Finite Group Databasebeta

← C43×#24467 #24944484

Subgroups — C43×#24467 #24944484

Order 11008.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3488C211yesmaximal, characteristic
2C43×#3056C211yesmaximal, characteristic, complemented
3C2×C43×#455C211yesmaximal, characteristic, complemented
4C43×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C43C211yesmaximal, characteristic, complemented
6C43×#2850C211yesmaximal, characteristic, complemented
7C43×#2040C211yesmaximal, characteristic, complemented
8C43×#2037C211yesmaximal, characteristic, complemented
9C43×#2007C211yesmaximal, characteristic, complemented
10C43×#2004C211yesmaximal, characteristic, complemented
11C43×#1900C211yesmaximal, characteristic, complemented
12C43×#1896C211yesmaximal, characteristic, complemented
13C43×#1882C211yesmaximal, characteristic, complemented
14C43×#1860C211yesmaximal, characteristic, complemented
15C43×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C2×#137×C43C2211yescharacteristic
19C2×#137×C43C2211yescharacteristic, complemented
20C2×#137×C43C2211yescharacteristic, complemented
21C22×M16×C43C2211yescharacteristic, complemented
22C43×#550—21no—
23C43×#548—21no—
24C43×#546—21no—
25C43×#546—22no—
26D42×C43—22no—
27D42×C43—21no—
28C43×#537—21no—
29C43×#537C2211yescharacteristic
30C43×#535—21no—
31C43×#535C2211yescharacteristic
32C2×#124×C43C2211yescharacteristic, complemented
33C43×#525—21no—
34C43×#525C2211yescharacteristic
35C2×C22⋊Q8×C43C2211yescharacteristic, complemented
36C2×#121×C43—21no—
37C2×#121×C43C2211yescharacteristic
38C43×#520C2211yescharacteristic
39C22×C42×C43C2211yescharacteristic, complemented
40C43×#470—21no—
41C43×#468—21no—
42C43×#467—21no—
43C43×#465—21no—
44C43×#455—24no—
45C43×#452—21no—
46C43×#452—21no—
47C43×#451—21no—
48C43×#450—21no—
49C43×#428C2211yescharacteristic, complemented
50C2×#104×C43—24no—
51C2×#104×C43C2211yescharacteristic
52C2×#104×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic, complemented
54C2×#104×C43C2211yescharacteristic, complemented
55C2×#104×C43C2211yescharacteristic, complemented
56C2×#104×C43C2211yescharacteristic, complemented
57C43×#419C2211yescharacteristic, complemented
58C43×#417C2211yescharacteristic
59C43×#417C2211yescharacteristic, complemented
60C43×#417C2211yescharacteristic, complemented
61C2×#100×C43C2211yescharacteristic, complemented
62C2×#100×C43C2211yescharacteristic, complemented
63C43×#407C2211yescharacteristic, complemented
64C43×#391C2211yescharacteristic, complemented
65C43×#390C2211yescharacteristic, complemented
66C43×#388—22no—
67C43×#386—22no—
68C43×#382C2211yescharacteristic, complemented
69C43×#343C2211yescharacteristic, complemented
70C43×#343C2211yescharacteristic, complemented
71C43×#339C2211yescharacteristic, complemented
72C43×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C43—22no—
74H(5,𝔽2)×C43—22no—
75H(5,𝔽2)×C43—41no—
76H(5,𝔽2)×C43—41no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—22no—
82C2×#41×C43—22no—
