Finite Group Databasebeta

← #25112083

Subgroups — #25112083

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×#14583540C211yesmaximal, characteristic
2C2×#14582970C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic, complemented
4C22×#13063247C211yesmaximal, characteristic, complemented
5#19137491C211yesmaximal, characteristic, complemented
6#19135524C211yesmaximal, characteristic, complemented
7#19135408C211yesmaximal, characteristic, complemented
8#19135032C211yesmaximal, characteristic, complemented
9#19134911C211yesmaximal, characteristic, complemented
10#19134903C211yesmaximal, characteristic, complemented
11#19134594C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic, complemented
13#19134525C211yesmaximal, characteristic, complemented
14#19134419C211yesmaximal, characteristic, complemented
15C43×#1892C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C23×D172C2211yescharacteristic
18C22×#10621872C2211yescharacteristic, complemented
19#14583540—24no—
20#14583540C418yescomplemented
21C2×#13063314C2211yescharacteristic
22C2×#13063310—21no—
23C2×#13063300—21no—
24C2×#13063300C2211yescharacteristic
25C2×#13063295—21no—
26C2×#13063287C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×(C22⋊D43)⋊C4—21no—
29C22×C4⋊Dic43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic, complemented
31C2×C22⋊C4×D43—21no—
32#14582970—24no—
33C2×Dic43⋊C8C2211yescharacteristic, complemented
34#14582899—24no—
35C2×#13063249C2211yescharacteristic, complemented
36C2×#13063249C2211yescharacteristic, complemented
37C2×#13063247—24no—
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×#13063245C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
48C2×#13063235C2211yescharacteristic, complemented
49#14582796—21no—
50#14582773—21no—
51#14582771—21no—
52#14582768C2211yescharacteristic, complemented
53#14582756C2211yescharacteristic, complemented
54C4⋊C4×Dic43C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C23×C8×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#103×C43C2211yescharacteristic, complemented
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—41no—
69C2×#10621902—41no—
70C2×#10621902C2×C414yescomplemented
71C22×D172—22no—
72C22×D172—22no—
73C22×D172—21no—
74C22×D172—21no—
75C22×D172—22no—
76C22×D172—21no—
77C22×D172—41no—
78C22×D172—41no—
79C22×D172C2×C414yescomplemented
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43D411yescharacteristic
83C23×Dic43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43C2311yescharacteristic
88C2×#10621872—22no—
89C2×#10621872—22no—
90C2×#10621872—41no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93#13063314—22no—
94#13063314C2×C414yescomplemented
95#13063310—28no—
96#13063300—22no—
97#13063300—28no—
98#13063300C2×C414yescomplemented
99#13063295—28no—
100#13063287—22no—
101#13063287C2×C414yescomplemented
102C4×C22⋊D43C2×C414yes—
103C4×C22⋊D43D414yes—
104(C22⋊D43)⋊C4—44no—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43—41no—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4D411yescharacteristic
114C4⋊C4×D43—22no—
115C4⋊C4×D43—41no—
116C2×C22⋊Dic43D411yescharacteristic
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4D411yescharacteristic
123C22⋊C4×D43—28no—
124C2×C4×Dic43—21no—
125C2×C4×Dic43C2311yescharacteristic
126Dic43⋊C8—22no—
127#13063249—22no—
128#13063249—41no—
129#13063247—22no—
130#13063247—22no—
131#13063247—22no—
132#13063247D414yescomplemented
133#13063245—22no—
134#13063245—22no—
135#13063245—41no—
136#13063245—41no—
137C22⋊(C43⋊C8)—22no—
138(C2×D43)⋊C8—22no—
139#13063235—22no—
140C43⋊#95—21no—
141C43⋊#95—21no—
142C22×Q8×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43—22no—
145C22×C8×C43—22no—
146C22×C8×C43—41no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22⋊Q8×C43—22no—
150C22⋊Q8×C43C2×C414yescomplemented
151C2×C4⋊C4×C43—21no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C22⋊C4×C43—21no—
