Finite Group Databasebeta

← C43×#14731 #24934748

Subgroups — C43×#14731 #24934748

Order 11008.

2254 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C43C211yesmaximal, characteristic
2C2×C43×#397C211yesmaximal, characteristic, complemented
3C2×C43×#394C211yesmaximal, characteristic
4C2×C43×#385C211yesmaximal, characteristic, complemented
5C2×C43×#385C211yesmaximal, characteristic, complemented
6C2×C43×#381C211yesmaximal, characteristic, complemented
7C43×#1444C211yesmaximal, characteristic, complemented
8C43×#1441C211yesmaximal, characteristic, complemented
9C43×#1440C211yesmaximal, characteristic, complemented
10C43×#1440C211yesmaximal, characteristic, complemented
11C43×#1439C211yesmaximal, characteristic, complemented
12C43×#1438C211yesmaximal, characteristic
13C43×#1436C211yesmaximal, characteristic, complemented
14C43×#1436C211yesmaximal, characteristic, complemented
15C43×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C24×C4×C43C2211yescharacteristic
18C24×C4×C43C2211yescharacteristic
19C2×C4×D4×C43—24no—
20C2×C4×D4×C43—24no—
21C2×C4×D4×C43—24no—
22C22×C4⋊C4×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C4⋊C4×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C22×C4⋊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×C22⋊C4×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C43×#397—24no—
39C43×#394—24no—
40C43×#385—24no—
41C43×#385—24no—
42C43×#381—24no—
43C2×#95×C43C2211yescharacteristic
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
58C2×#95×C43C2211yescharacteristic
59C25×C43C2311yescharacteristic
60C25×C43C2311yescharacteristic
61C22×D4×C43—22no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43D414yes—
68C23×C4×C43—22no—
69C23×C4×C43—22no—
70C23×C4×C43—22no—
71C23×C4×C43—22no—
72C23×C4×C43—22no—
73C23×C4×C43—22no—
74C23×C4×C43—22no—
75C23×C4×C43—22no—
76C23×C4×C43—22no—
77C23×C4×C43—41no—
78C23×C4×C43—41no—
79C23×C4×C43—41no—
80C23×C4×C43—41no—
81C23×C4×C43D414yes—
82C23×C4×C43C2311yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C4×D4×C43—232no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43—22no—
107C2×C4⋊C4×C43—22no—
108C2×C4⋊C4×C43—41no—
109C2×C4⋊C4×C43—41no—
110C2×C4⋊C4×C43—41no—
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—22no—
124C2×C22⋊C4×C43—22no—
125C2×C22⋊C4×C43—22no—
126C2×C22⋊C4×C43—22no—
127C2×C22⋊C4×C43—22no—
128C2×C22⋊C4×C43—22no—
129C2×C22⋊C4×C43—22no—
130C2×C22⋊C4×C43—22no—
131C2×C22⋊C4×C43—22no—
132C2×C22⋊C4×C43—22no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—22no—
135C2×C22⋊C4×C43—22no—
136C2×C22⋊C4×C43—41no—
137C2×C22⋊C4×C43—41no—
138C2×C22⋊C4×C43—41no—
139C2×C22⋊C4×C43—41no—
140C2×C22⋊C4×C43D414yes—
141C2×C42×C43—22no—
142C2×C42×C43—22no—
143C2×C42×C43—22no—
144#95×C43—22no—
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—22no—
156#95×C43—22no—
157#95×C43—22no—
158#95×C43—41no—
159#95×C43D414yescomplemented
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×C43C2×D412yes—
185C24×C43C2×D412yes—
186C24×C43C2×D412yes—
187C24×C43C2×D412yes—
188C24×C43#4112yes—
189C24×C43#4112yes—
190C24×C43C2411yescharacteristic
191C2×D4×C43—28no—
192C2×D4×C43—28no—
193C2×D4×C43—28no—
194C2×D4×C43—28no—
195C2×D4×C43—28no—
196C2×D4×C43—28no—
