Finite Group Databasebeta

← #25112078

Subgroups — #25112078

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×#14583537C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic, complemented
3C2×#102×D43C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D43C211yesmaximal, characteristic, complemented
5#19135524C211yesmaximal, characteristic, complemented
6#19135408C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135015C211yesmaximal, characteristic, complemented
9#19134912C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C2×C43×#417C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583537—24no—
19#14583537C418yescomplemented
20C2×#13063314C2211yescharacteristic
21C2×#13063308—21no—
22C2×#13063301C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063297—21no—
25C2×#13063293—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30C22×(C2×D43)⋊C4—21no—
31#14582968—24no—
32C2×Dic43⋊C8C2211yescharacteristic, complemented
33C2×#13063249C2211yescharacteristic, complemented
34C2×#13063249C2211yescharacteristic, complemented
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41#102×D43—24no—
42C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×#13063235C2211yescharacteristic, complemented
45#14582794—21no—
46#14582772—21no—
47#14582770—21no—
48#14582768C2211yescharacteristic, complemented
49#14582759C2211yescharacteristic, complemented
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C22×#41×C43C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic, complemented
58C22×C4⋊C4×C43C2211yescharacteristic, complemented
59C43×#417—24no—
60C2×#103×C43C2211yescharacteristic, complemented
61C2×#103×C43C2211yescharacteristic, complemented
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43D411yescharacteristic
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—41no—
73C2×D4×D43—41no—
74C2×D4×D43C2×C414yescomplemented
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C2×C8×D43—22no—
81C2×C8×D43—22no—
82C2×C8×D43—41no—
83#13063314—22no—
84#13063314C2×C414yescomplemented
85#13063308—28no—
86#13063301—22no—
87#13063301C2×C414yescomplemented
88#13063299—22no—
89#13063299C2×C414yescomplemented
90#13063297—28no—
91#13063293—28no—
92D4×Dic43—22no—
93D4×Dic43C2×C414yescomplemented
94C4×C22⋊D43—44no—
95C4×C22⋊D43C2×C414yes—
96C4×C22⋊D43D414yes—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4D411yescharacteristic
105C4⋊C4×D43—22no—
106C4⋊C4×D43—41no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43D411yescharacteristic
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—28no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×C4×Dic43—21no—
118C2×C4×Dic43C2311yescharacteristic
119Dic43⋊C8—22no—
120#13063249—41no—
121#13063249—41no—
122#13063247—22no—
123#13063247—41no—
124#13063246—22no—
125#13063246—22no—
126#13063245—22no—
127#13063245—41no—
128C22⋊(C43⋊C8)—22no—
129(C2×D43)⋊C8—22no—
130#13063235—22no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—22no—
137C2×#41×C43—41no—
138C2×#41×C43—41no—
139C2×#41×C43C2×C414yescomplemented
140C22×Q8×C43C2311yescharacteristic
141C22×D4×C43—21no—
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43—21no—
144C23×C4×C43—21no—
145C23×C4×C43C2311yescharacteristic
146C2×M16×C43—22no—
147C2×M16×C43—22no—
148C2×M16×C43—41no—
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C2×C4⋊C4×C43—22no—
152C2×C4⋊C4×C43—21no—
153C2×C4⋊C4×C43—41no—
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C4⋊C4×C43C2311yescharacteristic
156#103×C43—22no—
157#103×C43—22no—
158#102×C43—22no—
159#102×C43D414yescomplemented
160C24×C43—21no—
161C24×C43C2×D411yescharacteristic
162C23×D43—21no—
163C23×D43—24no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—42no—
168C23×D43—81no—
169C23×D43—81no—
170C23×D43C2×D411yescharacteristic
171#41×C43—28no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43C22×C412yes—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—24no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43C22×C412yes—
