Finite Group Databasebeta

← C43×#34392 #24954409

Subgroups — C43×#34392 #24954409

Order 11008.

2090 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#529C211yesmaximal, characteristic
2C43×#2376C214yesmaximal, complemented
3C43×#2363C212yesmaximal
4C43×#2362C212yesmaximal, complemented
5C43×#2357C211yesmaximal, characteristic, complemented
6C43×#2356C211yesmaximal, characteristic, complemented
7C43×#2351C211yesmaximal, characteristic, complemented
8C43×#2349C211yesmaximal, characteristic, complemented
9C43×#2347C212yesmaximal, complemented
10C43×#2343C212yesmaximal, complemented
11C43×#2334C214yesmaximal, complemented
12C43×#2330C212yesmaximal, complemented
13C43×#2326C212yesmaximal, complemented
14C43×#2319C212yesmaximal, complemented
15C43×#2318C212yesmaximal, complemented
16C43×#2285C211yesmaximal, characteristic, complemented
17C43×#2283C211yesmaximal, characteristic, complemented
18C43×#529C4116yescomplemented
19C2×#126×C43C2212yes—
20C2×#125×C43C2211yescharacteristic
21C2×#124×C43C2211yescharacteristic
22C2×#123×C43C2212yes—
23C2×C22⋊Q8×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×C4×Q8×C43C2212yes—
26C2×C4×Q8×C43C2211yescharacteristic
27C2×C4×D4×C43C2212yes—
28C2×C4×D4×C43C2211yescharacteristic
29C2×C4×D4×C43C2212yes—
30C2×#117×C43C2212yes—
31C2×#117×C43C2212yes—
32C22×C42×C43C2211yescharacteristic
33C43×#391C2212yes—
34C43×#390C2214yes—
35C43×#390C2212yes—
36C43×#389C2214yes—
37C43×#389C2214yes—
38C43×#389C2212yes—
39C43×#389C2212yes—
40C43×#389C2214yes—
41C43×#388C2214yes—
42C43×#388C2214yes—
43C43×#388C2214yes—
44C43×#388C2214yes—
45C43×#388C2214yes—
46C43×#388C2214yes—
47C43×#387C2214yes—
48C43×#387C2214yes—
49C43×#387C2214yes—
50C43×#387C2214yes—
51C43×#386C2214yes—
52C43×#385C2214yes—
53C43×#385C2214yes—
54C43×#385C2214yes—
55C43×#384C2212yes—
56C43×#383C2211yescharacteristic
57C43×#383C2211yescharacteristic
58C43×#383C2212yes—
59C43×#382C2212yes—
60C43×#382C2212yes—
61C43×#382C2211yescharacteristic
62C43×#382C2211yescharacteristic
63C43×#381C2211yescharacteristic
64C43×#381C2212yes—
65C43×#381C2211yescharacteristic
66C43×#380C2212yes—
67C43×#380C2212yes—
68C43×#380C2212yes—
69C43×#380C2212yes—
70C4×C4⋊C4×C43C2212yes—
71C4×C4⋊C4×C43C2212yes—
72C4×C4⋊C4×C43C2212yes—
73C4×C4⋊C4×C43C2212yes—
74C4×C4⋊C4×C43C2214yes—
75C4×C4⋊C4×C43C2212yes—
76C4×C4⋊C4×C43C2211yescharacteristic
77C4×C4⋊C4×C43C2211yescharacteristic
78C4×C22⋊C4×C43C2214yes—
79C4×C22⋊C4×C43C2212yes—
80C4×C22⋊C4×C43C2212yes—
81C43×#376C2212yes—
82C43×#376C2212yes—
83C2×#95×C43C2212yes—
84C22×Q8×C43C2311yescharacteristic
85C22×D4×C43C2311yescharacteristic
86C22×D4×C43C2312yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2314yes—
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2312yes—
92#126×C43C2×C4116yescomplemented
93#125×C43C2×C418yescomplemented
94#124×C43C2×C418yes—
95#123×C43C2×C4116yescomplemented