83C2×#41×C43—41no—
84C2×#41×C43—41no—
85C2×#41×C43D411yescharacteristic
86C2×#41×C43D411yescharacteristic
87C2×#41×C43C2311yescharacteristic
88C2×#41×C43C2311yescharacteristic
89C2×#41×C43C2311yescharacteristic
90C22×Q8×C43D411yescharacteristic
91C22×Q8×C43C2311yescharacteristic
92C22×D4×C43—21no—
93C22×D4×C43—22no—
94C22×D4×C43—22no—
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43D411yescharacteristic
98C22×D4×C43D412yes—
99C22×D4×C43C2311yescharacteristic
100C23×C4×C43—21no—
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103#137×C43—22no—
104#137×C43—22no—
105#137×C43—22no—
106#137×C43—41no—
107#137×C43—41no—
108#137×C43—41no—
109C2×Q16×C43—21no—
110C2×Q16×C43—21no—
111C2×Q16×C43—21no—
112C2×SD16×C43—21no—
113C2×SD16×C43—21no—
114C2×SD16×C43—21no—
115C2×M16×C43—21no—
116C2×M16×C43—22no—
117C2×M16×C43—41no—
118C2×M16×C43C2311yescharacteristic
119C2×M16×C43C2311yescharacteristic
120C2×M16×C43C2311yescharacteristic
121C2×M16×C43C2311yescharacteristic
122C22×C8×C43—21no—
123#127×C43—22no—
124#127×C43—21no—
125#124×C43—22no—
126#124×C43—21no—
127#124×C43—22no—
128#124×C43—41no—
129#123×C43—22no—
130#123×C43—21no—
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43—21no—
137C22⋊Q8×C43—21no—
138C22⋊Q8×C43D411yescharacteristic
139C22⋊Q8×C43D411yescharacteristic
140#121×C43—22no—
141#121×C43—22no—
142#121×C43—22no—
143#121×C43—22no—
144#121×C43—22no—
145#121×C43—21no—
146#121×C43—21no—
147#121×C43—21no—
148#121×C43—21no—
149#121×C43—21no—
150#121×C43—21no—
151#121×C43—22no—
152#121×C43—21no—
153#121×C43—21no—
154#121×C43D411yescharacteristic
155#121×C43D411yescharacteristic
156#120×C43—22no—
157#120×C43—22no—
158#120×C43—22no—
159#120×C43—21no—
160#120×C43—22no—
161C4×Q8×C43—21no—
162C4×D4×C43—22no—
163C4×D4×C43—22no—
164C4×D4×C43—21no—
165C4×D4×C43—22no—
166C4×D4×C43—21no—
167C4×D4×C43—21no—
168#117×C43—21no—
169#117×C43C2311yescharacteristic
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—22no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—22no—
177C2×C22⋊C4×C43—22no—
178C2×C22⋊C4×C43D412yes—
179C2×C42×C43—22no—
180C2×C42×C43—21no—
181C2×C42×C43—41no—
182C2×C42×C43C2311yescharacteristic
183C2×C42×C43C2311yescharacteristic
184#107×C43—21no—
185#106×C43—21no—
186#104×C43—22no—
187#104×C43—22no—
188#104×C43—22no—
189#104×C43—22no—
190#104×C43—41no—
191#104×C43D414yescomplemented
192#103×C43—21no—
193#103×C43—21no—
194#103×C43—21no—
195#103×C43—21no—
196#103×C43—21no—
197#102×C43—21no—
198#102×C43—21no—
199#102×C43—21no—
200#100×C43—22no—
201#100×C43—41no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43—21no—
204#95×C43—22no—
205#95×C43—22no—
206C24×C43—22no—
207C24×C43—21no—
208C24×C43C2×D411yescharacteristic
209C24×C43C2×D412yes—
210#41×C43—21no—
211#41×C43—21no—
212#41×C43—22no—
213#41×C43—22no—
214#41×C43—21no—
215#41×C43—21no—
216#41×C43—21no—
217#41×C43—21no—
218#41×C43—21no—
219#41×C43—21no—
220#41×C43—21no—
221#41×C43—21no—
222#41×C43—42no—
223#41×C43—42no—
224#41×C43—41no—
225#41×C43—41no—
