Finite Group Databasebeta

← C43×#34426 #24954443

Subgroups — C43×#34426 #24954443

Order 11008.

2442 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#538C211yesmaximal, characteristic
2C43×#2383C212yesmaximal, complemented
3C43×#2377C212yesmaximal, complemented
4C43×#2373C212yesmaximal, complemented
5C43×#2361C212yesmaximal, complemented
6C43×#2358C212yesmaximal, complemented
7C43×#2358C212yesmaximal, complemented
8C43×#2353C212yesmaximal, complemented
9D4×C4⋊C4×C43C212yesmaximal, complemented
10C43×#2337C212yesmaximal, complemented
11C43×#2335C212yesmaximal, complemented
12C43×#2329C211yesmaximal, characteristic, complemented
13C43×#2326C212yesmaximal, complemented
14C43×#2325C211yesmaximal, characteristic, complemented
15C43×#2322C212yesmaximal, complemented
16C43×#2315C211yesmaximal, characteristic, complemented
17C4×C22⋊Q8×C43C211yesmaximal, characteristic, complemented
18C4×#121×C43C211yesmaximal, characteristic, complemented
19C2×C43×#388C211yesmaximal, characteristic, complemented
20C43×#538C4116yescomplemented
21C2×#126×C43C2212yes—
22C2×#124×C43C2212yes—
23C2×#123×C43C2212yes—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic
26C2×#121×C43C2212yes—
27C2×#120×C43C2212yes—
28C2×C4×Q8×C43C2211yescharacteristic, complemented
29C2×C4×D4×C43C2212yes—
30C2×C4×D4×C43C2212yes—
31C2×C4×D4×C43C2212yes—
32C2×C4×D4×C43C2212yes—
33C2×C4×D4×C43C2212yes—
34C2×C4×D4×C43C2211yescharacteristic, complemented
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2212yescomplemented
37C22×C22⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2212yes—
40C22×C22⋊C4×C43C2211yescharacteristic
41C22×C42×C43C2211yescharacteristic
42C43×#391C2212yescomplemented
43C43×#391C2211yescharacteristic, complemented
44C43×#390C2212yes—
45C43×#390C2212yes—
46C43×#390C2211yescharacteristic, complemented
47C43×#389C2211yescharacteristic, complemented
48C43×#389C2212yescomplemented
49C43×#389C2212yescomplemented
50C43×#389C2212yescomplemented
51C43×#389C2211yescharacteristic, complemented
52C43×#388C2212yes—
53C43×#388C2212yes—
54C43×#388C2212yes—
55C43×#388C2212yes—
56C43×#388C2212yes—
57C43×#388C2212yes—
58C43×#388C2212yes—
59C43×#388C2212yes—
60C43×#388C2212yescomplemented
61C43×#388C2212yescomplemented
62C43×#388C2212yescomplemented
63C43×#388C2212yescomplemented
64C43×#387C2212yescomplemented
65C43×#387C2212yescomplemented
66C43×#387C2212yescomplemented
67C43×#387C2212yescomplemented
68C43×#387C2212yescomplemented
69C43×#387C2212yescomplemented
70C43×#386C2212yes—
71C43×#386C2212yes—
72C43×#386C2212yes—
73C43×#386C2212yes—
74C43×#386C2212yes—
75C43×#386C2212yes—
76C43×#386C2212yescomplemented
77C43×#385C2212yes—
78C43×#385C2212yes—
79C43×#385C2212yes—
80C43×#385C2212yes—
81C43×#385C2212yes—
82C43×#385C2212yes—
83C43×#385C2212yes—
84C43×#385C2212yes—
85C43×#385C2212yescomplemented
86C43×#385C2212yescomplemented
87C43×#385C2212yescomplemented
88C43×#384C2212yescomplemented
89C43×#383C2212yescomplemented
90C43×#381C2212yescomplemented
91C43×#380C2211yescharacteristic
92C43×#380C2211yescharacteristic
93C43×#380C2212yes—
94C43×#380C2212yescomplemented
95C4×C4⋊C4×C43C2211yescharacteristic, complemented
96C4×C4⋊C4×C43C2212yescomplemented
