Finite Group Databasebeta

← #25102312

Subgroups — #25102312

Order 11008.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583373C211yesmaximal, characteristic, complemented
2C2×#14583032C211yesmaximal, characteristic
3C2×#14583009C211yesmaximal, characteristic, complemented
4C2×C4×#10621882C211yesmaximal, characteristic, complemented
5#19134946C211yesmaximal, characteristic, complemented
6#19134946C211yesmaximal, characteristic, complemented
7#19134918C211yesmaximal, characteristic, complemented
8#19134855C211yesmaximal, characteristic, complemented
9#19134841C211yesmaximal, characteristic, complemented
10#19134792C211yesmaximal, characteristic, complemented
11#19134525C211yesmaximal, characteristic, complemented
12#19134423C211yesmaximal, characteristic, complemented
13C4×#13063245C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C43×#2324C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19#14583373—24no—
20#14583373—24no—
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×#13063287—21no—
26C2×#13063287—21no—
27C2×#13063284C2211yescharacteristic
28C2×C22⋊C4×D43—21no—
29C2×C22⋊C4×D43—21no—
30#14583032C418yescomplemented
31#14583009—24no—
32C4×#10621882—24no—
33C2×#13063258C2211yescharacteristic, complemented
34C2×#13063256C2211yescharacteristic, complemented
35C2×#13063246C2211yescharacteristic, complemented
36C2×#13063246C2211yescharacteristic, complemented
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×#13063236C2211yescharacteristic, complemented
46C2×C4×C43⋊C8C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53C2×#121×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic, complemented
55C2×#117×C43C2211yescharacteristic
56C43×#390—21no—
57C43×#390C2211yescharacteristic, complemented
58C43×#389C2211yescharacteristic, complemented
59C43×#388—21no—
60C43×#386—21no—
61C43×#385—21no—
62C43×#380C2211yescharacteristic
63C4×C4⋊C4×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172—21no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—22no—
69C22×D172—22no—
70C22×D172—22no—
71C22×D172C2×C414yescomplemented
72C22×D172C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C2×#10621882—22no—
79C2×#10621882—22no—
80C2×#10621882—22no—
81C2×#10621882—22no—
82C2×#10621882C2×C414yescomplemented
83C2×#10621882C2×C414yescomplemented
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C4×D172—22no—
89C4×D172—22no—
90C4×D172—22no—
91C4×D172—22no—
92C4×D172—22no—
93C4×D172—22no—
94C4×D172D414yescomplemented
95C4×D172D414yescomplemented
96#13063287—28no—
97#13063287—28no—
98#13063284—22no—
99#13063284—22no—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C22⋊C4×D43—28no—
108C22⋊C4×D43—28no—
109C2×C4×Dic43—21no—
110#13063258—22no—
111#13063256—22no—
112#13063246—22no—
113#13063246—22no—
114#13063245—22no—
115#13063245—22no—
116#13063245—22no—
117#13063245—22no—
118#13063245C2×C414yescomplemented
119#13063245C2×C414yescomplemented
120C22⋊(C43⋊C8)—22no—
121C22⋊(C43⋊C8)C2×C414yescomplemented
122#13063236—22no—
123C4×C43⋊C8—22no—
124C22×D4×C43—21no—
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C23×C4×C43C2311yescharacteristic
128#121×C43—22no—
129#121×C43C2×C414yescomplemented
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132#117×C43—22no—
133#117×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155C23×D43—21no—
156C23×D43—21no—
157C23×D43—24no—
158C23×D43—24no—
159C23×D43—24no—
160C23×D43—81no—
161C23×D43—81no—
162C23×D43—81no—
163C23×D43—81no—
164C2×D4×C43—21no—
165C2×D4×C43—24no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
172C2×D4×C43C22×C412yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—42no—
181C22×C4×C43—81no—
182C22×C4×C43—81no—
183C22×C4×C43C22×C412yes—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43#4112yes—
