Finite Group Databasebeta

← #25112009

Subgroups — #25112009

Order 11008.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583546C211yesmaximal, characteristic
2C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582896C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137517C211yesmaximal, characteristic, complemented
6#19135526C211yesmaximal, characteristic, complemented
7#19135405C211yesmaximal, characteristic, complemented
8#19135017C211yesmaximal, characteristic, complemented
9#19134918C211yesmaximal, characteristic, complemented
10#19134901C211yesmaximal, characteristic, complemented
11#19134604C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1893C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583546—24no—
20#14583546C418yescomplemented
21C2×#13063312C2211yescharacteristic
22C2×#13063307—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063296—21no—
25C2×#13063293—21no—
26C2×#13063287C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×#13063284C2211yescharacteristic, complemented
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C22⋊C4×D43—21no—
31C8×C22⋊D43—24no—
32C2×Dic43⋊C8C2211yescharacteristic, complemented
33#14582896—24no—
34C2×#13063250C2211yescharacteristic, complemented
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063248C2211yescharacteristic, complemented
37C2×#13063248C2211yescharacteristic, complemented
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44#102×D43—24no—
45C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×C8×Dic43C2211yescharacteristic, complemented
48#14582787—21no—
49#14582781—21no—
50#14582775—21no—
51#14582764C2211yescharacteristic, complemented
52#14582756C2211yescharacteristic
53C4⋊C4×Dic43C2211yescharacteristic, complemented
54#14582746—21no—
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C23×C8×C43C2211yescharacteristic, complemented
58C2×#121×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—41no—
69C2×#10621898—41no—
70C2×#10621898C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C22⋊D43D411yescharacteristic
76C2×D4×D43—22no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—41no—
80C2×D4×D43—41no—
81C2×D4×D43C2×C414yes—
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C2×C8×D43—22no—
89C2×C8×D43—22no—
90C2×C8×D43—41no—
91#13063312—22no—
92#13063312C2×C414yescomplemented
93#13063307—28no—
94#13063305—22no—
95#13063305C2×C414yes—
96#13063296—28no—
97#13063293—28no—
98#13063287—22no—
99#13063287C2×C414yescomplemented
100C4×C22⋊D43C2×C414yes—
101C4×C22⋊D43D414yes—
102#13063284—22no—
103#13063284—41no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4D411yescharacteristic
109C4⋊C4×D43—22no—
110C4⋊C4×D43—41no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43D411yescharacteristic
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4D411yescharacteristic
119C22⋊C4×D43—28no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123Dic43⋊C8—22no—
124#13063250—22no—
125#13063250—22no—
126#13063248—41no—
127#13063248—41no—
128#13063247—22no—
129#13063247D414yescomplemented
130#13063246—22no—
131#13063246—41no—
132#13063245—22no—
133#13063245—22no—
134C22⋊(C43⋊C8)—22no—
135(C2×D43)⋊C8—22no—
136C8×Dic43—22no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×D4×C43—21no—
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43—22no—
145C22×C8×C43—22no—
146C22×C8×C43—41no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149#121×C43—22no—
150#121×C43C2×C414yescomplemented
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156#102×C43—22no—
157#102×C43—41no—
158#95×C43—21no—
159C24×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43—24no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—81no—
168C23×D43—81no—
169C23×D43C2×D411yescharacteristic
170C2×D4×C43—21no—
171C2×D4×C43—24no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—81no—
177C2×D4×C43—81no—
178C2×D4×C43C22×C412yes—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43C22×C412yes—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—22no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43C22⋊C414yes—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205D4×D43—28no—
206D4×D43—44no—
207D4×D43—44no—
208D4×D43—44no—
209#10621898—28no—
210#10621898—44no—
211#10621898—44no—
212#10621898—44no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172C22×C412yes—
217C2×D172C2×D412yes—
218C2×D172#4112yes—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—42no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—81no—
230C2×C4×D43—81no—
231C2×C4×D43—81no—
232C2×C4×D43C22×C412yes—
233C2×C4×D43C2×D412yes—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22×C412yes—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—44no—
246C2×C8×C43C2×D412yes—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43C22×C412yes—
253C22⋊C4×C43—24no—
254C22⋊C4×C43—81no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257C22⋊Dic43—42no—
258C22⋊Dic43C22⋊C414yes—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—42no—
262(C2×D43)⋊C4C22⋊C414yes—
263C4⋊Dic43—21no—
264C4⋊Dic43—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43C2×D412yes—
