269C2×Dic86C22×C411yescharacteristic
270M16×C43—81no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—81no—
276C4⋊C4×C43C22×C411yescharacteristic
277C4⋊C4×C43C22×C411yescharacteristic
278C22⋊C4×C43—21no—
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊C4×C43—21no—
283C22⋊C4×C43—42no—
284C42×C43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43—21no—
287C22⋊Dic43—21no—
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290C22⋊Dic43C22⋊C411yescharacteristic
291C22⋊Dic43C22⋊C411yescharacteristic
292C22⋊Dic43C22⋊C411yescharacteristic
293C22⋊Dic43C22⋊C411yescharacteristic
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—42no—
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304(C2×D43)⋊C4C22⋊C411yescharacteristic
305(C2×D43)⋊C4C22⋊C411yescharacteristic
306(C2×D43)⋊C4C22⋊C411yescharacteristic
307C4⋊Dic43—21no—
308C4⋊Dic43—21no—
309C4⋊Dic43C22×C411yescharacteristic
310C4⋊Dic43C22×C411yescharacteristic
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—42no—
320Dic43⋊C4—42no—
321Dic43⋊C4—81no—
322Dic43⋊C4C22⋊C411yescharacteristic
323Dic43⋊C4C22⋊C411yescharacteristic
324Dic43⋊C4C22⋊C411yescharacteristic
325Dic43⋊C4C22⋊C411yescharacteristic
326C4×Dic43—21no—
327C4×Dic43—21no—
328C4×Dic43—21no—
329C4×Dic43—21no—
330C4×Dic43—21no—
331C4×Dic43—42no—
332C4×Dic43C22×C411yescharacteristic
333C4×Dic43C22×C411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335C4×Dic43C2×D411yescharacteristic
336#10621877—81no—
337C2×C43⋊C8—21no—
338C2×C43⋊C8—21no—
339#10621872—81no—
340#10621872—81no—
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43C2×C22⋊C411yescharacteristic
347C23×C43C2×C22⋊C411yescharacteristic
348C23×C43C22×D411yescharacteristic
349C22×D43—21no—
350C22×D43—21no—
351C22×D43—21no—
352C22×D43—41no—
353C22×D43—41no—
354C22×D43C2×C22⋊C411yescharacteristic
355C22×D43C2×C22⋊C411yescharacteristic
356Q8×C43—41no—
357D4×C43—41no—
358D4×C43—41no—
359D4×C43—41no—
360D4×C43—81no—
361D4×C43—81no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—81no—
378C2×C4×C43C2×C22⋊C411yescharacteristic
379C2×C4×C43C2×C22⋊C411yescharacteristic
380C2×C4×C43C23×C411yescharacteristic
381C2×C4×C43C22×D411yescharacteristic
382C22⋊D43—22no—
383C22⋊D43—22no—
384C22⋊D43—22no—
385C22⋊D43—22no—
386C22⋊D43—41no—
387C22⋊D43—41no—
388C22⋊D43—42no—
389C22⋊D43—81no—
390C22⋊D43—81no—
391C22⋊D43—81no—
392C22⋊D43—81no—
393C22⋊D43—81no—
394C2×Dic43—22no—
395C2×Dic43—21no—
396C2×Dic43—21no—
397C2×Dic43—21no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—42no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—81no—
407C2×Dic43—84no—
408C2×Dic43C2×C22⋊C411yescharacteristic
409C2×Dic43C2×C22⋊C411yescharacteristic
410C2×Dic43C2×C22⋊C411yescharacteristic
411C2×Dic43C2×C22⋊C411yescharacteristic
412C2×Dic43C2×C22⋊C411yescharacteristic
413C2×Dic43C2×C22⋊C411yescharacteristic
414C2×Dic43AGL(1,ℤ/8)12yes—
