Finite Group Databasebeta

← C43×#24867 #24944884

Subgroups — C43×#24867 #24944884

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#484C211yesmaximal, characteristic, complemented
2C22×#103×C43C211yesmaximal, characteristic, complemented
3C43×#2409C211yesmaximal, characteristic
4D4×C4⋊C4×C43C211yesmaximal, characteristic
5C43×#2095C211yesmaximal, characteristic, complemented
6C43×#2072C211yesmaximal, characteristic, complemented
7C43×#2036C211yesmaximal, characteristic, complemented
8C43×#2036C211yesmaximal, characteristic, complemented
9C43×#1928C211yesmaximal, characteristic, complemented
10C43×#1928C211yesmaximal, characteristic, complemented
11C43×#1872C211yesmaximal, characteristic, complemented
12C43×#1869C211yesmaximal, characteristic
13C43×#1852C211yesmaximal, characteristic, complemented
14C43×#1808C211yesmaximal, characteristic, complemented
15C43×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C43C2211yescharacteristic
17C23×C8×C43C2211yescharacteristic
18C2×C22⋊Q8×C43C2211yescharacteristic
19C2×C22⋊Q8×C43C2211yescharacteristic
20C2×C4×D4×C43—21no—
21C2×C4×D4×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C43×#484—24no—
25C2×#107×C43C2211yescharacteristic
26C2×#107×C43C2211yescharacteristic
27C2×#107×C43C2211yescharacteristic
28C2×#107×C43C2211yescharacteristic
29C2×#103×C43—24no—
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#103×C43C2211yescharacteristic
34C2×#103×C43C2211yescharacteristic
35C2×#103×C43C2211yescharacteristic
36C2×#103×C43C2211yescharacteristic
37C2×#103×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C2×C22⋊C8×C43C2211yescharacteristic
41C43×#395—21no—
42C43×#393—21no—
43C43×#391C2211yescharacteristic
44C43×#391C2211yescharacteristic
45C43×#389—21no—
46C43×#386—21no—
47C43×#385—21no—
48C43×#385—21no—
49C43×#385—21no—
50C43×#384C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C43×#380C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Q8×C43—21no—
62C22×Q8×C43—22no—
63C22×Q8×C43—22no—
64C22×Q8×C43—22no—
65C22×Q8×C43—22no—
66C22×Q8×C43—41no—
67C22×Q8×C43—41no—
68C22×Q8×C43C2311yescharacteristic
69C22×Q8×C43C2311yescharacteristic
70C22×D4×C43D411yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76C22×C8×C43—22no—
77C22×C8×C43—22no—
78C22×C8×C43—41no—
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22⋊Q8×C43—22no—
84C22⋊Q8×C43—22no—
85C22⋊Q8×C43—41no—
86C22⋊Q8×C43—41no—
87C4×D4×C43—22no—
88C4×D4×C43—22no—
89C4×D4×C43—44no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—41no—
99C2×C4⋊C4×C43—41no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#107×C43—22no—
117#107×C43—22no—
118#107×C43—41no—
119#107×C43—41no—
120#103×C43—22no—
121#103×C43—22no—
122#103×C43—22no—
123#103×C43—22no—
124#103×C43—22no—
125#103×C43—41no—
126#103×C43—41no—
127#103×C43D414yescomplemented
128C22⋊C8×C43—22no—
129C22⋊C8×C43—22no—
130C22⋊C8×C43—41no—
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43C2×D411yescharacteristic
140C24×C43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—28no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—42no—
153C2×Q8×C43—42no—
154C2×Q8×C43—44no—
155C2×Q8×C43—44no—
156C2×Q8×C43—44no—
157C2×Q8×C43—42no—
158C2×Q8×C43C2×D412yes—
159C2×Q8×C43#4112yes—
160C2×D4×C43—22no—
161C2×D4×C43—22no—
162C2×D4×C43Q1614yes—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43—42no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—81no—
189C22×C4×C43—81no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43#4112yes—
195C22×C4×C43#4112yes—
196C22×C4×C43C2411yescharacteristic
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—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—44no—
209C2×C8×C43C2×D412yes—
210C4⋊C4×C43—22no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—42no—
223C4⋊C4×C43—42no—
224C4⋊C4×C43—42no—
225C4⋊C4×C43—42no—
226C4⋊C4×C43—42no—
227C4⋊C4×C43—81no—
228C4⋊C4×C43C2×D412yes—
229C22⋊C4×C43—22no—
230C22⋊C4×C43—22no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C42×C43—21no—
237C42×C43—21no—
238C42×C43—42no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43#12312yes—
250C23×C43C2×Q1612yes—
251C23×C43C2×Q1612yes—
252C23×C43AGL(1,ℤ/8)12yes—
253C23×C43C22×D411yescharacteristic
254Q8×C43—22no—
255Q8×C43—22no—
256Q8×C43—22no—
257Q8×C43—22no—
258Q8×C43—48no—
259Q8×C43—41no—
260Q8×C43—41no—
261Q8×C43—41no—
