Finite Group Databasebeta

← C43×#18414 #24938431

Subgroups — C43×#18414 #24938431

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3534C211yesmaximal, characteristic, complemented
2C43×#3194C211yesmaximal, characteristic, complemented
3C43×#3186C211yesmaximal, characteristic, complemented
4C43×#2661C211yesmaximal, characteristic, complemented
5C43×#1612C211yesmaximal, characteristic, complemented
6C43×#1610C211yesmaximal, characteristic, complemented
7C43×#1609C211yesmaximal, characteristic, complemented
8C43×#1607C211yesmaximal, characteristic, complemented
9C43×#1600C211yesmaximal, characteristic, complemented
10C43×#1598C211yesmaximal, characteristic, complemented
11C43×#1597C211yesmaximal, characteristic, complemented
12C43×#1595C211yesmaximal, characteristic, complemented
13C43×#1507C211yesmaximal, characteristic, complemented
14C43×#1501C211yesmaximal, characteristic, complemented
15C43×#1468C211yesmaximal, characteristic, complemented
16C43×#562—21no—
17C43×#560—21no—
18C43×#553—21no—
19C43×#551—21no—
20C43×#546—21no—
21C43×#546—21no—
22C43×#546—21no—
23D42×C43—21no—
24C43×#540—21no—
25C43×#539—21no—
26C43×#539C2211yescharacteristic
27C43×#538—21no—
28C43×#538C2211yescharacteristic
29C43×#537C2211yescharacteristic
30C43×#534—21no—
31C43×#534C2211yescharacteristic
32C43×#525C2211yescharacteristic
33C2×#123×C43C2211yescharacteristic
34C2×#121×C43C2211yescharacteristic
35C2×#121×C43C2211yescharacteristic, complemented
36C43×#483C2211yescharacteristic, complemented
37C43×#482—21no—
38C43×#480—21no—
39C43×#480C2211yescharacteristic
40C43×#480C2211yescharacteristic, complemented
41C43×#480C2211yescharacteristic, complemented
42C43×#469—21no—
43C43×#468—21no—
44C43×#466—21no—
45C43×#466—21no—
46C43×#450C2211yescharacteristic, complemented
47C43×#449—21no—
48C43×#447—21no—
49C43×#447C2211yescharacteristic
50C43×#447C2211yescharacteristic, complemented
51C43×#447C2211yescharacteristic, complemented
52C43×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic, complemented
54C43×#398C2211yescharacteristic, complemented
55C43×#397C2211yescharacteristic, complemented
56C43×#394—21no—
57C43×#394C2211yescharacteristic, complemented
58C43×#392—21no—
59C43×#392C2211yescharacteristic, complemented
60C43×#390—21no—
61C43×#388—21no—
62C4×C22⋊C4×C43C2211yescharacteristic, complemented
63C43×#328C2211yescharacteristic, complemented
64C43×#328C2211yescharacteristic, complemented
65C43×#327C2211yescharacteristic
66C43×#327C2211yescharacteristic
67C43×#327C2211yescharacteristic, complemented
68C43×#327C2211yescharacteristic, complemented
69C43×#327C2211yescharacteristic, complemented
70C43×#327C2211yescharacteristic, complemented
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic, complemented
74C43×#323C2211yescharacteristic, complemented
75C2×#41×C43—21no—
76C2×#41×C43D411yescharacteristic, complemented
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—21no—
82C22×D4×C43D411yescharacteristic
83C22×D4×C43D411yescharacteristic, complemented
84C22×D4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C2×SD16×C43—21no—
87C2×D8×C43—21no—
88C2×D8×C43—21no—
89C2×D8×C43—21no—
90C2×M16×C43—21no—
91C22×C8×C43—21no—
92#127×C43—21no—
93#126×C43—21no—
94#126×C43—21no—
95#126×C43—21no—
96#126×C43—21no—
97#125×C43—21no—
98#125×C43—21no—
99#124×C43—21no—
100#124×C43—21no—
101#124×C43—21no—
102#123×C43—21no—
103#123×C43—21no—
104#123×C43—21no—
105#123×C43—21no—
106#123×C43—21no—
107#123×C43—21no—
108#123×C43—21no—
109#123×C43—21no—
110#123×C43—21no—
111#123×C43—21no—
112#123×C43—21no—
113#123×C43—21no—
114#123×C43—21no—
115#123×C43—21no—
116C22⋊Q8×C43—21no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—21no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43D411yescharacteristic, complemented
