Finite Group Databasebeta

← C43×#34511 #24954528

Subgroups — C43×#34511 #24954528

Order 11008.

2544 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#560C211yesmaximal, characteristic
2C43×#2375C211yesmaximal, characteristic, complemented
3C43×#2375C212yesmaximal, complemented
4C43×#2374C211yesmaximal, characteristic, complemented
5C43×#2373C212yesmaximal, complemented
6C43×#2366C211yesmaximal, characteristic, complemented
7C43×#2364C212yesmaximal, complemented
8C43×#2363C212yesmaximal, complemented
9C43×#2361C212yesmaximal, complemented
10C43×#2359C212yesmaximal, complemented
11C43×#2335C212yesmaximal, complemented
12C43×#2334C212yesmaximal, complemented
13C43×#2333C212yesmaximal, complemented
14C43×#2328C211yesmaximal, characteristic, complemented
15C43×#2325C212yesmaximal, complemented
16C43×#2324C212yesmaximal, complemented
17C43×#2322C211yesmaximal, characteristic, complemented
18C4×#120×C43C211yesmaximal, characteristic, complemented
19C4×#120×C43C212yesmaximal, complemented
20C24×C4×C43C2211yescharacteristic
21C43×#560C4116yescomplemented
22C2×#127×C43C2211yescharacteristic
23C2×#126×C43C2212yes—
24C2×#123×C43C2211yescharacteristic
25C2×#123×C43C2212yes—
26C2×#121×C43C2212yes—
27C2×#121×C43C2212yes—
28C2×#121×C43C2212yes—
29C2×#120×C43C2211yescharacteristic
30C2×#120×C43C2212yes—
31C2×C4×D4×C43C2211yescharacteristic
32C2×C4×D4×C43C2212yes—
33C2×C4×D4×C43C2212yes—
34C2×C4×D4×C43C2212yes—
35C2×C4×D4×C43C2212yes—
36C2×C4×D4×C43C2212yescomplemented
37C2×C4×D4×C43C2211yescharacteristic, complemented
38C2×#117×C43C2212yescomplemented
39C22×C4⋊C4×C43C2211yescharacteristic, complemented
40C43×#390C2212yes—
41C43×#390C2212yes—
42C43×#390C2211yescharacteristic
43C43×#390C2212yes—
44C43×#390C2212yes—
45C43×#390C2211yescharacteristic, complemented
46C43×#390C2212yescomplemented
47C43×#389C2212yescomplemented
48C43×#389C2212yescomplemented
49C43×#389C2212yescomplemented
50C43×#388C2212yes—
51C43×#388C2212yes—
52C43×#388C2212yes—
53C43×#388C2212yes—
54C43×#388C2212yes—
55C43×#388C2212yes—
56C43×#388C2212yes—
57C43×#388C2212yes—
58C43×#388C2212yes—
59C43×#388C2212yescomplemented
60C43×#388C2212yescomplemented
61C43×#388C2212yescomplemented
62C43×#387C2212yescomplemented
63C43×#387C2212yescomplemented
64C43×#387C2212yescomplemented
65C43×#387C2212yescomplemented
66C43×#387C2212yescomplemented
67C43×#387C2212yescomplemented
68C43×#386C2211yescharacteristic
69C43×#386C2212yes—
70C43×#386C2212yes—
71C43×#386C2212yes—
72C43×#386C2212yes—
73C43×#386C2212yes—
74C43×#386C2212yes—
75C43×#386C2212yes—
76C43×#386C2212yes—
77C43×#386C2211yescharacteristic
78C43×#386C2212yescomplemented
79C43×#386C2212yescomplemented
80C43×#386C2212yescomplemented
81C43×#385C2212yes—
82C43×#385C2212yes—
83C43×#385C2212yes—
84C43×#385C2211yescharacteristic
85C43×#385C2212yes—
86C43×#385C2211yescharacteristic, complemented
87C43×#385C2212yescomplemented
88C43×#382C2211yescharacteristic, complemented
89C43×#381C2211yescharacteristic, complemented
90C43×#380C2212yescomplemented
91C43×#379C2212yes—
92C43×#379C2211yescharacteristic
93C4×C4⋊C4×C43C2212yescomplemented
94C4×C4⋊C4×C43C2212yescomplemented
95C4×C4⋊C4×C43C2212yescomplemented
96C4×C4⋊C4×C43C2212yescomplemented
