Finite Group Databasebeta

← #25112071

Subgroups — #25112071

Order 11008.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583545C211yesmaximal, characteristic
2C2×#14582971C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4C22×#13063245C211yesmaximal, characteristic, complemented
5#19135527C211yesmaximal, characteristic, complemented
6#19135409C211yesmaximal, characteristic, complemented
7#19135031C211yesmaximal, characteristic, complemented
8#19135016C211yesmaximal, characteristic, complemented
9#19134912C211yesmaximal, characteristic, complemented
10#19134902C211yesmaximal, characteristic, complemented
11#19134592C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134525C211yesmaximal, characteristic, complemented
14#19134423C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×D172C2211yescharacteristic
18C22×#10621877C2211yescharacteristic, complemented
19C23×C43⋊C8C2211yescharacteristic
20#14583545—24no—
21#14583545C418yescomplemented
22C2×#13063313C2211yescharacteristic
23C2×#13063310—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063299C2211yescharacteristic
26C2×#13063298—21no—
27C2×#13063293—21no—
28C2×C4×D172C2211yescharacteristic
29C2×C22⋊C4×D43—21no—
30#14582971—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
32#14582898—24no—
33C2×#13063248C2211yescharacteristic, complemented
34C2×#13063248C2211yescharacteristic, complemented
35C2×#13063248C2211yescharacteristic, complemented
36C2×#13063248C2211yescharacteristic, complemented
37C2×#13063245—24no—
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×#13063245C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
48C2×#13063236C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53C2×C4×D4×C43—21no—
54C2×C4×D4×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C22×C4⋊C4×C43C2211yescharacteristic, complemented
57C43×#389—21no—
58C43×#385—21no—
59C43×#385—21no—
60C43×#384C2211yescharacteristic, complemented
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic, complemented
63C4×C4⋊C4×C43C2211yescharacteristic, 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×D172—22no—
73C22×D172—22no—
74C22×D172—21no—
75C22×D172—22no—
76C22×D172—41no—
77C22×D172—41no—
78C22×D172C2×C414yescomplemented
79C22×D172C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C2×#10621877—22no—
86C2×#10621877—22no—
87C2×#10621877—41no—
88C22×C43⋊C8—22no—
89C22×C43⋊C8—22no—
90C22×C43⋊C8—41no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95#13063313—22no—
96#13063313C2×C414yescomplemented
97#13063310—28no—
98#13063304—22no—
99#13063304C2×C414yescomplemented
100#13063299—22no—
101#13063299C2×C414yescomplemented
102#13063298—28no—
103#13063293—28no—
104C4×D172—22no—
105C4×D172C2×C414yescomplemented
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×C22⋊Dic43—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C22⋊C4×D43—28no—
114C4⋊(C43⋊C8)—22no—
115#13063248—22no—
116#13063248—22no—
117#13063248—41no—
118#13063248—41no—
119#13063245—22no—
120#13063245—22no—
121#13063245—22no—
122#13063245—22no—
123#13063245—22no—
124#13063245—41no—
125#13063245—41no—
126#13063245D414yescomplemented
127C22⋊(C43⋊C8)—22no—
128C22⋊(C43⋊C8)—22no—
129#13063236—22no—
130C22×D4×C43D411yescharacteristic
131C23×C4×C43—21no—
132C23×C4×C43—21no—