226#41×C43—42no—
227#41×C43—42no—
228#41×C43—42no—
229#41×C43—42no—
230#41×C43—42no—
231#41×C43—42no—
232#41×C43C2×D412yes—
233#41×C43#4112yes—
234C2×Q8×C43—21no—
235C2×Q8×C43—22no—
236C2×Q8×C43—21no—
237C2×Q8×C43—21no—
238C2×Q8×C43—21no—
239C2×Q8×C43—21no—
240C2×Q8×C43—21no—
241C2×Q8×C43—21no—
242C2×Q8×C43—41no—
243C2×Q8×C43C2×D411yescharacteristic
244C2×Q8×C43C2×D411yescharacteristic
245C2×Q8×C43C2×D411yescharacteristic
246C2×D4×C43—22no—
247C2×D4×C43—22no—
248C2×D4×C43—22no—
249C2×D4×C43—22no—
250C2×D4×C43—22no—
251C2×D4×C43—21no—
252C2×D4×C43—21no—
253C2×D4×C43—21no—
254C2×D4×C43—21no—
255C2×D4×C43—21no—
256C2×D4×C43—21no—
257C2×D4×C43—21no—
258C2×D4×C43—22no—
259C2×D4×C43—21no—
260C2×D4×C43—21no—
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—22no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—22no—
268C2×D4×C43—42no—
269C2×D4×C43—42no—
270C2×D4×C43—44no—
271C2×D4×C43—44no—
272C2×D4×C43—44no—
273C2×D4×C43—41no—
274C2×D4×C43—42no—
275C2×D4×C43—42no—
276C2×D4×C43—42no—
277C2×D4×C43—42no—
278C2×D4×C43—84no—
279C2×D4×C43C2×D411yescharacteristic
280C2×D4×C43C2×D411yescharacteristic
281C2×D4×C43C2×D411yescharacteristic
282C22×C4×C43—21no—
283C22×C4×C43—21no—
284C22×C4×C43—21no—
285C22×C4×C43—21no—
286C22×C4×C43—21no—
287C22×C4×C43—22no—
288C22×C4×C43—22no—
289C22×C4×C43—21no—
290C22×C4×C43—21no—
291C22×C4×C43—21no—
292C22×C4×C43—21no—
293C22×C4×C43—21no—
294C22×C4×C43—21no—
295C22×C4×C43—21no—
296C22×C4×C43—21no—
297C22×C4×C43—21no—
298C22×C4×C43—42no—
299C22×C4×C43—42no—
300C22×C4×C43—42no—
301C22×C4×C43—42no—
302C22×C4×C43—42no—
303C22×C4×C43C2×D411yescharacteristic
304C22×C4×C43C2×D411yescharacteristic
305C22×C4×C43C2×D411yescharacteristic
306C22×C4×C43C2×D411yescharacteristic
307C22×C4×C43C2×D411yescharacteristic
308C22×C4×C43C2×D412yes—
309C22×C4×C43C2411yescharacteristic
310Q16×C43—42no—
311Q16×C43—42no—
312Q16×C43—42no—
313SD16×C43—42no—
314SD16×C43—42no—
315SD16×C43—42no—
316M16×C43—21no—
317M16×C43—21no—
318M16×C43—21no—
319M16×C43—21no—
320M16×C43—21no—
321M16×C43—21no—
322M16×C43—21no—
323M16×C43—42no—
324M16×C43C2×D412yescomplemented
325C2×C8×C43—21no—
326C2×C8×C43—21no—
327C2×C8×C43—21no—
328C2×C8×C43—21no—
329C2×C8×C43—42no—
330C4⋊C4×C43—22no—
331C4⋊C4×C43—22no—
332C4⋊C4×C43—21no—
333C4⋊C4×C43—21no—
334C4⋊C4×C43—21no—
335C4⋊C4×C43—21no—
336C4⋊C4×C43—21no—
337C4⋊C4×C43—21no—
338C4⋊C4×C43—41no—
339C4⋊C4×C43—41no—
340C4⋊C4×C43C2×D411yescharacteristic
341C4⋊C4×C43C2×D411yescharacteristic
342C22⋊C4×C43—22no—
343C22⋊C4×C43—22no—
344C22⋊C4×C43—22no—
345C22⋊C4×C43—22no—
346C22⋊C4×C43—22no—
347C22⋊C4×C43—21no—
348C22⋊C4×C43—22no—
349C22⋊C4×C43—22no—
350C22⋊C4×C43—21no—
351C22⋊C4×C43—21no—
352C22⋊C4×C43—21no—
353C22⋊C4×C43—21no—
354C22⋊C4×C43—44no—
355C22⋊C4×C43—44no—
356C22⋊C4×C43—41no—
357C22⋊C4×C43—41no—
358C42×C43—22no—
359C42×C43—21no—
360C42×C43—21no—
361C42×C43—21no—
362C42×C43—21no—
363C42×C43—42no—
364C42×C43C2×D412yescomplemented
365C23×C43—21no—
366C23×C43—21no—
367C23×C43—21no—
368C23×C43—22no—