268Dic43⋊C4—42no—
269Dic43⋊C4C22⋊C414yes—
270C4×Dic43—42no—
271C4×Dic43—81no—
272C4×Dic43C22×C412yes—
273C4×Dic43C2×D412yes—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C8×D43—44no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—22no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43C2×C22⋊C412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—48no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—48no—
309C22×D43—84no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43C2×C22⋊C412yes—
315C22×D43#13512yes—
316C22×D43#13512yes—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—84no—
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—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43C2×C22⋊C412yes—
338C2×C4×C43C23×C411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C22⋊D43—28no—
345C22⋊D43—48no—
346C22⋊D43—48no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43C2×C22⋊C412yes—
363C2×Dic43C2×C22⋊C412yes—
364C2×Dic43C2×C22⋊C412yes—
365D172—22no—
366D172—22no—
367D172—22no—
368D172C4×D414yes—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—48no—
374C4×D43—84no—
375C4×D43—84no—
376Dic86—22no—
377Dic86—22no—
378Dic86—41no—
379Dic86—41no—
380C8×C43—22no—
381C8×C43—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22414—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43C22×C22⋊C411yescharacteristic
400C22×C43D4211yescharacteristic
401C22×C43#54611yescharacteristic
402C22×C43C2×#13511yescharacteristic
403C22×C43C2×#13511yescharacteristic
404C22×C43#57611yescharacteristic
405C22×C43#57711yescharacteristic
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—24no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—42no—
419C2×D43—816no—
420C2×D43#41614yescomplemented
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—81no—
424C4×C43—81no—
425C4×C43C2×C4×D411yescharacteristic
426C4×C43#51811yescharacteristic
427C4×C43D4211yescharacteristic
428C4×C43#54611yescharacteristic
429Dic43—22no—
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433Dic43—42no—
434Dic43—81no—
435C2×#546—431no—
436C2×C8×D4—431no—
437C2×#416—431no—
438C22×#102—431no—
439#2352—431no—
440#1983—431no—
441#1958—431no—
442#1893D4311yescharacteristic, complemented
443#1892—431no—
444#1875—431no—
445#1872—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—42no—
451C2×C43—82no—
452C2×C43D4×C22⋊C411yescharacteristic
453C2×C43C2×#41611yescharacteristic
454C2×C43#289711yescharacteristic
455C2×C43#328011yescharacteristic
456C2×C43#328211yescharacteristic
457C2×C43#329611yescharacteristic
458C2×C43#329711yescharacteristic
459D43—24no—
460D43—44no—
461C22×#41—431no—
462C23×D4—431no—
463C23×C8—431no—
464C23×C8C2×D4311yescharacteristic, complemented
465#546—438no—
466#546—864no—
467C2×#124—431no—
468C2×#123—861no—
469C2×C22⋊Q8—431no—
470C2×#121—861no—
471C2×#121C2×D4311yescharacteristic
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4—431no—
475C2×#117—431no—
476C22×C4⋊C4—431no—
477C22×C22⋊C4—861no—
478C8×D4—864no—
479C2×C4⋊C8—431no—
480#416—864no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—864no—
492C2×#102C2×D4311yescharacteristic
493C2×#102C2×D4311yescharacteristic
494C2×C22⋊C8—431no—
495C2×C22⋊C8—431no—
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380C2×D4311yescharacteristic, complemented
503C4×C4⋊C4—431no—
504C4×C22⋊C4—861no—
505#340—431no—
506#340—431no—
507#340C2×D4311yescharacteristic, complemented
508#340C2×D4311yescharacteristic, complemented
509C43#2241411yescharacteristic, complemented, Sylow
510C25—861no—
511C2×#41—434no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—862no—
515C2×#41—1721no—
516C2×#41—1721no—
517C22×Q8—431no—
518C22×D4—21no—
519C22×D4—431no—
520C22×D4—434no—
521C22×D4—431no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—862no—
525C22×D4—862no—
526C22×D4—861no—
527C22×D4—1721no—
528C22×D4—1721no—
529C22×D4C22×D4311yescharacteristic
530C23×C4—431no—
531C23×C4—861no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8—431no—
539C22×C8—431no—
540C22×C8—862no—
541C22×C8—862no—
542C22×C8—1721no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#124—434no—
546#124—862no—
547#123—868no—
548C22⋊Q8—434no—
549C22⋊Q8—862no—
550#121—22no—
551#121—868no—
552#121C4×D4314yescomplemented
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—862no—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—862no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—1721no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—431no—
574C2×C22⋊C4—868no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C42—431no—
582C2×C42—861no—
583C2×C42—861no—
584C4⋊C8—862no—
585#103—862no—
586#103—862no—
587#103—1721no—
588#103—1721no—
589#102—22no—
590#102—41no—
591#102—434no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—862no—
596#102—1721no—
597C22⋊C8—862no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—21no—
601#95—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—21no—
606C24—431no—
607C24—864no—
608C24—861no—
609C24—3441no—
610C24—3441no—
611C24—1722no—
612C24—1722no—
