Finite Group Databasebeta

← C43×#22062 #24942079

Subgroups — C43×#22062 #24942079

Order 11008.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3002C211yesmaximal, characteristic
2C43×#2930C211yesmaximal, characteristic, complemented
3C43×#2879C211yesmaximal, characteristic, complemented
4C43×#1975C211yesmaximal, characteristic, complemented
5C43×#1974C211yesmaximal, characteristic, complemented
6C43×#1938C211yesmaximal, characteristic, complemented
7C43×#1937C211yesmaximal, characteristic, complemented
8C43×#1929C211yesmaximal, characteristic, complemented
9C43×#1929C211yesmaximal, characteristic, complemented
10C43×#1876C211yesmaximal, characteristic, complemented
11C43×#1876C211yesmaximal, characteristic, complemented
12C43×#1871C211yesmaximal, characteristic, complemented
13C43×#1855C211yesmaximal, characteristic, complemented
14C43×#1789C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C2×#135×C43C2211yescharacteristic
18C2×#135×C43C2211yescharacteristic
19C2×#131×C43C2211yescharacteristic, complemented
20C22×M16×C43C2211yescharacteristic
21C22×M16×C43C2211yescharacteristic
22C43×#525C2211yescharacteristic
23C43×#452C411yescharacteristic, complemented
24C43×#452C411yescharacteristic, complemented
25C43×#451C411yescharacteristic, complemented
26C43×#450C411yescharacteristic, complemented
27C43×#449C411yescharacteristic, complemented
28C43×#449C411yescharacteristic, complemented
29C43×#448C411yescharacteristic, complemented
30C43×#447C411yescharacteristic, complemented
31C43×#436—21no—
32C43×#436—21no—
33C43×#435—21no—
34C43×#435—21no—
35C2×#108×C43C2211yescharacteristic, complemented
36C2×#108×C43C2211yescharacteristic, complemented
37C43×#424C2211yescharacteristic, complemented
38C2×#104×C43C2211yescharacteristic
39C2×#104×C43C2211yescharacteristic
40C2×#104×C43C2211yescharacteristic
41C2×#104×C43C2211yescharacteristic
42C2×#104×C43C2211yescharacteristic, complemented
43C2×#104×C43C2211yescharacteristic, complemented
44C43×#416C2211yescharacteristic
45C43×#416C2211yescharacteristic
46C43×#408—21no—
47C43×#408—21no—
48C43×#408C2211yescharacteristic
49C43×#408C2211yescharacteristic
50C43×#408C2211yescharacteristic
51C43×#408C2211yescharacteristic
52C43×#408C2211yescharacteristic, complemented
53C43×#407—21no—
54C43×#407—21no—
55C43×#407C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#405C2211yescharacteristic, complemented
58C2×#97×C43C2211yescharacteristic, complemented
59C2×C4×C8×C43C2211yescharacteristic, complemented
60C4×C22⋊C4×C43C2211yescharacteristic
61C43×#341C2211yescharacteristic, complemented
62C43×#341C2211yescharacteristic, complemented
63C43×#339C2211yescharacteristic, complemented
64C43×#339C2211yescharacteristic, complemented
65C43×#336C2211yescharacteristic, complemented
66C43×#336C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×#41×C43—41no—
70C2×#41×C43—41no—
71C2×#41×C43—41no—
72C2×#41×C43—41no—
73C2×#41×C43C2×C411yescharacteristic
74C2×#41×C43C2×C411yescharacteristic
75C2×#41×C43C2311yescharacteristic
76C2×#41×C43C2311yescharacteristic
77C2×#41×C43C2311yescharacteristic
78C22×Q8×C43C2×C411yescharacteristic
79C22×D4×C43—21no—
80C22×D4×C43C2×C411yescharacteristic
81C23×C4×C43—21no—
82C23×C4×C43C2311yescharacteristic
83#135×C43—41no—
84#135×C43—41no—
85#135×C43—41no—
86#135×C43—41no—
87C2×Q16×C43C2×C411yescharacteristic
88C2×Q16×C43C2×C411yescharacteristic
89C2×SD16×C43C2×C411yescharacteristic
90C2×SD16×C43C2×C411yescharacteristic
91C2×SD16×C43C2×C411yescharacteristic
92C2×SD16×C43C2×C411yescharacteristic
93C2×D8×C43C2×C411yescharacteristic
94C2×D8×C43C2×C411yescharacteristic
95#131×C43—41no—
96#131×C43—41no—
97C2×M16×C43—21no—
98C2×M16×C43—21no—
99C2×M16×C43—41no—
100C2×M16×C43—41no—
101C2×M16×C43—41no—
102C2×M16×C43—41no—