197C2×D4×C43—28no—
198C22×C4×C43—28no—
199C22×C4×C43—28no—
200C22×C4×C43—28no—
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—21no—
272C22×C4×C43—21no—
273C22×C4×C43—21no—
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—21no—
277C22×C4×C43—21no—
278C22×C4×C43—21no—
279C22×C4×C43—44no—
280C22×C4×C43—44no—
281C22×C4×C43—44no—
282C22×C4×C43—44no—
283C22×C4×C43—44no—
284C22×C4×C43—44no—
285C22×C4×C43—44no—
286C22×C4×C43—44no—
287C22×C4×C43—44no—
288C22×C4×C43—44no—
289C22×C4×C43—44no—
290C22×C4×C43C2×D412yes—
291C22×C4×C43C2×D412yes—
292C22×C4×C43C2×D412yes—
293C22×C4×C43C2×D412yes—
294C22×C4×C43C2×D412yes—
295C22×C4×C43C2×D412yes—
296C22×C4×C43C2×D412yes—
297C22×C4×C43C2×D412yes—
298C22×C4×C43#4112yes—
299C22×C4×C43#4112yes—
300C22×C4×C43#4112yes—
301C22×C4×C43#4112yes—
302C22×C4×C43#4112yes—
303C4⋊C4×C43—28no—
304C4⋊C4×C43—44no—
305C4⋊C4×C43—44no—
306C4⋊C4×C43—44no—
307C4⋊C4×C43—44no—
308C22⋊C4×C43—28no—
309C22⋊C4×C43—28no—
310C22⋊C4×C43—28no—
311C22⋊C4×C43—28no—
312C22⋊C4×C43—44no—
313C22⋊C4×C43—44no—
314C22⋊C4×C43—44no—
315C22⋊C4×C43—44no—
316C22⋊C4×C43—44no—
317C22⋊C4×C43—44no—
318C42×C43—28no—
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—22no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
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—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×C43—41no—
384C23×C43—41no—
385C23×C43—41no—
386C23×C43—41no—
387C23×C43#12014yes—
388C23×C43#12314yes—
389C23×C43C22×D411yescharacteristic
390C23×C43C22×D411yescharacteristic
391C23×C43C22×D411yescharacteristic
392C23×C43C22×D411yescharacteristic
393C23×C43C2×#4111yescharacteristic
394C23×C43C2×#4111yescharacteristic
395C23×C43C2×#4111yescharacteristic
396C23×C43C2×#4111yescharacteristic
397C23×C43C2×#4111yescharacteristic
398C23×C43C2×#4111yescharacteristic
399C23×C43C2×#4111yescharacteristic
400C23×C43H(5,𝔽2)11yescharacteristic
401C23×C43H(5,𝔽2)11yescharacteristic
402C23×C432−1+411yescharacteristic
403C23×C432−1+411yescharacteristic
404D4×C43—232no—
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—416no—
439C2×C4×C43—416no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
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×C43—41no—
489C2×C4×C43—41no—
490C2×C4×C43—41no—
491C2×C4×C43—41no—
492C2×C4×C43—41no—
493C2×C4×C43—41no—
494C2×C4×C43—41no—
495C2×C4×C43—41no—
496C2×C4×C43#12114yes—
497C2×C4×C43#12314yes—
498#14731C4311yesmaximal, characteristic, direct product factor, Sylow
499C22×C43—24no—
500C22×C43—24no—
501C22×C43—24no—
502C22×C43—24no—
503C22×C43—24no—
504C22×C43—24no—
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—42no—
516C22×C43—42no—
517C22×C43—42no—
518C22×C43—42no—
519C22×C43—42no—
520C22×C43—42no—
521C22×C43—42no—
522C22×C43—42no—
523C22×C43—42no—
524C22×C43—42no—
525C22×C43—42no—
526C22×C43—42no—
527C22×C43—42no—
528C22×C43—42no—
529C22×C43C2×#12011yescharacteristic
530C22×C43C2×#12111yescharacteristic
531C22×C43C2×#12311yescharacteristic
532C22×C43C2×#12311yescharacteristic
533C22×C43#52511yescharacteristic
534C22×C43#52511yescharacteristic
535C22×C43#52511yescharacteristic
536C22×C43#52511yescharacteristic
537C22×C43#52511yescharacteristic
538C22×C43#52511yescharacteristic
