Finite Group Databasebeta

← C43×#25159 #24945176

Subgroups — C43×#25159 #24945176

Order 11008.

1212 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#460C211yesmaximal, characteristic, complemented
2C2×C43×#449C211yesmaximal, characteristic, complemented
3C2×C43×#449C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
5C43×#2428C211yesmaximal, characteristic, complemented
6C43×#2341C211yesmaximal, characteristic, complemented
7C43×#2065C211yesmaximal, characteristic, complemented
8C43×#2034C211yesmaximal, characteristic, complemented
9C43×#2033C211yesmaximal, characteristic, complemented
10C43×#2011C211yesmaximal, characteristic, complemented
11C43×#1970C211yesmaximal, characteristic, complemented
12C43×#1923C211yesmaximal, characteristic, complemented
13C43×#1880C211yesmaximal, characteristic, complemented
14C43×#1879C211yesmaximal, characteristic, complemented
15C43×#1863C211yesmaximal, 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×Q8×C43C2211yescharacteristic
26C2×C4×Q8×C43C2211yescharacteristic
27C2×C4×D4×C43C2211yescharacteristic
28C43×#460—24no—
29C43×#449—24no—
30C43×#449—24no—
31C4×SD16×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×#390—21no—
49C43×#390—21no—
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#386—21no—
55C43×#380—21no—
56C43×#380C2211yescharacteristic
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—22no—
84C2×SD16×C43—22no—
85C2×SD16×C43—22no—
86C2×SD16×C43D414yescomplemented
87C2×D8×C43—22no—
88C2×D8×C43—22no—
89C2×D8×C43—22no—
90C2×D8×C43—22no—
91C2×D8×C43—41no—
92C2×D8×C43—41no—
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97#127×C43—22no—
98#127×C43—41no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—44no—
102#121×C43—41no—
103#121×C43—41no—
104C4×Q8×C43—22no—
105C4×Q8×C43—22no—
106C4×Q8×C43—41no—
107C4×Q8×C43—41no—
108C4×D4×C43—22no—
109C4×D4×C43—41no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
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×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133#107×C43—41no—
134#106×C43—22no—
135C4⋊C8×C43—22no—
136#103×C43—22no—
137#103×C43D414yescomplemented
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—41no—
144C22⋊C8×C43—22no—
145C22⋊C8×C43—22no—
146C4×C8×C43—22no—
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×C43C2×D412yes—
163C2×Q8×C43C2×D412yes—
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—21no—
181C2×D4×C43—21no—
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—42no—
191C2×D4×C43—42no—
192C2×D4×C43—81no—
193C2×D4×C43—81no—
194C2×D4×C43—81no—
195C2×D4×C43—81no—
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—81no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2411yescharacteristic
221SD16×C43—28no—
222SD16×C43—44no—
223D8×C43—44no—
224D8×C43—44no—
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—21no—
235C2×C8×C43C2×D412yes—
236C2×C8×C43C2×D412yes—
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—21no—
244C4⋊C4×C43—42no—
245C4⋊C4×C43—42no—
246C4⋊C4×C43—42no—
247C4⋊C4×C43C2×D412yes—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—81no—
257C22⋊C4×C43—81no—
258C22⋊C4×C43—81no—
259C22⋊C4×C43—81no—
260C42×C43—21no—
261C42×C43—21no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—42no—
265C42×C43—42no—
266C23×C43—21no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
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—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43C22×D411yescharacteristic
295Q8×C43—22no—
296Q8×C43—22no—
297Q8×C43—22no—
298Q8×C43#12114yescomplemented
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—48no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—41no—
309D4×C43—41no—
310D4×C43—41no—
311D4×C43—41no—
312D4×C43—84no—
313D4×C43—84no—
314D4×C43—84no—
315D4×C43—84no—
316C2×C4×C43—22no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
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—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—84no—
350C2×C4×C43#13512yes—
351C2×C4×C43AGL(1,ℤ/8)12yes—
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C2×#4111yescharacteristic
355C2×C4×C43C2×#4111yescharacteristic
