Finite Group Databasebeta

← C43×#22886 #24942903

Subgroups — C43×#22886 #24942903

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3002C211yesmaximal, characteristic
2C2×C43×#444C211yesmaximal, characteristic, complemented
3C43×#2933C211yesmaximal, characteristic, complemented
4C22×#104×C43C211yesmaximal, characteristic, complemented
5C43×#2880C211yesmaximal, characteristic, complemented
6C43×#1975C211yesmaximal, characteristic, complemented
7C43×#1938C211yesmaximal, characteristic, complemented
8C43×#1929C211yesmaximal, characteristic, complemented
9C43×#1896C211yesmaximal, characteristic, complemented
10C43×#1876C211yesmaximal, characteristic, complemented
11C43×#1876C211yesmaximal, characteristic, complemented
12C43×#1866C211yesmaximal, characteristic, complemented
13C43×#1855C211yesmaximal, characteristic, complemented
14C43×#1765C211yesmaximal, characteristic, complemented
15C43×#1749C211yesmaximal, 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
24C22×C42×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×#444—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
41C2×#104×C43—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×#97×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×C43—21no—
85C23×C4×C43C2311yescharacteristic
86#135×C43—22no—
87#135×C43—22no—
88#135×C43—41no—
89#135×C43—41no—
90C2×Q16×C43C2×C411yescharacteristic, complemented
91C2×Q16×C43C2×C411yescharacteristic, complemented
92C2×SD16×C43C2×C411yescharacteristic, complemented
93C2×SD16×C43C2×C411yescharacteristic, complemented
94C2×SD16×C43C2×C411yescharacteristic, complemented
95C2×SD16×C43C2×C411yescharacteristic, complemented
96C2×D8×C43C2×C411yescharacteristic, complemented
97C2×D8×C43C2×C411yescharacteristic, complemented
98#131×C43—22no—
99#131×C43—22no—
100#131×C43—22no—
101#131×C43—41no—
102#131×C43—41no—
103#131×C43—41no—
104C2×M16×C43—21no—
105C2×M16×C43—21no—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43—22no—
109C2×M16×C43—41no—
110C2×M16×C43C2311yescharacteristic
111C2×M16×C43C2311yescharacteristic
112C2×M16×C43C2311yescharacteristic
113C2×M16×C43C2311yescharacteristic
114C22×C8×C43—21no—
115C22×C8×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43C2×C411yescharacteristic
124C22⋊Q8×C43C2×C411yescharacteristic
125#121×C43C2×C411yescharacteristic
126#121×C43C2×C411yescharacteristic
127#120×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130#117×C43C2311yescharacteristic
131C2×C42×C43—22no—
132C2×C42×C43—21no—
133C2×C42×C43—41no—
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, complemented
147#103×C43C2×C411yescharacteristic, complemented
148#103×C43C2×C411yescharacteristic, complemented
149#103×C43C2×C411yescharacteristic, complemented
150#102×C43C2×C411yescharacteristic, complemented
151#102×C43C2×C411yescharacteristic, complemented
152#102×C43C2×C411yescharacteristic, complemented
153#102×C43C2×C411yescharacteristic, complemented
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—22no—
172#97×C43—41no—
173C4×C8×C43—21no—
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×C43—42no—
232C22×C4×C43—42no—
233C22×C4×C43—42no—
234C22×C4×C43C22×C411yescharacteristic
235C22×C4×C43C22×C411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43#4111yescharacteristic
239C22×C4×C43C2411yescharacteristic
240Q16×C43—22no—
241Q16×C43—41no—
242SD16×C43—22no—
243SD16×C43—22no—
244SD16×C43—41no—
245SD16×C43—41no—
246D8×C43—22no—
247D8×C43—41no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43—21no—
252M16×C43—21no—
253M16×C43—21no—
254M16×C43—21no—
255M16×C43—42no—
256M16×C43—42no—
