Finite Group Databasebeta

← C2×C43×#2520 #24954784

Subgroups — C2×C43×#2520 #24954784

Order 11008.

2030 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2520C2116yesmaximal, direct product factor
2C2×C43×#400C211yesmaximal, characteristic
3C2×C43×#398C211yesmaximal, characteristic
4C2×C43×#398C211yesmaximal, characteristic
5C2×C43×#395C211yesmaximal, characteristic
6C2×C43×#391C211yesmaximal, characteristic
7C2×C43×#391C211yesmaximal, characteristic
8C2×C43×#387C211yesmaximal, characteristic
9C2×C43×#387C211yesmaximal, characteristic
10C2×C43×#387C211yesmaximal, characteristic
11C2×C43×#387C211yesmaximal, characteristic
12C2×C43×#387C211yesmaximal, characteristic
13C2×C43×#387C211yesmaximal, characteristic
14C2×C43×#382C211yesmaximal, characteristic
15C2×C4×C4⋊C4×C43C211yesmaximal, characteristic
16C2×C4×C4⋊C4×C43C211yesmaximal, characteristic
17C23×Q8×C43C2211yescharacteristic
18C22×C4⋊C4×C43C2211yescharacteristic
19C22×C4⋊C4×C43C2211yescharacteristic
20C22×C4⋊C4×C43C2211yescharacteristic
21C22×C4⋊C4×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C4⋊C4×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C22×C4⋊C4×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C22×C42×C43C2211yescharacteristic
30C22×C42×C43C2211yescharacteristic
31C22×C42×C43C2211yescharacteristic
32C22×C42×C43C2211yescharacteristic
33C22×C42×C43C2211yescharacteristic
34C43×#400C2218yes—
35C43×#398C2218yes—
36C43×#398C2218yes—
37C43×#395C2218yes—
38C43×#391C2218yes—
39C43×#391C2218yes—
40C43×#387C2218yes—
41C43×#387C2218yes—
42C43×#387C2218yes—
43C43×#387C2218yes—
44C43×#387C2218yes—
45C43×#387C2218yes—
46C43×#382C2218yes—
47C4×C4⋊C4×C43C2218yes—
48C4×C4⋊C4×C43C2218yes—
49C2×#95×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C2×#95×C43C2211yescharacteristic
62C2×#95×C43C2211yescharacteristic
63C2×#95×C43C2211yescharacteristic
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C22×Q8×C43—24no—
68C22×Q8×C43—24no—
69C22×Q8×C43—42no—
70C22×Q8×C43C2314yes—
71C23×C4×C43C2311yescharacteristic
72C23×C4×C43C2311yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2311yescharacteristic
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C2×C4⋊C4×C43—24no—
87C2×C4⋊C4×C43—24no—
88C2×C4⋊C4×C43—24no—
89C2×C4⋊C4×C43—24no—
90C2×C4⋊C4×C43—24no—
91C2×C4⋊C4×C43—24no—
92C2×C4⋊C4×C43—24no—
93C2×C4⋊C4×C43—42no—
94C2×C4⋊C4×C43—42no—
95C2×C4⋊C4×C43—42no—
96C2×C4⋊C4×C43Q818yescomplemented
97C2×C4⋊C4×C43C2314yes—
98C2×C4⋊C4×C43C2314yes—
99C2×C4⋊C4×C43C2314yes—
100C2×C4⋊C4×C43C2314yes—
101C2×C4⋊C4×C43C2314yes—
102C2×C4⋊C4×C43C2314yes—
103C2×C4⋊C4×C43C2314yes—
104C2×C4⋊C4×C43C2314yes—
105C2×C4⋊C4×C43C2314yes—
106C2×C4⋊C4×C43C2314yes—
107C2×C4⋊C4×C43C2314yes—
108C2×C42×C43—24no—
109C2×C42×C43—24no—
110C2×C42×C43—24no—
111C2×C42×C43—42no—
112C2×C42×C43—42no—
113C2×C42×C43C2314yes—
114C2×C42×C43C2314yes—
115C2×C42×C43C2314yes—
116C2×C42×C43C2314yes—
117C2×C42×C43C2314yes—
118#95×C43C2314yes—
119#95×C43C2314yes—
120#95×C43C2314yes—
121#95×C43C2314yes—
122#95×C43C2314yes—
123#95×C43C2314yes—
124#95×C43C2314yes—
125#95×C43C2314yes—
126#95×C43C2314yes—
127#95×C43C2314yes—