97C4×C22⋊C4×C43C2212yes—
98C4×C22⋊C4×C43C2211yescharacteristic
99C4×C22⋊C4×C43C2212yes—
100C4×C22⋊C4×C43C2212yes—
101C4×C22⋊C4×C43C2212yes—
102C4×C22⋊C4×C43C2211yescharacteristic, complemented
103C4×C22⋊C4×C43C2212yescomplemented
104C4×C22⋊C4×C43C2212yescomplemented
105C4×C22⋊C4×C43C2212yescomplemented
106C43×#376C2211yescharacteristic, complemented
107C2×#95×C43C2212yescomplemented
108C25×C43C2311yescharacteristic
109C22×D4×C43C2312yes—
110C22×D4×C43C2312yes—
111C22×D4×C43C2312yes—
112C22×D4×C43C2311yescharacteristic
113C22×D4×C43C2312yes—
114C22×D4×C43C2312yes—
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—44no—
117C23×C4×C43—42no—
118C23×C4×C43C2311yescharacteristic
119C23×C4×C43C2312yes—
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2312yes—
122C23×C4×C43C2311yescharacteristic
123C23×C4×C43C2312yes—
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2312yes—
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2312yes—
128#127×C43C2×C418yescomplemented
129#126×C43C2×C4116yescomplemented
130#123×C43C2×C418yescomplemented
131#123×C43C2×C4116yescomplemented
132#121×C43C2×C4116yescomplemented
133#121×C43C2×C4116yescomplemented
134#121×C43C2×C4116yescomplemented
135#120×C43C2×C418yescomplemented
136#120×C43C2×C4116yescomplemented
137C4×D4×C43—42no—
138C4×D4×C43—44no—
139C4×D4×C43—42no—
140C4×D4×C43—44no—
141C4×D4×C43—44no—
142C4×D4×C43—44no—
143C4×D4×C43—44no—
144#117×C43—44no—
145C2×C4⋊C4×C43—42no—
146C2×C4⋊C4×C43C2312yes—
147C2×C4⋊C4×C43C2312yes—
148C2×C4⋊C4×C43C2312yes—
149C2×C4⋊C4×C43C2312yes—
150C2×C4⋊C4×C43C2312yes—
151C2×C4⋊C4×C43C2312yes—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2312yes—
155C2×C4⋊C4×C43C2312yes—
156C2×C4⋊C4×C43C2312yes—
157C2×C4⋊C4×C43C2312yes—
158C2×C4⋊C4×C43C2312yes—
159C2×C22⋊C4×C43C2312yes—
160C2×C22⋊C4×C43C2312yes—
161C2×C22⋊C4×C43C2312yes—
162C2×C22⋊C4×C43C2312yes—
163C2×C22⋊C4×C43C2311yescharacteristic
164C2×C22⋊C4×C43C2312yes—
165C2×C22⋊C4×C43C2312yes—
166C2×C22⋊C4×C43C2312yes—
167C2×C22⋊C4×C43C2312yes—
168C2×C22⋊C4×C43C2312yes—
169C2×C22⋊C4×C43C2311yescharacteristic
170C2×C22⋊C4×C43C2312yes—
171C2×C22⋊C4×C43C2312yes—
172C2×C22⋊C4×C43C2312yes—
173C2×C22⋊C4×C43C2312yes—
174C2×C22⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43C2312yes—
176C2×C22⋊C4×C43C2311yescharacteristic
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×C43C2311yescharacteristic
184C2×C22⋊C4×C43C2312yes—
185C2×C22⋊C4×C43C2311yescharacteristic
186C2×C42×C43C2312yes—
187C2×C42×C43C2311yescharacteristic
188C2×C42×C43C2312yes—
189C2×C42×C43C2312yes—
190C2×C42×C43C2312yes—
191C2×C42×C43C2312yes—
192C2×C42×C43C2312yes—
193C2×C42×C43C2311yescharacteristic
194C2×C42×C43C2312yes—
195C2×C42×C43C2312yes—
196C2×C42×C43C2311yescharacteristic
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—
215C24×C43—42no—
216C24×C43—41no—
217C24×C43—41no—
218C24×C43—42no—
219C24×C43C22×C414yes—
220C24×C43C2411yescharacteristic
221C24×C43C2412yes—
222C24×C43C2412yes—
223C24×C43C2411yescharacteristic
224C2×D4×C43—42no—
225C2×D4×C43—41no—
226C2×D4×C43—42no—
227C2×D4×C43—42no—
228C2×D4×C43—42no—
229C2×D4×C43—42no—
230C2×D4×C43—41no—
231C2×D4×C43—41no—
232C2×D4×C43—41no—
233C2×D4×C43—42no—