257M16×C43—42no—
258M16×C43—42no—
259M16×C43C2×D412yes—
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—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—42no—
273C2×C8×C43—42no—
274C2×C8×C43—42no—
275C2×C8×C43—42no—
276C2×C8×C43C22×C411yescharacteristic
277C2×C8×C43C22×C411yescharacteristic
278C2×C8×C43C22×C411yescharacteristic
279C2×C8×C43C22×C411yescharacteristic
280C2×C8×C43C2×D411yescharacteristic
281C2×C8×C43C2×D411yescharacteristic
282C2×C8×C43C2×D411yescharacteristic
283C2×C8×C43C2×D411yescharacteristic
284C4⋊C4×C43—21no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43C22×C411yescharacteristic
287C4⋊C4×C43C22×C411yescharacteristic
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C42×C43—21no—
294C42×C43—21no—
295C42×C43—21no—
296C42×C43—21no—
297C42×C43—42no—
298C42×C43C2×D412yes—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—22no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—41no—
306C23×C43—42no—
307C23×C43—42no—
308C23×C43—81no—
309C23×C43C4×D411yescharacteristic
310C23×C43C4×D411yescharacteristic
311C23×C43C2×#4111yescharacteristic
312Q8×C43—21no—
313Q8×C43—21no—
314Q8×C43—21no—
315Q8×C43—21no—
316Q8×C43—21no—
317Q8×C43—42no—
318Q8×C43C4×D412yes—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—21no—
322D4×C43—21no—
323D4×C43—21no—
324D4×C43—21no—
325D4×C43—21no—
326D4×C43—42no—
327D4×C43—42no—
328D4×C43—42no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—41no—
332D4×C43—41no—
333D4×C43—42no—
334D4×C43—81no—
335D4×C43C4×D412yes—
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—21no—
343C2×C4×C43—21no—
344C2×C4×C43—22no—
345C2×C4×C43—21no—
346C2×C4×C43—22no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—22no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—22no—
355C2×C4×C43—42no—
356C2×C4×C43—42no—
357C2×C4×C43—42no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—48no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43C4×D411yescharacteristic
368C2×C4×C43C4×D411yescharacteristic
369C2×C4×C43C23×C411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C2×C4×C43C22×D411yescharacteristic
372C2×C4×C43C2×#4111yescharacteristic
373C2×C4×C43H(5,𝔽2)11yescharacteristic
374C2×C4×C43H(5,𝔽2)11yescharacteristic
375C8×C43—21no—
376C8×C43—21no—
377C8×C43—21no—
378C8×C43—21no—
379C8×C43—21no—
380C8×C43—21no—
381C8×C43—22no—
382C8×C43—21no—
383C8×C43—21no—
384C8×C43—41no—
385C8×C43—41no—
386C8×C43—41no—
387#22886C4311yesmaximal, characteristic, direct product factor, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—22no—
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43—84no—
407C22×C43#44412yescomplemented
408C22×C43C2×C4×D411yescharacteristic
409C22×C43#54611yescharacteristic
410C22×C43#55111yescharacteristic
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—22no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43—41no—
417C4×C43—41no—
418C4×C43—41no—
419C4×C43—41no—
420C4×C43C2×C4×D411yescharacteristic
421C4×C43#51811yescharacteristic
422C4×C43D4211yescharacteristic
423C4×C43#54611yescharacteristic
424#3002C2×C4311yescharacteristic
425C2×#444C2×C4311yescharacteristic, complemented
426#2933C2×C4311yescharacteristic, complemented
427C22×#104C2×C4311yescharacteristic, complemented
428#2880C2×C4311yescharacteristic, complemented
429#1975C2×C4311yescharacteristic, complemented
430#1938C2×C4311yescharacteristic, complemented
431#1929C2×C4311yescharacteristic, complemented
432#1896C2×C4311yescharacteristic, complemented
433#1876C2×C4311yescharacteristic, complemented
434#1876C2×C4311yescharacteristic, complemented