539C22×C43#52911yescharacteristic
540C22×C43#52911yescharacteristic
541C22×C43#53211yescharacteristic
542C22×C43#53411yescharacteristic
543C22×C43#53611yescharacteristic
544C22×C43#53911yescharacteristic
545C22×C43#53911yescharacteristic
546C22×C43#54211yescharacteristic
547C22×C43#54211yescharacteristic
548C22×C43D4211yescharacteristic
549C22×C43D4211yescharacteristic
550C22×C43#54611yescharacteristic
551C22×C43#54611yescharacteristic
552C22×C43#54711yescharacteristic
553C22×C43#54711yescharacteristic
554C22×C43#54711yescharacteristic
555C22×C43#54711yescharacteristic
556C22×C43#54711yescharacteristic
557C22×C43#54811yescharacteristic
558C22×C43#55111yescharacteristic
559C22×C43#55211yescharacteristic
560C22×C43#55311yescharacteristic
561C22×C43#55311yescharacteristic
562C22×C43#55611yescharacteristic
563C22×C43#55911yescharacteristic
564C4×C43—24no—
565C4×C43—24no—
566C4×C43—42no—
567C4×C43—42no—
568C4×C43—42no—
569C4×C43—42no—
570C4×C43—42no—
571C4×C43—42no—
572C4×C43—42no—
573C4×C43—81no—
574C4×C43—81no—
575C4×C43—81no—
576C4×C43—81no—
577C22×C4×D4C2×C4311yescharacteristic
578C2×#397C2×C4311yescharacteristic, complemented
579C2×#394C2×C4311yescharacteristic
580C2×#385C2×C4311yescharacteristic, complemented
581C2×#385C2×C4311yescharacteristic, complemented
582C2×#381C2×C4311yescharacteristic, complemented
583#1444C2×C4311yescharacteristic, complemented
584#1441C2×C4311yescharacteristic, complemented
585#1440C2×C4311yescharacteristic, complemented
586#1440C2×C4311yescharacteristic, complemented
587#1439C2×C4311yescharacteristic, complemented
588#1438C2×C4311yescharacteristic
589#1436C2×C4311yescharacteristic, complemented
590#1436C2×C4311yescharacteristic, complemented
591C22⋊#95C2×C4311yescharacteristic, complemented
592C2×C43—44no—
593C2×C43—44no—
594C2×C43#239211yescharacteristic
595C2×C43#240611yescharacteristic
596C2×C43#241011yescharacteristic
597C2×C43#241511yescharacteristic
598C2×C43#241911yescharacteristic
599C2×C43#242211yescharacteristic
600C2×C43#244311yescharacteristic
601C2×C43#244711yescharacteristic
602C2×C43#245511yescharacteristic
603C2×C43#246111yescharacteristic
604C2×C43#246611yescharacteristic
605C2×C43#246811yescharacteristic
606C2×C43#260011yescharacteristic
607C2×C43#263811yescharacteristic
608C2×C43#284911yescharacteristic
609C23×D4C22×C4311yescharacteristic
610C24×C4C22×C4311yescharacteristic
611C24×C4C22×C4311yescharacteristic
612C2×C4×D4—24no—
613C2×C4×D4—24no—
614C2×C4×D4—24no—
615C22×C4⋊C4C22×C4311yescharacteristic
616C22×C4⋊C4C22×C4311yescharacteristic
617C22×C4⋊C4C22×C4311yescharacteristic
618C22×C4⋊C4C22×C4311yescharacteristic
619C22×C4⋊C4C22×C4311yescharacteristic
620C22×C22⋊C4C22×C4311yescharacteristic
621C22×C22⋊C4C22×C4311yescharacteristic
622C22×C22⋊C4C22×C4311yescharacteristic
623C22×C22⋊C4C22×C4311yescharacteristic
624C22×C22⋊C4C22×C4311yescharacteristic
625C22×C22⋊C4C22×C4311yescharacteristic
626C22×C22⋊C4C22×C4311yescharacteristic
627C22×C22⋊C4C22×C4311yescharacteristic
628C22×C22⋊C4C22×C4311yescharacteristic
629C22×C22⋊C4C22×C4311yescharacteristic
630C22×C42C22×C4311yescharacteristic
631#397—24no—
632#394—24no—
633#385—24no—
634#385—24no—
635#381—24no—
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
