Finite Group Databasebeta

← C43×#23876 #24943893

Subgroups — C43×#23876 #24943893

Order 11008.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
2C43×#3488C211yesmaximal, characteristic, complemented
3C2×C43×#453C212yesmaximal, complemented
4C43×#3003C211yesmaximal, characteristic, complemented
5C43×#2433C211yesmaximal, characteristic, complemented
6C43×#2006C212yesmaximal, complemented
7C43×#2002C212yesmaximal, complemented
8C43×#1900C211yesmaximal, characteristic, complemented
9C43×#1883C212yesmaximal, complemented
10C43×#1871C211yesmaximal, characteristic, complemented
11C43×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C43C2211yescharacteristic, complemented
13C22×#41×C43C2211yescharacteristic
14C23×D4×C43C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C43—21no—
16C2×AGL(1,ℤ/8)×C43—21no—
17C2×AGL(1,ℤ/8)×C43—28no—
18C2×AGL(1,ℤ/8)×C43C2212yes—
19C2×AGL(1,ℤ/8)×C43C2212yescomplemented
20C2×AGL(1,ℤ/8)×C43C2212yescomplemented
21C22×SD16×C43—21no—
22C22×D8×C43—21no—
23C22×M16×C43C2211yescharacteristic, complemented
24C43×#550—21no—
25C43×#548—21no—
26C43×#546—21no—
27C43×#546—22no—
28D42×C43—22no—
29D42×C43—21no—
30C43×#537—21no—
31C43×#537C2211yescharacteristic, complemented
32C43×#535—21no—
33C43×#535C2211yescharacteristic, complemented
34C2×#127×C43C2212yescomplemented
35C43×#525—21no—
36C43×#525C2211yescharacteristic
37C2×#121×C43—21no—
38C2×#121×C43C2211yescharacteristic
39C2×#120×C43—22no—
40C43×#520C2211yescharacteristic, complemented
41C43×#453—28no—
42C43×#450—21no—
43C43×#450—21no—
44C43×#447—21no—
45C43×#447—21no—
46C2×#104×C43C2212yescomplemented
47C2×#104×C43C2212yescomplemented
48C2×#104×C43C2212yescomplemented
49C43×#418C2212yescomplemented
50C2×#100×C43C2212yescomplemented
51C43×#407C2211yescharacteristic, complemented
52C43×#392—22no—
53C43×#390C2212yescomplemented
54C4×C22⋊C4×C43C2211yescharacteristic, complemented
55C43×#343C2212yescomplemented
56C43×#339C2212yescomplemented
57C25×C43—21no—
58H(5,𝔽2)×C43—24no—
59H(5,𝔽2)×C43—42no—
60C2×#41×C43—21no—
61C2×#41×C43—21no—
62C2×#41×C43—21no—
63C2×#41×C43—21no—
64C2×#41×C43—24no—
65C2×#41×C43—42no—
66C2×#41×C43D411yescharacteristic, complemented
67C2×#41×C43D411yescharacteristic, complemented
68C2×#41×C43C2311yescharacteristic
69C2×#41×C43C2311yescharacteristic
70C2×#41×C43C2311yescharacteristic
71C22×Q8×C43D411yescharacteristic, complemented
72C22×D4×C43—24no—
73C22×D4×C43—21no—
74C22×D4×C43—22no—
75C22×D4×C43—22no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—24no—
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—21no—
82C22×D4×C43—21no—
83C22×D4×C43—21no—
84C22×D4×C43—42no—
85C22×D4×C43D412yes—
86C22×D4×C43D411yescharacteristic, complemented
87C22×D4×C43C2311yescharacteristic
88C22×D4×C43C2312yes—
89C23×C4×C43—21no—
90C23×C4×C43C2311yescharacteristic
91AGL(1,ℤ/8)×C43—28no—
92AGL(1,ℤ/8)×C43—28no—
93AGL(1,ℤ/8)×C43—24no—
94AGL(1,ℤ/8)×C43—24no—
95AGL(1,ℤ/8)×C43—24no—
96AGL(1,ℤ/8)×C43—24no—
97AGL(1,ℤ/8)×C43—42no—
