Finite Group Databasebeta

← #25112070

Subgroups — #25112070

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×#14582973C211yesmaximal, characteristic, complemented
3C2×#14582900C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137491C211yesmaximal, characteristic, complemented
6#19135524C211yesmaximal, characteristic, complemented
7#19135408C211yesmaximal, characteristic, complemented
8#19135031C211yesmaximal, characteristic, complemented
9#19135015C211yesmaximal, characteristic, complemented
10#19134910C211yesmaximal, characteristic, complemented
11#19134899C211yesmaximal, characteristic, complemented
12#19134593C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621877C2211yescharacteristic, complemented
18C22×C8×D43C2211yescharacteristic
19#14583537—24no—
20#14583537C418yescomplemented
21C2×#13063314C2211yescharacteristic
22C2×#13063308—21no—
23C2×#13063301C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25C2×#13063297—21no—
26C2×#13063293—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×(C22⋊D43)⋊C4—21no—
30C22×C4⋊Dic43C2211yescharacteristic, complemented
31C2×C4⋊C4×D43C2211yescharacteristic
32C22×(C2×D43)⋊C4—21no—
33#14582973—24no—
34C2×Dic43⋊C8C2211yescharacteristic, complemented
35#14582900—24no—
36C2×#13063249C2211yescharacteristic, complemented
37C2×#13063249C2211yescharacteristic, complemented
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44#102×D43—24no—
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×#13063235C2211yescharacteristic, complemented
47#14582796—21no—
48#14582773—21no—
49#14582771—21no—
50#14582768C2211yescharacteristic, complemented
51#14582756C2211yescharacteristic
52C4⋊C4×Dic43C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C22×#41×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic, complemented
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C43×#380C2211yescharacteristic, complemented
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—
76C23×Dic43—21no—
77C22×C4×D43—21no—
78C22×C4×D43C2311yescharacteristic
79C2×#10621877—22no—
80C2×#10621877—22no—
81C2×#10621877—41no—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C2×C8×D43—22no—
85C2×C8×D43—22no—
86C2×C8×D43—41no—
87#13063314—22no—
88#13063314C2×C414yescomplemented
89#13063308—28no—
90#13063301—22no—
91#13063301C2×C414yescomplemented
92#13063299—22no—
93#13063299C2×C414yescomplemented
94#13063297—28no—
95#13063293—28no—
96D4×Dic43—22no—
97D4×Dic43C2×C414yescomplemented
98C4×C22⋊D43C2×C414yes—
99C4×C22⋊D43D414yes—
100(C22⋊D43)⋊C4—44no—
101C2×C4⋊Dic43—22no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43—41no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4D411yescharacteristic
112C4⋊C4×D43—22no—
113C4⋊C4×D43—41no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43D411yescharacteristic
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—28no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4D411yescharacteristic
123C2×C4×Dic43—21no—
124C2×C4×Dic43C2311yescharacteristic
125Dic43⋊C8—22no—
126#13063249—22no—
127#13063249—22no—
128#13063247—22no—
129#13063247—41no—
130#13063246—22no—
131#13063246D414yescomplemented
132#13063245—22no—
133#13063245—41no—
134(C2×D43)⋊C8—22no—
135#13063235—22no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C2×#41×C43—22no—
139C2×#41×C43—22no—
140C2×#41×C43—22no—
141C2×#41×C43—41no—
142C2×#41×C43—41no—
143C2×#41×C43C2×C414yescomplemented
144C22×Q8×C43C2311yescharacteristic
145C22×D4×C43—21no—
146C22×D4×C43C2311yescharacteristic
147C23×C4×C43—21no—
148C23×C4×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154#103×C43—41no—
155#103×C43—41no—
156#102×C43—22no—
157#102×C43—22no—
158C22⋊C8×C43—22no—
159#95×C43—21no—
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×C43C22×C412yes—
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—22no—
207C2×C22⋊D43—22no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—42no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43—81no—
212C2×C22⋊D43C22⋊C414yes—
213C22×Dic43—24no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—42no—
218C22×Dic43—42no—
219C22×Dic43—81no—
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—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C22⋊C4×C43—42no—
255C22⋊Dic43—24no—
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)⋊C4C22⋊C414yes—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—42no—
268C4⋊Dic43C22×C412yes—
269C4⋊Dic43C2×D412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—42no—
272Dic43⋊C4—42no—
273Dic43⋊C4—81no—
274Dic43⋊C4C22⋊C414yes—
275C4×Dic43—42no—
276C4×Dic43C22×C412yes—
277C4×Dic43C2×D412yes—
278#10621877—44no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8C2×D412yes—
285C8×D43—44no—
286C23×C43—22no—
287C23×C43—21no—
288C23×C43—22no—
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—48no—
339C2×C4×C43—41no—
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×C43C2×C22⋊C412yes—
348C2×C4×C43C23×C411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C2×#4111yescharacteristic
352C2×C4×C43H(5,𝔽2)11yescharacteristic
353C2×C4×C43H(5,𝔽2)11yescharacteristic
354C22⋊D43—28no—
355C22⋊D43—48no—
356C22⋊D43—84no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—22no—
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—84no—
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—41no—
387C8×C43—41no—
388C43⋊C8—22no—
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—81no—
430C4×C43—81no—
431C4×C43C2×C4×D411yescharacteristic
432C4×C43#51811yescharacteristic
433C4×C43D4211yescharacteristic
