Finite Group Databasebeta

← #25112378

Subgroups — #25112378

Order 11008.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063350C211yesmaximal, characteristic
2C2×#14582997C211yesmaximal, characteristic, complemented
3C2×C4×#10621884C211yesmaximal, characteristic, complemented
4C22⋊C4×D172C211yesmaximal, characteristic, complemented
5#19135470C211yesmaximal, characteristic, complemented
6#19135460C211yesmaximal, characteristic, complemented
7#19134950C211yesmaximal, characteristic, complemented
8#19134950C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic, complemented
11#19134626C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134525C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#2341C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C2×#13063350—24no—
18C2×#13063350—24no—
19C2×#13063350C418yescomplemented
20C22×#10621884C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621877C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×C22⋊C4×D43—21no—
28#14582997—24no—
29C4×#10621884—24no—
30C2×#13063258C2211yescharacteristic, complemented
31C2×#13063256C2211yescharacteristic, complemented
32C2×#13063249C2211yescharacteristic, complemented
33C2×#13063249C2211yescharacteristic, complemented
34C2×#13063246C2211yescharacteristic, complemented
35C2×#13063246C2211yescharacteristic, complemented
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×#13063236C2211yescharacteristic, complemented
42C2×C4×C43⋊C8C2211yescharacteristic, complemented
43#14582801C2211yescharacteristic
44#14582801C2211yescharacteristic
45#14582777—21no—
46#14582777—21no—
47#14582759C2211yescharacteristic
48#14582754—21no—
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53C22×#41×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic, complemented
55C2×C4×Q8×C43C2211yescharacteristic, complemented
56C43×#390—21no—
57C43×#390—21no—
58C43×#390C2211yescharacteristic, complemented
59C43×#390C2211yescharacteristic, complemented
60C43×#380—21no—
61C43×#380C2211yescharacteristic
62C4×C22⋊C4×C43—21no—
63C4×C22⋊C4×C43C2211yescharacteristic
64C24×D43—21no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—21no—
68C22×D172—22no—
69C22×D172—41no—
70C22×D172—41no—
71C22×D172C2×C414yes—
72C22×D172C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76#13063350—232no—
77C2×#10621884—22no—
78C2×#10621884—22no—
79C2×#10621884C2×C414yes—
80C2×#10621884C2×C414yescomplemented
81C2×#10621884D414yes—
82C2×#10621884D414yes—
83C2×#10621882—22no—
84C2×#10621882—22no—
85C2×#10621882—22no—
86C2×#10621882—22no—
87C2×#10621882C2×C414yes—
88C2×#10621882C2×C414yescomplemented
89C2×#10621877—22no—
90C2×#10621877—22no—
91C2×#10621877C2×C414yescomplemented
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C4×D172—22no—
97C4×D172—22no—
98C4×D172—41no—
99C4×D172—41no—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C22⋊C4×D43—44no—
110#13063258—22no—
111#13063256—22no—
112#13063249—22no—
113#13063249—22no—
114#13063246—41no—
115#13063246—41no—
116#13063245—22no—
117#13063245—22no—
118#13063245—41no—
119#13063245—41no—
120C22⋊(C43⋊C8)—22no—
121#13063236—22no—
122C4×C43⋊C8—22no—
123C43⋊#95—21no—
124C2×#41×C43—22no—
125C2×#41×C43—22no—
126C2×#41×C43—22no—
127C2×#41×C43—41no—
128C2×#41×C43—41no—
129C2×#41×C43C2×C414yescomplemented
130C22×Q8×C43C2311yescharacteristic
131C22×D4×C43—21no—
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134C23×C4×C43C2311yescharacteristic
135C4×Q8×C43—22no—
136C4×Q8×C43—22no—
137C4×Q8×C43—41no—
138C4×Q8×C43—41no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43D411yescharacteristic
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C42×C43—21no—
151C2×C42×C43—21no—
152C2×C42×C43C2311yescharacteristic
153C2×C42×C43C2311yescharacteristic
154#95×C43—21no—
155#95×C43D411yescharacteristic
156#95×C43D411yescharacteristic
157C24×C43—21no—
158C24×C43C2×D411yescharacteristic
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—24no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—81no—
167C23×D43—81no—
168#41×C43—28no—
169#41×C43—44no—