613C24—1722no—
614C24—1722no—
615C24D4×D4311yescharacteristic
616#41—868no—
617#41—1724no—
618#41—1724no—
619#41—1724no—
620C2×Q8—432no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—434no—
635C2×D4—432no—
636C2×D4—432no—
637C2×D4—432no—
638C2×D4—864no—
639C2×D4—868no—
640C2×D4—862no—
641C2×D4—862no—
642C2×D4—864no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—1724no—
647C2×D4—1724no—
648C2×D4—1724no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4—1722no—
652C2×D4—1722no—
653C2×D4C2×C4×D4312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—432no—
665C22×C4—432no—
666C22×C4—864no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—864no—
674C22×C4—861no—
675C22×C4—3441no—
676C22×C4—3441no—
677C22×C4—3441no—
678C22×C4—1722no—
679C22×C4—1722no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4C2×C4×D4312yes—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4312yes—
685C22×C4C23×D4311yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—44no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—1724no—
699C2×C8D4×D4312yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—434no—
706C4⋊C4—432no—
707C4⋊C4—864no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—1722no—
712C4⋊C4C2×C4×D4312yes—
713C22⋊C4—24no—
714C22⋊C4—81no—
715C22⋊C4—434no—
716C22⋊C4—434no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—864no—
721C22⋊C4—1722no—
722C22⋊C4—1722no—
723C42—432no—
724C42—432no—
725C42—3441no—
726C42—1722no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—432no—
741C23—432no—
742C23—432no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—862no—
748C23—862no—
749C23—862no—
750C23—3444no—
751C23—3444no—
752C23—3444no—
753C23—3444no—
754C23—3444no—
755C23—1728no—
756C23—1728no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23C22⋊C4×D4312yes—
762C23C2×D4×D4311yescharacteristic
763Q8—862no—
764Q8—862no—
765Q8—1721no—
766Q8—1721no—
767D4—22no—
768D4—22no—
769D4—41no—
770D4—41no—
771D4—84no—
772D4—434no—
773D4—868no—
774D4—862no—
775D4—862no—
776D4—862no—
777D4—1728no—
778D4—1728no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—432no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—3444no—
810C2×C4—3444no—
811C2×C4—1728no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4C22⋊C4×D4312yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4#41×D4311yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337111yescharacteristic
826C8—22no—
827C8—41no—
828C8—1721no—
829C8—1721no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—434no—
845C22—862no—
846C22—862no—
847C22—862no—
848C22—862no—
849C22—862no—
850C22—862no—
851C22—864no—
852C22—34416no—
853C22—1722no—
854C22—1722no—
855C22—1722no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22C2×C22⋊C4×D4311yescharacteristic
860C22#1458353311yescharacteristic
861C22#1458353811yescharacteristic
862C22#135×D4311yescharacteristic
863C22#135×D4311yescharacteristic
864C22#1458370011yescharacteristic
865C22#1458370511yescharacteristic
866C4—22no—
867C4—42no—
868C4—81no—
869C4—81no—
870C4—862no—
871C4—862no—
872C4—862no—
873C4—3441no—
874C4—1722no—
875C4—1722no—
876C4C4×D4×D4311yescharacteristic
877C4#1458337111yescharacteristic
878C4#1458353111yescharacteristic
879C4#1458354111yescharacteristic
880C2—42no—
881C2—82no—
882C2—864no—
883C2—1724no—
884C2#1913741311yescharacteristic
885C2#416×D4311yescharacteristic
886C2#1914311611yescharacteristic
887C2#1914628311yescharacteristic
888C2#1914630911yescharacteristic
889C2#1914642511yescharacteristic
890C2#1914644011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#14583546C2
cosocleC22×C4×C43C24
hypercenter#1893D43
hypocenterC43#22414
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D43C2semidirect
3. C2×#14582896C2semidirect
4. C2×#102×D43C2semidirect
5. #19137517C2semidirect
6. #19135526C2semidirect
7. #19135405C2semidirect
8. #19135017C2semidirect
9. #19134918C2semidirect
10. #19134901C2semidirect
11. #19134604C2semidirect
12. #19134533C2semidirect
13. #19134524C2semidirect
14. #19134409C2semidirect
15. C43×#1893C2semidirect
20. #14583546C4semidirect
28. C2×#13063284C22semidirect
32. C2×Dic43⋊C8C22semidirect
34. C2×#13063250C22semidirect
35. C2×#13063250C22semidirect
36. C2×#13063248C22semidirect
37. C2×#13063248C22semidirect
45. C2×C22⋊(C43⋊C8)C22semidirect
47. C2×C8×Dic43C22semidirect
51. #14582764C22semidirect
53. C4⋊C4×Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
57. C23×C8×C43C22semidirect
61. C43×#380C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
70. C2×#10621898C2×C4semidirect
92. #13063312C2×C4semidirect
99. #13063287C2×C4semidirect
129. #13063247D4semidirect
150. #121×C43C2×C4semidirect
420. C2×D43#416semidirect
442. #1893D43semidirect
464. C23×C8C2×D43semidirect
502. #380C2×D43semidirect
507. #340C2×D43semidirect
508. #340C2×D43semidirect
509. C43#22414semidirect
552. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835462
C2×C8×C22⋊D432
C2×#145828962
C2×#102×D432
#191375172
#191355262
#191354052
#191350172
#191349182
#191349012
#191346042
#191345332
#191345242
#191344092
C43×#18932
#2241443