Finite Group Databasebeta

← C43×#14095 #24934112

Subgroups — C43×#14095 #24934112

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C43C211yesmaximal, characteristic
2C2×C43×#390C211yesmaximal, characteristic
3C2×C43×#387C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
6C43×#1441C211yesmaximal, characteristic, complemented
7C43×#1439C211yesmaximal, characteristic, complemented
8C43×#1439C211yesmaximal, characteristic, complemented
9C43×#1438C211yesmaximal, characteristic
10C43×#1437C211yesmaximal, characteristic, complemented
11C43×#1437C211yesmaximal, characteristic, complemented
12C43×#1437C211yesmaximal, characteristic, complemented
13C43×#1437C211yesmaximal, characteristic, complemented
14C43×#1436C211yesmaximal, characteristic, complemented
15C43×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C24×C4×C43C2211yescharacteristic
18C2×#123×C43—24no—
19C2×#123×C43—24no—
20C2×#123×C43C418yescomplemented
21C22×C4⋊C4×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C4⋊C4×C43C2211yescharacteristic
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2211yescharacteristic
31C22×C22⋊C4×C43C2211yescharacteristic
32C22×C22⋊C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2211yescharacteristic
35C22×C22⋊C4×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C22×C42×C43C2211yescharacteristic
39C22×C42×C43C2211yescharacteristic
40C43×#390—24no—
41C43×#387—24no—
42C4×C4⋊C4×C43—24no—
43C4×C22⋊C4×C43—24no—
44C2×#95×C43C2211yescharacteristic
45C2×#95×C43C2211yescharacteristic
46C2×#95×C43C2211yescharacteristic
47C2×#95×C43C2211yescharacteristic
48C2×#95×C43C2211yescharacteristic
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
58C25×C43C2311yescharacteristic
59C25×C43C2311yescharacteristic
60C22×D4×C43—22no—
61C22×D4×C43—22no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—41no—
65C22×D4×C43—41no—
66C22×D4×C43C2×C414yes—
67C23×C4×C43—22no—
68C23×C4×C43—22no—
69C23×C4×C43—22no—
70C23×C4×C43—22no—
71C23×C4×C43—41no—
72C23×C4×C43—41no—
73C23×C4×C43C2×C414yes—
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
86C23×C4×C43C2311yescharacteristic
87#123×C43—232no—
88C2×C4⋊C4×C43—22no—
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—41no—
96C2×C4⋊C4×C43C2×C414yes—
97C2×C4⋊C4×C43C2×C414yes—
98C2×C4⋊C4×C43D414yes—
99C2×C4⋊C4×C43D414yes—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43—22no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—22no—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43—22no—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—22no—
117C2×C22⋊C4×C43—22no—
118C2×C22⋊C4×C43—22no—
119C2×C22⋊C4×C43—22no—
120C2×C22⋊C4×C43—22no—
121C2×C22⋊C4×C43—22no—
122C2×C22⋊C4×C43—22no—
123C2×C22⋊C4×C43—41no—
124C2×C22⋊C4×C43—41no—
125C2×C22⋊C4×C43—41no—
126C2×C22⋊C4×C43—41no—
127C2×C22⋊C4×C43—41no—
128C2×C22⋊C4×C43—41no—
129C2×C22⋊C4×C43C2×C414yes—
130C2×C22⋊C4×C43C2×C414yes—
131C2×C22⋊C4×C43C2×C414yes—
132C2×C22⋊C4×C43D414yes—
