Finite Group Databasebeta

← #25112077

Subgroups — #25112077

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×#14582971C211yesmaximal, characteristic, complemented
2C2×#14582900C211yesmaximal, characteristic, complemented
3C22×#13063246C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic43C211yesmaximal, characteristic, complemented
5#19135528C211yesmaximal, characteristic, complemented
6#19135412C211yesmaximal, characteristic, complemented
7#19135034C211yesmaximal, characteristic, complemented
8#19135019C211yesmaximal, characteristic, complemented
9#19134913C211yesmaximal, characteristic, complemented
10#19134903C211yesmaximal, characteristic, complemented
11#19134595C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic, complemented
17C23×C43⋊C8C2211yescharacteristic
18C2×D4×Dic43—21no—
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic, complemented
21#14582971—24no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
23#14582900—24no—
24C2×#13063249C2211yescharacteristic, complemented
25C2×#13063249C2211yescharacteristic, complemented
26C2×#13063249C2211yescharacteristic, complemented
27C2×#13063249C2211yescharacteristic, complemented
28C2×#13063246—24no—
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
39C2×#13063236C2211yescharacteristic, complemented
40#14582798—21no—
41#14582774—21no—
42#14582774—21no—
43#14582769C2211yescharacteristic, complemented
44#14582759C2211yescharacteristic
45#14582759C2211yescharacteristic, complemented
46C4×C4⋊Dic43C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51C22×#41×C43C2211yescharacteristic
52C23×D4×C43C2211yescharacteristic
53C43×#546—24no—
54C43×#546C418yescomplemented
55C2×#124×C43C2211yescharacteristic
56C2×#123×C43—21no—
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43—21no—
59C2×#121×C43C2211yescharacteristic
60C2×#120×C43—21no—
61C2×C4×D4×C43C2211yescharacteristic
62C2×C4×D4×C43C2211yescharacteristic
63C22×C22⋊C4×C43—21no—
64C23×Dic43—21no—
65C23×Dic43—21no—
66C2×#10621877—22no—
67C2×#10621877—22no—
68C2×#10621877—41no—
69C22×C43⋊C8—22no—
70C22×C43⋊C8—22no—
71C22×C43⋊C8—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76D4×Dic43—44no—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—41no—
84C2×C4⋊Dic43—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C4⋊(C43⋊C8)—22no—
93#13063249—22no—
94#13063249—22no—
95#13063249—41no—
96#13063249—41no—
97#13063246—22no—
98#13063246—22no—
99#13063246—22no—
100#13063246—22no—
101#13063246—22no—
102#13063246—41no—
103#13063246—41no—
104#13063246D414yescomplemented
105C22⋊(C43⋊C8)—22no—
106C22⋊(C43⋊C8)—22no—
107#13063236—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C25×C43—21no—
112C2×#41×C43—22no—
113C2×#41×C43—22no—
114C2×#41×C43—22no—
115C2×#41×C43—41no—
116C2×#41×C43—41no—
117C2×#41×C43C2×C414yescomplemented
118C22×Q8×C43C2311yescharacteristic
119C22×D4×C43—22no—
120C22×D4×C43—22no—
121C22×D4×C43—21no—
122C22×D4×C43—21no—
123C22×D4×C43—21no—
124C22×D4×C43—22no—
125C22×D4×C43—41no—
126C22×D4×C43—41no—
127C22×D4×C43C2×C414yescomplemented
128C22×D4×C43D411yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C22×D4×C43C2311yescharacteristic
131C23×C4×C43—21no—
132C23×C4×C43—21no—
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135#124×C43—22no—
136#124×C43C2×C414yescomplemented
137#123×C43—28no—
138C22⋊Q8×C43—22no—
139C22⋊Q8×C43C2×C414yescomplemented
140#121×C43—22no—
141#121×C43—28no—
142#121×C43C2×C414yescomplemented
143#120×C43—28no—
144C4×D4×C43—22no—
145C4×D4×C43C2×C414yes—
146C4×D4×C43C2×C414yescomplemented
147C4×D4×C43D414yes—