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C4×D4×C43—44no—
136C4×D4×C43C2×C414yes—
137C4×D4×C43D414yes—
138C2×C4⋊C4×C43—22no—
139C2×C4⋊C4×C43—22no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43—41no—
145C2×C4⋊C4×C43—41no—
146C2×C4⋊C4×C43D411yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C22⋊C4×C43—21no—
152C2×C22⋊C4×C43—21no—
153C2×C22⋊C4×C43D411yescharacteristic
154C2×C22⋊C4×C43D411yescharacteristic
155C2×C42×C43—21no—
156C2×C42×C43C2311yescharacteristic
157#95×C43—21no—
158#95×C43—21no—
159#95×C43—21no—
160C24×C43C2×D411yescharacteristic
161C24×C43C2×D411yescharacteristic
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—24no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—42no—
168C23×D43—42no—
169C23×D43—81no—
170C23×D43—81no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43C22⋊C414yes—
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—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—42no—
189C22×C4×C43—42no—
190C22×C4×C43—81no—
191C22×C4×C43—81no—
192C22×C4×C43C22×C412yes—
193C22×C4×C43C22×C412yes—
194C22×C4×C43C2×D412yes—
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—42no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43—81no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209#10621898—28no—
210#10621898—44no—
211#10621898—44no—
212#10621898—44no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—24no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—28no—
223C2×D172—42no—
224C2×D172—42no—
225C2×D172—44no—
226C2×D172—44no—
227C2×D172—44no—
228C2×D172C22×C412yes—
229C2×D172C22×C412yes—
230C2×D172C2×D412yes—
231C2×D172#4112yes—
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×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86C22×C412yes—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—42no—
252C4⋊C4×C43—42no—
253C4⋊C4×C43—42no—
254C4⋊C4×C43—81no—
255C4⋊C4×C43C22⋊C414yes—
256C4⋊C4×C43C2×D412yes—
257C22⋊C4×C43—42no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43C22⋊C414yes—
260C22⋊C4×C43C22⋊C414yes—
261C42×C43—42no—
262C42×C43C22×C412yes—
263C42×C43C2×D412yes—
264C22⋊Dic43—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269C4⋊Dic43—21no—
270C4⋊Dic43C22×C412yes—
271Dic43⋊C4—24no—
272#10621877—44no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—44no—
285C2×C43⋊C8C2×D412yes—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43C2×C22⋊C412yes—
297C23×C43C2×C22⋊C412yes—
298C23×C43AGL(1,ℤ/8)12yes—
299C23×C43#13712yes—
300C23×C43C22×D411yescharacteristic
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—48no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43—41no—
316C22×D43—48no—
317C22×D43—84no—
318C22×D43—84no—
319C22×D43—84no—
320C22×D43—84no—
321C22×D43—84no—
322D4×C43—28no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—84no—
352C2×C4×C43—84no—
353C2×C4×C43C2×C22⋊C412yes—
354C2×C4×C43C2×C22⋊C412yes—
355C2×C4×C43C2×C22⋊C412yes—
356C2×C4×C43C2×C22⋊C412yes—
357C2×C4×C43C23×C411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C2×#4111yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C2×C4×C43H(5,𝔽2)11yescharacteristic
363C22⋊D43—48no—
364C22⋊D43—84no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371D172—22no—
372D172—22no—
373D172—22no—
374D172—22no—
375D172—22no—
376D172—48no—
377D172—41no—
378D172—41no—