133C2×C42×C43—22no—
134C2×C42×C43—22no—
135C2×C42×C43—22no—
136C2×C42×C43—22no—
137C2×C42×C43—22no—
138C2×C42×C43—22no—
139C2×C42×C43—22no—
140C2×C42×C43—22no—
141C2×C42×C43—22no—
142C2×C42×C43—41no—
143C2×C42×C43—41no—
144C2×C42×C43—41no—
145#95×C43—22no—
146#95×C43—22no—
147#95×C43—22no—
148#95×C43—22no—
149#95×C43—22no—
150#95×C43—22no—
151#95×C43—22no—
152#95×C43—22no—
153#95×C43—22no—
154#95×C43—22no—
155#95×C43—41no—
156#95×C43—41no—
157#95×C43—41no—
158#95×C43—41no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43—21no—
178C24×C43—21no—
179C24×C43—21no—
180C24×C43—21no—
181C24×C43—21no—
182C24×C43—21no—
183C24×C43—21no—
184C24×C43—21no—
185C24×C43C22×C412yes—
186C24×C43C22×C412yes—
187C24×C43C2×D412yes—
188C24×C43#4112yes—
189C24×C43C2411yescharacteristic
190C2×D4×C43—28no—
191C2×D4×C43—28no—
192C2×D4×C43—44no—
193C2×D4×C43—44no—
194C2×D4×C43—44no—
195C2×D4×C43—44no—
196C2×D4×C43—44no—
197C22×C4×C43—28no—
198C22×C4×C43—28no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43—21no—
268C22×C4×C43—21no—
269C22×C4×C43—21no—
270C22×C4×C43—21no—
271C22×C4×C43—44no—
272C22×C4×C43—44no—
273C22×C4×C43—44no—
274C22×C4×C43—44no—
275C22×C4×C43—44no—
276C22×C4×C43C22×C412yes—
277C22×C4×C43C22×C412yes—
278C22×C4×C43C22×C412yes—
279C22×C4×C43C22×C412yes—
280C22×C4×C43C22×C412yes—
281C22×C4×C43C2×D412yes—
282C22×C4×C43C2×D412yes—
283C22×C4×C43C2×D412yes—
284C22×C4×C43C2×D412yes—
285C22×C4×C43C2×D412yes—
286C22×C4×C43C2×D412yes—
287C22×C4×C43C2×D412yes—
288C22×C4×C43C2×D412yes—
289C22×C4×C43#4112yes—
290C22×C4×C43#4112yes—
291C22×C4×C43#4112yes—
292C22×C4×C43#4112yes—
293C22×C4×C43#4112yes—
294C22×C4×C43#4112yes—
295C4⋊C4×C43—28no—
296C4⋊C4×C43—28no—
297C4⋊C4×C43—44no—
298C4⋊C4×C43C22⋊C4116yescomplemented
299C22⋊C4×C43—28no—
300C22⋊C4×C43—28no—
301C22⋊C4×C43—28no—
302C22⋊C4×C43—28no—
303C22⋊C4×C43—28no—
304C22⋊C4×C43—44no—
305C22⋊C4×C43—44no—
306C22⋊C4×C43—44no—
307C22⋊C4×C43—44no—
308C22⋊C4×C43—44no—
309C22⋊C4×C43—44no—
310C42×C43—28no—
311C42×C43—44no—
312C42×C43—44no—
313C42×C43—44no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—22no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43—22no—
335C23×C43—22no—
336C23×C43—22no—
337C23×C43—22no—
338C23×C43—22no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—41no—
354C23×C43—41no—
355C23×C43—41no—
356C23×C43—41no—
357C23×C43—41no—
358C23×C43—41no—
359C23×C43—41no—
360C23×C43—41no—
361C23×C43—41no—
362C23×C43—41no—
363C23×C43—41no—
364C23×C43—41no—
365C23×C43—41no—
366C23×C43—41no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43—41no—
371C23×C43—41no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43—41no—
377C23×C43—41no—
378C23×C43—41no—
379C23×C43—41no—
380C23×C43—41no—
381C23×C43—41no—
382C23×C43—41no—
383C23×C43C4×D414yes—
384C23×C43C23×C411yescharacteristic
385C23×C43C22×D411yescharacteristic
386C23×C43C22×D411yescharacteristic
387C23×C43C22×D411yescharacteristic
388C23×C43C2×#4111yescharacteristic