103C2×M16×C43D411yescharacteristic
104C2×M16×C43D411yescharacteristic
105C2×M16×C43D411yescharacteristic
106C2×M16×C43D411yescharacteristic
107C2×M16×C43C2311yescharacteristic
108C2×M16×C43C2311yescharacteristic
109C2×M16×C43C2311yescharacteristic
110C2×M16×C43C2311yescharacteristic
111C22×C8×C43—21no—
112C22×C8×C43—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117#123×C43—21no—
118C22⋊Q8×C43C2×C411yescharacteristic
119C22⋊Q8×C43C2×C411yescharacteristic
120#121×C43C2×C411yescharacteristic
121#121×C43C2×C411yescharacteristic
122#120×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125#117×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128C2×C42×C43C2311yescharacteristic
129#108×C43—41no—
130#108×C43—41no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133#104×C43—41no—
134#104×C43—41no—
135#104×C43—41no—
136#104×C43—41no—
137#104×C43—41no—
138#104×C43—41no—
139#103×C43C2×C411yescharacteristic
140#103×C43C2×C411yescharacteristic
141#103×C43C2×C411yescharacteristic
142#103×C43C2×C411yescharacteristic
143#102×C43C2×C411yescharacteristic
144#102×C43C2×C411yescharacteristic
145#102×C43C2×C411yescharacteristic
146#102×C43C2×C411yescharacteristic
147C22⋊C8×C43—21no—
148C22⋊C8×C43—21no—
149C22⋊C8×C43—21no—
150C22⋊C8×C43—21no—
151C22⋊C8×C43—21no—
152C22⋊C8×C43—21no—
153C22⋊C8×C43—21no—
154C22⋊C8×C43—21no—
155C22⋊C8×C43—21no—
156C22⋊C8×C43—21no—
157C22⋊C8×C43—21no—
158C22⋊C8×C43—21no—
159C22⋊C8×C43C2×C411yescharacteristic
160C22⋊C8×C43C2×C411yescharacteristic
161C22⋊C8×C43C2×C411yescharacteristic
162C22⋊C8×C43C2×C411yescharacteristic
163#97×C43—21no—
164#97×C43—41no—
165C4×C8×C43—21no—
166C4×C8×C43—41no—
167#95×C43—21no—
168C24×C43—21no—
169C24×C43#4111yescharacteristic
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174#41×C43—21no—
175#41×C43—21no—
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—41no—
183#41×C43—41no—
184#41×C43—41no—
185#41×C43—41no—
186#41×C43—42no—
187#41×C43—42no—
188#41×C43—42no—
189#41×C43—42no—
190C2×Q8×C43—21no—
191C2×Q8×C43—41no—
192C2×Q8×C43—41no—
193C2×Q8×C43C22×C411yescharacteristic
194C2×Q8×C43C22×C411yescharacteristic
195C2×Q8×C43C22×C411yescharacteristic
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43—41no—
207C2×D4×C43—41no—
208C2×D4×C43C22×C411yescharacteristic
209C2×D4×C43C22×C411yescharacteristic
210C2×D4×C43C22×C411yescharacteristic
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
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—42no—
224C22×C4×C43—42no—
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C22×C411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43#4111yescharacteristic
230C22×C4×C43C2411yescharacteristic
231Q16×C43—41no—
232Q16×C43—41no—
233SD16×C43—41no—
234SD16×C43—41no—
235SD16×C43—41no—
236SD16×C43—41no—
237D8×C43—41no—
238D8×C43—41no—
239M16×C43—21no—
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244M16×C43—21no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43—41no—
248M16×C43—41no—
249M16×C43—41no—
250M16×C43—41no—
251M16×C43—42no—
252M16×C43—42no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
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—42no—
266C2×C8×C43—42no—
267C2×C8×C43C22×C411yescharacteristic
268C2×C8×C43C22×C411yescharacteristic
269C2×C8×C43C22×C411yescharacteristic
270C2×C8×C43C22×C411yescharacteristic
271C2×C8×C43C2×D411yescharacteristic
272C2×C8×C43C2×D411yescharacteristic
273C2×C8×C43C2×D411yescharacteristic
274C2×C8×C43C2×D411yescharacteristic
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43C22×C411yescharacteristic
278C4⋊C4×C43C22×C411yescharacteristic
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊C4×C43—21no—
283C22⋊C4×C43—21no—
284C22⋊C4×C43—42no—
285C42×C43—21no—
286C42×C43—21no—
