Finite Group Databasebeta

← C43×#24017 #24944034

Subgroups — C43×#24017 #24944034

Order 11008.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#537C211yesmaximal, characteristic
2C2×C43×#485C211yesmaximal, characteristic, complemented
3C2×C43×#482C211yesmaximal, characteristic, complemented
4C43×#2311C211yesmaximal, characteristic, complemented
5C43×#2036C211yesmaximal, characteristic, complemented
6C43×#2035C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#1874C211yesmaximal, characteristic, complemented
10C43×#1872C211yesmaximal, characteristic, complemented
11C43×#1853C211yesmaximal, characteristic, complemented
12C43×#1852C211yesmaximal, characteristic, complemented
13C43×#1788C211yesmaximal, characteristic, complemented
14C43×#1788C211yesmaximal, characteristic, complemented
15C43×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C43×#537—24no—
19C43×#537—24no—
20C2×C22⋊Q8×C43—21no—
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×#121×C43—21no—
24C2×#121×C43—21no—
25C2×#121×C43—21no—
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×#117×C43C2211yescharacteristic
29C22×C4⋊C4×C43C2211yescharacteristic
30C22×C4⋊C4×C43C2211yescharacteristic
31C43×#485—24no—
32C43×#482—24no—
33C2×#107×C43C2211yescharacteristic
34C2×#107×C43C2211yescharacteristic
35C2×#106×C43C2211yescharacteristic
36C2×#106×C43C2211yescharacteristic
37C2×#103×C43C2211yescharacteristic
38C2×#103×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#103×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C2×C22⋊C8×C43C2211yescharacteristic
50C2×C22⋊C8×C43C2211yescharacteristic
51C43×#391—21no—
52C43×#390—21no—
53C43×#386—21no—
54C43×#386—21no—
55C43×#380C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C2×#41×C43—22no—
64C2×#41×C43—22no—
65C2×#41×C43—22no—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—22no—
71C2×#41×C43—41no—
72C2×#41×C43—41no—
73C2×#41×C43—41no—
74C2×#41×C43—41no—
75C22×Q8×C43D411yescharacteristic
76C22×Q8×C43C2311yescharacteristic
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43D411yescharacteristic
81C22×D4×C43D411yescharacteristic
82C22×D4×C43D411yescharacteristic
83C22×D4×C43C2311yescharacteristic
84C23×C4×C43—21no—
85C23×C4×C43—21no—
86C23×C4×C43—21no—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C22×C8×C43C2311yescharacteristic
91C22×C8×C43C2311yescharacteristic
92C22×C8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22⋊Q8×C43—28no—
95C22⋊Q8×C43—22no—
96C22⋊Q8×C43—22no—
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43D414yes—
99#121×C43—28no—
100#121×C43—28no—
101#121×C43—28no—
102#121×C43—22no—
103#121×C43—22no—
104#121×C43—22no—
105#121×C43D414yes—
106#117×C43—22no—
107#117×C43—22no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—41no—
115C2×C4⋊C4×C43—41no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C42×C43—21no—
132#107×C43—22no—
133#107×C43—22no—
134#106×C43—22no—
135#106×C43—22no—
136#103×C43—22no—
137#103×C43—22no—
138#103×C43—41no—
139#103×C43—41no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—41no—
143#102×C43—41no—
144C22⋊C8×C43—22no—
145C22⋊C8×C43—22no—
146C22⋊C8×C43—22no—
147C22⋊C8×C43—22no—
148C22⋊C8×C43—41no—
149C22⋊C8×C43—41no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157C24×C43C2×D411yescharacteristic
158#41×C43—44no—
159#41×C43—44no—
160#41×C43—44no—
161#41×C43—44no—
162#41×C43—44no—
163#41×C43—44no—
164#41×C43—44no—
165#41×C43—44no—
166C2×Q8×C43—22no—
167C2×Q8×C43—22no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—41no—
174C2×Q8×C43C2×D412yes—
175C2×D4×C43—24no—
176C2×D4×C43—24no—
177C2×D4×C43—22no—
178C2×D4×C43—22no—
179C2×D4×C43—21no—
180C2×D4×C43—22no—
181C2×D4×C43—22no—
182C2×D4×C43—24no—
183C2×D4×C43—22no—
184C2×D4×C43—22no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—41no—
190C2×D4×C43—41no—
191C2×D4×C43—41no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43—81no—
195C2×D4×C43—81no—
196C2×D4×C43—81no—
197C2×D4×C43—81no—
198C2×D4×C43C2×D412yes—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—24no—
208C22×C4×C43—24no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
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—42no—
223C22×C4×C43—42no—
224C22×C4×C43—42no—
225C22×C4×C43—81no—
226C22×C4×C43—81no—
227C22×C4×C43—81no—
228C22×C4×C43—81no—
229C22×C4×C43C2×D412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43#4112yes—
235C22×C4×C43#4112yes—
236C22×C4×C43C2411yescharacteristic
