Finite Group Databasebeta

← C43×#22889 #24942906

Subgroups — C43×#22889 #24942906

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3002C211yesmaximal, characteristic
2C2×C43×#443C211yesmaximal, characteristic, complemented
3C43×#2933C211yesmaximal, characteristic, complemented
4C2×C43×#421C211yesmaximal, characteristic, complemented
5C43×#2880C211yesmaximal, characteristic, complemented
6C43×#1975C211yesmaximal, characteristic, complemented
7C43×#1937C211yesmaximal, characteristic, complemented
8C43×#1929C211yesmaximal, characteristic, complemented
9C43×#1897C211yesmaximal, characteristic, complemented
10C43×#1876C211yesmaximal, characteristic, complemented
11C43×#1876C211yesmaximal, characteristic, complemented
12C43×#1866C211yesmaximal, characteristic, complemented
13C43×#1855C211yesmaximal, characteristic, complemented
14C43×#1765C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C2×#135×C43C2211yescharacteristic
18C2×#135×C43C2211yescharacteristic
19C2×#131×C43C2211yescharacteristic
20C2×#131×C43C2211yescharacteristic
21C2×#131×C43C2211yescharacteristic, complemented
22C22×M16×C43C2211yescharacteristic
23C43×#525C2211yescharacteristic
24C2×#117×C43C2211yescharacteristic
25C43×#452C411yescharacteristic, complemented
26C43×#452C411yescharacteristic, complemented
27C43×#451C411yescharacteristic, complemented
28C43×#450C411yescharacteristic, complemented
29C43×#449C411yescharacteristic, complemented
30C43×#449C411yescharacteristic, complemented
31C43×#448C411yescharacteristic, complemented
32C43×#447C411yescharacteristic, complemented
33C43×#443—24no—
34C43×#436—21no—
35C43×#435—21no—
36C43×#435—21no—
37C8×D4×C43—21no—
38C2×#108×C43C2211yescharacteristic, complemented
39C2×#108×C43C2211yescharacteristic, complemented
40C43×#424C2211yescharacteristic, complemented
41C43×#421—24no—
42C2×#104×C43C2211yescharacteristic
43C2×#104×C43C2211yescharacteristic
44C2×#104×C43C2211yescharacteristic
45C2×#104×C43C2211yescharacteristic
46C2×#104×C43C2211yescharacteristic, complemented
47C2×#104×C43C2211yescharacteristic, complemented
48C43×#416C2211yescharacteristic
49C43×#416C2211yescharacteristic
50C43×#408—21no—
51C43×#408—21no—
52C43×#408C2211yescharacteristic
53C43×#408C2211yescharacteristic
54C43×#408C2211yescharacteristic, complemented
55C43×#407—21no—
56C43×#407C2211yescharacteristic
57C2×C22⋊C8×C43—21no—
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C43×#405C2211yescharacteristic, complemented
61C2×#97×C43C2211yescharacteristic, complemented
62C2×C4×C8×C43C2211yescharacteristic, complemented
63C43×#341C2211yescharacteristic, complemented
64C43×#341C2211yescharacteristic, complemented
65C43×#339C2211yescharacteristic, complemented
66C43×#339C2211yescharacteristic, complemented
67C43×#336C2211yescharacteristic, complemented
68C43×#336C2211yescharacteristic, complemented
69C2×#41×C43—21no—
70C2×#41×C43—21no—
71C2×#41×C43—22no—
72C2×#41×C43—22no—
73C2×#41×C43—41no—
74C2×#41×C43—41no—
75C2×#41×C43C2×C411yescharacteristic
76C2×#41×C43C2×C411yescharacteristic
77C2×#41×C43C2311yescharacteristic
78C2×#41×C43C2311yescharacteristic
79C2×#41×C43C2311yescharacteristic
80C22×Q8×C43C2×C411yescharacteristic
81C22×D4×C43—21no—