287C42×C43—21no—
288C42×C43—21no—
289C42×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—42no—
298C23×C43—81no—
299C23×C43—81no—
300C23×C43C4×D411yescharacteristic
301C23×C43C4×D411yescharacteristic
302C23×C43C2×#4111yescharacteristic
303Q8×C43—21no—
304Q8×C43—21no—
305Q8×C43—21no—
306Q8×C43—21no—
307Q8×C43—21no—
308Q8×C43—21no—
309Q8×C43—42no—
310D4×C43—21no—
311D4×C43—21no—
312D4×C43—21no—
313D4×C43—21no—
314D4×C43—21no—
315D4×C43—21no—
316D4×C43—42no—
317D4×C43—42no—
318D4×C43—42no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43—81no—
326D4×C43—81no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—22no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—42no—
344C2×C4×C43—42no—
345C2×C4×C43—41no—
346C2×C4×C43—42no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43C4×D411yescharacteristic
358C2×C4×C43C4×D411yescharacteristic
359C2×C4×C43C23×C411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C2×C4×C43H(5,𝔽2)11yescharacteristic
363C2×C4×C43H(5,𝔽2)11yescharacteristic
364C2×C4×C43H(5,𝔽2)11yescharacteristic
365C8×C43—21no—
366C8×C43—21no—
367C8×C43—21no—
368C8×C43—21no—
369C8×C43—21no—
370C8×C43—21no—
371C8×C43—21no—
372C8×C43—21no—
373C8×C43—41no—
374C8×C43—41no—
375C8×C43—41no—
376C8×C43—41no—
377#22062C4311yesmaximal, characteristic, direct product factor, Sylow
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—21no—
385C22×C43—21no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—84no—
398C22×C43C2×C4×D411yescharacteristic
399C22×C43#53811yescharacteristic
400C22×C43#53811yescharacteristic
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—42no—
404C4×C43—41no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43—41no—
408C4×C43—41no—
409C4×C43—81no—
410C4×C43#51811yescharacteristic
411C4×C43#51811yescharacteristic
412C4×C43#53411yescharacteristic
413C4×C43#53511yescharacteristic
414#3002C2×C4311yescharacteristic
415#2930C2×C4311yescharacteristic, complemented
416#2879C2×C4311yescharacteristic, complemented
417#1975C2×C4311yescharacteristic, complemented
418#1974C2×C4311yescharacteristic, complemented
419#1938C2×C4311yescharacteristic, complemented
420#1937C2×C4311yescharacteristic, complemented
421#1929C2×C4311yescharacteristic, complemented
422#1929C2×C4311yescharacteristic, complemented
423#1876C2×C4311yescharacteristic, complemented
424#1876C2×C4311yescharacteristic, complemented
425#1871C2×C4311yescharacteristic, complemented
426#1855C2×C4311yescharacteristic, complemented
427#1789C2×C4311yescharacteristic, complemented
428#1753C2×C4311yescharacteristic, complemented
429C2×C43—21no—
430C2×C43—21no—
431C2×C43—41no—
432C2×C43—41no—
433C2×C43—81no—
434C2×C43—81no—
435C2×C43—81no—
436C2×C43#232111yescharacteristic
437C2×C43#295611yescharacteristic
438C2×C43#295711yescharacteristic
439C22×#41C22×C4311yescharacteristic
440C2×#135C22×C4311yescharacteristic
441C2×#135C22×C4311yescharacteristic
442C2×#131C22×C4311yescharacteristic, complemented
443C22×M16C22×C4311yescharacteristic
444C22×M16C22×C4311yescharacteristic
445#525C22×C4311yescharacteristic
446#452C4×C4311yescharacteristic, complemented
447#452C4×C4311yescharacteristic, complemented
448#451C4×C4311yescharacteristic, complemented
449#450C4×C4311yescharacteristic, complemented
450#449C4×C4311yescharacteristic, complemented
451#449C4×C4311yescharacteristic, complemented
452#448C4×C4311yescharacteristic, complemented
453#447C4×C4311yescharacteristic, complemented
454#436—21no—
455#436—21no—
456#435—21no—
457#435—21no—
458C2×#108C22×C4311yescharacteristic, complemented
459C2×#108C22×C4311yescharacteristic, complemented
460#424C22×C4311yescharacteristic, complemented
461C2×#104C22×C4311yescharacteristic
462C2×#104C22×C4311yescharacteristic
463C2×#104C22×C4311yescharacteristic