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—42no—
263C4⋊C4×C43C2×D412yes—
264C4⋊C4×C43C2×D412yes—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—24no—
267C22⋊C4×C43—24no—
268C22⋊C4×C43—24no—
269C22⋊C4×C43—42no—
270C22⋊C4×C43—81no—
271C22⋊C4×C43—81no—
272C22⋊C4×C43—81no—
273C22⋊C4×C43—81no—
274C42×C43—42no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—22no—
289C23×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—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43#12012yes—
302C23×C43#12312yes—
303C23×C43C22×D411yescharacteristic
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—44no—
307Q8×C43—41no—
308Q8×C43—41no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—44no—
312D4×C43—44no—
313D4×C43—44no—
314D4×C43—48no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—84no—
318D4×C43—84no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—48no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
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×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—84no—
361C2×C4×C43—84no—
362C2×C4×C43#12012yes—
363C2×C4×C43#12312yes—
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C2×#4111yescharacteristic
367C2×C4×C43C2×#4111yescharacteristic
368C2×C4×C43H(5,𝔽2)11yescharacteristic
369C2×C4×C43H(5,𝔽2)11yescharacteristic
370C8×C43—41no—
371C8×C43—41no—
372C8×C43—41no—
373C8×C43—41no—
374#24017C4311yesmaximal, characteristic, direct product factor, Sylow
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—42no—
397C22×C43—41no—
398C22×C43—42no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43C2×#12011yescharacteristic
404C22×C43C2×#12311yescharacteristic
405C22×C43#53411yescharacteristic
406C22×C43#57611yescharacteristic
407C22×C43#57711yescharacteristic
408C22×C43#57711yescharacteristic
409C22×C43#57811yescharacteristic
410C4×C43—22no—
411C4×C43—22no—
412C4×C43—41no—
413C4×C43—42no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43—81no—
417C4×C43—81no—
418C4×C43—81no—
419C4×C43—81no—
420C4×C43#54611yescharacteristic
421C4×C43#54611yescharacteristic
422C4×C43#54611yescharacteristic
423C4×C43#54611yescharacteristic
424C2×#537C2×C4311yescharacteristic
425C2×#485C2×C4311yescharacteristic, complemented
426C2×#482C2×C4311yescharacteristic, complemented
427#2311C2×C4311yescharacteristic, complemented
428#2036C2×C4311yescharacteristic, complemented
429#2035C2×C4311yescharacteristic, complemented
430#2034C2×C4311yescharacteristic, complemented
431#2033C2×C4311yescharacteristic, complemented
432#1874C2×C4311yescharacteristic, complemented
433#1872C2×C4311yescharacteristic, complemented
434#1853C2×C4311yescharacteristic, complemented
435#1852C2×C4311yescharacteristic, complemented
436#1788C2×C4311yescharacteristic, complemented
437#1788C2×C4311yescharacteristic, complemented
438#1780C2×C4311yescharacteristic, complemented
439C2×C43—42no—
440C2×C43—42no—
441C2×C43—81no—
442C2×C43—82no—
443C2×C43#240511yescharacteristic
444C2×C43#301211yescharacteristic
445C2×C43#301311yescharacteristic
446C2×C43#309811yescharacteristic
447C2×C43#309911yescharacteristic
448C2×C43#319811yescharacteristic
449C2×C43#320111yescharacteristic
450C22×#41C22×C4311yescharacteristic
451C22×#41C22×C4311yescharacteristic
452#537—24no—
453#537—24no—
454C2×C22⋊Q8—21no—
455C2×C22⋊Q8C22×C4311yescharacteristic
456C2×C22⋊Q8C22×C4311yescharacteristic
457C2×#121—21no—
458C2×#121—21no—
459C2×#121—21no—
460C2×#121C22×C4311yescharacteristic
461C2×#121C22×C4311yescharacteristic
462C2×#117C22×C4311yescharacteristic
463C22×C4⋊C4C22×C4311yescharacteristic
464C22×C4⋊C4C22×C4311yescharacteristic
465#485—24no—
466#482—24no—
467C2×#107C22×C4311yescharacteristic
468C2×#107C22×C4311yescharacteristic
469C2×#106C22×C4311yescharacteristic
470C2×#106C22×C4311yescharacteristic
471C2×#103C22×C4311yescharacteristic
472C2×#103C22×C4311yescharacteristic
473C2×#103C22×C4311yescharacteristic
474C2×#103C22×C4311yescharacteristic
475C2×#102C22×C4311yescharacteristic
476C2×#102C22×C4311yescharacteristic
477C2×#102C22×C4311yescharacteristic
478C2×#102C22×C4311yescharacteristic
479C2×C22⋊C8C22×C4311yescharacteristic
480C2×C22⋊C8C22×C4311yescharacteristic
481C2×C22⋊C8C22×C4311yescharacteristic
482C2×C22⋊C8C22×C4311yescharacteristic
483C2×C22⋊C8C22×C4311yescharacteristic
484C2×C22⋊C8C22×C4311yescharacteristic
485#391—21no—
486#390—21no—
487#386—21no—
488#386—21no—
489#380C22×C4311yescharacteristic