435#1866C2×C4311yescharacteristic, complemented
436#1855C2×C4311yescharacteristic, complemented
437#1765C2×C4311yescharacteristic, complemented
438#1749C2×C4311yescharacteristic, complemented
439C2×C43—21no—
440C2×C43—22no—
441C2×C43—21no—
442C2×C43—41no—
443C2×C43—42no—
444C2×C43—81no—
445C2×C43—81no—
446C2×C43#235811yescharacteristic
447C2×C43C2×#44411yescharacteristic
448C2×C43#295611yescharacteristic
449C22×#41C22×C4311yescharacteristic
450C2×#135C22×C4311yescharacteristic
451C2×#135C22×C4311yescharacteristic
452C2×#131C22×C4311yescharacteristic
453C2×#131C22×C4311yescharacteristic
454C2×#131C22×C4311yescharacteristic, complemented
455C22×M16C22×C4311yescharacteristic
456#525C22×C4311yescharacteristic
457C22×C42C22×C4311yescharacteristic
458#452C4×C4311yescharacteristic, complemented
459#452C4×C4311yescharacteristic, complemented
460#451C4×C4311yescharacteristic, complemented
461#450C4×C4311yescharacteristic, complemented
462#449C4×C4311yescharacteristic, complemented
463#449C4×C4311yescharacteristic, complemented
464#448C4×C4311yescharacteristic, complemented
465#447C4×C4311yescharacteristic, complemented
466#444—24no—
467#436—21no—
468#435—21no—
469#435—21no—
470C8×D4—21no—
471C2×#108C22×C4311yescharacteristic, complemented
472C2×#108C22×C4311yescharacteristic, complemented
473#424C22×C4311yescharacteristic, complemented
474C2×#104—24no—
475C2×#104C22×C4311yescharacteristic
476C2×#104C22×C4311yescharacteristic
477C2×#104C22×C4311yescharacteristic
478C2×#104C22×C4311yescharacteristic
479C2×#104C22×C4311yescharacteristic, complemented
480C2×#104C22×C4311yescharacteristic, complemented
481#416C22×C4311yescharacteristic
482#416C22×C4311yescharacteristic
483#408—21no—
484#408—21no—
485#408C22×C4311yescharacteristic
486#408C22×C4311yescharacteristic
487#408C22×C4311yescharacteristic, complemented
488#407—21no—
489#407C22×C4311yescharacteristic
490C2×C22⋊C8—21no—
491C2×C22⋊C8C22×C4311yescharacteristic
492C2×C22⋊C8C22×C4311yescharacteristic
493#405C22×C4311yescharacteristic, complemented
494C2×#97C22×C4311yescharacteristic, complemented
495C2×#97C22×C4311yescharacteristic, complemented
496#341C22×C4311yescharacteristic, complemented
497#341C22×C4311yescharacteristic, complemented
498#339C22×C4311yescharacteristic, complemented
499#339C22×C4311yescharacteristic, complemented
500#336C22×C4311yescharacteristic, complemented
501#336C22×C4311yescharacteristic, complemented
502C43#2288611yescharacteristic, direct product factor, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×C4×C4311yescharacteristic
510C2×#41C2×C4×C4311yescharacteristic
511C2×#41C23×C4311yescharacteristic
512C2×#41C23×C4311yescharacteristic
513C2×#41C23×C4311yescharacteristic
514C22×Q8C2×C4×C4311yescharacteristic
515C22×D4—21no—
516C22×D4C2×C4×C4311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C4311yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×C4×C4311yescharacteristic, complemented
525C2×Q16C2×C4×C4311yescharacteristic, complemented
526C2×SD16C2×C4×C4311yescharacteristic, complemented
527C2×SD16C2×C4×C4311yescharacteristic, complemented
528C2×SD16C2×C4×C4311yescharacteristic, complemented
529C2×SD16C2×C4×C4311yescharacteristic, complemented
530C2×D8C2×C4×C4311yescharacteristic, complemented
531C2×D8C2×C4×C4311yescharacteristic, complemented
532#131—22no—
533#131—22no—
534#131—22no—
535#131—41no—
536#131—41no—
537#131—41no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—21no—
541C2×M16—21no—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16C23×C4311yescharacteristic
545C2×M16C23×C4311yescharacteristic
546C2×M16C23×C4311yescharacteristic
