Finite Group Databasebeta

← C43×#24886 #24944903

Subgroups — C43×#24886 #24944903

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#482C211yesmaximal, characteristic, complemented
2C2×C43×#418C211yesmaximal, characteristic, complemented
3C43×#2408C211yesmaximal, characteristic
4C43×#2354C211yesmaximal, characteristic, complemented
5C43×#2094C211yesmaximal, characteristic, complemented
6C43×#2071C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#1925C211yesmaximal, characteristic, complemented
10C43×#1925C211yesmaximal, characteristic, complemented
11C43×#1875C211yesmaximal, characteristic, complemented
12C43×#1870C211yesmaximal, characteristic, complemented
13C43×#1854C211yesmaximal, characteristic, complemented
14C43×#1809C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×M16×C43C2211yescharacteristic
18C2×#121×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×#120×C43—21no—
21C2×C4×D4×C43C2211yescharacteristic
22C2×#117×C43C2211yescharacteristic
23C2×#117×C43C2211yescharacteristic, complemented
24C43×#482—24no—
25C2×#107×C43C2211yescharacteristic, complemented
26C2×#107×C43C2211yescharacteristic, complemented
27C2×#106×C43C2211yescharacteristic, complemented
28C2×#106×C43C2211yescharacteristic, complemented
29C43×#418—24no—
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic, complemented
40C2×C22⋊C8×C43C2211yescharacteristic, complemented
41C43×#394—21no—
42C43×#392—21no—
43C43×#390—21no—
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic
46C43×#388—21no—
47C43×#388—21no—
48C43×#384C2211yescharacteristic, complemented
49C43×#380C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#380C2211yescharacteristic, complemented
52C43×#379—21no—
53C4×C4⋊C4×C43—21no—
54C4×C4⋊C4×C43C2211yescharacteristic, complemented
55C43×#340C2211yescharacteristic, complemented
56C43×#340C2211yescharacteristic, complemented
57C43×#340C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C25×C43—21no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—22no—
68C22×D4×C43—22no—
69C22×D4×C43—41no—
70C22×D4×C43—41no—
71C22×D4×C43D411yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C22×D4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76C2×M16×C43—22no—
77C2×M16×C43—22no—
78C2×M16×C43—41no—
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83#121×C43—22no—
84#121×C43—22no—
85#121×C43—41no—
86#121×C43—41no—
87#120×C43—44no—
88C4×D4×C43—22no—
89C4×D4×C43—22no—
90#117×C43—22no—
91#117×C43—22no—
92#117×C43—41no—
93#117×C43—41no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43D411yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#107×C43—22no—
121#107×C43—41no—
122#106×C43—22no—
123#106×C43—41no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129#102×C43—41no—
130#102×C43—41no—
131#102×C43D414yescomplemented
132C22⋊C8×C43—22no—
133C22⋊C8×C43—22no—
134C22⋊C8×C43—41no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C2×D4×C43—22no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—22no—
154C2×D4×C43—28no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—41no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—44no—
171C2×D4×C43—44no—
172C2×D4×C43—44no—
173C2×D4×C43—42no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C2×D4×C43C2×D412yes—
177C2×D4×C43#4112yes—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43#4112yes—
199C22×C4×C43#4112yes—
200C22×C4×C43C2411yescharacteristic
201M16×C43—44no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43C2×D412yes—
214C4⋊C4×C43—22no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—42no—
227C4⋊C4×C43—81no—
228C4⋊C4×C43C2×D412yes—
229C22⋊C4×C43—22no—
230C22⋊C4×C43—22no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—81no—
239C22⋊C4×C43—81no—
240C22⋊C4×C43—81no—
241C22⋊C4×C43—81no—
242C42×C43—21no—
243C42×C43—21no—
244C42×C43—42no—
245C42×C43—42no—
246C42×C43—42no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—48no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—84no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43—84no—
279C23×C43—84no—
280C23×C43—84no—
281C23×C43#12312yes—
282C23×C43C22×D411yescharacteristic
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—44no—
288D4×C43—48no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—84no—
294D4×C43—84no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—22no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43#12312yes—
332C2×C4×C43AGL(1,ℤ/8)12yes—