234C2×D4×C43—42no—
235C2×D4×C43—42no—
236C2×D4×C43—42no—
237C2×D4×C43—42no—
238C2×D4×C43C22×C418yes—
239C2×D4×C43C22×C418yes—
240C2×D4×C43C22×C418yes—
241C2×D4×C43C22×C414yes—
242C2×D4×C43C22×C418yes—
243C2×D4×C43C22×C414yescomplemented
244C2×D4×C43C22×C418yescomplemented
245C22×C4×C43—24no—
246C22×C4×C43—24no—
247C22×C4×C43—24no—
248C22×C4×C43—24no—
249C22×C4×C43—22no—
250C22×C4×C43—22no—
251C22×C4×C43—24no—
252C22×C4×C43—41no—
253C22×C4×C43—42no—
254C22×C4×C43—42no—
255C22×C4×C43—41no—
256C22×C4×C43—42no—
257C22×C4×C43—42no—
258C22×C4×C43—42no—
259C22×C4×C43—41no—
260C22×C4×C43—42no—
261C22×C4×C43—41no—
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—42no—
269C22×C4×C43—416no—
270C22×C4×C43C22×C414yescomplemented
271C22×C4×C43C22×C418yescomplemented
272C22×C4×C43C2411yescharacteristic
273C22×C4×C43C2412yes—
274C22×C4×C43C2411yescharacteristic
275C22×C4×C43C2412yes—
276C22×C4×C43C2412yes—
277C22×C4×C43C2412yes—
278C22×C4×C43C2412yes—
279C22×C4×C43C2411yescharacteristic
280C22×C4×C43C2411yescharacteristic
281C22×C4×C43C2412yes—
282C22×C4×C43C2412yes—
283C22×C4×C43C2412yes—
284C22×C4×C43C2412yes—
285C22×C4×C43C2412yes—
286C22×C4×C43C2411yescharacteristic
287C4⋊C4×C43—24no—
288C4⋊C4×C43—24no—
289C4⋊C4×C43—24no—
290C4⋊C4×C43—42no—
291C4⋊C4×C43—42no—
292C4⋊C4×C43—42no—
293C4⋊C4×C43—42no—
294C4⋊C4×C43—42no—
295C4⋊C4×C43—41no—
296C4⋊C4×C43—41no—
297C4⋊C4×C43C22×C418yescomplemented
298C4⋊C4×C43C22×C418yescomplemented
299C4⋊C4×C43C22×C418yescomplemented
300C22⋊C4×C43—24no—
301C22⋊C4×C43—24no—
302C22⋊C4×C43—24no—
303C22⋊C4×C43—41no—
304C22⋊C4×C43—42no—
305C22⋊C4×C43—42no—
306C22⋊C4×C43—42no—
307C22⋊C4×C43—41no—
308C22⋊C4×C43—42no—
309C22⋊C4×C43—42no—
310C22⋊C4×C43—42no—
311C22⋊C4×C43—42no—
312C22⋊C4×C43—42no—
313C22⋊C4×C43—42no—
314C22⋊C4×C43—41no—
315C22⋊C4×C43—42no—
316C22⋊C4×C43—41no—
317C22⋊C4×C43—42no—
318C22⋊C4×C43—42no—
319C22⋊C4×C43—42no—
320C22⋊C4×C43C22×C418yes—
321C22⋊C4×C43C22×C418yes—
322C22⋊C4×C43C22×C418yes—
323C22⋊C4×C43C22×C418yes—
324C22⋊C4×C43C22×C414yes—
325C22⋊C4×C43C22×C418yescomplemented
326C22⋊C4×C43C22×C414yescomplemented
327C42×C43—24no—
328C42×C43—22no—
329C42×C43—42no—
330C42×C43—42no—
331C42×C43—41no—
332C42×C43—42no—
333C42×C43—42no—
334C42×C43—42no—
335C42×C43—42no—
336C42×C43—42no—
337C42×C43C22×C414yescomplemented
338C23×C43—22no—
339C23×C43—22no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—21no—
343C23×C43—22no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—21no—
347C23×C43—22no—
348C23×C43—21no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—21no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—48no—
359C23×C43—44no—
360C23×C43—44no—
361C23×C43—48no—
362C23×C43—44no—
363C23×C43C23×C414yes—
364C23×C43C23×C412yes—
365C23×C43C23×C414yes—
366C23×C43C23×C412yes—
367C23×C43C2511yescharacteristic
368D4×C43—48no—
369D4×C43—48no—
370D4×C43—48no—
371D4×C43—44no—
372D4×C43—48no—
373D4×C43—44no—
374D4×C43—48no—
375C2×C4×C43—22no—
376C2×C4×C43—21no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—21no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—21no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—21no—
398C2×C4×C43—22no—
399C2×C4×C43—21no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—44no—