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43D411yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C22⋊C4×C43—21no—
152C2×C22⋊C4×C43—21no—
153C2×C22⋊C4×C43—21no—
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156C2×C22⋊C4×C43—28no—
157C2×C22⋊C4×C43D411yescharacteristic
158C2×C22⋊C4×C43D411yescharacteristic
159C2×C42×C43C2311yescharacteristic
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—24no—
163C24×C43—42no—
164C24×C43—42no—
165C24×C43—42no—
166C24×C43—42no—
167C24×C43—81no—
168C24×C43—81no—
169C24×C43C2×D411yescharacteristic
170C24×C43C2×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—24no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—24no—
187C2×D4×C43—24no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—28no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—42no—
199C2×D4×C43—44no—
200C2×D4×C43—44no—
201C2×D4×C43—44no—
202C2×D4×C43—81no—
203C2×D4×C43—81no—
204C2×D4×C43C22⋊C414yes—
205C2×D4×C43C22×C412yes—
206C2×D4×C43C22×C412yes—
207C2×D4×C43C2×D412yes—
208C2×D4×C43#4112yes—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—24no—
218C22×C4×C43—24no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43—81no—
224C22×C4×C43—81no—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C22×C412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—42no—
239C22×Dic43—42no—
240C22×Dic43—42no—
241C22×Dic43—42no—
242C22×Dic43—81no—
243C22×Dic43—81no—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43C22⋊C414yes—
247C4⋊C4×C43C22×C412yes—
248C22⋊C4×C43—24no—
249C22⋊C4×C43—24no—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—24no—
253C22⋊C4×C43C22⋊C414yes—
254C22⋊C4×C43C22⋊C414yes—
255C42×C43C22×C412yes—
256C42×C43C2×D412yes—
257C22⋊Dic43—42no—
258C22⋊Dic43—42no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—42no—
267C4⋊Dic43—42no—
268C4⋊Dic43—42no—
269C4⋊Dic43—81no—
270C4⋊Dic43C2×D412yes—
271C4×Dic43—42no—
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—22no—
291C23×C43—21no—
292C23×C43—22no—
293C23×C43—21no—
294C23×C43—22no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—22no—
300C23×C43—48no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—48no—
312C23×C43—84no—
313C23×C43—84no—
314C23×C43—84no—
315C23×C43—84no—
316C23×C43—84no—
317C23×C43C2×C22⋊C412yes—
318C23×C43C2×C22⋊C412yes—
319C23×C43AGL(1,ℤ/8)12yes—
320C23×C43#13712yes—
321C23×C43C22×D411yescharacteristic
322Q8×C43—22no—
323Q8×C43—22no—
324Q8×C43—41no—
325Q8×C43—41no—
326D4×C43—28no—
327D4×C43—22no—
328D4×C43—22no—
329D4×C43—22no—
330D4×C43—22no—
331D4×C43—22no—
332D4×C43—48no—
333D4×C43—48no—
334D4×C43—41no—
335D4×C43—41no—
336D4×C43—84no—
337D4×C43C4×D414yescomplemented
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—48no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—84no—
362C2×C4×C43C2×C22⋊C412yes—
363C2×C4×C43C2×C22⋊C412yes—
364C2×C4×C43C2×C22⋊C412yes—
365C2×C4×C43C2×C22⋊C412yes—
366C2×C4×C43C23×C411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C2×#4111yescharacteristic
370C2×C4×C43H(5,𝔽2)11yescharacteristic
371C2×C4×C43H(5,𝔽2)11yescharacteristic
372C2×Dic43—22no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—41no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—84no—
385C2×Dic43—84no—
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—24no—
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—41no—
404C22×C43—42no—
405C22×C43—41no—
406C22×C43—42no—
407C22×C43—41no—
408C22×C43—42no—
409C22×C43—41no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—816no—
415C22×C43—81no—
416C22×C43—81no—
417C22×C43—81no—
418C22×C43—81no—
419C22×C43#41714yescomplemented