97C4×C4⋊C4×C43C2212yescomplemented
98C4×C4⋊C4×C43C2211yescharacteristic, complemented
99C4×C22⋊C4×C43C2212yes—
100C4×C22⋊C4×C43C2212yes—
101C4×C22⋊C4×C43C2212yes—
102C4×C22⋊C4×C43C2212yes—
103C4×C22⋊C4×C43C2212yescomplemented
104C4×C22⋊C4×C43C2212yescomplemented
105C43×#376C2212yescomplemented
106C2×#95×C43C2211yescharacteristic
107C2×#95×C43C2211yescharacteristic
108C25×C43C2311yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2312yes—
111C22×D4×C43C2312yes—
112C22×D4×C43C2312yes—
113C22×D4×C43C2311yescharacteristic
114C23×C4×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C23×C4×C43C2312yes—
119C23×C4×C43C2312yes—
120C23×C4×C43C2312yes—
121C23×C4×C43C2312yes—
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2312yes—
125#126×C43C2×C4116yescomplemented
126#124×C43C2×C4116yescomplemented
127#123×C43C2×C4116yescomplemented
128C22⋊Q8×C43C2×C418yescomplemented
129#121×C43C2×C4116yescomplemented
130#121×C43C2×C418yescomplemented
131#120×C43C2×C4116yescomplemented
132C4×Q8×C43—42no—
133C4×D4×C43—44no—
134C4×D4×C43—42no—
135C4×D4×C43—44no—
136C4×D4×C43—44no—
137C4×D4×C43—44no—
138C4×D4×C43C2×C4116yescomplemented
139C2×C4⋊C4×C43—42no—
140C2×C4⋊C4×C43—44no—
141C2×C4⋊C4×C43C2312yes—
142C2×C4⋊C4×C43C2312yes—
143C2×C4⋊C4×C43C2312yes—
144C2×C4⋊C4×C43C2312yes—
145C2×C4⋊C4×C43C2312yes—
146C2×C4⋊C4×C43C2312yes—
147C2×C4⋊C4×C43C2312yes—
148C2×C4⋊C4×C43C2312yes—
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2312yes—
152C2×C4⋊C4×C43C2312yes—
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C4⋊C4×C43C2312yes—
156C2×C4⋊C4×C43C2312yes—
157C2×C4⋊C4×C43C2311yescharacteristic
158C2×C4⋊C4×C43C2311yescharacteristic
159C2×C22⋊C4×C43—42no—
160C2×C22⋊C4×C43—42no—
161C2×C22⋊C4×C43—44no—
162C2×C22⋊C4×C43C2×C418yescomplemented
163C2×C22⋊C4×C43C2312yes—
164C2×C22⋊C4×C43C2312yes—
165C2×C22⋊C4×C43C2312yes—
166C2×C22⋊C4×C43C2312yes—
167C2×C22⋊C4×C43C2312yes—
168C2×C22⋊C4×C43C2312yes—
169C2×C22⋊C4×C43C2312yes—
170C2×C22⋊C4×C43C2312yes—
171C2×C22⋊C4×C43C2312yes—
172C2×C22⋊C4×C43C2312yes—
173C2×C22⋊C4×C43C2312yes—
174C2×C22⋊C4×C43C2312yes—
175C2×C22⋊C4×C43C2312yes—
176C2×C22⋊C4×C43C2312yes—
177C2×C22⋊C4×C43C2312yes—
178C2×C22⋊C4×C43C2312yes—
179C2×C22⋊C4×C43C2312yes—
180C2×C22⋊C4×C43C2312yes—
181C2×C22⋊C4×C43C2312yes—
182C2×C22⋊C4×C43C2312yes—
183C2×C22⋊C4×C43C2312yes—
184C2×C42×C43—42no—
185C2×C42×C43C2311yescharacteristic
186C2×C42×C43C2311yescharacteristic
187C2×C42×C43C2312yes—
188C2×C42×C43C2311yescharacteristic
189C2×C42×C43C2311yescharacteristic
190C2×C42×C43C2312yes—
191C2×C42×C43C2312yes—
192C2×C42×C43C2312yes—
193C2×C42×C43C2312yes—
194C2×C42×C43C2312yes—
195C2×C42×C43C2312yes—
196#95×C43C2312yes—
197#95×C43C2312yes—
198#95×C43C2312yes—
199#95×C43C2312yes—
200#95×C43C2312yes—
201#95×C43C2312yes—
202#95×C43C2312yes—
203#95×C43C2312yes—
204#95×C43C2312yes—
205#95×C43C2312yes—
206#95×C43C2312yes—
207#95×C43C2312yes—
208#95×C43C2312yes—
209#95×C43C2312yes—
210#95×C43C2312yes—
211#95×C43C2312yes—
212#95×C43C2312yes—
213#95×C43C2312yes—
214#95×C43C2312yes—
215#95×C43C2312yes—
216C24×C43—22no—
217C24×C43—22no—
218C24×C43—41no—
219C24×C43—41no—
220C24×C43—41no—
221C24×C43—41no—
222C24×C43C22×C414yes—
223C24×C43C2412yes—