389C23×C43C2×#4111yescharacteristic
390C23×C43C2×#4111yescharacteristic
391C23×C43C2×#4111yescharacteristic
392C23×C43C2×#4111yescharacteristic
393C23×C43C2×#4111yescharacteristic
394C23×C43C2×#4111yescharacteristic
395C23×C43H(5,𝔽2)11yescharacteristic
396C23×C43H(5,𝔽2)11yescharacteristic
397C23×C43H(5,𝔽2)11yescharacteristic
398C23×C432−1+411yescharacteristic
399D4×C43—416no—
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—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—22no—
441C2×C4×C43—22no—
442C2×C4×C43—22no—
443C2×C4×C43—22no—
444C2×C4×C43—22no—
445C2×C4×C43—416no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—41no—
465C2×C4×C43—41no—
466C2×C4×C43—41no—
467C2×C4×C43—41no—
468C2×C4×C43—41no—
469C2×C4×C43—41no—
470C2×C4×C43—41no—
471C2×C4×C43—41no—
472C2×C4×C43—41no—
473C2×C4×C43—41no—
474C2×C4×C43—41no—
475C2×C4×C43—41no—
476C2×C4×C43—41no—
477C2×C4×C43—41no—
478C2×C4×C43—41no—
479C2×C4×C43—41no—
480C2×C4×C43—41no—
481C2×C4×C43—41no—
482C2×C4×C43—41no—
483C2×C4×C43—41no—
484C2×C4×C43—41no—
485C2×C4×C43—41no—
486C2×C4×C43—41no—
487C2×C4×C43—41no—
488C2×C4×C43C2×C22⋊C414yes—
489C2×C4×C43C2×C22⋊C414yes—
490C2×C4×C43C2×C22⋊C414yes—
491C2×C4×C43#12314yescomplemented
492#14095C4311yesmaximal, characteristic, direct product factor, Sylow
493C22×C43—24no—
494C22×C43—24no—
495C22×C43—24no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43—42no—
499C22×C43—42no—
500C22×C43—42no—
501C22×C43—42no—
502C22×C43—42no—
503C22×C43—42no—
504C22×C43—42no—
505C22×C43—42no—
506C22×C43—42no—
507C22×C43—42no—
508C22×C43—42no—
509C22×C43—42no—
510C22×C43—42no—
511C22×C43—42no—
512C22×C43—42no—
513C22×C43—42no—
514C22×C43—42no—
515C22×C43—81no—
516C22×C43—81no—
517C22×C43—81no—
518C22×C43—81no—
519C22×C43—81no—
520C22×C43—81no—
521C22×C43—81no—
522C22×C43—81no—
523C22×C43C22×C22⋊C411yescharacteristic
524C22×C43C2×C4×D411yescharacteristic
525C22×C43C4×#4111yescharacteristic
526C22×C43C4×#4111yescharacteristic
527C22×C43C4×#4111yescharacteristic
528C22×C43#51811yescharacteristic
529C22×C43#52011yescharacteristic
530C22×C43C2×#12311yescharacteristic
531C22×C43#52511yescharacteristic
532C22×C43#52511yescharacteristic
533C22×C43#52511yescharacteristic
534C22×C43#52911yescharacteristic
535C22×C43#52911yescharacteristic
536C22×C43#53211yescharacteristic
537C22×C43#53211yescharacteristic
538C22×C43#53811yescharacteristic
539C22×C43#53911yescharacteristic
540C22×C43#54011yescharacteristic
541C22×C43#54211yescharacteristic
542C22×C43D4211yescharacteristic
543C22×C43D4211yescharacteristic
544C22×C43#54611yescharacteristic
545C22×C43#54611yescharacteristic
546C22×C43#54611yescharacteristic
547C22×C43#54711yescharacteristic
548C22×C43#54811yescharacteristic
549C22×C43#54811yescharacteristic
550C22×C43#55011yescharacteristic
551C22×C43#55011yescharacteristic
552C22×C43#55111yescharacteristic
553C22×C43#55111yescharacteristic
554C22×C43#55211yescharacteristic
