Finite Group Databasebeta

← C43×#14733 #24934750

Subgroups — C43×#14733 #24934750

Order 11008.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C43C211yesmaximal, characteristic
2C2×C43×#398C211yesmaximal, characteristic, complemented
3C2×C43×#396C211yesmaximal, characteristic, complemented
4C2×C43×#385C211yesmaximal, characteristic, complemented
5C2×C43×#385C211yesmaximal, characteristic, complemented
6C2×C43×#380C211yesmaximal, characteristic, complemented
7C43×#1441C211yesmaximal, characteristic, complemented
8C43×#1439C211yesmaximal, characteristic, complemented
9C43×#1439C211yesmaximal, characteristic, complemented
10C43×#1439C211yesmaximal, characteristic, complemented
11C43×#1438C211yesmaximal, characteristic
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×C4⋊C4×C43C2211yescharacteristic
28C22×C4⋊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×C22⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C42×C43C2211yescharacteristic
40C43×#398—24no—
41C43×#396—24no—
42C43×#385—24no—
43C43×#385—24no—
44C43×#380—24no—
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×C43Q814yes—
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—22no—
109C2×C4⋊C4×C43—22no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—41no—
113C2×C4⋊C4×C43—41no—
114C2×C4⋊C4×C43—41no—
115C2×C4⋊C4×C43—41no—
116C2×C4⋊C4×C43D414yes—
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—22no—
137C2×C22⋊C4×C43—22no—
138C2×C22⋊C4×C43—41no—
139C2×C22⋊C4×C43—41no—
140C2×C22⋊C4×C43—41no—
141C2×C22⋊C4×C43—41no—
142C2×C22⋊C4×C43—41no—
143C2×C22⋊C4×C43—41no—
144C2×C22⋊C4×C43—41no—
145C2×C22⋊C4×C43—41no—
146C2×C22⋊C4×C43D414yes—
147C2×C42×C43—22no—
148C2×C42×C43—22no—
149C2×C42×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—22no—
159#95×C43—22no—
160#95×C43—22no—
161#95×C43—41no—
162#95×C43—41no—
163#95×C43D414yescomplemented
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×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43C2×D412yes—
189C24×C43C2×D412yes—
190C24×C43C2×Q812yes—
191C24×C43C2×Q812yes—
192C24×C43#4112yes—
193C24×C43#4112yes—
194C24×C43C2411yescharacteristic
195C2×D4×C43—28no—
196C2×D4×C43—28no—
197C2×D4×C43—28no—
198C2×D4×C43—28no—
199C2×D4×C43—28no—
200C2×D4×C43—28no—
201C2×D4×C43—28no—
202C22×C4×C43—28no—
203C22×C4×C43—28no—
204C22×C4×C43—28no—
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—21no—
280C22×C4×C43—21no—
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×C43—44no—
291C22×C4×C43—44no—
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×C43C2×D412yes—
299C22×C4×C43C2×D412yes—
300C22×C4×C43C2×D412yes—
301C22×C4×C43C2×D412yes—
302C22×C4×C43C2×Q812yes—
303C22×C4×C43#4112yes—
304C22×C4×C43#4112yes—
305C22×C4×C43#4112yes—
306C22×C4×C43#4112yes—
307C4⋊C4×C43—28no—
308C4⋊C4×C43—44no—
309C4⋊C4×C43—44no—
310C4⋊C4×C43—44no—
311C4⋊C4×C43—44no—
312C4⋊C4×C43—44no—
313C4⋊C4×C43—44no—
314C22⋊C4×C43—28no—
315C22⋊C4×C43—28no—
316C22⋊C4×C43—28no—
317C22⋊C4×C43—28no—
318C22⋊C4×C43—44no—
319C22⋊C4×C43—44no—
320C22⋊C4×C43—44no—
321C22⋊C4×C43—44no—
322C22⋊C4×C43—44no—
323C22⋊C4×C43—44no—
324C42×C43—28no—
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—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—22no—
360C23×C43—22no—
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—41no—
388C23×C43—41no—
389C23×C43—41no—
390C23×C43—41no—
391C23×C43—41no—
392C23×C43—41no—
393C23×C43C22⋊Q814yes—
394C23×C43C22⋊Q814yes—
395C23×C43C22×D411yescharacteristic
396C23×C43C22×D411yescharacteristic
397C23×C43C22×D411yescharacteristic
398C23×C43C22×D411yescharacteristic
399C23×C43C22×Q811yescharacteristic
400C23×C43C2×#4111yescharacteristic
401C23×C43C2×#4111yescharacteristic
402C23×C43C2×#4111yescharacteristic
403C23×C43C2×#4111yescharacteristic
404C23×C43C2×#4111yescharacteristic
405C23×C43C2×#4111yescharacteristic
406C23×C43H(5,𝔽2)11yescharacteristic
407C23×C43H(5,𝔽2)11yescharacteristic
408C23×C43H(5,𝔽2)11yescharacteristic
409C23×C432−1+411yescharacteristic
410D4×C43—232no—