128#95×C43C2314yes—
129#95×C43C2314yes—
130#95×C43C2314yes—
131#95×C43C2314yes—
132#95×C43C2314yes—
133#95×C43C2314yes—
134#95×C43C2314yes—
135#95×C43C2314yes—
136C24×C43C2411yescharacteristic
137C2×Q8×C43—28no—
138C2×Q8×C43—28no—
139C2×Q8×C43—44no—
140C2×Q8×C43—416no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43C2×Q814yes—
180C22×C4×C43C2×Q814yes—
181C22×C4×C43C2×Q814yes—
182C22×C4×C43#4114yes—
183C22×C4×C43#4114yes—
184C22×C4×C43#4114yes—
185C22×C4×C43#4114yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2412yes—
201C4⋊C4×C43—28no—
202C4⋊C4×C43—28no—
203C4⋊C4×C43—28no—
204C4⋊C4×C43—28no—
205C4⋊C4×C43—28no—
206C4⋊C4×C43—28no—
207C4⋊C4×C43—28no—
208C4⋊C4×C43—44no—
209C4⋊C4×C43—44no—
210C4⋊C4×C43—44no—
211C4⋊C4×C43C2×Q8116yescomplemented
212C42×C43—28no—
213C42×C43—28no—
214C42×C43—28no—
215C42×C43—44no—
216C42×C43—44no—
217C23×C43C22×Q812yes—
218C23×C43C2×#4112yes—
219C23×C43C2×#4112yes—
220C23×C43C2×#4112yes—
221C23×C43C2×#4112yes—
222C23×C43H(5,𝔽2)12yes—
223C23×C432−1+412yes—
224C23×C43C2511yescharacteristic
225Q8×C43—416no—
226C2×C4×C43—28no—
227C2×C4×C43—28no—
228C2×C4×C43—28no—
229C2×C4×C43—28no—
230C2×C4×C43—28no—
231C2×C4×C43—28no—
232C2×C4×C43—28no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—44no—
272C2×C4×C43—44no—
273C2×C4×C43—44no—
274C2×C4×C43—44no—
275C2×C4×C43—44no—
276C2×C4×C43—44no—
277C2×C4×C43—44no—
278C2×C4×C43—44no—
279C2×C4×C43C22×Q814yes—
280C2×C4×C43C22×Q814yes—
281C2×C4×C43C22×Q814yes—
282C2×C4×C43C2×#4114yes—
283C2×C4×C43C2×#4114yes—
284C2×C4×C43C2×#4114yes—
285C2×C4×C43C2×#4114yes—
286C2×#2520C4311yesmaximal, characteristic, direct product factor, Sylow
287C22×C43#52914yes—
288C22×C43#53314yes—
289C22×C43#54214yes—
290C22×C43#55114yes—
291C22×C43#55214yes—
292C22×C43#55414yes—
293C22×C43#55714yes—
294C22×C43C23×Q811yescharacteristic
295C22×C43C22×#4111yescharacteristic
296C22×C43C22×#4111yescharacteristic
297C22×C43C22×#4111yescharacteristic
298C22×C43C22×#4111yescharacteristic
299C22×C43C2×H(5,𝔽2)11yescharacteristic
300C22×C43C2×2−1+411yescharacteristic
301C4×C43—24no—
302C4×C43—24no—
303C4×C43—24no—
304C4×C43—24no—
305C4×C43—24no—
306C4×C43—24no—
307C4×C43—24no—
308C4×C43—42no—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43—42no—
312C4×C43—42no—
313C4×C43—42no—
314C4×C43—42no—
315C4×C43—42no—
316#2520C2×C43116yesdirect product factor
317C2×#400C2×C4311yescharacteristic
318C2×#398C2×C4311yescharacteristic
319C2×#398C2×C4311yescharacteristic
320C2×#395C2×C4311yescharacteristic
321C2×#391C2×C4311yescharacteristic
322C2×#391C2×C4311yescharacteristic
323C2×#387C2×C4311yescharacteristic
324C2×#387C2×C4311yescharacteristic
325C2×#387C2×C4311yescharacteristic
326C2×#387C2×C4311yescharacteristic
327C2×#387C2×C4311yescharacteristic
328C2×#387C2×C4311yescharacteristic
329C2×#382C2×C4311yescharacteristic
330C2×C4×C4⋊C4C2×C4311yescharacteristic
331C2×C4×C4⋊C4C2×C4311yescharacteristic
332C2×C43#252018yesdirect product factor
333C2×C43C2×#52911yescharacteristic
334C2×C43C2×#53311yescharacteristic
335C2×C43C2×#54211yescharacteristic
336C2×C43C2×#55111yescharacteristic
