Finite Group Databasebeta

← C43×#24142 #24944159

Subgroups — C43×#24142 #24944159

Order 11008.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3505C211yesmaximal, characteristic, complemented
2C43×#2626C211yesmaximal, characteristic, complemented
3C43×#2617C211yesmaximal, characteristic, complemented
4C43×#2321C211yesmaximal, characteristic, complemented
5C43×#2044C212yesmaximal, complemented
6C43×#2021C212yesmaximal, complemented
7C43×#1996C211yesmaximal, characteristic, complemented
8C43×#1964C211yesmaximal, characteristic, complemented
9C43×#1889C212yesmaximal, complemented
10C43×#1867C212yesmaximal, complemented
11C43×#1799C211yesmaximal, characteristic, complemented
12C43×#553—22no—
13C43×#553—21no—
14C43×#552—21no—
15C43×#551—22no—
16C43×#548—21no—
17C43×#546—21no—
18C43×#539—21no—
19C43×#538—21no—
20C43×#534C2212yes—
21C43×#529—21no—
22C43×#525—21no—
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#120×C43C2211yescharacteristic
26C2×#120×C43C2212yes—
27C43×#518C2212yes—
28C2×C4×D4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2211yescharacteristic
30C2×#99×C43C2212yes—
31C2×#99×C43C2212yes—
32C2×#99×C43C2212yes—
33C43×#399—21no—
34C43×#397—21no—
35C43×#396—22no—
36C43×#394—22no—
37C43×#393—21no—
38C43×#392—21no—
39C43×#390—21no—
40C43×#388—21no—
41C43×#388—21no—
42C43×#386—21no—
43C43×#386C2211yescharacteristic
44C43×#386C2212yes—
45C43×#385C2211yescharacteristic
46C43×#385C2212yes—
47C43×#380C2211yescharacteristic
48C43×#380C2211yescharacteristic
49C43×#379C2211yescharacteristic
50C43×#379C2212yes—
51C4×C22⋊C4×C43C2211yescharacteristic
52C43×#342C2212yes—
53C43×#342C2212yes—
54C43×#342C2212yes—
55C25×C43C2311yescharacteristic
56C2×#41×C43—21no—
57C22×Q8×C43D411yescharacteristic, complemented
58C22×D4×C43—21no—
59C22×D4×C43—22no—
60C22×D4×C43D411yescharacteristic, complemented
61C22×D4×C43C2311yescharacteristic
62C22×D4×C43C2312yes—
63C23×C4×C43D411yescharacteristic, complemented
64C23×C4×C43C2311yescharacteristic
65C23×C4×C43C2311yescharacteristic
66#126×C43—22no—
67#126×C43—22no—
68#126×C43—22no—
69#125×C43—21no—
70#125×C43—22no—
71#124×C43—21no—
72#124×C43—22no—
73#123×C43—22no—
74#123×C43—22no—
75#123×C43—22no—
76#123×C43—22no—
77#123×C43—22no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—21no—
82C22⋊Q8×C43—21no—
83C22⋊Q8×C43—21no—
84#121×C43—21no—
85#121×C43—22no—
86#121×C43—21no—
87#121×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43—22no—
91#121×C43—22no—
92#120×C43—22no—
93#120×C43—22no—
94#120×C43—22no—
95#120×C43—22no—
96#120×C43—24no—
97#120×C43—42no—
98C4×Q8×C43—21no—
99C4×D4×C43—22no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109#117×C43—21no—
110#117×C43—22no—
111#117×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—22no—
116C2×C4⋊C4×C43D411yescharacteristic, complemented
117C2×C4⋊C4×C43D411yescharacteristic, complemented
118C2×C4⋊C4×C43D412yescomplemented
119C2×C4⋊C4×C43D411yescharacteristic, complemented
120C2×C22⋊C4×C43—22no—
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×C43—21no—
128C2×C22⋊C4×C43—22no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—22no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—22no—
135C2×C22⋊C4×C43D411yescharacteristic, complemented
136C2×C22⋊C4×C43D412yescomplemented
137C2×C22⋊C4×C43C2312yes—
138C2×C22⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43C2312yes—
140C2×C22⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43C2312yes—
142C2×C22⋊C4×C43C2311yescharacteristic
143C2×C42×C43—21no—
144C2×C42×C43D411yescharacteristic, complemented
