Finite Group Databasebeta

← C43×#24471 #24944488

Subgroups — C43×#24471 #24944488

Order 11008.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 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
5C2×C43×#421C211yesmaximal, characteristic, complemented
6C43×#2620C211yesmaximal, characteristic, complemented
7C43×#2039C211yesmaximal, characteristic, complemented
8C43×#2037C211yesmaximal, characteristic, complemented
9C43×#2007C211yesmaximal, characteristic, complemented
10C43×#2004C211yesmaximal, characteristic, complemented
11C43×#1900C211yesmaximal, characteristic, complemented
12C43×#1897C211yesmaximal, characteristic, complemented
13C43×#1882C211yesmaximal, characteristic, complemented
14C43×#1859C211yesmaximal, 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
39C2×#117×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
50C43×#421—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×#396—22no—
65C43×#394—22no—
66C43×#391C2211yescharacteristic, complemented
67C43×#390C2211yescharacteristic, complemented
68C43×#384C2211yescharacteristic, 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×C43C2311yescharacteristic
102#137×C43—22no—
103#137×C43—22no—
104#137×C43—22no—
105#137×C43—41no—
106#137×C43—41no—
107#137×C43—41no—
108C2×Q16×C43—21no—
109C2×Q16×C43—21no—
110C2×Q16×C43—21no—
111C2×SD16×C43—21no—
112C2×SD16×C43—21no—
113C2×SD16×C43—21no—
114C2×M16×C43—21no—
115C2×M16×C43—22no—
116C2×M16×C43—41no—
117C2×M16×C43C2311yescharacteristic
118C2×M16×C43C2311yescharacteristic
119C2×M16×C43C2311yescharacteristic
120C2×M16×C43C2311yescharacteristic
121C22×C8×C43—21no—
122#127×C43—22no—
123#127×C43—21no—
124#124×C43—22no—
125#124×C43—21no—
126#124×C43—22no—
127#124×C43—41no—
128#123×C43—22no—
129#123×C43—21no—
130C22⋊Q8×C43—22no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43—21no—
137C22⋊Q8×C43D411yescharacteristic
138C22⋊Q8×C43D411yescharacteristic
139#121×C43—22no—
140#121×C43—22no—
141#121×C43—22no—
142#121×C43—22no—
143#121×C43—22no—
144#121×C43—21no—
145#121×C43—21no—
146#121×C43—21no—
147#121×C43—21no—
148#121×C43—21no—
149#121×C43—21no—
150#121×C43—22no—
151#121×C43—21no—
152#121×C43—21no—
153#121×C43D411yescharacteristic
154#121×C43D411yescharacteristic
155#120×C43—22no—
156#120×C43—22no—
157#120×C43—22no—
158#120×C43—21no—
159#120×C43—22no—
160C4×Q8×C43—21no—
161C4×D4×C43—22no—
162C4×D4×C43—22no—
163C4×D4×C43—21no—
164C4×D4×C43—22no—
165C4×D4×C43—21no—
166C4×D4×C43—21no—
167#117×C43—21no—
168#117×C43—22no—
169#117×C43—41no—
170#117×C43C2311yescharacteristic
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—22no—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—22no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—22no—
181C2×C22⋊C4×C43—22no—
182C2×C22⋊C4×C43D412yes—
183C2×C42×C43C2311yescharacteristic
184C2×C42×C43C2311yescharacteristic
185#107×C43—21no—
186#106×C43—21no—
187#104×C43—22no—
188#104×C43—22no—
189#104×C43—22no—
190#104×C43—22no—
191#104×C43—41no—
192#104×C43D414yescomplemented
193#103×C43—21no—
194#103×C43—21no—
195#103×C43—21no—
196#103×C43—21no—
197#103×C43—21no—
198#102×C43—21no—
199#102×C43—21no—
200#102×C43—21no—
201#100×C43—22no—