369C23×C43—22no—
370C23×C43—21no—
371C23×C43—21no—
372C23×C43—22no—
373C23×C43—22no—
374C23×C43—41no—
375C23×C43—42no—
376C23×C43—44no—
377C23×C43—42no—
378C23×C43—42no—
379C23×C43—42no—
380C23×C43—81no—
381C23×C43—82no—
382C23×C43—82no—
383C23×C43#12011yescharacteristic
384C23×C43#12011yescharacteristic
385C23×C43C22×D411yescharacteristic
386Q8×C43—21no—
387Q8×C43—21no—
388Q8×C43—21no—
389Q8×C43—21no—
390Q8×C43—21no—
391Q8×C43—42no—
392Q8×C43—41no—
393Q8×C43—41no—
394Q8×C43—41no—
395Q8×C43—41no—
396Q8×C43#12112yes—
397D4×C43—22no—
398D4×C43—22no—
399D4×C43—21no—
400D4×C43—21no—
401D4×C43—21no—
402D4×C43—21no—
403D4×C43—21no—
404D4×C43—42no—
405D4×C43—42no—
406D4×C43—44no—
407D4×C43—42no—
408D4×C43—44no—
409D4×C43—41no—
410D4×C43—41no—
411D4×C43—41no—
412D4×C43—41no—
413D4×C43—44no—
414D4×C43—42no—
415D4×C43—41no—
416D4×C43—41no—
417D4×C43—41no—
418D4×C43—41no—
419D4×C43—81no—
420D4×C43—82no—
421D4×C43—82no—
422D4×C43—82no—
423D4×C43—82no—
424D4×C43#12112yes—
425C2×C4×C43—21no—
426C2×C4×C43—21no—
427C2×C4×C43—21no—
428C2×C4×C43—21no—
429C2×C4×C43—21no—
430C2×C4×C43—21no—
431C2×C4×C43—21no—
432C2×C4×C43—21no—
433C2×C4×C43—21no—
434C2×C4×C43—22no—
435C2×C4×C43—21no—
436C2×C4×C43—21no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—21no—
440C2×C4×C43—22no—
441C2×C4×C43—21no—
442C2×C4×C43—21no—
443C2×C4×C43—21no—
444C2×C4×C43—22no—
445C2×C4×C43—42no—
446C2×C4×C43—42no—
447C2×C4×C43—42no—
448C2×C4×C43—44no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—48no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43—42no—
459C2×C4×C43—42no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—82no—
465C2×C4×C43#12011yescharacteristic
466C2×C4×C43#12011yescharacteristic
467C2×C4×C43C22×D411yescharacteristic
468C2×C4×C43C22×D411yescharacteristic
469C2×C4×C43C22×D411yescharacteristic
470C2×C4×C43C2×#4111yescharacteristic
471C2×C4×C43H(5,𝔽2)11yescharacteristic
472C2×C4×C43H(5,𝔽2)11yescharacteristic
473C8×C43—22no—
474C8×C43—41no—
475C8×C43—41no—
476C8×C43—41no—
477#24467C4311yesmaximal, characteristic, direct product factor, Sylow
478C22×C43—21no—
479C22×C43—21no—
480C22×C43—21no—
481C22×C43—21no—
482C22×C43—21no—
483C22×C43—22no—
484C22×C43—21no—
485C22×C43—21no—
486C22×C43—42no—
487C22×C43—42no—
488C22×C43—41no—
489C22×C43—41no—
490C22×C43—42no—
491C22×C43—41no—
492C22×C43—41no—
493C22×C43—41no—
494C22×C43—42no—
495C22×C43—41no—
496C22×C43—42no—
497C22×C43—41no—
498C22×C43—41no—
499C22×C43—84no—
500C22×C43—82no—
501C22×C43—82no—
502C22×C43—164no—
503C22×C43#45512yescomplemented
504C22×C43C2×#12011yescharacteristic
505C22×C43D4211yescharacteristic
506C22×C43#54611yescharacteristic
507C4×C43—21no—
508C4×C43—21no—
509C4×C43—22no—
510C4×C43—42no—
511C4×C43—42no—
512C4×C43—41no—
513C4×C43—41no—
514C4×C43—42no—
515C4×C43—41no—
516C4×C43—41no—
517C4×C43—81no—
518C4×C43—81no—
519C4×C43C2×#12111yescharacteristic
520C4×C43#53411yescharacteristic
521C4×C43D4211yescharacteristic
522C4×C43#54611yescharacteristic
523#3488C2×C4311yescharacteristic