98AGL(1,ℤ/8)×C43D418yescomplemented
99C2×SD16×C43—28no—
100C2×SD16×C43—22no—
101C2×SD16×C43—22no—
102C2×SD16×C43—22no—
103C2×D8×C43—28no—
104C2×D8×C43—22no—
105C2×D8×C43—22no—
106C2×D8×C43—22no—
107C2×M16×C43—21no—
108C2×M16×C43—24no—
109C2×M16×C43C2312yes—
110C2×M16×C43C2312yes—
111C22×C8×C43—21no—
112#127×C43—22no—
113#127×C43—21no—
114#127×C43—24no—
115#127×C43—42no—
116#124×C43—22no—
117#124×C43—21no—
118#123×C43—22no—
119#123×C43—21no—
120C22⋊Q8×C43—22no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43D411yescharacteristic, complemented
124C22⋊Q8×C43D411yescharacteristic, complemented
125#121×C43—22no—
126#121×C43—22no—
127#121×C43—22no—
128#121×C43—22no—
129#121×C43—22no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134#121×C43—21no—
135#121×C43—21no—
136#121×C43—22no—
137#121×C43—21no—
138#121×C43—21no—
139#121×C43D411yescharacteristic, complemented
140#121×C43D411yescharacteristic, complemented
141#120×C43—22no—
142#120×C43—22no—
143#120×C43—22no—
144#120×C43—21no—
145#120×C43—22no—
146#120×C43—48no—
147C4×Q8×C43—21no—
148C4×D4×C43—22no—
149C4×D4×C43—22no—
150C4×D4×C43—21no—
151C4×D4×C43—22no—
152C4×D4×C43—21no—
153C4×D4×C43—21no—
154#117×C43—21no—
155#117×C43C2311yescharacteristic
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43C2311yescharacteristic
158C2×C22⋊C4×C43—22no—
159C2×C22⋊C4×C43—21no—
160C2×C22⋊C4×C43—24no—
161C2×C22⋊C4×C43D412yes—
162C2×C42×C43C2312yes—
163#104×C43—24no—
164#104×C43—24no—
165#104×C43—42no—
166#102×C43—22no—
167#102×C43—22no—
168#100×C43—24no—
169C22⋊C8×C43—21no—
170C22⋊C8×C43—21no—
171#95×C43—21no—
172C24×C43—22no—
173C24×C43—22no—
174C24×C43—21no—
175C24×C43—44no—
176C24×C43—44no—
177C24×C43—41no—
178C24×C43—41no—
179C24×C43—82no—
180C24×C43C2×D411yescharacteristic
181C24×C43C2×D412yes—
182#41×C43—22no—
183#41×C43—22no—
184#41×C43—22no—
185#41×C43—22no—
186#41×C43—22no—
187#41×C43—22no—
188#41×C43—22no—
189#41×C43—44no—
190#41×C43—41no—
191#41×C43—41no—
192#41×C43—44no—
193#41×C43—44no—
194#41×C43—42no—
195#41×C43—42no—
196#41×C43C2×D414yes—
197C2×Q8×C43—21no—
198C2×Q8×C43—22no—
199C2×Q8×C43—41no—
200C2×Q8×C43C2×D411yescharacteristic
201C2×Q8×C43C2×D411yescharacteristic
202C2×Q8×C43C2×D411yescharacteristic
203C2×D4×C43—22no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—22no—
208C2×D4×C43—21no—
209C2×D4×C43—22no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—22no—
213C2×D4×C43—22no—
214C2×D4×C43—22no—
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—22no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—24no—
224C2×D4×C43—24no—
225C2×D4×C43—22no—
226C2×D4×C43—22no—
227C2×D4×C43—22no—
228C2×D4×C43—22no—
229C2×D4×C43—22no—
230C2×D4×C43—48no—
231C2×D4×C43—44no—
232C2×D4×C43—44no—
233C2×D4×C43—48no—
234C2×D4×C43—44no—
235C2×D4×C43—41no—
236C2×D4×C43—44no—
237C2×D4×C43—44no—
238C2×D4×C43—44no—
239C2×D4×C43—42no—
240C2×D4×C43—42no—
241C2×D4×C43—48no—
242C2×D4×C43—42no—
243C2×D4×C43—42no—
244C2×D4×C43—41no—
245C2×D4×C43—41no—
