Finite Group Databasebeta

← #25112012

Subgroups — #25112012

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×#14583540C211yesmaximal, characteristic
2C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
3C2×#14582894C211yesmaximal, characteristic, complemented
4C22×#13063245C211yesmaximal, characteristic, complemented
5#19137520C211yesmaximal, characteristic, complemented
6#19135524C211yesmaximal, characteristic, complemented
7#19135403C211yesmaximal, characteristic, complemented
8#19135022C211yesmaximal, characteristic, complemented
9#19135019C211yesmaximal, characteristic, complemented
10#19134916C211yesmaximal, characteristic, complemented
11#19134604C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic, complemented
13#19134527C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1872C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C23×D172C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic, complemented
20#14583540—24no—
21#14583540C418yescomplemented
22C2×#13063314C2211yescharacteristic
23C2×#13063310—21no—
24C2×#13063300—21no—
25C2×#13063300C2211yescharacteristic
26C2×#13063295—21no—
27C2×#13063287C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic, complemented
30C2×C22⋊C4×D43—21no—
31(C22⋊D43)⋊C8—24no—
32C2×Dic43⋊C8C2211yescharacteristic, complemented
33#14582894—24no—
34C2×#13063249C2211yescharacteristic, complemented
35C2×#13063249C2211yescharacteristic, complemented
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063245—24no—
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
46C2×C8×Dic43C2211yescharacteristic, complemented
47#14582789—21no—
48#14582780—21no—
49#14582778—21no—
50#14582764C2211yescharacteristic, complemented
51#14582759C2211yescharacteristic
52#14582756C2211yescharacteristic, complemented
53C4⋊C4×Dic43C2211yescharacteristic, complemented
54C4×C22⋊Dic43—21no—
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×C22⋊Q8×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#103×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—41no—
69C2×#10621902—41no—
70C2×#10621902C2×C414yescomplemented
71C22×D172—22no—
72C22×D172—22no—
73C22×D172—21no—
74C22×D172—21no—
75C22×D172—22no—
76C22×D172—21no—
77C22×D172—41no—
78C22×D172—41no—
79C22×D172C2×C414yes—
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43D411yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C22×C43⋊C8—22no—
87C22×C43⋊C8—22no—
88C22×C43⋊C8—41no—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—22no—
92C2×C8×D43—22no—
93C2×C8×D43—41no—
94#13063314—22no—
95#13063314C2×C414yescomplemented
96#13063310—28no—
97#13063300—22no—
98#13063300—28no—
99#13063300C2×C414yescomplemented
100#13063295—28no—
101#13063287—22no—
102#13063287C2×C414yescomplemented
103C4×C22⋊D43C2×C414yes—
104C4×C22⋊D43D414yes—
105#13063283—22no—
106#13063283—41no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4D411yescharacteristic
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
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#13063249—22no—
125#13063249—41no—
126#13063247—22no—
127#13063247—22no—
128#13063247—41no—
129#13063247—41no—
130#13063245—22no—
131#13063245—22no—
132#13063245—22no—
133#13063245D414yescomplemented
134(C2×D43)⋊C8—22no—
135C8×Dic43—22no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×Q8×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43C2×C414yes—
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43—22no—
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43—41no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C22⋊C4×C43—21no—
156#103×C43—22no—
157#103×C43—41no—
158C22⋊C8×C43—22no—
159C24×C43C2×D411yescharacteristic
160C23×D43—21no—
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×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C22×C412yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43—81no—
187C22×C4×C43C22×C412yes—
188C22×C4×C43C2×D412yes—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43C22⋊C414yes—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199#10621902—28no—
200#10621902—44no—
201#10621902—44no—
202#10621902—44no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—24no—
207C2×D172—21no—
208C2×D172—24no—
209C2×D172—24no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—28no—
215C2×D172—42no—
216C2×D172—42no—
217C2×D172—42no—
218C2×D172—42no—
219C2×D172—44no—
220C2×D172—44no—
221C2×D172—44no—
222C2×D172—81no—
223C2×D172—81no—
224C2×D172C22×C412yes—
225C2×D172C22×C412yes—
226C2×D172C2×D412yes—
227C2×D172#4112yes—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—42no—
235C2×C4×D43—42no—
236C2×C4×D43—81no—
237C2×C4×D43—81no—
238C2×C4×D43C22×C412yes—
239C2×C4×D43C2×D412yes—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C4⋊C4×C43—24no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—42no—
252C4⋊C4×C43C22×C412yes—
253C4⋊C4×C43C2×D412yes—
254C22⋊C4×C43—24no—
255C22⋊Dic43—42no—
256C22⋊Dic43C22⋊C414yes—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—42no—
