Finite Group Databasebeta

← C43×#28916 #24948933

Subgroups — C43×#28916 #24948933

Order 11008.

996 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#490C211yesmaximal, characteristic, complemented
2C2×C43×#469C211yesmaximal, characteristic, complemented
3C43×#2490C211yesmaximal, characteristic, complemented
4C43×#2428C211yesmaximal, characteristic, complemented
5C43×#2059C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#2011C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1970C211yesmaximal, characteristic, complemented
10C43×#1936C211yesmaximal, characteristic, complemented
11C43×#1926C211yesmaximal, characteristic, complemented
12C43×#1895C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C4×#102×C43C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C2×#127×C43C2211yescharacteristic
20C2×#125×C43C2211yescharacteristic
21C2×#121×C43—21no—
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C43×#490—24no—
27C43×#469—24no—
28C2×#107×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#97×C43C2211yescharacteristic
40C2×C4×C8×C43C2211yescharacteristic
41C43×#397—21no—
42C43×#394—21no—
43C43×#394—21no—
44C43×#392—21no—
45C43×#390—21no—
46C43×#390C2211yescharacteristic
47C43×#390C2211yescharacteristic
48C43×#390C2211yescharacteristic
49C43×#389C2211yescharacteristic
50C43×#388—21no—
51C43×#386—21no—
52C43×#380C2211yescharacteristic
53C4×C4⋊C4×C43C2211yescharacteristic
54C4×C22⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43C2311yescharacteristic
67C22×D4×C43C2311yescharacteristic
68C22×D4×C43C2311yescharacteristic
69C23×C4×C43—21no—
70C23×C4×C43C2311yescharacteristic
71C2×D8×C43—22no—
72C2×D8×C43—22no—
73C2×D8×C43—22no—
74C2×D8×C43—41no—
75C2×D8×C43—41no—
76C2×D8×C43—41no—
77C2×M16×C43—22no—
78C2×M16×C43—22no—
79C2×M16×C43—41no—
80C22×C8×C43C2311yescharacteristic
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84#127×C43—22no—
85#127×C43—41no—
86#125×C43—22no—
87#125×C43—41no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43—22no—
91#121×C43—44no—
92#121×C43—41no—
93#121×C43—41no—
94#121×C43—41no—
95C4×D4×C43—22no—
96C4×D4×C43—41no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
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×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#107×C43—41no—
122#106×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130#102×C43D414yescomplemented
131C22⋊C8×C43—22no—
132#97×C43—22no—
133C4×C8×C43—41no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43D411yescharacteristic
138#95×C43D411yescharacteristic
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43C2×D411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×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—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
172C2×D4×C43—81no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43C2×D412yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—42no—
188C22×C4×C43—42no—
189C22×C4×C43—81no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196D8×C43—44no—
197D8×C43—44no—
198M16×C43—44no—
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×C43C2×D412yes—
209C2×C8×C43#4112yes—
210C2×C8×C43#4112yes—
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—42no—
220C4⋊C4×C43—42no—
221C4⋊C4×C43—42no—
222C4⋊C4×C43C2×D412yes—
223C4⋊C4×C43#4112yes—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—41no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—81no—
233C22⋊C4×C43—81no—
234C22⋊C4×C43—81no—
235C22⋊C4×C43—81no—
236C22⋊C4×C43—81no—
237C42×C43—21no—
238C42×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—81no—
242C23×C43—21no—
243C23×C43—22no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C22×D411yescharacteristic
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—84no—
284D4×C43—84no—
285D4×C43—84no—
286D4×C43—84no—
287D4×C43—84no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—21no—
296C2×C4×C43—22no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—84no—
322C2×C4×C43AGL(1,ℤ/8)12yes—
