Finite Group Databasebeta

← C43×#25087 #24945104

Subgroups — C43×#25087 #24945104

Order 11008.

1192 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#466C211yesmaximal, characteristic, complemented
2C2×C43×#463C211yesmaximal, characteristic, complemented
3C2×C43×#449C211yesmaximal, characteristic, complemented
4C2×C43×#416C211yesmaximal, characteristic, complemented
5C43×#2431C211yesmaximal, characteristic, complemented
6C43×#2363C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic, complemented
8C43×#2055C211yesmaximal, characteristic, complemented
9C43×#2042C211yesmaximal, characteristic, complemented
10C43×#2011C211yesmaximal, characteristic, complemented
11C43×#1982C211yesmaximal, characteristic, complemented
12C43×#1928C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1875C211yesmaximal, characteristic, complemented
15C43×#1850C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C23×C8×C43C2211yescharacteristic
21C2×#127×C43C2211yescharacteristic
22C2×#124×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C2×#117×C43C2211yescharacteristic
27C43×#466—24no—
28C43×#463—24no—
29C43×#449—24no—
30C2×#107×C43C2211yescharacteristic
31C2×C4⋊C8×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×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic
45C43×#392—21no—
46C43×#392—21no—
47C43×#391C2211yescharacteristic
48C43×#390—21no—
49C43×#390C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#388—21no—
53C43×#386—21no—
54C43×#386—21no—
55C43×#386—21no—
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C22⋊C4×C43—21no—
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
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×C43—21no—
75C22×D4×C43C2311yescharacteristic
76C22×D4×C43C2311yescharacteristic
77C22×D4×C43C2311yescharacteristic
78C23×C4×C43—21no—
79C23×C4×C43—21no—
80C23×C4×C43C2311yescharacteristic
81C2×SD16×C43—22no—
82C2×SD16×C43—22no—
83C2×SD16×C43—41no—
84C2×D8×C43—22no—
85C2×D8×C43—22no—
86C2×D8×C43—22no—
87C2×D8×C43—22no—
88C2×D8×C43—41no—
89C2×D8×C43—41no—
90C22×C8×C43—22no—
91C22×C8×C43—22no—
92C22×C8×C43—41no—
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97#127×C43—22no—
98#127×C43—41no—
99#124×C43—22no—
100#124×C43—41no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—22no—
104#121×C43D414yescomplemented
105C4×D4×C43—22no—
106C4×D4×C43—41no—
107#117×C43—22no—
108#117×C43—41no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
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×C43D411yescharacteristic
125C2×C22⋊C4×C43D411yescharacteristic
126C2×C42×C43—21no—
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130#107×C43—22no—
131C4⋊C8×C43—22no—
132C4⋊C8×C43—41no—
133#103×C43—22no—
134#103×C43—22no—
135#103×C43D414yescomplemented
136#102×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—41no—
143C22⋊C8×C43—22no—
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43D411yescharacteristic
149#95×C43D411yescharacteristic
150C24×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
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—21no—
166C2×D4×C43—24no—
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—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—42no—
182C2×D4×C43—42no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—81no—
190C2×D4×C43—81no—
191C2×D4×C43—81no—
192C2×D4×C43—81no—
193C2×D4×C43—81no—
194C2×D4×C43—81no—
195C2×D4×C43C2×D412yes—
196C2×D4×C43#4112yes—
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—42no—
207C22×C4×C43—42no—
208C22×C4×C43—42no—
209C22×C4×C43—42no—
210C22×C4×C43—42no—
211C22×C4×C43—81no—
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43#4112yes—
219C22×C4×C43C2411yescharacteristic
220SD16×C43—44no—
221D8×C43—44no—
222D8×C43—44no—
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—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—44no—
235C2×C8×C43C2×D412yes—
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—81no—
243C4⋊C4×C43C2×D412yes—
244C4⋊C4×C43C2×D412yes—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—41no—
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—81no—
255C22⋊C4×C43—81no—
256C22⋊C4×C43—81no—
257C42×C43—21no—
258C42×C43—21no—
259C42×C43—21no—
260C42×C43—21no—
261C42×C43—42no—
262C42×C43—81no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
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—41no—
290C23×C43#12112yes—