379D172C4×D414yescomplemented
380C4×D43—48no—
381C4×D43—84no—
382Dic86—22no—
383Dic86—22no—
384Dic86—41no—
385Dic86—41no—
386C43⋊C8—22no—
387C43⋊C8—41no—
388C43⋊C8—41no—
389C43⋊C8—41no—
390#22419—431nomaximal, Sylow
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43#41714yescomplemented
405C22×C43C22×C22⋊C411yescharacteristic
406C22×C43D4211yescharacteristic
407C22×C43#54611yescharacteristic
408C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C43C2×#13711yescharacteristic
410C22×C43#57611yescharacteristic
411C22×C43#57711yescharacteristic
412C2×D43—24no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—816no—
423C2×D43—81no—
424C2×D43—81no—
425C2×D43—81no—
426C2×D43—81no—
427C4×C43—22no—
428C4×C43—22no—
429C4×C43—22no—
430C4×C43—22no—
431C4×C43—42no—
432C4×C43—81no—
433C4×C43—81no—
434C4×C43—81no—
435C4×C43C2×C4×D411yescharacteristic
436C4×C43#51811yescharacteristic
437C4×C43D4211yescharacteristic
438C4×C43#54611yescharacteristic
439Dic43—42no—
440Dic43—42no—
441C2×#546—431no—
442C2×#435—431no—
443C2×#417—431no—
444C22×#102—431no—
445D4×C4⋊C4D4311yescharacteristic, complemented
446#1983—431no—
447#1959—431no—
448#1895—431no—
449#1892—431no—
450#1874—431no—
451#1872—431no—
452#1802—431no—
453#1788—431no—
454#1786—431no—
455#1762—431no—
456C2×C43—24no—
457C2×C43—42no—
458C2×C43D4×C22⋊C411yescharacteristic
459C2×C43C2×#41711yescharacteristic
460C2×C43#289711yescharacteristic
461C2×C43#326411yescharacteristic
462C2×C43#326611yescharacteristic
463C2×C43#330611yescharacteristic
464C2×C43#331411yescharacteristic
465D43—44no—
466D43—82no—
467C22×#41—431no—
468C23×D4—431no—
469C22×M16—431no—
470C23×C8—431no—
471#546—438no—
472#546—864no—
473C2×#124—431no—
474C2×#123—861no—
475C2×C22⋊Q8—431no—
476C2×#121—431no—
477C2×#121—861no—
478C2×#120—861no—
479C2×C4×D4—21no—
480C2×C4×D4—431no—
481C2×C4×D4C2×D4311yescharacteristic
482C22×C4⋊C4C2×D4311yescharacteristic
483C22×C4⋊C4C2×D4311yescharacteristic, complemented
484C22×C22⋊C4—861no—
485#435—864no—
486C2×C4⋊C8—431no—
487#417—864no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103—431no—
491C2×#103—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102—431no—
496C2×#102—431no—
497C2×#102—431no—
498C2×#102—431no—
499C2×#102—431no—
500C2×#102—864no—
501C2×C22⋊C8—431no—
502C2×C22⋊C8—431no—
503C2×#97—431no—
504#389—21no—
505#385—21no—
506#385—21no—
507#384C2×D4311yescharacteristic, complemented
508#380C2×D4311yescharacteristic
509#380C2×D4311yescharacteristic, complemented
510C4×C4⋊C4C2×D4311yescharacteristic, complemented
511#340—431no—
512#340—431no—
513#340—431no—
514#340—431no—
515C43#2241911yescharacteristic, complemented, Sylow
516C25—861no—
517C2×#41—434no—
518C2×#41—862no—
519C2×#41—862no—
520C2×#41—862no—
521C2×#41—1721no—
522C2×#41—1721no—
523C22×Q8—431no—
524C22×D4—434no—
525C22×D4—431no—
526C22×D4—431no—
527C22×D4—862no—
528C22×D4—862no—
529C22×D4—861no—
530C22×D4—861no—
531C22×D4—862no—
532C22×D4—861no—
533C22×D4—1721no—
534C22×D4—1721no—
535C22×D4C22⋊D4311yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4C22×D4311yescharacteristic
541C23×C4C22×D4311yescharacteristic
542C2×M16—862no—
543C2×M16—862no—
544C2×M16—1721no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—431no—
548C22×C8—431no—
549C22×C8—862no—
550C22×C8—862no—
551C22×C8—1721no—
552#124—434no—