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C2×#4111yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43H(5,𝔽2)11yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C8×C43—22no—
340C8×C43—41no—
341C8×C43—41no—
342C8×C43—41no—
343#24886C4311yesmaximal, characteristic, direct product factor, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—41no—
357C22×C43—42no—
358C22×C43—41no—
359C22×C43—42no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—41no—
363C22×C43—42no—
364C22×C43—816no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43C2×#12311yescharacteristic
374C22×C43D4211yescharacteristic
375C22×C43#54611yescharacteristic
376C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C43#57511yescharacteristic
378C22×C43#57611yescharacteristic
379C22×C43#57711yescharacteristic
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—42no—
385C4×C43—81no—
386C4×C43—81no—
387C4×C43—81no—
388C4×C43—81no—
389C4×C43—81no—
390C4×C43#52511yescharacteristic
391C4×C43#53811yescharacteristic
392C4×C43#54611yescharacteristic
393C4×C43#55111yescharacteristic
394C2×#482C2×C4311yescharacteristic, complemented
395C2×#418C2×C4311yescharacteristic, complemented
396#2408C2×C4311yescharacteristic
397#2354C2×C4311yescharacteristic, complemented
398#2094C2×C4311yescharacteristic, complemented
399#2071C2×C4311yescharacteristic, complemented
400#2034C2×C4311yescharacteristic, complemented
401#2033C2×C4311yescharacteristic, complemented
402#1925C2×C4311yescharacteristic, complemented
403#1925C2×C4311yescharacteristic, complemented
404#1875C2×C4311yescharacteristic, complemented
405#1870C2×C4311yescharacteristic, complemented
406#1854C2×C4311yescharacteristic, complemented
407#1809C2×C4311yescharacteristic, complemented
408#1786C2×C4311yescharacteristic, complemented
409C2×C43—42no—
410C2×C43—81no—
411C2×C43—82no—
412C2×C43—82no—
413C2×C43#241811yescharacteristic
414C2×C43#309411yescharacteristic
415C2×C43#309611yescharacteristic
416C2×C43#326811yescharacteristic
417C2×C43#327211yescharacteristic
418C2×C43#331111yescharacteristic
419C2×C43#332511yescharacteristic
420C23×D4C22×C4311yescharacteristic
421C22×M16C22×C4311yescharacteristic
422C2×#121C22×C4311yescharacteristic
423C2×#121C22×C4311yescharacteristic
424C2×#120—21no—
425C2×C4×D4C22×C4311yescharacteristic
426C2×#117C22×C4311yescharacteristic
427C2×#117C22×C4311yescharacteristic, complemented
428#482—24no—
429C2×#107C22×C4311yescharacteristic, complemented
430C2×#107C22×C4311yescharacteristic, complemented
431C2×#106C22×C4311yescharacteristic, complemented
432C2×#106C22×C4311yescharacteristic, complemented
433#418—24no—
434C2×#102C22×C4311yescharacteristic
435C2×#102C22×C4311yescharacteristic
436C2×#102C22×C4311yescharacteristic
437C2×#102C22×C4311yescharacteristic
438C2×#102C22×C4311yescharacteristic
439C2×#102C22×C4311yescharacteristic
440C2×#102C22×C4311yescharacteristic
441C2×#102C22×C4311yescharacteristic
442C2×C22⋊C8C22×C4311yescharacteristic
443C2×C22⋊C8C22×C4311yescharacteristic, complemented
444C2×C22⋊C8C22×C4311yescharacteristic, complemented
445#394—21no—
446#392—21no—
447#390—21no—
448#390C22×C4311yescharacteristic
449#390C22×C4311yescharacteristic
450#388—21no—
451#388—21no—
452#384C22×C4311yescharacteristic, complemented
453#380C22×C4311yescharacteristic
454#380C22×C4311yescharacteristic
455#380C22×C4311yescharacteristic, complemented
456#379—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C22×C4311yescharacteristic, complemented
459#340C22×C4311yescharacteristic, complemented
460#340C22×C4311yescharacteristic, complemented
461#340C22×C4311yescharacteristic, complemented
462#340C22×C4311yescharacteristic, complemented
463#336C22×C4311yescharacteristic, complemented
464#336C22×C4311yescharacteristic, complemented
465C43#2488611yescharacteristic, direct product factor, Sylow
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4D4×C4311yescharacteristic
477C22×D4C23×C4311yescharacteristic
478C22×D4C23×C4311yescharacteristic
479C23×C4C23×C4311yescharacteristic
480C23×C4C23×C4311yescharacteristic
481C2×M16—22no—
482C2×M16—22no—
483C2×M16—41no—
484C22×C8C23×C4311yescharacteristic
485C22×C8C23×C4311yescharacteristic
486C22×C8C23×C4311yescharacteristic
487C22×C8C23×C4311yescharacteristic
488#121—22no—
489#121—22no—
490#121—41no—
491#121—41no—
492#120—44no—
493C4×D4—22no—
494C4×D4—22no—
495#117—22no—
496#117—22no—
497#117—41no—
498#117—41no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C4311yescharacteristic
502C2×C4⋊C4C23×C4311yescharacteristic