224C24×C43C2412yes—
225C24×C43C2411yescharacteristic
226C2×Q8×C43—41no—
227C2×Q8×C43—41no—
228C2×Q8×C43C22×C414yes—
229C2×D4×C43—24no—
230C2×D4×C43—24no—
231C2×D4×C43—42no—
232C2×D4×C43—42no—
233C2×D4×C43—41no—
234C2×D4×C43—42no—
235C2×D4×C43—41no—
236C2×D4×C43—42no—
237C2×D4×C43C22×C418yes—
238C2×D4×C43C22×C418yes—
239C2×D4×C43C22×C418yes—
240C2×D4×C43C22×C414yes—
241C22×C4×C43—22no—
242C22×C4×C43—22no—
243C22×C4×C43—24no—
244C22×C4×C43—22no—
245C22×C4×C43—22no—
246C22×C4×C43—22no—
247C22×C4×C43—22no—
248C22×C4×C43—41no—
249C22×C4×C43—41no—
250C22×C4×C43—41no—
251C22×C4×C43—42no—
252C22×C4×C43—41no—
253C22×C4×C43—41no—
254C22×C4×C43—41no—
255C22×C4×C43—42no—
256C22×C4×C43—41no—
257C22×C4×C43—41no—
258C22×C4×C43—42no—
259C22×C4×C43—42no—
260C22×C4×C43—41no—
261C22×C4×C43—42no—
262C22×C4×C43—42no—
263C22×C4×C43—42no—
264C22×C4×C43—42no—
265C22×C4×C43—42no—
266C22×C4×C43—42no—
267C22×C4×C43—42no—
268C22×C4×C43—41no—
269C22×C4×C43—42no—
270C22×C4×C43—42no—
271C22×C4×C43C22×C414yes—
272C22×C4×C43C22×C414yes—
273C22×C4×C43C22×C418yes—
274C22×C4×C43C2411yescharacteristic
275C22×C4×C43C2412yes—
276C22×C4×C43C2412yes—
277C22×C4×C43C2412yes—
278C22×C4×C43C2412yes—
279C22×C4×C43C2412yes—
280C22×C4×C43C2412yes—
281C22×C4×C43C2411yescharacteristic
282C22×C4×C43C2412yes—
283C22×C4×C43C2412yes—
284C22×C4×C43C2411yescharacteristic
285C22×C4×C43C2411yescharacteristic
286C22×C4×C43C2412yes—
287C22×C4×C43C2412yes—
288C22×C4×C43C2411yescharacteristic
289C22×C4×C43C2411yescharacteristic
290C4⋊C4×C43—24no—
291C4⋊C4×C43—24no—
292C4⋊C4×C43—42no—
293C4⋊C4×C43—42no—
294C4⋊C4×C43—42no—
295C4⋊C4×C43—42no—
296C4⋊C4×C43—41no—
297C4⋊C4×C43—41no—
298C4⋊C4×C43—41no—
299C4⋊C4×C43—42no—
300C4⋊C4×C43—42no—
301C4⋊C4×C43—42no—
302C4⋊C4×C43—41no—
303C4⋊C4×C43—42no—
304C4⋊C4×C43C22×C418yes—
305C4⋊C4×C43C22×C418yes—
306C4⋊C4×C43C22×C414yes—
307C4⋊C4×C43C22×C414yes—
308C22⋊C4×C43—24no—
309C22⋊C4×C43—24no—
310C22⋊C4×C43—24no—
311C22⋊C4×C43—24no—
312C22⋊C4×C43—24no—
313C22⋊C4×C43—42no—
314C22⋊C4×C43—42no—
315C22⋊C4×C43—42no—
316C22⋊C4×C43—42no—
317C22⋊C4×C43—42no—
318C22⋊C4×C43—42no—
319C22⋊C4×C43—42no—
320C22⋊C4×C43—42no—
321C22⋊C4×C43—42no—
322C22⋊C4×C43C22×C418yes—
323C22⋊C4×C43C22×C418yes—
324C22⋊C4×C43C22×C418yes—
325C22⋊C4×C43C22×C418yes—
326C22⋊C4×C43C22×C418yes—
327C22⋊C4×C43C22×C418yes—
328C22⋊C4×C43C22×C418yes—
329C42×C43—22no—
330C42×C43—22no—
331C42×C43—24no—
332C42×C43—41no—
333C42×C43—41no—
334C42×C43—42no—
335C42×C43—42no—
336C42×C43—42no—
337C42×C43—42no—
338C42×C43—42no—
339C42×C43C22×C418yes—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—28no—
357C23×C43—44no—
358C23×C43—44no—
359C23×C43—82no—
360C23×C43—82no—
361C23×C43—82no—
362C23×C43—82no—
363C23×C43C23×C414yes—
364C23×C43C23×C414yes—
365C23×C43C23×C412yes—
366C23×C43H(5,𝔽2)12yes—
367C23×C432−1+412yes—
368C23×C43C2511yescharacteristic
369Q8×C43—44no—
370D4×C43—216no—
371D4×C43—48no—
372D4×C43—44no—
373D4×C43—48no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—21no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—21no—
383C2×C4×C43—22no—
384C2×C4×C43—21no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—22no—
392C2×C4×C43—21no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—21no—