145#99×C43—24no—
146#99×C43—42no—
147#99×C43—42no—
148#95×C43—21no—
149#95×C43—21no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—22no—
153#95×C43—21no—
154#95×C43—22no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—81no—
162C24×C43—81no—
163C24×C43C2×D412yes—
164C24×C43C2×D411yescharacteristic
165C24×C43#4112yescomplemented
166C24×C43C2411yescharacteristic
167#41×C43—82no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—81no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43—24no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—22no—
178C2×D4×C43—21no—
179C2×D4×C43—22no—
180C2×D4×C43—22no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—22no—
184C2×D4×C43—21no—
185C2×D4×C43—22no—
186C2×D4×C43—21no—
187C2×D4×C43—22no—
188C2×D4×C43—44no—
189C2×D4×C43—81no—
190C2×D4×C43—81no—
191C2×D4×C43—81no—
192C2×D4×C43—82no—
193C2×D4×C43—82no—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
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—22no—
203C22×C4×C43—22no—
204C22×C4×C43—21no—
205C22×C4×C43—81no—
206C22×C4×C43—81no—
207C22×C4×C43—81no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C4⋊C4×C43—22no—
221C4⋊C4×C43—22no—
222C4⋊C4×C43—22no—
223C4⋊C4×C43—22no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—22no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—22no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—81no—
233C4⋊C4×C43—81no—
234C4⋊C4×C43—81no—
235C4⋊C4×C43—82no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—22no—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—22no—
240C22⋊C4×C43—22no—
241C22⋊C4×C43—22no—
242C22⋊C4×C43—22no—
243C22⋊C4×C43—22no—
244C22⋊C4×C43—21no—
245C22⋊C4×C43—21no—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—21no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—21no—
250C22⋊C4×C43—22no—
251C22⋊C4×C43—21no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—22no—
254C22⋊C4×C43—21no—
255C22⋊C4×C43—22no—
256C22⋊C4×C43—22no—
257C22⋊C4×C43—21no—
258C22⋊C4×C43—44no—
259C22⋊C4×C43—41no—
260C22⋊C4×C43—41no—
261C22⋊C4×C43—41no—
262C22⋊C4×C43—41no—
263C22⋊C4×C43—81no—
264C22⋊C4×C43—81no—
265C22⋊C4×C43—82no—
266C22⋊C4×C43—81no—
267C22⋊C4×C43—82no—
268C22⋊C4×C43—82no—
269C22⋊C4×C43#4112yescomplemented
270C42×C43—22no—
271C42×C43—22no—
272C42×C43—21no—
273C42×C43—21no—
274C42×C43—81no—
275C23×C43—21no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—21no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—21no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—42no—
290C23×C43—41no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—41no—
294C23×C43—42no—
295C23×C43—41no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—82no—
303C23×C43—82no—
304C23×C43—82no—
305C23×C43—82no—
306C23×C43C22×D411yescharacteristic
307C23×C43C22×D411yescharacteristic
308C23×C43C22×D411yescharacteristic
309C23×C43C2×#4111yescharacteristic
310C23×C43C2×#4111yescharacteristic
311C23×C43H(5,𝔽2)11yescharacteristic
312C23×C432−1+411yescharacteristic
313Q8×C43—42no—
314Q8×C43—81no—
315D4×C43—42no—
316D4×C43—42no—
317D4×C43—42no—
318D4×C43—41no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—42no—
322D4×C43—42no—
323D4×C43—41no—
324D4×C43—81no—
325D4×C43—82no—
326D4×C43—84no—
327D4×C43—82no—
328D4×C43—88no—
329C2×C4×C43—21no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—21no—
336C2×C4×C43—22no—
337C2×C4×C43—21no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
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—42no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—42no—