555C22×C43#55311yescharacteristic
556C22×C43#55311yescharacteristic
557C22×C43#55911yescharacteristic
558C4×C43—24no—
559C4×C43—24no—
560C4×C43—24no—
561C4×C43—24no—
562C4×C43—42no—
563C4×C43—42no—
564C4×C43—42no—
565C4×C43—42no—
566C4×C43—42no—
567C4×C43—42no—
568C4×C43—42no—
569C4×C43—81no—
570C4×C43—81no—
571C22×#123C2×C4311yescharacteristic
572C2×#390C2×C4311yescharacteristic
573C2×#387C2×C4311yescharacteristic, complemented
574C2×C4×C4⋊C4C2×C4311yescharacteristic, complemented
575C2×C4×C22⋊C4C2×C4311yescharacteristic, complemented
576#1441C2×C4311yescharacteristic, complemented
577#1439C2×C4311yescharacteristic, complemented
578#1439C2×C4311yescharacteristic, complemented
579#1438C2×C4311yescharacteristic
580#1437C2×C4311yescharacteristic, complemented
581#1437C2×C4311yescharacteristic, complemented
582#1437C2×C4311yescharacteristic, complemented
583#1437C2×C4311yescharacteristic, complemented
584#1436C2×C4311yescharacteristic, complemented
585C22⋊#95C2×C4311yescharacteristic, complemented
586C2×C43—44no—
587C2×C43—82no—
588C2×C43#229711yescharacteristic
589C2×C43C4×#12311yescharacteristic
590C2×C43#233511yescharacteristic
591C2×C43D4×C22⋊C411yescharacteristic
592C2×C43#234111yescharacteristic
593C2×C43#235911yescharacteristic
594C2×C43#237411yescharacteristic
595C2×C43#244311yescharacteristic
596C2×C43#244511yescharacteristic
597C2×C43#245611yescharacteristic
598C2×C43#245811yescharacteristic
599C2×C43#246111yescharacteristic
600C2×C43#247111yescharacteristic
601C2×C43#255411yescharacteristic
602C2×C43#255811yescharacteristic
603C23×D4C22×C4311yescharacteristic
604C24×C4C22×C4311yescharacteristic
605C2×#123—24no—
606C2×#123—24no—
607C2×#123C4×C4318yescomplemented
608C22×C4⋊C4C22×C4311yescharacteristic
609C22×C4⋊C4C22×C4311yescharacteristic
610C22×C4⋊C4C22×C4311yescharacteristic
611C22×C4⋊C4C22×C4311yescharacteristic
612C22×C22⋊C4C22×C4311yescharacteristic
613C22×C22⋊C4C22×C4311yescharacteristic
614C22×C22⋊C4C22×C4311yescharacteristic
615C22×C22⋊C4C22×C4311yescharacteristic
616C22×C22⋊C4C22×C4311yescharacteristic
617C22×C22⋊C4C22×C4311yescharacteristic
618C22×C22⋊C4C22×C4311yescharacteristic
619C22×C22⋊C4C22×C4311yescharacteristic
620C22×C22⋊C4C22×C4311yescharacteristic
621C22×C22⋊C4C22×C4311yescharacteristic
622C22×C22⋊C4C22×C4311yescharacteristic
623C22×C42C22×C4311yescharacteristic
624C22×C42C22×C4311yescharacteristic
625C22×C42C22×C4311yescharacteristic
626C22×C42C22×C4311yescharacteristic
627#390—24no—
628#387—24no—
629C4×C4⋊C4—24no—
630C4×C22⋊C4—24no—
631C2×#95C22×C4311yescharacteristic
632C2×#95C22×C4311yescharacteristic
633C2×#95C22×C4311yescharacteristic
634C2×#95C22×C4311yescharacteristic
635C2×#95C22×C4311yescharacteristic
636C2×#95C22×C4311yescharacteristic
637C2×#95C22×C4311yescharacteristic
638C2×#95C22×C4311yescharacteristic
639C2×#95C22×C4311yescharacteristic
640C2×#95C22×C4311yescharacteristic
641C2×#95C22×C4311yescharacteristic
