Finite Group Databasebeta

← C43×#25131 #24945148

Subgroups — C43×#25131 #24945148

Order 11008.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#468C211yesmaximal, characteristic, complemented
2C2×C43×#449C211yesmaximal, characteristic, complemented
3C2×C43×#435C211yesmaximal, characteristic, complemented
4C2×C43×#416C211yesmaximal, characteristic, complemented
5C43×#2414C211yesmaximal, characteristic, complemented
6C43×#2407C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic, complemented
8C43×#2055C211yesmaximal, characteristic, complemented
9C43×#2035C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1972C211yesmaximal, characteristic, complemented
12C43×#1935C211yesmaximal, characteristic, complemented
13C43×#1895C211yesmaximal, characteristic, complemented
14C43×#1893C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×M16×C43C2211yescharacteristic
20C23×C8×C43C2211yescharacteristic
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C2×#117×C43C2211yescharacteristic
27C43×#468—24no—
28C43×#449—24no—
29C43×#435—24no—
30C2×#107×C43C2211yescharacteristic
31C2×#106×C43C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C43×#416—24no—
34C2×#103×C43C2211yescharacteristic
35C2×#103×C43C2211yescharacteristic
36C2×#103×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×C22⋊C8×C43C2211yescharacteristic
43C2×C22⋊C8×C43C2211yescharacteristic
44C2×#97×C43C2211yescharacteristic
45C43×#394—21no—
46C43×#394—21no—
47C43×#392—21no—
48C43×#392—21no—
49C43×#391C2211yescharacteristic
50C43×#390—21no—
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#386—21no—
56C43×#385—21no—
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—41no—
68C2×#41×C43—41no—
69C22×Q8×C43C2311yescharacteristic
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43D411yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C22×D4×C43C2311yescharacteristic
77C23×C4×C43—21no—
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2311yescharacteristic
80C2×SD16×C43—22no—
81C2×SD16×C43—22no—
82C2×SD16×C43—41no—
83C2×D8×C43—22no—
84C2×D8×C43—22no—
85C2×D8×C43—41no—
86C2×M16×C43—22no—
87C2×M16×C43—22no—
88C2×M16×C43—41no—
89C22×C8×C43—22no—
90C22×C8×C43—22no—
91C22×C8×C43—41no—
92C22×C8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22⋊Q8×C43—22no—
97C22⋊Q8×C43—41no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—41no—
103#121×C43—41no—
104C4×D4×C43—22no—
105C4×D4×C43—22no—
106#117×C43—22no—
107#117×C43—41no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
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×C43D411yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#107×C43—22no—
132#106×C43—41no—
133C4⋊C8×C43—22no—
134#103×C43—22no—
135#103×C43—22no—
136#103×C43D414yescomplemented
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—41no—
142C22⋊C8×C43—22no—
143C22⋊C8×C43D414yescomplemented
144#97×C43—22no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43—21no—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43C2×D411yescharacteristic
153C24×C43C2×D411yescharacteristic
154#41×C43—28no—
155#41×C43—44no—
156#41×C43—44no—
157#41×C43—44no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43C2×D412yes—
164C2×D4×C43—21no—
165C2×D4×C43—22no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—41no—
177C2×D4×C43—41no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—81no—
187C2×D4×C43—81no—
188C2×D4×C43—81no—
189C2×D4×C43—81no—
190C2×D4×C43#4112yes—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
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—42no—
208C22×C4×C43—42no—
209C22×C4×C43—42no—
210C22×C4×C43C2×D412yes—
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43#4112yes—
216C22×C4×C43C2411yescharacteristic
217SD16×C43—44no—
218D8×C43—44no—
219M16×C43—44no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—44no—
230C2×C8×C43C2×D412yes—
231C2×C8×C43C2×D412yes—
232C2×C8×C43C2×D412yes—
233C4⋊C4×C43—22no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—42no—
244C4⋊C4×C43—81no—
245C4⋊C4×C43C2×D412yes—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—42no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—81no—
256C22⋊C4×C43—81no—
257C22⋊C4×C43—81no—
258C22⋊C4×C43—81no—
259C42×C43—21no—
260C42×C43—21no—
261C42×C43—42no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—22no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43#12112yes—
