Finite Group Databasebeta

← C43×#34381 #24954398

Subgroups — C43×#34381 #24954398

Order 11008.

2134 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C43C211yesmaximal, characteristic
2C43×#2383C214yesmaximal, complemented
3C43×#2373C214yesmaximal, complemented
4C43×#2345C212yesmaximal, complemented
5C43×#2344C212yesmaximal, complemented
6C43×#2342C212yesmaximal
7C43×#2342C212yesmaximal
8C43×#2334C214yesmaximal, complemented
9C43×#2334C214yesmaximal, complemented
10C43×#2316C211yesmaximal, characteristic, complemented
11C43×#2315C211yesmaximal, characteristic
12C43×#2313C211yesmaximal, characteristic, complemented
13C43×#2312C211yesmaximal, characteristic
14C43×#2285C211yesmaximal, characteristic, complemented
15C43×#2283C211yesmaximal, characteristic, complemented
16C2×#126×C43C4116yescomplemented
17C2×#126×C43C2212yes—
18C2×#126×C43C2212yes—
19C2×#126×C43C2212yes—
20C2×#126×C43C2212yes—
21C2×#117×C43C2212yes—
22C2×#117×C43C2212yes—
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C4⋊C4×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2212yes—
27C22×C22⋊C4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2211yescharacteristic
30C22×C42×C43C2211yescharacteristic
31C43×#389C2214yescomplemented
32C43×#389C2214yescomplemented
33C43×#389C2214yescomplemented
34C43×#389C2214yescomplemented
35C43×#388C2214yes—
36C43×#388C2214yes—
37C43×#388C2214yes—
38C43×#388C2214yes—
39C43×#388C2214yes—
40C43×#388C2214yes—
41C43×#387C2214yescomplemented
42C43×#387C2214yescomplemented
43C43×#387C2214yescomplemented
44C43×#387C2214yescomplemented
45C43×#387C2214yescomplemented
46C43×#387C2214yescomplemented
47C43×#385C2214yes—
48C43×#385C2214yes—
49C43×#385C2214yes—
50C43×#385C2214yes—
51C43×#384C2212yescomplemented
52C43×#383C2212yescomplemented
53C43×#382C2212yescomplemented
54C43×#382C2212yescomplemented
55C43×#381C2212yes—
56C43×#381C2212yes—
57C43×#380C2212yes—
58C43×#380C2212yes—
59C43×#380C2212yes—
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C43×#379C2212yes—
65C4×C4⋊C4×C43C2212yescomplemented
66C4×C4⋊C4×C43C2212yescomplemented
67C4×C4⋊C4×C43C2214yescomplemented
68C4×C4⋊C4×C43C2214yescomplemented
69C4×C4⋊C4×C43C2212yescomplemented
70C4×C22⋊C4×C43C2214yes—
71C4×C22⋊C4×C43C2214yes—
72C4×C22⋊C4×C43C2212yes—
73C4×C22⋊C4×C43C2212yes—
74C4×C22⋊C4×C43C2212yes—
75C43×#376C2212yescomplemented
76C25×C43C2311yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2314yes—
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2311yescharacteristic
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84#126×C43C2×C4116yescomplemented
85#126×C43C2×C4116yescomplemented
86#126×C43C2×C4116yescomplemented
87#126×C43C2×C4116yescomplemented
88#117×C43—44no—
89#117×C43—44no—
90C2×C4⋊C4×C43C2×C418yescomplemented
91C2×C4⋊C4×C43C2×C418yescomplemented
92C2×C4⋊C4×C43C2×C418yescomplemented