122C22⋊Q8×C43C2311yescharacteristic
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#121×C43—21no—
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—21no—
137#121×C43—21no—
138#121×C43—21no—
139#121×C43—21no—
140#121×C43—21no—
141#121×C43—21no—
142#121×C43D411yescharacteristic, complemented
143#121×C43D411yescharacteristic, complemented
144#121×C43D411yescharacteristic, complemented
145#121×C43C2311yescharacteristic
146#121×C43C2311yescharacteristic
147#121×C43C2311yescharacteristic
148#120×C43—21no—
149#120×C43—21no—
150#120×C43—21no—
151#120×C43—21no—
152#120×C43—21no—
153#120×C43—21no—
154#120×C43—21no—
155#120×C43—21no—
156C4×D4×C43—21no—
157C4×D4×C43—21no—
158C4×D4×C43—21no—
159C4×D4×C43—21no—
160C4×D4×C43—21no—
161C4×D4×C43—21no—
162C4×D4×C43—21no—
163C4×D4×C43—21no—
164#117×C43—21no—
165#117×C43D411yescharacteristic, complemented
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43D411yescharacteristic
168C2×C4⋊C4×C43D411yescharacteristic, complemented
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43D411yescharacteristic
181C2×C22⋊C4×C43D411yescharacteristic
182C2×C22⋊C4×C43C2311yescharacteristic
183C2×C42×C43—21no—
184#107×C43—21no—
185#107×C43—21no—
186#107×C43—21no—
187#106×C43—21no—
188#103×C43—21no—
189#102×C43—21no—
190#102×C43—21no—
191#102×C43—21no—
192#102×C43—21no—
193#102×C43—21no—
194#102×C43—21no—
195#102×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43C2311yescharacteristic
199C22⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202#95×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43—21no—
207C24×C43—21no—
208C24×C43—21no—
209C24×C43C2×D411yescharacteristic
210C24×C43C2×D411yescharacteristic
211#41×C43—81no—
212#41×C43—81no—
213#41×C43—81no—
214C2×Q8×C43—21no—
215C2×Q8×C43C2×D411yescharacteristic
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—42no—
236C2×D4×C43—41no—
237C2×D4×C43—41no—
238C2×D4×C43—81no—
239C2×D4×C43—81no—
240C2×D4×C43—81no—
241C2×D4×C43—81no—
242C2×D4×C43—81no—
243C2×D4×C43—81no—
244C2×D4×C43—81no—
245C2×D4×C43—81no—
246C2×D4×C43—81no—
247C2×D4×C43—81no—
248C2×D4×C43—81no—
249C2×D4×C43—82no—
250C2×D4×C43C2×D411yescharacteristic
251C2×D4×C43C2×D411yescharacteristic
252C2×D4×C43C2×D411yescharacteristic
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—81no—
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2×D411yescharacteristic
266C22×C4×C43C2×D411yescharacteristic
267C22×C4×C43C2×D411yescharacteristic
268C22×C4×C43C2×D411yescharacteristic
269C22×C4×C43C2×D411yescharacteristic
270C22×C4×C43C2×D411yescharacteristic
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2411yescharacteristic
273SD16×C43—81no—
274D8×C43—81no—
275D8×C43—81no—
276D8×C43—81no—
277M16×C43—81no—
278C2×C8×C43—21no—
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C2×C8×C43—21no—
282C2×C8×C43—81no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43—21no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43—21no—
290C4⋊C4×C43—21no—
291C4⋊C4×C43—21no—
292C4⋊C4×C43—21no—
293C4⋊C4×C43—21no—
294C4⋊C4×C43—21no—
295C4⋊C4×C43—21no—
296C4⋊C4×C43—21no—
297C4⋊C4×C43—21no—
298C4⋊C4×C43—81no—
299C4⋊C4×C43C2×D411yescharacteristic
300C4⋊C4×C43C2×D411yescharacteristic
301C4⋊C4×C43C2×D411yescharacteristic
302C4⋊C4×C43C2×D411yescharacteristic
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—21no—
310C22⋊C4×C43—21no—
311C22⋊C4×C43—21no—
312C22⋊C4×C43—21no—
313C22⋊C4×C43—21no—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—21no—
316C22⋊C4×C43—21no—
317C22⋊C4×C43—21no—
318C22⋊C4×C43—21no—
319C22⋊C4×C43—21no—
320C22⋊C4×C43—21no—
321C22⋊C4×C43—21no—
322C22⋊C4×C43—21no—
323C22⋊C4×C43—21no—
324C22⋊C4×C43—21no—
325C22⋊C4×C43—21no—