170#41×C43—44no—
171#41×C43—44no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C22×C412yes—
176C2×Q8×C43C2×D412yes—
177C2×Q8×C43C2×D412yes—
178C2×D4×C43—21no—
179C2×D4×C43—24no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43C22×C412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43C22×C412yes—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43#4112yes—
204C22×C4×C43C2411yescharacteristic
205C22×Dic43—21no—
206C22×Dic43—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—24no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—28no—
217C2×D172—42no—
218C2×D172—42no—
219C2×D172—44no—
220C2×D172—44no—
221C2×D172—44no—
222C2×D172C22×C412yes—
223C2×D172C22×C412yes—
224C2×D172C2×D412yes—
225C2×D172C2×D412yes—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43—81no—
231C2×C4×D43—81no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—42no—
237C4⋊C4×C43—42no—
238C22⋊C4×C43—22no—
239C22⋊C4×C43—41no—
240C22⋊C4×C43—42no—
241C22⋊C4×C43—42no—
242C22⋊C4×C43—81no—
243C22⋊C4×C43—81no—
244C22⋊C4×C43—81no—
245C42×C43—21no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—21no—
249C42×C43—42no—
250C42×C43—42no—
251C22⋊Dic43—42no—
252#10621884—28no—
253#10621884C22⋊C4116yescomplemented
254#10621882—28no—
255#10621882—28no—
256(C2×D43)⋊C4—42no—
257(C2×D43)⋊C4—42no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—81no—
261(C2×D43)⋊C4—81no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266#10621877—28no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8C22×C412yes—
276C2×C43⋊C8C22×C412yes—
277C2×C43⋊C8C2×D412yes—
278C2×C43⋊C8C2×D412yes—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—22no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43C4×D412yes—
293C23×C43C22×D411yescharacteristic
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—48no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—48no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315Q8×C43—22no—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43C2×C22⋊C414yescomplemented
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—48no—
322D4×C43—41no—
323D4×C43—41no—
324C2×C4×C43—22no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
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—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
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—48no—
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×C43C4×D412yes—
352C2×C4×C43AGL(1,ℤ/8)12yescomplemented
353C2×C4×C43C23×C411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
358C2×C4×C43H(5,𝔽2)11yescharacteristic
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365D172—22no—
366D172—22no—
367D172—22no—
368D172—22no—
369D172—22no—
370D172—48no—
371D172—41no—
372D172—41no—
373D172C2×C22⋊C414yes—
374C4×D43—84no—
375C4×D43—84no—
376C43⋊C8—22no—
377C43⋊C8—41no—
378C43⋊C8—41no—
379C43⋊C8C2×C22⋊C414yescomplemented
380#22443—431nomaximal, Sylow
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43C2×C4×D411yescharacteristic
396C22×C43D4211yescharacteristic
397C22×C43D4211yescharacteristic
398C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C43#57511yescharacteristic
400C22×C43#57611yescharacteristic
401C22×C43#57711yescharacteristic
402C2×D43—24no—
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—816no—
413C2×D43—81no—
414C2×D43—81no—
415C2×D43—81no—
416C2×D43—81no—
417C4×C43—22no—
418C4×C43—24no—
419C4×C43—22no—
420C4×C43—41no—
421C4×C43—41no—
422C4×C43—41no—
423C4×C43—81no—
424C4×C43—81no—
425C4×C43C22×C22⋊C411yescharacteristic
426C4×C43#51811yescharacteristic
427C4×C43#54611yescharacteristic
428C4×C43#54611yescharacteristic
429Dic43—81no—
430Dic43—81no—
431C22×AGL(1,ℤ/8)—431no—
432C2×#440—431no—
433C2×C4×SD16—431no—
434#2341D4311yescharacteristic, complemented
435D4×C22⋊C4—431no—
436#1972—431no—
437#1970—431no—
438#1880—431no—
439#1880—431no—
440#1879—431no—
441#1879—431no—
442#1809—431no—
443#1788—431no—
444#1786—431no—
445#1753—431no—
446C2×C43—42no—
447C2×C43—82no—
448C2×C43D4×C22⋊C411yescharacteristic
449C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