93C2×C4⋊C4×C43C2314yes—
94C2×C4⋊C4×C43C2314yes—
95C2×C4⋊C4×C43C2312yes—
96C2×C4⋊C4×C43C2312yes—
97C2×C4⋊C4×C43C2312yes—
98C2×C4⋊C4×C43C2314yes—
99C2×C4⋊C4×C43C2312yes—
100C2×C4⋊C4×C43C2314yes—
101C2×C4⋊C4×C43C2314yes—
102C2×C4⋊C4×C43C2312yes—
103C2×C4⋊C4×C43C2312yes—
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2312yes—
107C2×C4⋊C4×C43C2312yes—
108C2×C22⋊C4×C43—44no—
109C2×C22⋊C4×C43C2×C418yes—
110C2×C22⋊C4×C43C2×C418yes—
111C2×C22⋊C4×C43C2×C418yes—
112C2×C22⋊C4×C43C2312yes—
113C2×C22⋊C4×C43C2312yes—
114C2×C22⋊C4×C43C2312yes—
115C2×C22⋊C4×C43C2312yes—
116C2×C22⋊C4×C43C2314yes—
117C2×C22⋊C4×C43C2314yes—
118C2×C22⋊C4×C43C2314yes—
119C2×C22⋊C4×C43C2312yes—
120C2×C22⋊C4×C43C2312yes—
121C2×C22⋊C4×C43C2312yes—
122C2×C22⋊C4×C43C2312yes—
123C2×C22⋊C4×C43C2312yes—
124C2×C22⋊C4×C43C2312yes—
125C2×C42×C43C2×C418yescomplemented
126C2×C42×C43C2314yes—
127C2×C42×C43C2314yes—
128C2×C42×C43C2314yes—
129C2×C42×C43C2314yes—
130C2×C42×C43C2314yes—
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#95×C43C2314yes—
136#95×C43C2312yes—
137#95×C43C2312yes—
138#95×C43C2314yes—
139#95×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142#95×C43C2314yes—
143#95×C43C2314yes—
144#95×C43C2312yes—
145#95×C43C2312yes—
146#95×C43C2314yes—
147#95×C43C2314yes—
148#95×C43C2314yes—
149C24×C43—22no—
150C24×C43—22no—
151C24×C43—42no—
152C24×C43—42no—
153C24×C43C22×C414yes—
154C24×C43C2412yes—
155C24×C43C2411yescharacteristic
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43—42no—
163C22×C4×C43—42no—
164C22×C4×C43—44no—
165C22×C4×C43—44no—
166C22×C4×C43—44no—
167C22×C4×C43C22×C414yes—
168C22×C4×C43C22×C414yes—
169C22×C4×C43C22×C414yes—
170C22×C4×C43C22×C414yes—
171C22×C4×C43C22×C414yes—
172C22×C4×C43C22×C414yes—
173C22×C4×C43C2414yes—
174C22×C4×C43C2414yes—
175C22×C4×C43C2414yes—
176C22×C4×C43C2414yes—
177C22×C4×C43C2411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C22×C4×C43C2412yes—
180C22×C4×C43C2411yescharacteristic
181C22×C4×C43C2412yes—
182C22×C4×C43C2412yes—
183C22×C4×C43C2411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C4⋊C4×C43—44no—
187C4⋊C4×C43—44no—
188C4⋊C4×C43—42no—
189C4⋊C4×C43—44no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43—42no—
193C4⋊C4×C43—44no—
194C4⋊C4×C43—44no—
195C4⋊C4×C43C22×C418yes—
196C4⋊C4×C43C22×C418yes—
197C4⋊C4×C43C22×C418yes—
198C4⋊C4×C43C22×C418yes—
199C4⋊C4×C43C22×C418yes—
200C4⋊C4×C43C22×C418yes—
201C22⋊C4×C43—24no—
202C22⋊C4×C43—24no—
203C22⋊C4×C43—24no—
204C22⋊C4×C43—24no—
205C22⋊C4×C43—44no—
206C22⋊C4×C43—44no—
207C22⋊C4×C43—44no—
208C22⋊C4×C43C22×C418yes—
209C22⋊C4×C43C22×C418yes—
210C22⋊C4×C43C22×C418yes—
211C22⋊C4×C43C22×C418yes—
212C22⋊C4×C43C22×C418yes—
213C22⋊C4×C43C22×C418yes—
214C42×C43—44no—
215C42×C43—44no—
216C42×C43—44no—
217C42×C43—44no—
218C42×C43—44no—
219C42×C43C22×C414yes—
220C42×C43C22×C414yes—
221C42×C43C22×C414yes—