434C4×C43#54611yescharacteristic
435Dic43—22no—
436Dic43—22no—
437Dic43—22no—
438Dic43—42no—
439Dic43—42no—
440Dic43—81no—
441C2×#546—431no—
442C2×#435—431no—
443C2×#417—431no—
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#1788D4311yescharacteristic, complemented
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×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—431no—
480C2×C4×D4—431no—
481C2×C4×D4—861no—
482C22×C4⋊C4—431no—
483C22×C4⋊C4—431no—
484C22×C22⋊C4—861no—
485#435—864no—
486C2×C4⋊C8—431no—
487#417—864no—
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⋊C8C2×D4311yescharacteristic, complemented
503C2×#97—431no—
504#389—861no—
505#385—861no—
506#385—861no—
507#384—431no—
508#380—431no—
509#380C2×D4311yescharacteristic, complemented
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—431no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4C22×D4311yescharacteristic
542C2×M16—862no—
543C2×M16—862no—
544C2×M16—1721no—
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—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—862no—
571C2×C4⋊C4—862no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—1721no—
578C2×C4⋊C4—1721no—
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—431no—
583C2×C22⋊C4—431no—
584C2×C22⋊C4—868no—
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—41no—
595#103—41no—
596#103—862no—
597#103—862no—
598#102—22no—
599#102—22no—
600#102—434no—
601#102—862no—
602#102—862no—
603#102—862no—
604#102—1721no—
605#102—1721no—
606C22⋊C8—22no—
607C22⋊C8—862no—
608#97—862no—
609#95—21no—
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×D4D4×D4312yes—
660C2×D4#1062190012yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—24no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—432no—
675C22×C4—432no—
676C22×C4—864no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—3441no—
685C22×C4—3441no—
686C22×C4—3441no—
687C22×C4—3441no—
688C22×C4—1722no—
689C22×C4—1722no—
690C22×C4—1722no—
691C22×C4—1722no—
692C22×C4C2×C4×D4312yes—
693C22×C4D4×D4311yescharacteristic
694C22×C4D4×D4312yes—
695C22×C4C23×D4311yescharacteristic
696M16—1724no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—432no—
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—434no—
715C4⋊C4—432no—
716C4⋊C4—432no—
717C4⋊C4—864no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—3441no—
723C4⋊C4—1722no—
724C4⋊C4—1722no—
725C4⋊C4—1722no—
726C22⋊C4—42no—
727C22⋊C4—434no—
728C22⋊C4—434no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—864no—
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—
789D4(C22⋊D43)⋊C414yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—432no—
807C2×C4—432no—
808C2×C4—432no—
809C2×C4—861no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—3444no—
822C2×C4—3444no—
823C2×C4—3444no—
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×C4C2×D4×D4311yescharacteristic
835C2×C4C2×#1062190011yescharacteristic
836C2×C4#1306337011yescharacteristic
837C2×C4#1306337011yescharacteristic
838C8—41no—
839C8—41no—
840C8—862no—
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
872C22#1458353111yescharacteristic
873C22#1458353611yescharacteristic
874C22AGL(1,ℤ/8)×D4311yescharacteristic
875C22#137×D4311yescharacteristic
876C22#1458370111yescharacteristic
877C22#1458370611yescharacteristic
878C4—22no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—862no—
883C4—862no—
884C4—862no—
885C4—3441no—
886C4—1722no—
887C4—1722no—
888C4C2×(C22⋊D43)⋊C411yescharacteristic
889C4#1458337211yescharacteristic
890C4#1458353111yescharacteristic
891C4#1458353611yescharacteristic
892C2—42no—
893C2—44no—
894C2—864no—
895C2—3442no—
896C2#1913741111yescharacteristic
897C2#417×D4311yescharacteristic
898C2#1914311711yescharacteristic
899C2#1914607811yescharacteristic
900C2#1914610311yescharacteristic
901C2#1914654911yescharacteristic
902C2#1914666911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583537C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#22419
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14582973C2semidirect
3. C2×#14582900C2semidirect
4. C2×#102×D43C2semidirect
5. #19137491C2semidirect
6. #19135524C2semidirect
7. #19135408C2semidirect
8. #19135031C2semidirect
9. #19135015C2semidirect
10. #19134910C2semidirect
11. #19134899C2semidirect
12. #19134593C2semidirect
13. #19134524C2semidirect
14. #19134422C2semidirect
15. C43×#1788C2semidirect
17. C22×#10621877C22semidirect
20. #14583537C4semidirect
30. C22×C4⋊Dic43C22semidirect
34. C2×Dic43⋊C8C22semidirect
36. C2×#13063249C22semidirect
37. C2×#13063249C22semidirect
46. C2×#13063235C22semidirect
50. #14582768C22semidirect
52. C4⋊C4×Dic43C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×#103×C43C22semidirect
59. C2×#103×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C43×#380C22semidirect
74. C2×D4×D43C2×C4semidirect
88. #13063314C2×C4semidirect
91. #13063301C2×C4semidirect
93. #13063299C2×C4semidirect
97. D4×Dic43C2×C4semidirect
131. #13063246D4semidirect
143. C2×#41×C43C2×C4semidirect
330. D4×C43C4×D4semidirect
426. C2×D43#417semidirect
453. #1788D43semidirect
490. C2×#103C2×D43semidirect
491. C2×#103C2×D43semidirect
502. C2×C22⋊C8C2×D43semidirect
509. #380C2×D43semidirect
515. C43#22419semidirect
522. C2×#41C4×D43semidirect
789. D4(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145835372
C2×#145829732
C2×#145829002
C2×#102×D432
#191374912
#191355242
#191354082
#191350312
#191350152
#191349102
#191348992
#191345932
#191345242
#191344222
C43×#17882
#2241943