403C2×C4×C43—21no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—21no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—21no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—44no—
415C2×C4×C43—48no—
416C2×C4×C43—44no—
417C2×C4×C43—44no—
418C2×C4×C43—44no—
419C2×C4×C43—84no—
420C2×C4×C43—82no—
421C2×C4×C43—82no—
422C2×C4×C43—84no—
423C2×C4×C43—84no—
424C2×C4×C43—84no—
425C2×C4×C43C23×C414yes—
426C2×C4×C43C23×C414yes—
427C2×C4×C43C23×C414yes—
428C2×C4×C43C23×C412yes—
429C2×C4×C43C23×C412yes—
430C2×C4×C43C23×C414yes—
431C2×C4×C43H(5,𝔽2)12yes—
432C2×C4×C43H(5,𝔽2)12yes—
433#34426C4311yesmaximal, characteristic, direct product factor, Sylow
434C22×C43—22no—
435C22×C43—22no—
436C22×C43—22no—
437C22×C43—22no—
438C22×C43—22no—
439C22×C43—22no—
440C22×C43—24no—
441C22×C43—24no—
442C22×C43—24no—
443C22×C43—24no—
444C22×C43—24no—
445C22×C43—24no—
446C22×C43—42no—
447C22×C43—42no—
448C22×C43—42no—
449C22×C43—42no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43—42no—
453C22×C43—42no—
454C22×C43—88no—
455C22×C43#52014yes—
456C22×C43C24×C411yescharacteristic
457C22×C43C2×H(5,𝔽2)11yescharacteristic
458C22×C43C2×H(5,𝔽2)11yescharacteristic
459C22×C43C2×H(5,𝔽2)11yescharacteristic
460C22×C43C2×2−1+411yescharacteristic
461C22×C43#58511yescharacteristic
462C22×C43#58511yescharacteristic
463C4×C43—24no—
464C4×C43—24no—
465C4×C43—22no—
466C4×C43—24no—
467C4×C43—22no—
468C4×C43—24no—
469C4×C43—22no—
470C4×C43—22no—
471C4×C43—41no—
472C4×C43—41no—
473C4×C43—42no—
474C4×C43—42no—
475C4×C43—42no—
476C4×C43—42no—
477C4×C43—42no—
478C4×C43—42no—
479C2×#538C2×C4311yescharacteristic
480#2383C2×C4312yescomplemented
481#2377C2×C4312yescomplemented
482#2373C2×C4312yescomplemented
483#2361C2×C4312yescomplemented
484#2358C2×C4312yescomplemented
485#2358C2×C4312yescomplemented
486#2353C2×C4312yescomplemented
487D4×C4⋊C4C2×C4312yescomplemented
488#2337C2×C4312yescomplemented
489#2335C2×C4312yescomplemented
490#2329C2×C4311yescharacteristic, complemented
491#2326C2×C4312yescomplemented
492#2325C2×C4311yescharacteristic, complemented
493#2322C2×C4312yescomplemented
494#2315C2×C4311yescharacteristic, complemented
495C4×C22⋊Q8C2×C4311yescharacteristic, complemented
496C4×#121C2×C4311yescharacteristic, complemented
497C2×#388C2×C4311yescharacteristic, complemented
498C2×C43—24no—
499C2×C43—44no—
500C2×C43—44no—
501C2×C43C2×#52011yescharacteristic
502C2×C43C4×H(5,𝔽2)11yescharacteristic
503C2×C43C4×H(5,𝔽2)11yescharacteristic
504C2×C43#353511yescharacteristic
505C2×C43#353711yescharacteristic
506C2×C43#356011yescharacteristic
507C2×C43#356111yescharacteristic
508#538C4×C43116yescomplemented
509C2×#126C22×C4312yes—
510C2×#124C22×C4312yes—
511C2×#123C22×C4312yes—
512C2×C22⋊Q8C22×C4311yescharacteristic
513C2×#121C22×C4311yescharacteristic
514C2×#121C22×C4312yes—
515C2×#120C22×C4312yes—
516C2×C4×Q8C22×C4311yescharacteristic, complemented
517C2×C4×D4C22×C4312yes—
518C2×C4×D4C22×C4312yes—
519C2×C4×D4C22×C4312yes—
520C2×C4×D4C22×C4312yes—
521C2×C4×D4C22×C4312yes—
522C2×C4×D4C22×C4311yescharacteristic, complemented
523C22×C4⋊C4C22×C4311yescharacteristic
524C22×C4⋊C4C22×C4312yescomplemented
525C22×C22⋊C4C22×C4312yes—
526C22×C22⋊C4C22×C4311yescharacteristic
