Finite Group Databasebeta

← C43×#24634 #24944651

Subgroups — C43×#24634 #24944651

Order 11008.

952 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#463C211yesmaximal, characteristic, complemented
2C2×C4×D8×C43C211yesmaximal, characteristic, complemented
3C43×#2544C211yesmaximal, characteristic, complemented
4C43×#2357C211yesmaximal, characteristic, complemented
5C43×#2055C211yesmaximal, characteristic, complemented
6C43×#2054C211yesmaximal, characteristic, complemented
7C43×#2012C211yesmaximal, characteristic, complemented
8C43×#2011C211yesmaximal, characteristic
9C43×#1983C211yesmaximal, characteristic, complemented
10C43×#1982C211yesmaximal, characteristic, complemented
11C43×#1958C211yesmaximal, characteristic, complemented
12C43×#1939C211yesmaximal, characteristic, complemented
13C43×#1928C211yesmaximal, characteristic, complemented
14C43×#1925C211yesmaximal, characteristic, complemented
15C43×#1804C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C2×#127×C43C2211yescharacteristic
20C2×#124×C43C2211yescharacteristic
21C2×#124×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C2×C4×D4×C43C2211yescharacteristic
24C43×#463—24no—
25C4×D8×C43—24no—
26C2×#107×C43C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×C4×C8×C43C2211yescharacteristic
41C43×#394—21no—
42C43×#394—21no—
43C43×#391C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic
46C43×#390C2211yescharacteristic
47C43×#388—21no—
48C43×#388—21no—
49C43×#386—21no—
50C43×#386—21no—
51C43×#382C2211yescharacteristic
52C43×#381—21no—
53C4×C4⋊C4×C43C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C4×C22⋊C4×C43—21no—
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43C2311yescharacteristic
65C22×D4×C43C2311yescharacteristic
66C22×D4×C43C2311yescharacteristic
67C23×C4×C43—21no—
68C23×C4×C43—21no—
69C2×SD16×C43—22no—
70C2×SD16×C43—41no—
71C2×SD16×C43—41no—
72C2×D8×C43—22no—
73C2×D8×C43—22no—
74C2×D8×C43—22no—
75C2×D8×C43—22no—
76C2×D8×C43—41no—
77C2×D8×C43—41no—
78C22×C8×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82#127×C43—22no—
83#127×C43—41no—
84#124×C43—22no—
85#124×C43—22no—
86#124×C43—22no—
87#124×C43—41no—
88C4×D4×C43—22no—
89C4×D4×C43—22no—
90C4×D4×C43—22no—
91C4×D4×C43D414yescomplemented
92C2×C4⋊C4×C43D411yescharacteristic
93C2×C4⋊C4×C43D411yescharacteristic
94C2×C4⋊C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#107×C43—22no—
116C4⋊C8×C43—22no—
117C4⋊C8×C43—41no—
118C4⋊C8×C43—41no—
119#103×C43—22no—
120#103×C43—22no—
121#103×C43—41no—
122#102×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—41no—
127#102×C43—41no—
128#102×C43—41no—
129C4×C8×C43—22no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—81no—
168C2×D4×C43—81no—
169C2×D4×C43C2×D412yes—
170C2×D4×C43#4112yes—
171C22×C4×C43—24no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—42no—
178C22×C4×C43—81no—
179C22×C4×C43—81no—
180C22×C4×C43—81no—
181C22×C4×C43—81no—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189SD16×C43—44no—
190D8×C43—28no—
191D8×C43—44no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43#4112yes—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—41no—
213C4⋊C4×C43C2×D412yes—
214C22⋊C4×C43—24no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—42no—
219C22⋊C4×C43—42no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—81no—
223C22⋊C4×C43—81no—
224C22⋊C4×C43—81no—
225C22⋊C4×C43—81no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—81no—
231C42×C43—81no—
232C42×C43C2×D412yes—
233C42×C43#4112yes—
234C23×C43—22no—
235C23×C43—22no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43C22×D411yescharacteristic
256Q8×C43—41no—
257Q8×C43—41no—
258Q8×C43—41no—
259Q8×C43—41no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—41no—
265D4×C43—41no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—41no—
271D4×C43—41no—
272D4×C43—84no—
273D4×C43—84no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—84no—
305C2×C4×C43—84no—
306C2×C4×C43#12112yes—
307C2×C4×C43#12112yes—
308C2×C4×C43#13512yes—