524#3056C2×C4311yescharacteristic, complemented
525C2×#455C2×C4311yescharacteristic, complemented
526#3007C2×C4311yescharacteristic, complemented
527C22×#104C2×C4311yescharacteristic, complemented
528#2850C2×C4311yescharacteristic, complemented
529#2040C2×C4311yescharacteristic, complemented
530#2037C2×C4311yescharacteristic, complemented
531#2007C2×C4311yescharacteristic, complemented
532#2004C2×C4311yescharacteristic, complemented
533#1900C2×C4311yescharacteristic, complemented
534#1896C2×C4311yescharacteristic, complemented
535#1882C2×C4311yescharacteristic, complemented
536#1860C2×C4311yescharacteristic, complemented
537#1792C2×C4311yescharacteristic, complemented
538C2×C43—21no—
539C2×C43—21no—
540C2×C43—22no—
541C2×C43—41no—
542C2×C43—42no—
543C2×C43—81no—
544C2×C43—82no—
545C2×C43—81no—
546C2×C43#241011yescharacteristic
547C2×C43C2×#45511yescharacteristic
548C2×C43#301811yescharacteristic
549C2×H(5,𝔽2)C22×C4311yescharacteristic
550C22×#41C22×C4311yescharacteristic
551C2×#137C22×C4311yescharacteristic
552C2×#137C22×C4311yescharacteristic, complemented
553C2×#137C22×C4311yescharacteristic, complemented
554C22×M16C22×C4311yescharacteristic, complemented
555#550—21no—
556#548—21no—
557#546—21no—
558#546—22no—
559D42—22no—
560D42—21no—
561#537—21no—
562#537C22×C4311yescharacteristic
563#535—21no—
564#535C22×C4311yescharacteristic
565C2×#124C22×C4311yescharacteristic, complemented
566#525—21no—
567#525C22×C4311yescharacteristic
568C2×C22⋊Q8C22×C4311yescharacteristic, complemented
569C2×#121—21no—
570C2×#121C22×C4311yescharacteristic
571#520C22×C4311yescharacteristic
572C22×C42C22×C4311yescharacteristic, complemented
573#470—21no—
574#468—21no—
575#467—21no—
576#465—21no—
577#455—24no—
578#452—21no—
579#452—21no—
580#451—21no—
581#450—21no—
582#428C22×C4311yescharacteristic, complemented
583C2×#104—24no—
584C2×#104C22×C4311yescharacteristic
585C2×#104C22×C4311yescharacteristic
586C2×#104C22×C4311yescharacteristic, complemented
587C2×#104C22×C4311yescharacteristic, complemented
588C2×#104C22×C4311yescharacteristic, complemented
589C2×#104C22×C4311yescharacteristic, complemented
590#419C22×C4311yescharacteristic, complemented
591#417C22×C4311yescharacteristic
592#417C22×C4311yescharacteristic, complemented
593#417C22×C4311yescharacteristic, complemented
594C2×#100C22×C4311yescharacteristic, complemented
595C2×#100C22×C4311yescharacteristic, complemented
596#407C22×C4311yescharacteristic, complemented
597#391C22×C4311yescharacteristic, complemented
598#390C22×C4311yescharacteristic, complemented
599#388—22no—
600#386—22no—
601#382C22×C4311yescharacteristic, complemented
602#343C22×C4311yescharacteristic, complemented
603#343C22×C4311yescharacteristic, complemented
604#339C22×C4311yescharacteristic, complemented
605#339C22×C4311yescharacteristic, complemented
606C43#2446711yescharacteristic, direct product factor, Sylow
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C4311yescharacteristic