96C22⋊Q8×C43C2×C418yescomplemented
97#121×C43C2×C418yes—
98C4×Q8×C43—44no—
99C4×Q8×C43C2×C418yescomplemented
100C4×D4×C43—44no—
101C4×D4×C43C2×C418yes—
102C4×D4×C43C2×C4116yescomplemented
103#117×C43—44no—
104#117×C43C2×C4116yescomplemented
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2312yes—
107C2×C4⋊C4×C43C2314yes—
108C2×C4⋊C4×C43C2312yes—
109C2×C4⋊C4×C43C2312yes—
110C2×C4⋊C4×C43C2314yes—
111C2×C4⋊C4×C43C2314yes—
112C2×C4⋊C4×C43C2314yes—
113C2×C4⋊C4×C43C2314yes—
114C2×C4⋊C4×C43C2312yes—
115C2×C4⋊C4×C43C2312yes—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2312yes—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2312yes—
120C2×C22⋊C4×C43C2314yes—
121C2×C22⋊C4×C43C2314yes—
122C2×C22⋊C4×C43C2312yes—
123C2×C22⋊C4×C43C2312yes—
124C2×C22⋊C4×C43C2314yes—
125C2×C22⋊C4×C43C2314yes—
126C2×C22⋊C4×C43C2312yes—
127C2×C22⋊C4×C43C2312yes—
128C2×C22⋊C4×C43C2312yes—
129C2×C22⋊C4×C43C2312yes—
130C2×C22⋊C4×C43C2312yes—
131C2×C42×C43C2×C418yescomplemented
132C2×C42×C43C2312yes—
133C2×C42×C43C2312yes—
134C2×C42×C43C2314yes—
135C2×C42×C43C2314yes—
136C2×C42×C43C2314yes—
137C2×C42×C43C2314yes—
138C2×C42×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141C2×C42×C43C2311yescharacteristic
142C2×C42×C43C2312yes—
143#95×C43C2311yescharacteristic
144#95×C43C2312yes—
145#95×C43C2314yes—
146#95×C43C2311yescharacteristic
147#95×C43C2312yes—
148#95×C43C2312yes—
149#95×C43C2312yes—
150#95×C43C2312yes—
151#95×C43C2314yes—
152#95×C43C2312yes—
153#95×C43C2311yescharacteristic
154#95×C43C2312yes—
155#95×C43C2312yes—
156#95×C43C2314yes—
157#95×C43C2311yescharacteristic
158#95×C43C2312yes—
159#95×C43C2312yes—
160#95×C43C2314yes—
161#95×C43C2314yes—
162#95×C43C2314yes—
163C24×C43C2411yescharacteristic
164C24×C43C2412yes—
165C2×Q8×C43—22no—
166C2×Q8×C43—22no—
167C2×Q8×C43C22×C414yes—
168C2×D4×C43—22no—
169C2×D4×C43—22no—
170C2×D4×C43—44no—
171C2×D4×C43C22×C414yes—
172C2×D4×C43C22×C418yes—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—42no—
176C22×C4×C43—44no—
177C22×C4×C43—42no—
178C22×C4×C43—44no—
179C22×C4×C43—44no—
180C22×C4×C43—44no—
181C22×C4×C43C22×C414yes—
182C22×C4×C43C22×C414yes—
183C22×C4×C43C22×C414yes—
184C22×C4×C43C22×C418yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2414yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2414yes—
191C22×C4×C43C2411yescharacteristic
192C22×C4×C43C2411yescharacteristic
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C4⋊C4×C43—24no—
201C4⋊C4×C43—24no—
202C4⋊C4×C43—44no—
203C4⋊C4×C43—44no—
204C4⋊C4×C43—42no—
205C4⋊C4×C43—44no—
206C4⋊C4×C43—44no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43—44no—
209C4⋊C4×C43C22×C418yes—
210C4⋊C4×C43C22×C418yes—
211C4⋊C4×C43C22×C414yes—
212C4⋊C4×C43C22×C418yes—
213C4⋊C4×C43C22×C414yes—
214C4⋊C4×C43C22×C418yes—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—44no—
218C22⋊C4×C43—44no—