337C2×C43C2×#55211yescharacteristic
338C2×C43C2×#55411yescharacteristic
339C2×C43C2×#55711yescharacteristic
340C23×Q8C22×C4311yescharacteristic
341C22×C4⋊C4C22×C4311yescharacteristic
342C22×C4⋊C4C22×C4311yescharacteristic
343C22×C4⋊C4C22×C4311yescharacteristic
344C22×C4⋊C4C22×C4311yescharacteristic
345C22×C4⋊C4C22×C4311yescharacteristic
346C22×C4⋊C4C22×C4311yescharacteristic
347C22×C4⋊C4C22×C4311yescharacteristic
348C22×C4⋊C4C22×C4311yescharacteristic
349C22×C4⋊C4C22×C4311yescharacteristic
350C22×C4⋊C4C22×C4311yescharacteristic
351C22×C4⋊C4C22×C4311yescharacteristic
352C22×C42C22×C4311yescharacteristic
353C22×C42C22×C4311yescharacteristic
354C22×C42C22×C4311yescharacteristic
355C22×C42C22×C4311yescharacteristic
356C22×C42C22×C4311yescharacteristic
357#400C22×C4318yes—
358#398C22×C4318yes—
359#398C22×C4318yes—
360#395C22×C4318yes—
361#391C22×C4318yes—
362#391C22×C4318yes—
363#387C22×C4318yes—
364#387C22×C4318yes—
365#387C22×C4318yes—
366#387C22×C4318yes—
367#387C22×C4318yes—
368#387C22×C4318yes—
369#382C22×C4318yes—
370C4×C4⋊C4C22×C4318yes—
371C4×C4⋊C4C22×C4318yes—
372C2×#95C22×C4311yescharacteristic
373C2×#95C22×C4311yescharacteristic
374C2×#95C22×C4311yescharacteristic
375C2×#95C22×C4311yescharacteristic
376C2×#95C22×C4311yescharacteristic
377C2×#95C22×C4311yescharacteristic
378C2×#95C22×C4311yescharacteristic
379C2×#95C22×C4311yescharacteristic
380C2×#95C22×C4311yescharacteristic
381C2×#95C22×C4311yescharacteristic
382C2×#95C22×C4311yescharacteristic
383C2×#95C22×C4311yescharacteristic
384C2×#95C22×C4311yescharacteristic
385C2×#95C22×C4311yescharacteristic
386C2×#95C22×C4311yescharacteristic
387C2×#95C22×C4311yescharacteristic
388C2×#95C22×C4311yescharacteristic
389C2×#95C22×C4311yescharacteristic
390C43C2×#252011yescharacteristic, direct product factor, Sylow
391C22×Q8—24no—
392C22×Q8—24no—
393C22×Q8—42no—
394C22×Q8C23×C4314yes—
395C23×C4C23×C4311yescharacteristic
396C23×C4C23×C4311yescharacteristic
397C23×C4C23×C4311yescharacteristic
398C23×C4C23×C4311yescharacteristic
399C23×C4C23×C4311yescharacteristic
400C23×C4C23×C4311yescharacteristic
401C23×C4C23×C4311yescharacteristic
402C23×C4C23×C4311yescharacteristic
403C23×C4C23×C4311yescharacteristic
404C23×C4C23×C4311yescharacteristic
405C23×C4C23×C4311yescharacteristic
406C23×C4C23×C4311yescharacteristic
407C23×C4C23×C4311yescharacteristic
408C23×C4C23×C4311yescharacteristic
409C23×C4C23×C4311yescharacteristic
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4Q8×C4318yescomplemented
421C2×C4⋊C4C23×C4314yes—
422C2×C4⋊C4C23×C4314yes—
423C2×C4⋊C4C23×C4314yes—
424C2×C4⋊C4C23×C4314yes—
425C2×C4⋊C4C23×C4314yes—
426C2×C4⋊C4C23×C4314yes—
427C2×C4⋊C4C23×C4314yes—
428C2×C4⋊C4C23×C4314yes—
429C2×C4⋊C4C23×C4314yes—
430C2×C4⋊C4C23×C4314yes—
431C2×C4⋊C4C23×C4314yes—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—24no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42C23×C4314yes—
438C2×C42C23×C4314yes—
439C2×C42C23×C4314yes—
440C2×C42C23×C4314yes—
441C2×C42C23×C4314yes—
442#95C23×C4314yes—
443#95C23×C4314yes—
444#95C23×C4314yes—
445#95C23×C4314yes—
446#95C23×C4314yes—
447#95C23×C4314yes—