188C2×D4×C43C2×D412yes—
189C2×D4×C43#4112yes—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—24no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—42no—
199C22×C4×C43—42no—
200C22×C4×C43—42no—
201C22×C4×C43—42no—
202C22×C4×C43—81no—
203C22×C4×C43C22×C412yes—
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—22no—
210C2×C22⋊D43—22no—
211C2×C22⋊D43—42no—
212C2×C22⋊D43—42no—
213C2×C22⋊D43—81no—
214C2×C22⋊D43—81no—
215C2×C22⋊D43C22⋊C414yes—
216C22×Dic43—24no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—81no—
221C22×Dic43—81no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225D4×D43—28no—
226D4×D43—44no—
227D4×D43—44no—
228D4×D43—44no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172C22×C412yes—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—42no—
240C2×C4×D43—42no—
241C2×C4×D43—81no—
242C2×C4×D43C22×C412yes—
243C2×C4×D43C2×D412yes—
244M16×C43—44no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43C2×D412yes—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—42no—
255C4⋊C4×C43C2×D412yes—
256C22⋊Dic43—24no—
257C22⋊Dic43—42no—
258C22⋊Dic43C22⋊C414yes—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—42no—
264(C2×D43)⋊C4C22⋊C414yes—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43C22×C412yes—
271Dic43⋊C4—24no—
272Dic43⋊C4—42no—
273Dic43⋊C4—42no—
274Dic43⋊C4—81no—
275Dic43⋊C4C22⋊C414yes—
276C4×Dic43—42no—
277C4×Dic43C22×C412yes—
278C4×Dic43C2×D412yes—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C8×D43—44no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—21no—
289C23×C43—22no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43C2×C22⋊C412yes—
300C23×C43C22×D411yescharacteristic
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—22no—
306C22×D43—48no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—48no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43—84no—
317C22×D43—84no—
318C22×D43—84no—
319C22×D43C2×C22⋊C412yes—
320C22×D43AGL(1,ℤ/8)12yes—
321C22×D43#13712yes—
322Q8×C43—22no—
323Q8×C43—22no—
324Q8×C43—41no—
325Q8×C43—41no—
326D4×C43—22no—
327D4×C43—22no—
328D4×C43—22no—
329D4×C43—48no—
330D4×C43C4×D414yescomplemented
331C2×C4×C43—21no—
332C2×C4×C43—21no—
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—48no—
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—84no—
348C2×C4×C43C2×C22⋊C412yes—
349C2×C4×C43C23×C411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43H(5,𝔽2)11yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C22⋊D43—28no—
356C22⋊D43—48no—
357C22⋊D43—84no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—22no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—84no—
374C2×Dic43C2×C22⋊C412yes—
375C2×Dic43C2×C22⋊C412yes—
376C2×Dic43C2×C22⋊C412yes—
377D172—22no—
378D172—22no—
379D172—41no—
380D172—41no—
381C4×D43—22no—
382C4×D43—22no—
383C4×D43—22no—
384C4×D43—22no—
385C4×D43—84no—
386C8×C43—22no—
387C8×C43—41no—
388C43⋊C8—41no—
389C43⋊C8—41no—
390#22419—431nomaximal, Sylow
391C22×C43—24no—
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—41no—
399C22×C43—42no—
400C22×C43—41no—
401C22×C43—42no—
402C22×C43—41no—
403C22×C43—42no—
404C22×C43—41no—
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—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—816no—
422C2×D43—81no—
423C2×D43—81no—
424C2×D43—81no—
425C2×D43—81no—
426C2×D43#41714yescomplemented
427C4×C43—22no—
428C4×C43—42no—
429C4×C43—42no—
430C4×C43—81no—
431C4×C43C2×C4×D411yescharacteristic
432C4×C43#51811yescharacteristic
433C4×C43D4211yescharacteristic
434C4×C43#54611yescharacteristic
435Dic43—22no—
436Dic43—22no—
437Dic43—22no—
438Dic43—42no—
439Dic43—81no—
440Dic43—81no—
441C2×#546—431no—
442C2×#435—431no—
443C2×#417D4311yescharacteristic, complemented
444C22×#102—431no—
445D4×C4⋊C4—431no—
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—44no—
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—24no—
466D43—82no—
467C22×#41C2×D4311yescharacteristic