82C22×D4×C43C2×C411yescharacteristic
83C23×C4×C43—21no—
84C23×C4×C43C2311yescharacteristic
85#135×C43—22no—
86#135×C43—22no—
87#135×C43—41no—
88#135×C43—41no—
89C2×Q16×C43C2×C411yescharacteristic
90C2×Q16×C43C2×C411yescharacteristic
91C2×SD16×C43C2×C411yescharacteristic
92C2×SD16×C43C2×C411yescharacteristic
93C2×SD16×C43C2×C411yescharacteristic
94C2×SD16×C43C2×C411yescharacteristic
95C2×D8×C43C2×C411yescharacteristic
96C2×D8×C43C2×C411yescharacteristic
97#131×C43—22no—
98#131×C43—22no—
99#131×C43—22no—
100#131×C43—41no—
101#131×C43—41no—
102#131×C43—41no—
103C2×M16×C43—21no—
104C2×M16×C43—21no—
105C2×M16×C43—21no—
106C2×M16×C43—21no—
107C2×M16×C43—22no—
108C2×M16×C43—41no—
109C2×M16×C43C2311yescharacteristic
110C2×M16×C43C2311yescharacteristic
111C2×M16×C43C2311yescharacteristic
112C2×M16×C43C2311yescharacteristic
113C22×C8×C43—21no—
114C22×C8×C43—21no—
115C22×C8×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121#123×C43—21no—
122C22⋊Q8×C43C2×C411yescharacteristic
123C22⋊Q8×C43C2×C411yescharacteristic
124#121×C43C2×C411yescharacteristic
125#121×C43C2×C411yescharacteristic
126#120×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129#117×C43—22no—
130#117×C43—41no—
131#117×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#108×C43—22no—
137#108×C43—41no—
138C4⋊C8×C43—21no—
139C4⋊C8×C43—21no—
140#104×C43—22no—
141#104×C43—22no—
142#104×C43—22no—
143#104×C43—22no—
144#104×C43—41no—
145#104×C43D414yescomplemented
146#103×C43C2×C411yescharacteristic
147#103×C43C2×C411yescharacteristic
148#103×C43C2×C411yescharacteristic
149#103×C43C2×C411yescharacteristic
150#102×C43C2×C411yescharacteristic
151#102×C43C2×C411yescharacteristic
152#102×C43C2×C411yescharacteristic
153#102×C43C2×C411yescharacteristic
154C22⋊C8×C43—21no—
155C22⋊C8×C43—21no—
156C22⋊C8×C43—21no—
157C22⋊C8×C43—21no—
158C22⋊C8×C43—21no—
159C22⋊C8×C43—21no—
160C22⋊C8×C43—21no—
161C22⋊C8×C43—21no—
162C22⋊C8×C43C2×C411yescharacteristic
163C22⋊C8×C43C2×C411yescharacteristic
164C22⋊C8×C43C2×C411yescharacteristic
165C22⋊C8×C43C2×C411yescharacteristic
166C22⋊C8×C43D411yescharacteristic
167C22⋊C8×C43D411yescharacteristic
168C22⋊C8×C43D411yescharacteristic
169C22⋊C8×C43D411yescharacteristic
170#97×C43—21no—
171#97×C43—41no—
172C4×C8×C43—21no—
173C4×C8×C43—22no—
174C24×C43—21no—
175C24×C43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—22no—
179#41×C43—22no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184#41×C43—21no—
185#41×C43—21no—
186#41×C43—21no—
187#41×C43—21no—
188#41×C43—42no—
189#41×C43—42no—
190#41×C43—41no—
191#41×C43—41no—
192#41×C43—42no—
193#41×C43—42no—
194#41×C43C2×D412yes—
195#41×C43#4112yes—
196C2×Q8×C43—21no—
197C2×Q8×C43—22no—
198C2×Q8×C43—41no—
199C2×Q8×C43C22×C411yescharacteristic
200C2×Q8×C43C22×C411yescharacteristic
201C2×Q8×C43C22×C411yescharacteristic
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—22no—
211C2×D4×C43—42no—
212C2×D4×C43—42no—
213C2×D4×C43—41no—
214C2×D4×C43C22×C411yescharacteristic
215C2×D4×C43C22×C411yescharacteristic
216C2×D4×C43C22×C411yescharacteristic
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—42no—
230C22×C4×C43—42no—
231C22×C4×C43C22×C411yescharacteristic
232C22×C4×C43C22×C411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43#4111yescharacteristic