450C2×C43#294611yescharacteristic
451C2×C43#326511yescharacteristic
452C2×C43#326811yescharacteristic
453C2×C43#327411yescharacteristic
454C2×C43#327511yescharacteristic
455D43—44no—
456D43—82no—
457C22×#41C2×D4311yescharacteristic
458C23×D4—431no—
459C2×AGL(1,ℤ/8)—438no—
460C2×AGL(1,ℤ/8)—864no—
461C2×AGL(1,ℤ/8)—864no—
462C22×SD16—431no—
463C22×SD16—431no—
464C22×D8—431no—
465C22×D8—431no—
466C22×M16—431no—
467C2×C4×Q8C2×D4311yescharacteristic, complemented
468C2×C4×Q8C2×D4311yescharacteristic, complemented
469C2×C4×D4—431no—
470C2×C4×D4—431no—
471C22×C22⋊C4—861no—
472#440—864no—
473C4×SD16—864no—
474C2×#107—431no—
475C2×#106—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×C22⋊C8—431no—
485C2×#97—431no—
486C2×C4×C8—431no—
487#390—21no—
488#390—21no—
489#390—431no—
490#390—431no—
491#390C2×D4311yescharacteristic, complemented
492#390C2×D4311yescharacteristic, complemented
493#386—861no—
494#386—861no—
495#380—21no—
496#380—431no—
497#380C2×D4311yescharacteristic
498#379—861no—
499C4×C22⋊C4—21no—
500C4×C22⋊C4C2×D4311yescharacteristic
501#340—431no—
502#340—431no—
503#336—431no—
504#336—431no—
505C43#2244311yescharacteristic, complemented, Sylow
506C25—861no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41C4×D4314yescomplemented
513C22×Q8C22×D4311yescharacteristic
514C22×D4—21no—
515C22×D4—434no—
516C22×D4—431no—
517C22×D4—431no—
518C22×D4—862no—
519C22×D4—862no—
520C22×D4—862no—
521C22×D4—861no—
522C22×D4—1721no—
523C22×D4—1721no—
524C22×D4C22×D4311yescharacteristic
525C23×C4—21no—
526C23×C4—861no—
527C23×C4—861no—
528C23×C4C22×D4311yescharacteristic
529AGL(1,ℤ/8)—8632no—
530C2×SD16—434no—
531C2×SD16—434no—
532C2×SD16—434no—
533C2×SD16—434no—
534C2×SD16—862no—
535C2×SD16—862no—
536C2×D8—434no—
537C2×D8—434no—
538C2×D8—862no—
539C2×D8—862no—
540C2×D8—862no—
541C2×D8—862no—
542C2×M16—434no—
543C2×M16—862no—
544C2×M16—862no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—431no—
548C22×C8—431no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×D4—862no—
554C4×D4—862no—
555C4×D4—1721no—
556C4×D4—1721no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—1724no—
576C2×C22⋊C4C22⋊D4311yescharacteristic
577C2×C22⋊C4C22⋊D4311yescharacteristic
578C2×C42—21no—
579C2×C42—21no—
580C2×C42C22×D4311yescharacteristic
581C2×C42C22×D4311yescharacteristic
582#107—862no—
583#106—862no—
584#103—862no—
585#103—862no—
586#102—862no—
587#102—862no—
588#102—1721no—
589#102—1721no—
590#102—1721no—
591#102—1721no—
592C22⋊C8—862no—
593#97—862no—
594C4×C8—862no—
595#95—21no—
596#95—861no—
597#95C22⋊D4311yescharacteristic
598#95C22⋊D4311yescharacteristic
599C24—21no—
600C24—861no—
601C24—864no—
602C24—861no—
603C24—3441no—
604C24—3441no—
605C24—1722no—
606C24—1722no—
607C24—1722no—
608C24—1722no—
609C24C2×C22⋊D4311yescharacteristic
610#41—28no—
611#41—44no—
612#41—44no—
613#41—44no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8C2×C4×D4312yes—
618C2×Q8D4×D4312yes—
619C2×Q8D4×D4312yes—
620C2×D4—24no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—432no—
629C2×D4—432no—
630C2×D4—432no—
631C2×D4—432no—
632C2×D4—868no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—1724no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1722no—
646C2×D4—1722no—
647C2×D4C2×C4×D4312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—3441no—
661C22×C4—3441no—
662C22×C4—1722no—
663C22×C4—1722no—
664C22×C4—1722no—
665C22×C4—1722no—
666C22×C4C2×C4×D4312yes—
667C22×C4#1062189812yes—
668C22×C4C2×C22⋊D4311yescharacteristic
669C22×C4C2×C22⋊D4311yescharacteristic
670C22×C4C2×C22⋊D4311yescharacteristic
671C22×C4C2×C22⋊D4311yescharacteristic
672C22×C4C2×C22⋊D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674SD16—4316no—
675SD16—868no—
676D8—868no—
677D8—868no—
678M16—868no—
679C2×C8—432no—
680C2×C8—432no—
681C2×C8—432no—
682C2×C8—432no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C22⋊C4—22no—
702C22⋊C4—41no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—3441no—
709C22⋊C4—3441no—
710C22⋊C4—1722no—
711C22⋊C4—1722no—
712C22⋊C4—1722no—