448#95C23×C4314yes—
449#95C23×C4314yes—
450#95C23×C4314yes—
451#95C23×C4314yes—
452#95C23×C4314yes—
453#95C23×C4314yes—
454#95C23×C4314yes—
455#95C23×C4314yes—
456#95C23×C4314yes—
457#95C23×C4314yes—
458#95C23×C4314yes—
459#95C23×C4314yes—
460C24C24×C4311yescharacteristic
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—44no—
464C2×Q8—416no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4C2×Q8×C4314yes—
504C22×C4C2×Q8×C4314yes—
505C22×C4C2×Q8×C4314yes—
506C22×C4#41×C4314yes—
507C22×C4#41×C4314yes—
508C22×C4#41×C4314yes—
509C22×C4#41×C4314yes—
510C22×C4C24×C4312yes—
511C22×C4C24×C4312yes—
512C22×C4C24×C4312yes—
513C22×C4C24×C4312yes—
514C22×C4C24×C4312yes—
515C22×C4C24×C4312yes—
516C22×C4C24×C4312yes—
517C22×C4C24×C4312yes—
518C22×C4C24×C4312yes—
519C22×C4C24×C4312yes—
520C22×C4C24×C4312yes—
521C22×C4C24×C4312yes—
522C22×C4C24×C4312yes—
523C22×C4C24×C4312yes—
524C22×C4C24×C4312yes—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—28no—
529C4⋊C4—28no—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—44no—
533C4⋊C4—44no—
534C4⋊C4—44no—
535C4⋊C4C2×Q8×C43116yescomplemented
536C42—28no—
537C42—28no—
538C42—28no—
539C42—44no—
540C42—44no—
541C23C22×Q8×C4312yes—
542C23C2×#41×C4312yes—
543C23C2×#41×C4312yes—
544C23C2×#41×C4312yes—
545C23C2×#41×C4312yes—
546C23H(5,𝔽2)×C4312yes—
547C232−1+4×C4312yes—
548C23C25×C4311yescharacteristic
549Q8—416no—
550C2×C4—28no—
551C2×C4—28no—
552C2×C4—28no—
553C2×C4—28no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4C22×Q8×C4314yes—
604C2×C4C22×Q8×C4314yes—
605C2×C4C22×Q8×C4314yes—
606C2×C4C2×#41×C4314yes—
607C2×C4C2×#41×C4314yes—
608C2×C4C2×#41×C4314yes—
609C2×C4C2×#41×C4314yes—
610C22C43×#52914yes—
611C22C43×#53314yes—
612C22C43×#54214yes—
613C22C43×#55114yes—
614C22C43×#55214yes—
615C22C43×#55414yes—
616C22C43×#55714yes—
617C22C23×Q8×C4311yescharacteristic
618C22C22×#41×C4311yescharacteristic
619C22C22×#41×C4311yescharacteristic
620C22C22×#41×C4311yescharacteristic
621C22C22×#41×C4311yescharacteristic
622C22C2×H(5,𝔽2)×C4311yescharacteristic
623C22C2×2−1+4×C4311yescharacteristic
624C4—24no—
625C4—24no—
626C4—24no—
627C4—24no—
628C4—24no—
629C4—24no—
630C4—24no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—42no—
639C2C43×#252018yesdirect product factor
640C2C2×C43×#52911yescharacteristic
641C2C2×C43×#53311yescharacteristic
642C2C2×C43×#54211yescharacteristic
643C2C2×C43×#55111yescharacteristic
644C2C2×C43×#55211yescharacteristic
645C2C2×C43×#55411yescharacteristic
646C2C2×C43×#55711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C43C24
commutator, Frattini, cosocleC23C25×C43
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2520C2direct (N × H)
96. C2×C4⋊C4×C43Q8semidirect
211. C4⋊C4×C43C2×Q8semidirect
286. C2×#2520C43direct (N × H)
316. #2520C2×C43direct (N × H)
332. C2×C43#2520direct (N × H)
390. C43C2×#2520direct (N × H)
420. C2×C4⋊C4Q8×C43semidirect
535. C4⋊C4C2×Q8×C43semidirect
639. C2C43×#2520direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#25202
C2×C43×#4002
C2×C43×#3982
C2×C43×#3952
C2×C43×#3912
C2×C43×#3872
C2×C43×#3822
C2×C4×C4⋊C4×C432
C2×#252043