290C23×C43C22×D411yescharacteristic
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—41no—
294Q8×C43—41no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—44no—
298D4×C43—48no—
299D4×C43—41no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—84no—
306D4×C43—84no—
307D4×C43—84no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—21no—
319C2×C4×C43—22no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—48no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
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#12112yes—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C2×C4×C43C2×#4111yescharacteristic
351C2×C4×C43H(5,𝔽2)11yescharacteristic
352C2×C4×C43H(5,𝔽2)11yescharacteristic
353C8×C43—22no—
354C8×C43—22no—
355C8×C43—22no—
356C8×C43—41no—
357#25131C4311yesmaximal, characteristic, direct product factor, Sylow
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—42no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—42no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—42no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43—81no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43—81no—
386C22×C43C2×#12111yescharacteristic
387C22×C43D4211yescharacteristic
388C22×C43#54611yescharacteristic
389C22×C43#57511yescharacteristic
390C22×C43#57511yescharacteristic
391C22×C43#57611yescharacteristic
392C22×C43#57711yescharacteristic
393C4×C43—22no—
394C4×C43—41no—
395C4×C43—42no—
396C4×C43—42no—
397C4×C43—41no—
398C4×C43—41no—
399C4×C43—81no—
400C4×C43—81no—
401C4×C43—81no—
402C4×C43—81no—
403C4×C43#52511yescharacteristic
404C4×C43#53811yescharacteristic
405C4×C43D4211yescharacteristic
406C4×C43#54611yescharacteristic
407C2×#468C2×C4311yescharacteristic, complemented
408C2×#449C2×C4311yescharacteristic, complemented
409C2×#435C2×C4311yescharacteristic, complemented
410C2×#416C2×C4311yescharacteristic, complemented
411#2414C2×C4311yescharacteristic, complemented
412#2407C2×C4311yescharacteristic, complemented
413#2067C2×C4311yescharacteristic, complemented
414#2055C2×C4311yescharacteristic, complemented
415#2035C2×C4311yescharacteristic, complemented
416#1999C2×C4311yescharacteristic, complemented
417#1972C2×C4311yescharacteristic, complemented
418#1935C2×C4311yescharacteristic, complemented
419#1895C2×C4311yescharacteristic, complemented
420#1893C2×C4311yescharacteristic, complemented
421#1854C2×C4311yescharacteristic, complemented
422C2×C43—42no—
423C2×C43—81no—
424C2×C43—82no—
425C2×C43—161no—
426C2×C43#242411yescharacteristic
427C2×C43#305411yescharacteristic
428C2×C43#306211yescharacteristic
429C2×C43#326811yescharacteristic
430C2×C43#327111yescharacteristic
431C2×C43#330711yescharacteristic
432C2×C43#331911yescharacteristic
433C22×#41C22×C4311yescharacteristic
434C22×SD16C22×C4311yescharacteristic
435C22×D8C22×C4311yescharacteristic
436C22×M16C22×C4311yescharacteristic
437C23×C8C22×C4311yescharacteristic
438C2×C22⋊Q8C22×C4311yescharacteristic
439C2×#121C22×C4311yescharacteristic
440C2×#121C22×C4311yescharacteristic
441C2×#121C22×C4311yescharacteristic
442C2×C4×D4C22×C4311yescharacteristic
443C2×#117C22×C4311yescharacteristic
444#468—24no—
445#449—24no—
446#435—24no—
447C2×#107C22×C4311yescharacteristic
448C2×#106C22×C4311yescharacteristic
449C2×C4⋊C8C22×C4311yescharacteristic
450#416—24no—
451C2×#103C22×C4311yescharacteristic
452C2×#103C22×C4311yescharacteristic
453C2×#103C22×C4311yescharacteristic
454C2×#102C22×C4311yescharacteristic
455C2×#102C22×C4311yescharacteristic
456C2×#102C22×C4311yescharacteristic
457C2×#102C22×C4311yescharacteristic
458C2×#102C22×C4311yescharacteristic
459C2×C22⋊C8C22×C4311yescharacteristic
460C2×C22⋊C8C22×C4311yescharacteristic
461C2×#97C22×C4311yescharacteristic
462#394—21no—
463#394—21no—
464#392—21no—
465#392—21no—
466#391C22×C4311yescharacteristic
467#390—21no—
468#390C22×C4311yescharacteristic
469#390C22×C4311yescharacteristic
470#389C22×C4311yescharacteristic
471#388—21no—
472#386—21no—
473#385—21no—
474#380C22×C4311yescharacteristic
475#380C22×C4311yescharacteristic
476#340C22×C4311yescharacteristic
477#340C22×C4311yescharacteristic
478#340C22×C4311yescharacteristic
479#340C22×C4311yescharacteristic
480C43#2513111yescharacteristic, direct product factor, Sylow