410C2×C4×C43—48no—
411C2×C4×C43—48no—
412C2×C4×C43—44no—
413C2×C4×C43—44no—
414C2×C4×C43—48no—
415C2×C4×C43—82no—
416C2×C4×C43—84no—
417C2×C4×C43—82no—
418C2×C4×C43—84no—
419C2×C4×C43C23×C412yes—
420C2×C4×C43C23×C414yes—
421C2×C4×C43C23×C414yes—
422C2×C4×C43C23×C414yes—
423C2×C4×C43C23×C414yes—
424C2×C4×C43H(5,𝔽2)14yes—
425C2×C4×C43H(5,𝔽2)12yes—
426#34511C4311yesmaximal, characteristic, direct product factor, Sylow
427C22×C43—24no—
428C22×C43—24no—
429C22×C43—24no—
430C22×C43—24no—
431C22×C43—22no—
432C22×C43—24no—
433C22×C43—22no—
434C22×C43—24no—
435C22×C43—24no—
436C22×C43—24no—
437C22×C43—416no—
438C22×C43—42no—
439C22×C43—41no—
440C22×C43—42no—
441C22×C43—41no—
442C22×C43—42no—
443C22×C43—42no—
444C22×C43—42no—
445C22×C43—42no—
446C22×C43—42no—
447C22×C43—42no—
448C22×C43—41no—
449C22×C43—41no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43C24×C411yescharacteristic
453C22×C43C2×H(5,𝔽2)12yes—
454C22×C43C2×H(5,𝔽2)11yescharacteristic
455C22×C43#58511yescharacteristic
456C22×C43#58512yes—
457C4×C43—24no—
458C4×C43—24no—
459C4×C43—24no—
460C4×C43—22no—
461C4×C43—24no—
462C4×C43—22no—
463C4×C43—24no—
464C4×C43—41no—
465C4×C43—41no—
466C4×C43—42no—
467C4×C43—42no—
468C4×C43—42no—
469C4×C43—42no—
470C4×C43—42no—
471C4×C43—41no—
472C2×#560C2×C4311yescharacteristic
473#2375C2×C4311yescharacteristic, complemented
474#2375C2×C4312yescomplemented
475#2374C2×C4311yescharacteristic, complemented
476#2373C2×C4312yescomplemented
477#2366C2×C4311yescharacteristic, complemented
478#2364C2×C4312yescomplemented
479#2363C2×C4312yescomplemented
480#2361C2×C4312yescomplemented
481#2359C2×C4312yescomplemented
482#2335C2×C4312yescomplemented
483#2334C2×C4312yescomplemented
484#2333C2×C4312yescomplemented
485#2328C2×C4311yescharacteristic, complemented
486#2325C2×C4312yescomplemented
487#2324C2×C4312yescomplemented
488#2322C2×C4311yescharacteristic, complemented
489C4×#120C2×C4311yescharacteristic, complemented
490C4×#120C2×C4312yescomplemented
491C2×C43—44no—
492C2×C43—42no—
493C2×C43—44no—
494C2×C43—42no—
495C2×C43C4×H(5,𝔽2)12yes—
496C2×C43C4×H(5,𝔽2)11yescharacteristic
497C2×C43#353211yescharacteristic
498C2×C43#353912yes—
499C2×C43#354011yescharacteristic
500C24×C4C22×C4311yescharacteristic
501#560C4×C43116yescomplemented
502C2×#127C22×C4311yescharacteristic
503C2×#126C22×C4312yes—
504C2×#123C22×C4311yescharacteristic
505C2×#123C22×C4312yes—
506C2×#121C22×C4312yes—
507C2×#121C22×C4312yes—
508C2×#121C22×C4312yes—
509C2×#120C22×C4311yescharacteristic
510C2×#120C22×C4312yes—
511C2×C4×D4C22×C4311yescharacteristic
512C2×C4×D4C22×C4312yes—
513C2×C4×D4C22×C4312yes—
514C2×C4×D4C22×C4312yes—
515C2×C4×D4C22×C4312yes—
516C2×C4×D4C22×C4312yescomplemented
517C2×C4×D4C22×C4311yescharacteristic, complemented
518C2×#117C22×C4312yescomplemented
519C22×C4⋊C4C22×C4311yescharacteristic, complemented
520#390C22×C4312yes—
521#390C22×C4312yes—
522#390C22×C4311yescharacteristic
523#390C22×C4312yes—
524#390C22×C4312yes—
525#390C22×C4311yescharacteristic, complemented
526#390C22×C4312yescomplemented
527#389C22×C4312yescomplemented
528#389C22×C4312yescomplemented
529#389C22×C4312yescomplemented
530#388C22×C4312yes—