262Q8×C43—41no—
263D4×C43—28no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—48no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
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—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—84no—
308C2×C4×C43—84no—
309C2×C4×C43#12312yes—
310C2×C4×C43C2×Q1612yes—
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43H(5,𝔽2)11yescharacteristic
316C2×C4×C43H(5,𝔽2)11yescharacteristic
317C8×C43—22no—
318C8×C43—41no—
319C8×C43—41no—
320C8×C43—41no—
321#24867C4311yesmaximal, characteristic, direct product factor, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43#48414yescomplemented
336C22×C43C2×#12311yescharacteristic
337C22×C43D4211yescharacteristic
338C22×C43#54611yescharacteristic
339C22×C43C22×Q1611yescharacteristic
340C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C43#57711yescharacteristic
342C22×C43#57811yescharacteristic
343C4×C43—22no—
344C4×C43—22no—
345C4×C43—41no—
346C4×C43—41no—
347C4×C43—42no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—81no—
351C4×C43—81no—
352C4×C43—81no—
353C4×C43—81no—
354C4×C43—81no—
355C4×C43#52511yescharacteristic
356C4×C43#53811yescharacteristic
357C4×C43#54611yescharacteristic
358C4×C43#55111yescharacteristic
359C2×#484C2×C4311yescharacteristic, complemented
360C22×#103C2×C4311yescharacteristic, complemented
361#2409C2×C4311yescharacteristic
362D4×C4⋊C4C2×C4311yescharacteristic
363#2095C2×C4311yescharacteristic, complemented
364#2072C2×C4311yescharacteristic, complemented
365#2036C2×C4311yescharacteristic, complemented
366#2036C2×C4311yescharacteristic, complemented
367#1928C2×C4311yescharacteristic, complemented
368#1928C2×C4311yescharacteristic, complemented
369#1872C2×C4311yescharacteristic, complemented
370#1869C2×C4311yescharacteristic
371#1852C2×C4311yescharacteristic, complemented
372#1808C2×C4311yescharacteristic, complemented
373#1787C2×C4311yescharacteristic, complemented
374C2×C43—24no—
375C2×C43—42no—
376C2×C43#241811yescharacteristic
377C2×C43C2×#48411yescharacteristic
378C2×C43#309711yescharacteristic
379C2×C43#326511yescharacteristic
380C2×C43D4×Q1611yescharacteristic
381C2×C43#329911yescharacteristic
382C2×C43#330811yescharacteristic
383C23×Q8C22×C4311yescharacteristic
384C23×C8C22×C4311yescharacteristic
385C2×C22⋊Q8C22×C4311yescharacteristic
386C2×C22⋊Q8C22×C4311yescharacteristic
387C2×C4×D4—21no—
388C2×C4×D4C22×C4311yescharacteristic
389C22×C4⋊C4C22×C4311yescharacteristic
390C22×C4⋊C4C22×C4311yescharacteristic
391#484—24no—
392C2×#107C22×C4311yescharacteristic
393C2×#107C22×C4311yescharacteristic
394C2×#107C22×C4311yescharacteristic
395C2×#107C22×C4311yescharacteristic
396C2×#103—24no—
397C2×#103C22×C4311yescharacteristic
398C2×#103C22×C4311yescharacteristic
399C2×#103C22×C4311yescharacteristic
400C2×#103C22×C4311yescharacteristic
401C2×#103C22×C4311yescharacteristic
402C2×#103C22×C4311yescharacteristic
403C2×#103C22×C4311yescharacteristic
404C2×#103C22×C4311yescharacteristic
405C2×C22⋊C8C22×C4311yescharacteristic
406C2×C22⋊C8C22×C4311yescharacteristic
407C2×C22⋊C8C22×C4311yescharacteristic
408#395—21no—
409#393—21no—
410#391C22×C4311yescharacteristic
411#391C22×C4311yescharacteristic
412#389—21no—
413#386—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384C22×C4311yescharacteristic
418#380C22×C4311yescharacteristic
419#380C22×C4311yescharacteristic
420#380C22×C4311yescharacteristic
421C4×C4⋊C4C22×C4311yescharacteristic
422#340C22×C4311yescharacteristic
423#340C22×C4311yescharacteristic
424#340C22×C4311yescharacteristic
425#340C22×C4311yescharacteristic
426#336C22×C4311yescharacteristic
427#336C22×C4311yescharacteristic
428C43#2486711yescharacteristic, direct product factor, Sylow
429C22×Q8—21no—
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—22no—
434C22×Q8—41no—
435C22×Q8—41no—
436C22×Q8C23×C4311yescharacteristic
437C22×Q8C23×C4311yescharacteristic
438C22×D4D4×C4311yescharacteristic
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—21no—
442C23×C4C23×C4311yescharacteristic
443C23×C4C23×C4311yescharacteristic
444C22×C8—22no—
445C22×C8—22no—
446C22×C8—41no—
447C22×C8C23×C4311yescharacteristic
448C22×C8C23×C4311yescharacteristic
449C22×C8C23×C4311yescharacteristic
450C22×C8C23×C4311yescharacteristic
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—41no—