219C22⋊C4×C43—44no—
220C22⋊C4×C43—44no—
221C22⋊C4×C43C22×C418yes—
222C22⋊C4×C43C22×C418yes—
223C22⋊C4×C43C22×C418yes—
224C22⋊C4×C43C22×C418yes—
225C22⋊C4×C43C22×C418yes—
226C42×C43—24no—
227C42×C43—24no—
228C42×C43—44no—
229C42×C43—44no—
230C42×C43—44no—
231C42×C43—44no—
232C42×C43C22×C414yes—
233C42×C43C22×C414yes—
234C42×C43C22×C414yes—
235C42×C43C22×C414yes—
236C42×C43C22×C418yes—
237C23×C43—21no—
238C23×C43—22no—
239C23×C43—21no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—24no—
243C23×C43—24no—
244C23×C43—22no—
245C23×C43C23×C414yes—
246C23×C43C23×C412yes—
247C23×C43C2511yescharacteristic
248Q8×C43—28no—
249D4×C43—28no—
250D4×C43—48no—
251C2×C4×C43—21no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—22no—
255C2×C4×C43—24no—
256C2×C4×C43—24no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—28no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—24no—
265C2×C4×C43—24no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—24no—
271C2×C4×C43—24no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—24no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—24no—
279C2×C4×C43—22no—
280C2×C4×C43—44no—
281C2×C4×C43—48no—
282C2×C4×C43—44no—
283C2×C4×C43—88no—
284C2×C4×C43C23×C412yes—
285C2×C4×C43C23×C412yes—
286C2×C4×C43C23×C412yes—
287C2×C4×C43C23×C412yes—
288C2×C4×C43C23×C412yes—
289C2×C4×C43C23×C414yes—
290C2×C4×C43C23×C414yes—
291C2×C4×C43C23×C414yes—
292C2×C4×C43C23×C412yes—
293C2×C4×C43H(5,𝔽2)12yes—
294C2×C4×C432−1+412yes—
295#34392C4311yesmaximal, characteristic, direct product factor, Sylow
296C22×C43—22no—
297C22×C43—24no—
298C22×C43—22no—
299C22×C43—24no—
300C22×C43—22no—
301C22×C43—24no—
302C22×C43—42no—
303C22×C43—44no—
304C22×C43—42no—
305C22×C43—44no—
306C22×C43C24×C411yescharacteristic
307C22×C43C2×H(5,𝔽2)11yescharacteristic
308C22×C43C2×2−1+411yescharacteristic
309C22×C43#58512yes—
310C22×C43#58512yes—
311C4×C43—22no—
312C4×C43—24no—
313C4×C43—22no—
314C4×C43—24no—
315C4×C43—22no—
316C4×C43—22no—
317C4×C43—22no—
318C4×C43—24no—
319C4×C43—42no—
320C4×C43—44no—
321C4×C43—44no—
322C4×C43—42no—
323C4×C43—42no—
324C4×C43—42no—
325C4×C43#52014yes—
326C2×#529C2×C4311yescharacteristic
327#2376C2×C4314yescomplemented
328#2363C2×C4312yes—
329#2362C2×C4312yescomplemented
330#2357C2×C4311yescharacteristic, complemented
331#2356C2×C4311yescharacteristic, complemented
332#2351C2×C4311yescharacteristic, complemented
333#2349C2×C4311yescharacteristic, complemented
334#2347C2×C4312yescomplemented
335#2343C2×C4312yescomplemented
336#2334C2×C4314yescomplemented
337#2330C2×C4312yescomplemented
338#2326C2×C4312yescomplemented
339#2319C2×C4312yescomplemented
340#2318C2×C4312yescomplemented
341#2285C2×C4311yescharacteristic, complemented
342#2283C2×C4311yescharacteristic, complemented
343C2×C43—42no—
344C2×C43—44no—
345C2×C43C2×#52011yescharacteristic
346C2×C43#342811yescharacteristic
