Finite Group Databasebeta

← C43×#25162 #24945179

Subgroups — C43×#25162 #24945179

Order 11008.

1240 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#459C211yesmaximal, characteristic, complemented
2C2×C43×#449C211yesmaximal, characteristic, complemented
3C2×C43×#449C211yesmaximal, characteristic, complemented
4C2×C4×D8×C43C211yesmaximal, characteristic, complemented
5C43×#2428C211yesmaximal, characteristic, complemented
6C43×#2339C211yesmaximal, characteristic, complemented
7C43×#2068C211yesmaximal, characteristic, complemented
8C43×#2034C211yesmaximal, characteristic, complemented
9C43×#2033C211yesmaximal, characteristic, complemented
10C43×#2014C211yesmaximal, characteristic, complemented
11C43×#1968C211yesmaximal, characteristic, complemented
12C43×#1923C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1877C211yesmaximal, characteristic, complemented
15C43×#1864C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C2×#127×C43C2211yescharacteristic
22C2×#121×C43—21no—
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic
27C2×C4×D4×C43C2211yescharacteristic
28C43×#459—24no—
29C43×#449—24no—
30C43×#449—24no—
31C4×D8×C43—24no—
32C2×#107×C43C2211yescharacteristic
33C2×#106×C43C2211yescharacteristic
34C2×C4⋊C8×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×C22⋊C8×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic
45C2×C4×C8×C43C2211yescharacteristic
46C43×#394—21no—
47C43×#392—21no—
48C43×#391C2211yescharacteristic
49C43×#391C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#386—21no—
53C43×#386—21no—
54C43×#386—21no—
55C43×#381—21no—
56C43×#380C2211yescharacteristic
57C4×C22⋊C4×C43C2211yescharacteristic
58C2×#95×C43—21no—
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×C43—21no—
81C23×C4×C43—21no—
82C23×C4×C43C2311yescharacteristic
83C2×SD16×C43—22no—
84C2×SD16×C43—22no—
85C2×SD16×C43—22no—
86C2×SD16×C43—22no—
87C2×SD16×C43—41no—
88C2×SD16×C43—41no—
89C2×D8×C43—22no—
90C2×D8×C43—22no—
91C2×D8×C43—22no—
92C2×D8×C43—22no—
93C2×D8×C43—22no—
94C2×D8×C43D414yescomplemented
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98C22×C8×C43C2311yescharacteristic
99#127×C43—22no—
100#127×C43—41no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—44no—
104#121×C43—41no—
105#121×C43—41no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43—41no—
110C4×D4×C43—41no—
111C4×D4×C43—41no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
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×C43D411yescharacteristic
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C42×C43C2311yescharacteristic
128C2×C42×C43C2311yescharacteristic
129#107×C43—22no—
130#106×C43—41no—
131C4⋊C8×C43—22no—
132#103×C43—22no—
133#103×C43—22no—
134#102×C43—22no—
135#102×C43—22no—
136#102×C43—22no—
137#102×C43—22no—
138#102×C43—41no—
139#102×C43D414yescomplemented
140C22⋊C8×C43—22no—
141C22⋊C8×C43—22no—
142C4×C8×C43—22no—
143#95×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43D411yescharacteristic
150#95×C43D411yescharacteristic
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155#41×C43—44no—
156#41×C43—44no—
157#41×C43—44no—
158#41×C43—44no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43#4112yes—
165C2×D4×C43—24no—
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—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
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—42no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43—42no—
190C2×D4×C43—81no—
191C2×D4×C43—81no—
192C2×D4×C43—81no—
193C2×D4×C43—81no—
194C2×D4×C43C2×D412yes—
195C2×D4×C43C2×D412yes—
196C2×D4×C43C2×D412yes—
197C2×D4×C43#4112yes—
198C22×C4×C43—24no—
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—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—42no—
211C22×C4×C43—42no—
212C22×C4×C43—42no—
213C22×C4×C43—42no—
214C22×C4×C43—42no—
215C22×C4×C43—42no—
216C22×C4×C43—42no—
217C22×C4×C43—42no—
218C22×C4×C43—81no—
219C22×C4×C43—81no—
220C22×C4×C43—81no—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227SD16×C43—44no—
228SD16×C43—44no—
229D8×C43—28no—
230D8×C43—44no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43C2×D412yes—
242C2×C8×C43C2×D412yes—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—42no—
251C4⋊C4×C43C2×D412yes—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—22no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—42no—
258C22⋊C4×C43—42no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—81no—