553#124—862no—
554#123—868no—
555C22⋊Q8—434no—
556C22⋊Q8—862no—
557#121—434no—
558#121—862no—
559#121—868no—
560#120—868no—
561C4×D4—44no—
562C4×D4—434no—
563C4×D4—862no—
564C4×D4C4×D4314yes—
565C4×D4D17214yes—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4C22⋊D4311yescharacteristic
577C2×C4⋊C4C22×D4311yescharacteristic
578C2×C4⋊C4C22×D4311yescharacteristic
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—868no—
589C2×C22⋊C4C22⋊D4311yescharacteristic
590C2×C22⋊C4C22⋊D4311yescharacteristic
591C2×C42—21no—
592C2×C42C22×D4311yescharacteristic
593C4⋊C8—862no—
594#103—862no—
595#103—862no—
596#103—1721no—
597#103—1721no—
598#102—434no—
599#102—862no—
600#102—862no—
601#102—862no—
602#102—862no—
603#102—862no—
604#102—1721no—
605#102—1721no—
606C22⋊C8—862no—
607C22⋊C8—862no—
608#97—862no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—861no—
613C24—864no—
614C24—861no—
615C24—3441no—
616C24—3441no—
617C24—1722no—
618C24—1722no—
619C24—1722no—
620C24—1722no—
621C24C2×C22⋊D4311yescharacteristic
622C24C2×C22⋊D4311yescharacteristic
623#41—868no—
624#41—1724no—
625#41—1724no—
626#41—1724no—
627C2×Q8—432no—
628C2×Q8—861no—
629C2×Q8—861no—
630C2×Q8—861no—
631C2×Q8—861no—
632C2×Q8—861no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—432no—
636C2×D4—432no—
637C2×D4—432no—
638C2×D4—432no—
639C2×D4—868no—
640C2×D4—864no—
641C2×D4—864no—
642C2×D4—864no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4—3441no—
652C2×D4—3441no—
653C2×D4—1724no—
654C2×D4—1724no—
655C2×D4—1724no—
656C2×D4—1722no—
657C2×D4—1722no—
658C2×D4—1722no—
659C2×D4—1722no—
660C2×D4(C2×D43)⋊C414yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—81no—
678C22×C4—81no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—864no—
682C22×C4—864no—
683C22×C4—3441no—
684C22×C4—3441no—
685C22×C4—1722no—
686C22×C4—1722no—
687C22×C4C2×C4×D4312yes—
688C22×C4C2×C4×D4312yes—
689C22×C4C2×D17212yes—
690C22×C4C2×D17212yes—
691C22×C4C2×C22⋊D4311yescharacteristic
692C22×C4C2×C22⋊D4311yescharacteristic
693C22×C4C2×C22⋊D4311yescharacteristic
694C22×C4C2×C22⋊D4311yescharacteristic
695C22×C4C23×D4311yescharacteristic
696M16—1724no—
697C2×C8—432no—
698C2×C8—861no—
699C2×C8—861no—
700C2×C8—861no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—1724no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—42no—
720C4⋊C4—81no—
721C4⋊C4—432no—
722C4⋊C4—864no—
723C4⋊C4—861no—
724C4⋊C4(C2×D43)⋊C414yes—
725C4⋊C4D4×D4312yes—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—864no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4(C2×D43)⋊C414yes—
734C22⋊C4(C2×D43)⋊C414yes—
735C42—42no—
736C42C2×C4×D4312yes—
737C42C2×D17212yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—862no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—3444no—
753C23—3444no—
754C23—3444no—
755C23—3444no—
756C23—3444no—
757C23—1728no—
758C23—1728no—
759C23—1721no—
760C23—1721no—
761C23—1721no—
762C23—1721no—
763C23—1721no—
764C23—1721no—
765C23—1721no—
766C23—1721no—
767C23—1721no—
768C23—1721no—
769C23C2×(C2×D43)⋊C412yes—
770C23C2×(C2×D43)⋊C412yes—
771C23#1306335112yes—
772C23#1306335612yes—
773C23C22×C22⋊D4311yescharacteristic
774Q8—862no—
775Q8—862no—
776Q8—1721no—
777Q8—1721no—
778D4—28no—
779D4—434no—
780D4—862no—
781D4—862no—
782D4—862no—
783D4—862no—
784D4—862no—
785D4—3444no—