351C2×C4×C43—41no—
352C2×C4×C43—42no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—42no—
356C2×C4×C43—42no—
357C2×C4×C43—42no—
358C2×C4×C43—41no—
359C2×C4×C43—42no—
360C2×C4×C43—41no—
361C2×C4×C43—42no—
362C2×C4×C43—42no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43—81no—
368C2×C4×C43—82no—
369C2×C4×C43—82no—
370C2×C4×C43#12011yescharacteristic
371C2×C4×C43#12011yescharacteristic
372C2×C4×C43#12011yescharacteristic
373C2×C4×C43#12011yescharacteristic
374#24142C4311yesmaximal, characteristic, direct product factor, Sylow
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—42no—
386C22×C43—44no—
387C22×C43—42no—
388C22×C43—44no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—41no—
397C22×C43—81no—
398C22×C43—82no—
399C22×C43—82no—
400C22×C43—82no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—82no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43C2×#12011yescharacteristic
407C22×C43#52511yescharacteristic
408C22×C43#53711yescharacteristic
409C22×C43#54611yescharacteristic
410C22×C43#54711yescharacteristic
411C22×C43#54811yescharacteristic
412C22×C43#55011yescharacteristic
413C4×C43—21no—
414C4×C43—21no—
415C4×C43—21no—
416C4×C43—21no—
417C4×C43—42no—
418C4×C43—41no—
419C4×C43—42no—
420C4×C43—41no—
421C4×C43—42no—
422C4×C43—41no—
423C4×C43—42no—
424C4×C43—82no—
425C4×C43—81no—
426C4×C43—82no—
427C4×C43—81no—
428#3505C2×C4311yescharacteristic, complemented
429#2626C2×C4311yescharacteristic, complemented
430#2617C2×C4311yescharacteristic, complemented
431#2321C2×C4311yescharacteristic, complemented
432#2044C2×C4312yescomplemented
433#2021C2×C4312yescomplemented
434#1996C2×C4311yescharacteristic, complemented
435#1964C2×C4311yescharacteristic, complemented
436#1889C2×C4312yescomplemented
437#1867C2×C4312yescomplemented
438#1799C2×C4311yescharacteristic, complemented
439C2×C43—21no—
440C2×C43—21no—
441C2×C43—21no—
442C2×C43—21no—
443C2×C43—21no—
444C2×C43—21no—
445C2×C43—82no—
446C2×C43—81no—
447C2×C43—82no—
448C2×C43#240711yescharacteristic
449C2×C43#302611yescharacteristic
450C2×C43#302711yescharacteristic
451#553—22no—
452#553—21no—
453#552—21no—
454#551—22no—
455#548—21no—
456#546—21no—
457#539—21no—
458#538—21no—
459#534C22×C4312yes—
460#529—21no—
461#525—21no—
462C2×C22⋊Q8C22×C4311yescharacteristic
463C2×#121C22×C4311yescharacteristic
464C2×#120C22×C4311yescharacteristic
465C2×#120C22×C4312yes—
466#518C22×C4312yes—
467C2×C4×D4C22×C4311yescharacteristic
468C22×C22⋊C4C22×C4311yescharacteristic
469C2×#99C22×C4312yes—
470C2×#99C22×C4312yes—
471C2×#99C22×C4312yes—
472#399—21no—
473#397—21no—
474#396—22no—
475#394—22no—
476#393—21no—
477#392—21no—
478#390—21no—
479#388—21no—
480#388—21no—
481#386—21no—
482#386C22×C4311yescharacteristic
483#386C22×C4312yes—
484#385C22×C4311yescharacteristic
485#385C22×C4312yes—
486#380C22×C4311yescharacteristic
487#380C22×C4311yescharacteristic
488#379C22×C4311yescharacteristic
489#379C22×C4312yes—
490C4×C22⋊C4C22×C4311yescharacteristic
491#342C22×C4312yes—
492#342C22×C4312yes—
493#342C22×C4312yes—
494C43#2414211yescharacteristic, direct product factor, Sylow
495C25C23×C4311yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C4311yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C4311yescharacteristic, complemented
501C22×D4C23×C4311yescharacteristic
502C22×D4C23×C4312yes—
503C23×C4D4×C4311yescharacteristic, complemented
504C23×C4C23×C4311yescharacteristic
505C23×C4C23×C4311yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C4311yescharacteristic, complemented