527C22×C22⋊C4C22×C4311yescharacteristic
528C22×C22⋊C4C22×C4311yescharacteristic
529C22×C42C22×C4311yescharacteristic
530#391C22×C4312yescomplemented
531#391C22×C4311yescharacteristic, complemented
532#390C22×C4312yes—
533#390C22×C4312yes—
534#390C22×C4311yescharacteristic, complemented
535#389C22×C4311yescharacteristic, complemented
536#389C22×C4312yescomplemented
537#389C22×C4312yescomplemented
538#389C22×C4312yescomplemented
539#389C22×C4311yescharacteristic, complemented
540#388C22×C4312yes—
541#388C22×C4312yes—
542#388C22×C4312yes—
543#388C22×C4312yes—
544#388C22×C4312yes—
545#388C22×C4312yes—
546#388C22×C4312yes—
547#388C22×C4312yes—
548#388C22×C4312yescomplemented
549#388C22×C4312yescomplemented
550#388C22×C4312yescomplemented
551#388C22×C4312yescomplemented
552#387C22×C4312yescomplemented
553#387C22×C4312yescomplemented
554#387C22×C4312yescomplemented
555#387C22×C4312yescomplemented
556#387C22×C4312yescomplemented
557#387C22×C4312yescomplemented
558#386C22×C4312yes—
559#386C22×C4312yes—
560#386C22×C4312yes—
561#386C22×C4312yes—
562#386C22×C4312yes—
563#386C22×C4312yes—
564#386C22×C4312yescomplemented
565#385C22×C4312yes—
566#385C22×C4312yes—
567#385C22×C4312yes—
568#385C22×C4312yes—
569#385C22×C4312yes—
570#385C22×C4312yes—
571#385C22×C4312yes—
572#385C22×C4312yes—
573#385C22×C4312yescomplemented
574#385C22×C4312yescomplemented
575#385C22×C4312yescomplemented
576#384C22×C4312yescomplemented
577#383C22×C4312yescomplemented
578#381C22×C4312yescomplemented
579#380C22×C4311yescharacteristic
580#380C22×C4311yescharacteristic
581#380C22×C4312yes—
582#380C22×C4312yescomplemented
583C4×C4⋊C4C22×C4311yescharacteristic, complemented
584C4×C4⋊C4C22×C4312yescomplemented
585C4×C4⋊C4C22×C4312yescomplemented
586C4×C4⋊C4C22×C4311yescharacteristic, complemented
587C4×C22⋊C4C22×C4312yes—
588C4×C22⋊C4C22×C4312yes—
589C4×C22⋊C4C22×C4312yes—
590C4×C22⋊C4C22×C4312yes—
591C4×C22⋊C4C22×C4312yescomplemented
592C4×C22⋊C4C22×C4312yescomplemented
593#376C22×C4312yescomplemented
594C2×#95C22×C4311yescharacteristic
595C2×#95C22×C4311yescharacteristic
596C43#3442611yescharacteristic, direct product factor, Sylow
597C25C23×C4311yescharacteristic
598C22×Q8C23×C4311yescharacteristic
599C22×D4C23×C4312yes—
600C22×D4C23×C4312yes—
601C22×D4C23×C4312yes—
602C22×D4C23×C4311yescharacteristic
603C23×C4C23×C4311yescharacteristic
604C23×C4C23×C4311yescharacteristic
605C23×C4C23×C4311yescharacteristic
606C23×C4C23×C4311yescharacteristic
607C23×C4C23×C4312yes—
608C23×C4C23×C4312yes—
609C23×C4C23×C4312yes—
610C23×C4C23×C4312yes—
611C23×C4C23×C4311yescharacteristic
612C23×C4C23×C4311yescharacteristic
613C23×C4C23×C4312yes—
614#126C2×C4×C43116yescomplemented
615#124C2×C4×C43116yescomplemented
616#123C2×C4×C43116yescomplemented
617C22⋊Q8C2×C4×C4318yescomplemented
618#121C2×C4×C43116yescomplemented
619#121C2×C4×C4318yescomplemented
620#120C2×C4×C43116yescomplemented
621C4×Q8—42no—
622C4×D4—44no—
623C4×D4—42no—
624C4×D4—44no—
625C4×D4—44no—
626C4×D4—44no—
627C4×D4C2×C4×C43116yescomplemented
628C2×C4⋊C4—42no—
629C2×C4⋊C4—44no—
630C2×C4⋊C4C23×C4312yes—
631C2×C4⋊C4C23×C4312yes—
632C2×C4⋊C4C23×C4312yes—
633C2×C4⋊C4C23×C4312yes—
634C2×C4⋊C4C23×C4312yes—