222C42×C43C22×C414yes—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—22no—
227C23×C43—24no—
228C23×C43—24no—
229C23×C43—28no—
230C23×C43—44no—
231C23×C43—44no—
232C23×C43—84no—
233C23×C43—84no—
234C23×C43C23×C414yes—
235C23×C43C23×C412yes—
236C23×C43H(5,𝔽2)12yes—
237C23×C432−1+412yes—
238C23×C43C2511yescharacteristic
239C2×C4×C43—28no—
240C2×C4×C43—28no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—24no—
249C2×C4×C43—24no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—24no—
254C2×C4×C43—24no—
255C2×C4×C43—24no—
256C2×C4×C43—24no—
257C2×C4×C43—24no—
258C2×C4×C43—24no—
259C2×C4×C43—24no—
260C2×C4×C43—24no—
261C2×C4×C43—24no—
262C2×C4×C43—24no—
263C2×C4×C43—24no—
264C2×C4×C43—24no—
265C2×C4×C43—44no—
266C2×C4×C43—44no—
267C2×C4×C43—44no—
268C2×C4×C43—44no—
269C2×C4×C43—88no—
270C2×C4×C43C23×C412yes—
271C2×C4×C43C23×C412yes—
272C2×C4×C43C23×C412yes—
273C2×C4×C43C23×C412yes—
274C2×C4×C43C23×C412yes—
275C2×C4×C43C23×C412yes—
276C2×C4×C43C23×C414yes—
277C2×C4×C43C23×C414yes—
278C2×C4×C43C23×C414yes—
279#34381C4311yesmaximal, characteristic, direct product factor, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—24no—
283C22×C43—24no—
284C22×C43—24no—
285C22×C43—24no—
286C22×C43—24no—
287C22×C43—44no—
288C22×C43—44no—
289C22×C43—88no—
290C22×C43#52014yes—
291C22×C43C24×C411yescharacteristic
292C22×C43C2×H(5,𝔽2)11yescharacteristic
293C22×C43C2×2−1+411yescharacteristic
294C22×C43#58512yes—
295C22×C43#58512yes—
296C4×C43—22no—
297C4×C43—24no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—24no—
301C4×C43—24no—
302C4×C43—22no—
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—44no—
306C4×C43—44no—
307C4×C43—44no—
308C4×C43—44no—
309C22×#126C2×C4311yescharacteristic
310#2383C2×C4314yescomplemented
311#2373C2×C4314yescomplemented
312#2345C2×C4312yescomplemented
313#2344C2×C4312yescomplemented
314#2342C2×C4312yes—
315#2342C2×C4312yes—
316#2334C2×C4314yescomplemented
317#2334C2×C4314yescomplemented
318#2316C2×C4311yescharacteristic, complemented
319#2315C2×C4311yescharacteristic
320#2313C2×C4311yescharacteristic, complemented
321#2312C2×C4311yescharacteristic
322#2285C2×C4311yescharacteristic, complemented
323#2283C2×C4311yescharacteristic, complemented
324C2×C43—24no—
325C2×C43—44no—
326C2×C43C2×#52011yescharacteristic
327C2×C43#342811yescharacteristic
328C2×C43#342811yescharacteristic
329C2×C43#356012yes—
330C2×C43#356412yes—
331C2×#126C4×C43116yescomplemented
332C2×#126C22×C4312yes—
333C2×#126C22×C4312yes—
334C2×#126C22×C4312yes—
335C2×#126C22×C4312yes—
336C2×#117C22×C4312yes—
337C2×#117C22×C4312yes—
338C22×C4⋊C4C22×C4311yescharacteristic
339C22×C4⋊C4C22×C4311yescharacteristic
340C22×C4⋊C4C22×C4311yescharacteristic
341C22×C22⋊C4C22×C4312yes—
342C22×C22⋊C4C22×C4311yescharacteristic
343C22×C22⋊C4C22×C4311yescharacteristic
344C22×C22⋊C4C22×C4311yescharacteristic