531#388C22×C4312yes—
532#388C22×C4312yes—
533#388C22×C4312yes—
534#388C22×C4312yes—
535#388C22×C4312yes—
536#388C22×C4312yes—
537#388C22×C4312yes—
538#388C22×C4312yes—
539#388C22×C4312yescomplemented
540#388C22×C4312yescomplemented
541#388C22×C4312yescomplemented
542#387C22×C4312yescomplemented
543#387C22×C4312yescomplemented
544#387C22×C4312yescomplemented
545#387C22×C4312yescomplemented
546#387C22×C4312yescomplemented
547#387C22×C4312yescomplemented
548#386C22×C4311yescharacteristic
549#386C22×C4312yes—
550#386C22×C4312yes—
551#386C22×C4312yes—
552#386C22×C4312yes—
553#386C22×C4312yes—
554#386C22×C4312yes—
555#386C22×C4312yes—
556#386C22×C4312yes—
557#386C22×C4311yescharacteristic
558#386C22×C4312yescomplemented
559#386C22×C4312yescomplemented
560#386C22×C4312yescomplemented
561#385C22×C4312yes—
562#385C22×C4312yes—
563#385C22×C4312yes—
564#385C22×C4311yescharacteristic
565#385C22×C4312yes—
566#385C22×C4311yescharacteristic, complemented
567#385C22×C4312yescomplemented
568#382C22×C4311yescharacteristic, complemented
569#381C22×C4311yescharacteristic, complemented
570#380C22×C4312yescomplemented
571#379C22×C4312yes—
572#379C22×C4311yescharacteristic
573C4×C4⋊C4C22×C4312yescomplemented
574C4×C4⋊C4C22×C4312yescomplemented
575C4×C4⋊C4C22×C4312yescomplemented
576C4×C4⋊C4C22×C4312yescomplemented
577C4×C22⋊C4C22×C4312yes—
578C4×C22⋊C4C22×C4311yescharacteristic
579C4×C22⋊C4C22×C4312yes—
580C4×C22⋊C4C22×C4312yes—
581C4×C22⋊C4C22×C4312yes—
582C4×C22⋊C4C22×C4311yescharacteristic, complemented
583C4×C22⋊C4C22×C4312yescomplemented
584C4×C22⋊C4C22×C4312yescomplemented
585C4×C22⋊C4C22×C4312yescomplemented
586#376C22×C4311yescharacteristic, complemented
587C2×#95C22×C4312yescomplemented
588C43#3451111yescharacteristic, direct product factor, Sylow
589C25C23×C4311yescharacteristic
590C22×D4C23×C4312yes—
591C22×D4C23×C4312yes—
592C22×D4C23×C4312yes—
593C22×D4C23×C4311yescharacteristic
594C22×D4C23×C4312yes—
595C22×D4C23×C4312yes—
596C22×D4C23×C4311yescharacteristic
597C23×C4—44no—
598C23×C4—42no—
599C23×C4C23×C4311yescharacteristic
600C23×C4C23×C4312yes—
601C23×C4C23×C4311yescharacteristic
602C23×C4C23×C4312yes—
603C23×C4C23×C4311yescharacteristic
604C23×C4C23×C4312yes—
605C23×C4C23×C4311yescharacteristic
606C23×C4C23×C4312yes—
607C23×C4C23×C4311yescharacteristic
608C23×C4C23×C4312yes—
609#127C2×C4×C4318yescomplemented
610#126C2×C4×C43116yescomplemented
611#123C2×C4×C4318yescomplemented
612#123C2×C4×C43116yescomplemented
613#121C2×C4×C43116yescomplemented
614#121C2×C4×C43116yescomplemented
615#121C2×C4×C43116yescomplemented
616#120C2×C4×C4318yescomplemented
617#120C2×C4×C43116yescomplemented
618C4×D4—42no—
619C4×D4—44no—
620C4×D4—42no—
621C4×D4—44no—
622C4×D4—44no—
623C4×D4—44no—
624C4×D4—44no—
625#117—44no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4C23×C4312yes—
628C2×C4⋊C4C23×C4312yes—
629C2×C4⋊C4C23×C4312yes—
630C2×C4⋊C4C23×C4312yes—
631C2×C4⋊C4C23×C4312yes—
632C2×C4⋊C4C23×C4312yes—
633C2×C4⋊C4C23×C4311yescharacteristic
634C2×C4⋊C4C23×C4311yescharacteristic
635C2×C4⋊C4C23×C4312yes—
636C2×C4⋊C4C23×C4312yes—
637C2×C4⋊C4C23×C4312yes—
638C2×C4⋊C4C23×C4312yes—
639C2×C4⋊C4C23×C4312yes—
640C2×C22⋊C4C23×C4312yes—
641C2×C22⋊C4C23×C4312yes—