415C2×Dic43#13712yes—
416D172—41no—
417D172—81no—
418D172—81no—
419C4×D43—41no—
420C4×D43—41no—
421C4×D43—41no—
422C4×D43—41no—
423C4×D43—42no—
424C4×D43—81no—
425C4×D43—81no—
426C4×D43—84no—
427Dic86—42no—
428Dic86—41no—
429Dic86—81no—
430C8×C43—41no—
431C8×C43—41no—
432C43⋊C8—41no—
433C43⋊C8—41no—
434#17630—431nomaximal, Sylow
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—21no—
438C22×C43—21no—
439C22×C43—21no—
440C22×C43—21no—
441C22×C43—21no—
442C22×C43—21no—
443C22×C43—42no—
444C22×C43—42no—
445C22×C43—41no—
446C22×C43—41no—
447C22×C43—41no—
448C22×C43C22×C22⋊C411yescharacteristic
449C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C43C2×#13711yescharacteristic
451C2×D43—21no—
452C2×D43—21no—
453C2×D43—21no—
454C2×D43—21no—
455C2×D43—21no—
456C2×D43—21no—
457C2×D43—42no—
458C2×D43—42no—
459C2×D43—41no—
460C2×D43—41no—
461C2×D43—41no—
462C4×C43—21no—
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—41no—
467C4×C43—41no—
468C4×C43—41no—
469C4×C43—81no—
470C4×C43—81no—
471Dic43—21no—
472Dic43—21no—
473Dic43—21no—
474Dic43—21no—
475Dic43—42no—
476Dic43—41no—
477Dic43—41no—
478Dic43—41no—
479Dic43—81no—
480Dic43#41712yes—
481Dic43#41712yes—
482#3506—431no—
483#2975—431no—
484#2349—431no—
485#1518—431no—
486#1517—431no—
487#1513—431no—
488#1513—431no—
489#1513—431no—
490#1513D4311yescharacteristic, complemented
491#1504—431no—
492#1504—431no—
493#1504—431no—
494#1504—431no—
495#1503—431no—
496#1502—431no—
497C2×C43—21no—
498C2×C43—21no—
499C2×C43—41no—
500C2×C43—41no—
501C2×C43—81no—
502C2×C43#288311yescharacteristic
503C2×C43C2×#41711yescharacteristic
504C2×C43#290111yescharacteristic
505D43—41no—
506D43—41no—
507D43—81no—
508#559—861no—
509#559—861no—
510#556—431no—
511#556—431no—
512#555—431no—
513#555—431no—
514#553—861no—
515#553—861no—
516#550—431no—
517#550—431no—
518#547—431no—
519#547—431no—
520#538—861no—
521#538—861no—
522#535—861no—
523#533—431no—
524#532—431no—
525#525—431no—
526#525—431no—
527#525—431no—
528#525C2×D4311yescharacteristic
529#520—861no—
530C2×C4×D4—431no—
531C2×C4×D4—861no—
532#436—861no—
533#436—861no—
534#436—861no—
535#436—861no—
536#431—431no—
537#431—431no—
538#407—431no—
539#407—431no—
540#407—431no—
541#407C2×D4311yescharacteristic
542#389—861no—
543#385—861no—
544#385—861no—
545#382—431no—
546#380—431no—
547#380C2×D4311yescharacteristic
548C4×C4⋊C4—431no—
549C2×#95—431no—
550C2×#95—431no—
551#328—431no—
552#328—431no—
553#328—431no—
554#328—431no—
555#328—431no—
556#328—431no—
557#328C2×D4311yescharacteristic
558#328C2×D4311yescharacteristic
559#327—431no—
560#327—431no—
561#327—431no—
562#327—431no—
563#327—431no—
564#327—431no—
565#327C2×D4311yescharacteristic
566#327C2×D4311yescharacteristic
567C43#1763011yescharacteristic, complemented, Sylow
568C2×#41—431no—
569C2×#41—431no—
570C2×#41—431no—
571C2×#41—861no—
572C2×#41C4×D4311yescharacteristic, complemented