345C22×C42C22×C4311yescharacteristic
346#389C22×C4314yescomplemented
347#389C22×C4314yescomplemented
348#389C22×C4314yescomplemented
349#389C22×C4314yescomplemented
350#388C22×C4314yes—
351#388C22×C4314yes—
352#388C22×C4314yes—
353#388C22×C4314yes—
354#388C22×C4314yes—
355#388C22×C4314yes—
356#387C22×C4314yescomplemented
357#387C22×C4314yescomplemented
358#387C22×C4314yescomplemented
359#387C22×C4314yescomplemented
360#387C22×C4314yescomplemented
361#387C22×C4314yescomplemented
362#385C22×C4314yes—
363#385C22×C4314yes—
364#385C22×C4314yes—
365#385C22×C4314yes—
366#384C22×C4312yescomplemented
367#383C22×C4312yescomplemented
368#382C22×C4312yescomplemented
369#382C22×C4312yescomplemented
370#381C22×C4312yes—
371#381C22×C4312yes—
372#380C22×C4311yescharacteristic
373#380C22×C4311yescharacteristic
374#380C22×C4311yescharacteristic
375#380C22×C4311yescharacteristic
376#380C22×C4312yes—
377#380C22×C4312yes—
378#380C22×C4312yes—
379#379C22×C4312yes—
380C4×C4⋊C4C22×C4312yescomplemented
381C4×C4⋊C4C22×C4312yescomplemented
382C4×C4⋊C4C22×C4314yescomplemented
383C4×C4⋊C4C22×C4314yescomplemented
384C4×C4⋊C4C22×C4312yescomplemented
385C4×C22⋊C4C22×C4312yes—
386C4×C22⋊C4C22×C4312yes—
387C4×C22⋊C4C22×C4314yes—
388C4×C22⋊C4C22×C4314yes—
389C4×C22⋊C4C22×C4312yes—
390#376C22×C4312yescomplemented
391C43#3438111yescharacteristic, direct product factor, Sylow
392C25C23×C4311yescharacteristic
393C23×C4C23×C4311yescharacteristic
394C23×C4C23×C4311yescharacteristic
395C23×C4C23×C4314yes—
396C23×C4C23×C4311yescharacteristic
397C23×C4C23×C4311yescharacteristic
398C23×C4C23×C4311yescharacteristic
399C23×C4C23×C4311yescharacteristic
400#126C2×C4×C43116yescomplemented
401#126C2×C4×C43116yescomplemented
402#126C2×C4×C43116yescomplemented
403#126C2×C4×C43116yescomplemented
404#117—44no—
405#117—44no—
406C2×C4⋊C4C2×C4×C4318yescomplemented
407C2×C4⋊C4C2×C4×C4318yescomplemented
408C2×C4⋊C4C2×C4×C4318yescomplemented
409C2×C4⋊C4C23×C4314yes—
410C2×C4⋊C4C23×C4314yes—
411C2×C4⋊C4C23×C4312yes—
412C2×C4⋊C4C23×C4312yes—
413C2×C4⋊C4C23×C4312yes—
414C2×C4⋊C4C23×C4314yes—
415C2×C4⋊C4C23×C4312yes—
416C2×C4⋊C4C23×C4314yes—
417C2×C4⋊C4C23×C4314yes—
418C2×C4⋊C4C23×C4312yes—
419C2×C4⋊C4C23×C4312yes—
420C2×C4⋊C4C23×C4312yes—
421C2×C4⋊C4C23×C4312yes—
422C2×C4⋊C4C23×C4312yes—
423C2×C4⋊C4C23×C4312yes—
424C2×C22⋊C4—44no—
425C2×C22⋊C4C2×C4×C4318yes—
426C2×C22⋊C4C2×C4×C4318yes—
427C2×C22⋊C4C2×C4×C4318yes—
428C2×C22⋊C4C23×C4312yes—
429C2×C22⋊C4C23×C4312yes—
430C2×C22⋊C4C23×C4312yes—
431C2×C22⋊C4C23×C4312yes—
432C2×C22⋊C4C23×C4314yes—
433C2×C22⋊C4C23×C4314yes—
434C2×C22⋊C4C23×C4314yes—
435C2×C22⋊C4C23×C4312yes—
436C2×C22⋊C4C23×C4312yes—
437C2×C22⋊C4C23×C4312yes—
438C2×C22⋊C4C23×C4312yes—
439C2×C22⋊C4C23×C4312yes—
440C2×C22⋊C4C23×C4312yes—
441C2×C42C2×C4×C4318yescomplemented
442C2×C42C23×C4314yes—
443C2×C42C23×C4314yes—
444C2×C42C23×C4314yes—