356C2×C4×C43H(5,𝔽2)11yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
358C8×C43—22no—
359C8×C43—22no—
360C8×C43—41no—
361C8×C43—41no—
362#25159C4311yesmaximal, characteristic, direct product factor, Sylow
363C22×C43—41no—
364C22×C43—42no—
365C22×C43—41no—
366C22×C43—42no—
367C22×C43—41no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—42no—
373C22×C43—41no—
374C22×C43—42no—
375C22×C43—41no—
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×C43—81no—
389C22×C43—81no—
390C22×C43—81no—
391C22×C43#52511yescharacteristic
392C22×C43D4211yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43C2×#13511yescharacteristic
395C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C43#57611yescharacteristic
397C22×C43#57711yescharacteristic
398C4×C43—24no—
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—41no—
402C4×C43—42no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43—81no—
406C4×C43—81no—
407C4×C43—81no—
408C4×C43C2×#12111yescharacteristic
409C4×C43#53811yescharacteristic
410C4×C43#54611yescharacteristic
411C4×C43#54611yescharacteristic
412C2×#460C2×C4311yescharacteristic, complemented
413C2×#449C2×C4311yescharacteristic, complemented
414C2×#449C2×C4311yescharacteristic, complemented
415C2×C4×SD16C2×C4311yescharacteristic, complemented
416#2428C2×C4311yescharacteristic, complemented
417#2341C2×C4311yescharacteristic, complemented
418#2065C2×C4311yescharacteristic, complemented
419#2034C2×C4311yescharacteristic, complemented
420#2033C2×C4311yescharacteristic, complemented
421#2011C2×C4311yescharacteristic, complemented
422#1970C2×C4311yescharacteristic, complemented
423#1923C2×C4311yescharacteristic, complemented
424#1880C2×C4311yescharacteristic, complemented
425#1879C2×C4311yescharacteristic, complemented
426#1863C2×C4311yescharacteristic, complemented
427C2×C43—81no—
428C2×C43—82no—
429C2×C43—82no—
430C2×C43—161no—
431C2×C43#242411yescharacteristic
432C2×C43#310611yescharacteristic
433C2×C43#311911yescharacteristic
434C2×C43#326511yescharacteristic
435C2×C43#327411yescharacteristic
436C2×C43#328211yescharacteristic
437C2×C43#328711yescharacteristic
438C22×#41C22×C4311yescharacteristic
439C22×SD16C22×C4311yescharacteristic
440C22×SD16C22×C4311yescharacteristic
441C22×D8C22×C4311yescharacteristic
442C22×D8C22×C4311yescharacteristic
443C2×#127C22×C4311yescharacteristic
444C2×#121—21no—
445C2×#121C22×C4311yescharacteristic
446C2×#121C22×C4311yescharacteristic
447C2×C4×Q8C22×C4311yescharacteristic
448C2×C4×Q8C22×C4311yescharacteristic
449C2×C4×D4C22×C4311yescharacteristic
450#460—24no—
451#449—24no—
452#449—24no—
453C4×SD16—24no—
454C2×#107C22×C4311yescharacteristic
455C2×#106C22×C4311yescharacteristic
456C2×C4⋊C8C22×C4311yescharacteristic
457C2×#103C22×C4311yescharacteristic
458C2×#103C22×C4311yescharacteristic
459C2×#102C22×C4311yescharacteristic
460C2×#102C22×C4311yescharacteristic
461C2×#102C22×C4311yescharacteristic
462C2×#102C22×C4311yescharacteristic
463C2×#102C22×C4311yescharacteristic
464C2×#102C22×C4311yescharacteristic
465C2×C22⋊C8C22×C4311yescharacteristic
466C2×C22⋊C8C22×C4311yescharacteristic
467C2×C4×C8C22×C4311yescharacteristic
468#394—21no—
469#392—21no—
470#390—21no—
471#390—21no—
472#390C22×C4311yescharacteristic
473#390C22×C4311yescharacteristic
474#390C22×C4311yescharacteristic
475#389C22×C4311yescharacteristic
476#386—21no—
477#380—21no—
478#380C22×C4311yescharacteristic
479C4×C22⋊C4—21no—
480C4×C22⋊C4C22×C4311yescharacteristic
481#340C22×C4311yescharacteristic
482#340C22×C4311yescharacteristic
483#336C22×C4311yescharacteristic
484#336C22×C4311yescharacteristic
485C43#2515911yescharacteristic, direct product factor, Sylow
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C4311yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C4311yescharacteristic
499C22×D4C23×C4311yescharacteristic
500C22×D4C23×C4311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C4311yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C4314yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C4311yescharacteristic
517C22×C8C23×C4311yescharacteristic
518C22×C8C23×C4311yescharacteristic
519C22×C8C23×C4311yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C4311yescharacteristic
