Finite Group Databasebeta

← C43×#21458 #24941475

Subgroups — C43×#21458 #24941475

Order 11008.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#518C211yesmaximal, characteristic, complemented
2C2×C43×#447C211yesmaximal, characteristic
3C2×C43×#442C211yesmaximal, characteristic, complemented
4C2×C4×D8×C43C211yesmaximal, characteristic, complemented
5C43×#2324C211yesmaximal, characteristic, complemented
6C43×#1879C211yesmaximal, characteristic, complemented
7C43×#1879C211yesmaximal, characteristic, complemented
8C43×#1875C211yesmaximal, characteristic, complemented
9C43×#1864C211yesmaximal, characteristic, complemented
10C43×#1862C211yesmaximal, characteristic, complemented
11C43×#1854C211yesmaximal, characteristic, complemented
12C43×#1786C211yesmaximal, characteristic, complemented
13C43×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C43C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C43×#518—24no—
21C43×#518—24no—
22C2×C4×D4×C43—21no—
23C2×C4×D4×C43—21no—
24C2×C4×D4×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic
27C2×C4×D4×C43C2211yescharacteristic
28C2×C4×D4×C43C2211yescharacteristic, complemented
29C2×#117×C43C2211yescharacteristic
30C2×#117×C43C2211yescharacteristic
31C22×C22⋊C4×C43—21no—
32C22×C22⋊C4×C43—21no—
33C43×#447C418yescomplemented
34C43×#442—24no—
35C4×D8×C43—24no—
36C2×#107×C43C2211yescharacteristic, complemented
37C2×#106×C43C2211yescharacteristic, complemented
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic, complemented
45C2×#102×C43C2211yescharacteristic, complemented
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×#97×C43C2211yescharacteristic, complemented
49C2×C4×C8×C43C2211yescharacteristic, complemented
50C43×#390—21no—
51C43×#390C2211yescharacteristic, complemented
52C43×#389C2211yescharacteristic, complemented
53C43×#388—21no—
54C43×#386—21no—
55C43×#385—21no—
56C43×#380C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#336C2211yescharacteristic, complemented
63C43×#336C2211yescharacteristic, complemented
64C25×C43—21no—
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43—22no—
68C22×D4×C43—22no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—22no—
72C22×D4×C43C2×C414yescomplemented
73C22×D4×C43C2311yescharacteristic
74C22×D4×C43C2311yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C23×C4×C43—21no—
77C23×C4×C43—21no—
78C23×C4×C43—21no—
79C23×C4×C43—21no—
80C23×C4×C43—21no—
81C23×C4×C43C2311yescharacteristic
82C2×D8×C43—22no—
83C2×D8×C43—22no—
84C2×D8×C43—22no—
85C2×D8×C43—22no—
86C2×D8×C43C2×C414yescomplemented
87C2×D8×C43C2×C414yescomplemented
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90C22×C8×C43C2311yescharacteristic
91C22×C8×C43C2311yescharacteristic
92#121×C43—22no—
93#121×C43C2×C414yescomplemented
94C4×D4×C43—28no—
95C4×D4×C43—28no—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43D414yescomplemented
105C4×D4×C43D414yescomplemented
106#117×C43—22no—
107#117×C43—22no—
108#117×C43—22no—
109#117×C43—22no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—28no—
119C2×C22⋊C4×C43—28no—
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×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#107×C43—22no—
137#106×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—22no—
144#102×C43C2×C414yescomplemented
145#102×C43C2×C414yescomplemented