642C2×C22⋊C4C23×C4312yes—
643C2×C22⋊C4C23×C4312yes—
644C2×C22⋊C4C23×C4311yescharacteristic
645C2×C22⋊C4C23×C4312yes—
646C2×C22⋊C4C23×C4312yes—
647C2×C22⋊C4C23×C4312yes—
648C2×C22⋊C4C23×C4312yes—
649C2×C22⋊C4C23×C4312yes—
650C2×C22⋊C4C23×C4311yescharacteristic
651C2×C22⋊C4C23×C4312yes—
652C2×C22⋊C4C23×C4312yes—
653C2×C22⋊C4C23×C4312yes—
654C2×C22⋊C4C23×C4312yes—
655C2×C22⋊C4C23×C4311yescharacteristic
656C2×C22⋊C4C23×C4312yes—
657C2×C22⋊C4C23×C4311yescharacteristic
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×C4311yescharacteristic
665C2×C22⋊C4C23×C4312yes—
666C2×C22⋊C4C23×C4311yescharacteristic
667C2×C42C23×C4312yes—
668C2×C42C23×C4311yescharacteristic
669C2×C42C23×C4312yes—
670C2×C42C23×C4312yes—
671C2×C42C23×C4312yes—
672C2×C42C23×C4312yes—
673C2×C42C23×C4312yes—
674C2×C42C23×C4311yescharacteristic
675C2×C42C23×C4312yes—
676C2×C42C23×C4312yes—
677C2×C42C23×C4311yescharacteristic
678#95C23×C4312yes—
679#95C23×C4312yes—
680#95C23×C4312yes—
681#95C23×C4312yes—
682#95C23×C4312yes—
683#95C23×C4312yes—
684#95C23×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—
696C24—42no—
697C24—41no—
698C24—41no—
699C24—42no—
700C24C22×C4×C4314yes—
701C24C24×C4311yescharacteristic
702C24C24×C4312yes—
703C24C24×C4312yes—
704C24C24×C4311yescharacteristic
705C2×D4—42no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4C22×C4×C4318yes—
720C2×D4C22×C4×C4318yes—
721C2×D4C22×C4×C4318yes—
722C2×D4C22×C4×C4314yes—
723C2×D4C22×C4×C4318yes—
724C2×D4C22×C4×C4314yescomplemented
725C2×D4C22×C4×C4318yescomplemented
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—24no—
733C22×C4—41no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—41no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—41no—
741C22×C4—42no—
742C22×C4—41no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—416no—
751C22×C4C22×C4×C4314yescomplemented
752C22×C4C22×C4×C4318yescomplemented
753C22×C4C24×C4311yescharacteristic
754C22×C4C24×C4312yes—
755C22×C4C24×C4311yescharacteristic
756C22×C4C24×C4312yes—
757C22×C4C24×C4312yes—
758C22×C4C24×C4312yes—
759C22×C4C24×C4312yes—
760C22×C4C24×C4311yescharacteristic
761C22×C4C24×C4311yescharacteristic
762C22×C4C24×C4312yes—
763C22×C4C24×C4312yes—
764C22×C4C24×C4312yes—
765C22×C4C24×C4312yes—
766C22×C4C24×C4312yes—
767C22×C4C24×C4311yescharacteristic
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—42no—
772C4⋊C4—42no—
773C4⋊C4—42no—
774C4⋊C4—41no—
775C4⋊C4—41no—
776C4⋊C4—42no—
777C4⋊C4—42no—
778C4⋊C4C22×C4×C4318yescomplemented
779C4⋊C4C22×C4×C4318yescomplemented
780C4⋊C4C22×C4×C4318yescomplemented
781C22⋊C4—24no—
782C22⋊C4—24no—
783C22⋊C4—24no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—41no—
788C22⋊C4—41no—
789C22⋊C4—42no—
790C22⋊C4—42no—
791C22⋊C4—42no—
792C22⋊C4—42no—
793C22⋊C4—42no—
794C22⋊C4—41no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—41no—
799C22⋊C4—42no—
800C22⋊C4—42no—
801C22⋊C4C22×C4×C4318yes—
802C22⋊C4C22×C4×C4318yes—
803C22⋊C4C22×C4×C4318yes—
804C22⋊C4C22×C4×C4318yes—
805C22⋊C4C22×C4×C4314yes—
806C22⋊C4C22×C4×C4318yescomplemented
807C22⋊C4C22×C4×C4314yescomplemented
808C42—24no—
809C42—22no—
810C42—42no—
811C42—42no—
812C42—42no—
813C42—42no—
814C42—42no—
815C42—42no—