326C22⋊C4×C43—21no—
327C22⋊C4×C43—21no—
328C22⋊C4×C43—42no—
329C22⋊C4×C43—42no—
330C22⋊C4×C43—41no—
331C22⋊C4×C43—41no—
332C22⋊C4×C43—81no—
333C22⋊C4×C43—81no—
334C22⋊C4×C43—81no—
335C42×C43—21no—
336C42×C43—21no—
337C42×C43—21no—
338C42×C43—81no—
339C23×C43—21no—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43—21no—
345C23×C43—21no—
346C23×C43—21no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—42no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—41no—
354C23×C43—41no—
355C23×C43—41no—
356C23×C43—41no—
357C23×C43—41no—
358C23×C43—41no—
359C23×C43—81no—
360C23×C43—81no—
361C23×C43—81no—
362C23×C43—81no—
363C23×C43—81no—
364C23×C43#12011yescharacteristic
365C23×C43#12011yescharacteristic
366C23×C43C22×D411yescharacteristic
367Q8×C43—41no—
368Q8×C43—81no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—41no—
372D4×C43—41no—
373D4×C43—41no—
374D4×C43—41no—
375D4×C43—41no—
376D4×C43—42no—
377D4×C43—42no—
378D4×C43—41no—
379D4×C43—41no—
380D4×C43—41no—
381D4×C43—41no—
382D4×C43—41no—
383D4×C43—41no—
384D4×C43—81no—
385D4×C43—81no—
386D4×C43—81no—
387D4×C43—81no—
388D4×C43—81no—
389D4×C43—81no—
390D4×C43—81no—
391D4×C43—81no—
392D4×C43—81no—
393D4×C43—81no—
394D4×C43—81no—
395D4×C43—81no—
396D4×C43—84no—
397D4×C43—82no—
398D4×C43—82no—
399C2×C4×C43—22no—
400C2×C4×C43—21no—
401C2×C4×C43—21no—
402C2×C4×C43—21no—
403C2×C4×C43—21no—
404C2×C4×C43—21no—
405C2×C4×C43—21no—
406C2×C4×C43—21no—
407C2×C4×C43—21no—
408C2×C4×C43—21no—
409C2×C4×C43—21no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—81no—
427C2×C4×C43—81no—
428C2×C4×C43—81no—
429C2×C4×C43—81no—
430C2×C4×C43—81no—
431C2×C4×C43—81no—
432C2×C4×C43—81no—
433C2×C4×C43#12011yescharacteristic
434C2×C4×C43#12011yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C8×C43—41no—
438C8×C43—41no—
439C8×C43—41no—
440C8×C43—41no—
441#18414C4311yesmaximal, characteristic, direct product factor, Sylow
442C22×C43—21no—
443C22×C43—21no—
444C22×C43—21no—
445C22×C43—21no—
446C22×C43—21no—
447C22×C43—21no—
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—41no—
451C22×C43—41no—
452C22×C43—41no—
453C22×C43—41no—
454C22×C43—41no—
455C22×C43—41no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43—41no—
460C22×C43—41no—
461C22×C43—41no—
462C22×C43—81no—
463C22×C43—81no—
464C22×C43—81no—
465C22×C43—81no—
466C22×C43—81no—
467C22×C43—81no—
468C22×C43—81no—
469C22×C43—81no—
470C22×C43—81no—
471C22×C43—81no—
472C22×C43—81no—
473C22×C43—162no—
474C22×C43—162no—
475C22×C43C2×#12011yescharacteristic
476C22×C43#57611yescharacteristic
477C22×C43#57611yescharacteristic
478C4×C43—21no—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—42no—
483C4×C43—41no—
484C4×C43—41no—
485C4×C43—41no—
486C4×C43—41no—
487C4×C43—41no—
488C4×C43—41no—
489C4×C43—41no—
490C4×C43—41no—
491C4×C43—81no—
492C4×C43—81no—
493#3534C2×C4311yescharacteristic, complemented
494#3194C2×C4311yescharacteristic, complemented
495#3186C2×C4311yescharacteristic, complemented
496#2661C2×C4311yescharacteristic, complemented
497#1612C2×C4311yescharacteristic, complemented
498#1610C2×C4311yescharacteristic, complemented
499#1609C2×C4311yescharacteristic, complemented
500#1607C2×C4311yescharacteristic, complemented
501#1600C2×C4311yescharacteristic, complemented
502#1598C2×C4311yescharacteristic, complemented
503#1597C2×C4311yescharacteristic, complemented
504#1595C2×C4311yescharacteristic, complemented
505#1507C2×C4311yescharacteristic, complemented
506#1501C2×C4311yescharacteristic, complemented
507#1468C2×C4311yescharacteristic, complemented
508C2×C43—21no—
509C2×C43—21no—
510C2×C43—41no—
511C2×C43—41no—
512C2×C43—81no—
513C2×C43—81no—
514C2×C43—81no—
515C2×C43—81no—
516C2×C43—161no—
517C2×C43#300811yescharacteristic