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C2×C4×C43H(5,𝔽2)11yescharacteristic
315C8×C43—22no—
316C8×C43—41no—
317C8×C43—41no—
318C8×C43—41no—
319#24634C4311yesmaximal, characteristic, direct product factor, Sylow
320C22×C43—42no—
321C22×C43—42no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43—81no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43C2×#12111yescharacteristic
342C22×C43#54611yescharacteristic
343C22×C43#55011yescharacteristic
344C22×C43C2×#13511yescharacteristic
345C22×C43#57511yescharacteristic
346C22×C43#57611yescharacteristic
347C22×C43#57611yescharacteristic
348C4×C43—22no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—42no—
352C4×C43—41no—
353C4×C43—41no—
354C4×C43—41no—
355C4×C43—81no—
356C4×C43—81no—
357C4×C43—81no—
358C4×C43—81no—
359C4×C43#52511yescharacteristic
360C4×C43#53511yescharacteristic
361C4×C43#55311yescharacteristic
362C4×C43#55511yescharacteristic
363C2×#463C2×C4311yescharacteristic, complemented
364C2×C4×D8C2×C4311yescharacteristic, complemented
365#2544C2×C4311yescharacteristic, complemented
366#2357C2×C4311yescharacteristic, complemented
367#2055C2×C4311yescharacteristic, complemented
368#2054C2×C4311yescharacteristic, complemented
369#2012C2×C4311yescharacteristic, complemented
370#2011C2×C4311yescharacteristic
371#1983C2×C4311yescharacteristic, complemented
372#1982C2×C4311yescharacteristic, complemented
373#1958C2×C4311yescharacteristic, complemented
374#1939C2×C4311yescharacteristic, complemented
375#1928C2×C4311yescharacteristic, complemented
376#1925C2×C4311yescharacteristic, complemented
377#1804C2×C4311yescharacteristic, complemented
378C2×C43—82no—
379C2×C43—82no—
380C2×C43—161no—
381C2×C43#241411yescharacteristic
382C2×C43#303511yescharacteristic
383C2×C43#304111yescharacteristic
384C2×C43#329711yescharacteristic
385C2×C43#332211yescharacteristic
386C2×C43#339611yescharacteristic
387C2×C43#340311yescharacteristic
388C22×SD16C22×C4311yescharacteristic
389C22×D8C22×C4311yescharacteristic
390C22×D8C22×C4311yescharacteristic
391C2×#127C22×C4311yescharacteristic
392C2×#124C22×C4311yescharacteristic
393C2×#124C22×C4311yescharacteristic
394C2×C4×D4C22×C4311yescharacteristic
395C2×C4×D4C22×C4311yescharacteristic
396#463—24no—
397C4×D8—24no—
398C2×#107C22×C4311yescharacteristic
399C2×C4⋊C8C22×C4311yescharacteristic
400C2×C4⋊C8C22×C4311yescharacteristic
401C2×C4⋊C8C22×C4311yescharacteristic
402C2×#103C22×C4311yescharacteristic
403C2×#103C22×C4311yescharacteristic
404C2×#103C22×C4311yescharacteristic
405C2×#102C22×C4311yescharacteristic
406C2×#102C22×C4311yescharacteristic
407C2×#102C22×C4311yescharacteristic
408C2×#102C22×C4311yescharacteristic
409C2×#102C22×C4311yescharacteristic
410C2×#102C22×C4311yescharacteristic
411C2×#102C22×C4311yescharacteristic
412C2×C4×C8C22×C4311yescharacteristic
413#394—21no—
414#394—21no—
415#391C22×C4311yescharacteristic
416#390C22×C4311yescharacteristic
417#390C22×C4311yescharacteristic
418#390C22×C4311yescharacteristic
419#388—21no—
420#388—21no—
421#386—21no—
422#386—21no—
423#382C22×C4311yescharacteristic
424#381—21no—
425C4×C4⋊C4C22×C4311yescharacteristic
426C4×C4⋊C4C22×C4311yescharacteristic
427C4×C4⋊C4C22×C4311yescharacteristic
428C4×C22⋊C4—21no—
429#340C22×C4311yescharacteristic
430#340C22×C4311yescharacteristic
431#336C22×C4311yescharacteristic
432#336C22×C4311yescharacteristic
433C43#2463411yescharacteristic, direct product factor, Sylow
434C22×Q8C23×C4311yescharacteristic
435C22×D4—21no—
436C22×D4—21no—
437C22×D4C23×C4311yescharacteristic
438C22×D4C23×C4311yescharacteristic
439C22×D4C23×C4311yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C2×SD16—22no—
443C2×SD16—41no—
444C2×SD16—41no—
445C2×D8—22no—
446C2×D8—22no—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—41no—
450C2×D8—41no—
451C22×C8C23×C4311yescharacteristic
452C22×C8C23×C4311yescharacteristic
453C22×C8C23×C4311yescharacteristic
454C22×C8C23×C4311yescharacteristic
455#127—22no—
456#127—41no—
457#124—22no—
458#124—22no—
459#124—22no—