635C2×C4⋊C4C23×C4312yes—
636C2×C4⋊C4C23×C4312yes—
637C2×C4⋊C4C23×C4312yes—
638C2×C4⋊C4C23×C4311yescharacteristic
639C2×C4⋊C4C23×C4311yescharacteristic
640C2×C4⋊C4C23×C4312yes—
641C2×C4⋊C4C23×C4312yes—
642C2×C4⋊C4C23×C4311yescharacteristic
643C2×C4⋊C4C23×C4311yescharacteristic
644C2×C4⋊C4C23×C4312yes—
645C2×C4⋊C4C23×C4312yes—
646C2×C4⋊C4C23×C4311yescharacteristic
647C2×C4⋊C4C23×C4311yescharacteristic
648C2×C22⋊C4—42no—
649C2×C22⋊C4—42no—
650C2×C22⋊C4—44no—
651C2×C22⋊C4C2×C4×C4318yescomplemented
652C2×C22⋊C4C23×C4312yes—
653C2×C22⋊C4C23×C4312yes—
654C2×C22⋊C4C23×C4312yes—
655C2×C22⋊C4C23×C4312yes—
656C2×C22⋊C4C23×C4312yes—
657C2×C22⋊C4C23×C4312yes—
658C2×C22⋊C4C23×C4312yes—
659C2×C22⋊C4C23×C4312yes—
660C2×C22⋊C4C23×C4312yes—
661C2×C22⋊C4C23×C4312yes—
662C2×C22⋊C4C23×C4312yes—
663C2×C22⋊C4C23×C4312yes—
664C2×C22⋊C4C23×C4312yes—
665C2×C22⋊C4C23×C4312yes—
666C2×C22⋊C4C23×C4312yes—
667C2×C22⋊C4C23×C4312yes—
668C2×C22⋊C4C23×C4312yes—
669C2×C22⋊C4C23×C4312yes—
670C2×C22⋊C4C23×C4312yes—
671C2×C22⋊C4C23×C4312yes—
672C2×C22⋊C4C23×C4312yes—
673C2×C42—42no—
674C2×C42C23×C4312yes—
675C2×C42C23×C4311yescharacteristic
676C2×C42C23×C4311yescharacteristic
677C2×C42C23×C4312yes—
678C2×C42C23×C4312yes—
679C2×C42C23×C4312yes—
680C2×C42C23×C4312yes—
681C2×C42C23×C4312yes—
682C2×C42C23×C4311yescharacteristic
683C2×C42C23×C4311yescharacteristic
684C2×C42C23×C4312yes—
685#95C23×C4312yes—
686#95C23×C4312yes—
687#95C23×C4312yes—
688#95C23×C4312yes—
689#95C23×C4312yes—
690#95C23×C4312yes—
691#95C23×C4312yes—
692#95C23×C4312yes—
693#95C23×C4312yes—
694#95C23×C4312yes—
695#95C23×C4312yes—
696#95C23×C4312yes—
697#95C23×C4312yes—
698#95C23×C4312yes—
699#95C23×C4312yes—
700#95C23×C4312yes—
701#95C23×C4312yes—
702#95C23×C4312yes—
703#95C23×C4312yes—
704#95C23×C4312yes—
705C24—22no—
706C24—22no—
707C24—41no—
708C24—41no—
709C24—41no—
710C24—41no—
711C24C22×C4×C4314yes—
712C24C24×C4312yes—
713C24C24×C4312yes—
714C24C24×C4311yescharacteristic
715C2×Q8—41no—
716C2×Q8—41no—
717C2×Q8C22×C4×C4314yes—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—41no—
726C2×D4C22×C4×C4318yes—
727C2×D4C22×C4×C4318yes—
728C2×D4C22×C4×C4318yes—
729C2×D4C22×C4×C4314yes—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—24no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—42no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—42no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—42no—
747C22×C4—41no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—41no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—41no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4C22×C4×C4314yes—
761C22×C4C22×C4×C4314yes—
762C22×C4C22×C4×C4318yes—
763C22×C4C24×C4311yescharacteristic
764C22×C4C24×C4312yes—
765C22×C4C24×C4312yes—
766C22×C4C24×C4312yes—
767C22×C4C24×C4312yes—
768C22×C4C24×C4312yes—
769C22×C4C24×C4312yes—
770C22×C4C24×C4311yescharacteristic
771C22×C4C24×C4312yes—
772C22×C4C24×C4312yes—
773C22×C4C24×C4311yescharacteristic
774C22×C4C24×C4311yescharacteristic
775C22×C4C24×C4312yes—
776C22×C4C24×C4312yes—
777C22×C4C24×C4311yescharacteristic
778C22×C4C24×C4311yescharacteristic
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—42no—
782C4⋊C4—42no—
783C4⋊C4—42no—