261C22⋊C4×C43—81no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—21no—
265C42×C43—21no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—21no—
270C23×C43—22no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
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—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43C22×D411yescharacteristic
295Q8×C43—22no—
296Q8×C43—22no—
297Q8×C43—41no—
298Q8×C43—41no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—48no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—84no—
312D4×C43—84no—
313D4×C43—84no—
314D4×C43—84no—
315D4×C43#12114yescomplemented
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—48no—
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—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—84no—
350C2×C4×C43—84no—
351C2×C4×C43—84no—
352C2×C4×C43#13512yes—
353C2×C4×C43AGL(1,ℤ/8)12yes—
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C2×#4111yescharacteristic
357C2×C4×C43C2×#4111yescharacteristic
358C2×C4×C43H(5,𝔽2)11yescharacteristic
359C2×C4×C43H(5,𝔽2)11yescharacteristic
360C8×C43—22no—
361C8×C43—22no—
362C8×C43—41no—
363C8×C43—41no—
364#25162C4311yesmaximal, characteristic, direct product factor, Sylow
365C22×C43—24no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—42no—
379C22×C43—41no—
380C22×C43—42no—
381C22×C43—41no—
382C22×C43—81no—
383C22×C43—81no—
384C22×C43—81no—
385C22×C43—81no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43#52511yescharacteristic
394C22×C43D4211yescharacteristic
395C22×C43D4211yescharacteristic
396C22×C43C2×#13511yescharacteristic
397C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C43#57611yescharacteristic
399C22×C43#57711yescharacteristic
400C4×C43—22no—
401C4×C43—22no—
402C4×C43—41no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43—81no—
408C4×C43—81no—
409C4×C43—81no—
410C4×C43C2×#12111yescharacteristic
411C4×C43#53811yescharacteristic
412C4×C43#54611yescharacteristic
413C4×C43#54611yescharacteristic
414C2×#459C2×C4311yescharacteristic, complemented
415C2×#449C2×C4311yescharacteristic, complemented
416C2×#449C2×C4311yescharacteristic, complemented
417C2×C4×D8C2×C4311yescharacteristic, complemented
418#2428C2×C4311yescharacteristic, complemented
419#2339C2×C4311yescharacteristic, complemented
420#2068C2×C4311yescharacteristic, complemented
421#2034C2×C4311yescharacteristic, complemented
422#2033C2×C4311yescharacteristic, complemented
423#2014C2×C4311yescharacteristic, complemented
424#1968C2×C4311yescharacteristic, complemented
425#1923C2×C4311yescharacteristic, complemented
426#1879C2×C4311yescharacteristic, complemented
427#1877C2×C4311yescharacteristic, complemented
428#1864C2×C4311yescharacteristic, complemented
429C2×C43—44no—
430C2×C43—81no—
431C2×C43—82no—
432C2×C43—161no—
433C2×C43#242411yescharacteristic
434C2×C43#310611yescharacteristic
435C2×C43#311911yescharacteristic
436C2×C43#326411yescharacteristic
437C2×C43#327211yescharacteristic
438C2×C43#328011yescharacteristic
439C2×C43#328411yescharacteristic
440C22×#41C22×C4311yescharacteristic
441C22×SD16C22×C4311yescharacteristic
442C22×SD16C22×C4311yescharacteristic
443C22×D8C22×C4311yescharacteristic
444C22×D8C22×C4311yescharacteristic
445C2×#127C22×C4311yescharacteristic
446C2×#121—21no—
447C2×#121C22×C4311yescharacteristic
448C2×#121C22×C4311yescharacteristic
449C2×C4×D4C22×C4311yescharacteristic
450C2×C4×D4C22×C4311yescharacteristic
451C2×C4×D4C22×C4311yescharacteristic
452#459—24no—
453#449—24no—
454#449—24no—
455C4×D8—24no—
456C2×#107C22×C4311yescharacteristic
457C2×#106C22×C4311yescharacteristic
458C2×C4⋊C8C22×C4311yescharacteristic
459C2×#103C22×C4311yescharacteristic
460C2×#103C22×C4311yescharacteristic
461C2×#102C22×C4311yescharacteristic
462C2×#102C22×C4311yescharacteristic
463C2×#102C22×C4311yescharacteristic
464C2×#102C22×C4311yescharacteristic
465C2×#102C22×C4311yescharacteristic
466C2×#102C22×C4311yescharacteristic
467C2×C22⋊C8C22×C4311yescharacteristic
468C2×C22⋊C8C22×C4311yescharacteristic
469C2×C4×C8C22×C4311yescharacteristic
470#394—21no—
471#392—21no—
472#391C22×C4311yescharacteristic
473#391C22×C4311yescharacteristic
474#390C22×C4311yescharacteristic
475#389C22×C4311yescharacteristic
476#386—21no—
477#386—21no—
478#386—21no—
479#381—21no—
480#380C22×C4311yescharacteristic
481C4×C22⋊C4C22×C4311yescharacteristic
482C2×#95—21no—
483#340C22×C4311yescharacteristic
484#340C22×C4311yescharacteristic
485#336C22×C4311yescharacteristic
486#336C22×C4311yescharacteristic