262(C2×D43)⋊C4—81no—
263(C2×D43)⋊C4C22⋊C414yes—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268Dic43⋊C4C22⋊C414yes—
269C4×Dic43—42no—
270C4×Dic43—81no—
271C4×Dic43C22×C412yes—
272C4×Dic43C2×D412yes—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—44no—
279C2×C43⋊C8C2×D412yes—
280C8×D43—44no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43C2×C22⋊C412yes—
286C23×C43#13512yes—
287C23×C43#13512yes—
288C23×C43C22×D411yescharacteristic
289C22×D43—22no—
290C22×D43—21no—
291C22×D43—22no—
292C22×D43—21no—
293C22×D43—22no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—22no—
299C22×D43—48no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—48no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43C2×C22⋊C412yes—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—41no—
320Q8×C43—41no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
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×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—84no—
340C2×C4×C43C2×C22⋊C412yes—
341C2×C4×C43C23×C411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C22⋊D43—28no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43C2×C22⋊C412yes—
361C2×Dic43C2×C22⋊C412yes—
362C2×Dic43C2×C22⋊C412yes—
363D172—22no—
364D172—22no—
365D172—22no—
366D172—22no—
367D172—22no—
368D172—48no—
369D172—48no—
370D172—41no—
371D172—41no—
372D172—84no—
373D172C4×D414yes—
374C4×D43—22no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—48no—
379C4×D43—84no—
380C8×C43—41no—
381C8×C43—41no—
382C43⋊C8—22no—
383C43⋊C8—41no—
384#22414—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43#41614yescomplemented
392C22×C43C22×C22⋊C411yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43C2×#13511yescharacteristic
396C22×C43C2×#13511yescharacteristic
397C22×C43#57611yescharacteristic
398C22×C43#57711yescharacteristic
399C2×D43—24no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—41no—
406C2×D43—42no—
407C2×D43—41no—
408C2×D43—42no—
409C2×D43—41no—
410C2×D43—42no—
411C2×D43—41no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—816no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43—81no—
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—42no—
424C4×C43—42no—
425C4×C43—81no—
426C4×C43C2×C4×D411yescharacteristic
427C4×C43#51811yescharacteristic
428C4×C43D4211yescharacteristic
429C4×C43#54611yescharacteristic
430Dic43—22no—
431Dic43—22no—
432Dic43—22no—
433Dic43—81no—
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#1893—431no—
443#1892—431no—
444#1875—431no—
445#1872D4311yescharacteristic, complemented
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—24no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43C2×#41611yescharacteristic
453C2×C43#289711yescharacteristic
454C2×C43#328011yescharacteristic
455C2×C43#328211yescharacteristic
456C2×C43#329611yescharacteristic
457C2×C43#329711yescharacteristic
458D43—42no—
459D43—44no—
460D43—82no—
461C22×#41—431no—
462C23×D4—431no—
463C23×C8—431no—
464C23×C8—431no—
465#546—438no—
466#546—864no—
467C2×#124—431no—
468C2×#123—861no—
469C2×C22⋊Q8C2×D4311yescharacteristic
470C2×#121—431no—
471C2×#121—861no—
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4—431no—
475C2×#117—431no—
476C22×C4⋊C4C2×D4311yescharacteristic
477C22×C22⋊C4—861no—
478C8×D4—864no—
479C2×C4⋊C8—431no—
480#416—864no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103C2×D4311yescharacteristic, complemented
484C2×#103C2×D4311yescharacteristic, complemented
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102—431no—
493C2×#102—864no—
494C2×C22⋊C8—431no—
495C2×C22⋊C8C2×D4311yescharacteristic
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380—431no—
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×Q8C22×D4311yescharacteristic
518C22×D4—431no—
519C22×D4—434no—
520C22×D4—431no—
521C22×D4—431no—
522C22×D4—862no—
523C22×D4—862no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4—861no—
527C22×D4—862no—
528C22×D4—1721no—
529C22×D4—1721no—
530C23×C4—21no—
531C23×C4—431no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—862no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—862no—
541C22×C8—1721no—
542C22×C8—1721no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#124—434no—
546#124—862no—
547#123—868no—
548C22⋊Q8—22no—
549C22⋊Q8C4×D4314yes—
550#121—434no—
551#121—868no—
552#121—862no—
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—862no—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—868no—
574C2×C22⋊C4—861no—
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—22no—
586#103—41no—
587#103—862no—
588#103—1721no—
589#102—434no—
590#102—862no—
591#102—862no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—1721no—
596#102—1721no—
597C22⋊C8—22no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—861no—
601#95—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—431no—
606C24—861no—