784C4⋊C4—41no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4—42no—
788C4⋊C4—41no—
789C4⋊C4—42no—
790C4⋊C4—42no—
791C4⋊C4—41no—
792C4⋊C4—41no—
793C4⋊C4C22×C4×C4318yes—
794C4⋊C4C22×C4×C4318yes—
795C4⋊C4C22×C4×C4314yes—
796C4⋊C4C22×C4×C4314yes—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—24no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4—42no—
808C22⋊C4—42no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4C22×C4×C4318yes—
812C22⋊C4C22×C4×C4318yes—
813C22⋊C4C22×C4×C4318yes—
814C22⋊C4C22×C4×C4318yes—
815C22⋊C4C22×C4×C4318yes—
816C22⋊C4C22×C4×C4318yes—
817C22⋊C4C22×C4×C4318yes—
818C42—22no—
819C42—22no—
820C42—24no—
821C42—41no—
822C42—41no—
823C42—42no—
824C42—42no—
825C42—42no—
826C42—42no—
827C42—42no—
828C42C22×C4×C4318yes—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—28no—
846C23—44no—
847C23—44no—
848C23—82no—
849C23—82no—
850C23—82no—
851C23—82no—
852C23C23×C4×C4314yes—
853C23C23×C4×C4314yes—
854C23C23×C4×C4312yes—
855C23H(5,𝔽2)×C4312yes—
856C232−1+4×C4312yes—
857C23C25×C4311yescharacteristic
858Q8—44no—
859D4—216no—
860D4—48no—
861D4—44no—
862D4—48no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—21no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—48no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—84no—
909C2×C4—82no—
910C2×C4—82no—
911C2×C4—84no—
912C2×C4—84no—
913C2×C4—84no—
914C2×C4C23×C4×C4314yes—
915C2×C4C23×C4×C4314yes—
916C2×C4C23×C4×C4314yes—
917C2×C4C23×C4×C4312yes—
918C2×C4C23×C4×C4312yes—
919C2×C4C23×C4×C4314yes—
920C2×C4H(5,𝔽2)×C4312yes—
921C2×C4H(5,𝔽2)×C4312yes—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—88no—
943C22C43×#52014yes—
944C22C24×C4×C4311yescharacteristic
945C22C2×H(5,𝔽2)×C4311yescharacteristic
946C22C2×H(5,𝔽2)×C4311yescharacteristic
947C22C2×H(5,𝔽2)×C4311yescharacteristic
948C22C2×2−1+4×C4311yescharacteristic
949C22C43×#58511yescharacteristic
950C22C43×#58511yescharacteristic
951C4—24no—
952C4—24no—
953C4—22no—
954C4—24no—
955C4—22no—
956C4—24no—
957C4—22no—
958C4—22no—
959C4—41no—
960C4—41no—
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C2—24no—
968C2—44no—
969C2—44no—
970C2C2×C43×#52011yescharacteristic
971C2C4×H(5,𝔽2)×C4311yescharacteristic
972C2C4×H(5,𝔽2)×C4311yescharacteristic
973C2C43×#353511yescharacteristic
974C2C43×#353711yescharacteristic
975C2C43×#356011yescharacteristic
976C2C43×#356111yescharacteristic
subgroupG/H
center, socleC23×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC23C25×C43
prime radicalC2×C43×#538C2
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×#2377C2semidirect
4. C43×#2373C2semidirect
5. C43×#2361C2semidirect
6. C43×#2358C2semidirect
7. C43×#2358C2semidirect
8. C43×#2353C2semidirect
9. D4×C4⋊C4×C43C2semidirect
10. C43×#2337C2semidirect
11. C43×#2335C2semidirect
12. C43×#2329C2semidirect
13. C43×#2326C2semidirect
14. C43×#2325C2semidirect
15. C43×#2322C2semidirect
16. C43×#2315C2semidirect
17. C4×C22⋊Q8×C43C2semidirect
18. C4×#121×C43C2semidirect
19. C2×C43×#388C2semidirect
20. C43×#538C4semidirect
28. C2×C4×Q8×C43C22semidirect
34. C2×C4×D4×C43C22semidirect
36. C22×C4⋊C4×C43C22semidirect
42. C43×#391C22semidirect
43. C43×#391C22semidirect
46. C43×#390C22semidirect