487C43#2516211yescharacteristic, direct product factor, Sylow
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C4311yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C4311yescharacteristic
501C22×D4C23×C4311yescharacteristic
502C22×D4C23×C4311yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C4311yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C4314yescomplemented
520C22×C8C23×C4311yescharacteristic
521C22×C8C23×C4311yescharacteristic
522C22×C8C23×C4311yescharacteristic
523C22×C8C23×C4311yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C4311yescharacteristic
539C2×C4⋊C4C23×C4311yescharacteristic
540C2×C4⋊C4C23×C4311yescharacteristic
541C2×C4⋊C4C23×C4311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C4311yescharacteristic
551C2×C22⋊C4D4×C4311yescharacteristic
552C2×C42C23×C4311yescharacteristic
553C2×C42C23×C4311yescharacteristic
554#107—22no—
555#106—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C4314yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C4311yescharacteristic
575#95D4×C4311yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C4311yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C4312yes—
590C2×D4—24no—
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—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C4312yes—
620C2×D4C2×D4×C4312yes—
621C2×D4C2×D4×C4312yes—
622C2×D4#41×C4312yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
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×C4C2×D4×C4311yescharacteristic
647C22×C4C2×D4×C4311yescharacteristic
648C22×C4C2×D4×C4311yescharacteristic
649C22×C4C2×D4×C4311yescharacteristic
650C22×C4C2×D4×C4311yescharacteristic
651C22×C4C24×C4311yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C4312yes—
667C2×C8C2×D4×C4312yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C4312yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C4311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C4314yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
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—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4#135×C4312yes—
778C2×C4AGL(1,ℤ/8)×C4312yes—
779C2×C4C22×D4×C4311yescharacteristic
780C2×C4C22×D4×C4311yescharacteristic
781C2×C4C2×#41×C4311yescharacteristic
782C2×C4C2×#41×C4311yescharacteristic
783C2×C4H(5,𝔽2)×C4311yescharacteristic
784C2×C4H(5,𝔽2)×C4311yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22C43×#52511yescharacteristic
818C22D42×C4311yescharacteristic
819C22D42×C4311yescharacteristic
820C22C2×#135×C4311yescharacteristic
821C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
822C22C43×#57611yescharacteristic
823C22C43×#57711yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—41no—
830C4—41no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C4311yescharacteristic
835C4C43×#53811yescharacteristic
836C4C43×#54611yescharacteristic
837C4C43×#54611yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C43×#242411yescharacteristic
843C2C43×#310611yescharacteristic
844C2C43×#311911yescharacteristic
845C2C43×#326411yescharacteristic
846C2C43×#327211yescharacteristic
847C2C43×#328011yescharacteristic
848C2C43×#328411yescharacteristic
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×#459C2semidirect
2. C2×C43×#449C2semidirect
3. C2×C43×#449C2semidirect
4. C2×C4×D8×C43C2semidirect
5. C43×#2428C2semidirect
6. C43×#2339C2semidirect
7. C43×#2068C2semidirect
8. C43×#2034C2semidirect
9. C43×#2033C2semidirect
10. C43×#2014C2semidirect
11. C43×#1968C2semidirect
12. C43×#1923C2semidirect
13. C43×#1879C2semidirect
14. C43×#1877C2semidirect
15. C43×#1864C2semidirect
94. C2×D8×C43D4semidirect
139. #102×C43D4semidirect
315. D4×C43#121semidirect
364. #25162C43direct (N × H)
414. C2×#459C2×C43semidirect
415. C2×#449C2×C43semidirect
416. C2×#449C2×C43semidirect
417. C2×C4×D8C2×C43semidirect
418. #2428C2×C43semidirect
419. #2339C2×C43semidirect
420. #2068C2×C43semidirect
421. #2034C2×C43semidirect
422. #2033C2×C43semidirect
423. #2014C2×C43semidirect
424. #1968C2×C43semidirect
425. #1923C2×C43semidirect
426. #1879C2×C43semidirect
427. #1877C2×C43semidirect
428. #1864C2×C43semidirect
487. C43#25162direct (N × H)
519. C2×D8D4×C43semidirect
564. #102D4×C43semidirect
740. D4#121×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4592
C2×C43×#4492
C2×C4×D8×C432
C43×#24282
C43×#23392
C43×#20682
C43×#20342
C43×#20332
C43×#20142
C43×#19682
C43×#19232
C43×#18792
C43×#18772
C43×#18642
#2516243