146C22⋊C8×C43—22no—
147C22⋊C8×C43C2×C414yescomplemented
148#97×C43—22no—
149C4×C8×C43—22no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153C24×C43—24no—
154C24×C43—24no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—24no—
158C24×C43—21no—
159C24×C43—81no—
160C24×C43—81no—
161C24×C43—81no—
162C24×C43—81no—
163C24×C43C2×D411yescharacteristic
164C2×D4×C43—24no—
165C2×D4×C43—28no—
166C2×D4×C43—28no—
167C2×D4×C43—24no—
168C2×D4×C43—28no—
169C2×D4×C43—28no—
170C2×D4×C43—24no—
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—24no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—81no—
184C2×D4×C43—81no—
185C2×D4×C43C22×C412yes—
186C2×D4×C43C22×C412yes—
187C2×D4×C43C22×C412yes—
188C2×D4×C43C2×D412yes—
189C2×D4×C43C2×D412yes—
190C2×D4×C43#4112yes—
191C2×D4×C43#4112yes—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—24no—
197C22×C4×C43—24no—
198C22×C4×C43—24no—
199C22×C4×C43—24no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—42no—
206C22×C4×C43—81no—
207C22×C4×C43—81no—
208C22×C4×C43—81no—
209C22×C4×C43—81no—
210C22×C4×C43—81no—
211C22×C4×C43—81no—
212C22×C4×C43—81no—
213C22×C4×C43—81no—
214C22×C4×C43—81no—
215C22×C4×C43—81no—
216C22×C4×C43C22×C412yes—
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43#4112yes—
223C22×C4×C43C2411yescharacteristic
224D8×C43—28no—
225D8×C43—28no—
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×C43—21no—
236C2×C8×C43C22×C412yes—
237C2×C8×C43C22×C412yes—
238C4⋊C4×C43—22no—
239C4⋊C4×C43—22no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—81no—
248C4⋊C4×C43C22×C412yes—
249C4⋊C4×C43C2×D412yes—
250C4⋊C4×C43C2×D412yes—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—24no—
253C22⋊C4×C43—24no—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—22no—
256C22⋊C4×C43—22no—
257C22⋊C4×C43—24no—
258C22⋊C4×C43—24no—
259C22⋊C4×C43—42no—
260C22⋊C4×C43—81no—
261C22⋊C4×C43—81no—
262C22⋊C4×C43—81no—
263C42×C43—24no—
264C42×C43—21no—
265C42×C43—21no—
266C42×C43—81no—
267C42×C43C2×D412yes—
268C42×C43C2×D412yes—
269C23×C43—216no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—21no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—21no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—22no—
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×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—84no—
298C23×C43—84no—
299C23×C43—84no—
300C23×C43—84no—
301C23×C43—84no—
302C23×C43—84no—
303C23×C43C4×D412yes—
304C23×C43C22×D411yescharacteristic
305D4×C43—216no—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—41no—
315D4×C43—41no—
316D4×C43—84no—
317D4×C43C4×D414yes—
318D4×C43C4×D414yes—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
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—41no—
350C2×C4×C43—84no—
351C2×C4×C43—84no—
352C2×C4×C43—84no—
353C2×C4×C43—84no—
354C2×C4×C43—84no—
355C2×C4×C43C4×D412yes—
356C2×C4×C43#12012yes—
357C2×C4×C43#12012yes—
358C2×C4×C43C23×C411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C2×#4111yescharacteristic
362C2×C4×C43C2×#4111yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C8×C43—22no—
365C8×C43—22no—
366C8×C43—41no—
367C8×C43—41no—
368#21458C4311yesmaximal, characteristic, direct product factor, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—24no—