503C2×C4⋊C4C23×C4311yescharacteristic
504C2×C4⋊C4C23×C4311yescharacteristic
505C2×C4⋊C4C23×C4311yescharacteristic
506C2×C4⋊C4C23×C4311yescharacteristic
507C2×C4⋊C4C23×C4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C4311yescharacteristic
520C2×C22⋊C4D4×C4311yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C23×C4311yescharacteristic
525#107—22no—
526#107—41no—
527#106—22no—
528#106—41no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—41no—
535#102—41no—
536#102D4×C4314yescomplemented
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—41no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24C2×D4×C4311yescharacteristic
554C24C2×D4×C4311yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4C2×D4×C4312yes—
582C2×D4#41×C4312yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4C2×D4×C4311yescharacteristic
600C22×C4C2×D4×C4311yescharacteristic
601C22×C4C2×D4×C4311yescharacteristic
602C22×C4C2×D4×C4311yescharacteristic
603C22×C4#41×C4312yes—
604C22×C4#41×C4312yes—
605C22×C4C24×C4311yescharacteristic
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×D4×C4312yes—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—81no—
633C4⋊C4C2×D4×C4312yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—42no—
651C42—42no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#123×C4312yes—
687C23C22×D4×C4311yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4#123×C4312yes—
737C2×C4AGL(1,ℤ/8)×C4312yes—
738C2×C4C22×D4×C4311yescharacteristic
739C2×C4C2×#41×C4311yescharacteristic
740C2×C4C2×#41×C4311yescharacteristic
741C2×C4C2×#41×C4311yescharacteristic
742C2×C4H(5,𝔽2)×C4311yescharacteristic
743C2×C4H(5,𝔽2)×C4311yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—42no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#123×C4311yescharacteristic
778C22D42×C4311yescharacteristic
779C22C43×#54611yescharacteristic
780C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
781C22C43×#57511yescharacteristic
782C22C43×#57611yescharacteristic
783C22C43×#57711yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—42no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4C43×#52511yescharacteristic
795C4C43×#53811yescharacteristic
796C4C43×#54611yescharacteristic
797C4C43×#55111yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2C43×#241811yescharacteristic
803C2C43×#309411yescharacteristic
804C2C43×#309611yescharacteristic
805C2C43×#326811yescharacteristic
806C2C43×#327211yescharacteristic
807C2C43×#331111yescharacteristic
808C2C43×#332511yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#482C2semidirect
2. C2×C43×#418C2semidirect
4. C43×#2354C2semidirect
5. C43×#2094C2semidirect
6. C43×#2071C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#1925C2semidirect
10. C43×#1925C2semidirect
11. C43×#1875C2semidirect
12. C43×#1870C2semidirect
13. C43×#1854C2semidirect
14. C43×#1809C2semidirect
15. C43×#1786C2semidirect
23. C2×#117×C43C22semidirect
25. C2×#107×C43C22semidirect
26. C2×#107×C43C22semidirect
27. C2×#106×C43C22semidirect
28. C2×#106×C43C22semidirect
39. C2×C22⋊C8×C43C22semidirect
40. C2×C22⋊C8×C43C22semidirect
48. C43×#384C22semidirect
51. C43×#380C22semidirect
54. C4×C4⋊C4×C43C22semidirect
55. C43×#340C22semidirect
56. C43×#340C22semidirect
57. C43×#340C22semidirect
58. C43×#340C22semidirect
59. C43×#336C22semidirect
60. C43×#336C22semidirect
131. #102×C43D4semidirect
343. #24886C43direct (N × H)
394. C2×#482C2×C43semidirect
395. C2×#418C2×C43semidirect
397. #2354C2×C43semidirect
398. #2094C2×C43semidirect
399. #2071C2×C43semidirect
400. #2034C2×C43semidirect
401. #2033C2×C43semidirect
402. #1925C2×C43semidirect
403. #1925C2×C43semidirect
404. #1875C2×C43semidirect
405. #1870C2×C43semidirect
406. #1854C2×C43semidirect
407. #1809C2×C43semidirect
408. #1786C2×C43semidirect
427. C2×#117C22×C43semidirect
429. C2×#107C22×C43semidirect
430. C2×#107C22×C43semidirect
431. C2×#106C22×C43semidirect
432. C2×#106C22×C43semidirect
443. C2×C22⋊C8C22×C43semidirect
444. C2×C22⋊C8C22×C43semidirect
452. #384C22×C43semidirect
455. #380C22×C43semidirect
458. C4×C4⋊C4C22×C43semidirect
459. #340C22×C43semidirect
460. #340C22×C43semidirect
461. #340C22×C43semidirect
462. #340C22×C43semidirect
463. #336C22×C43semidirect
464. #336C22×C43semidirect
465. C43#24886direct (N × H)
536. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4822
C2×C43×#4182
C43×#24082
C43×#23542
C43×#20942
C43×#20712
C43×#20342
C43×#20332
C43×#19252
C43×#18752
C43×#18702
C43×#18542
C43×#18092
C43×#17862
#2488643