347C2×C43#342811yescharacteristic
348C2×C43#356212yes—
349C2×C43#356512yes—
350#529C4×C43116yescomplemented
351C2×#126C22×C4312yes—
352C2×#125C22×C4311yescharacteristic
353C2×#124C22×C4311yescharacteristic
354C2×#123C22×C4312yes—
355C2×C22⋊Q8C22×C4311yescharacteristic
356C2×#121C22×C4311yescharacteristic
357C2×C4×Q8C22×C4312yes—
358C2×C4×Q8C22×C4311yescharacteristic
359C2×C4×D4C22×C4312yes—
360C2×C4×D4C22×C4311yescharacteristic
361C2×C4×D4C22×C4312yes—
362C2×#117C22×C4312yes—
363C2×#117C22×C4312yes—
364C22×C42C22×C4311yescharacteristic
365#391C22×C4312yes—
366#390C22×C4314yes—
367#390C22×C4312yes—
368#389C22×C4314yes—
369#389C22×C4314yes—
370#389C22×C4312yes—
371#389C22×C4312yes—
372#389C22×C4314yes—
373#388C22×C4314yes—
374#388C22×C4314yes—
375#388C22×C4314yes—
376#388C22×C4314yes—
377#388C22×C4314yes—
378#388C22×C4314yes—
379#387C22×C4314yes—
380#387C22×C4314yes—
381#387C22×C4314yes—
382#387C22×C4314yes—
383#386C22×C4314yes—
384#385C22×C4314yes—
385#385C22×C4314yes—
386#385C22×C4314yes—
387#384C22×C4312yes—
388#383C22×C4312yes—
389#383C22×C4311yescharacteristic
390#383C22×C4311yescharacteristic
391#382C22×C4312yes—
392#382C22×C4312yes—
393#382C22×C4311yescharacteristic
394#382C22×C4311yescharacteristic
395#381C22×C4311yescharacteristic
396#381C22×C4311yescharacteristic
397#381C22×C4312yes—
398#380C22×C4312yes—
399#380C22×C4312yes—
400#380C22×C4312yes—
401#380C22×C4312yes—
402C4×C4⋊C4C22×C4312yes—
403C4×C4⋊C4C22×C4312yes—
404C4×C4⋊C4C22×C4312yes—
405C4×C4⋊C4C22×C4312yes—
406C4×C4⋊C4C22×C4314yes—
407C4×C4⋊C4C22×C4312yes—
408C4×C4⋊C4C22×C4311yescharacteristic
409C4×C4⋊C4C22×C4311yescharacteristic
410C4×C22⋊C4C22×C4312yes—
411C4×C22⋊C4C22×C4314yes—
412C4×C22⋊C4C22×C4312yes—
413#376C22×C4312yes—
414#376C22×C4312yes—
415C2×#95C22×C4312yes—
416C43#3439211yescharacteristic, direct product factor, Sylow
417C22×Q8C23×C4311yescharacteristic
418C22×D4C23×C4311yescharacteristic
419C22×D4C23×C4312yes—
420C23×C4C23×C4311yescharacteristic
421C23×C4C23×C4314yes—
422C23×C4C23×C4312yes—
423C23×C4C23×C4311yescharacteristic
424C23×C4C23×C4311yescharacteristic
425#126C2×C4×C43116yescomplemented
426#125C2×C4×C4318yescomplemented
427#124C2×C4×C4318yes—
428#123C2×C4×C43116yescomplemented
429C22⋊Q8C2×C4×C4318yescomplemented
430#121C2×C4×C4318yes—
431C4×Q8—44no—
432C4×Q8C2×C4×C4318yescomplemented
433C4×D4—44no—
434C4×D4C2×C4×C4318yes—
435C4×D4C2×C4×C43116yescomplemented
436#117—44no—
437#117C2×C4×C43116yescomplemented
438C2×C4⋊C4C23×C4312yes—
439C2×C4⋊C4C23×C4312yes—
440C2×C4⋊C4C23×C4314yes—
441C2×C4⋊C4C23×C4312yes—
442C2×C4⋊C4C23×C4312yes—
443C2×C4⋊C4C23×C4314yes—
444C2×C4⋊C4C23×C4314yes—
445C2×C4⋊C4C23×C4314yes—
446C2×C4⋊C4C23×C4314yes—
447C2×C4⋊C4C23×C4312yes—
448C2×C4⋊C4C23×C4312yes—
449C2×C4⋊C4C23×C4311yescharacteristic
450C2×C4⋊C4C23×C4312yes—
451C2×C4⋊C4C23×C4311yescharacteristic