445C2×C42C23×C4314yes—
446C2×C42C23×C4314yes—
447C2×C42C23×C4311yescharacteristic
448C2×C42C23×C4311yescharacteristic
449C2×C42C23×C4311yescharacteristic
450C2×C42C23×C4311yescharacteristic
451#95C23×C4314yes—
452#95C23×C4312yes—
453#95C23×C4312yes—
454#95C23×C4314yes—
455#95C23×C4314yes—
456#95C23×C4314yes—
457#95C23×C4314yes—
458#95C23×C4314yes—
459#95C23×C4314yes—
460#95C23×C4312yes—
461#95C23×C4312yes—
462#95C23×C4314yes—
463#95C23×C4314yes—
464#95C23×C4314yes—
465C24—22no—
466C24—22no—
467C24—42no—
468C24—42no—
469C24C22×C4×C4314yes—
470C24C24×C4312yes—
471C24C24×C4311yescharacteristic
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4C22×C4×C4314yes—
484C22×C4C22×C4×C4314yes—
485C22×C4C22×C4×C4314yes—
486C22×C4C22×C4×C4314yes—
487C22×C4C22×C4×C4314yes—
488C22×C4C22×C4×C4314yes—
489C22×C4C24×C4314yes—
490C22×C4C24×C4314yes—
491C22×C4C24×C4314yes—
492C22×C4C24×C4314yes—
493C22×C4C24×C4311yescharacteristic
494C22×C4C24×C4311yescharacteristic
495C22×C4C24×C4312yes—
496C22×C4C24×C4311yescharacteristic
497C22×C4C24×C4312yes—
498C22×C4C24×C4312yes—
499C22×C4C24×C4311yescharacteristic
500C22×C4C24×C4311yescharacteristic
501C22×C4C24×C4311yescharacteristic
502C4⋊C4—44no—
503C4⋊C4—44no—
504C4⋊C4—44no—
505C4⋊C4—44no—
506C4⋊C4—42no—
507C4⋊C4—44no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4C22×C4×C4318yes—
512C4⋊C4C22×C4×C4318yes—
513C4⋊C4C22×C4×C4318yes—
514C4⋊C4C22×C4×C4318yes—
515C4⋊C4C22×C4×C4318yes—
516C4⋊C4C22×C4×C4318yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—44no—
522C22⋊C4—44no—
523C22⋊C4—44no—
524C22⋊C4C22×C4×C4318yes—
525C22⋊C4C22×C4×C4318yes—
526C22⋊C4C22×C4×C4318yes—
527C22⋊C4C22×C4×C4318yes—
528C22⋊C4C22×C4×C4318yes—
529C22⋊C4C22×C4×C4318yes—
530C42—44no—
531C42—44no—
532C42—44no—
533C42—44no—
534C42—44no—
535C42C22×C4×C4314yes—
536C42C22×C4×C4314yes—
537C42C22×C4×C4314yes—
538C42C22×C4×C4314yes—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—24no—
544C23—24no—
545C23—28no—
546C23—44no—
547C23—44no—
548C23—84no—
549C23—84no—
550C23C23×C4×C4314yes—
551C23C23×C4×C4312yes—
552C23H(5,𝔽2)×C4312yes—
553C232−1+4×C4312yes—
554C23C25×C4311yescharacteristic
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—44no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4—88no—
586C2×C4C23×C4×C4312yes—
587C2×C4C23×C4×C4312yes—
588C2×C4C23×C4×C4312yes—
589C2×C4C23×C4×C4312yes—
590C2×C4C23×C4×C4312yes—
591C2×C4C23×C4×C4312yes—
592C2×C4C23×C4×C4314yes—
593C2×C4C23×C4×C4314yes—
594C2×C4C23×C4×C4314yes—
595C22—22no—
596C22—22no—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—24no—
601C22—24no—
602C22—44no—
603C22—44no—
604C22—88no—
605C22C43×#52014yes—
606C22C24×C4×C4311yescharacteristic
607C22C2×H(5,𝔽2)×C4311yescharacteristic
608C22C2×2−1+4×C4311yescharacteristic
609C22C43×#58512yes—
610C22C43×#58512yes—
611C4—22no—
612C4—24no—
613C4—22no—
614C4—22no—
615C4—24no—