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—22no—
446C2×C4×C43—22no—
447C2×C4×C43—416no—
448C2×C4×C43—416no—
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—41no—
497C2×C4×C43—41no—
498C2×C4×C43—41no—
499C2×C4×C43—41no—
500C2×C4×C43—41no—
501C2×C4×C43#12014yes—
502C2×C4×C43#12114yes—
503C2×C4×C43C22⋊Q814yes—
504#14733C4311yesmaximal, characteristic, direct product factor, Sylow
505C22×C43—24no—
506C22×C43—24no—
507C22×C43—24no—
508C22×C43—24no—
509C22×C43—24no—
510C22×C43—24no—
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×C43—42no—
530C22×C43—42no—
531C22×C43—42no—
532C22×C43—42no—
533C22×C43—42no—
534C22×C43—42no—
535C22×C43C2×#12011yescharacteristic
536C22×C43C2×#12111yescharacteristic
537C22×C43C2×C22⋊Q811yescharacteristic
538C22×C43C2×C22⋊Q811yescharacteristic
539C22×C43C2×C22⋊Q811yescharacteristic
540C22×C43#52511yescharacteristic
541C22×C43#52511yescharacteristic
542C22×C43#52511yescharacteristic
543C22×C43#52511yescharacteristic
544C22×C43#52511yescharacteristic
545C22×C43#52911yescharacteristic
546C22×C43#52911yescharacteristic
547C22×C43#53211yescharacteristic
548C22×C43#53411yescharacteristic
549C22×C43#53711yescharacteristic
550C22×C43#53811yescharacteristic
551C22×C43#53911yescharacteristic
552C22×C43#54011yescharacteristic
553C22×C43#54211yescharacteristic
554C22×C43D4211yescharacteristic
555C22×C43D4211yescharacteristic
556C22×C43#54611yescharacteristic
557C22×C43#54611yescharacteristic
558C22×C43#54611yescharacteristic
559C22×C43#54611yescharacteristic
560C22×C43#54711yescharacteristic
561C22×C43#54811yescharacteristic
562C22×C43D4×Q811yescharacteristic
563C22×C43#55011yescharacteristic
564C22×C43#55211yescharacteristic
565C22×C43#55311yescharacteristic
566C22×C43#55311yescharacteristic
567C22×C43#55411yescharacteristic
568C22×C43#55411yescharacteristic
569C22×C43#55411yescharacteristic
570C4×C43—24no—
571C4×C43—24no—
572C4×C43—24no—
573C4×C43—42no—
574C4×C43—42no—
575C4×C43—42no—
576C4×C43—42no—
577C4×C43—42no—
578C4×C43—42no—
579C4×C43—81no—
580C4×C43—81no—
581C4×C43—81no—
582C4×C43—81no—
583C22×C4×D4C2×C4311yescharacteristic
584C2×#398C2×C4311yescharacteristic, complemented
585C2×#396C2×C4311yescharacteristic, complemented
586C2×#385C2×C4311yescharacteristic, complemented
587C2×#385C2×C4311yescharacteristic, complemented
588C2×#380C2×C4311yescharacteristic, complemented
589#1441C2×C4311yescharacteristic, complemented
590#1439C2×C4311yescharacteristic, complemented
591#1439C2×C4311yescharacteristic, complemented
592#1439C2×C4311yescharacteristic, complemented
593#1438C2×C4311yescharacteristic
594#1438C2×C4311yescharacteristic
595#1436C2×C4311yescharacteristic, complemented
596#1436C2×C4311yescharacteristic, complemented
597C22⋊#95C2×C4311yescharacteristic, complemented
598C2×C43—44no—
599C2×C43—44no—
600C2×C43#239211yescharacteristic
601C2×C43#240711yescharacteristic
602C2×C43#241011yescharacteristic
603C2×C43#241711yescharacteristic
604C2×C43#244911yescharacteristic
605C2×C43#245011yescharacteristic
606C2×C43#245211yescharacteristic
607C2×C43#245411yescharacteristic
608C2×C43#245611yescharacteristic
609C2×C43#246011yescharacteristic
610C2×C43#246411yescharacteristic
611C2×C43#246811yescharacteristic
612C2×C43#257911yescharacteristic
613C2×C43#263011yescharacteristic
614C2×C43#284811yescharacteristic
615C23×D4C22×C4311yescharacteristic
616C24×C4C22×C4311yescharacteristic
617C24×C4C22×C4311yescharacteristic
618C2×C4×D4—24no—
619C2×C4×D4—24no—
620C2×C4×D4—24no—
621C22×C4⋊C4C22×C4311yescharacteristic
622C22×C4⋊C4C22×C4311yescharacteristic
623C22×C4⋊C4C22×C4311yescharacteristic
624C22×C4⋊C4C22×C4311yescharacteristic
625C22×C4⋊C4C22×C4311yescharacteristic
626C22×C4⋊C4C22×C4311yescharacteristic
627C22×C4⋊C4C22×C4311yescharacteristic
628C22×C22⋊C4C22×C4311yescharacteristic
629C22×C22⋊C4C22×C4311yescharacteristic
630C22×C22⋊C4C22×C4311yescharacteristic
631C22×C22⋊C4C22×C4311yescharacteristic
632C22×C22⋊C4C22×C4311yescharacteristic
633C22×C22⋊C4C22×C4311yescharacteristic