373C22×C43—24no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—41no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—41no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—816no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43C2×C4×D411yescharacteristic
399C22×C43C2×#12011yescharacteristic
400C22×C43#52511yescharacteristic
401C22×C43#57611yescharacteristic
402C22×C43#57611yescharacteristic
403C22×C43#57611yescharacteristic
404C22×C43#57711yescharacteristic
405C4×C43—22no—
406C4×C43—22no—
407C4×C43—22no—
408C4×C43—42no—
409C4×C43—41no—
410C4×C43—42no—
411C4×C43—41no—
412C4×C43—42no—
413C4×C43—81no—
414C4×C43—81no—
415C4×C43C2×C4×D411yescharacteristic
416C4×C43C2×C4×D411yescharacteristic
417C4×C43#52511yescharacteristic
418C4×C43#52511yescharacteristic
419C2×#518C2×C4311yescharacteristic, complemented
420C2×#447C2×C4311yescharacteristic
421C2×#442C2×C4311yescharacteristic, complemented
422C2×C4×D8C2×C4311yescharacteristic, complemented
423#2324C2×C4311yescharacteristic, complemented
424#1879C2×C4311yescharacteristic, complemented
425#1879C2×C4311yescharacteristic, complemented
426#1875C2×C4311yescharacteristic, complemented
427#1864C2×C4311yescharacteristic, complemented
428#1862C2×C4311yescharacteristic, complemented
429#1854C2×C4311yescharacteristic, complemented
430#1786C2×C4311yescharacteristic, complemented
431#1762C2×C4311yescharacteristic, complemented
432C4×#102C2×C4311yescharacteristic, complemented
433#1750C2×C4311yescharacteristic, complemented
434C2×C43—42no—
435C2×C43—44no—
436C2×C43—44no—
437C2×C43—82no—
438C2×C43C4×#12011yescharacteristic
439C2×C43#294611yescharacteristic
440C2×C43#294811yescharacteristic
441C2×C43#300811yescharacteristic
442C2×C43#301211yescharacteristic
443C2×C43#311811yescharacteristic
444C2×C43#312211yescharacteristic
445C23×D4C22×C4311yescharacteristic
446C22×D8C22×C4311yescharacteristic
447C22×D8C22×C4311yescharacteristic
448C2×#121C22×C4311yescharacteristic
449#518—24no—
450#518—24no—
451C2×C4×D4—21no—
452C2×C4×D4—21no—
453C2×C4×D4C22×C4311yescharacteristic
454C2×C4×D4C22×C4311yescharacteristic
455C2×C4×D4C22×C4311yescharacteristic
456C2×C4×D4C22×C4311yescharacteristic
457C2×C4×D4C22×C4311yescharacteristic, complemented
458C2×#117C22×C4311yescharacteristic
459C2×#117C22×C4311yescharacteristic
460C22×C22⋊C4—21no—
461C22×C22⋊C4—21no—
462#447C4×C4318yescomplemented
463#442—24no—
464C4×D8—24no—
465C2×#107C22×C4311yescharacteristic, complemented
466C2×#106C22×C4311yescharacteristic, complemented
467C2×#102C22×C4311yescharacteristic
468C2×#102C22×C4311yescharacteristic
469C2×#102C22×C4311yescharacteristic
470C2×#102C22×C4311yescharacteristic
471C2×#102C22×C4311yescharacteristic
472C2×#102C22×C4311yescharacteristic
473C2×#102C22×C4311yescharacteristic, complemented
474C2×#102C22×C4311yescharacteristic, complemented
475C2×C22⋊C8C22×C4311yescharacteristic
476C2×C22⋊C8C22×C4311yescharacteristic
477C2×#97C22×C4311yescharacteristic, complemented
478C2×C4×C8C22×C4311yescharacteristic, complemented
479#390—21no—
480#390C22×C4311yescharacteristic, complemented
481#389C22×C4311yescharacteristic, complemented
482#388—21no—
483#386—21no—
484#385—21no—
485#380C22×C4311yescharacteristic
486C4×C4⋊C4C22×C4311yescharacteristic, complemented
487#340C22×C4311yescharacteristic, complemented
488#340C22×C4311yescharacteristic, complemented
489#340C22×C4311yescharacteristic, complemented
