Finite Group Databasebeta

← #25106248

Subgroups — #25106248

Order 11008.

1200 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2#423×D43C211yesmaximal, characteristic, complemented
3C4×#13063283C211yesmaximal, characteristic, complemented
4#19135570C212yesmaximal, complemented
5#19135421C212yesmaximal, complemented
6#19134896C212yesmaximal, complemented
7#19134894C212yesmaximal, complemented
8#19134616C211yesmaximal, characteristic, complemented
9#19134615C211yesmaximal, characteristic, complemented
10#19134612C211yesmaximal, characteristic, complemented
11C43×#1806C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583453C411yescharacteristic, complemented
14#14583453C411yescharacteristic, complemented
15#14583452C2211yescharacteristic
16#14583446C411yescharacteristic, complemented
17#14583446C411yescharacteristic, complemented
18#14583445C2211yescharacteristic
19#14583436C411yescharacteristic, complemented
20#14583436C411yescharacteristic, complemented
21#14583431C411yescharacteristic, complemented
22#14583431C411yescharacteristic, complemented
23#14583429—21no—
24#14583429—21no—
25#14583427—21no—
26#14583427—21no—
27#14583411C2211yescharacteristic
28#14583408—21no—
29#14583408—21no—
30#14583406C2211yescharacteristic
31C4×#10621898—21no—
32C4×#10621898—21no—
33C4×#10621898C2211yescharacteristic
34C2×#13063283—21no—
35C2×C42×D43C2211yescharacteristic
36#14582923C2211yescharacteristic
37#14582922C2212yes—
38#14582921—21no—
39#14582921—21no—
40C4⋊C8×D43—21no—
41C4⋊C8×D43—21no—
42C2×#13063253C2212yes—
43C2×#13063252C2212yes—
44C2×#13063251C2212yes—
45C4⋊C4×Dic43—21no—
46C4×C4⋊Dic43C2211yescharacteristic
47C4×(C2×D43)⋊C4C2212yes—
48#14582746—21no—
49#14582744—21no—
50C42×Dic43C2212yes—
51#14582660C2212yes—
52#14582659C2212yes—
53#14582658C2212yes—
54C4×#41×C43C2211yescharacteristic
55C43×#423C2211yescharacteristic
56C2×#104×C43C2212yes—
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#339C2212yes—
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2311yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621877C2312yes—
66C2×#10621872—22no—
67M16×D43—42no—
68M16×D43—42no—
69C2×C8×D43—22no—
70#13063324C2×C411yescharacteristic
71#13063324C2×C411yescharacteristic
72#13063323C2×C411yescharacteristic
73#13063321C2×C411yescharacteristic
74#13063320—21no—
75#13063320—21no—
76#13063318—21no—
77#13063318—21no—
78#13063316C2×C411yescharacteristic
79#13063316C2×C411yescharacteristic
80#13063315—21no—
81#13063315—21no—
82#13063314C2×C411yescharacteristic
83#13063312C2×C411yescharacteristic
84#13063311—21no—
85#13063311—21no—
86#13063310—21no—
87#13063310—21no—
88#13063309—21no—
89#13063307—21no—
90#13063307—21no—
91#13063306—21no—
92#13063305C2×C411yescharacteristic
93#13063305C2×C411yescharacteristic
94#13063303—21no—
95#13063303—21no—
96#13063302—21no—
97#13063302—21no—
98#13063301C2×C411yescharacteristic
99#13063301C2×C411yescharacteristic
100#13063300C2×C411yescharacteristic
101#13063300C2×C411yescharacteristic
102#13063298—21no—
103#13063298—21no—
104#13063297—21no—
105#13063297—21no—
106#13063296C2×C411yescharacteristic
107#13063296C2×C411yescharacteristic