645C2×#95C22×C4311yescharacteristic
646C2×#95C22×C4311yescharacteristic
647C2×#95C22×C4311yescharacteristic
648C2×#95C22×C4311yescharacteristic
649C2×#95C22×C4311yescharacteristic
650C2×#95C22×C4311yescharacteristic
651C2×#95C22×C4311yescharacteristic
652C43#1473111yescharacteristic, direct product factor, Sylow
653C25C23×C4311yescharacteristic
654C25C23×C4311yescharacteristic
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—22no—
658C22×D4—22no—
659C22×D4—22no—
660C22×D4—22no—
661C22×D4D4×C4314yes—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4—41no—
675C23×C4D4×C4314yes—
676C23×C4C23×C4311yescharacteristic
677C23×C4C23×C4311yescharacteristic
678C23×C4C23×C4311yescharacteristic
679C23×C4C23×C4311yescharacteristic
680C23×C4C23×C4311yescharacteristic
681C23×C4C23×C4311yescharacteristic
682C23×C4C23×C4311yescharacteristic
683C23×C4C23×C4311yescharacteristic
684C23×C4C23×C4311yescharacteristic
685C23×C4C23×C4311yescharacteristic
686C23×C4C23×C4311yescharacteristic
687C23×C4C23×C4311yescharacteristic
688C23×C4C23×C4311yescharacteristic
689C4×D4—232no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—41no—
703C2×C4⋊C4—41no—
704C2×C4⋊C4—41no—
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—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4D4×C4314yes—
735C2×C42—22no—
736C2×C42—22no—
737C2×C42—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—22no—
749#95—22no—
750#95—22no—
751#95—22no—
752#95—41no—
753#95D4×C4314yescomplemented
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—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C2×D4×C4312yes—
779C24C2×D4×C4312yes—
780C24C2×D4×C4312yes—
781C24C2×D4×C4312yes—
782C24#41×C4312yes—
783C24#41×C4312yes—
784C24C24×C4311yescharacteristic
785C2×D4—28no—
786C2×D4—28no—
787C2×D4—28no—
788C2×D4—28no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—28no—
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—28no—
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—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4C2×D4×C4312yes—
885C22×C4C2×D4×C4312yes—
886C22×C4C2×D4×C4312yes—
887C22×C4C2×D4×C4312yes—
888C22×C4C2×D4×C4312yes—
889C22×C4C2×D4×C4312yes—
890C22×C4C2×D4×C4312yes—
891C22×C4C2×D4×C4312yes—
892C22×C4#41×C4312yes—
893C22×C4#41×C4312yes—
894C22×C4#41×C4312yes—
895C22×C4#41×C4312yes—
896C22×C4#41×C4312yes—
897C4⋊C4—28no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C42—28no—
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—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
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—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23#120×C4314yes—
982C23#123×C4314yes—
983C23C22×D4×C4311yescharacteristic
984C23C22×D4×C4311yescharacteristic
985C23C22×D4×C4311yescharacteristic
986C23C22×D4×C4311yescharacteristic
987C23C2×#41×C4311yescharacteristic
988C23C2×#41×C4311yescharacteristic
989C23C2×#41×C4311yescharacteristic
990C23C2×#41×C4311yescharacteristic
991C23C2×#41×C4311yescharacteristic
992C23C2×#41×C4311yescharacteristic
993C23C2×#41×C4311yescharacteristic
994C23H(5,𝔽2)×C4311yescharacteristic
995C23H(5,𝔽2)×C4311yescharacteristic
996C232−1+4×C4311yescharacteristic
997C232−1+4×C4311yescharacteristic
