Finite Group Databasebeta

← C43×#25708 #24945725

Subgroups — C43×#25708 #24945725

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#552C211yesmaximal, characteristic
2C2×C43×#499C211yesmaximal, characteristic, complemented
3C2×C43×#479C211yesmaximal, characteristic, complemented
4C43×#2562C211yesmaximal, characteristic
5C43×#2036C211yesmaximal, characteristic, complemented
6C43×#2036C211yesmaximal, characteristic, complemented
7C43×#2035C211yesmaximal, characteristic, complemented
8C43×#2035C211yesmaximal, characteristic, complemented
9C43×#1989C211yesmaximal, characteristic, complemented
10C43×#1954C211yesmaximal, characteristic
11C43×#1854C211yesmaximal, characteristic, complemented
12C43×#1854C211yesmaximal, characteristic, complemented
13C43×#1853C211yesmaximal, characteristic, complemented
14C43×#1852C211yesmaximal, characteristic, complemented
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C43×#552—24no—
17C43×#552—24no—
18C2×#126×C43—21no—
19C2×#125×C43—21no—
20C2×#125×C43C2211yescharacteristic
21C2×#125×C43C2211yescharacteristic
22C2×#123×C43—21no—
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×C22⋊Q8×C43C2211yescharacteristic
25C2×C4×Q8×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic
27C2×#117×C43—21no—
28C2×#117×C43C2211yescharacteristic
29C22×C4⋊C4×C43C2211yescharacteristic
30C43×#499—24no—
31C43×#479—24no—
32C2×#107×C43C2211yescharacteristic
33C2×#107×C43C2211yescharacteristic
34C2×#107×C43C2211yescharacteristic
35C2×#106×C43C2211yescharacteristic
36C2×#106×C43C2211yescharacteristic
37C2×#106×C43C2211yescharacteristic
38C2×C4⋊C8×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#103×C43C2211yescharacteristic
41C2×#103×C43C2211yescharacteristic
42C2×#103×C43C2211yescharacteristic
43C2×C22⋊C8×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C4×C8×C43C2211yescharacteristic
48C43×#400—21no—
49C43×#394—21no—
50C43×#388—21no—
51C43×#388—21no—
52C43×#380C2211yescharacteristic
53C43×#380C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Q8×C43C2311yescharacteristic
64C22×D4×C43D411yescharacteristic
65C23×C4×C43—21no—
66C23×C4×C43C2311yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43C2311yescharacteristic
69C22×C8×C43C2311yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72#126×C43—28no—
73#125×C43—28no—
74#125×C43—22no—
75#125×C43—22no—
76#125×C43—22no—
77#125×C43D414yes—
78#123×C43—28no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—22no—
81C22⋊Q8×C43—22no—
82C22⋊Q8×C43—22no—
83C4×Q8×C43—22no—
84C4×Q8×C43D414yes—
85C4×D4×C43—22no—
86C4×D4×C43—22no—
87#117×C43—28no—
88#117×C43—22no—
89#117×C43—22no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
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×C4⋊C4×C43C2311yescharacteristic
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×C43D411yescharacteristic
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C42×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#107×C43—22no—
123#107×C43—22no—
124#106×C43—22no—
125#106×C43—22no—
126#106×C43—22no—
127C4⋊C8×C43—22no—
128#103×C43—22no—
129#103×C43—22no—
130#103×C43—22no—
131#103×C43—22no—
132C22⋊C8×C43—22no—
133C22⋊C8×C43—22no—
134C22⋊C8×C43—22no—
135C22⋊C8×C43—22no—
136C4×C8×C43—22no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43—21no—
142C24×C43C2×D411yescharacteristic
143C24×C43C2×D411yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C2×D412yes—
150C2×D4×C43—22no—
151C2×D4×C43—22no—
152C2×D4×C43—41no—
153C22×C4×C43—24no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
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—42no—
175C22×C4×C43—42no—
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2411yescharacteristic
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43#4112yes—
192C2×C8×C43#4112yes—
193C4⋊C4×C43—24no—
194C4⋊C4×C43—24no—
195C4⋊C4×C43—24no—
196C4⋊C4×C43—24no—
197C4⋊C4×C43—24no—
198C4⋊C4×C43—24no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
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—42no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43C2×D412yes—
214C4⋊C4×C43C2×D412yes—
215C4⋊C4×C43C2×D412yes—
216C22⋊C4×C43—24no—
217C22⋊C4×C43—24no—
218C22⋊C4×C43—24no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—81no—