156C2×C22⋊C4×C43—21no—
157#103×C43—22no—
158#103×C43—41no—
159#95×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
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
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43C22×C412yes—
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×C43C22×C412yes—
186C22×C4×C43C2×D412yes—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43C22⋊C414yes—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—81no—
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200#10621902—28no—
201#10621902—44no—
202#10621902—44no—
203#10621902—44no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—24no—
208C2×D172—21no—
209C2×D172—24no—
210C2×D172—24no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—28no—
216C2×D172—42no—
217C2×D172—42no—
218C2×D172—42no—
219C2×D172—42no—
220C2×D172—44no—
221C2×D172—44no—
222C2×D172—44no—
223C2×D172—81no—
224C2×D172—81no—
225C2×D172C22×C412yes—
226C2×D172C22×C412yes—
227C2×D172C2×D412yes—
228C2×D172#4112yes—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—24no—
234C2×C4×D43—24no—
235C2×C4×D43—42no—
236C2×C4×D43—42no—
237C2×C4×D43—42no—
238C2×C4×D43—42no—
239C2×C4×D43—81no—
240C2×C4×D43—81no—
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—44no—
250C2×C8×C43C2×D412yes—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C22×C412yes—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—42no—
260C22⋊Dic43C22⋊C414yes—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—42no—
266(C2×D43)⋊C4C22⋊C414yes—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—42no—
271C4⋊Dic43C2×D412yes—
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—
285#10621872—44no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43C2×C22⋊C412yes—
291C23×C43AGL(1,ℤ/8)12yes—
292C23×C43#13712yes—
293C23×C43C22×D411yescharacteristic
294C22×D43—22no—
295C22×D43—21no—
296C22×D43—22no—
297C22×D43—21no—
298C22×D43—22no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—22no—
304C22×D43—48no—
305C22×D43—41no—
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—48no—
316C22×D43—84no—
317C22×D43—84no—
318C22×D43—84no—
319C22×D43—84no—
320C22×D43—84no—
321C22×D43C2×C22⋊C412yes—
322Q8×C43—22no—
323Q8×C43—22no—
324Q8×C43—41no—
325Q8×C43—41no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43C2×C22⋊C412yes—
345C2×C4×C43C23×C411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4111yescharacteristic
349C2×C4×C43H(5,𝔽2)11yescharacteristic
350C2×C4×C43H(5,𝔽2)11yescharacteristic
351C22⋊D43—28no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—22no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—84no—
365C2×Dic43C2×C22⋊C412yes—
366C2×Dic43C2×C22⋊C412yes—
367C2×Dic43C2×C22⋊C412yes—
368D172—22no—
369D172—22no—
370D172—22no—
371D172—22no—
372D172—22no—
373D172—48no—
374D172—48no—
375D172—41no—
376D172—41no—
377D172—84no—
378D172C4×D414yescomplemented
379C4×D43—22no—
380C4×D43—22no—
381C4×D43—22no—
382C4×D43—22no—
383C4×D43—48no—
384C4×D43—84no—
385C4×D43—84no—
386C8×C43—22no—
387C8×C43—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#41714yescomplemented
398C22×C43C22×C22⋊C411yescharacteristic
399C22×C43D4211yescharacteristic
400C22×C43#54611yescharacteristic
401C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C43C2×#13711yescharacteristic
403C22×C43#57611yescharacteristic
404C22×C43#57711yescharacteristic
405C2×D43—24no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—41no—
412C2×D43—42no—
413C2×D43—41no—
414C2×D43—42no—
415C2×D43—41no—
416C2×D43—42no—
417C2×D43—41no—
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—42no—
429C4×C43—42no—
430C4×C43—81no—
431C4×C43—81no—
432C4×C43C2×C4×D411yescharacteristic
433C4×C43#51811yescharacteristic
434C4×C43D4211yescharacteristic
435C4×C43#54611yescharacteristic
436Dic43—22no—
437Dic43—22no—
438Dic43—22no—
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#1892D4311yescharacteristic, complemented