786D4—1728no—
787D4—1728no—
788D4—1721no—
789D4—1721no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—3444no—
823C2×C4—1728no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4C2×(C2×D43)⋊C412yes—
829C2×C4C2×(C2×D43)⋊C412yes—
830C2×C4C2×(C2×D43)⋊C412yes—
831C2×C4C2×(C2×D43)⋊C412yes—
832C2×C4C22×C4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C22×D17211yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4#1306337011yescharacteristic
837C2×C4#1306337111yescharacteristic
838C8—862no—
839C8—1721no—
840C8—1721no—
841C8—1721no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—864no—
856C22—34416no—
857C22—3441no—
858C22—3441no—
859C22—3441no—
860C22—3441no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1722no—
865C22—1722no—
866C22—1722no—
867C22—1722no—
868C22—1722no—
869C22—1722no—
870C22#1458289814yescomplemented
871C22C22×(C2×D43)⋊C411yescharacteristic
872C22D4×C22⋊D4311yescharacteristic
873C22#1458353711yescharacteristic
874C22C2×#1306335111yescharacteristic
875C22C2×#1306335611yescharacteristic
876C22#1458370211yescharacteristic
877C22#1458370711yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—1722no—
887C4—1722no—
888C4C4×D4×D4311yescharacteristic
889C4#1458337111yescharacteristic
890C4D4×D17211yescharacteristic
891C4#1458354411yescharacteristic
892C2—24no—
893C2—42no—
894C2—3442no—
895C2—1724no—
896C2D4×(C2×D43)⋊C411yescharacteristic
897C2C2×#1458289811yescharacteristic
898C2#1914311811yescharacteristic
899C2#1914607111yescharacteristic
900C2#1914610611yescharacteristic
901C2#1914655011yescharacteristic
902C2#1914667011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×C4⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583545C2
cosocleC22×C4×C43C24
hypercenterD4×C4⋊C4D43
hypocenterC43#22419
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14582971C2semidirect
3. C2×#14582898C2semidirect
4. C22×#13063245C2semidirect
5. #19135527C2semidirect
6. #19135409C2semidirect
7. #19135031C2semidirect
8. #19135016C2semidirect
9. #19134912C2semidirect
10. #19134902C2semidirect
11. #19134592C2semidirect
12. #19134533C2semidirect
13. #19134525C2semidirect
14. #19134423C2semidirect
15. D4×C4⋊C4×C43C2semidirect
18. C22×#10621877C22semidirect
21. #14583545C4semidirect
31. C2×C4⋊(C43⋊C8)C22semidirect
33. C2×#13063248C22semidirect
34. C2×#13063248C22semidirect
35. C2×#13063248C22semidirect
36. C2×#13063248C22semidirect
47. C2×C22⋊(C43⋊C8)C22semidirect
48. C2×#13063236C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
56. C22×C4⋊C4×C43C22semidirect
60. C43×#384C22semidirect
62. C43×#380C22semidirect
63. C4×C4⋊C4×C43C22semidirect
70. C2×#10621898C2×C4semidirect
78. C22×D172C2×C4semidirect
96. #13063313C2×C4semidirect
99. #13063304C2×C4semidirect
101. #13063299C2×C4semidirect
105. C4×D172C2×C4semidirect
126. #13063245D4semidirect
379. D172C4×D4semidirect
404. C22×C43#417semidirect
445. D4×C4⋊C4D43semidirect
483. C22×C4⋊C4C2×D43semidirect
507. #384C2×D43semidirect
509. #380C2×D43semidirect
510. C4×C4⋊C4C2×D43semidirect
515. C43#22419semidirect
870. C22#14582898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835452
C2×#145829712
C2×#145828982
C22×#130632452
#191355272
#191354092
#191350312
#191350162
#191349122
#191349022
#191345922
#191345332
#191345252
#191344232
D4×C4⋊C4×C432
#2241943