420C22×C43C22×C22⋊C411yescharacteristic
421C22×C43D4211yescharacteristic
422C22×C43#54611yescharacteristic
423C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C43C2×#13711yescharacteristic
425C22×C43#57611yescharacteristic
426C22×C43#57711yescharacteristic
427C4×C43—22no—
428C4×C43—22no—
429C4×C43—22no—
430C4×C43—22no—
431C4×C43—42no—
432C4×C43—42no—
433C4×C43C2×C4×D411yescharacteristic
434C4×C43#51811yescharacteristic
435C4×C43D4211yescharacteristic
436C4×C43#54611yescharacteristic
437Dic43—42no—
438Dic43—81no—
439Dic43—81no—
440Dic43—81no—
441C2×#546D4311yescharacteristic
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#1788—431no—
454#1786—431no—
455#1762—431no—
456C2×C43—24no—
457C2×C43—42no—
458C2×C43—44no—
459C2×C43—82no—
460C2×C43D4×C22⋊C411yescharacteristic
461C2×C43C2×#41711yescharacteristic
462C2×C43#289711yescharacteristic
463C2×C43#326411yescharacteristic
464C2×C43#326611yescharacteristic
465C2×C43#330611yescharacteristic
466C2×C43#331411yescharacteristic
467C22×#41C2×D4311yescharacteristic
468C23×D4C2×D4311yescharacteristic
469C22×M16—431no—
470C23×C8—431no—
471#546—24no—
472#546Dic4318yescomplemented
473C2×#124C2×D4311yescharacteristic
474C2×#123—21no—
475C2×C22⋊Q8C2×D4311yescharacteristic
476C2×#121—21no—
477C2×#121C2×D4311yescharacteristic
478C2×#120—21no—
479C2×C4×D4—861no—
480C2×C4×D4C2×D4311yescharacteristic
481C2×C4×D4C2×D4311yescharacteristic
482C22×C4⋊C4—431no—
483C22×C4⋊C4—431no—
484C22×C22⋊C4—21no—
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—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—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×Dic4314yescomplemented
523C22×Q8C22×D4311yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×Dic4314yescomplemented
533C22×D4C22⋊D4311yescharacteristic
534C22×D4C22×D4311yescharacteristic
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—22no—
553#124C2×Dic4314yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×Dic4314yescomplemented
557#121—22no—
558#121—28no—
559#121C2×Dic4314yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—1724no—
563C4×D4C2×Dic4314yes—
564C4×D4C2×Dic4314yescomplemented
565C4×D4C22⋊D4314yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—862no—
572C2×C4⋊C4—862no—
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—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4C22⋊D4311yescharacteristic
590C2×C22⋊C4C22⋊D4311yescharacteristic
591C2×C42—861no—
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—861no—
610#95—861no—
611#95—861no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×C22⋊D4311yescharacteristic
622C24C2×C22⋊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×Q8C22×Dic4312yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊Dic4314yes—
657C2×D4D4×D4312yes—
658C2×D4#1062190012yes—
659C2×D4C22×Dic4312yes—
660C2×D4C22×Dic4312yes—
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—24no—
672C22×C4—24no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—3441no—
682C22×C4—3441no—
683C22×C4—1722no—
684C22×C4—1722no—
685C22×C4—1722no—
686C22×C4—1722no—
687C22×C4C22×Dic4312yes—
688C22×C4C22×Dic4312yes—
689C22×C4C2×C22⋊D4311yescharacteristic
690C22×C4C2×C22⋊D4311yescharacteristic
691C22×C4C2×C22⋊D4311yescharacteristic
692C22×C4C2×C22⋊D4311yescharacteristic
693C22×C4C2×C22⋊D4312yes—
694C22×C4C2×C22⋊D4312yes—
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—24no—
711C4⋊C4—21no—
712C4⋊C4—432no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—3441no—
721C4⋊C4—1722no—
722C4⋊C4—1722no—
723C4⋊C4—1722no—
724C4⋊C4C22⋊Dic4314yes—
725C4⋊C4C22×Dic4312yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—1722no—