202#100×C43—41no—
203C22⋊C8×C43—21no—
204C22⋊C8×C43—21no—
205#95×C43—22no—
206C24×C43—22no—
207C24×C43—21no—
208C24×C43C2×D412yes—
209C24×C43C2×D411yescharacteristic
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—41no—
273C2×D4×C43—42no—
274C2×D4×C43—42no—
275C2×D4×C43—42no—
276C2×D4×C43—42no—
277C2×D4×C43—82no—
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×C43C2×D411yescharacteristic
301C22×C4×C43C2×D411yescharacteristic
302C22×C4×C43C2×D411yescharacteristic
303C22×C4×C43C2×D411yescharacteristic
304C22×C4×C43C2×D411yescharacteristic
305C22×C4×C43C2×D412yes—
306C22×C4×C43C2411yescharacteristic
307Q16×C43—42no—
308Q16×C43—42no—
309Q16×C43—42no—
310SD16×C43—42no—
311SD16×C43—42no—
312SD16×C43—42no—
313M16×C43—21no—
314M16×C43—21no—
315M16×C43—21no—
316M16×C43—21no—
317M16×C43—21no—
318M16×C43—21no—
319M16×C43—21no—
320M16×C43—42no—
321M16×C43C2×D412yescomplemented
322C2×C8×C43—21no—
323C2×C8×C43—21no—
324C2×C8×C43—21no—
325C2×C8×C43—21no—
326C2×C8×C43—42no—
327C4⋊C4×C43—22no—
328C4⋊C4×C43—22no—
329C4⋊C4×C43—21no—
330C4⋊C4×C43—21no—
331C4⋊C4×C43—21no—
332C4⋊C4×C43—21no—
333C4⋊C4×C43—21no—
334C4⋊C4×C43—21no—
335C4⋊C4×C43—42no—
336C4⋊C4×C43—41no—
337C4⋊C4×C43—41no—
338C4⋊C4×C43—82no—
339C4⋊C4×C43C2×D411yescharacteristic
340C4⋊C4×C43C2×D411yescharacteristic
341C22⋊C4×C43—22no—
342C22⋊C4×C43—22no—
343C22⋊C4×C43—22no—
344C22⋊C4×C43—22no—
345C22⋊C4×C43—22no—
346C22⋊C4×C43—21no—
347C22⋊C4×C43—22no—
348C22⋊C4×C43—22no—
349C22⋊C4×C43—21no—
350C22⋊C4×C43—21no—
351C22⋊C4×C43—21no—
352C22⋊C4×C43—21no—
353C22⋊C4×C43—42no—
354C22⋊C4×C43—44no—
355C22⋊C4×C43—41no—
356C22⋊C4×C43—41no—
357C22⋊C4×C43—82no—
358C42×C43—22no—
359C42×C43—21no—
360C42×C43—21no—
361C42×C43—21no—
362C42×C43—21no—
363C42×C43C2×D412yescomplemented
364C23×C43—21no—
365C23×C43—21no—
366C23×C43—21no—
367C23×C43—22no—
368C23×C43—21no—
369C23×C43—21no—
370C23×C43—22no—
371C23×C43—22no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43—42no—
375C23×C43—42no—
376C23×C43—44no—
377C23×C43—42no—
378C23×C43—42no—
379C23×C43—81no—
380C23×C43—82no—
381C23×C43—82no—
382C23×C43#12011yescharacteristic
383C23×C43#12011yescharacteristic
384C23×C43C22×D411yescharacteristic
385Q8×C43—21no—
386Q8×C43—21no—
387Q8×C43—21no—
388Q8×C43—21no—
389Q8×C43—21no—
390Q8×C43—42no—
391Q8×C43—41no—
392Q8×C43—41no—
393Q8×C43—41no—
394Q8×C43—41no—
395Q8×C43#12112yes—
396D4×C43—22no—
397D4×C43—22no—
398D4×C43—21no—
399D4×C43—21no—
400D4×C43—21no—
401D4×C43—21no—
402D4×C43—21no—
403D4×C43—42no—
404D4×C43—42no—
405D4×C43—44no—
406D4×C43—42no—
407D4×C43—44no—
408D4×C43—44no—
409D4×C43—42no—
410D4×C43—41no—
411D4×C43—41no—
412D4×C43—41no—
413D4×C43—41no—
414D4×C43—41no—
415D4×C43—41no—
416D4×C43—41no—
417D4×C43—41no—
418D4×C43—81no—
419D4×C43—82no—
420D4×C43—82no—
421D4×C43—82no—
422D4×C43—82no—
423D4×C43#12112yes—
424C2×C4×C43—21no—
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—22no—
434C2×C4×C43—21no—
435C2×C4×C43—21no—
436C2×C4×C43—22no—
437C2×C4×C43—21no—
438C2×C4×C43—22no—
439C2×C4×C43—21no—
440C2×C4×C43—21no—
441C2×C4×C43—21no—
442C2×C4×C43—22no—
443C2×C4×C43—42no—
444C2×C4×C43—42no—
445C2×C4×C43—42no—
446C2×C4×C43—44no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—42no—