47. C43×#389C22semidirect
48. C43×#389C22semidirect
49. C43×#389C22semidirect
50. C43×#389C22semidirect
51. C43×#389C22semidirect
60. C43×#388C22semidirect
61. C43×#388C22semidirect
62. C43×#388C22semidirect
63. C43×#388C22semidirect
64. C43×#387C22semidirect
65. C43×#387C22semidirect
66. C43×#387C22semidirect
67. C43×#387C22semidirect
68. C43×#387C22semidirect
69. C43×#387C22semidirect
76. C43×#386C22semidirect
85. C43×#385C22semidirect
86. C43×#385C22semidirect
87. C43×#385C22semidirect
88. C43×#384C22semidirect
89. C43×#383C22semidirect
90. C43×#381C22semidirect
94. C43×#380C22semidirect
95. C4×C4⋊C4×C43C22semidirect
96. C4×C4⋊C4×C43C22semidirect
97. C4×C4⋊C4×C43C22semidirect
98. C4×C4⋊C4×C43C22semidirect
103. C4×C22⋊C4×C43C22semidirect
104. C4×C22⋊C4×C43C22semidirect
105. C43×#376C22semidirect
125. #126×C43C2×C4semidirect
126. #124×C43C2×C4semidirect
127. #123×C43C2×C4semidirect
128. C22⋊Q8×C43C2×C4semidirect
129. #121×C43C2×C4semidirect
130. #121×C43C2×C4semidirect
131. #120×C43C2×C4semidirect
138. C4×D4×C43C2×C4semidirect
162. C2×C22⋊C4×C43C2×C4semidirect
433. #34426C43direct (N × H)
480. #2383C2×C43semidirect
481. #2377C2×C43semidirect
482. #2373C2×C43semidirect
483. #2361C2×C43semidirect
484. #2358C2×C43semidirect
485. #2358C2×C43semidirect
486. #2353C2×C43semidirect
487. D4×C4⋊C4C2×C43semidirect
488. #2337C2×C43semidirect
489. #2335C2×C43semidirect
490. #2329C2×C43semidirect
491. #2326C2×C43semidirect
492. #2325C2×C43semidirect
493. #2322C2×C43semidirect
494. #2315C2×C43semidirect
495. C4×C22⋊Q8C2×C43semidirect
496. C4×#121C2×C43semidirect
497. C2×#388C2×C43semidirect
508. #538C4×C43semidirect
516. C2×C4×Q8C22×C43semidirect
522. C2×C4×D4C22×C43semidirect
524. C22×C4⋊C4C22×C43semidirect
530. #391C22×C43semidirect
531. #391C22×C43semidirect
534. #390C22×C43semidirect
535. #389C22×C43semidirect
536. #389C22×C43semidirect
537. #389C22×C43semidirect
538. #389C22×C43semidirect
539. #389C22×C43semidirect
548. #388C22×C43semidirect
549. #388C22×C43semidirect
550. #388C22×C43semidirect
551. #388C22×C43semidirect
552. #387C22×C43semidirect
553. #387C22×C43semidirect
554. #387C22×C43semidirect
555. #387C22×C43semidirect
556. #387C22×C43semidirect
557. #387C22×C43semidirect
564. #386C22×C43semidirect
573. #385C22×C43semidirect
574. #385C22×C43semidirect
575. #385C22×C43semidirect
576. #384C22×C43semidirect
577. #383C22×C43semidirect
578. #381C22×C43semidirect
582. #380C22×C43semidirect
583. C4×C4⋊C4C22×C43semidirect
584. C4×C4⋊C4C22×C43semidirect
585. C4×C4⋊C4C22×C43semidirect
586. C4×C4⋊C4C22×C43semidirect
591. C4×C22⋊C4C22×C43semidirect
592. C4×C22⋊C4C22×C43semidirect
593. #376C22×C43semidirect
596. C43#34426direct (N × H)
614. #126C2×C4×C43semidirect
615. #124C2×C4×C43semidirect
616. #123C2×C4×C43semidirect
617. C22⋊Q8C2×C4×C43semidirect
618. #121C2×C4×C43semidirect
619. #121C2×C4×C43semidirect
620. #120C2×C4×C43semidirect
627. C4×D4C2×C4×C43semidirect
651. C2×C22⋊C4C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5382
C43×#23832
C43×#23772
C43×#23732
C43×#23612
C43×#23582
C43×#23532
D4×C4⋊C4×C432
C43×#23372
C43×#23352
C43×#23292
C43×#23262
C43×#23252
C43×#23222
C43×#23152
C4×C22⋊Q8×C432
C4×#121×C432
C2×C43×#3882
#3442643