547C2×M16C23×C4311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8—21no—
552C22×C8C23×C4311yescharacteristic
553C22×C8C23×C4311yescharacteristic
554C22×C8C23×C4311yescharacteristic
555C22×C8C23×C4311yescharacteristic
556#123—21no—
557C22⋊Q8C2×C4×C4311yescharacteristic
558C22⋊Q8C2×C4×C4311yescharacteristic
559#121C2×C4×C4311yescharacteristic
560#121C2×C4×C4311yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C23×C4311yescharacteristic
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C23×C4311yescharacteristic
569C2×C42C23×C4311yescharacteristic
570#108—22no—
571#108—41no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—22no—
578#104—41no—
579#104D4×C4314yescomplemented
580#103C2×C4×C4311yescharacteristic, complemented
581#103C2×C4×C4311yescharacteristic, complemented
582#103C2×C4×C4311yescharacteristic, complemented
583#103C2×C4×C4311yescharacteristic, complemented
584#102C2×C4×C4311yescharacteristic, complemented
585#102C2×C4×C4311yescharacteristic, complemented
586#102C2×C4×C4311yescharacteristic, complemented
587#102C2×C4×C4311yescharacteristic, complemented
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8C2×C4×C4311yescharacteristic
597C22⋊C8C2×C4×C4311yescharacteristic
598C22⋊C8C2×C4×C4311yescharacteristic
599C22⋊C8C2×C4×C4311yescharacteristic
600C22⋊C8D4×C4311yescharacteristic
601C22⋊C8D4×C4311yescharacteristic
602C22⋊C8D4×C4311yescharacteristic
603C22⋊C8D4×C4311yescharacteristic
604#97—21no—
605#97—22no—
606#97—41no—
607C4×C8—21no—
608C24—21no—
609C24#41×C4311yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41C2×D4×C4312yes—
629#41#41×C4312yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×C4×C4311yescharacteristic
634C2×Q8C22×C4×C4311yescharacteristic
635C2×Q8C22×C4×C4311yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×C4×C4311yescharacteristic
649C2×D4C22×C4×C4311yescharacteristic
650C2×D4C22×C4×C4311yescharacteristic
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—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22×C4×C4311yescharacteristic
669C22×C4C22×C4×C4311yescharacteristic
670C22×C4C2×D4×C4311yescharacteristic
671C22×C4C2×D4×C4311yescharacteristic
672C22×C4#41×C4311yescharacteristic
673C22×C4C24×C4311yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—42no—
690M16—42no—
691M16—42no—
692M16—42no—
693M16C2×D4×C4312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—42no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—42no—
710C2×C8C22×C4×C4311yescharacteristic
711C2×C8C22×C4×C4311yescharacteristic
712C2×C8C22×C4×C4311yescharacteristic
713C2×C8C22×C4×C4311yescharacteristic
714C2×C8C2×D4×C4311yescharacteristic
715C2×C8C2×D4×C4311yescharacteristic
716C2×C8C2×D4×C4311yescharacteristic
717C2×C8C2×D4×C4311yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×C4×C4311yescharacteristic
721C4⋊C4C22×C4×C4311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42C2×D4×C4312yes—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23C4×D4×C4311yescharacteristic
744C23C4×D4×C4311yescharacteristic
745C23C2×#41×C4311yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8C4×D4×C4312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—42no—
768D4—81no—
769D4C4×D4×C4312yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4C4×D4×C4311yescharacteristic
802C2×C4C4×D4×C4311yescharacteristic
803C2×C4C23×C4×C4311yescharacteristic
804C2×C4C22×D4×C4311yescharacteristic
805C2×C4C22×D4×C4311yescharacteristic
806C2×C4C2×#41×C4311yescharacteristic
807C2×C4H(5,𝔽2)×C4311yescharacteristic
808C2×C4H(5,𝔽2)×C4311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—22no—