732C22⋊C4—1722no—
733C22⋊C4C22⋊Dic4314yes—
734C22⋊C4C22⋊Dic4314yes—
735C42—1722no—
736C42C22×Dic4312yes—
737C42C2×C22⋊D4312yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊Dic4312yes—
770C23C2×C22⋊Dic4312yes—
771C23#1306335012yes—
772C23#1306335512yes—
773C23C22×C22⋊D4311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4D4×Dic4314yescomplemented
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—22no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4—862no—
815C2×C4—3444no—
816C2×C4—3444no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4C2×C22⋊Dic4312yes—
829C2×C4C2×C22⋊Dic4312yes—
830C2×C4C2×C22⋊Dic4312yes—
831C2×C4C2×C22⋊Dic4312yes—
832C2×C4C23×Dic4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C22×C22⋊D4311yescharacteristic
835C2×C4C2×#1062190011yescharacteristic
836C2×C4#1306337011yescharacteristic
837C2×C4#1306337011yescharacteristic
838C8—862no—
839C8—1721no—
840C8—1721no—
841C8—1721no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#1458290014yescomplemented
871C22C22×C22⋊Dic4311yescharacteristic
872C22D4×C22⋊D4311yescharacteristic
873C22#1458354311yescharacteristic
874C22C2×#1306335011yescharacteristic
875C22C2×#1306335511yescharacteristic
876C22#1458370211yescharacteristic
877C22#1458371011yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—3441no—
885C4—3441no—
886C4—3441no—
887C4—1722no—
888C4C2×D4×Dic4311yescharacteristic
889C4#1458337411yescharacteristic
890C4D4×C22⋊D4311yescharacteristic
891C4#1458354311yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊Dic4311yescharacteristic
897C2C2×#1458290011yescharacteristic
898C2#1914312111yescharacteristic
899C2#1914607611yescharacteristic
900C2#1914610111yescharacteristic
901C2#1914655611yescharacteristic
902C2#1914667611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#546C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#546D43
hypocenterC43#22419
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#14582971C2semidirect
2. C2×#14582900C2semidirect
3. C22×#13063246C2semidirect
4. D4×C4⋊Dic43C2semidirect
5. #19135528C2semidirect
6. #19135412C2semidirect
7. #19135034C2semidirect
8. #19135019C2semidirect
9. #19134913C2semidirect
10. #19134903C2semidirect
11. #19134595C2semidirect
12. #19134535C2semidirect
13. #19134526C2semidirect
14. #19134420C2semidirect
16. C22×#10621877C22semidirect
20. C22×C4⋊Dic43C22semidirect
22. C2×C4⋊(C43⋊C8)C22semidirect
24. C2×#13063249C22semidirect
25. C2×#13063249C22semidirect
26. C2×#13063249C22semidirect
27. C2×#13063249C22semidirect
38. C2×C22⋊(C43⋊C8)C22semidirect
39. C2×#13063236C22semidirect
43. #14582769C22semidirect
45. #14582759C22semidirect
46. C4×C4⋊Dic43C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
54. C43×#546C4semidirect
104. #13063246D4semidirect
117. C2×#41×C43C2×C4semidirect
127. C22×D4×C43C2×C4semidirect
136. #124×C43C2×C4semidirect
139. C22⋊Q8×C43C2×C4semidirect
142. #121×C43C2×C4semidirect
146. C4×D4×C43C2×C4semidirect
337. D4×C43C4×D4semidirect
419. C22×C43#417semidirect
472. #546Dic43semidirect
515. C43#22419semidirect
522. C2×#41C2×Dic43semidirect
532. C22×D4C2×Dic43semidirect
553. #124C2×Dic43semidirect
556. C22⋊Q8C2×Dic43semidirect
559. #121C2×Dic43semidirect
564. C4×D4C2×Dic43semidirect
789. D4D4×Dic43semidirect
870. C22#14582900semidirect

Maximal subgroups

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

subgroupindex
C2×#145829712
C2×#145829002
C22×#130632462
D4×C4⋊Dic432
#191355282
#191354122
#191350342
#191350192
#191349132
#191349032
#191345952
#191345352
#191345262
#191344202
C2×C43×#5462
#2241943