108#13063295—21no—
109#13063293—21no—
110C4×Dic86—21no—
111C4×Dic86—21no—
112C4×Dic86—21no—
113C4×Dic86—21no—
114C4×Dic86C2×C411yescharacteristic
115C4×Dic86C2×C411yescharacteristic
116C4×D172—21no—
117C4×D172—21no—
118C4×D172—21no—
119C4×D172—21no—
120C4×D172C2×C411yescharacteristic
121C4×D172C2×C411yescharacteristic
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129C4×C22⋊D43—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132#13063284—21no—
133#13063284—21no—
134#13063284C2311yescharacteristic
135#13063283—28no—
136#13063282—21no—
137#13063282—21no—
138#13063282—21no—
139#13063282—21no—
140#13063282—21no—
141C2×C4⋊Dic43—21no—
142C2×(C2×D43)⋊C4—22no—
143C2×C4×Dic43—22no—
144C2×C4×Dic43—22no—
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43C2312yes—
148C2×C4×Dic43C2311yescharacteristic
149C42×D43—21no—
150C42×D43C2×C411yescharacteristic
151C42×D43C2×C411yescharacteristic
152C42×D43C2×C411yescharacteristic
153C42×D43C2×C411yescharacteristic
154C42×D43D411yescharacteristic
155C42×D43D411yescharacteristic
156C42×D43D411yescharacteristic
157C42×D43D411yescharacteristic
158C4⋊(C43⋊C8)—21no—
159C4⋊(C43⋊C8)—21no—
160Dic43⋊C8—22no—
161Dic43⋊C8—22no—
162#13063253—42no—
163#13063252—42no—
164#13063251—42no—
165C43⋊#95—21no—
166C43⋊#95—22no—
167C2×#41×C43C2311yescharacteristic
168C2×M16×C43C2312yes—
169C4×Q8×C43C2×C411yescharacteristic
170C4×Q8×C43C2×C411yescharacteristic
171C4×D4×C43—21no—
172C4×D4×C43—21no—
173C4×D4×C43C2×C411yescharacteristic
174C4×D4×C43C2×C411yescharacteristic
175#117×C43—21no—
176#117×C43C2311yescharacteristic
177C2×C4⋊C4×C43—21no—
178C2×C42×C43—21no—
179C2×C42×C43C2312yes—
180C2×C42×C43C2311yescharacteristic
181C4⋊C8×C43—21no—
182C4⋊C8×C43—21no—
183#104×C43—42no—
184#95×C43—21no—
185C23×D43C2×D411yescharacteristic
186#41×C43—21no—
187#41×C43—21no—
188#41×C43—21no—
189#41×C43—21no—
190C2×Q8×C43C22×C411yescharacteristic
191C2×D4×C43—21no—
192C2×D4×C43C22×C411yescharacteristic
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—22no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C2×C22⋊D43—21no—
203C2×C22⋊D43—21no—
204C2×C22⋊D43—21no—
205C22×Dic43—22no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209#10621898—21no—
210#10621898—21no—
211#10621898—21no—
212#10621898—21no—
213#10621898—44no—
214#10621898—44no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172C22×C411yescharacteristic
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—24no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—42no—
227C2×C4×D43C22⋊C411yescharacteristic
228C2×C4×D43C22⋊C411yescharacteristic
229C2×C4×D43C22⋊C411yescharacteristic
230C2×C4×D43C22⋊C411yescharacteristic
231C2×C4×D43C22⋊C411yescharacteristic
232C2×C4×D43C22⋊C411yescharacteristic
233C2×C4×D43C22⋊C411yescharacteristic
234C2×C4×D43C22⋊C411yescharacteristic
235C2×C4×D43C22×C411yescharacteristic
236C2×C4×D43C22×C411yescharacteristic
237C2×C4×D43C2×D411yescharacteristic
238C2×C4×D43C2×D411yescharacteristic
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86C22×C411yescharacteristic
242M16×C43—22no—
243M16×C43—22no—
244C2×C8×C43—22no—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43C22×C411yescharacteristic