537C2×C4⋊C4C23×C4311yescharacteristic
538C2×C4⋊C4C23×C4311yescharacteristic
539C2×C4⋊C4C23×C4311yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
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×C42—21no—
553C2×C42—21no—
554C2×C42C23×C4311yescharacteristic
555C2×C42C23×C4311yescharacteristic
556#107—41no—
557#106—22no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C4314yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C4×C8—22no—
570#95—21no—
571#95—21no—
572#95D4×C4311yescharacteristic
573#95D4×C4311yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C4311yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C4312yes—
586C2×Q8C2×D4×C4312yes—
587C2×Q8#41×C4312yes—
588C2×D4—24no—
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—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×D4#41×C4312yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
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—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C4311yescharacteristic
639C22×C4C2×D4×C4311yescharacteristic
640C22×C4C2×D4×C4311yescharacteristic
641C22×C4C2×D4×C4311yescharacteristic
642C22×C4C2×D4×C4311yescharacteristic
643C22×C4C24×C4311yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C4312yes—
659C2×C8C2×D4×C4312yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C4312yes—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
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—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C4311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C4314yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
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—84no—
773C2×C4#135×C4312yes—
774C2×C4AGL(1,ℤ/8)×C4312yes—
775C2×C4C22×D4×C4311yescharacteristic
776C2×C4C22×D4×C4311yescharacteristic
777C2×C4C2×#41×C4311yescharacteristic
778C2×C4C2×#41×C4311yescharacteristic
779C2×C4H(5,𝔽2)×C4311yescharacteristic
780C2×C4H(5,𝔽2)×C4311yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—41no—
786C22—42no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C43×#52511yescharacteristic
814C22D42×C4311yescharacteristic
815C22D42×C4311yescharacteristic
816C22C2×#135×C4311yescharacteristic
817C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
818C22C43×#57611yescharacteristic
819C22C43×#57711yescharacteristic
820C4—24no—
821C4—22no—
822C4—22no—
823C4—41no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C4311yescharacteristic
831C4C43×#53811yescharacteristic
832C4C43×#54611yescharacteristic
833C4C43×#54611yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C43×#242411yescharacteristic
839C2C43×#310611yescharacteristic
840C2C43×#311911yescharacteristic
841C2C43×#326511yescharacteristic
842C2C43×#327411yescharacteristic
843C2C43×#328211yescharacteristic
844C2C43×#328711yescharacteristic
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×#460C2semidirect
2. C2×C43×#449C2semidirect
3. C2×C43×#449C2semidirect
4. C2×C4×SD16×C43C2semidirect
5. C43×#2428C2semidirect
6. C43×#2341C2semidirect
7. C43×#2065C2semidirect
8. C43×#2034C2semidirect
9. C43×#2033C2semidirect
10. C43×#2011C2semidirect
11. C43×#1970C2semidirect
12. C43×#1923C2semidirect
13. C43×#1880C2semidirect
14. C43×#1879C2semidirect
15. C43×#1863C2semidirect
86. C2×SD16×C43D4semidirect
137. #103×C43D4semidirect
298. Q8×C43#121semidirect
362. #25159C43direct (N × H)
412. C2×#460C2×C43semidirect
413. C2×#449C2×C43semidirect
414. C2×#449C2×C43semidirect
415. C2×C4×SD16C2×C43semidirect
416. #2428C2×C43semidirect
417. #2341C2×C43semidirect
418. #2065C2×C43semidirect
419. #2034C2×C43semidirect
420. #2033C2×C43semidirect
421. #2011C2×C43semidirect
422. #1970C2×C43semidirect
423. #1923C2×C43semidirect
424. #1880C2×C43semidirect
425. #1879C2×C43semidirect
426. #1863C2×C43semidirect
485. C43#25159direct (N × H)
509. C2×SD16D4×C43semidirect
560. #103D4×C43semidirect
721. Q8#121×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4602
C2×C43×#4492
C2×C4×SD16×C432
C43×#24282
C43×#23412
C43×#20652
C43×#20342
C43×#20332
C43×#20112
C43×#19702
C43×#19232
C43×#18802
C43×#18792
C43×#18632
#2515943