452C2×C4⋊C4C23×C4312yes—
453C2×C22⋊C4C23×C4314yes—
454C2×C22⋊C4C23×C4314yes—
455C2×C22⋊C4C23×C4312yes—
456C2×C22⋊C4C23×C4312yes—
457C2×C22⋊C4C23×C4314yes—
458C2×C22⋊C4C23×C4314yes—
459C2×C22⋊C4C23×C4312yes—
460C2×C22⋊C4C23×C4312yes—
461C2×C22⋊C4C23×C4312yes—
462C2×C22⋊C4C23×C4312yes—
463C2×C22⋊C4C23×C4312yes—
464C2×C42C2×C4×C4318yescomplemented
465C2×C42C23×C4312yes—
466C2×C42C23×C4312yes—
467C2×C42C23×C4314yes—
468C2×C42C23×C4314yes—
469C2×C42C23×C4314yes—
470C2×C42C23×C4314yes—
471C2×C42C23×C4311yescharacteristic
472C2×C42C23×C4312yes—
473C2×C42C23×C4311yescharacteristic
474C2×C42C23×C4311yescharacteristic
475C2×C42C23×C4311yescharacteristic
476#95C23×C4311yescharacteristic
477#95C23×C4312yes—
478#95C23×C4314yes—
479#95C23×C4311yescharacteristic
480#95C23×C4312yes—
481#95C23×C4312yes—
482#95C23×C4312yes—
483#95C23×C4312yes—
484#95C23×C4314yes—
485#95C23×C4312yes—
486#95C23×C4311yescharacteristic
487#95C23×C4312yes—
488#95C23×C4312yes—
489#95C23×C4314yes—
490#95C23×C4311yescharacteristic
491#95C23×C4312yes—
492#95C23×C4312yes—
493#95C23×C4314yes—
494#95C23×C4314yes—
495#95C23×C4314yes—
496C24C24×C4311yescharacteristic
497C24C24×C4312yes—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8C22×C4×C4314yes—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—44no—
504C2×D4C22×C4×C4314yes—
505C2×D4C22×C4×C4318yes—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4C22×C4×C4314yes—
515C22×C4C22×C4×C4314yes—
516C22×C4C22×C4×C4314yes—
517C22×C4C22×C4×C4318yes—
518C22×C4C24×C4312yes—
519C22×C4C24×C4312yes—
520C22×C4C24×C4312yes—
521C22×C4C24×C4314yes—
522C22×C4C24×C4312yes—
523C22×C4C24×C4314yes—
524C22×C4C24×C4311yescharacteristic
525C22×C4C24×C4311yescharacteristic
526C22×C4C24×C4312yes—
527C22×C4C24×C4312yes—
528C22×C4C24×C4312yes—
529C22×C4C24×C4311yescharacteristic
530C22×C4C24×C4311yescharacteristic
531C22×C4C24×C4311yescharacteristic
532C22×C4C24×C4311yescharacteristic
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—44no—
536C4⋊C4—44no—
537C4⋊C4—44no—
538C4⋊C4—42no—
539C4⋊C4—44no—
540C4⋊C4—44no—
541C4⋊C4—42no—
542C4⋊C4C22×C4×C4318yes—
543C4⋊C4C22×C4×C4318yes—
544C4⋊C4C22×C4×C4314yes—
545C4⋊C4C22×C4×C4318yes—
546C4⋊C4C22×C4×C4314yes—
547C4⋊C4C22×C4×C4318yes—
548C22⋊C4—44no—
549C22⋊C4—44no—
550C22⋊C4—42no—
551C22⋊C4—44no—
552C22⋊C4—42no—
553C22⋊C4—44no—
554C22⋊C4C22×C4×C4318yes—
555C22⋊C4C22×C4×C4318yes—
556C22⋊C4C22×C4×C4318yes—
557C22⋊C4C22×C4×C4318yes—
558C22⋊C4C22×C4×C4318yes—
559C42—24no—
560C42—24no—
561C42—44no—
562C42—44no—
563C42—44no—
564C42—44no—
565C42C22×C4×C4314yes—
566C42C22×C4×C4314yes—
567C42C22×C4×C4314yes—
568C42C22×C4×C4314yes—
569C42C22×C4×C4318yes—
570C23—21no—
571C23—22no—
572C23—21no—
573C23—22no—
574C23—22no—
575C23—24no—
576C23—24no—
577C23—22no—
578C23C23×C4×C4314yes—
579C23C23×C4×C4312yes—
580C23C25×C4311yescharacteristic
581Q8—28no—
582D4—28no—