518C2×C43#301811yescharacteristic
519C2×C43#302611yescharacteristic
520#562—21no—
521#560—21no—
522#553—21no—
523#551—21no—
524#546—21no—
525#546—21no—
526#546—21no—
527D42—21no—
528#540—21no—
529#539—21no—
530#539C22×C4311yescharacteristic
531#538—21no—
532#538C22×C4311yescharacteristic
533#537C22×C4311yescharacteristic
534#534—21no—
535#534C22×C4311yescharacteristic
536#525C22×C4311yescharacteristic
537C2×#123C22×C4311yescharacteristic
538C2×#121C22×C4311yescharacteristic
539C2×#121C22×C4311yescharacteristic, complemented
540#483C22×C4311yescharacteristic, complemented
541#482—21no—
542#480—21no—
543#480C22×C4311yescharacteristic
544#480C22×C4311yescharacteristic, complemented
545#480C22×C4311yescharacteristic, complemented
546#469—21no—
547#468—21no—
548#466—21no—
549#466—21no—
550#450C22×C4311yescharacteristic, complemented
551#449—21no—
552#447—21no—
553#447C22×C4311yescharacteristic
554#447C22×C4311yescharacteristic, complemented
555#447C22×C4311yescharacteristic, complemented
556#407C22×C4311yescharacteristic, complemented
557C2×C22⋊C8C22×C4311yescharacteristic, complemented
558#398C22×C4311yescharacteristic, complemented
559#397C22×C4311yescharacteristic, complemented
560#394—21no—
561#394C22×C4311yescharacteristic, complemented
562#392—21no—
563#392C22×C4311yescharacteristic, complemented
564#390—21no—
565#388—21no—
566C4×C22⋊C4C22×C4311yescharacteristic, complemented
567#328C22×C4311yescharacteristic, complemented
568#328C22×C4311yescharacteristic, complemented
569#327C22×C4311yescharacteristic
570#327C22×C4311yescharacteristic
571#327C22×C4311yescharacteristic, complemented
572#327C22×C4311yescharacteristic, complemented
573#327C22×C4311yescharacteristic, complemented
574#327C22×C4311yescharacteristic, complemented
575#324C22×C4311yescharacteristic, complemented
576#324C22×C4311yescharacteristic, complemented
577#323C22×C4311yescharacteristic, complemented
578#323C22×C4311yescharacteristic, complemented
579C43#1841411yescharacteristic, direct product factor, Sylow
580C2×#41—21no—
581C2×#41D4×C4311yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C4311yescharacteristic
588C22×D4D4×C4311yescharacteristic, complemented
589C22×D4C23×C4311yescharacteristic
590C23×C4C23×C4311yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C4311yescharacteristic, complemented
627C22⋊Q8C23×C4311yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C4311yescharacteristic, complemented
648#121D4×C4311yescharacteristic, complemented
649#121D4×C4311yescharacteristic, complemented
650#121C23×C4311yescharacteristic
651#121C23×C4311yescharacteristic
652#121C23×C4311yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C4311yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C4311yescharacteristic
673C2×C4⋊C4D4×C4311yescharacteristic, complemented
674C2×C4⋊C4C23×C4311yescharacteristic
675C2×C4⋊C4C23×C4311yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C4311yescharacteristic
686C2×C22⋊C4D4×C4311yescharacteristic
687C2×C22⋊C4C23×C4311yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C4311yescharacteristic
704C22⋊C8C23×C4311yescharacteristic
705C22⋊C8C23×C4311yescharacteristic
706C22⋊C8C23×C4311yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C4311yescharacteristic
710#95C23×C4311yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C4311yescharacteristic
715C24C2×D4×C4311yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C4311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C4311yescharacteristic
756C2×D4C2×D4×C4311yescharacteristic
757C2×D4C2×D4×C4311yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C4311yescharacteristic
770C22×C4C2×D4×C4311yescharacteristic
771C22×C4C2×D4×C4311yescharacteristic
772C22×C4C2×D4×C4311yescharacteristic
