Finite Group Databasebeta

← C43×#25236 #24945253

Subgroups — C43×#25236 #24945253

Order 11008.

918 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#483C211yesmaximal, characteristic, complemented
2C2×C8×D4×C43C211yesmaximal, characteristic
3C43×#2486C211yesmaximal, characteristic
4C43×#2417C211yesmaximal, characteristic
5C43×#2088C211yesmaximal, characteristic, complemented
6C43×#2077C211yesmaximal, characteristic, complemented
7C43×#2066C211yesmaximal, characteristic, complemented
8C43×#2035C211yesmaximal, characteristic, complemented
9C43×#1941C211yesmaximal, characteristic, complemented
10C43×#1933C211yesmaximal, characteristic, complemented
11C43×#1892C211yesmaximal, characteristic, complemented
12C43×#1892C211yesmaximal, characteristic, complemented
13C43×#1853C211yesmaximal, characteristic, complemented
14C43×#1807C211yesmaximal, characteristic, complemented
15C2×C43×#340C211yesmaximal, characteristic, complemented
16C23×C8×C43C2211yescharacteristic
17C23×C8×C43C2211yescharacteristic
18C2×#123×C43—21no—
19C2×C22⋊Q8×C43C2211yescharacteristic
20C2×C22⋊Q8×C43C2211yescharacteristic
21C2×C4×D4×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C43×#483—24no—
25C8×D4×C43—24no—
26C2×#106×C43C2211yescharacteristic
27C2×#106×C43C2211yescharacteristic
28C2×#106×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#103×C43C2211yescharacteristic
34C2×#103×C43C2211yescharacteristic
35C2×C22⋊C8×C43C2211yescharacteristic
36C2×C22⋊C8×C43C2211yescharacteristic
37C2×C4×C8×C43C2211yescharacteristic
38C43×#398—21no—
39C43×#398—21no—
40C43×#397—21no—
41C43×#396—21no—
42C43×#391C2211yescharacteristic
43C43×#389C2211yescharacteristic
44C43×#389C2211yescharacteristic
45C43×#389C2211yescharacteristic
46C43×#386—21no—
47C43×#381—21no—
48C43×#380—21no—
49C43×#380C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Q8×C43C2311yescharacteristic
62C22×D4×C43D411yescharacteristic
63C23×C4×C43—21no—
64C23×C4×C43—21no—
65C23×C4×C43C2311yescharacteristic
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43—22no—
68C22×C8×C43—22no—
69C22×C8×C43—22no—
70C22×C8×C43—22no—
71C22×C8×C43—41no—
72C22×C8×C43—41no—
73C22×C8×C43C2311yescharacteristic
74C22×C8×C43C2311yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C22×C8×C43C2311yescharacteristic
77#123×C43—44no—
78C22⋊Q8×C43—22no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—22no—
81C22⋊Q8×C43—41no—
82C4×D4×C43—22no—
83C4×D4×C43—22no—
84C2×C4⋊C4×C43—22no—
85C2×C4⋊C4×C43—22no—
86C2×C4⋊C4×C43—22no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—41no—
95C2×C4⋊C4×C43D411yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43D411yescharacteristic
110C2×C22⋊C4×C43D411yescharacteristic
111C2×C42×C43C2311yescharacteristic
112#106×C43—22no—
113#106×C43—22no—
114#106×C43—22no—
115#106×C43—41no—
116C4⋊C8×C43—22no—
117#103×C43—22no—
118#103×C43—22no—
119#103×C43—22no—
120#103×C43—41no—
121C22⋊C8×C43—22no—
122C22⋊C8×C43D414yes—
123C4×C8×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133C24×C43C2×D411yescharacteristic
134C24×C43C2×D411yescharacteristic
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×D4×C43—22no—
142C2×D4×C43—22no—
143C2×D4×C43SD1614yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
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—42no—
163C22×C4×C43—42no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43—81no—
168C22×C4×C43C2×D412yes—
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43#4112yes—
174C22×C4×C43C2411yescharacteristic
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—44no—
185C2×C8×C43—44no—
186C2×C8×C43C2×D412yes—
187C2×C8×C43C2×D412yes—
188C2×C8×C43#4112yes—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—42no—
204C4⋊C4×C43—42no—
205C4⋊C4×C43—42no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43—42no—
209C4⋊C4×C43—81no—
210C4⋊C4×C43#4112yes—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—81no—
219C42×C43—21no—
220C42×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43#12112yes—
232C23×C43C2×SD1612yes—
233C23×C43C2×SD1612yes—
234C23×C43#13512yes—