190C22×C4×C43C2411yescharacteristic
191C22×Dic43—21no—
192C22×Dic43—21no—
193C2×D172—24no—
194C2×D172—24no—
195C2×D172—28no—
196C2×D172—28no—
197C2×D172—24no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—28no—
205C2×D172—28no—
206C2×D172C22×C412yes—
207C2×D172C22×C412yes—
208C2×D172C2×D412yes—
209C2×D172C2×D412yes—
210C2×D172#4112yes—
211C2×D172#4112yes—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—81no—
217C2×C4×D43—81no—
218C2×C4×D43—81no—
219C2×C4×D43—81no—
220C2×C4×D43—81no—
221C2×C4×D43—81no—
222C2×C4×D43—81no—
223C2×C4×D43—81no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—22no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—81no—
232C4⋊C4×C43C22×C412yes—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—22no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—81no—
238C22⋊C4×C43—81no—
239C22⋊C4×C43—81no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—81no—
243C42×C43C2×D412yes—
244C42×C43C2×D412yes—
245C22⋊Dic43—24no—
246#10621882—28no—
247#10621882—28no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43C2×D412yes—
255C4⋊Dic43C2×D412yes—
256C4×Dic43—24no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8C22×C412yes—
268C2×C43⋊C8C22×C412yes—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—22no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43C4×D412yes—
283C23×C43C22×D411yescharacteristic
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—216no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—84no—
300C22×D43—84no—
301C22×D43—84no—
302C22×D43—84no—
303C22×D43—84no—
304C22×D43—84no—
305D4×C43—22no—
306D4×C43—22no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—84no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
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—84no—
336C2×C4×C43C4×D412yes—
337C2×C4×C43#12012yes—
338C2×C4×C43#12012yes—
339C2×C4×C43C23×C411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351D172—216no—
352D172—22no—
353D172—22no—
354D172—22no—
355D172—22no—
356D172—22no—
357D172—22no—
358D172C4×D414yes—
359D172C4×D414yes—
360C4×D43—84no—
361C4×D43—84no—
362C4×D43—84no—
363C4×D43—84no—
364C43⋊C8—22no—
365C43⋊C8—22no—
366C43⋊C8—41no—
367C43⋊C8—41no—
368#21458—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43C2×C4×D411yescharacteristic
384C22×C43C2×#12011yescharacteristic
385C22×C43#52511yescharacteristic
386C22×C43#57611yescharacteristic
387C22×C43#57611yescharacteristic
388C22×C43#57611yescharacteristic
389C22×C43#57711yescharacteristic
390C2×D43—24no—
391C2×D43—24no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—42no—
404C2×D43—816no—
405C4×C43—22no—
406C4×C43—22no—
407C4×C43—22no—
408C4×C43—42no—
409C4×C43—41no—
410C4×C43—41no—
411C4×C43—81no—
412C4×C43—81no—
413C4×C43C2×C4×D411yescharacteristic
414C4×C43C2×C4×D411yescharacteristic
415C4×C43#52511yescharacteristic
416C4×C43#52511yescharacteristic
417Dic43—42no—
418Dic43—42no—
419C2×#518—431no—
420C2×#447—431no—
421C2×#442—431no—
422C2×C4×D8—431no—
423#2324D4311yescharacteristic, complemented
424#1879—431no—
425#1879—431no—
426#1875—431no—
427#1864—431no—
428#1862—431no—
429#1854—431no—
430#1786—431no—
431#1762—431no—
432C4×#102—431no—
433#1750—431no—
434C2×C43—42no—
435C2×C43—82no—
436C2×C43C4×#12011yescharacteristic
437C2×C43#294611yescharacteristic
438C2×C43#294811yescharacteristic
439C2×C43#300811yescharacteristic
440C2×C43#301211yescharacteristic
441C2×C43#311811yescharacteristic
442C2×C43#312211yescharacteristic
443D43—44no—
444D43—44no—
445C23×D4—431no—
446C22×D8—431no—
447C22×D8—431no—
448C2×#121C2×D4311yescharacteristic
449#518—864no—
450#518—864no—
451C2×C4×D4—431no—
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C2×C4×D4—431no—
455C2×C4×D4—861no—
456C2×C4×D4—861no—