249C4⋊C4×C43C22×C411yescharacteristic
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C42×C43—21no—
254C42×C43—21no—
255C42×C43—21no—
256C42×C43—22no—
257C42×C43—22no—
258C42×C43C22×C411yescharacteristic
259C42×C43C22×C411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C42×C43C2×D411yescharacteristic
262C22⋊Dic43—21no—
263C22⋊Dic43—21no—
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266C22⋊Dic43—21no—
267(C2×D43)⋊C4—28no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4—21no—
278C4⋊Dic43—24no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43C22×C411yescharacteristic
284C4⋊Dic43C22×C411yescharacteristic
285Dic43⋊C4—21no—
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295C4×Dic43—28no—
296C4×Dic43—21no—
297C4×Dic43—21no—
298C4×Dic43—21no—
299C4×Dic43—22no—
300C4×Dic43—22no—
301C4×Dic43—44no—
302C4×Dic43C22⋊C411yescharacteristic
303C4×Dic43C22⋊C411yescharacteristic
304C4×Dic43C22⋊C411yescharacteristic
305C4×Dic43C22⋊C411yescharacteristic
306C4×Dic43C22⋊C411yescharacteristic
307C4×Dic43C22⋊C411yescharacteristic
308C4×Dic43C22⋊C411yescharacteristic
309C4×Dic43C22⋊C411yescharacteristic
310C4×Dic43C22×C411yescharacteristic
311C4×Dic43C22×C411yescharacteristic
312C4×Dic43C2×D411yescharacteristic
313C4×Dic43C2×D411yescharacteristic
314#10621877—22no—
315#10621877—22no—
316C2×C43⋊C8—22no—
317#10621872—44no—
318C8×D43—44no—
319C23×C43—21no—
320C23×C43C22×D411yescharacteristic
321C22×D43—21no—
322C22×D43—21no—
323C22×D43—22no—
324C22×D43—21no—
325C22×D43—41no—
326C22×D43C2×C22⋊C411yescharacteristic
327C22×D43C2×C22⋊C411yescharacteristic
328Q8×C43—21no—
329Q8×C43—21no—
330D4×C43—21no—
331D4×C43—21no—
332D4×C43—41no—
333D4×C43—41no—
334C2×C4×C43—22no—
335C2×C4×C43—24no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—41no—
340C2×C4×C43—42no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—42no—
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C2×C22⋊C411yescharacteristic
348C2×C4×C43C2×C22⋊C411yescharacteristic
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C23×C411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43H(5,𝔽2)11yescharacteristic
353C2×C4×C43H(5,𝔽2)11yescharacteristic
354C2×C4×C432−1+411yescharacteristic
355C2×C4×C432−1+411yescharacteristic
356C22⋊D43—42no—
357C22⋊D43—41no—
358C22⋊D43—41no—
359C22⋊D43—42no—
360C22⋊D43—42no—
361C22⋊D43—42no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—24no—
367C2×Dic43—21no—
368C2×Dic43—21no—
369C2×Dic43—21no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378D172—21no—
379D172—21no—
380D172—42no—
381D172—42no—
382C4×D43—22no—
383C4×D43—21no—
384C4×D43—21no—
385C4×D43—21no—
386C4×D43—21no—
387C4×D43—21no—
388C4×D43—21no—
389C4×D43—21no—
390C4×D43—21no—
391C4×D43—22no—
392C4×D43—22no—
393C4×D43—22no—
394C4×D43—22no—
395C4×D43—41no—
396C4×D43—41no—
397C4×D43—42no—
398C4×D43—41no—
399C4×D43—41no—
400C4×D43—42no—
401C4×D43#10414yescomplemented
402Dic86—21no—
403Dic86—21no—
404Dic86—42no—
405Dic86—42no—
406C8×C43—42no—
407C43⋊C8—42no—
408#21856—431nomaximal, Sylow
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43C22×C22⋊C411yescharacteristic
415C22×C43#53711yescharacteristic