291C23×C43C22×D411yescharacteristic
292Q8×C43—22no—
293Q8×C43—22no—
294Q8×C43—41no—
295Q8×C43—41no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43—48no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—84no—
310D4×C43—84no—
311D4×C43—84no—
312D4×C43—84no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—21no—
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—48no—
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—84no—
347C2×C4×C43#12112yes—
348C2×C4×C43#13512yes—
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C2×#4111yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43H(5,𝔽2)11yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C8×C43—22no—
356C8×C43—41no—
357C8×C43—41no—
358C8×C43—41no—
359#25087C4311yesmaximal, characteristic, direct product factor, Sylow
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—81no—
374C22×C43—81no—
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×C43—81no—
387C22×C43—81no—
388C22×C43C2×#12111yescharacteristic
389C22×C43D4211yescharacteristic
390C22×C43#54611yescharacteristic
391C22×C43C2×#13511yescharacteristic
392C22×C43#57511yescharacteristic
393C22×C43#57611yescharacteristic
394C22×C43#57611yescharacteristic
395C4×C43—22no—
396C4×C43—22no—
397C4×C43—42no—
398C4×C43—41no—
399C4×C43—42no—
400C4×C43—41no—
401C4×C43—42no—
402C4×C43—41no—
403C4×C43—81no—
404C4×C43—81no—
405C4×C43#52511yescharacteristic
406C4×C43#53811yescharacteristic
407C4×C43D4211yescharacteristic
408C4×C43#54611yescharacteristic
409C2×#466C2×C4311yescharacteristic, complemented
410C2×#463C2×C4311yescharacteristic, complemented
411C2×#449C2×C4311yescharacteristic, complemented
412C2×#416C2×C4311yescharacteristic, complemented
413#2431C2×C4311yescharacteristic, complemented
414#2363C2×C4311yescharacteristic, complemented
415#2067C2×C4311yescharacteristic, complemented
416#2055C2×C4311yescharacteristic, complemented
417#2042C2×C4311yescharacteristic, complemented
418#2011C2×C4311yescharacteristic, complemented
419#1982C2×C4311yescharacteristic, complemented
420#1928C2×C4311yescharacteristic, complemented
421#1879C2×C4311yescharacteristic, complemented
422#1875C2×C4311yescharacteristic, complemented
423#1850C2×C4311yescharacteristic, complemented
424C2×C43—42no—
425C2×C43—82no—
426C2×C43—82no—
427C2×C43—161no—
428C2×C43#242411yescharacteristic
429C2×C43#303511yescharacteristic
430C2×C43#304111yescharacteristic
431C2×C43#326811yescharacteristic
432C2×C43#328711yescharacteristic
433C2×C43#329711yescharacteristic
434C2×C43#331911yescharacteristic
435C22×#41C22×C4311yescharacteristic
436C22×SD16C22×C4311yescharacteristic
437C22×D8C22×C4311yescharacteristic
438C22×D8C22×C4311yescharacteristic
439C23×C8C22×C4311yescharacteristic
440C2×#127C22×C4311yescharacteristic
441C2×#124C22×C4311yescharacteristic
442C2×#121C22×C4311yescharacteristic
443C2×#121C22×C4311yescharacteristic
444C2×C4×D4C22×C4311yescharacteristic
445C2×#117C22×C4311yescharacteristic
446#466—24no—
447#463—24no—
448#449—24no—
449C2×#107C22×C4311yescharacteristic
450C2×C4⋊C8C22×C4311yescharacteristic
451C2×C4⋊C8C22×C4311yescharacteristic
452#416—24no—
453C2×#103C22×C4311yescharacteristic
454C2×#103C22×C4311yescharacteristic
455C2×#103C22×C4311yescharacteristic
456C2×#102C22×C4311yescharacteristic
457C2×#102C22×C4311yescharacteristic
458C2×#102C22×C4311yescharacteristic
459C2×#102C22×C4311yescharacteristic
460C2×#102C22×C4311yescharacteristic
461C2×#102C22×C4311yescharacteristic
462C2×#102C22×C4311yescharacteristic
463C2×C22⋊C8C22×C4311yescharacteristic
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#386—21no—
474#386—21no—
475C4×C4⋊C4C22×C4311yescharacteristic
476C4×C22⋊C4—21no—
477C4×C22⋊C4C22×C4311yescharacteristic
478#340C22×C4311yescharacteristic
479#340C22×C4311yescharacteristic
480#336C22×C4311yescharacteristic
481#336C22×C4311yescharacteristic
482C43#2508711yescharacteristic, direct product factor, Sylow
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C22×Q8C23×C4311yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4C23×C4311yescharacteristic
496C22×D4C23×C4311yescharacteristic
497C22×D4C23×C4311yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C4311yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C23×C4311yescharacteristic
514C22×C8C23×C4311yescharacteristic
515C22×C8C23×C4311yescharacteristic
516C22×C8C23×C4311yescharacteristic
517#127—22no—
518#127—41no—