457C2×C4×D4C2×D4311yescharacteristic, complemented
458C2×#117—431no—
459C2×#117C2×D4311yescharacteristic
460C22×C22⋊C4—861no—
461C22×C22⋊C4—861no—
462#447—438no—
463#442—864no—
464C4×D8—864no—
465C2×#107—431no—
466C2×#106—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102—431no—
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×C22⋊C8—431no—
476C2×C22⋊C8—431no—
477C2×#97—431no—
478C2×C4×C8—431no—
479#390—21no—
480#390C2×D4311yescharacteristic, complemented
481#389C2×D4311yescharacteristic, complemented
482#388—21no—
483#386—21no—
484#385—21no—
485#380C2×D4311yescharacteristic
486C4×C4⋊C4C2×D4311yescharacteristic, complemented
487#340—431no—
488#340—431no—
489#340—431no—
490#340—431no—
491#336—431no—
492#336—431no—
493C43#2145811yescharacteristic, complemented, Sylow
494C25—861no—
495C22×D4—21no—
496C22×D4—434no—
497C22×D4—431no—
498C22×D4—431no—
499C22×D4—862no—
500C22×D4—862no—
501C22×D4—862no—
502C22×D4—862no—
503C22×D4—862no—
504C22×D4—861no—
505C22×D4C22×D4311yescharacteristic
506C23×C4—21no—
507C23×C4—861no—
508C23×C4—861no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4C22×D4311yescharacteristic
512C2×D8—434no—
513C2×D8—434no—
514C2×D8—862no—
515C2×D8—862no—
516C2×D8—862no—
517C2×D8—862no—
518C22×C8—431no—
519C22×C8—431no—
520C22×C8—431no—
521C22×C8—431no—
522#121—22no—
523#121C4×D4314yescomplemented
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—434no—
527C4×D4—434no—
528C4×D4—862no—
529C4×D4—862no—
530C4×D4—862no—
531C4×D4—862no—
532C4×D4—868no—
533C4×D4—868no—
534C4×D4—862no—
535C4×D4—862no—
536#117—22no—
537#117—22no—
538#117—862no—
539#117—862no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4C22⋊D4311yescharacteristic
544C2×C4⋊C4C22⋊D4311yescharacteristic
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—868no—
554C2×C22⋊C4—868no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4C22⋊D4311yescharacteristic
561C2×C22⋊C4C22⋊D4311yescharacteristic
562C2×C42—21no—
563C2×C42—861no—
564C2×C42C22×D4311yescharacteristic
565C2×C42C22×D4311yescharacteristic
566#107—862no—
567#106—862no—
568#102—434no—
569#102—434no—
570#102—862no—
571#102—862no—
572#102—862no—
573#102—862no—
574#102—862no—
575#102—862no—
576C22⋊C8—434no—
577C22⋊C8—862no—
578#97—862no—
579C4×C8—862no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—864no—
585C24—864no—
586C24—864no—
587C24—861no—
588C24—861no—
589C24—3441no—
590C24—3441no—
591C24—3441no—
592C24—3441no—
593C24C2×C22⋊D4311yescharacteristic
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—432no—
603C2×D4—432no—
604C2×D4—432no—
605C2×D4—432no—
606C2×D4—432no—
607C2×D4—432no—
608C2×D4—868no—
609C2×D4—868no—
610C2×D4—864no—
611C2×D4—864no—
612C2×D4—868no—
613C2×D4—868no—
614C2×D4—864no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—861no—
621C2×D4C2×C4×D4312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—42no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4—864no—
633C22×C4—864no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—864no—
637C22×C4—864no—
638C22×C4—3441no—
639C22×C4—3441no—
640C22×C4—3441no—
641C22×C4—3441no—
642C22×C4—3441no—
643C22×C4—3441no—
644C22×C4—3441no—
645C22×C4—3441no—
646C22×C4C2×C4×D4312yes—
647C22×C4#1062189812yes—
648C22×C4C2×C22⋊D4311yescharacteristic
649C22×C4C2×C22⋊D4311yescharacteristic
650C22×C4C2×C22⋊D4311yescharacteristic
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C23×D4311yescharacteristic
654D8—868no—
655D8—868no—
656C2×C8—432no—
657C2×C8—432no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—81no—
676C4⋊C4—432no—
677C4⋊C4—432no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4C2×C4×D4312yes—
681C22⋊C4—24no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—864no—
697C42D4×D4312yes—