416C22×C43#53711yescharacteristic
417C2×D43—21no—
418C2×D43—21no—
419C2×D43—21no—
420C2×D43—21no—
421C2×D43—21no—
422C2×D43—42no—
423C2×D43—42no—
424C2×D43—41no—
425C2×D43—41no—
426C2×D43—41no—
427C2×D43C2×#10412yes—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—44no—
432C4×C43—41no—
433C4×C43—41no—
434C4×C43—41no—
435C4×C43C2×#10412yes—
436C4×C43#52011yescharacteristic
437C4×C43#52011yescharacteristic
438C4×C43#53511yescharacteristic
439C4×C43#53611yescharacteristic
440Dic43—21no—
441Dic43—21no—
442Dic43—21no—
443Dic43—21no—
444Dic43—44no—
445Dic43—41no—
446Dic43—41no—
447Dic43—41no—
448Dic43C2×#10412yes—
449Dic43#42112yes—
450#3444—431no—
451C2×#423—431no—
452C4×#117—431no—
453#1994—432no—
454#1962—432no—
455#1871—432no—
456#1871—432no—
457#1806—431no—
458#1806—431no—
459#1806—431no—
460#1806D4311yescharacteristic, complemented
461C2×C43—21no—
462C2×C43—21no—
463C2×C43—81no—
464C2×C43#231111yescharacteristic
465C2×C43C22×#10411yescharacteristic
466C2×C43C2×#42111yescharacteristic
467D43—22no—
468D43—41no—
469D43—81no—
470C22×M16—432no—
471#533—431no—
472#533—431no—
473#533—431no—
474#532—431no—
475#532—431no—
476#532—431no—
477#529—431no—
478#529—431no—
479#529—431no—
480#529—431no—
481#529—861no—
482#529—861no—
483#529—861no—
484#529—861no—
485#525—431no—
486#525—431no—
487#525—861no—
488#525—861no—
489C4×#41—431no—
490C4×#41—861no—
491C4×#41—861no—
492C4×#41C2×D4311yescharacteristic
493C2×#117—861no—
494C22×C42—431no—
495#423—432no—
496#423—431no—
497#423—861no—
498#423—861no—
499#423C2×D4311yescharacteristic
500C2×C4⋊C8—861no—
501C2×C4⋊C8—861no—
502C2×#104—432no—
503C2×#104—432no—
504C2×#104—432no—
505C2×#104C2×D4312yes—
506C4×C4⋊C4—431no—
507C4×C4⋊C4—861no—
508C4×C4⋊C4C2×D4311yescharacteristic
509C4×C22⋊C4—432no—
510C4×C22⋊C4—861no—
511#376—861no—
512C43—432no—
513#339—432no—
514#339—432no—
515#339—432no—
516#339C2×D4312yes—
517C43#2185611yescharacteristic, complemented, Sylow
518C2×#41—431no—
519C2×#41—861no—
520C2×#41—861no—
521C2×#41C22×D4311yescharacteristic
522C23×C4—431no—
523C23×C4—431no—
524C23×C4—431no—
525C2×M16—432no—
526C2×M16—862no—
527C2×M16—1722no—
528C2×M16—1722no—
529C2×M16C22×D4312yes—
530C22×C8—862no—
531C4⋊Q8—431no—
532C4⋊Q8—431no—
533C4⋊Q8—431no—
534#127—431no—
535#126—861no—
536#126—861no—
537#126—861no—
538#126—861no—
539#125—431no—
540#125—431no—
541#125—861no—
542#125—861no—
543#124—431no—
544#124—431no—
545#124—861no—
546#124—861no—
547#123—861no—
548#123—861no—
549#123—861no—
550#123—861no—
551#123—861no—
552#123—861no—
553C22⋊Q8—431no—
554C22⋊Q8—431no—
555C22⋊Q8—431no—
556C22⋊Q8—431no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561#121—431no—
562#121—431no—
563#121—431no—
564#121—431no—
565#121—861no—
566#121—861no—
567#121—861no—
568#121—861no—
569#120—861no—
570#120—861no—
571C4×Q8—431no—
572C4×Q8—431no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8—861no—
576C4×Q8—861no—
577C4×Q8C4×D4311yescharacteristic
578C4×Q8C4×D4311yescharacteristic
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—431no—
582C4×D4—431no—
583C4×D4—861no—
584C4×D4—861no—
585C4×D4—861no—
586C4×D4—861no—
587C4×D4—861no—