224C22⋊C4×C43—81no—
225C42×C43—24no—
226C42×C43—24no—
227C42×C43—81no—
228C42×C43C2×D412yes—
229C42×C43C2×D412yes—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43#13512yes—
244C23×C43C22×D411yescharacteristic
245Q8×C43—22no—
246Q8×C43—22no—
247Q8×C43—41no—
248Q8×C43—41no—
249D4×C43—44no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—21no—
259C2×C4×C43—22no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—48no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
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#12012yes—
294C2×C4×C43#12012yes—
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C432−1+411yescharacteristic
300C2×C4×C432−1+411yescharacteristic
301C8×C43—22no—
302C8×C43—22no—
303C8×C43—41no—
304C8×C43—41no—
305#25708C4311yesmaximal, characteristic, direct product factor, Sylow
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43—41no—
320C22×C43C2×#12011yescharacteristic
321C22×C43#54711yescharacteristic
322C22×C43#54711yescharacteristic
323C22×C43C2×#13511yescharacteristic
324C22×C43#57511yescharacteristic
325C22×C43#57711yescharacteristic
326C22×C43#57811yescharacteristic
327C4×C43—22no—
328C4×C43—22no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43—42no—
332C4×C43—42no—
333C4×C43—42no—
334C4×C43—42no—
335C4×C43—81no—
336C4×C43—81no—
337C4×C43—81no—
338C4×C43—81no—
339C4×C43#53211yescharacteristic
340C4×C43#53611yescharacteristic
341C4×C43#54811yescharacteristic
342C4×C43#54811yescharacteristic
343C2×#552C2×C4311yescharacteristic
344C2×#499C2×C4311yescharacteristic, complemented
345C2×#479C2×C4311yescharacteristic, complemented
346#2562C2×C4311yescharacteristic
347#2036C2×C4311yescharacteristic, complemented
348#2036C2×C4311yescharacteristic, complemented
349#2035C2×C4311yescharacteristic, complemented
350#2035C2×C4311yescharacteristic, complemented
351#1989C2×C4311yescharacteristic, complemented
352#1954C2×C4311yescharacteristic
353#1854C2×C4311yescharacteristic, complemented
354#1854C2×C4311yescharacteristic, complemented
355#1853C2×C4311yescharacteristic, complemented
356#1852C2×C4311yescharacteristic, complemented
357C4×#103C2×C4311yescharacteristic, complemented
358C2×C43—42no—
359C2×C43—81no—
360C2×C43#243211yescharacteristic
361C2×C43#300211yescharacteristic
362C2×C43#301311yescharacteristic
363C2×C43#333611yescharacteristic
364C2×C43#333711yescharacteristic
365C2×C43#335111yescharacteristic
366C2×C43#335211yescharacteristic
367#552—24no—
368#552—24no—
369C2×#126—21no—
370C2×#125—21no—
371C2×#125C22×C4311yescharacteristic
372C2×#125C22×C4311yescharacteristic
373C2×#123—21no—
374C2×C22⋊Q8C22×C4311yescharacteristic
375C2×C22⋊Q8C22×C4311yescharacteristic
376C2×C4×Q8C22×C4311yescharacteristic
377C2×C4×D4C22×C4311yescharacteristic
378C2×#117—21no—
379C2×#117C22×C4311yescharacteristic
380C22×C4⋊C4C22×C4311yescharacteristic
381#499—24no—
382#479—24no—
383C2×#107C22×C4311yescharacteristic
384C2×#107C22×C4311yescharacteristic
385C2×#107C22×C4311yescharacteristic
386C2×#106C22×C4311yescharacteristic
387C2×#106C22×C4311yescharacteristic
388C2×#106C22×C4311yescharacteristic
389C2×C4⋊C8C22×C4311yescharacteristic
390C2×#103C22×C4311yescharacteristic
391C2×#103C22×C4311yescharacteristic
392C2×#103C22×C4311yescharacteristic
393C2×#103C22×C4311yescharacteristic
394C2×C22⋊C8C22×C4311yescharacteristic
395C2×C22⋊C8C22×C4311yescharacteristic
396C2×C22⋊C8C22×C4311yescharacteristic
397C2×C22⋊C8C22×C4311yescharacteristic
398C2×C4×C8C22×C4311yescharacteristic
399#400—21no—
400#394—21no—
401#388—21no—
402#388—21no—
403#380C22×C4311yescharacteristic
404#380C22×C4311yescharacteristic
405#380C22×C4311yescharacteristic
406#380C22×C4311yescharacteristic
407C4×C4⋊C4C22×C4311yescharacteristic
408#340C22×C4311yescharacteristic
409#340C22×C4311yescharacteristic
410#340C22×C4311yescharacteristic
411#340C22×C4311yescharacteristic
412#340C22×C4311yescharacteristic
413#340C22×C4311yescharacteristic
414C43#2570811yescharacteristic, direct product factor, Sylow
415C22×Q8C23×C4311yescharacteristic
416C22×D4D4×C4311yescharacteristic
417C23×C4—21no—
418C23×C4C23×C4311yescharacteristic
419C23×C4C23×C4311yescharacteristic
420C22×C8C23×C4311yescharacteristic
421C22×C8C23×C4311yescharacteristic