773C22×C4C2×D4×C4311yescharacteristic
774C22×C4C2×D4×C4311yescharacteristic
775C22×C4C2×D4×C4311yescharacteristic
776C22×C4C2×D4×C4311yescharacteristic
777C22×C4C24×C4311yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C4311yescharacteristic
805C4⋊C4C2×D4×C4311yescharacteristic
806C4⋊C4C2×D4×C4311yescharacteristic
807C4⋊C4C2×D4×C4311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C4311yescharacteristic
870C23#120×C4311yescharacteristic
871C23C22×D4×C4311yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C4311yescharacteristic
939C2×C4#120×C4311yescharacteristic
940C2×C4C22×D4×C4311yescharacteristic
941C2×C4C22×D4×C4311yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C4311yescharacteristic
980C22C43×#57611yescharacteristic
981C22C43×#57611yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C43×#300811yescharacteristic
1007C2C43×#301811yescharacteristic
1008C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3534C2semidirect
2. C43×#3194C2semidirect
3. C43×#3186C2semidirect
4. C43×#2661C2semidirect
5. C43×#1612C2semidirect
6. C43×#1610C2semidirect
7. C43×#1609C2semidirect
8. C43×#1607C2semidirect
9. C43×#1600C2semidirect
10. C43×#1598C2semidirect
11. C43×#1597C2semidirect
12. C43×#1595C2semidirect
13. C43×#1507C2semidirect
14. C43×#1501C2semidirect
15. C43×#1468C2semidirect
35. C2×#121×C43C22semidirect
36. C43×#483C22semidirect
40. C43×#480C22semidirect
41. C43×#480C22semidirect
46. C43×#450C22semidirect
50. C43×#447C22semidirect
51. C43×#447C22semidirect
52. C43×#407C22semidirect
53. C2×C22⋊C8×C43C22semidirect
54. C43×#398C22semidirect
55. C43×#397C22semidirect
57. C43×#394C22semidirect
59. C43×#392C22semidirect
62. C4×C22⋊C4×C43C22semidirect
63. C43×#328C22semidirect
64. C43×#328C22semidirect
67. C43×#327C22semidirect
68. C43×#327C22semidirect
69. C43×#327C22semidirect
70. C43×#327C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
73. C43×#323C22semidirect
74. C43×#323C22semidirect
76. C2×#41×C43D4semidirect
83. C22×D4×C43D4semidirect
121. C22⋊Q8×C43D4semidirect
142. #121×C43D4semidirect
143. #121×C43D4semidirect
144. #121×C43D4semidirect
165. #117×C43D4semidirect
168. C2×C4⋊C4×C43D4semidirect
441. #18414C43direct (N × H)
493. #3534C2×C43semidirect
494. #3194C2×C43semidirect
495. #3186C2×C43semidirect
496. #2661C2×C43semidirect
497. #1612C2×C43semidirect
498. #1610C2×C43semidirect
499. #1609C2×C43semidirect
500. #1607C2×C43semidirect
501. #1600C2×C43semidirect
502. #1598C2×C43semidirect
503. #1597C2×C43semidirect
504. #1595C2×C43semidirect
505. #1507C2×C43semidirect
506. #1501C2×C43semidirect
507. #1468C2×C43semidirect
539. C2×#121C22×C43semidirect
540. #483C22×C43semidirect
544. #480C22×C43semidirect
545. #480C22×C43semidirect
550. #450C22×C43semidirect
554. #447C22×C43semidirect
555. #447C22×C43semidirect
556. #407C22×C43semidirect
557. C2×C22⋊C8C22×C43semidirect
558. #398C22×C43semidirect
559. #397C22×C43semidirect
561. #394C22×C43semidirect
563. #392C22×C43semidirect
566. C4×C22⋊C4C22×C43semidirect
567. #328C22×C43semidirect
568. #328C22×C43semidirect
571. #327C22×C43semidirect
572. #327C22×C43semidirect
573. #327C22×C43semidirect
574. #327C22×C43semidirect
575. #324C22×C43semidirect
576. #324C22×C43semidirect
577. #323C22×C43semidirect
578. #323C22×C43semidirect
579. C43#18414direct (N × H)
581. C2×#41D4×C43semidirect
588. C22×D4D4×C43semidirect
626. C22⋊Q8D4×C43semidirect
647. #121D4×C43semidirect
648. #121D4×C43semidirect
649. #121D4×C43semidirect
670. #117D4×C43semidirect
673. C2×C4⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35342
C43×#31942
C43×#31862
C43×#26612
C43×#16122
C43×#16102
C43×#16092
C43×#16072
C43×#16002
C43×#15982
C43×#15972
C43×#15952
C43×#15072
C43×#15012
C43×#14682
#1841443