464C2×#104C22×C4311yescharacteristic
465C2×#104C22×C4311yescharacteristic, complemented
466C2×#104C22×C4311yescharacteristic, complemented
467#416C22×C4311yescharacteristic
468#416C22×C4311yescharacteristic
469#408—21no—
470#408—21no—
471#408C22×C4311yescharacteristic
472#408C22×C4311yescharacteristic
473#408C22×C4311yescharacteristic
474#408C22×C4311yescharacteristic
475#408C22×C4311yescharacteristic, complemented
476#407—21no—
477#407—21no—
478#407C22×C4311yescharacteristic
479C2×C22⋊C8C22×C4311yescharacteristic
480#405C22×C4311yescharacteristic, complemented
481C2×#97C22×C4311yescharacteristic, complemented
482C2×C4×C8C22×C4311yescharacteristic, complemented
483C4×C22⋊C4C22×C4311yescharacteristic
484#341C22×C4311yescharacteristic, complemented
485#341C22×C4311yescharacteristic, complemented
486#339C22×C4311yescharacteristic, complemented
487#339C22×C4311yescharacteristic, complemented
488#336C22×C4311yescharacteristic, complemented
489#336C22×C4311yescharacteristic, complemented
490C43#2206211yescharacteristic, direct product factor, Sylow
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×C4×C4311yescharacteristic
498C2×#41C2×C4×C4311yescharacteristic
499C2×#41C23×C4311yescharacteristic
500C2×#41C23×C4311yescharacteristic
501C2×#41C23×C4311yescharacteristic
502C22×Q8C2×C4×C4311yescharacteristic
503C22×D4—21no—
504C22×D4C2×C4×C4311yescharacteristic
505C23×C4—21no—
506C23×C4C23×C4311yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×C4×C4311yescharacteristic
512C2×Q16C2×C4×C4311yescharacteristic
513C2×SD16C2×C4×C4311yescharacteristic
514C2×SD16C2×C4×C4311yescharacteristic
515C2×SD16C2×C4×C4311yescharacteristic
516C2×SD16C2×C4×C4311yescharacteristic
517C2×D8C2×C4×C4311yescharacteristic
518C2×D8C2×C4×C4311yescharacteristic
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16D4×C4311yescharacteristic
528C2×M16D4×C4311yescharacteristic
529C2×M16D4×C4311yescharacteristic
530C2×M16D4×C4311yescharacteristic
531C2×M16C23×C4311yescharacteristic
532C2×M16C23×C4311yescharacteristic
533C2×M16C23×C4311yescharacteristic
534C2×M16C23×C4311yescharacteristic
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C4311yescharacteristic
538C22×C8C23×C4311yescharacteristic
539C22×C8C23×C4311yescharacteristic
540C22×C8C23×C4311yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C4311yescharacteristic
543C22⋊Q8C2×C4×C4311yescharacteristic
544#121C2×C4×C4311yescharacteristic
545#121C2×C4×C4311yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C23×C4311yescharacteristic
550C2×C22⋊C4—21no—
551C2×C42C23×C4311yescharacteristic
552C2×C42C23×C4311yescharacteristic
553#108—41no—
554#108—41no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#104—41no—
563#103C2×C4×C4311yescharacteristic
564#103C2×C4×C4311yescharacteristic
565#103C2×C4×C4311yescharacteristic
566#103C2×C4×C4311yescharacteristic
567#102C2×C4×C4311yescharacteristic
568#102C2×C4×C4311yescharacteristic
569#102C2×C4×C4311yescharacteristic
570#102C2×C4×C4311yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C2×C4×C4311yescharacteristic
584C22⋊C8C2×C4×C4311yescharacteristic
585C22⋊C8C2×C4×C4311yescharacteristic
586C22⋊C8C2×C4×C4311yescharacteristic
587#97—21no—
588#97—41no—
589C4×C8—21no—
590C4×C8—41no—
591#95—21no—
592C24—21no—
593C24#41×C4311yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C4311yescharacteristic
618C2×Q8C22×C4×C4311yescharacteristic
619C2×Q8C22×C4×C4311yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C4311yescharacteristic
633C2×D4C22×C4×C4311yescharacteristic
634C2×D4C22×C4×C4311yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C4311yescharacteristic
650C22×C4C22×C4×C4311yescharacteristic
651C22×C4C2×D4×C4311yescharacteristic
652C22×C4C2×D4×C4311yescharacteristic