557C2×C4⋊C4D4×C4311yescharacteristic, complemented
558C2×C4⋊C4D4×C4312yescomplemented
559C2×C4⋊C4D4×C4311yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C4311yescharacteristic, complemented
576C2×C22⋊C4D4×C4312yescomplemented
577C2×C22⋊C4C23×C4312yes—
578C2×C22⋊C4C23×C4311yescharacteristic
579C2×C22⋊C4C23×C4312yes—
580C2×C22⋊C4C23×C4311yescharacteristic
581C2×C22⋊C4C23×C4312yes—
582C2×C22⋊C4C23×C4311yescharacteristic
583C2×C42—21no—
584C2×C42D4×C4311yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C4312yes—
604C24C2×D4×C4311yescharacteristic
605C24#41×C4312yescomplemented
606C24C24×C4311yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C4311yescharacteristic
649C22×C4C2×D4×C4312yes—
650C22×C4C2×D4×C4311yescharacteristic
651C22×C4C2×D4×C4312yes—
652C22×C4C2×D4×C4311yescharacteristic
653C22×C4C2×D4×C4312yes—
654C22×C4C2×D4×C4311yescharacteristic
655C22×C4C2×D4×C4311yescharacteristic
656C22×C4C2×D4×C4311yescharacteristic
657C22×C4C2×D4×C4311yescharacteristic
658C22×C4C2×D4×C4311yescharacteristic
659C22×C4C2×D4×C4311yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C4312yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C4311yescharacteristic
747C23C22×D4×C4311yescharacteristic
748C23C22×D4×C4311yescharacteristic
749C23C2×#41×C4311yescharacteristic
750C23C2×#41×C4311yescharacteristic
751C23H(5,𝔽2)×C4311yescharacteristic
752C232−1+4×C4311yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C4311yescharacteristic
811C2×C4#120×C4311yescharacteristic
812C2×C4#120×C4311yescharacteristic
813C2×C4#120×C4311yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C4311yescharacteristic
846C22C43×#52511yescharacteristic
847C22C43×#53711yescharacteristic
848C22C43×#54611yescharacteristic
849C22C43×#54711yescharacteristic
850C22C43×#54811yescharacteristic
851C22C43×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C43×#240711yescharacteristic
877C2C43×#302611yescharacteristic
878C2C43×#302711yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3505C2semidirect
2. C43×#2626C2semidirect
3. C43×#2617C2semidirect
4. C43×#2321C2semidirect
5. C43×#2044C2semidirect
6. C43×#2021C2semidirect
7. C43×#1996C2semidirect
8. C43×#1964C2semidirect
9. C43×#1889C2semidirect
10. C43×#1867C2semidirect
11. C43×#1799C2semidirect
57. C22×Q8×C43D4semidirect
60. C22×D4×C43D4semidirect
63. C23×C4×C43D4semidirect
116. C2×C4⋊C4×C43D4semidirect
117. C2×C4⋊C4×C43D4semidirect
118. C2×C4⋊C4×C43D4semidirect
119. C2×C4⋊C4×C43D4semidirect
135. C2×C22⋊C4×C43D4semidirect
136. C2×C22⋊C4×C43D4semidirect
144. C2×C42×C43D4semidirect
165. C24×C43#41semidirect
269. C22⋊C4×C43#41semidirect
374. #24142C43direct (N × H)
428. #3505C2×C43semidirect
429. #2626C2×C43semidirect
430. #2617C2×C43semidirect
431. #2321C2×C43semidirect
432. #2044C2×C43semidirect
433. #2021C2×C43semidirect
434. #1996C2×C43semidirect
435. #1964C2×C43semidirect
436. #1889C2×C43semidirect
437. #1867C2×C43semidirect
438. #1799C2×C43semidirect
494. C43#24142direct (N × H)
497. C22×Q8D4×C43semidirect
500. C22×D4D4×C43semidirect
503. C23×C4D4×C43semidirect
556. C2×C4⋊C4D4×C43semidirect
557. C2×C4⋊C4D4×C43semidirect
558. C2×C4⋊C4D4×C43semidirect
559. C2×C4⋊C4D4×C43semidirect
575. C2×C22⋊C4D4×C43semidirect
576. C2×C22⋊C4D4×C43semidirect
584. C2×C42D4×C43semidirect
605. C24#41×C43semidirect
709. C22⋊C4#41×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35052
C43×#26262
C43×#26172
C43×#23212
C43×#20442
C43×#20212
C43×#19962
C43×#19642
C43×#18892
C43×#18672
C43×#17992
#2414243