468C23×D4—431no—
469C22×M16C2×D4311yescharacteristic, complemented
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—431no—
480C2×C4×D4—431no—
481C2×C4×D4—861no—
482C22×C4⋊C4—431no—
483C22×C4⋊C4C2×D4311yescharacteristic, complemented
484C22×C22⋊C4—861no—
485#435—864no—
486C2×C4⋊C8—431no—
487#417—24no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103C2×D4311yescharacteristic, complemented
491C2×#103C2×D4311yescharacteristic, complemented
492C2×#102—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102—431no—
496C2×#102—431no—
497C2×#102—431no—
498C2×#102—864no—
499C2×#102C2×D4311yescharacteristic
500C2×#102C2×D4311yescharacteristic
501C2×C22⋊C8—431no—
502C2×C22⋊C8—431no—
503C2×#97—431no—
504#389—861no—
505#385—861no—
506#385—861no—
507#384—431no—
508#380—431no—
509#380—431no—
510C4×C4⋊C4—431no—
511#340—431no—
512#340—431no—
513#340—431no—
514#340—431no—
515C43#2241911yescharacteristic, complemented, Sylow
516C25—861no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C4×D4314yescomplemented
523C22×Q8C22×D4311yescharacteristic
524C22×D4—21no—
525C22×D4—431no—
526C22×D4—434no—
527C22×D4—431no—
528C22×D4—862no—
529C22×D4—861no—
530C22×D4—862no—
531C22×D4—862no—
532C22×D4—861no—
533C22×D4—1721no—
534C22×D4—1721no—
535C22×D4C22×D4311yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—431no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4C22×D4311yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—862no—
548C22×C8—862no—
549C22×C8—1721no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#124—434no—
553#124—862no—
554#123—868no—
555C22⋊Q8—434no—
556C22⋊Q8—862no—
557#121—434no—
558#121—868no—
559#121—862no—
560#120—868no—
561C4×D4—434no—
562C4×D4—434no—
563C4×D4—434no—
564C4×D4—862no—
565C4×D4—1724no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—431no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—862no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4—1721no—
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C22⋊C4—431no—
582C2×C22⋊C4—431no—
583C2×C22⋊C4—868no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C42—431no—
592C2×C42—861no—
593C4⋊C8—862no—
594#103—22no—
595#103—22no—
596#103—1721no—
597#103—1721no—
598#102—22no—
599#102—862no—
600#102—862no—
601#102—862no—
602#102—862no—
603#102—1721no—
604#102—1721no—
605#102C22⋊D4314yescomplemented
606C22⋊C8—862no—
607C22⋊C8—862no—
608#97—862no—
609#95—861no—
610#95—861no—
611#95—861no—
612C24—21no—
613C24—431no—
614C24—864no—
615C24—861no—
616C24—3441no—
617C24—3441no—
618C24—1722no—
619C24—1722no—
620C24—1722no—
621C24—1722no—
622C24D4×D4311yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×C4×D4312yes—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—434no—
640C2×D4—432no—
641C2×D4—864no—
642C2×D4—862no—
643C2×D4—862no—
644C2×D4—868no—
645C2×D4—864no—
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×D4C2×C4×D4312yes—
659C2×D4#1062189812yes—
660C2×D4C2×C22⋊D4312yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—24no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—81no—
674C22×C4—431no—
675C22×C4—431no—
676C22×C4—431no—
677C22×C4—432no—
678C22×C4—432no—
679C22×C4—864no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—3441no—
688C22×C4—3441no—
689C22×C4—3441no—
690C22×C4—1722no—
691C22×C4—1722no—
692C22×C4C2×C4×D4312yes—
693C22×C4D4×D4311yescharacteristic
694C22×C4D4×D4312yes—
695C22×C4C23×D4311yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—1724no—
709C2×C8C2×C22⋊D4312yes—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—42no—
714C4⋊C4—434no—
715C4⋊C4—432no—
716C4⋊C4—864no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—3441no—
723C4⋊C4—1722no—
724C4⋊C4—1722no—
725C4⋊C4C2×C22⋊D4312yes—
726C22⋊C4—434no—
727C22⋊C4—434no—
728C22⋊C4—864no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—1722no—
734C22⋊C4—1722no—
735C42—432no—
736C42—432no—
737C42—1722no—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—432no—