620C2×#41D4×C4311yescharacteristic
621C2×#41C23×C4311yescharacteristic
622C2×#41C23×C4311yescharacteristic
623C2×#41C23×C4311yescharacteristic
624C22×Q8D4×C4311yescharacteristic
625C22×Q8C23×C4311yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C4311yescharacteristic
632C22×D4D4×C4312yes—
633C22×D4C23×C4311yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C4311yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C4311yescharacteristic
653C2×M16C23×C4311yescharacteristic
654C2×M16C23×C4311yescharacteristic
655C2×M16C23×C4311yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C4311yescharacteristic
673C22⋊Q8D4×C4311yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C4311yescharacteristic
689#121D4×C4311yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C4311yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C4311yescharacteristic
707C2×C4⋊C4C23×C4311yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C4312yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C4311yescharacteristic
717C2×C42C23×C4311yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C4314yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C4311yescharacteristic
743C24C2×D4×C4312yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C4312yes—
767#41#41×C4312yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C4311yescharacteristic
778C2×Q8C2×D4×C4311yescharacteristic
779C2×Q8C2×D4×C4311yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C4311yescharacteristic
814C2×D4C2×D4×C4311yescharacteristic
815C2×D4C2×D4×C4311yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C4311yescharacteristic
838C22×C4C2×D4×C4311yescharacteristic
839C22×C4C2×D4×C4311yescharacteristic
840C22×C4C2×D4×C4311yescharacteristic
841C22×C4C2×D4×C4311yescharacteristic
842C22×C4C2×D4×C4312yes—
843C22×C4C24×C4311yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C4312yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C4311yescharacteristic
875C4⋊C4C2×D4×C4311yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C4312yescomplemented
899C23—21no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C4311yescharacteristic
918C23#120×C4311yescharacteristic
919C23C22×D4×C4311yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C4312yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—44no—
948D4—42no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C4312yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C4311yescharacteristic
1000C2×C4#120×C4311yescharacteristic
1001C2×C4C22×D4×C4311yescharacteristic
1002C2×C4C22×D4×C4311yescharacteristic
1003C2×C4C22×D4×C4311yescharacteristic
1004C2×C4C2×#41×C4311yescharacteristic
1005C2×C4H(5,𝔽2)×C4311yescharacteristic
1006C2×C4H(5,𝔽2)×C4311yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C43×#45512yescomplemented
1037C22C2×#120×C4311yescharacteristic
1038C22D42×C4311yescharacteristic
1039C22C43×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C4311yescharacteristic
1053C4C43×#53411yescharacteristic
1054C4D42×C4311yescharacteristic