490#340C22×C4311yescharacteristic, complemented
491#336C22×C4311yescharacteristic, complemented
492#336C22×C4311yescharacteristic, complemented
493C43#2145811yescharacteristic, direct product factor, Sylow
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4C2×C4×C4314yescomplemented
503C22×D4C23×C4311yescharacteristic
504C22×D4C23×C4311yescharacteristic
505C22×D4C23×C4311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C23×C4311yescharacteristic
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8C2×C4×C4314yescomplemented
517C2×D8C2×C4×C4314yescomplemented
518C22×C8C23×C4311yescharacteristic
519C22×C8C23×C4311yescharacteristic
520C22×C8C23×C4311yescharacteristic
521C22×C8C23×C4311yescharacteristic
522#121—22no—
523#121C2×C4×C4314yescomplemented
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4D4×C4314yescomplemented
535C4×D4D4×C4314yescomplemented
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C4311yescharacteristic
542C2×C4⋊C4D4×C4311yescharacteristic
543C2×C4⋊C4C23×C4311yescharacteristic
544C2×C4⋊C4C23×C4311yescharacteristic
545C2×C4⋊C4C23×C4311yescharacteristic
546C2×C4⋊C4C23×C4311yescharacteristic
547C2×C4⋊C4C23×C4311yescharacteristic
548C2×C22⋊C4—28no—
549C2×C22⋊C4—28no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4D4×C4311yescharacteristic
561C2×C22⋊C4D4×C4311yescharacteristic
562C2×C42—21no—
563C2×C42—21no—
564C2×C42C23×C4311yescharacteristic
565C2×C42C23×C4311yescharacteristic
566#107—22no—
567#106—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102C2×C4×C4314yescomplemented
575#102C2×C4×C4314yescomplemented
576C22⋊C8—22no—
577C22⋊C8C2×C4×C4314yescomplemented
578#97—22no—
579C4×C8—22no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—21no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—81no—
593C24C2×D4×C4311yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C22×C4×C4312yes—
616C2×D4C22×C4×C4312yes—
617C2×D4C22×C4×C4312yes—
618C2×D4C2×D4×C4312yes—
619C2×D4C2×D4×C4312yes—
620C2×D4#41×C4312yes—
621C2×D4#41×C4312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C22×C4×C4312yes—
647C22×C4C2×D4×C4311yescharacteristic
648C22×C4C2×D4×C4311yescharacteristic
649C22×C4C2×D4×C4311yescharacteristic
650C22×C4C2×D4×C4311yescharacteristic
651C22×C4C2×D4×C4311yescharacteristic
652C22×C4#41×C4312yes—
653C22×C4C24×C4311yescharacteristic
654D8—28no—
655D8—28no—
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×C8C22×C4×C4312yes—
667C2×C8C22×C4×C4312yes—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—81no—
678C4⋊C4C22×C4×C4312yes—
679C4⋊C4C2×D4×C4312yes—
680C4⋊C4C2×D4×C4312yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—42no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—81no—
697C42C2×D4×C4312yes—
698C42C2×D4×C4312yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23C4×D4×C4312yes—
734C23C22×D4×C4311yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4C4×D4×C4314yes—
748D4C4×D4×C4314yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4C4×D4×C4312yes—
786C2×C4#120×C4312yes—
787C2×C4#120×C4312yes—
788C2×C4C23×C4×C4311yescharacteristic
789C2×C4C22×D4×C4311yescharacteristic
790C2×C4C22×D4×C4311yescharacteristic
791C2×C4C2×#41×C4311yescharacteristic
792C2×C4C2×#41×C4311yescharacteristic
793C2×C4C2×#41×C4311yescharacteristic
794C8—22no—
795C8—22no—