588C4×D4—861no—
589C4×D4—861no—
590C4×D4—861no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4C4×D4311yescharacteristic
598C4×D4C4×D4311yescharacteristic
599#117—21no—
600#117—431no—
601#117—861no—
602#117—861no—
603#117—861no—
604#117—861no—
605#117—861no—
606#117—861no—
607#117—868no—
608#117—861no—
609#117C22×D4311yescharacteristic
610C2×C4⋊C4—21no—
611C2×C4⋊C4—861no—
612C2×C22⋊C4—862no—
613C2×C42—21no—
614C2×C42—431no—
615C2×C42—431no—
616C2×C42—431no—
617C2×C42—431no—
618C2×C42—431no—
619C2×C42—431no—
620C2×C42—431no—
621C2×C42—431no—
622C2×C42—431no—
623C2×C42—431no—
624C2×C42—431no—
625C2×C42—432no—
626C2×C42—862no—
627C2×C42—861no—
628C2×C42—862no—
629C2×C42C22×D4312yes—
630C2×C42C22×D4311yescharacteristic
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—862no—
634C4⋊C8—862no—
635C4⋊C8—861no—
636C4⋊C8—861no—
637#104—42no—
638#104—1722no—
639#104—1722no—
640#104—1722no—
641#95—21no—
642#95—862no—
643#95—861no—
644C24—431no—
645#41—21no—
646#41—21no—
647#41—21no—
648#41—21no—
649#41—861no—
650#41—861no—
651#41—861no—
652#41—861no—
653#41—1724no—
654#41—1724no—
655C2×Q8—431no—
656C2×Q8—861no—
657C2×Q8—861no—
658C2×Q8C2×C4×D4311yescharacteristic
659C2×D4—21no—
660C2×D4—431no—
661C2×D4—861no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4—861no—
666C2×D4—861no—
667C2×D4—861no—
668C2×D4C2×C4×D4311yescharacteristic
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—431no—
674C22×C4—431no—
675C22×C4—431no—
676C22×C4—431no—
677C22×C4—431no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—431no—
681C22×C4—431no—
682C22×C4—431no—
683C22×C4—431no—
684C22×C4—431no—
685C22×C4—431no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—864no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—861no—
693C22×C4—862no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—1722no—
698C22×C4D4×D4311yescharacteristic
699C22×C4D4×D4311yescharacteristic
700C22×C4C23×D4311yescharacteristic
701M16—22no—
702M16—22no—
703M16—862no—
704M16—862no—
705M16—1724no—
706C2×C8—22no—
707C2×C8—862no—
708C2×C8—1724no—
709C4⋊C4—24no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—431no—
713C4⋊C4—431no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4—864no—
727C4⋊C4—861no—
728C4⋊C4—861no—
729C4⋊C4C2×C4×D4311yescharacteristic
730C4⋊C4C2×C4×D4311yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C22⋊C4—861no—
738C22⋊C4—861no—
739C22⋊C4—861no—
740C22⋊C4—861no—
741C22⋊C4—861no—
742C22⋊C4—868no—
743C22⋊C4—861no—
744C22⋊C4—861no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4—861no—
748C22⋊C4—861no—
749C22⋊C4—861no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—22no—
754C42—22no—
755C42—431no—
756C42—431no—
757C42—431no—
758C42—431no—
759C42—431no—
760C42—431no—
761C42—431no—
762C42—431no—
763C42—431no—
764C42—431no—
765C42—431no—
766C42—431no—
767C42—868no—
768C42—861no—
769C42—861no—
770C42—861no—
771C42—862no—
772C42—862no—
773C42—1724no—
774C42C2×C4×D4311yescharacteristic
775C42C2×C4×D4311yescharacteristic
776C42D4×D4311yescharacteristic
777C42D4×D4311yescharacteristic
778C23—21no—
779C23—431no—
780C23—431no—
781C23—862no—
782C23—861no—
783C23—861no—
784C23—861no—