454C22⋊Q8—41no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—44no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4D4×C4311yescharacteristic
469C2×C4⋊C4C23×C4311yescharacteristic
470C2×C4⋊C4C23×C4311yescharacteristic
471C2×C4⋊C4C23×C4311yescharacteristic
472C2×C4⋊C4C23×C4311yescharacteristic
473C2×C4⋊C4C23×C4311yescharacteristic
474C2×C4⋊C4C23×C4311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4D4×C4311yescharacteristic
481C2×C22⋊C4D4×C4311yescharacteristic
482C2×C42—21no—
483C2×C42C23×C4311yescharacteristic
484#107—22no—
485#107—22no—
486#107—41no—
487#107—41no—
488#103—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#103—41no—
494#103—41no—
495#103D4×C4314yescomplemented
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—41no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507C24C2×D4×C4311yescharacteristic
508C24C2×D4×C4311yescharacteristic
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—28no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—44no—
523C2×Q8—44no—
524C2×Q8—44no—
525C2×Q8—42no—
526C2×Q8C2×D4×C4312yes—
527C2×Q8#41×C4312yes—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4Q16×C4314yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4C2×D4×C4311yescharacteristic
559C22×C4C2×D4×C4311yescharacteristic
560C22×C4C2×D4×C4311yescharacteristic
561C22×C4C2×D4×C4311yescharacteristic
562C22×C4#41×C4312yes—
563C22×C4#41×C4312yes—
564C22×C4C24×C4311yescharacteristic
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—44no—
577C2×C8C2×D4×C4312yes—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—81no—
596C4⋊C4C2×D4×C4312yes—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C42—21no—
605C42—21no—
606C42—42no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23#123×C4312yes—
618C23C2×Q16×C4312yes—
619C23C2×Q16×C4312yes—
620C23AGL(1,ℤ/8)×C4312yes—
621C23C22×D4×C4311yescharacteristic
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—48no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—28no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—48no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
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—84no—
676C2×C4—84no—
677C2×C4#123×C4312yes—
678C2×C4C2×Q16×C4312yes—
679C2×C4C22×D4×C4311yescharacteristic
680C2×C4C2×#41×C4311yescharacteristic
681C2×C4C2×#41×C4311yescharacteristic
682C2×C4C2×#41×C4311yescharacteristic
683C2×C4H(5,𝔽2)×C4311yescharacteristic
684C2×C4H(5,𝔽2)×C4311yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22C43×#48414yescomplemented
703C22C2×#123×C4311yescharacteristic
704C22D42×C4311yescharacteristic
705C22C43×#54611yescharacteristic
706C22C22×Q16×C4311yescharacteristic
707C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
708C22C43×#57711yescharacteristic
709C22C43×#57811yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4C43×#52511yescharacteristic
723C4C43×#53811yescharacteristic
724C4C43×#54611yescharacteristic
725C4C43×#55111yescharacteristic
726C2—24no—
727C2—42no—
728C2C43×#241811yescharacteristic
729C2C2×C43×#48411yescharacteristic
730C2C43×#309711yescharacteristic
731C2C43×#326511yescharacteristic
732C2D4×Q16×C4311yescharacteristic
733C2C43×#329911yescharacteristic
734C2C43×#330811yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC22×D4×C43D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#484C2semidirect
2. C22×#103×C43C2semidirect
5. C43×#2095C2semidirect
6. C43×#2072C2semidirect
7. C43×#2036C2semidirect
8. C43×#2036C2semidirect
9. C43×#1928C2semidirect
10. C43×#1928C2semidirect
11. C43×#1872C2semidirect
13. C43×#1852C2semidirect
14. C43×#1808C2semidirect
15. C43×#1787C2semidirect
127. #103×C43D4semidirect
321. #24867C43direct (N × H)
335. C22×C43#484semidirect
359. C2×#484C2×C43semidirect
360. C22×#103C2×C43semidirect
363. #2095C2×C43semidirect
364. #2072C2×C43semidirect
365. #2036C2×C43semidirect
366. #2036C2×C43semidirect
367. #1928C2×C43semidirect
368. #1928C2×C43semidirect
369. #1872C2×C43semidirect
371. #1852C2×C43semidirect
372. #1808C2×C43semidirect
373. #1787C2×C43semidirect
428. C43#24867direct (N × H)
495. #103D4×C43semidirect
702. C22C43×#484semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4842
C22×#103×C432
C43×#24092
D4×C4⋊C4×C432
C43×#20952
C43×#20722
C43×#20362
C43×#19282
C43×#18722
C43×#18692
C43×#18522
C43×#18082
C43×#17872
#2486743