450#1874—431no—
451#1872—431no—
452#1802—431no—
453#1788—431no—
454#1786—431no—
455#1762—431no—
456C2×C43—24no—
457C2×C43D4×C22⋊C411yescharacteristic
458C2×C43C2×#41711yescharacteristic
459C2×C43#289711yescharacteristic
460C2×C43#326411yescharacteristic
461C2×C43#326611yescharacteristic
462C2×C43#330611yescharacteristic
463C2×C43#331411yescharacteristic
464D43—42no—
465D43—44no—
466D43—82no—
467C22×#41—431no—
468C23×D4—431no—
469C22×M16—431no—
470C23×C8C2×D4311yescharacteristic
471#546—438no—
472#546—864no—
473C2×#124—431no—
474C2×#123—861no—
475C2×C22⋊Q8C2×D4311yescharacteristic
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—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#380C2×D4311yescharacteristic
510C4×C4⋊C4—431no—
511#340—431no—
512#340—431no—
513#340C2×D4311yescharacteristic, complemented
514#340C2×D4311yescharacteristic, complemented
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×Q8C22×D4311yescharacteristic
524C22×D4—431no—
525C22×D4—434no—
526C22×D4—431no—
527C22×D4—431no—
528C22×D4—862no—
529C22×D4—862no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4—862no—
534C22×D4—1721no—
535C22×D4—1721no—
536C23×C4—431no—
537C23×C4—861no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4C22×D4311yescharacteristic
542C2×M16—862no—
543C2×M16—862no—
544C2×M16—1721no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8—431no—
549C22×C8—431no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#124—434no—
553#124—862no—
554#123—868no—
555C22⋊Q8—22no—
556C22⋊Q8C4×D4314yescomplemented
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—21no—
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—1721no—
577C2×C4⋊C4—1721no—
578C2×C4⋊C4C22×D4311yescharacteristic
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—431no—
584C2×C22⋊C4—431no—
585C2×C22⋊C4—868no—
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—41no—
596#103—862no—
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—861no—
611#95—861no—
612C24—431no—
613C24—861no—
614C24—864no—
615C24—861no—
616C24—3441no—
617C24—3441no—
618C24—1722no—
619C24—1722no—
620C24—1722no—
621C24—1722no—
622C24D4×D4311yescharacteristic
623#41—868no—
624#41—1724no—
625#41—1724no—
626#41—1724no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×C4×D4312yes—
633C2×D4—434no—
634C2×D4—432no—
635C2×D4—432no—
636C2×D4—432no—
637C2×D4—432no—
638C2×D4—868no—
639C2×D4—864no—
640C2×D4—864no—
641C2×D4—862no—
642C2×D4—862no—
643C2×D4—864no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4—861no—
652C2×D4—3441no—
653C2×D4—3441no—
654C2×D4—1724no—
655C2×D4—1724no—
656C2×D4—1724no—
657C2×D4—1722no—
658C2×D4—1722no—
659C2×D4—1722no—
660C2×D4—1722no—
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—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—432no—
673C22×C4—432no—
674C22×C4—864no—
675C22×C4—864no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—3441no—
683C22×C4—3441no—
684C22×C4—3441no—
685C22×C4—3441no—
686C22×C4—1722no—
687C22×C4—1722no—
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—44no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8D4×D4312yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—434no—
717C4⋊C4—432no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—3441no—
722C4⋊C4—1722no—
723C4⋊C4—1722no—
724C4⋊C4—1722no—
725C4⋊C4C2×C4×D4312yes—
726C22⋊C4—24no—
727C22⋊C4—42no—
728C22⋊C4—434no—
729C22⋊C4—434no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—1722no—
735C42—432no—
736C42—432no—
737C42—1722no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—432no—
743C23—862no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—861no—
748C23—861no—
749C23—862no—
750C23—861no—
751C23—862no—
752C23—862no—
753C23—3444no—
754C23—3444no—
755C23—3444no—
756C23—3444no—
757C23—3444no—
758C23—1728no—
759C23—1728no—
760C23—1721no—
761C23—1721no—
762C23—1721no—
763C23—1721no—