454C2×C4×C43—41no—
455C2×C4×C43—42no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—82no—
463C2×C4×C43#12011yescharacteristic
464C2×C4×C43#12011yescharacteristic
465C2×C4×C43C22×D411yescharacteristic
466C2×C4×C43C22×D411yescharacteristic
467C2×C4×C43C22×D411yescharacteristic
468C2×C4×C43C2×#4111yescharacteristic
469C2×C4×C43H(5,𝔽2)11yescharacteristic
470C2×C4×C43H(5,𝔽2)11yescharacteristic
471C8×C43—22no—
472C8×C43—41no—
473C8×C43—41no—
474C8×C43—41no—
475#24471C4311yesmaximal, characteristic, direct product factor, Sylow
476C22×C43—21no—
477C22×C43—21no—
478C22×C43—21no—
479C22×C43—21no—
480C22×C43—22no—
481C22×C43—21no—
482C22×C43—21no—
483C22×C43—21no—
484C22×C43—21no—
485C22×C43—41no—
486C22×C43—41no—
487C22×C43—42no—
488C22×C43—41no—
489C22×C43—41no—
490C22×C43—41no—
491C22×C43—42no—
492C22×C43—41no—
493C22×C43—42no—
494C22×C43—41no—
495C22×C43—41no—
496C22×C43—81no—
497C22×C43—81no—
498C22×C43—82no—
499C22×C43—82no—
500C22×C43—84no—
501C22×C43—164no—
502C22×C43C2×#12011yescharacteristic
503C22×C43D4211yescharacteristic
504C22×C43#54611yescharacteristic
505C4×C43—21no—
506C4×C43—21no—
507C4×C43—22no—
508C4×C43—42no—
509C4×C43—41no—
510C4×C43—41no—
511C4×C43—42no—
512C4×C43—41no—
513C4×C43—41no—
514C4×C43—81no—
515C4×C43—81no—
516C4×C43—81no—
517C4×C43C2×#12111yescharacteristic
518C4×C43#53411yescharacteristic
519C4×C43D4211yescharacteristic
520C4×C43#54611yescharacteristic
521#3488C2×C4311yescharacteristic
522#3056C2×C4311yescharacteristic, complemented
523C2×#455C2×C4311yescharacteristic, complemented
524#3007C2×C4311yescharacteristic, complemented
525C2×#421C2×C4311yescharacteristic, complemented
526#2620C2×C4311yescharacteristic, complemented
527#2039C2×C4311yescharacteristic, complemented
528#2037C2×C4311yescharacteristic, complemented
529#2007C2×C4311yescharacteristic, complemented
530#2004C2×C4311yescharacteristic, complemented
531#1900C2×C4311yescharacteristic, complemented
532#1897C2×C4311yescharacteristic, complemented
533#1882C2×C4311yescharacteristic, complemented
534#1859C2×C4311yescharacteristic, complemented
535#1792C2×C4311yescharacteristic, complemented
536C2×C43—21no—
537C2×C43—21no—
538C2×C43—41no—
539C2×C43—41no—
540C2×C43—42no—
541C2×C43—81no—
542C2×C43—82no—
543C2×C43—81no—
544C2×C43#241011yescharacteristic
545C2×C43#301911yescharacteristic
546C2×C43#302211yescharacteristic
547C2×H(5,𝔽2)C22×C4311yescharacteristic
548C22×#41C22×C4311yescharacteristic
549C2×#137C22×C4311yescharacteristic
550C2×#137C22×C4311yescharacteristic, complemented
551C2×#137C22×C4311yescharacteristic, complemented
552C22×M16C22×C4311yescharacteristic, complemented
553#550—21no—
554#548—21no—
555#546—21no—
556#546—22no—
557D42—22no—
558D42—21no—
559#537—21no—
560#537C22×C4311yescharacteristic
561#535—21no—
562#535C22×C4311yescharacteristic
563C2×#124C22×C4311yescharacteristic, complemented
564#525—21no—
565#525C22×C4311yescharacteristic
566C2×C22⋊Q8C22×C4311yescharacteristic, complemented
567C2×#121—21no—
568C2×#121C22×C4311yescharacteristic
569#520C22×C4311yescharacteristic
570C2×#117C22×C4311yescharacteristic, complemented
571#470—21no—
572#468—21no—
573#467—21no—