235C23×C43C22×D411yescharacteristic
236Q8×C43—41no—
237Q8×C43—41no—
238Q8×C43—41no—
239Q8×C43—41no—
240D4×C43—28no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
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—84no—
284C2×C4×C43—84no—
285C2×C4×C43#12112yes—
286C2×C4×C43C2×SD1612yes—
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C432−1+411yescharacteristic
293C8×C43—22no—
294C8×C43—22no—
295C8×C43—22no—
296C8×C43—41no—
297#25236C4311yesmaximal, characteristic, direct product factor, Sylow
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—22no—
301C22×C43—22no—
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43#46514yes—
312C22×C43C2×#12111yescharacteristic
313C22×C43#54611yescharacteristic
314C22×C43#54711yescharacteristic
315C22×C43C22×SD1611yescharacteristic
316C22×C43C2×#13511yescharacteristic
317C22×C43#57711yescharacteristic
318C22×C43#57811yescharacteristic
319C4×C43—22no—
320C4×C43—22no—
321C4×C43—41no—
322C4×C43—42no—
323C4×C43—41no—
324C4×C43—81no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43—81no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43—81no—
331C4×C43#52911yescharacteristic
332C4×C43#53911yescharacteristic
333C4×C43#54611yescharacteristic
334C4×C43#54711yescharacteristic
335C2×#483C2×C4311yescharacteristic, complemented
336C2×C8×D4C2×C4311yescharacteristic
337#2486C2×C4311yescharacteristic
338#2417C2×C4311yescharacteristic
339#2088C2×C4311yescharacteristic, complemented
340#2077C2×C4311yescharacteristic, complemented
341#2066C2×C4311yescharacteristic, complemented
342#2035C2×C4311yescharacteristic, complemented
343#1941C2×C4311yescharacteristic, complemented
344#1933C2×C4311yescharacteristic, complemented
345#1892C2×C4311yescharacteristic, complemented
346#1892C2×C4311yescharacteristic, complemented
347#1853C2×C4311yescharacteristic, complemented
348#1807C2×C4311yescharacteristic, complemented
349C2×#340C2×C4311yescharacteristic, complemented
350C2×C43—24no—
351C2×C43—42no—
352C2×C43#242511yescharacteristic
353C2×C43C2×#46511yescharacteristic
354C2×C43#306311yescharacteristic
355C2×C43#329611yescharacteristic
356C2×C43#329811yescharacteristic
357C2×C43#333511yescharacteristic
358C2×C43#333611yescharacteristic
359C23×C8C22×C4311yescharacteristic
360C23×C8C22×C4311yescharacteristic
361C2×#123—21no—
362C2×C22⋊Q8C22×C4311yescharacteristic
363C2×C22⋊Q8C22×C4311yescharacteristic
364C2×C4×D4C22×C4311yescharacteristic
365C22×C4⋊C4C22×C4311yescharacteristic
366C22×C4⋊C4C22×C4311yescharacteristic
367#483—24no—
368C8×D4—24no—
369C2×#106C22×C4311yescharacteristic
370C2×#106C22×C4311yescharacteristic
371C2×#106C22×C4311yescharacteristic
372C2×#106C22×C4311yescharacteristic
373C2×C4⋊C8C22×C4311yescharacteristic
374C2×#103C22×C4311yescharacteristic
375C2×#103C22×C4311yescharacteristic
376C2×#103C22×C4311yescharacteristic
377C2×#103C22×C4311yescharacteristic
378C2×C22⋊C8C22×C4311yescharacteristic
379C2×C22⋊C8C22×C4311yescharacteristic
380C2×C4×C8C22×C4311yescharacteristic
381#398—21no—
382#398—21no—
383#397—21no—
384#396—21no—
385#391C22×C4311yescharacteristic
386#389C22×C4311yescharacteristic
387#389C22×C4311yescharacteristic
388#389C22×C4311yescharacteristic
389#386—21no—
390#381—21no—
391#380—21no—
392#380C22×C4311yescharacteristic
393#380C22×C4311yescharacteristic
394#380C22×C4311yescharacteristic
395#380C22×C4311yescharacteristic
396#340C22×C4311yescharacteristic
397#340C22×C4311yescharacteristic
398#340C22×C4311yescharacteristic
399#340C22×C4311yescharacteristic
400#340C22×C4311yescharacteristic
401#340C22×C4311yescharacteristic
402#340C22×C4311yescharacteristic
403#340C22×C4311yescharacteristic
404C43#2523611yescharacteristic, direct product factor, Sylow
405C22×Q8C23×C4311yescharacteristic
406C22×D4D4×C4311yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C23×C4C23×C4311yescharacteristic
410C23×C4C23×C4311yescharacteristic
411C22×C8—22no—
412C22×C8—22no—
413C22×C8—22no—
414C22×C8—22no—
415C22×C8—41no—
416C22×C8—41no—
417C22×C8C23×C4311yescharacteristic
418C22×C8C23×C4311yescharacteristic