653C22×C4#41×C4311yescharacteristic
654C22×C4C24×C4311yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C4311yescharacteristic
692C2×C8C22×C4×C4311yescharacteristic
693C2×C8C22×C4×C4311yescharacteristic
694C2×C8C22×C4×C4311yescharacteristic
695C2×C8C2×D4×C4311yescharacteristic
696C2×C8C2×D4×C4311yescharacteristic
697C2×C8C2×D4×C4311yescharacteristic
698C2×C8C2×D4×C4311yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C4311yescharacteristic
702C4⋊C4C22×C4×C4311yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C4311yescharacteristic
725C23C4×D4×C4311yescharacteristic
726C23C2×#41×C4311yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4C4×D4×C4311yescharacteristic
782C2×C4C4×D4×C4311yescharacteristic
783C2×C4C23×C4×C4311yescharacteristic
784C2×C4C22×D4×C4311yescharacteristic
785C2×C4H(5,𝔽2)×C4311yescharacteristic
786C2×C4H(5,𝔽2)×C4311yescharacteristic
787C2×C4H(5,𝔽2)×C4311yescharacteristic
788C2×C4H(5,𝔽2)×C4311yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C4311yescharacteristic
822C22C43×#53811yescharacteristic
823C22C43×#53811yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4C43×#51811yescharacteristic
834C4C43×#51811yescharacteristic
835C4C43×#53411yescharacteristic
836C4C43×#53511yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2C43×#232111yescharacteristic
845C2C43×#295611yescharacteristic
846C2C43×#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 ◁ C22×M16×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2930C2semidirect
3. C43×#2879C2semidirect
4. C43×#1975C2semidirect
5. C43×#1974C2semidirect
6. C43×#1938C2semidirect
7. C43×#1937C2semidirect
8. C43×#1929C2semidirect
9. C43×#1929C2semidirect
10. C43×#1876C2semidirect
11. C43×#1876C2semidirect
12. C43×#1871C2semidirect
13. C43×#1855C2semidirect
14. C43×#1789C2semidirect
15. C43×#1753C2semidirect
19. C2×#131×C43C22semidirect
23. C43×#452C4semidirect
24. C43×#452C4semidirect
25. C43×#451C4semidirect
26. C43×#450C4semidirect
27. C43×#449C4semidirect
28. C43×#449C4semidirect
29. C43×#448C4semidirect
30. C43×#447C4semidirect
35. C2×#108×C43C22semidirect
36. C2×#108×C43C22semidirect
37. C43×#424C22semidirect
42. C2×#104×C43C22semidirect
43. C2×#104×C43C22semidirect
52. C43×#408C22semidirect
57. C43×#405C22semidirect
58. C2×#97×C43C22semidirect
59. C2×C4×C8×C43C22semidirect
61. C43×#341C22semidirect
62. C43×#341C22semidirect
63. C43×#339C22semidirect
64. C43×#339C22semidirect
65. C43×#336C22semidirect
66. C43×#336C22semidirect
377. #22062C43direct (N × H)
415. #2930C2×C43semidirect
416. #2879C2×C43semidirect
417. #1975C2×C43semidirect
418. #1974C2×C43semidirect
419. #1938C2×C43semidirect
420. #1937C2×C43semidirect
421. #1929C2×C43semidirect
422. #1929C2×C43semidirect
423. #1876C2×C43semidirect
424. #1876C2×C43semidirect
425. #1871C2×C43semidirect
426. #1855C2×C43semidirect
427. #1789C2×C43semidirect
428. #1753C2×C43semidirect
442. C2×#131C22×C43semidirect
446. #452C4×C43semidirect
447. #452C4×C43semidirect
448. #451C4×C43semidirect
449. #450C4×C43semidirect
450. #449C4×C43semidirect
451. #449C4×C43semidirect
452. #448C4×C43semidirect
453. #447C4×C43semidirect
458. C2×#108C22×C43semidirect
459. C2×#108C22×C43semidirect
460. #424C22×C43semidirect
465. C2×#104C22×C43semidirect
466. C2×#104C22×C43semidirect
475. #408C22×C43semidirect
480. #405C22×C43semidirect
481. C2×#97C22×C43semidirect
482. C2×C4×C8C22×C43semidirect
484. #341C22×C43semidirect
485. #341C22×C43semidirect
486. #339C22×C43semidirect
487. #339C22×C43semidirect
488. #336C22×C43semidirect
489. #336C22×C43semidirect
490. C43#22062direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30022
C43×#29302
C43×#28792
C43×#19752
C43×#19742
C43×#19382
C43×#19372
C43×#19292
C43×#18762
C43×#18712
C43×#18552
C43×#17892
C43×#17532
#2206243