816C42—42no—
817C42—41no—
818C42C22×C4×C4314yescomplemented
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—21no—
828C23—22no—
829C23—21no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—21no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—48no—
840C23—44no—
841C23—44no—
842C23—48no—
843C23—44no—
844C23C23×C4×C4314yes—
845C23C23×C4×C4312yes—
846C23C23×C4×C4314yes—
847C23C23×C4×C4312yes—
848C23C25×C4311yescharacteristic
849D4—48no—
850D4—48no—
851D4—48no—
852D4—44no—
853D4—48no—
854D4—44no—
855D4—48no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—22no—
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—44no—
891C2×C4—48no—
892C2×C4—48no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—48no—
896C2×C4—84no—
897C2×C4—82no—
898C2×C4—82no—
899C2×C4—84no—
900C2×C4C23×C4×C4312yes—
901C2×C4C23×C4×C4314yes—
902C2×C4C23×C4×C4314yes—
903C2×C4C23×C4×C4314yes—
904C2×C4C23×C4×C4314yes—
905C2×C4H(5,𝔽2)×C4314yes—
906C2×C4H(5,𝔽2)×C4312yes—
907C22—24no—
908C22—22no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—22no—
917C22—416no—
918C22—42no—
919C22—41no—
920C22—41no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—41no—
930C22—42no—
931C22—41no—
932C22C24×C4×C4311yescharacteristic
933C22C2×H(5,𝔽2)×C4312yes—
934C22C2×H(5,𝔽2)×C4311yescharacteristic
935C22C43×#58511yescharacteristic
936C22C43×#58512yes—
937C4—24no—
938C4—24no—
939C4—24no—
940C4—22no—
941C4—24no—
942C4—22no—
943C4—24no—
944C4—41no—
945C4—42no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—42no—
950C4—41no—
951C4—42no—
952C2—44no—
953C2—42no—
954C2—42no—
955C2—44no—
956C2C4×H(5,𝔽2)×C4312yes—
957C2C4×H(5,𝔽2)×C4311yescharacteristic
958C2C43×#353211yescharacteristic
959C2C43×#353912yes—
960C2C43×#354011yescharacteristic
subgroupG/H
center, socleC23×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC23C25×C43
prime radicalC2×C43×#560C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2375C2semidirect
3. C43×#2375C2semidirect
4. C43×#2374C2semidirect
5. C43×#2373C2semidirect
6. C43×#2366C2semidirect
7. C43×#2364C2semidirect
8. C43×#2363C2semidirect
9. C43×#2361C2semidirect
10. C43×#2359C2semidirect
11. C43×#2335C2semidirect
12. C43×#2334C2semidirect
13. C43×#2333C2semidirect
14. C43×#2328C2semidirect
15. C43×#2325C2semidirect
16. C43×#2324C2semidirect
17. C43×#2322C2semidirect
18. C4×#120×C43C2semidirect
19. C4×#120×C43C2semidirect
21. C43×#560C4semidirect
36. C2×C4×D4×C43C22semidirect
37. C2×C4×D4×C43C22semidirect
38. C2×#117×C43C22semidirect
39. C22×C4⋊C4×C43C22semidirect
45. C43×#390C22semidirect
46. C43×#390C22semidirect
47. C43×#389C22semidirect
48. C43×#389C22semidirect
49. C43×#389C22semidirect
59. C43×#388C22semidirect
60. C43×#388C22semidirect
61. C43×#388C22semidirect
62. C43×#387C22semidirect
63. C43×#387C22semidirect
64. C43×#387C22semidirect
65. C43×#387C22semidirect
66. C43×#387C22semidirect
67. C43×#387C22semidirect
78. C43×#386C22semidirect
79. C43×#386C22semidirect
80. C43×#386C22semidirect
86. C43×#385C22semidirect
87. C43×#385C22semidirect
88. C43×#382C22semidirect
89. C43×#381C22semidirect
90. C43×#380C22semidirect
93. C4×C4⋊C4×C43C22semidirect
94. C4×C4⋊C4×C43C22semidirect
95. C4×C4⋊C4×C43C22semidirect