246C2×D4×C43—84no—
247C2×D4×C43—84no—
248C2×D4×C43C2×D411yescharacteristic
249C2×D4×C43C2×D411yescharacteristic
250C2×D4×C43C2×D411yescharacteristic
251C2×D4×C43C2×D414yescomplemented
252C22×C4×C43—21no—
253C22×C4×C43—22no—
254C22×C4×C43—22no—
255C22×C4×C43—22no—
256C22×C4×C43—22no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—22no—
263C22×C4×C43—44no—
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2×D411yescharacteristic
266C22×C4×C43C2×D411yescharacteristic
267C22×C4×C43C2×D411yescharacteristic
268C22×C4×C43C2×D411yescharacteristic
269C22×C4×C43C2×D412yes—
270C22×C4×C43C2411yescharacteristic
271SD16×C43—28no—
272SD16×C43—28no—
273SD16×C43—44no—
274D8×C43—28no—
275D8×C43—28no—
276D8×C43—44no—
277M16×C43—24no—
278M16×C43—22no—
279M16×C43—22no—
280M16×C43—22no—
281M16×C43C2×D414yescomplemented
282C2×C8×C43—24no—
283C2×C8×C43—22no—
284C2×C8×C43—22no—
285C4⋊C4×C43—22no—
286C4⋊C4×C43—22no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43—21no—
290C4⋊C4×C43—21no—
291C4⋊C4×C43C2×D411yescharacteristic
292C4⋊C4×C43C2×D411yescharacteristic
293C22⋊C4×C43—22no—
294C22⋊C4×C43—22no—
295C22⋊C4×C43—24no—
296C22⋊C4×C43—22no—
297C22⋊C4×C43—22no—
298C22⋊C4×C43—22no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—22no—
301C22⋊C4×C43—22no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—48no—
307C42×C43—22no—
308C42×C43—21no—
309C42×C43—22no—
310C42×C43—22no—
311C23×C43—21no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—24no—
318C23×C43—24no—
319C23×C43—41no—
320C23×C43—42no—
321C23×C43—44no—
322C23×C43—44no—
323C23×C43—44no—
324C23×C43—44no—
325C23×C43—44no—
326C23×C43—42no—
327C23×C43—42no—
328C23×C43—42no—
329C23×C43—42no—
330C23×C43—42no—
331C23×C43—81no—
332C23×C43—82no—
333C23×C43—82no—
334C23×C43—82no—
335C23×C43—82no—
336C23×C43—82no—
337C23×C43—816no—
338C23×C43—82no—
339C23×C43#12011yescharacteristic
340C23×C43#12011yescharacteristic
341C23×C43C22×D411yescharacteristic
342Q8×C43—21no—
343Q8×C43—21no—
344Q8×C43—21no—
345Q8×C43—22no—
346Q8×C43—42no—
347Q8×C43#12012yescomplemented
348D4×C43—24no—
349D4×C43—21no—
350D4×C43—24no—
351D4×C43—21no—
352D4×C43—21no—
353D4×C43—22no—
354D4×C43—24no—
355D4×C43—42no—
356D4×C43—42no—
357D4×C43—44no—
358D4×C43—44no—
359D4×C43—44no—
360D4×C43—42no—
361D4×C43—44no—
362D4×C43—42no—
363D4×C43—42no—
364D4×C43—44no—
365D4×C43—42no—
366D4×C43—41no—
367D4×C43—42no—
368D4×C43—41no—
369D4×C43—42no—
370D4×C43—42no—
371D4×C43—81no—
372D4×C43—82no—
373D4×C43—82no—
374D4×C43—82no—
375D4×C43—82no—
376D4×C43—816no—
377D4×C43#12012yescomplemented
378C2×C4×C43—21no—
379C2×C4×C43—22no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—24no—
387C2×C4×C43—24no—
388C2×C4×C43—21no—
389C2×C4×C43—22no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—42no—
394C2×C4×C43—42no—
395C2×C4×C43—42no—
396C2×C4×C43—44no—
397C2×C4×C43—42no—
398C2×C4×C43—42no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—42no—
402C2×C4×C43—42no—
403C2×C4×C43—82no—
404C2×C4×C43#12011yescharacteristic