460#124—41no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4D4×C4314yescomplemented
465C2×C4⋊C4D4×C4311yescharacteristic
466C2×C4⋊C4D4×C4311yescharacteristic
467C2×C4⋊C4C23×C4311yescharacteristic
468C2×C4⋊C4C23×C4311yescharacteristic
469C2×C4⋊C4C23×C4311yescharacteristic
470C2×C4⋊C4C23×C4311yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42C23×C4311yescharacteristic
486C2×C42C23×C4311yescharacteristic
487C2×C42C23×C4311yescharacteristic
488#107—22no—
489C4⋊C8—22no—
490C4⋊C8—41no—
491C4⋊C8—41no—
492#103—22no—
493#103—22no—
494#103—41no—
495#102—22no—
496#102—22no—
497#102—22no—
498#102—22no—
499#102—41no—
500#102—41no—
501#102—41no—
502C4×C8—22no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95D4×C4311yescharacteristic
510#95D4×C4311yescharacteristic
511C24—21no—
512C24—21no—
513C24—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4C2×D4×C4312yes—
543C2×D4#41×C4312yes—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4C2×D4×C4311yescharacteristic
556C22×C4C2×D4×C4311yescharacteristic
557C22×C4C2×D4×C4311yescharacteristic
558C22×C4C2×D4×C4311yescharacteristic
559C22×C4C2×D4×C4311yescharacteristic
560C22×C4C2×D4×C4311yescharacteristic
561C22×C4C24×C4311yescharacteristic
562SD16—44no—
563D8—28no—
564D8—44no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8#41×C4312yes—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—41no—
586C4⋊C4C2×D4×C4312yes—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—81no—
604C42—81no—
605C42C2×D4×C4312yes—
606C42#41×C4312yes—
607C23—22no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C22×D4×C4311yescharacteristic
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—84no—
646D4—84no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4#121×C4312yes—
680C2×C4#121×C4312yes—
681C2×C4#135×C4312yes—
682C2×C4C22×D4×C4311yescharacteristic
683C2×C4C2×#41×C4311yescharacteristic
684C2×C4C2×#41×C4311yescharacteristic
685C2×C4C2×#41×C4311yescharacteristic
686C2×C4H(5,𝔽2)×C4311yescharacteristic
687C2×C4H(5,𝔽2)×C4311yescharacteristic
688C8—22no—
689C8—41no—
690C8—41no—
691C8—41no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×#121×C4311yescharacteristic
714C22C43×#54611yescharacteristic
715C22C43×#55011yescharacteristic
716C22C2×#135×C4311yescharacteristic
717C22C43×#57511yescharacteristic
718C22C43×#57611yescharacteristic
719C22C43×#57611yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—42no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4C43×#52511yescharacteristic
732C4C43×#53511yescharacteristic
733C4C43×#55311yescharacteristic
734C4C43×#55511yescharacteristic
735C2—82no—
736C2—82no—
737C2—161no—
738C2C43×#241411yescharacteristic
739C2C43×#303511yescharacteristic
740C2C43×#304111yescharacteristic
741C2C43×#329711yescharacteristic
742C2C43×#332211yescharacteristic
743C2C43×#339611yescharacteristic
744C2C43×#340311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C4⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#463C2semidirect
2. C2×C4×D8×C43C2semidirect
3. C43×#2544C2semidirect
4. C43×#2357C2semidirect
5. C43×#2055C2semidirect
6. C43×#2054C2semidirect
7. C43×#2012C2semidirect
9. C43×#1983C2semidirect
10. C43×#1982C2semidirect
11. C43×#1958C2semidirect
12. C43×#1939C2semidirect
13. C43×#1928C2semidirect
14. C43×#1925C2semidirect
15. C43×#1804C2semidirect
91. C4×D4×C43D4semidirect
319. #24634C43direct (N × H)
363. C2×#463C2×C43semidirect
364. C2×C4×D8C2×C43semidirect
365. #2544C2×C43semidirect
366. #2357C2×C43semidirect
367. #2055C2×C43semidirect
368. #2054C2×C43semidirect
369. #2012C2×C43semidirect
371. #1983C2×C43semidirect
372. #1982C2×C43semidirect
373. #1958C2×C43semidirect
374. #1939C2×C43semidirect
375. #1928C2×C43semidirect
376. #1925C2×C43semidirect
377. #1804C2×C43semidirect
433. C43#24634direct (N × H)
464. C4×D4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4632
C2×C4×D8×C432
C43×#25442
C43×#23572
C43×#20552
C43×#20542
C43×#20122
C43×#20112
C43×#19832
C43×#19822
C43×#19582
C43×#19392
C43×#19282
C43×#19252
C43×#18042
#2463443