642C2×#95C22×C4311yescharacteristic
643C2×#95C22×C4311yescharacteristic
644C2×#95C22×C4311yescharacteristic
645C43#1409511yescharacteristic, direct product factor, Sylow
646C25C23×C4311yescharacteristic
647C25C23×C4311yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C2×C4×C4314yes—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4C2×C4×C4314yes—
662C23×C4C23×C4311yescharacteristic
663C23×C4C23×C4311yescharacteristic
664C23×C4C23×C4311yescharacteristic
665C23×C4C23×C4311yescharacteristic
666C23×C4C23×C4311yescharacteristic
667C23×C4C23×C4311yescharacteristic
668C23×C4C23×C4311yescharacteristic
669C23×C4C23×C4311yescharacteristic
670C23×C4C23×C4311yescharacteristic
671C23×C4C23×C4311yescharacteristic
672C23×C4C23×C4311yescharacteristic
673C23×C4C23×C4311yescharacteristic
674C23×C4C23×C4311yescharacteristic
675#123—232no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4C2×C4×C4314yes—
685C2×C4⋊C4C2×C4×C4314yes—
686C2×C4⋊C4D4×C4314yes—
687C2×C4⋊C4D4×C4314yes—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4C2×C4×C4314yes—
718C2×C22⋊C4C2×C4×C4314yes—
719C2×C22⋊C4C2×C4×C4314yes—
720C2×C22⋊C4D4×C4314yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42—41no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C22×C4×C4312yes—
774C24C22×C4×C4312yes—
775C24C2×D4×C4312yes—
776C24#41×C4312yes—
777C24C24×C4311yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—28no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4C22×C4×C4312yes—
865C22×C4C22×C4×C4312yes—
866C22×C4C22×C4×C4312yes—
867C22×C4C22×C4×C4312yes—
868C22×C4C22×C4×C4312yes—
869C22×C4C2×D4×C4312yes—
870C22×C4C2×D4×C4312yes—
871C22×C4C2×D4×C4312yes—
872C22×C4C2×D4×C4312yes—
873C22×C4C2×D4×C4312yes—
874C22×C4C2×D4×C4312yes—
875C22×C4C2×D4×C4312yes—
876C22×C4C2×D4×C4312yes—
877C22×C4#41×C4312yes—
878C22×C4#41×C4312yes—
879C22×C4#41×C4312yes—
880C22×C4#41×C4312yes—
881C22×C4#41×C4312yes—
882C22×C4#41×C4312yes—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—44no—
886C4⋊C4C22⋊C4×C43116yescomplemented
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—44no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C4×D4×C4314yes—
972C23C23×C4×C4311yescharacteristic
973C23C22×D4×C4311yescharacteristic
974C23C22×D4×C4311yescharacteristic
975C23C22×D4×C4311yescharacteristic
976C23C2×#41×C4311yescharacteristic
977C23C2×#41×C4311yescharacteristic
978C23C2×#41×C4311yescharacteristic
979C23C2×#41×C4311yescharacteristic
980C23C2×#41×C4311yescharacteristic
981C23C2×#41×C4311yescharacteristic
982C23C2×#41×C4311yescharacteristic
983C23H(5,𝔽2)×C4311yescharacteristic
984C23H(5,𝔽2)×C4311yescharacteristic
985C23H(5,𝔽2)×C4311yescharacteristic
986C232−1+4×C4311yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4C2×C22⋊C4×C4314yes—
1077C2×C4C2×C22⋊C4×C4314yes—
1078C2×C4C2×C22⋊C4×C4314yes—
1079C2×C4#123×C4314yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C22⋊C4×C4311yescharacteristic
1111C22C2×C4×D4×C4311yescharacteristic