816C8—21no—
817C8—21no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22C43×#44412yescomplemented
841C22C2×C4×D4×C4311yescharacteristic
842C22C43×#54611yescharacteristic
843C22C43×#55111yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4C2×C4×D4×C4311yescharacteristic
854C4C43×#51811yescharacteristic
855C4D42×C4311yescharacteristic
856C4C43×#54611yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2C43×#235811yescharacteristic
865C2C2×C43×#44411yescharacteristic
866C2C43×#295611yescharacteristic
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×#444C2semidirect
3. C43×#2933C2semidirect
4. C22×#104×C43C2semidirect
5. C43×#2880C2semidirect
6. C43×#1975C2semidirect
7. C43×#1938C2semidirect
8. C43×#1929C2semidirect
9. C43×#1896C2semidirect
10. C43×#1876C2semidirect
11. C43×#1876C2semidirect
12. C43×#1866C2semidirect
13. C43×#1855C2semidirect
14. C43×#1765C2semidirect
15. C43×#1749C2semidirect
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×#97×C43C22semidirect
63. C43×#341C22semidirect
64. C43×#341C22semidirect
65. C43×#339C22semidirect
66. C43×#339C22semidirect
67. C43×#336C22semidirect
68. C43×#336C22semidirect
90. C2×Q16×C43C2×C4semidirect
91. C2×Q16×C43C2×C4semidirect
92. C2×SD16×C43C2×C4semidirect
93. C2×SD16×C43C2×C4semidirect
94. C2×SD16×C43C2×C4semidirect
95. C2×SD16×C43C2×C4semidirect
96. C2×D8×C43C2×C4semidirect
97. C2×D8×C43C2×C4semidirect
145. #104×C43D4semidirect
146. #103×C43C2×C4semidirect
147. #103×C43C2×C4semidirect
148. #103×C43C2×C4semidirect
149. #103×C43C2×C4semidirect
150. #102×C43C2×C4semidirect
151. #102×C43C2×C4semidirect
152. #102×C43C2×C4semidirect
153. #102×C43C2×C4semidirect
387. #22886C43direct (N × H)
407. C22×C43#444semidirect
425. C2×#444C2×C43semidirect
426. #2933C2×C43semidirect
427. C22×#104C2×C43semidirect
428. #2880C2×C43semidirect
429. #1975C2×C43semidirect
430. #1938C2×C43semidirect
431. #1929C2×C43semidirect
432. #1896C2×C43semidirect
433. #1876C2×C43semidirect
434. #1876C2×C43semidirect
435. #1866C2×C43semidirect
436. #1855C2×C43semidirect
437. #1765C2×C43semidirect
438. #1749C2×C43semidirect
454. C2×#131C22×C43semidirect
458. #452C4×C43semidirect
459. #452C4×C43semidirect
460. #451C4×C43semidirect
461. #450C4×C43semidirect
462. #449C4×C43semidirect
463. #449C4×C43semidirect
464. #448C4×C43semidirect
465. #447C4×C43semidirect
471. C2×#108C22×C43semidirect
472. C2×#108C22×C43semidirect
473. #424C22×C43semidirect
479. C2×#104C22×C43semidirect
480. C2×#104C22×C43semidirect
487. #408C22×C43semidirect
493. #405C22×C43semidirect
494. C2×#97C22×C43semidirect
495. C2×#97C22×C43semidirect
496. #341C22×C43semidirect
497. #341C22×C43semidirect
498. #339C22×C43semidirect
499. #339C22×C43semidirect
500. #336C22×C43semidirect
501. #336C22×C43semidirect
502. C43#22886direct (N × H)
524. C2×Q16C2×C4×C43semidirect
525. C2×Q16C2×C4×C43semidirect
526. C2×SD16C2×C4×C43semidirect
527. C2×SD16C2×C4×C43semidirect
528. C2×SD16C2×C4×C43semidirect
529. C2×SD16C2×C4×C43semidirect
530. C2×D8C2×C4×C43semidirect
531. C2×D8C2×C4×C43semidirect
579. #104D4×C43semidirect
580. #103C2×C4×C43semidirect
581. #103C2×C4×C43semidirect
582. #103C2×C4×C43semidirect
583. #103C2×C4×C43semidirect
584. #102C2×C4×C43semidirect
585. #102C2×C4×C43semidirect
586. #102C2×C4×C43semidirect
587. #102C2×C4×C43semidirect
840. C22C43×#444semidirect

Maximal subgroups

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

subgroupindex
C43×#30022
C2×C43×#4442
C43×#29332
C22×#104×C432
C43×#28802
C43×#19752
C43×#19382
C43×#19292
C43×#18962
C43×#18762
C43×#18662
C43×#18552
C43×#17652
C43×#17492
#2288643