583D4—48no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—28no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—44no—
614C2×C4—48no—
615C2×C4—44no—
616C2×C4—88no—
617C2×C4C23×C4×C4312yes—
618C2×C4C23×C4×C4312yes—
619C2×C4C23×C4×C4312yes—
620C2×C4C23×C4×C4312yes—
621C2×C4C23×C4×C4312yes—
622C2×C4C23×C4×C4314yes—
623C2×C4C23×C4×C4314yes—
624C2×C4C23×C4×C4314yes—
625C2×C4C23×C4×C4312yes—
626C2×C4H(5,𝔽2)×C4312yes—
627C2×C42−1+4×C4312yes—
628C22—22no—
629C22—24no—
630C22—22no—
631C22—22no—
632C22—24no—
633C22—24no—
634C22—44no—
635C22—42no—
636C22—42no—
637C22—44no—
638C22C24×C4×C4311yescharacteristic
639C22C2×H(5,𝔽2)×C4311yescharacteristic
640C22C2×2−1+4×C4311yescharacteristic
641C22C43×#58512yes—
642C22C43×#58512yes—
643C4—22no—
644C4—24no—
645C4—22no—
646C4—24no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—24no—
651C4—42no—
652C4—44no—
653C4—42no—
654C4—44no—
655C4—42no—
656C4—42no—
657C4C43×#52014yes—
658C2—42no—
659C2—44no—
660C2C2×C43×#52011yescharacteristic
661C2C43×#342811yescharacteristic
662C2C43×#342811yescharacteristic
663C2C43×#356212yes—
664C2C43×#356512yes—
subgroupG/H
center, socleC23×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC23C25×C43
prime radicalC2×#121×C43C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2376C2semidirect
4. C43×#2362C2semidirect
5. C43×#2357C2semidirect
6. C43×#2356C2semidirect
7. C43×#2351C2semidirect
8. C43×#2349C2semidirect
9. C43×#2347C2semidirect
10. C43×#2343C2semidirect
11. C43×#2334C2semidirect
12. C43×#2330C2semidirect
13. C43×#2326C2semidirect
14. C43×#2319C2semidirect
15. C43×#2318C2semidirect
16. C43×#2285C2semidirect
17. C43×#2283C2semidirect
18. C43×#529C4semidirect
92. #126×C43C2×C4semidirect
93. #125×C43C2×C4semidirect
95. #123×C43C2×C4semidirect
96. C22⋊Q8×C43C2×C4semidirect
99. C4×Q8×C43C2×C4semidirect
102. C4×D4×C43C2×C4semidirect
104. #117×C43C2×C4semidirect
131. C2×C42×C43C2×C4semidirect
295. #34392C43direct (N × H)
327. #2376C2×C43semidirect
329. #2362C2×C43semidirect
330. #2357C2×C43semidirect
331. #2356C2×C43semidirect
332. #2351C2×C43semidirect
333. #2349C2×C43semidirect
334. #2347C2×C43semidirect
335. #2343C2×C43semidirect
336. #2334C2×C43semidirect
337. #2330C2×C43semidirect
338. #2326C2×C43semidirect
339. #2319C2×C43semidirect
340. #2318C2×C43semidirect
341. #2285C2×C43semidirect
342. #2283C2×C43semidirect
350. #529C4×C43semidirect
416. C43#34392direct (N × H)
425. #126C2×C4×C43semidirect
426. #125C2×C4×C43semidirect
428. #123C2×C4×C43semidirect
429. C22⋊Q8C2×C4×C43semidirect
432. C4×Q8C2×C4×C43semidirect
435. C4×D4C2×C4×C43semidirect
437. #117C2×C4×C43semidirect
464. C2×C42C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5292
C43×#23762
C43×#23632
C43×#23622
C43×#23572
C43×#23562
C43×#23512
C43×#23492
C43×#23472
C43×#23432
C43×#23342
C43×#23302
C43×#23262
C43×#23192
C43×#23182
C43×#22852
C43×#22832
#3439243