573C22×D4—431no—
574C23×C4—431no—
575C23×C4—861no—
576C23×C4—861no—
577C23×C4C22×D4311yescharacteristic
578C2×M16—21no—
579C2×M16—861no—
580C2×M16—861no—
581C2×M16—861no—
582C4⋊Q8—431no—
583C4⋊Q8—431no—
584C4⋊Q8—431no—
585#127—431no—
586#127—861no—
587#127—861no—
588#126—861no—
589#126—861no—
590#126—861no—
591#126—861no—
592#125—861no—
593#124—861no—
594#124—861no—
595#124—861no—
596#124—861no—
597#124—861no—
598#124—861no—
599#124—861no—
600#123—21no—
601#123—861no—
602#123—861no—
603#123—861no—
604#123—861no—
605#123—861no—
606#123—861no—
607#123—861no—
608C22⋊Q8—431no—
609C22⋊Q8—431no—
610C22⋊Q8—431no—
611C22⋊Q8—431no—
612C22⋊Q8—861no—
613C22⋊Q8C4×D4311yescharacteristic, complemented
614C22⋊Q8C22×D4311yescharacteristic
615#121—431no—
616#121—431no—
617#121—431no—
618#121—431no—
619#121—861no—
620#121—861no—
621#121—861no—
622#121—861no—
623#121—861no—
624#121—861no—
625#121—861no—
626#121—861no—
627#121—861no—
628#121C4×D4311yescharacteristic, complemented
629#121C22×D4311yescharacteristic
630#120—21no—
631#120—861no—
632#120—861no—
633#120—861no—
634C4×Q8—431no—
635C4×Q8—431no—
636C4×Q8—861no—
637C4×Q8—861no—
638C4×Q8—861no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—431no—
642C4×D4—431no—
643C4×D4—431no—
644C4×D4—431no—
645C4×D4—431no—
646C4×D4—431no—
647C4×D4—431no—
648C4×D4—431no—
649C4×D4—431no—
650C4×D4—431no—
651C4×D4—861no—
652C4×D4—861no—
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—861no—
657C4×D4—861no—
658C4×D4—861no—
659C4×D4—861no—
660C4×D4—1724no—
661#117—431no—
662#117—431no—
663#117—431no—
664#117—861no—
665#117—861no—
666#117—861no—
667#117C4×D4311yescharacteristic, complemented
668C2×C4⋊C4—21no—
669C2×C4⋊C4—431no—
670C2×C4⋊C4—861no—
671C2×C4⋊C4—861no—
672C2×C4⋊C4—861no—
673C2×C4⋊C4—861no—
674C2×C4⋊C4—861no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—431no—
677C2×C22⋊C4—431no—
678C2×C22⋊C4—861no—
679C2×C42—431no—
680C2×C42—861no—
681C4⋊C8—861no—
682C4⋊C8—861no—
683C22⋊C8—21no—
684C22⋊C8—431no—
685C22⋊C8—431no—
686C22⋊C8—861no—
687C22⋊C8—861no—
688C22⋊C8—861no—
689C22⋊C8C22×D4311yescharacteristic
690C22⋊C8C22×D4311yescharacteristic
691C4×C8—861no—
692C4×C8—861no—
693#95—431no—
694#95—431no—
695#95—861no—
696#95—861no—
697#95—861no—
698#95C22×D4311yescharacteristic
699#95C22×D4311yescharacteristic
700C24—431no—
701C24D4×D4311yescharacteristic
702#41—81no—
703#41—3441no—
704#41—3441no—
705#41—3441no—
706#41—1722no—
707#41—1722no—
708C2×Q8—431no—
709C2×Q8—861no—
710C2×Q8—861no—
711C2×Q8C2×C4×D4311yescharacteristic
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—431no—
716C2×D4—431no—
717C2×D4—431no—
718C2×D4—431no—
719C2×D4—431no—
720C2×D4—861no—
721C2×D4—861no—
722C2×D4—862no—
723C2×D4—862no—
724C2×D4—861no—
725C2×D4—861no—
726C2×D4—861no—
727C2×D4—861no—
728C2×D4—861no—
729C2×D4—861no—
730C2×D4—861no—
731C2×D4C2×C4×D4311yescharacteristic