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—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C2×C4×D4312yes—
626C2×D4—434no—
627C2×D4—432no—
628C2×D4—432no—
629C2×D4—432no—
630C2×D4—432no—
631C2×D4—868no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—862no—
635C2×D4—862no—
636C2×D4—864no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—3441no—
646C2×D4—3441no—
647C2×D4—1724no—
648C2×D4—1724no—
649C2×D4—1724no—
650C2×D4—1722no—
651C2×D4—1722no—
652C2×D4—1722no—
653C2×D4—1722no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—81no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—432no—
669C22×C4—432no—
670C22×C4—864no—
671C22×C4—864no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—3441no—
679C22×C4—3441no—
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—21no—
692C2×C8—432no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—1724no—
699C2×C8—1724no—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—434no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4C2×C4×D4312yes—
712C4⋊C4D4×D4312yes—
713C22⋊C4—24no—
714C22⋊C4—434no—
715C22⋊C4—434no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—3441no—
721C22⋊C4—1722no—
722C22⋊C4—1722no—
723C42—432no—
724C42—432no—
725C42—3441no—
726C42—1722no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—432no—
732C23—862no—
733C23—861no—
734C23—861no—
735C23—861no—
736C23—861no—
737C23—861no—
738C23—862no—
739C23—861no—
740C23—862no—
741C23—862no—
742C23—3444no—
743C23—3444no—
744C23—3444no—
745C23—3444no—
746C23—3444no—
747C23—1728no—
748C23—1728no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23C22⋊C4×D4312yes—
760C23#1306334612yes—
761C23#1306334812yes—
762C23C2×D4×D4311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—434no—
768D4—868no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—862no—
774D4—3444no—
775D4—1728no—
776D4—1728no—
777D4—1721no—
778D4—1721no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4—432no—
799C2×C4—432no—
800C2×C4—432no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—3444no—
812C2×C4—1728no—
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—41no—
827C8—41no—
828C8—862no—
829C8—1721no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—862no—
837C22—864no—
838C22—862no—
839C22—862no—
840C22—34416no—
841C22—3441no—
842C22—3441no—
843C22—3441no—
844C22—3441no—
845C22—1722no—
846C22—1722no—
847C22—1722no—
848C22—1721no—
849C22—1722no—
850C22—1721no—
851C22—1722no—
852C22—1722no—
853C22—1721no—
854C22—1722no—
855C22—1721no—
856C22—1722no—
857C22—1722no—
858C22#1458289414yescomplemented
859C22C2×C22⋊C4×D4311yescharacteristic
860C22#1458353111yescharacteristic
861C22#1458354111yescharacteristic
862C22C2×#1306334611yescharacteristic
863C22C2×#1306334811yescharacteristic
864C22#1458370311yescharacteristic
865C22#1458370811yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—862no—
872C4—862no—
873C4—862no—
874C4—3441no—
875C4—3441no—
876C4C4×D4×D4311yescharacteristic
877C4#1458337111yescharacteristic
878C4#1458353311yescharacteristic
879C4#1458353811yescharacteristic
880C2—24no—
881C2—3442no—
882C2—1722no—
883C2—1724no—
884C2#1913741311yescharacteristic
885C2C2×#1458289411yescharacteristic
886C2#1914311911yescharacteristic
887C2#1914627311yescharacteristic
888C2#1914629511yescharacteristic
889C2#1914642811yescharacteristic
890C2#1914644311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC2×#14583540C2
cosocleC22×C4×C43C24
hypercenter#1872D43
hypocenterC43#22414
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D43)⋊C8C2semidirect
3. C2×#14582894C2semidirect
4. C22×#13063245C2semidirect
5. #19137520C2semidirect
6. #19135524C2semidirect
7. #19135403C2semidirect
8. #19135022C2semidirect
9. #19135019C2semidirect
10. #19134916C2semidirect
11. #19134604C2semidirect
12. #19134534C2semidirect
13. #19134527C2semidirect
14. #19134409C2semidirect
15. C43×#1872C2semidirect
19. C22×C8×D43C22semidirect
21. #14583540C4semidirect
29. C2×#13063283C22semidirect
32. C2×Dic43⋊C8C22semidirect
34. C2×#13063249C22semidirect
35. C2×#13063249C22semidirect
45. C2×(C2×D43)⋊C8C22semidirect
46. C2×C8×Dic43C22semidirect
50. #14582764C22semidirect
52. #14582756C22semidirect
53. C4⋊C4×Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
59. C2×#103×C43C22semidirect
60. C2×#103×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
70. C2×#10621902C2×C4semidirect
95. #13063314C2×C4semidirect
99. #13063300C2×C4semidirect
102. #13063287C2×C4semidirect
133. #13063245D4semidirect
391. C22×C43#416semidirect
445. #1872D43semidirect
483. C2×#103C2×D43semidirect
484. C2×#103C2×D43semidirect
507. #340C2×D43semidirect
508. #340C2×D43semidirect
509. C43#22414semidirect
858. C22#14582894semidirect

Maximal subgroups

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

subgroupindex
C2×#145835402
C2×(C22⋊D43)⋊C82
C2×#145828942
C22×#130632452
#191375202
#191355242
#191354032
#191350222
#191350192
#191349162
#191346042
#191345342
#191345272
#191344092
C43×#18722
#2241443