405C2×C4×C43#12011yescharacteristic
406C2×C4×C43C22×D411yescharacteristic
407C2×C4×C43C22×D412yes—
408C2×C4×C43C22×D411yescharacteristic
409C2×C4×C43H(5,𝔽2)12yes—
410C8×C43—24no—
411C8×C43—42no—
412#23876C4311yesmaximal, characteristic, direct product factor, Sylow
413C22×C43—21no—
414C22×C43—21no—
415C22×C43—21no—
416C22×C43—21no—
417C22×C43—21no—
418C22×C43—22no—
419C22×C43—21no—
420C22×C43—21no—
421C22×C43—44no—
422C22×C43—48no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—42no—
426C22×C43—44no—
427C22×C43—41no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43—42no—
431C22×C43—41no—
432C22×C43—42no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—84no—
436C22×C43—84no—
437C22×C43—84no—
438C22×C43—88no—
439C22×C43—88no—
440C22×C43—82no—
441C22×C43—82no—
442C22×C43—164no—
443C22×C43#45312yescomplemented
444C22×C43C2×#12011yescharacteristic
445C22×C43D4212yes—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—22no—
449C4×C43—44no—
450C4×C43—41no—
451C4×C43—41no—
452C4×C43—42no—
453C4×C43—41no—
454C4×C43—41no—
455C4×C43C2×#12011yescharacteristic
456C4×C43#53411yescharacteristic
457C4×C43D4212yes—
458C22×AGL(1,ℤ/8)C2×C4311yescharacteristic, complemented
459#3488C2×C4311yescharacteristic, complemented
460C2×#453C2×C4312yescomplemented
461#3003C2×C4311yescharacteristic, complemented
462#2433C2×C4311yescharacteristic, complemented
463#2006C2×C4312yescomplemented
464#2002C2×C4312yescomplemented
465#1900C2×C4311yescharacteristic, complemented
466#1883C2×C4312yescomplemented
467#1871C2×C4311yescharacteristic, complemented
468#1789C2×C4311yescharacteristic, complemented
469C2×C43—22no—
470C2×C43—22no—
471C2×C43—41no—
472C2×C43—42no—
473C2×C43—81no—
474C2×C43—84no—
475C2×C43—82no—
476C2×C43—81no—
477C2×C43#240311yescharacteristic
478C2×C43C2×#45311yescharacteristic
479C2×C43#302111yescharacteristic
480C2×H(5,𝔽2)C22×C4311yescharacteristic, complemented
481C22×#41C22×C4311yescharacteristic
482C23×D4C22×C4311yescharacteristic, complemented
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—28no—
486C2×AGL(1,ℤ/8)C22×C4312yes—
487C2×AGL(1,ℤ/8)C22×C4312yescomplemented
488C2×AGL(1,ℤ/8)C22×C4312yescomplemented
489C22×SD16—21no—
490C22×D8—21no—
491C22×M16C22×C4311yescharacteristic, complemented
492#550—21no—
493#548—21no—
494#546—21no—
495#546—22no—
496D42—22no—
497D42—21no—
498#537—21no—
499#537C22×C4311yescharacteristic, complemented
500#535—21no—
501#535C22×C4311yescharacteristic, complemented
502C2×#127C22×C4312yescomplemented
503#525—21no—
504#525C22×C4311yescharacteristic
505C2×#121—21no—
506C2×#121C22×C4311yescharacteristic
507C2×#120—22no—
508#520C22×C4311yescharacteristic, complemented
509#453—28no—
510#450—21no—
511#450—21no—
512#447—21no—
513#447—21no—
514C2×#104C22×C4312yescomplemented
515C2×#104C22×C4312yescomplemented
516C2×#104C22×C4312yescomplemented
517#418C22×C4312yescomplemented
518C2×#100C22×C4312yescomplemented
519#407C22×C4311yescharacteristic, complemented