764C23—1721no—
765C23—1721no—
766C23—1721no—
767C23—1721no—
768C23—1721no—
769C23—1721no—
770C23C22⋊C4×D4312yes—
771C23#1306335212yes—
772C23#1306335712yes—
773C23C2×D4×D4311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—434no—
779D4—868no—
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—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
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—41no—
807C2×C4—41no—
808C2×C4—432no—
809C2×C4—432no—
810C2×C4—432no—
811C2×C4—861no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—861no—
816C2×C4—861no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—3444no—
823C2×C4—3444no—
824C2×C4—3444no—
825C2×C4—1728no—
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×C4#41×D4311yescharacteristic
836C2×C4#1306337011yescharacteristic
837C2×C4#1306337111yescharacteristic
838C8—22no—
839C8—41no—
840C8—1721no—
841C8—1721no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—862no—
849C22—864no—
850C22—862no—
851C22—862no—
852C22—34416no—
853C22—3441no—
854C22—3441no—
855C22—3441no—
856C22—3441no—
857C22—1722no—
858C22—1722no—
859C22—1722no—
860C22—1721no—
861C22—1722no—
862C22—1721no—
863C22—1722no—
864C22—1721no—
865C22—1722no—
866C22—1721no—
867C22—1722no—
868C22—1722no—
869C22—1722no—
870C22#1458289914yescomplemented
871C22C2×C22⋊C4×D4311yescharacteristic
872C22#1458353311yescharacteristic
873C22#1458353811yescharacteristic
874C22C2×#1306335211yescharacteristic
875C22C2×#1306335711yescharacteristic
876C22#1458370111yescharacteristic
877C22#1458370611yescharacteristic
878C4—22no—
879C4—42no—
880C4—42no—
881C4—81no—
882C4—81no—
883C4—862no—
884C4—862no—
885C4—862no—
886C4—3441no—
887C4—1722no—
888C4C4×D4×D4311yescharacteristic
889C4#1458337111yescharacteristic
890C4#1458353111yescharacteristic
891C4#1458354111yescharacteristic
892C2—24no—
893C2—3442no—
894C2—1722no—
895C2—1724no—
896C2#1913741311yescharacteristic
897C2C2×#1458289911yescharacteristic
898C2#1914311711yescharacteristic
899C2#1914607211yescharacteristic
900C2#1914610211yescharacteristic
901C2#1914656211yescharacteristic
902C2#1914668211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1892C2
socleC23×C43C22×D4
prime radicalC2×#14583540C2
cosocleC22×C4×C43C24
hypercenter#1892D43
hypocenterC43#22419
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
2. C2×#14582970C2semidirect
3. C2×#14582899C2semidirect
4. C22×#13063247C2semidirect
5. #19137491C2semidirect
6. #19135524C2semidirect
7. #19135408C2semidirect
8. #19135032C2semidirect
9. #19134911C2semidirect
10. #19134903C2semidirect
11. #19134594C2semidirect
12. #19134534C2semidirect
13. #19134525C2semidirect
14. #19134419C2semidirect
15. C43×#1892C2semidirect
18. C22×#10621872C22semidirect
20. #14583540C4semidirect
30. C2×C4⋊C4×D43C22semidirect
33. C2×Dic43⋊C8C22semidirect
35. C2×#13063249C22semidirect
36. C2×#13063249C22semidirect
47. C2×(C2×D43)⋊C8C22semidirect
48. C2×#13063235C22semidirect
52. #14582768C22semidirect
53. #14582756C22semidirect
54. C4⋊C4×Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
59. C2×#103×C43C22semidirect
60. C2×#103×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
70. C2×#10621902C2×C4semidirect
79. C22×D172C2×C4semidirect
94. #13063314C2×C4semidirect
98. #13063300C2×C4semidirect
101. #13063287C2×C4semidirect
132. #13063247D4semidirect
150. C22⋊Q8×C43C2×C4semidirect
378. D172C4×D4semidirect
397. C22×C43#417semidirect
449. #1892D43semidirect
490. C2×#103C2×D43semidirect
491. C2×#103C2×D43semidirect
513. #340C2×D43semidirect
514. #340C2×D43semidirect
515. C43#22419semidirect
556. C22⋊Q8C4×D43semidirect
870. C22#14582899semidirect

Maximal subgroups

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

subgroupindex
C2×#145835402
C2×#145829702
C2×#145828992
C22×#130632472
#191374912
#191355242
#191354082
#191350322
#191349112
#191349032
#191345942
#191345342
#191345252
#191344192
C43×#18922
#2241943