419C22×C8C23×C4311yescharacteristic
420C22×C8C23×C4311yescharacteristic
421#123—44no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—41no—
426C4×D4—22no—
427C4×D4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4D4×C4311yescharacteristic
440C2×C4⋊C4C23×C4311yescharacteristic
441C2×C4⋊C4C23×C4311yescharacteristic
442C2×C4⋊C4C23×C4311yescharacteristic
443C2×C4⋊C4C23×C4311yescharacteristic
444C2×C4⋊C4C23×C4311yescharacteristic
445C2×C4⋊C4C23×C4311yescharacteristic
446C2×C4⋊C4C23×C4311yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4D4×C4311yescharacteristic
454C2×C22⋊C4D4×C4311yescharacteristic
455C2×C42C23×C4311yescharacteristic
456#106—22no—
457#106—22no—
458#106—22no—
459#106—41no—
460C4⋊C8—22no—
461#103—22no—
462#103—22no—
463#103—22no—
464#103—41no—
465C22⋊C8—22no—
466C22⋊C8D4×C4314yes—
467C4×C8—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477C24C2×D4×C4311yescharacteristic
478C24C2×D4×C4311yescharacteristic
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4SD16×C4314yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—81no—
512C22×C4C2×D4×C4311yescharacteristic
513C22×C4C2×D4×C4311yescharacteristic
514C22×C4C2×D4×C4311yescharacteristic
515C22×C4C2×D4×C4312yes—
516C22×C4C2×D4×C4311yescharacteristic
517C22×C4#41×C4312yes—
518C22×C4C24×C4311yescharacteristic
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—44no—
529C2×C8—44no—
530C2×C8C2×D4×C4312yes—
531C2×C8C2×D4×C4312yes—
532C2×C8#41×C4312yes—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—81no—
554C4⋊C4#41×C4312yes—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—81no—
563C42—21no—
564C42—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23#121×C4312yes—
576C23C2×SD16×C4312yes—
577C23C2×SD16×C4312yes—
578C23#135×C4312yes—
579C23C22×D4×C4311yescharacteristic
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584D4—28no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
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—84no—
628C2×C4—84no—
629C2×C4#121×C4312yes—
630C2×C4C2×SD16×C4312yes—
631C2×C4C22×D4×C4311yescharacteristic
632C2×C4C2×#41×C4311yescharacteristic
633C2×C4C2×#41×C4311yescharacteristic
634C2×C4C2×#41×C4311yescharacteristic
635C2×C4H(5,𝔽2)×C4311yescharacteristic
636C2×C42−1+4×C4311yescharacteristic
637C8—22no—
638C8—22no—
639C8—22no—
640C8—41no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22C43×#46514yes—
655C22C2×#121×C4311yescharacteristic
656C22C43×#54611yescharacteristic
657C22C43×#54711yescharacteristic
658C22C22×SD16×C4311yescharacteristic
659C22C2×#135×C4311yescharacteristic
660C22C43×#57711yescharacteristic
661C22C43×#57811yescharacteristic
662C4—22no—
663C4—22no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4C43×#52911yescharacteristic
675C4C43×#53911yescharacteristic
676C4C43×#54611yescharacteristic
677C4C43×#54711yescharacteristic
678C2—24no—
679C2—42no—
680C2C43×#242511yescharacteristic
681C2C2×C43×#46511yescharacteristic
682C2C43×#306311yescharacteristic
683C2C43×#329611yescharacteristic
684C2C43×#329811yescharacteristic
685C2C43×#333511yescharacteristic
686C2C43×#333611yescharacteristic
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×#483C2semidirect
5. C43×#2088C2semidirect
6. C43×#2077C2semidirect
7. C43×#2066C2semidirect
8. C43×#2035C2semidirect
9. C43×#1941C2semidirect
10. C43×#1933C2semidirect
11. C43×#1892C2semidirect
12. C43×#1892C2semidirect
13. C43×#1853C2semidirect
14. C43×#1807C2semidirect
15. C2×C43×#340C2semidirect
297. #25236C43direct (N × H)
335. C2×#483C2×C43semidirect
339. #2088C2×C43semidirect
340. #2077C2×C43semidirect
341. #2066C2×C43semidirect
342. #2035C2×C43semidirect
343. #1941C2×C43semidirect
344. #1933C2×C43semidirect
345. #1892C2×C43semidirect
346. #1892C2×C43semidirect
347. #1853C2×C43semidirect
348. #1807C2×C43semidirect
349. C2×#340C2×C43semidirect
404. C43#25236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4832
C2×C8×D4×C432
C43×#24862
C43×#24172
C43×#20882
C43×#20772
C43×#20662
C43×#20352
C43×#19412
C43×#19332
C43×#18922
C43×#18532
C43×#18072
C2×C43×#3402
#2523643