796C8—41no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22C2×C4×D4×C4311yescharacteristic
828C22C2×#120×C4311yescharacteristic
829C22C43×#52511yescharacteristic
830C22C43×#57611yescharacteristic
831C22C43×#57611yescharacteristic
832C22C43×#57611yescharacteristic
833C22C43×#57711yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—42no—
838C4—41no—
839C4—42no—
840C4—41no—
841C4—42no—
842C4—81no—
843C4—81no—
844C4C2×C4×D4×C4311yescharacteristic
845C4C2×C4×D4×C4311yescharacteristic
846C4C43×#52511yescharacteristic
847C4C43×#52511yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—82no—
852C2C4×#120×C4311yescharacteristic
853C2C43×#294611yescharacteristic
854C2C43×#294811yescharacteristic
855C2C43×#300811yescharacteristic
856C2C43×#301211yescharacteristic
857C2C43×#311811yescharacteristic
858C2C43×#312211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#447C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#518C2semidirect
3. C2×C43×#442C2semidirect
4. C2×C4×D8×C43C2semidirect
5. C43×#2324C2semidirect
6. C43×#1879C2semidirect
7. C43×#1879C2semidirect
8. C43×#1875C2semidirect
9. C43×#1864C2semidirect
10. C43×#1862C2semidirect
11. C43×#1854C2semidirect
12. C43×#1786C2semidirect
13. C43×#1762C2semidirect
14. C4×#102×C43C2semidirect
15. C43×#1750C2semidirect
28. C2×C4×D4×C43C22semidirect
33. C43×#447C4semidirect
36. C2×#107×C43C22semidirect
37. C2×#106×C43C22semidirect
44. C2×#102×C43C22semidirect
45. C2×#102×C43C22semidirect
48. C2×#97×C43C22semidirect
49. C2×C4×C8×C43C22semidirect
51. C43×#390C22semidirect
52. C43×#389C22semidirect
57. C4×C4⋊C4×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
62. C43×#336C22semidirect
63. C43×#336C22semidirect
72. C22×D4×C43C2×C4semidirect
86. C2×D8×C43C2×C4semidirect
87. C2×D8×C43C2×C4semidirect
93. #121×C43C2×C4semidirect
104. C4×D4×C43D4semidirect
105. C4×D4×C43D4semidirect
144. #102×C43C2×C4semidirect
145. #102×C43C2×C4semidirect
147. C22⋊C8×C43C2×C4semidirect
368. #21458C43direct (N × H)
419. C2×#518C2×C43semidirect
421. C2×#442C2×C43semidirect
422. C2×C4×D8C2×C43semidirect
423. #2324C2×C43semidirect
424. #1879C2×C43semidirect
425. #1879C2×C43semidirect
426. #1875C2×C43semidirect
427. #1864C2×C43semidirect
428. #1862C2×C43semidirect
429. #1854C2×C43semidirect
430. #1786C2×C43semidirect
431. #1762C2×C43semidirect
432. C4×#102C2×C43semidirect
433. #1750C2×C43semidirect
457. C2×C4×D4C22×C43semidirect
462. #447C4×C43semidirect
465. C2×#107C22×C43semidirect
466. C2×#106C22×C43semidirect
473. C2×#102C22×C43semidirect
474. C2×#102C22×C43semidirect
477. C2×#97C22×C43semidirect
478. C2×C4×C8C22×C43semidirect
480. #390C22×C43semidirect
481. #389C22×C43semidirect
486. C4×C4⋊C4C22×C43semidirect
487. #340C22×C43semidirect
488. #340C22×C43semidirect
489. #340C22×C43semidirect
490. #340C22×C43semidirect
491. #336C22×C43semidirect
492. #336C22×C43semidirect
493. C43#21458direct (N × H)
502. C22×D4C2×C4×C43semidirect
516. C2×D8C2×C4×C43semidirect
517. C2×D8C2×C4×C43semidirect
523. #121C2×C4×C43semidirect
534. C4×D4D4×C43semidirect
535. C4×D4D4×C43semidirect
574. #102C2×C4×C43semidirect
575. #102C2×C4×C43semidirect
577. C22⋊C8C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5182
C2×C43×#4472
C2×C43×#4422
C2×C4×D8×C432
C43×#23242
C43×#18792
C43×#18752
C43×#18642
C43×#18622
C43×#18542
C43×#17862
C43×#17622
C4×#102×C432
C43×#17502
#2145843