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C8×C43—22no—
330C8×C43—22no—
331C8×C43—22no—
332C8×C43—41no—
333#28916C4311yesmaximal, characteristic, direct product factor, Sylow
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—42no—
338C22×C43—41no—
339C22×C43—42no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—42no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43#53211yescharacteristic
363C22×C43D4211yescharacteristic
364C22×C43#54611yescharacteristic
365C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C43#57511yescharacteristic
367C22×C43#57611yescharacteristic
368C22×C43#57611yescharacteristic
369C4×C43—22no—
370C4×C43—41no—
371C4×C43—42no—
372C4×C43—41no—
373C4×C43—41no—
374C4×C43—42no—
375C4×C43—41no—
376C4×C43—81no—
377C4×C43—81no—
378C4×C43—81no—
379C4×C43#53211yescharacteristic
380C4×C43#53811yescharacteristic
381C4×C43#54611yescharacteristic
382C4×C43#55511yescharacteristic
383C2×#490C2×C4311yescharacteristic, complemented
384C2×#469C2×C4311yescharacteristic, complemented
385#2490C2×C4311yescharacteristic, complemented
386#2428C2×C4311yescharacteristic, complemented
387#2059C2×C4311yescharacteristic, complemented
388#2033C2×C4311yescharacteristic, complemented
389#2011C2×C4311yescharacteristic, complemented
390#1999C2×C4311yescharacteristic, complemented
391#1970C2×C4311yescharacteristic, complemented
392#1936C2×C4311yescharacteristic, complemented
393#1926C2×C4311yescharacteristic, complemented
394#1895C2×C4311yescharacteristic, complemented
395#1879C2×C4311yescharacteristic, complemented
396C4×#102C2×C4311yescharacteristic, complemented
397#1753C2×C4311yescharacteristic, complemented
398C2×C43—81no—
399C2×C43—82no—
400C2×C43—161no—
401C2×C43—161no—
402C2×C43#255511yescharacteristic
403C2×C43#317111yescharacteristic
404C2×C43#317611yescharacteristic
405C2×C43#327311yescharacteristic
406C2×C43#327411yescharacteristic
407C2×C43#330911yescharacteristic
408C2×C43#331811yescharacteristic
409C22×D8C22×C4311yescharacteristic
410C22×D8C22×C4311yescharacteristic
411C22×M16C22×C4311yescharacteristic
412C2×#127C22×C4311yescharacteristic
413C2×#125C22×C4311yescharacteristic
414C2×#121—21no—
415C2×#121C22×C4311yescharacteristic
416C2×#121C22×C4311yescharacteristic
417C2×#121C22×C4311yescharacteristic
418C2×C4×D4C22×C4311yescharacteristic
419#490—24no—
420#469—24no—
421C2×#107C22×C4311yescharacteristic
422C2×#106C22×C4311yescharacteristic
423C2×#102C22×C4311yescharacteristic
424C2×#102C22×C4311yescharacteristic
425C2×#102C22×C4311yescharacteristic
426C2×#102C22×C4311yescharacteristic
427C2×#102C22×C4311yescharacteristic
428C2×#102C22×C4311yescharacteristic
429C2×#102C22×C4311yescharacteristic
430C2×#102C22×C4311yescharacteristic
431C2×C22⋊C8C22×C4311yescharacteristic
432C2×#97C22×C4311yescharacteristic
433C2×C4×C8C22×C4311yescharacteristic
434#397—21no—
435#394—21no—
436#394—21no—
437#392—21no—
438#390—21no—
439#390C22×C4311yescharacteristic
440#390C22×C4311yescharacteristic
441#390C22×C4311yescharacteristic
442#389C22×C4311yescharacteristic
443#388—21no—
444#386—21no—
445#380C22×C4311yescharacteristic
446C4×C4⋊C4C22×C4311yescharacteristic
447C4×C22⋊C4C22×C4311yescharacteristic
448#340C22×C4311yescharacteristic
449#340C22×C4311yescharacteristic
450#340C22×C4311yescharacteristic
451#340C22×C4311yescharacteristic
452#336C22×C4311yescharacteristic
453#336C22×C4311yescharacteristic
454C43#2891611yescharacteristic, direct product factor, Sylow
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C23×C4311yescharacteristic
461C22×D4C23×C4311yescharacteristic
462C22×D4C23×C4311yescharacteristic
463C23×C4—21no—
464C23×C4C23×C4311yescharacteristic
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—22no—
468C2×D8—41no—
469C2×D8—41no—
470C2×D8—41no—
471C2×M16—22no—
472C2×M16—22no—
473C2×M16—41no—
474C22×C8C23×C4311yescharacteristic
475C22×C8C23×C4311yescharacteristic
476C22×C8C23×C4311yescharacteristic
477C22×C8C23×C4311yescharacteristic
478#127—22no—
479#127—41no—
480#125—22no—