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—81no—
736C22×C4—431no—
737C22×C4—431no—
738C22×C4—431no—
739C22×C4—431no—
740C22×C4—431no—
741C22×C4—431no—
742C22×C4—431no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—3441no—
751C22×C4—3441no—
752C22×C4—3441no—
753C22×C4—1722no—
754C22×C4—1722no—
755C22×C4—1722no—
756C22×C4—1722no—
757C22×C4C2×C4×D4311yescharacteristic
758C22×C4C2×C4×D4311yescharacteristic
759C22×C4D4×D4311yescharacteristic
760C22×C4D4×D4311yescharacteristic
761C22×C4D4×D4311yescharacteristic
762C22×C4C23×D4311yescharacteristic
763M16—81no—
764M16—3441no—
765M16—3441no—
766M16—3441no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—861no—
770C2×C8—861no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—81no—
774C4⋊C4—431no—
775C4⋊C4—431no—
776C4⋊C4—431no—
777C4⋊C4—431no—
778C4⋊C4—431no—
779C4⋊C4—431no—
780C4⋊C4—861no—
781C4⋊C4—861no—
782C4⋊C4—861no—
783C4⋊C4—861no—
784C4⋊C4—861no—
785C4⋊C4—861no—
786C4⋊C4—861no—
787C4⋊C4—861no—
788C4⋊C4—861no—
789C4⋊C4—861no—
790C4⋊C4—3441no—
791C4⋊C4—1722no—
792C4⋊C4—1722no—
793C4⋊C4C2×C4×D4311yescharacteristic
794C4⋊C4C2×C4×D4311yescharacteristic
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—42no—
801C22⋊C4—431no—
802C22⋊C4—431no—
803C22⋊C4—431no—
804C22⋊C4—431no—
805C22⋊C4—431no—
806C22⋊C4—431no—
807C22⋊C4—431no—
808C22⋊C4—431no—
809C22⋊C4—861no—
810C22⋊C4—861no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C22⋊C4—861no—
815C22⋊C4—861no—
816C22⋊C4—861no—
817C22⋊C4—861no—
818C22⋊C4—861no—
819C22⋊C4—861no—
820C22⋊C4—861no—
821C22⋊C4—861no—
822C22⋊C4—1722no—
823C42—21no—
824C42—431no—
825C42—431no—
826C42—431no—
827C42—431no—
828C42—861no—
829C42—861no—
830C42—861no—
831C42—861no—
832C42—861no—
833C42—1722no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—41no—
838C23—41no—
839C23—431no—
840C23—431no—
841C23—861no—
842C23—861no—
843C23—861no—
844C23—1721no—
845C23—1721no—
846C23C22⋊C4×D4311yescharacteristic
847C23C22⋊C4×D4311yescharacteristic
848C23C2×D4×D4311yescharacteristic
849Q8—41no—
850Q8—3441no—
851Q8—1721no—
852Q8—1722no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—862no—
859D4—862no—
860D4—862no—
861D4—862no—
862D4—3441no—
863D4—3441no—
864D4—3441no—
865D4—3441no—
866D4—3441no—
867D4—3441no—
868D4—3441no—
869D4—1721no—
870D4—1722no—
871D4—1721no—
872D4—1721no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—81no—
889C2×C4—431no—
890C2×C4—431no—
891C2×C4—432no—
892C2×C4—432no—
893C2×C4—431no—
894C2×C4—431no—
895C2×C4—431no—
896C2×C4—431no—
897C2×C4—862no—
898C2×C4—861no—
899C2×C4—861no—
900C2×C4—861no—
901C2×C4—3441no—
902C2×C4—3441no—
903C2×C4—3444no—
904C2×C4—3441no—
905C2×C4—3444no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1722no—
911C2×C4—1722no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4—1721no—
916C2×C4—1721no—
917C2×C4—1721no—
918C2×C4—1721no—