519#124—22no—
520#124—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121D4×C4314yescomplemented
525C4×D4—22no—
526C4×D4—41no—
527#117—22no—
528#117—41no—
529C2×C4⋊C4—21no—
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⋊C4D4×C4311yescharacteristic
545C2×C22⋊C4D4×C4311yescharacteristic
546C2×C42—21no—
547C2×C42—21no—
548C2×C42C23×C4311yescharacteristic
549C2×C42C23×C4311yescharacteristic
550#107—22no—
551C4⋊C8—22no—
552C4⋊C8—41no—
553#103—22no—
554#103—22no—
555#103D4×C4314yescomplemented
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—41no—
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95D4×C4311yescharacteristic
569#95D4×C4311yescharacteristic
570C24—21no—
571C24—21no—
572C24—21no—
573C24C2×D4×C4311yescharacteristic
574#41—28no—
575#41—44no—
576#41—44no—
577#41—44no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8C2×D4×C4312yes—
584C2×D4—24no—
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—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C4312yes—
616C2×D4#41×C4312yes—
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—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—81no—
632C22×C4C2×D4×C4311yescharacteristic
633C22×C4C2×D4×C4311yescharacteristic
634C22×C4C2×D4×C4311yescharacteristic
635C22×C4C2×D4×C4311yescharacteristic
636C22×C4C2×D4×C4312yes—
637C22×C4C2×D4×C4311yescharacteristic
638C22×C4#41×C4312yes—
639C22×C4C24×C4311yescharacteristic
640SD16—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8C2×D4×C4312yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C4312yes—
664C4⋊C4C2×D4×C4312yes—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—81no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
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—41no—
708C23—41no—
709C23—41no—
710C23#121×C4312yes—
711C23C22×D4×C4311yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—84no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—48no—
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—41no—
765C2×C4—41no—
766C2×C4—84no—
767C2×C4#121×C4312yes—
768C2×C4#135×C4312yes—
769C2×C4C22×D4×C4311yescharacteristic
770C2×C4C22×D4×C4311yescharacteristic
771C2×C4C2×#41×C4311yescharacteristic
772C2×C4C2×#41×C4311yescharacteristic
773C2×C4H(5,𝔽2)×C4311yescharacteristic
774C2×C4H(5,𝔽2)×C4311yescharacteristic
775C8—22no—
776C8—41no—
777C8—41no—
778C8—41no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C4311yescharacteristic
808C22D42×C4311yescharacteristic
809C22C43×#54611yescharacteristic
810C22C2×#135×C4311yescharacteristic
811C22C43×#57511yescharacteristic
812C22C43×#57611yescharacteristic
813C22C43×#57611yescharacteristic
814C4—22no—
815C4—22no—
816C4—42no—
817C4—41no—
818C4—42no—
819C4—41no—
820C4—42no—
821C4—41no—
822C4—81no—
823C4—81no—
824C4C43×#52511yescharacteristic
825C4C43×#53811yescharacteristic
826C4D42×C4311yescharacteristic
827C4C43×#54611yescharacteristic
828C2—42no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C43×#242411yescharacteristic
833C2C43×#303511yescharacteristic
834C2C43×#304111yescharacteristic
835C2C43×#326811yescharacteristic
836C2C43×#328711yescharacteristic
837C2C43×#329711yescharacteristic
838C2C43×#331911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#466C2semidirect
2. C2×C43×#463C2semidirect
3. C2×C43×#449C2semidirect
4. C2×C43×#416C2semidirect
5. C43×#2431C2semidirect
6. C43×#2363C2semidirect
7. C43×#2067C2semidirect
8. C43×#2055C2semidirect
9. C43×#2042C2semidirect
10. C43×#2011C2semidirect
11. C43×#1982C2semidirect
12. C43×#1928C2semidirect
13. C43×#1879C2semidirect
14. C43×#1875C2semidirect
15. C43×#1850C2semidirect
104. #121×C43D4semidirect
135. #103×C43D4semidirect
359. #25087C43direct (N × H)
409. C2×#466C2×C43semidirect
410. C2×#463C2×C43semidirect
411. C2×#449C2×C43semidirect
412. C2×#416C2×C43semidirect
413. #2431C2×C43semidirect
414. #2363C2×C43semidirect
415. #2067C2×C43semidirect
416. #2055C2×C43semidirect
417. #2042C2×C43semidirect
418. #2011C2×C43semidirect
419. #1982C2×C43semidirect
420. #1928C2×C43semidirect
421. #1879C2×C43semidirect
422. #1875C2×C43semidirect
423. #1850C2×C43semidirect
482. C43#25087direct (N × H)
524. #121D4×C43semidirect
555. #103D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4662
C2×C43×#4632
C2×C43×#4492
C2×C43×#4162
C43×#24312
C43×#23632
C43×#20672
C43×#20552
C43×#20422
C43×#20112
C43×#19822
C43×#19282
C43×#18792
C43×#18752
C43×#18502
#2508743