236C22×C4×C43C2411yescharacteristic
237Q16×C43—22no—
238Q16×C43—41no—
239SD16×C43—22no—
240SD16×C43—22no—
241SD16×C43—41no—
242SD16×C43—41no—
243D8×C43—22no—
244D8×C43—41no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43—21no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43—21no—
252M16×C43—42no—
253M16×C43—42no—
254M16×C43—42no—
255M16×C43—42no—
256M16×C43C2×D412yes—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—42no—
270C2×C8×C43—42no—
271C2×C8×C43—42no—
272C2×C8×C43—42no—
273C2×C8×C43C22×C411yescharacteristic
274C2×C8×C43C22×C411yescharacteristic
275C2×C8×C43C22×C411yescharacteristic
276C2×C8×C43C22×C411yescharacteristic
277C2×C8×C43C2×D411yescharacteristic
278C2×C8×C43C2×D411yescharacteristic
279C2×C8×C43C2×D411yescharacteristic
280C2×C8×C43C2×D411yescharacteristic
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—42no—
284C4⋊C4×C43C22×C411yescharacteristic
285C4⋊C4×C43C22×C411yescharacteristic
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—42no—
292C42×C43—21no—
293C42×C43—21no—
294C42×C43—21no—
295C42×C43—21no—
296C42×C43C2×D412yes—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—42no—
305C23×C43—42no—
306C23×C43—81no—
307C23×C43C4×D411yescharacteristic
308C23×C43C4×D411yescharacteristic
309C23×C43C2×#4111yescharacteristic
310Q8×C43—21no—
311Q8×C43—21no—
312Q8×C43—21no—
313Q8×C43—21no—
314Q8×C43—21no—
315Q8×C43—42no—
316Q8×C43C4×D412yes—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—21no—
320D4×C43—21no—
321D4×C43—21no—
322D4×C43—21no—
323D4×C43—21no—
324D4×C43—42no—
325D4×C43—42no—
326D4×C43—42no—
327D4×C43—42no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—41no—
332D4×C43—81no—
333D4×C43C4×D412yes—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—22no—
343C2×C4×C43—21no—
344C2×C4×C43—22no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—22no—
352C2×C4×C43—42no—
353C2×C4×C43—42no—
354C2×C4×C43—42no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43C4×D411yescharacteristic
365C2×C4×C43C4×D411yescharacteristic
366C2×C4×C43C23×C411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C2×#4111yescharacteristic
370C2×C4×C43H(5,𝔽2)11yescharacteristic
371C2×C4×C43H(5,𝔽2)11yescharacteristic
372C8×C43—21no—
373C8×C43—21no—
374C8×C43—21no—
375C8×C43—21no—
376C8×C43—21no—
377C8×C43—21no—
378C8×C43—22no—
379C8×C43—21no—
380C8×C43—21no—
381C8×C43—41no—
382C8×C43—41no—
383C8×C43—41no—
384#22889C4311yesmaximal, characteristic, direct product factor, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—22no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—84no—
405C22×C43C2×C4×D411yescharacteristic
406C22×C43#54611yescharacteristic
407C22×C43#55111yescharacteristic
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—22no—
411C4×C43—42no—
412C4×C43—41no—
413C4×C43—41no—
414C4×C43—41no—
415C4×C43—41no—
416C4×C43—81no—
417C4×C43C2×C4×D411yescharacteristic
418C4×C43#51811yescharacteristic
419C4×C43D4211yescharacteristic
420C4×C43#54611yescharacteristic
421#3002C2×C4311yescharacteristic
422C2×#443C2×C4311yescharacteristic, complemented
423#2933C2×C4311yescharacteristic, complemented
424C2×#421C2×C4311yescharacteristic, complemented