785C23—1721no—
786C23C2×D4×D4311yescharacteristic
787Q8—21no—
788Q8—21no—
789Q8—861no—
790Q8—861no—
791Q8—1722no—
792Q8—1722no—
793D4—21no—
794D4—21no—
795D4—41no—
796D4—41no—
797D4—861no—
798D4—861no—
799D4—1722no—
800D4—1722no—
801D4—1722no—
802D4—1722no—
803D4—1722no—
804D4—1722no—
805D4—1721no—
806D4—1721no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—431no—
820C2×C4—431no—
821C2×C4—434no—
822C2×C4—431no—
823C2×C4—431no—
824C2×C4—431no—
825C2×C4—431no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—862no—
831C2×C4—862no—
832C2×C4—861no—
833C2×C4—861no—
834C2×C4—861no—
835C2×C4—861no—
836C2×C4—861no—
837C2×C4—861no—
838C2×C4—862no—
839C2×C4—861no—
840C2×C4—861no—
841C2×C4—861no—
842C2×C4—861no—
843C2×C4—864no—
844C2×C4—861no—
845C2×C4—861no—
846C2×C4—861no—
847C2×C4—1721no—
848C2×C4—1721no—
849C2×C4—1722no—
850C2×C4—1722no—
851C2×C4—1722no—
852C2×C4—1722no—
853C2×C4—1721no—
854C2×C4—1721no—
855C2×C4C22⋊C4×D4311yescharacteristic
856C2×C4C22⋊C4×D4311yescharacteristic
857C2×C4C22⋊C4×D4311yescharacteristic
858C2×C4C22⋊C4×D4311yescharacteristic
859C2×C4C22×C4×D4311yescharacteristic
860C2×C4C2×D4×D4311yescharacteristic
861C2×C4#1306337011yescharacteristic
862C2×C4#1306337111yescharacteristic
863C2×C4#1306337211yescharacteristic
864C2×C4#1306337311yescharacteristic
865C8—42no—
866C8—1722no—
867C22—21no—
868C22—21no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—432no—
873C22—861no—
874C22—861no—
875C22—861no—
876C22—861no—
877C22—861no—
878C22—1722no—
879C22—1722no—
880C22—1721no—
881C22—1721no—
882C22—1721no—
883C22C2×C22⋊C4×D4311yescharacteristic
884C22#1458347811yescharacteristic
885C22#1458347911yescharacteristic
886C4—21no—
887C4—21no—
888C4—21no—
889C4—44no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—432no—
894C4—432no—
895C4—861no—
896C4—861no—
897C4—861no—
898C4—861no—
899C4—1724no—
900C4—1721no—
901C4—1721no—
902C4—1721no—
903C4#104×D4312yes—
904C4#1458337911yescharacteristic
905C4#1458338011yescharacteristic
906C4#1458346511yescharacteristic
907C4#1458347211yescharacteristic
908C2—21no—
909C2—21no—
910C2—81no—
911C2—862no—
912C2—3441no—
913C2—1721no—
914C2#1913718411yescharacteristic
915C2C2×#104×D4311yescharacteristic
916C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radical#19147888C2
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#21856
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #423×D43C2semidirect
3. C4×#13063283C2semidirect
4. #19135570C2semidirect
5. #19135421C2semidirect
6. #19134896C2semidirect
7. #19134894C2semidirect
8. #19134616C2semidirect
9. #19134615C2semidirect
10. #19134612C2semidirect
11. C43×#1806C2semidirect
13. #14583453C4semidirect
14. #14583453C4semidirect
16. #14583446C4semidirect
17. #14583446C4semidirect
19. #14583436C4semidirect
20. #14583436C4semidirect
21. #14583431C4semidirect
22. #14583431C4semidirect
401. C4×D43#104semidirect
460. #1806D43semidirect
517. C43#21856semidirect

Maximal subgroups

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

subgroupindex
#191478882
#423×D432
C4×#130632832
#191355702
#191354212
#191348962
#191348942
#191346162
#191346152
#191346122
C43×#18062
#2185643