919C2×C4C22⋊C4×D4311yescharacteristic
920C2×C4C22⋊C4×D4311yescharacteristic
921C2×C4C22×C4×D4311yescharacteristic
922C2×C4C2×D4×D4311yescharacteristic
923C8—41no—
924C8—41no—
925C8—1721no—
926C8—1721no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—42no—
936C22—42no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—861no—
941C22—861no—
942C22—861no—
943C22—861no—
944C22—861no—
945C22—861no—
946C22—1722no—
947C22—1722no—
948C22—1721no—
949C22—1721no—
950C22—1721no—
951C22C2×C22⋊C4×D4311yescharacteristic
952C22AGL(1,ℤ/8)×D4311yescharacteristic
953C22#137×D4311yescharacteristic
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—81no—
962C4—81no—
963C4—432no—
964C4—432no—
965C4—861no—
966C4—861no—
967C4—861no—
968C4—861no—
969C4—3441no—
970C4—1722no—
971C4—1721no—
972C4—1721no—
973C4—1721no—
974C2—21no—
975C2—21no—
976C2—41no—
977C2—41no—
978C2—81no—
979C2—3441no—
980C2—1721no—
981C2—1721no—
982C2#1914305311yescharacteristic
983C2#417×D4311yescharacteristic
984C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1513C2
socleC22×C43C22×C22⋊C4
prime radical#19148438C2
cosocleC22×C4×C43C24
hypercenter#1513D43
hypocenterC43#17630
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #19143634C2semidirect
3. #19137499C2semidirect
4. #19133157C2semidirect
5. #19133153C2semidirect
6. #19133137C2semidirect
7. #19133136C2semidirect
8. #19133135C2semidirect
9. #19133100C2semidirect
10. #19133099C2semidirect
11. #19133098C2semidirect
12. #19133096C2semidirect
13. #19133092C2semidirect
14. #19133088C2semidirect
15. C43×#1513C2semidirect
18. #14583620C4semidirect
19. #14583617C4semidirect
20. #14583613C4semidirect
21. #14583612C4semidirect
24. #14583568C4semidirect
25. #14583567C4semidirect
26. #14583551C4semidirect
27. #14583548C4semidirect
75. C2×#10621902C2×C4semidirect
76. C2×#10621898C2×C4semidirect
78. C2×#10621900C2×C4semidirect
86. #13063324C2×C4semidirect
87. #13063324C2×C4semidirect
88. #13063323C2×C4semidirect
91. #13063321C2×C4semidirect
111. #13063305C2×C4semidirect
112. #13063304C2×C4semidirect
115. #13063301C2×C4semidirect
116. #13063300C2×C4semidirect
118. #13063299C2×C4semidirect
128. #13063296C2×C4semidirect
132. Q8×Dic43C2×C4semidirect
136. #13063290C2×C4semidirect
138. D4×Dic43C2×C4semidirect
140. #13063287C2×C4semidirect
157. #13063284C2×C4semidirect
158. #13063283C2×C4semidirect
159. #13063283C2×C4semidirect
188. C2×#41×C43C2×C4semidirect
192. C22⋊Q8×C43C2×C4semidirect
194. #121×C43C2×C4semidirect
199. #117×C43C2×C4semidirect
490. #1513D43semidirect
567. C43#17630semidirect
572. C2×#41C4×D43semidirect
613. C22⋊Q8C4×D43semidirect
628. #121C4×D43semidirect
667. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191484382
#191436342
#191374992
#191331572
#191331532
#191331372
#191331362
#191331352
#191331002
#191330992
#191330982
#191330962
#191330922
#191330882
C43×#15132
#1763043