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8C23×C4311yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C4311yescharacteristic
493C22×D4C23×C4311yescharacteristic
494C22×D4C23×C4311yescharacteristic
495C23×C4—21no—
496C23×C4C23×C4311yescharacteristic
497C23×C4C23×C4311yescharacteristic
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C23×C4311yescharacteristic
511C22×C8C23×C4311yescharacteristic
512C22×C8C23×C4311yescharacteristic
513C22×C8C23×C4311yescharacteristic
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522C4×D4—22no—
523C4×D4—22no—
524#117—22no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4D4×C4311yescharacteristic
529C2×C4⋊C4C23×C4311yescharacteristic
530C2×C4⋊C4C23×C4311yescharacteristic
531C2×C4⋊C4C23×C4311yescharacteristic
532C2×C4⋊C4C23×C4311yescharacteristic
533C2×C4⋊C4C23×C4311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C4311yescharacteristic
546C2×C22⋊C4D4×C4311yescharacteristic
547C2×C42—21no—
548C2×C42C23×C4311yescharacteristic
549#107—22no—
550#106—41no—
551C4⋊C8—22no—
552#103—22no—
553#103—22no—
554#103D4×C4314yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8D4×C4314yescomplemented
562#97—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C4311yescharacteristic
571C24C2×D4×C4311yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C4312yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4#41×C4312yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×D4×C4311yescharacteristic
629C22×C4C2×D4×C4311yescharacteristic
630C22×C4C2×D4×C4311yescharacteristic
631C22×C4C2×D4×C4311yescharacteristic
632C22×C4C2×D4×C4312yes—
633C22×C4#41×C4312yes—
634C22×C4C24×C4311yescharacteristic
635SD16—44no—
636D8—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C4312yes—
649C2×C8C2×D4×C4312yes—
650C2×C8C2×D4×C4312yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C4312yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—42no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23#121×C4312yes—
708C23C22×D4×C4311yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4#121×C4312yes—
765C2×C4C22×D4×C4311yescharacteristic
766C2×C4C22×D4×C4311yescharacteristic
767C2×C4C2×#41×C4311yescharacteristic
768C2×C4C2×#41×C4311yescharacteristic
769C2×C4H(5,𝔽2)×C4311yescharacteristic
770C2×C4H(5,𝔽2)×C4311yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C4311yescharacteristic
804C22D42×C4311yescharacteristic
805C22C43×#54611yescharacteristic
806C22C43×#57511yescharacteristic
807C22C43×#57511yescharacteristic
808C22C43×#57611yescharacteristic
809C22C43×#57711yescharacteristic
810C4—22no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—41no—
815C4—41no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C43×#52511yescharacteristic
821C4C43×#53811yescharacteristic
822C4D42×C4311yescharacteristic
823C4C43×#54611yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—161no—
828C2C43×#242411yescharacteristic
829C2C43×#305411yescharacteristic
830C2C43×#306211yescharacteristic
831C2C43×#326811yescharacteristic
832C2C43×#327111yescharacteristic
833C2C43×#330711yescharacteristic
834C2C43×#331911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
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×#468C2semidirect
2. C2×C43×#449C2semidirect
3. C2×C43×#435C2semidirect
4. C2×C43×#416C2semidirect
5. C43×#2414C2semidirect
6. C43×#2407C2semidirect
7. C43×#2067C2semidirect
8. C43×#2055C2semidirect
9. C43×#2035C2semidirect
10. C43×#1999C2semidirect
11. C43×#1972C2semidirect
12. C43×#1935C2semidirect
13. C43×#1895C2semidirect
14. C43×#1893C2semidirect
15. C43×#1854C2semidirect
136. #103×C43D4semidirect
143. C22⋊C8×C43D4semidirect
357. #25131C43direct (N × H)
407. C2×#468C2×C43semidirect
408. C2×#449C2×C43semidirect
409. C2×#435C2×C43semidirect
410. C2×#416C2×C43semidirect
411. #2414C2×C43semidirect
412. #2407C2×C43semidirect
413. #2067C2×C43semidirect
414. #2055C2×C43semidirect
415. #2035C2×C43semidirect
416. #1999C2×C43semidirect
417. #1972C2×C43semidirect
418. #1935C2×C43semidirect
419. #1895C2×C43semidirect
420. #1893C2×C43semidirect
421. #1854C2×C43semidirect
480. C43#25131direct (N × H)
554. #103D4×C43semidirect
561. C22⋊C8D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4682
C2×C43×#4492
C2×C43×#4352
C2×C43×#4162
C43×#24142
C43×#24072
C43×#20672
C43×#20552
C43×#20352
C43×#19992
C43×#19722
C43×#19352
C43×#18952
C43×#18932
C43×#18542
#2513143