425#2880C2×C4311yescharacteristic, complemented
426#1975C2×C4311yescharacteristic, complemented
427#1937C2×C4311yescharacteristic, complemented
428#1929C2×C4311yescharacteristic, complemented
429#1897C2×C4311yescharacteristic, complemented
430#1876C2×C4311yescharacteristic, complemented
431#1876C2×C4311yescharacteristic, complemented
432#1866C2×C4311yescharacteristic, complemented
433#1855C2×C4311yescharacteristic, complemented
434#1765C2×C4311yescharacteristic, complemented
435#1750C2×C4311yescharacteristic, complemented
436C2×C43—21no—
437C2×C43—21no—
438C2×C43—41no—
439C2×C43—41no—
440C2×C43—42no—
441C2×C43—81no—
442C2×C43—81no—
443C2×C43#235811yescharacteristic
444C2×C43#295511yescharacteristic
445C2×C43#295711yescharacteristic
446C22×#41C22×C4311yescharacteristic
447C2×#135C22×C4311yescharacteristic
448C2×#135C22×C4311yescharacteristic
449C2×#131C22×C4311yescharacteristic
450C2×#131C22×C4311yescharacteristic
451C2×#131C22×C4311yescharacteristic, complemented
452C22×M16C22×C4311yescharacteristic
453#525C22×C4311yescharacteristic
454C2×#117C22×C4311yescharacteristic
455#452C4×C4311yescharacteristic, complemented
456#452C4×C4311yescharacteristic, complemented
457#451C4×C4311yescharacteristic, complemented
458#450C4×C4311yescharacteristic, complemented
459#449C4×C4311yescharacteristic, complemented
460#449C4×C4311yescharacteristic, complemented
461#448C4×C4311yescharacteristic, complemented
462#447C4×C4311yescharacteristic, complemented
463#443—24no—
464#436—21no—
465#435—21no—
466#435—21no—
467C8×D4—21no—
468C2×#108C22×C4311yescharacteristic, complemented
469C2×#108C22×C4311yescharacteristic, complemented
470#424C22×C4311yescharacteristic, complemented
471#421—24no—
472C2×#104C22×C4311yescharacteristic
473C2×#104C22×C4311yescharacteristic
474C2×#104C22×C4311yescharacteristic
475C2×#104C22×C4311yescharacteristic
476C2×#104C22×C4311yescharacteristic, complemented
477C2×#104C22×C4311yescharacteristic, complemented
478#416C22×C4311yescharacteristic
479#416C22×C4311yescharacteristic
480#408—21no—
481#408—21no—
482#408C22×C4311yescharacteristic
483#408C22×C4311yescharacteristic
484#408C22×C4311yescharacteristic, complemented
485#407—21no—
486#407C22×C4311yescharacteristic
487C2×C22⋊C8—21no—
488C2×C22⋊C8C22×C4311yescharacteristic
489C2×C22⋊C8C22×C4311yescharacteristic
490#405C22×C4311yescharacteristic, complemented
491C2×#97C22×C4311yescharacteristic, complemented
492C2×C4×C8C22×C4311yescharacteristic, complemented
493#341C22×C4311yescharacteristic, complemented
494#341C22×C4311yescharacteristic, complemented
495#339C22×C4311yescharacteristic, complemented
496#339C22×C4311yescharacteristic, complemented
497#336C22×C4311yescharacteristic, complemented
498#336C22×C4311yescharacteristic, complemented
499C43#2288911yescharacteristic, direct product factor, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C4311yescharacteristic
507C2×#41C2×C4×C4311yescharacteristic
508C2×#41C23×C4311yescharacteristic
509C2×#41C23×C4311yescharacteristic
510C2×#41C23×C4311yescharacteristic
511C22×Q8C2×C4×C4311yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C4311yescharacteristic
514C23×C4—21no—
515C23×C4C23×C4311yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C4311yescharacteristic