481#125—41no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—44no—
486#121—41no—
487#121—41no—
488#121—41no—
489C4×D4—22no—
490C4×D4—41no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4C23×C4311yescharacteristic
495C2×C4⋊C4C23×C4311yescharacteristic
496C2×C4⋊C4C23×C4311yescharacteristic
497C2×C4⋊C4C23×C4311yescharacteristic
498C2×C4⋊C4C23×C4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C4311yescharacteristic
511C2×C22⋊C4D4×C4311yescharacteristic
512C2×C42—21no—
513C2×C42C23×C4311yescharacteristic
514C2×C42C23×C4311yescharacteristic
515#107—41no—
516#106—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102D4×C4314yescomplemented
525C22⋊C8—22no—
526#97—22no—
527C4×C8—41no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95D4×C4311yescharacteristic
532#95D4×C4311yescharacteristic
533C24—21no—
534C24—21no—
535C24—21no—
536C24C2×D4×C4311yescharacteristic
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4C2×D4×C4312yes—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4C2×D4×C4311yescharacteristic
585C22×C4C2×D4×C4311yescharacteristic
586C22×C4C2×D4×C4311yescharacteristic
587C22×C4C2×D4×C4311yescharacteristic
588C22×C4C2×D4×C4311yescharacteristic
589C22×C4C24×C4311yescharacteristic
590D8—44no—
591D8—44no—
592M16—44no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8C2×D4×C4312yes—
603C2×C8#41×C4312yes—
604C2×C8#41×C4312yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4C2×D4×C4312yes—
617C4⋊C4#41×C4312yes—
618C22⋊C4—22no—
619C22⋊C4—41no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—81no—
636C23—21no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23C22×D4×C4311yescharacteristic
665D4—22no—
666D4—22no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—84no—
716C2×C4AGL(1,ℤ/8)×C4312yes—
717C2×C4C22×D4×C4311yescharacteristic
718C2×C4C2×#41×C4311yescharacteristic
719C2×C4C2×#41×C4311yescharacteristic
720C2×C4C2×#41×C4311yescharacteristic
721C2×C4H(5,𝔽2)×C4311yescharacteristic
722C2×C4H(5,𝔽2)×C4311yescharacteristic
723C8—22no—
724C8—22no—
725C8—22no—
726C8—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C43×#53211yescharacteristic
756C22D42×C4311yescharacteristic
757C22C43×#54611yescharacteristic
758C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
759C22C43×#57511yescharacteristic
760C22C43×#57611yescharacteristic
761C22C43×#57611yescharacteristic
762C4—22no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4C43×#53211yescharacteristic
773C4C43×#53811yescharacteristic
774C4C43×#54611yescharacteristic
775C4C43×#55511yescharacteristic
776C2—81no—
777C2—82no—
778C2—161no—
779C2—161no—
780C2C43×#255511yescharacteristic
781C2C43×#317111yescharacteristic
782C2C43×#317611yescharacteristic
783C2C43×#327311yescharacteristic
784C2C43×#327411yescharacteristic
785C2C43×#330911yescharacteristic
786C2C43×#331811yescharacteristic
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×#490C2semidirect
2. C2×C43×#469C2semidirect
3. C43×#2490C2semidirect
4. C43×#2428C2semidirect
5. C43×#2059C2semidirect
6. C43×#2033C2semidirect
7. C43×#2011C2semidirect
8. C43×#1999C2semidirect
9. C43×#1970C2semidirect
10. C43×#1936C2semidirect
11. C43×#1926C2semidirect
12. C43×#1895C2semidirect
13. C43×#1879C2semidirect
14. C4×#102×C43C2semidirect
15. C43×#1753C2semidirect
130. #102×C43D4semidirect
333. #28916C43direct (N × H)
383. C2×#490C2×C43semidirect
384. C2×#469C2×C43semidirect
385. #2490C2×C43semidirect
386. #2428C2×C43semidirect
387. #2059C2×C43semidirect
388. #2033C2×C43semidirect
389. #2011C2×C43semidirect
390. #1999C2×C43semidirect
391. #1970C2×C43semidirect
392. #1936C2×C43semidirect
393. #1926C2×C43semidirect
394. #1895C2×C43semidirect
395. #1879C2×C43semidirect
396. C4×#102C2×C43semidirect
397. #1753C2×C43semidirect
454. C43#28916direct (N × H)
524. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4902
C2×C43×#4692
C43×#24902
C43×#24282
C43×#20592
C43×#20332
C43×#20112
C43×#19992
C43×#19702
C43×#19362
C43×#19262
C43×#18952
C43×#18792
C4×#102×C432
C43×#17532
#2891643