698C42D4×D4312yes—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—8616no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—862no—
719C23—3444no—
720C23—3444no—
721C23—3444no—
722C23—3444no—
723C23—3444no—
724C23—3444no—
725C23—1721no—
726C23—1721no—
727C23—1721no—
728C23—1721no—
729C23—1721no—
730C23—1721no—
731C23—1721no—
732C23—1721no—
733C23C4×C22⋊D4312yes—
734C23C22×C22⋊D4311yescharacteristic
735D4—22no—
736D4—22no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—434no—
741D4—434no—
742D4—8616no—
743D4—862no—
744D4—862no—
745D4—862no—
746D4—862no—
747D4—862no—
748D4—862no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—3444no—
778C2×C4—3444no—
779C2×C4—3444no—
780C2×C4—3444no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4C4×C22⋊D4312yes—
786C2×C4#1306329312yes—
787C2×C4#1306329312yes—
788C2×C4C22×C4×D4311yescharacteristic
789C2×C4C2×D4×D4311yescharacteristic
790C2×C4C2×D4×D4311yescharacteristic
791C2×C4#41×D4311yescharacteristic
792C2×C4#41×D4311yescharacteristic
793C2×C4C2×#1062189811yescharacteristic
794C8—862no—
795C8—862no—
796C8—1721no—
797C8—1721no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—864no—
813C22—864no—
814C22—34416no—
815C22—1722no—
816C22—1722no—
817C22—1722no—
818C22—1722no—
819C22—1722no—
820C22—1722no—
821C22—1722no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22—1722no—
826C22—1722no—
827C22C2×C4×C22⋊D4311yescharacteristic
828C22C2×#1306329311yescharacteristic
829C22#1458340611yescharacteristic
830C22#1458370211yescharacteristic
831C22#1458370211yescharacteristic
832C22#1458370211yescharacteristic
833C22#1458370711yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—42no—
838C4—41no—
839C4—41no—
840C4—81no—
841C4—81no—
842C4—1722no—
843C4—1722no—
844C4C4×D4×D4311yescharacteristic
845C4C4×D4×D4311yescharacteristic
846C4#1458340811yescharacteristic
847C4#1458340811yescharacteristic
848C2—42no—
849C2—82no—
850C2—1724no—
851C2—1724no—
852C2C4×#1306329311yescharacteristic
853C2#1914342311yescharacteristic
854C2#1914344511yescharacteristic
855C2#1914386111yescharacteristic
856C2#1914389611yescharacteristic
857C2#1914477311yescharacteristic
858C2#1914483311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2324C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
cosocleC22×C4×C43C24
hypercenter#2324D43
hypocenterC43#21458
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#14583373C2semidirect
3. C2×#14583009C2semidirect
4. C2×C4×#10621882C2semidirect
5. #19134946C2semidirect
6. #19134946C2semidirect
7. #19134918C2semidirect
8. #19134855C2semidirect
9. #19134841C2semidirect
10. #19134792C2semidirect
11. #19134525C2semidirect
12. #19134423C2semidirect
13. C4×#13063245C2semidirect
14. #19134361C2semidirect
15. C43×#2324C2semidirect
30. #14583032C4semidirect
33. C2×#13063258C22semidirect
34. C2×#13063256C22semidirect
35. C2×#13063246C22semidirect
36. C2×#13063246C22semidirect
45. C2×#13063236C22semidirect
46. C2×C4×C43⋊C8C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582654C22semidirect
52. #14582654C22semidirect
54. C2×C4×D4×C43C22semidirect
57. C43×#390C22semidirect
58. C43×#389C22semidirect
63. C4×C4⋊C4×C43C22semidirect
71. C22×D172C2×C4semidirect
82. C2×#10621882C2×C4semidirect
83. C2×#10621882C2×C4semidirect
94. C4×D172D4semidirect
95. C4×D172D4semidirect
118. #13063245C2×C4semidirect
119. #13063245C2×C4semidirect
121. C22⋊(C43⋊C8)C2×C4semidirect
129. #121×C43C2×C4semidirect
423. #2324D43semidirect
457. C2×C4×D4C2×D43semidirect
480. #390C2×D43semidirect
481. #389C2×D43semidirect
486. C4×C4⋊C4C2×D43semidirect
493. C43#21458semidirect
523. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833732
C2×#145830322
C2×#145830092
C2×C4×#106218822
#191349462
#191349182
#191348552
#191348412
#191347922
#191345252
#191344232
C4×#130632452
#191343612
C43×#23242
#2145843