521C2×Q16C2×C4×C4311yescharacteristic
522C2×SD16C2×C4×C4311yescharacteristic
523C2×SD16C2×C4×C4311yescharacteristic
524C2×SD16C2×C4×C4311yescharacteristic
525C2×SD16C2×C4×C4311yescharacteristic
526C2×D8C2×C4×C4311yescharacteristic
527C2×D8C2×C4×C4311yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C4311yescharacteristic
541C2×M16C23×C4311yescharacteristic
542C2×M16C23×C4311yescharacteristic
543C2×M16C23×C4311yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C4311yescharacteristic
549C22×C8C23×C4311yescharacteristic
550C22×C8C23×C4311yescharacteristic
551C22×C8C23×C4311yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C4311yescharacteristic
554C22⋊Q8C2×C4×C4311yescharacteristic
555#121C2×C4×C4311yescharacteristic
556#121C2×C4×C4311yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C4311yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C4311yescharacteristic
566C2×C42C23×C4311yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C4314yescomplemented
577#103C2×C4×C4311yescharacteristic
578#103C2×C4×C4311yescharacteristic
579#103C2×C4×C4311yescharacteristic
580#103C2×C4×C4311yescharacteristic
581#102C2×C4×C4311yescharacteristic
582#102C2×C4×C4311yescharacteristic
583#102C2×C4×C4311yescharacteristic
584#102C2×C4×C4311yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C4311yescharacteristic
594C22⋊C8C2×C4×C4311yescharacteristic
595C22⋊C8C2×C4×C4311yescharacteristic
596C22⋊C8C2×C4×C4311yescharacteristic
597C22⋊C8D4×C4311yescharacteristic
598C22⋊C8D4×C4311yescharacteristic
599C22⋊C8D4×C4311yescharacteristic
600C22⋊C8D4×C4311yescharacteristic
601#97—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—22no—
605C24—21no—
606C24#41×C4311yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C4312yes—
626#41#41×C4312yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C4311yescharacteristic
631C2×Q8C22×C4×C4311yescharacteristic
632C2×Q8C22×C4×C4311yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C4311yescharacteristic
646C2×D4C22×C4×C4311yescharacteristic
647C2×D4C22×C4×C4311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C4311yescharacteristic
663C22×C4C22×C4×C4311yescharacteristic
664C22×C4C2×D4×C4311yescharacteristic
665C22×C4C2×D4×C4311yescharacteristic
666C22×C4#41×C4311yescharacteristic
667C22×C4C24×C4311yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C4312yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C4311yescharacteristic
705C2×C8C22×C4×C4311yescharacteristic
706C2×C8C22×C4×C4311yescharacteristic
707C2×C8C22×C4×C4311yescharacteristic
708C2×C8C2×D4×C4311yescharacteristic
709C2×C8C2×D4×C4311yescharacteristic
710C2×C8C2×D4×C4311yescharacteristic
711C2×C8C2×D4×C4311yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C4311yescharacteristic
716C4⋊C4C22×C4×C4311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C4312yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C4311yescharacteristic
739C23C4×D4×C4311yescharacteristic
740C23C2×#41×C4311yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C4312yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C4312yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C4311yescharacteristic
796C2×C4C4×D4×C4311yescharacteristic