574#465—21no—
575#455—24no—
576#452—21no—
577#452—21no—
578#451—21no—
579#450—21no—
580#428C22×C4311yescharacteristic, complemented
581#421—24no—
582C2×#104C22×C4311yescharacteristic
583C2×#104C22×C4311yescharacteristic
584C2×#104C22×C4311yescharacteristic, complemented
585C2×#104C22×C4311yescharacteristic, complemented
586C2×#104C22×C4311yescharacteristic, complemented
587C2×#104C22×C4311yescharacteristic, complemented
588#419C22×C4311yescharacteristic, complemented
589#417C22×C4311yescharacteristic
590#417C22×C4311yescharacteristic, complemented
591#417C22×C4311yescharacteristic, complemented
592C2×#100C22×C4311yescharacteristic, complemented
593C2×#100C22×C4311yescharacteristic, complemented
594#407C22×C4311yescharacteristic, complemented
595#396—22no—
596#394—22no—
597#391C22×C4311yescharacteristic, complemented
598#390C22×C4311yescharacteristic, complemented
599#384C22×C4311yescharacteristic, complemented
600#343C22×C4311yescharacteristic, complemented
601#343C22×C4311yescharacteristic, complemented
602#339C22×C4311yescharacteristic, complemented
603#339C22×C4311yescharacteristic, complemented
604C43#2447111yescharacteristic, direct product factor, Sylow
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C4311yescharacteristic
618C2×#41D4×C4311yescharacteristic
619C2×#41C23×C4311yescharacteristic
620C2×#41C23×C4311yescharacteristic
621C2×#41C23×C4311yescharacteristic
622C22×Q8D4×C4311yescharacteristic
623C22×Q8C23×C4311yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C4311yescharacteristic
630C22×D4D4×C4312yes—
631C22×D4C23×C4311yescharacteristic
632C23×C4—21no—
633C23×C4C23×C4311yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C4311yescharacteristic
650C2×M16C23×C4311yescharacteristic
651C2×M16C23×C4311yescharacteristic
652C2×M16C23×C4311yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C4311yescharacteristic
670C22⋊Q8D4×C4311yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C4311yescharacteristic
686#121D4×C4311yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C4311yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C4311yescharacteristic
708C2×C4⋊C4C23×C4311yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C4312yes—
715C2×C42C23×C4311yescharacteristic
716C2×C42C23×C4311yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C4314yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C4312yes—
741C24C2×D4×C4311yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C4312yes—
765#41#41×C4312yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C4311yescharacteristic
776C2×Q8C2×D4×C4311yescharacteristic
777C2×Q8C2×D4×C4311yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C4311yescharacteristic
812C2×D4C2×D4×C4311yescharacteristic
813C2×D4C2×D4×C4311yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C4311yescharacteristic
833C22×C4C2×D4×C4311yescharacteristic
834C22×C4C2×D4×C4311yescharacteristic
835C22×C4C2×D4×C4311yescharacteristic
836C22×C4C2×D4×C4311yescharacteristic
837C22×C4C2×D4×C4312yes—
838C22×C4C24×C4311yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C4312yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C4311yescharacteristic