520#392—22no—
521#390C22×C4312yescomplemented
522C4×C22⋊C4C22×C4311yescharacteristic, complemented
523#343C22×C4312yescomplemented
524#339C22×C4312yescomplemented
525C43#2387611yescharacteristic, direct product factor, Sylow
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C4311yescharacteristic, complemented
536C2×#41D4×C4311yescharacteristic, complemented
537C2×#41C23×C4311yescharacteristic
538C2×#41C23×C4311yescharacteristic
539C2×#41C23×C4311yescharacteristic
540C22×Q8D4×C4311yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C4312yes—
555C22×D4D4×C4311yescharacteristic, complemented
556C22×D4C23×C4311yescharacteristic
557C22×D4C23×C4312yes—
558C23×C4—21no—
559C23×C4C23×C4311yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C4318yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C4312yes—
579C2×M16C23×C4312yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C4311yescharacteristic, complemented
593C22⋊Q8D4×C4311yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C4311yescharacteristic, complemented
609#121D4×C4311yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C4311yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C4311yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C4312yes—
631C2×C42C23×C4312yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C4311yescharacteristic
650C24C2×D4×C4312yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C4314yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C4311yescharacteristic
670C2×Q8C2×D4×C4311yescharacteristic
671C2×Q8C2×D4×C4311yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C4311yescharacteristic
718C2×D4C2×D4×C4311yescharacteristic
719C2×D4C2×D4×C4311yescharacteristic
720C2×D4C2×D4×C4314yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C4311yescharacteristic
734C22×C4C2×D4×C4311yescharacteristic
735C22×C4C2×D4×C4311yescharacteristic
736C22×C4C2×D4×C4311yescharacteristic
737C22×C4C2×D4×C4311yescharacteristic
738C22×C4C2×D4×C4312yes—
739C22×C4C24×C4311yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C4314yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C4311yescharacteristic
761C4⋊C4C2×D4×C4311yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C4311yescharacteristic
809C23#120×C4311yescharacteristic
810C23C22×D4×C4311yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C4312yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—42no—
832D4—42no—
833D4—44no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—82no—
841D4—81no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C4312yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C4311yescharacteristic
874C2×C4#120×C4311yescharacteristic
875C2×C4C22×D4×C4311yescharacteristic
876C2×C4C22×D4×C4312yes—
877C2×C4C22×D4×C4311yescharacteristic
878C2×C4H(5,𝔽2)×C4312yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22C43×#45312yescomplemented
912C22C2×#120×C4311yescharacteristic
913C22D42×C4312yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×#120×C4311yescharacteristic