797C2×C4C23×C4×C4311yescharacteristic
798C2×C4C22×D4×C4311yescharacteristic
799C2×C4C22×D4×C4311yescharacteristic
800C2×C4C2×#41×C4311yescharacteristic
801C2×C4H(5,𝔽2)×C4311yescharacteristic
802C2×C4H(5,𝔽2)×C4311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C4311yescharacteristic
836C22C43×#54611yescharacteristic
837C22C43×#55111yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C4311yescharacteristic
848C4C43×#51811yescharacteristic
849C4D42×C4311yescharacteristic
850C4C43×#54611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2C43×#235811yescharacteristic
859C2C43×#295511yescharacteristic
860C2C43×#295711yescharacteristic
subgroupG/H
centerC2×C4×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
socleC22×C43C2×C4×D4
prime radicalC43×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C22⋊C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#443C2semidirect
3. C43×#2933C2semidirect
4. C2×C43×#421C2semidirect
5. C43×#2880C2semidirect
6. C43×#1975C2semidirect
7. C43×#1937C2semidirect
8. C43×#1929C2semidirect
9. C43×#1897C2semidirect
10. C43×#1876C2semidirect
11. C43×#1876C2semidirect
12. C43×#1866C2semidirect
13. C43×#1855C2semidirect
14. C43×#1765C2semidirect
15. C43×#1750C2semidirect
21. C2×#131×C43C22semidirect
25. C43×#452C4semidirect
26. C43×#452C4semidirect
27. C43×#451C4semidirect
28. C43×#450C4semidirect
29. C43×#449C4semidirect
30. C43×#449C4semidirect
31. C43×#448C4semidirect
32. C43×#447C4semidirect
38. C2×#108×C43C22semidirect
39. C2×#108×C43C22semidirect
40. C43×#424C22semidirect
46. C2×#104×C43C22semidirect
47. C2×#104×C43C22semidirect
54. C43×#408C22semidirect
60. C43×#405C22semidirect
61. C2×#97×C43C22semidirect
62. C2×C4×C8×C43C22semidirect
63. C43×#341C22semidirect
64. C43×#341C22semidirect
65. C43×#339C22semidirect
66. C43×#339C22semidirect
67. C43×#336C22semidirect
68. C43×#336C22semidirect
145. #104×C43D4semidirect
384. #22889C43direct (N × H)
422. C2×#443C2×C43semidirect
423. #2933C2×C43semidirect
424. C2×#421C2×C43semidirect
425. #2880C2×C43semidirect
426. #1975C2×C43semidirect
427. #1937C2×C43semidirect
428. #1929C2×C43semidirect
429. #1897C2×C43semidirect
430. #1876C2×C43semidirect
431. #1876C2×C43semidirect
432. #1866C2×C43semidirect
433. #1855C2×C43semidirect
434. #1765C2×C43semidirect
435. #1750C2×C43semidirect
451. C2×#131C22×C43semidirect
455. #452C4×C43semidirect
456. #452C4×C43semidirect
457. #451C4×C43semidirect
458. #450C4×C43semidirect
459. #449C4×C43semidirect
460. #449C4×C43semidirect
461. #448C4×C43semidirect
462. #447C4×C43semidirect
468. C2×#108C22×C43semidirect
469. C2×#108C22×C43semidirect
470. #424C22×C43semidirect
476. C2×#104C22×C43semidirect
477. C2×#104C22×C43semidirect
484. #408C22×C43semidirect
490. #405C22×C43semidirect
491. C2×#97C22×C43semidirect
492. C2×C4×C8C22×C43semidirect
493. #341C22×C43semidirect
494. #341C22×C43semidirect
495. #339C22×C43semidirect
496. #339C22×C43semidirect
497. #336C22×C43semidirect
498. #336C22×C43semidirect
499. C43#22889direct (N × H)
576. #104D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#30022
C2×C43×#4432
C43×#29332
C2×C43×#4212
C43×#28802
C43×#19752
C43×#19372
C43×#19292
C43×#18972
C43×#18762
C43×#18662
C43×#18552
C43×#17652
C43×#17502
#2288943