616C4—24no—
617C4—22no—
618C4—22no—
619C4—22no—
620C4—44no—
621C4—44no—
622C4—44no—
623C4—44no—
624C2—24no—
625C2—44no—
626C2C2×C43×#52011yescharacteristic
627C2C43×#342811yescharacteristic
628C2C43×#342811yescharacteristic
629C2C43×#356012yes—
630C2C43×#356412yes—
subgroupG/H
center, socleC23×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC23C25×C43
prime radicalC25×C43C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2383C2semidirect
3. C43×#2373C2semidirect
4. C43×#2345C2semidirect
5. C43×#2344C2semidirect
8. C43×#2334C2semidirect
9. C43×#2334C2semidirect
10. C43×#2316C2semidirect
12. C43×#2313C2semidirect
14. C43×#2285C2semidirect
15. C43×#2283C2semidirect
16. C2×#126×C43C4semidirect
31. C43×#389C22semidirect
32. C43×#389C22semidirect
33. C43×#389C22semidirect
34. C43×#389C22semidirect
41. C43×#387C22semidirect
42. C43×#387C22semidirect
43. C43×#387C22semidirect
44. C43×#387C22semidirect
45. C43×#387C22semidirect
46. C43×#387C22semidirect
51. C43×#384C22semidirect
52. C43×#383C22semidirect
53. C43×#382C22semidirect
54. C43×#382C22semidirect
65. C4×C4⋊C4×C43C22semidirect
66. C4×C4⋊C4×C43C22semidirect
67. C4×C4⋊C4×C43C22semidirect
68. C4×C4⋊C4×C43C22semidirect
69. C4×C4⋊C4×C43C22semidirect
75. C43×#376C22semidirect
84. #126×C43C2×C4semidirect
85. #126×C43C2×C4semidirect
86. #126×C43C2×C4semidirect
87. #126×C43C2×C4semidirect
90. C2×C4⋊C4×C43C2×C4semidirect
91. C2×C4⋊C4×C43C2×C4semidirect
92. C2×C4⋊C4×C43C2×C4semidirect
125. C2×C42×C43C2×C4semidirect
279. #34381C43direct (N × H)
310. #2383C2×C43semidirect
311. #2373C2×C43semidirect
312. #2345C2×C43semidirect
313. #2344C2×C43semidirect
316. #2334C2×C43semidirect
317. #2334C2×C43semidirect
318. #2316C2×C43semidirect
320. #2313C2×C43semidirect
322. #2285C2×C43semidirect
323. #2283C2×C43semidirect
331. C2×#126C4×C43semidirect
346. #389C22×C43semidirect
347. #389C22×C43semidirect
348. #389C22×C43semidirect
349. #389C22×C43semidirect
356. #387C22×C43semidirect
357. #387C22×C43semidirect
358. #387C22×C43semidirect
359. #387C22×C43semidirect
360. #387C22×C43semidirect
361. #387C22×C43semidirect
366. #384C22×C43semidirect
367. #383C22×C43semidirect
368. #382C22×C43semidirect
369. #382C22×C43semidirect
380. C4×C4⋊C4C22×C43semidirect
381. C4×C4⋊C4C22×C43semidirect
382. C4×C4⋊C4C22×C43semidirect
383. C4×C4⋊C4C22×C43semidirect
384. C4×C4⋊C4C22×C43semidirect
390. #376C22×C43semidirect
391. C43#34381direct (N × H)
400. #126C2×C4×C43semidirect
401. #126C2×C4×C43semidirect
402. #126C2×C4×C43semidirect
403. #126C2×C4×C43semidirect
406. C2×C4⋊C4C2×C4×C43semidirect
407. C2×C4⋊C4C2×C4×C43semidirect
408. C2×C4⋊C4C2×C4×C43semidirect
441. C2×C42C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C432
C43×#23832
C43×#23732
C43×#23452
C43×#23442
C43×#23422
C43×#23342
C43×#23162
C43×#23152
C43×#23132
C43×#23122
C43×#22852
C43×#22832
#3438143