872C4⋊C4C2×D4×C4311yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C4312yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C4311yescharacteristic
915C23#120×C4311yescharacteristic
916C23C22×D4×C4311yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C4312yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C4312yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C4311yescharacteristic
996C2×C4#120×C4311yescharacteristic
997C2×C4C22×D4×C4311yescharacteristic
998C2×C4C22×D4×C4311yescharacteristic
999C2×C4C22×D4×C4311yescharacteristic
1000C2×C4C2×#41×C4311yescharacteristic
1001C2×C4H(5,𝔽2)×C4311yescharacteristic
1002C2×C4H(5,𝔽2)×C4311yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C4311yescharacteristic
1034C22D42×C4311yescharacteristic
1035C22C43×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C4311yescharacteristic
1049C4C43×#53411yescharacteristic
1050C4D42×C4311yescharacteristic
1051C4C43×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C43×#241011yescharacteristic
1061C2C43×#301911yescharacteristic
1062C2C43×#302211yescharacteristic
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. C2×C43×#421C2semidirect
6. C43×#2620C2semidirect
7. C43×#2039C2semidirect
8. C43×#2037C2semidirect
9. C43×#2007C2semidirect
10. C43×#2004C2semidirect
11. C43×#1900C2semidirect
12. C43×#1897C2semidirect
13. C43×#1882C2semidirect
14. C43×#1859C2semidirect
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. C2×#117×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
66. C43×#391C22semidirect
67. C43×#390C22semidirect
68. C43×#384C22semidirect
69. C43×#343C22semidirect
70. C43×#343C22semidirect
71. C43×#339C22semidirect
72. C43×#339C22semidirect
192. #104×C43D4semidirect
321. M16×C43C2×D4semidirect
363. C42×C43C2×D4semidirect
475. #24471C43direct (N × H)
522. #3056C2×C43semidirect
523. C2×#455C2×C43semidirect
524. #3007C2×C43semidirect
525. C2×#421C2×C43semidirect
526. #2620C2×C43semidirect
527. #2039C2×C43semidirect
528. #2037C2×C43semidirect
529. #2007C2×C43semidirect
530. #2004C2×C43semidirect
531. #1900C2×C43semidirect
532. #1897C2×C43semidirect
533. #1882C2×C43semidirect
534. #1859C2×C43semidirect
535. #1792C2×C43semidirect
550. C2×#137C22×C43semidirect
551. C2×#137C22×C43semidirect
552. C22×M16C22×C43semidirect
563. C2×#124C22×C43semidirect
566. C2×C22⋊Q8C22×C43semidirect
570. C2×#117C22×C43semidirect
580. #428C22×C43semidirect
584. C2×#104C22×C43semidirect
585. C2×#104C22×C43semidirect
586. C2×#104C22×C43semidirect
587. C2×#104C22×C43semidirect
588. #419C22×C43semidirect
590. #417C22×C43semidirect
591. #417C22×C43semidirect
592. C2×#100C22×C43semidirect
593. C2×#100C22×C43semidirect
594. #407C22×C43semidirect
597. #391C22×C43semidirect
598. #390C22×C43semidirect
599. #384C22×C43semidirect
600. #343C22×C43semidirect
601. #343C22×C43semidirect
602. #339C22×C43semidirect
603. #339C22×C43semidirect
604. C43#24471direct (N × H)
724. #104D4×C43semidirect
853. M16C2×D4×C43semidirect
895. C42C2×D4×C43semidirect

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
C2×C43×#4212
C43×#26202
C43×#20392
C43×#20372
C43×#20072
C43×#20042
C43×#19002
C43×#18972
C43×#18822
C43×#18592
C43×#17922
#2447143