1112C22C4×#41×C4311yescharacteristic
1113C22C4×#41×C4311yescharacteristic
1114C22C4×#41×C4311yescharacteristic
1115C22C43×#51811yescharacteristic
1116C22C43×#52011yescharacteristic
1117C22C2×#123×C4311yescharacteristic
1118C22C43×#52511yescharacteristic
1119C22C43×#52511yescharacteristic
1120C22C43×#52511yescharacteristic
1121C22C43×#52911yescharacteristic
1122C22C43×#52911yescharacteristic
1123C22C43×#53211yescharacteristic
1124C22C43×#53211yescharacteristic
1125C22C43×#53811yescharacteristic
1126C22C43×#53911yescharacteristic
1127C22C43×#54011yescharacteristic
1128C22C43×#54211yescharacteristic
1129C22D42×C4311yescharacteristic
1130C22D42×C4311yescharacteristic
1131C22C43×#54611yescharacteristic
1132C22C43×#54611yescharacteristic
1133C22C43×#54611yescharacteristic
1134C22C43×#54711yescharacteristic
1135C22C43×#54811yescharacteristic
1136C22C43×#54811yescharacteristic
1137C22C43×#55011yescharacteristic
1138C22C43×#55011yescharacteristic
1139C22C43×#55111yescharacteristic
1140C22C43×#55111yescharacteristic
1141C22C43×#55211yescharacteristic
1142C22C43×#55311yescharacteristic
1143C22C43×#55311yescharacteristic
1144C22C43×#55911yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C43×#229711yescharacteristic
1161C2C4×#123×C4311yescharacteristic
1162C2C43×#233511yescharacteristic
1163C2D4×C22⋊C4×C4311yescharacteristic
1164C2C43×#234111yescharacteristic
1165C2C43×#235911yescharacteristic
1166C2C43×#237411yescharacteristic
1167C2C43×#244311yescharacteristic
1168C2C43×#244511yescharacteristic
1169C2C43×#245611yescharacteristic
1170C2C43×#245811yescharacteristic
1171C2C43×#246111yescharacteristic
1172C2C43×#247111yescharacteristic
1173C2C43×#255411yescharacteristic
1174C2C43×#255811yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
prime radicalC23×D4×C43C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C43×#387C2semidirect
4. C2×C4×C4⋊C4×C43C2semidirect
5. C2×C4×C22⋊C4×C43C2semidirect
6. C43×#1441C2semidirect
7. C43×#1439C2semidirect
8. C43×#1439C2semidirect
10. C43×#1437C2semidirect
11. C43×#1437C2semidirect
12. C43×#1437C2semidirect
13. C43×#1437C2semidirect
14. C43×#1436C2semidirect
15. C43×C22⋊#95C2semidirect
20. C2×#123×C43C4semidirect
298. C4⋊C4×C43C22⋊C4semidirect
491. C2×C4×C43#123semidirect
492. #14095C43direct (N × H)
573. C2×#387C2×C43semidirect
574. C2×C4×C4⋊C4C2×C43semidirect
575. C2×C4×C22⋊C4C2×C43semidirect
576. #1441C2×C43semidirect
577. #1439C2×C43semidirect
578. #1439C2×C43semidirect
580. #1437C2×C43semidirect
581. #1437C2×C43semidirect
582. #1437C2×C43semidirect
583. #1437C2×C43semidirect
584. #1436C2×C43semidirect
585. C22⋊#95C2×C43semidirect
607. C2×#123C4×C43semidirect
645. C43#14095direct (N × H)
886. C4⋊C4C22⋊C4×C43semidirect
1079. C2×C4#123×C43semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C432
C2×C43×#3902
C2×C43×#3872
C2×C4×C4⋊C4×C432
C2×C4×C22⋊C4×C432
C43×#14412
C43×#14392
C43×#14382
C43×#14372
C43×#14362
C43×C22⋊#952
#1409543