96. C4×C4⋊C4×C43C22semidirect
102. C4×C22⋊C4×C43C22semidirect
103. C4×C22⋊C4×C43C22semidirect
104. C4×C22⋊C4×C43C22semidirect
105. C4×C22⋊C4×C43C22semidirect
106. C43×#376C22semidirect
107. C2×#95×C43C22semidirect
128. #127×C43C2×C4semidirect
129. #126×C43C2×C4semidirect
130. #123×C43C2×C4semidirect
131. #123×C43C2×C4semidirect
132. #121×C43C2×C4semidirect
133. #121×C43C2×C4semidirect
134. #121×C43C2×C4semidirect
135. #120×C43C2×C4semidirect
136. #120×C43C2×C4semidirect
243. C2×D4×C43C22×C4semidirect
244. C2×D4×C43C22×C4semidirect
270. C22×C4×C43C22×C4semidirect
271. C22×C4×C43C22×C4semidirect
297. C4⋊C4×C43C22×C4semidirect
298. C4⋊C4×C43C22×C4semidirect
299. C4⋊C4×C43C22×C4semidirect
325. C22⋊C4×C43C22×C4semidirect
326. C22⋊C4×C43C22×C4semidirect
337. C42×C43C22×C4semidirect
426. #34511C43direct (N × H)
473. #2375C2×C43semidirect
474. #2375C2×C43semidirect
475. #2374C2×C43semidirect
476. #2373C2×C43semidirect
477. #2366C2×C43semidirect
478. #2364C2×C43semidirect
479. #2363C2×C43semidirect
480. #2361C2×C43semidirect
481. #2359C2×C43semidirect
482. #2335C2×C43semidirect
483. #2334C2×C43semidirect
484. #2333C2×C43semidirect
485. #2328C2×C43semidirect
486. #2325C2×C43semidirect
487. #2324C2×C43semidirect
488. #2322C2×C43semidirect
489. C4×#120C2×C43semidirect
490. C4×#120C2×C43semidirect
501. #560C4×C43semidirect
516. C2×C4×D4C22×C43semidirect
517. C2×C4×D4C22×C43semidirect
518. C2×#117C22×C43semidirect
519. C22×C4⋊C4C22×C43semidirect
525. #390C22×C43semidirect
526. #390C22×C43semidirect
527. #389C22×C43semidirect
528. #389C22×C43semidirect
529. #389C22×C43semidirect
539. #388C22×C43semidirect
540. #388C22×C43semidirect
541. #388C22×C43semidirect
542. #387C22×C43semidirect
543. #387C22×C43semidirect
544. #387C22×C43semidirect
545. #387C22×C43semidirect
546. #387C22×C43semidirect
547. #387C22×C43semidirect
558. #386C22×C43semidirect
559. #386C22×C43semidirect
560. #386C22×C43semidirect
566. #385C22×C43semidirect
567. #385C22×C43semidirect
568. #382C22×C43semidirect
569. #381C22×C43semidirect
570. #380C22×C43semidirect
573. C4×C4⋊C4C22×C43semidirect
574. C4×C4⋊C4C22×C43semidirect
575. C4×C4⋊C4C22×C43semidirect
576. C4×C4⋊C4C22×C43semidirect
582. C4×C22⋊C4C22×C43semidirect
583. C4×C22⋊C4C22×C43semidirect
584. C4×C22⋊C4C22×C43semidirect
585. C4×C22⋊C4C22×C43semidirect
586. #376C22×C43semidirect
587. C2×#95C22×C43semidirect
588. C43#34511direct (N × H)
609. #127C2×C4×C43semidirect
610. #126C2×C4×C43semidirect
611. #123C2×C4×C43semidirect
612. #123C2×C4×C43semidirect
613. #121C2×C4×C43semidirect
614. #121C2×C4×C43semidirect
615. #121C2×C4×C43semidirect
616. #120C2×C4×C43semidirect
617. #120C2×C4×C43semidirect
724. C2×D4C22×C4×C43semidirect
725. C2×D4C22×C4×C43semidirect
751. C22×C4C22×C4×C43semidirect
752. C22×C4C22×C4×C43semidirect
778. C4⋊C4C22×C4×C43semidirect
779. C4⋊C4C22×C4×C43semidirect
780. C4⋊C4C22×C4×C43semidirect
806. C22⋊C4C22×C4×C43semidirect
807. C22⋊C4C22×C4×C43semidirect
818. C42C22×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5602
C43×#23752
C43×#23742
C43×#23732
C43×#23662
C43×#23642
C43×#23632
C43×#23612
C43×#23592
C43×#23352
C43×#23342
C43×#23332
C43×#23282
C43×#23252
C43×#23242
C43×#23222
C4×#120×C432
#3451143