422C22×C8C23×C4311yescharacteristic
423C22×C8C23×C4311yescharacteristic
424#126—28no—
425#125—28no—
426#125—22no—
427#125—22no—
428#125—22no—
429#125D4×C4314yes—
430#123—28no—
431C22⋊Q8—22no—
432C22⋊Q8—22no—
433C22⋊Q8—22no—
434C22⋊Q8—22no—
435C4×Q8—22no—
436C4×Q8D4×C4314yes—
437C4×D4—22no—
438C4×D4—22no—
439#117—28no—
440#117—22no—
441#117—22no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4D4×C4311yescharacteristic
453C2×C4⋊C4C23×C4311yescharacteristic
454C2×C4⋊C4C23×C4311yescharacteristic
455C2×C4⋊C4C23×C4311yescharacteristic
456C2×C4⋊C4C23×C4311yescharacteristic
457C2×C4⋊C4C23×C4311yescharacteristic
458C2×C4⋊C4C23×C4311yescharacteristic
459C2×C4⋊C4C23×C4311yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4D4×C4311yescharacteristic
468C2×C22⋊C4D4×C4311yescharacteristic
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42C23×C4311yescharacteristic
473#107—22no—
474#107—22no—
475#107—22no—
476#106—22no—
477#106—22no—
478#106—22no—
479C4⋊C8—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—22no—
484C22⋊C8—22no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C4×C8—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494C24C2×D4×C4311yescharacteristic
495C24C2×D4×C4311yescharacteristic
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8C2×D4×C4312yes—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—41no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4C2×D4×C4311yescharacteristic
529C22×C4C2×D4×C4311yescharacteristic
530C22×C4C2×D4×C4311yescharacteristic
531C22×C4C2×D4×C4311yescharacteristic
532C22×C4C24×C4311yescharacteristic
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8#41×C4312yes—
544C2×C8#41×C4312yes—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4C2×D4×C4312yes—
566C4⋊C4C2×D4×C4312yes—
567C4⋊C4C2×D4×C4312yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C42—24no—
578C42—24no—
579C42—81no—
580C42C2×D4×C4312yes—
581C42C2×D4×C4312yes—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23#135×C4312yes—
596C23C22×D4×C4311yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—44no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—48no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4#120×C4312yes—
646C2×C4#120×C4312yes—
647C2×C4C22×D4×C4311yescharacteristic
648C2×C4C22×D4×C4311yescharacteristic
649C2×C4C2×#41×C4311yescharacteristic
650C2×C4C2×#41×C4311yescharacteristic
651C2×C42−1+4×C4311yescharacteristic
652C2×C42−1+4×C4311yescharacteristic
653C8—22no—
654C8—22no—
655C8—41no—
656C8—41no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22C2×#120×C4311yescharacteristic
672C22C43×#54711yescharacteristic
673C22C43×#54711yescharacteristic
674C22C2×#135×C4311yescharacteristic
675C22C43×#57511yescharacteristic
676C22C43×#57711yescharacteristic
677C22C43×#57811yescharacteristic
678C4—22no—
679C4—22no—
680C4—41no—
681C4—41no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4C43×#53211yescharacteristic
691C4C43×#53611yescharacteristic
692C4C43×#54811yescharacteristic
693C4C43×#54811yescharacteristic
694C2—42no—
695C2—81no—
696C2C43×#243211yescharacteristic
697C2C43×#300211yescharacteristic
698C2C43×#301311yescharacteristic
699C2C43×#333611yescharacteristic
700C2C43×#333711yescharacteristic
701C2C43×#335111yescharacteristic
702C2C43×#335211yescharacteristic
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
2. C2×C43×#499C2semidirect
3. C2×C43×#479C2semidirect
5. C43×#2036C2semidirect
6. C43×#2036C2semidirect
7. C43×#2035C2semidirect
8. C43×#2035C2semidirect
9. C43×#1989C2semidirect
11. C43×#1854C2semidirect
12. C43×#1854C2semidirect
13. C43×#1853C2semidirect
14. C43×#1852C2semidirect
15. C4×#103×C43C2semidirect
305. #25708C43direct (N × H)
344. C2×#499C2×C43semidirect
345. C2×#479C2×C43semidirect
347. #2036C2×C43semidirect
348. #2036C2×C43semidirect
349. #2035C2×C43semidirect
350. #2035C2×C43semidirect
351. #1989C2×C43semidirect
353. #1854C2×C43semidirect
354. #1854C2×C43semidirect
355. #1853C2×C43semidirect
356. #1852C2×C43semidirect
357. C4×#103C2×C43semidirect
414. C43#25708direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5522
C2×C43×#4992
C2×C43×#4792
C43×#25622
C43×#20362
C43×#20352
C43×#19892
C43×#19542
C43×#18542
C43×#18532
C43×#18522
C4×#103×C432
#2570843