924C4C43×#53411yescharacteristic
925C4D42×C4312yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C43×#240311yescharacteristic
935C2C2×C43×#45311yescharacteristic
936C2C43×#302111yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C43C2semidirect
2. C43×#3488C2semidirect
3. C2×C43×#453C2semidirect
4. C43×#3003C2semidirect
5. C43×#2433C2semidirect
6. C43×#2006C2semidirect
7. C43×#2002C2semidirect
8. C43×#1900C2semidirect
9. C43×#1883C2semidirect
10. C43×#1871C2semidirect
11. C43×#1789C2semidirect
12. C2×H(5,𝔽2)×C43C22semidirect
14. C23×D4×C43C22semidirect
19. C2×AGL(1,ℤ/8)×C43C22semidirect
20. C2×AGL(1,ℤ/8)×C43C22semidirect
23. C22×M16×C43C22semidirect
31. C43×#537C22semidirect
33. C43×#535C22semidirect
34. C2×#127×C43C22semidirect
40. C43×#520C22semidirect
46. C2×#104×C43C22semidirect
47. C2×#104×C43C22semidirect
48. C2×#104×C43C22semidirect
49. C43×#418C22semidirect
50. C2×#100×C43C22semidirect
51. C43×#407C22semidirect
53. C43×#390C22semidirect
54. C4×C22⋊C4×C43C22semidirect
55. C43×#343C22semidirect
56. C43×#339C22semidirect
66. C2×#41×C43D4semidirect
67. C2×#41×C43D4semidirect
71. C22×Q8×C43D4semidirect
86. C22×D4×C43D4semidirect
98. AGL(1,ℤ/8)×C43D4semidirect
123. C22⋊Q8×C43D4semidirect
124. C22⋊Q8×C43D4semidirect
139. #121×C43D4semidirect
140. #121×C43D4semidirect
251. C2×D4×C43C2×D4semidirect
281. M16×C43C2×D4semidirect
347. Q8×C43#120semidirect
377. D4×C43#120semidirect
412. #23876C43direct (N × H)
443. C22×C43#453semidirect
458. C22×AGL(1,ℤ/8)C2×C43semidirect
459. #3488C2×C43semidirect
460. C2×#453C2×C43semidirect
461. #3003C2×C43semidirect
462. #2433C2×C43semidirect
463. #2006C2×C43semidirect
464. #2002C2×C43semidirect
465. #1900C2×C43semidirect
466. #1883C2×C43semidirect
467. #1871C2×C43semidirect
468. #1789C2×C43semidirect
480. C2×H(5,𝔽2)C22×C43semidirect
482. C23×D4C22×C43semidirect
487. C2×AGL(1,ℤ/8)C22×C43semidirect
488. C2×AGL(1,ℤ/8)C22×C43semidirect
491. C22×M16C22×C43semidirect
499. #537C22×C43semidirect
501. #535C22×C43semidirect
502. C2×#127C22×C43semidirect
508. #520C22×C43semidirect
514. C2×#104C22×C43semidirect
515. C2×#104C22×C43semidirect
516. C2×#104C22×C43semidirect
517. #418C22×C43semidirect
518. C2×#100C22×C43semidirect
519. #407C22×C43semidirect
521. #390C22×C43semidirect
522. C4×C22⋊C4C22×C43semidirect
523. #343C22×C43semidirect
524. #339C22×C43semidirect
525. C43#23876direct (N × H)
535. C2×#41D4×C43semidirect
536. C2×#41D4×C43semidirect
540. C22×Q8D4×C43semidirect
555. C22×D4D4×C43semidirect
567. AGL(1,ℤ/8)D4×C43semidirect
592. C22⋊Q8D4×C43semidirect
593. C22⋊Q8D4×C43semidirect
608. #121D4×C43semidirect
609. #121D4×C43semidirect
720. C2×D4C2×D4×C43semidirect
750. M16C2×D4×C43semidirect
816. Q8#120×C43semidirect
846. D4#120×C43semidirect
911. C22C43×#453semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C432
C43×#34882
C2×C43×#4532
C43×#30032
C43×#24332
C43×#20062
C43×#20022
C43×#19002
C43×#18832
C43×#18712
C43×#17892
#2387643