713C22⋊C4—1722no—
714C22⋊C4—1722no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—42no—
720C42—42no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—862no—
735C23—862no—
736C23—862no—
737C23—862no—
738C23—3444no—
739C23—3444no—
740C23—3444no—
741C23—3444no—
742C23—3444no—
743C23—1728no—
744C23—1728no—
745C23—1721no—
746C23—1721no—
747C23—1721no—
748C23—1721no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23C4×C22⋊D4312yes—
756C23C22×C22⋊D4311yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C22⋊C4×D4314yescomplemented
761D4—22no—
762D4—22no—
763D4—48no—
764D4—41no—
765D4—41no—
766D4—434no—
767D4—862no—
768D4—862no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—1728no—
773D4—1721no—
774D4—1721no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—3444no—
803C2×C4—3444no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4C4×C22⋊D4312yes—
811C2×C4#1306335012yescomplemented
812C2×C4C22×C4×D4311yescharacteristic
813C2×C4C2×D4×D4311yescharacteristic
814C2×C4C2×D4×D4311yescharacteristic
815C2×C4C2×#1062189811yescharacteristic
816C2×C4#1306337011yescharacteristic
817C2×C4#1306337011yescharacteristic
818C8—434no—
819C8—862no—
820C8—1721no—
821C8—1721no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—864no—
837C22—34416no—
838C22—3441no—
839C22—3441no—
840C22—3441no—
841C22—3441no—
842C22—1722no—
843C22—1722no—
844C22—1722no—
845C22—1722no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22C2×C4×C22⋊D4311yescharacteristic
852C22D4×C22⋊D4311yescharacteristic
853C22D4×C22⋊D4311yescharacteristic
854C22C2×#1306335011yescharacteristic
855C22#1458369711yescharacteristic
856C22#1458370211yescharacteristic
857C22#1458370711yescharacteristic
858C4—22no—
859C4—22no—
860C4—24no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—3441no—
867C4—3441no—
868C4C2×C22⋊C4×D4311yescharacteristic
869C4#1458337211yescharacteristic
870C4#1458353911yescharacteristic
871C4#1458353911yescharacteristic
872C2—42no—
873C2—82no—
874C2—3442no—
875C2—1724no—
876C2C22⋊C4×C22⋊D4311yescharacteristic
877C2C4×#1306335011yescharacteristic
878C2#1914342311yescharacteristic
879C2#1914609111yescharacteristic
880C2#1914613611yescharacteristic
881C2#1914621511yescharacteristic
882C2#1914622711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2341C2
socleC23×C43C22×D4
prime radicalC22×#13063350C2
cosocleC22×C4×C43C24
hypercenter#2341D43
hypocenterC43#22443
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#14582997C2semidirect
3. C2×C4×#10621884C2semidirect
4. C22⋊C4×D172C2semidirect
5. #19135470C2semidirect
6. #19135460C2semidirect
7. #19134950C2semidirect
8. #19134950C2semidirect
9. #19134946C2semidirect
10. #19134946C2semidirect
11. #19134626C2semidirect
12. #19134535C2semidirect
13. #19134525C2semidirect
14. #19134379C2semidirect
15. C43×#2341C2semidirect
19. C2×#13063350C4semidirect
30. C2×#13063258C22semidirect
31. C2×#13063256C22semidirect
32. C2×#13063249C22semidirect
33. C2×#13063249C22semidirect
34. C2×#13063246C22semidirect
35. C2×#13063246C22semidirect
41. C2×#13063236C22semidirect
42. C2×C4×C43⋊C8C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582654C22semidirect
52. #14582654C22semidirect
54. C2×C4×Q8×C43C22semidirect
55. C2×C4×Q8×C43C22semidirect
58. C43×#390C22semidirect
59. C43×#390C22semidirect
80. C2×#10621884C2×C4semidirect
88. C2×#10621882C2×C4semidirect
91. C2×#10621877C2×C4semidirect
129. C2×#41×C43C2×C4semidirect
253. #10621884C22⋊C4semidirect
318. Q8×C43C2×C22⋊C4semidirect
352. C2×C4×C43AGL(1,ℤ/8)semidirect
379. C43⋊C8C2×C22⋊C4semidirect
434. #2341D43semidirect
467. C2×C4×Q8C2×D43semidirect
468. C2×C4×Q8C2×D43semidirect
491. #390C2×D43semidirect
492. #390C2×D43semidirect
505. C43#22443semidirect
512. C2×#41C4×D43semidirect
760. Q8C22⋊C4×D43semidirect
811. C2×C4#13063350semidirect

Maximal subgroups

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

subgroupindex
C22×#130633502
C2×#145829972
C2×C4×#106218842
C22⋊C4×D1722
#191354702
#191354602
#191349502
#191349462
#191346262
#191345352
#191345252
#191343792
C43×#23412
#2244343