752C23—432no—
753C23—432no—
754C23—861no—
755C23—861no—
756C23—861no—
757C23—861no—
758C23—862no—
759C23—3444no—
760C23—3444no—
761C23—3444no—
762C23—3444no—
763C23—3444no—
764C23—1728no—
765C23—1728no—
766C23—1721no—
767C23—1721no—
768C23—1721no—
769C23—1721no—
770C23—1721no—
771C23—1721no—
772C23C22⋊C4×D4312yes—
773C23C2×D4×D4311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—868no—
783D4—862no—
784D4—862no—
785D4—3444no—
786D4—1728no—
787D4—1721no—
788D4—1721no—
789D4C4×C22⋊D4314yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—84no—
807C2×C4—432no—
808C2×C4—432no—
809C2×C4—432no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—861no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—3444no—
822C2×C4—3444no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4C22⋊C4×D4312yes—
832C2×C4C22×C4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C22×C22⋊D4311yescharacteristic
835C2×C4C2×#1062189811yescharacteristic
836C2×C4#1306337011yescharacteristic
837C2×C4#1306337011yescharacteristic
838C8—22no—
839C8—41no—
840C8—1721no—
841C8—1721no—
842C22—22no—
843C22—24no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—41no—
851C22—42no—
852C22—41no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—434no—
857C22—862no—
858C22—862no—
859C22—862no—
860C22—862no—
861C22—862no—
862C22—862no—
863C22—34416no—
864C22—3441no—
865C22—3441no—
866C22—3441no—
867C22—3441no—
868C22—1722no—
869C22—1722no—
870C22—1722no—
871C22C2×C22⋊C4×D4311yescharacteristic
872C22D4×C22⋊D4311yescharacteristic
873C22#1458353911yescharacteristic
874C22AGL(1,ℤ/8)×D4311yescharacteristic
875C22#137×D4311yescharacteristic
876C22#1458370311yescharacteristic
877C22#1458370811yescharacteristic
878C4—22no—
879C4—42no—
880C4—42no—
881C4—81no—
882C4—862no—
883C4—862no—
884C4—862no—
885C4—3441no—
886C4—3441no—
887C4—1722no—
888C4C2×C4×C22⋊D4311yescharacteristic
889C4#1458337211yescharacteristic
890C4D4×C22⋊D4311yescharacteristic
891C4#1458353911yescharacteristic
892C2—42no—
893C2—44no—
894C2—864no—
895C2—3442no—
896C2C22⋊C4×C22⋊D4311yescharacteristic
897C2#417×D4311yescharacteristic
898C2#1914311911yescharacteristic
899C2#1914606911yescharacteristic
900C2#1914609911yescharacteristic
901C2#1914655711yescharacteristic
902C2#1914667711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583537C2
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43#22419
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582968C2semidirect
3. C2×#102×D43C2semidirect
4. C4⋊C4×C22⋊D43C2semidirect
5. #19135524C2semidirect
6. #19135408C2semidirect
7. #19135033C2semidirect
8. #19135015C2semidirect
9. #19134912C2semidirect
10. #19134899C2semidirect
11. #19134593C2semidirect
12. #19134535C2semidirect
13. #19134524C2semidirect
14. #19134422C2semidirect
15. C2×C43×#417C2semidirect
19. #14583537C4semidirect
32. C2×Dic43⋊C8C22semidirect
33. C2×#13063249C22semidirect
34. C2×#13063249C22semidirect
42. C2×C22⋊(C43⋊C8)C22semidirect
44. C2×#13063235C22semidirect
48. #14582768C22semidirect
49. #14582759C22semidirect
51. C4⋊C4×Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
57. C22×M16×C43C22semidirect
58. C22×C4⋊C4×C43C22semidirect
60. C2×#103×C43C22semidirect
61. C2×#103×C43C22semidirect
74. C2×D4×D43C2×C4semidirect
84. #13063314C2×C4semidirect
87. #13063301C2×C4semidirect
89. #13063299C2×C4semidirect
93. D4×Dic43C2×C4semidirect
139. C2×#41×C43C2×C4semidirect
159. #102×C43D4semidirect
330. D4×C43C4×D4semidirect
426. C2×D43#417semidirect
443. C2×#417D43semidirect
469. C22×M16C2×D43semidirect
483. C22×C4⋊C4C2×D43semidirect
490. C2×#103C2×D43semidirect
491. C2×#103C2×D43semidirect
515. C43#22419semidirect
522. C2×#41C4×D43semidirect
605. #102C22⋊D43semidirect
789. D4C4×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835372
C2×#145829682
C2×#102×D432
C4⋊C4×C22⋊D432
#191355242
#191354082
#191350332
#191350152
#191349122
#191348992
#191345932
#191345352
#191345242
#191344222
C2×C43×#4172
#2241943