1055C4C43×#54611yescharacteristic
1056C2—21no—
1057C2—21no—
1058C2—22no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C43×#241011yescharacteristic
1065C2C2×C43×#45511yescharacteristic
1066C2C43×#301811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3488C2
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
2. C43×#3056C2semidirect
3. C2×C43×#455C2semidirect
4. C43×#3007C2semidirect
5. C22×#104×C43C2semidirect
6. C43×#2850C2semidirect
7. C43×#2040C2semidirect
8. C43×#2037C2semidirect
9. C43×#2007C2semidirect
10. C43×#2004C2semidirect
11. C43×#1900C2semidirect
12. C43×#1896C2semidirect
13. C43×#1882C2semidirect
14. C43×#1860C2semidirect
15. C43×#1792C2semidirect
19. C2×#137×C43C22semidirect
20. C2×#137×C43C22semidirect
21. C22×M16×C43C22semidirect
32. C2×#124×C43C22semidirect
35. C2×C22⋊Q8×C43C22semidirect
39. C22×C42×C43C22semidirect
49. C43×#428C22semidirect
53. C2×#104×C43C22semidirect
54. C2×#104×C43C22semidirect
55. C2×#104×C43C22semidirect
56. C2×#104×C43C22semidirect
57. C43×#419C22semidirect
59. C43×#417C22semidirect
60. C43×#417C22semidirect
61. C2×#100×C43C22semidirect
62. C2×#100×C43C22semidirect
63. C43×#407C22semidirect
64. C43×#391C22semidirect
65. C43×#390C22semidirect
68. C43×#382C22semidirect
69. C43×#343C22semidirect
70. C43×#343C22semidirect
71. C43×#339C22semidirect
72. C43×#339C22semidirect
191. #104×C43D4semidirect
324. M16×C43C2×D4semidirect
364. C42×C43C2×D4semidirect
477. #24467C43direct (N × H)
503. C22×C43#455semidirect
524. #3056C2×C43semidirect
525. C2×#455C2×C43semidirect
526. #3007C2×C43semidirect
527. C22×#104C2×C43semidirect
528. #2850C2×C43semidirect
529. #2040C2×C43semidirect
530. #2037C2×C43semidirect
531. #2007C2×C43semidirect
532. #2004C2×C43semidirect
533. #1900C2×C43semidirect
534. #1896C2×C43semidirect
535. #1882C2×C43semidirect
536. #1860C2×C43semidirect
537. #1792C2×C43semidirect
552. C2×#137C22×C43semidirect
553. C2×#137C22×C43semidirect
554. C22×M16C22×C43semidirect
565. C2×#124C22×C43semidirect
568. C2×C22⋊Q8C22×C43semidirect
572. C22×C42C22×C43semidirect
582. #428C22×C43semidirect
586. C2×#104C22×C43semidirect
587. C2×#104C22×C43semidirect
588. C2×#104C22×C43semidirect
589. C2×#104C22×C43semidirect
590. #419C22×C43semidirect
592. #417C22×C43semidirect
593. #417C22×C43semidirect
594. C2×#100C22×C43semidirect
595. C2×#100C22×C43semidirect
596. #407C22×C43semidirect
597. #391C22×C43semidirect
598. #390C22×C43semidirect
601. #382C22×C43semidirect
602. #343C22×C43semidirect
603. #343C22×C43semidirect
604. #339C22×C43semidirect
605. #339C22×C43semidirect
606. C43#24467direct (N × H)
725. #104D4×C43semidirect
858. M16C2×D4×C43semidirect
898. C42C2×D4×C43semidirect
1036. C22C43×#455semidirect

Maximal subgroups

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

subgroupindex
C43×#34882
C43×#30562
C2×C43×#4552
C43×#30072
C22×#104×C432
C43×#28502
C43×#20402
C43×#20372
C43×#20072
C43×#20042
C43×#19002
C43×#18962
C43×#18822
C43×#18602
C43×#17922
#2446743