998D4—232no—
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—416no—
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×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4#121×C4314yes—
1091C2×C4#123×C4314yes—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22C2×#120×C4311yescharacteristic
1123C22C2×#121×C4311yescharacteristic
1124C22C2×#123×C4311yescharacteristic
1125C22C2×#123×C4311yescharacteristic
1126C22C43×#52511yescharacteristic
1127C22C43×#52511yescharacteristic
1128C22C43×#52511yescharacteristic
1129C22C43×#52511yescharacteristic
1130C22C43×#52511yescharacteristic
1131C22C43×#52511yescharacteristic
1132C22C43×#52911yescharacteristic
1133C22C43×#52911yescharacteristic
1134C22C43×#53211yescharacteristic
1135C22C43×#53411yescharacteristic
1136C22C43×#53611yescharacteristic
1137C22C43×#53911yescharacteristic
1138C22C43×#53911yescharacteristic
1139C22C43×#54211yescharacteristic
1140C22C43×#54211yescharacteristic
1141C22D42×C4311yescharacteristic
1142C22D42×C4311yescharacteristic
1143C22C43×#54611yescharacteristic
1144C22C43×#54611yescharacteristic
1145C22C43×#54711yescharacteristic
1146C22C43×#54711yescharacteristic
1147C22C43×#54711yescharacteristic
1148C22C43×#54711yescharacteristic
1149C22C43×#54711yescharacteristic
1150C22C43×#54811yescharacteristic
1151C22C43×#55111yescharacteristic
1152C22C43×#55211yescharacteristic
1153C22C43×#55311yescharacteristic
1154C22C43×#55311yescharacteristic
1155C22C43×#55611yescharacteristic
1156C22C43×#55911yescharacteristic
1157C4—24no—
1158C4—24no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—44no—
1172C2C43×#239211yescharacteristic
1173C2C43×#240611yescharacteristic
1174C2C43×#241011yescharacteristic
1175C2C43×#241511yescharacteristic
1176C2C43×#241911yescharacteristic
1177C2C43×#242211yescharacteristic
1178C2C43×#244311yescharacteristic
1179C2C43×#244711yescharacteristic
1180C2C43×#245511yescharacteristic
1181C2C43×#246111yescharacteristic
1182C2C43×#246611yescharacteristic
1183C2C43×#246811yescharacteristic
1184C2C43×#260011yescharacteristic
1185C2C43×#263811yescharacteristic
1186C2C43×#284911yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutator, Frattini, cosocleC24C24×C43
prime radicalC23×D4×C43C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#397C2semidirect
4. C2×C43×#385C2semidirect
5. C2×C43×#385C2semidirect
6. C2×C43×#381C2semidirect
7. C43×#1444C2semidirect
8. C43×#1441C2semidirect
9. C43×#1440C2semidirect
10. C43×#1440C2semidirect
11. C43×#1439C2semidirect
13. C43×#1436C2semidirect
14. C43×#1436C2semidirect
15. C43×C22⋊#95C2semidirect
159. #95×C43D4semidirect
498. #14731C43direct (N × H)
578. C2×#397C2×C43semidirect
580. C2×#385C2×C43semidirect
581. C2×#385C2×C43semidirect
582. C2×#381C2×C43semidirect
583. #1444C2×C43semidirect
584. #1441C2×C43semidirect
585. #1440C2×C43semidirect
586. #1440C2×C43semidirect
587. #1439C2×C43semidirect
589. #1436C2×C43semidirect
590. #1436C2×C43semidirect
591. C22⋊#95C2×C43semidirect
652. C43#14731direct (N × H)
753. #95D4×C43semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C432
C2×C43×#3972
C2×C43×#3942
C2×C43×#3852
C2×C43×#3812
C43×#14442
C43×#14412
C43×#14402
C43×#14392
C43×#14382
C43×#14362
C43×C22⋊#952
#1473143