490#380C22×C4311yescharacteristic
491#380C22×C4311yescharacteristic
492#380C22×C4311yescharacteristic
493#340C22×C4311yescharacteristic
494#340C22×C4311yescharacteristic
495#340C22×C4311yescharacteristic
496#340C22×C4311yescharacteristic
497C43#2401711yescharacteristic, direct product factor, Sylow
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8D4×C4311yescharacteristic
511C22×Q8C23×C4311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C4311yescharacteristic
516C22×D4D4×C4311yescharacteristic
517C22×D4D4×C4311yescharacteristic
518C22×D4C23×C4311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C4311yescharacteristic
523C23×C4C23×C4311yescharacteristic
524C23×C4C23×C4311yescharacteristic
525C22×C8C23×C4311yescharacteristic
526C22×C8C23×C4311yescharacteristic
527C22×C8C23×C4311yescharacteristic
528C22×C8C23×C4311yescharacteristic
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8D4×C4314yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C4314yes—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C4311yescharacteristic
552C2×C4⋊C4C23×C4311yescharacteristic
553C2×C4⋊C4C23×C4311yescharacteristic
554C2×C4⋊C4C23×C4311yescharacteristic
555C2×C4⋊C4C23×C4311yescharacteristic
556C2×C4⋊C4C23×C4311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C42—21no—
567#107—22no—
568#107—22no—
569#106—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C4311yescharacteristic
591C24C2×D4×C4311yescharacteristic
592C24C2×D4×C4311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C4312yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C4312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
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—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C4311yescharacteristic
665C22×C4C2×D4×C4311yescharacteristic
666C22×C4C2×D4×C4312yes—
667C22×C4C2×D4×C4312yes—
668C22×C4C2×D4×C4311yescharacteristic
669C22×C4#41×C4312yes—
670C22×C4#41×C4312yes—
671C22×C4C24×C4311yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—42no—
698C4⋊C4C2×D4×C4312yes—
699C4⋊C4C2×D4×C4312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#120×C4312yes—
737C23#123×C4312yes—
738C23C22×D4×C4311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
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×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
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×C4—84no—
796C2×C4—84no—
797C2×C4#120×C4312yes—
798C2×C4#123×C4312yes—
799C2×C4C22×D4×C4311yescharacteristic
800C2×C4C22×D4×C4311yescharacteristic
801C2×C4C2×#41×C4311yescharacteristic
802C2×C4C2×#41×C4311yescharacteristic
803C2×C4H(5,𝔽2)×C4311yescharacteristic
804C2×C4H(5,𝔽2)×C4311yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#120×C4311yescharacteristic
838C22C2×#123×C4311yescharacteristic
839C22C43×#53411yescharacteristic
840C22C43×#57611yescharacteristic
841C22C43×#57711yescharacteristic
842C22C43×#57711yescharacteristic
843C22C43×#57811yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4C43×#54611yescharacteristic
855C4C43×#54611yescharacteristic
856C4C43×#54611yescharacteristic
857C4C43×#54611yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C43×#240511yescharacteristic
863C2C43×#301211yescharacteristic
864C2C43×#301311yescharacteristic
865C2C43×#309811yescharacteristic
866C2C43×#309911yescharacteristic
867C2C43×#319811yescharacteristic
868C2C43×#320111yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#485C2semidirect
3. C2×C43×#482C2semidirect
4. C43×#2311C2semidirect
5. C43×#2036C2semidirect
6. C43×#2035C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#1874C2semidirect
10. C43×#1872C2semidirect
11. C43×#1853C2semidirect
12. C43×#1852C2semidirect
13. C43×#1788C2semidirect
14. C43×#1788C2semidirect
15. C43×#1780C2semidirect
374. #24017C43direct (N × H)
425. C2×#485C2×C43semidirect
426. C2×#482C2×C43semidirect
427. #2311C2×C43semidirect
428. #2036C2×C43semidirect
429. #2035C2×C43semidirect
430. #2034C2×C43semidirect
431. #2033C2×C43semidirect
432. #1874C2×C43semidirect
433. #1872C2×C43semidirect
434. #1853C2×C43semidirect
435. #1852C2×C43semidirect
436. #1788C2×C43semidirect
437. #1788C2×C43semidirect
438. #1780C2×C43semidirect
497. C43#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5372
C2×C43×#4852
C2×C43×#4822
C43×#23112
C43×#20362
C43×#20352
C43×#20342
C43×#20332
C43×#18742
C43×#18722
C43×#18532
C43×#18522
C43×#17882
C43×#17802
#2401743