634C22×C22⋊C4C22×C4311yescharacteristic
635C22×C22⋊C4C22×C4311yescharacteristic
636C22×C22⋊C4C22×C4311yescharacteristic
637C22×C22⋊C4C22×C4311yescharacteristic
638C22×C42C22×C4311yescharacteristic
639#398—24no—
640#396—24no—
641#385—24no—
642#385—24no—
643#380—24no—
644C2×#95C22×C4311yescharacteristic
645C2×#95C22×C4311yescharacteristic
646C2×#95C22×C4311yescharacteristic
647C2×#95C22×C4311yescharacteristic
648C2×#95C22×C4311yescharacteristic
649C2×#95C22×C4311yescharacteristic
650C2×#95C22×C4311yescharacteristic
651C2×#95C22×C4311yescharacteristic
652C2×#95C22×C4311yescharacteristic
653C2×#95C22×C4311yescharacteristic
654C2×#95C22×C4311yescharacteristic
655C2×#95C22×C4311yescharacteristic
656C2×#95C22×C4311yescharacteristic
657C2×#95C22×C4311yescharacteristic
658C43#1473311yescharacteristic, direct product factor, Sylow
659C25C23×C4311yescharacteristic
660C25C23×C4311yescharacteristic
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4—22no—
667C22×D4Q8×C4314yes—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—41no—
678C23×C4—41no—
679C23×C4—41no—
680C23×C4—41no—
681C23×C4D4×C4314yes—
682C23×C4C23×C4311yescharacteristic
683C23×C4C23×C4311yescharacteristic
684C23×C4C23×C4311yescharacteristic
685C23×C4C23×C4311yescharacteristic
686C23×C4C23×C4311yescharacteristic
687C23×C4C23×C4311yescharacteristic
688C23×C4C23×C4311yescharacteristic
689C23×C4C23×C4311yescharacteristic
690C23×C4C23×C4311yescharacteristic
691C23×C4C23×C4311yescharacteristic
692C23×C4C23×C4311yescharacteristic
693C23×C4C23×C4311yescharacteristic
694C23×C4C23×C4311yescharacteristic
695C4×D4—232no—
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—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—41no—
713C2×C4⋊C4—41no—
714C2×C4⋊C4—41no—
715C2×C4⋊C4—41no—
716C2×C4⋊C4D4×C4314yes—
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—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C22⋊C4—41no—
741C2×C22⋊C4—41no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4D4×C4314yes—
747C2×C42—22no—
748C2×C42—22no—
749C2×C42—22no—
750#95—22no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—22no—
761#95—41no—
762#95—41no—
763#95D4×C4314yescomplemented
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—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24C2×D4×C4312yes—
789C24C2×D4×C4312yes—
790C24C2×Q8×C4312yes—
791C24C2×Q8×C4312yes—
792C24#41×C4312yes—
793C24#41×C4312yes—
794C24C24×C4311yescharacteristic
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—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—28no—
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—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—28no—
852C22×C4—28no—
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—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4C2×D4×C4312yes—
893C22×C4C2×D4×C4312yes—
894C22×C4C2×D4×C4312yes—
895C22×C4C2×D4×C4312yes—
896C22×C4C2×D4×C4312yes—
897C22×C4C2×D4×C4312yes—
898C22×C4C2×D4×C4312yes—
899C22×C4C2×D4×C4312yes—
900C22×C4C2×D4×C4312yes—
901C22×C4C2×D4×C4312yes—
902C22×C4C2×Q8×C4312yes—
903C22×C4#41×C4312yes—
904C22×C4#41×C4312yes—
905C22×C4#41×C4312yes—
906C22×C4#41×C4312yes—
907C4⋊C4—28no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C42—28no—
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—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
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—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23C22⋊Q8×C4314yes—
994C23C22⋊Q8×C4314yes—
995C23C22×D4×C4311yescharacteristic
996C23C22×D4×C4311yescharacteristic
997C23C22×D4×C4311yescharacteristic
998C23C22×D4×C4311yescharacteristic
999C23C22×Q8×C4311yescharacteristic
1000C23C2×#41×C4311yescharacteristic
1001C23C2×#41×C4311yescharacteristic
1002C23C2×#41×C4311yescharacteristic
1003C23C2×#41×C4311yescharacteristic
1004C23C2×#41×C4311yescharacteristic
1005C23C2×#41×C4311yescharacteristic
1006C23H(5,𝔽2)×C4311yescharacteristic
1007C23H(5,𝔽2)×C4311yescharacteristic
1008C23H(5,𝔽2)×C4311yescharacteristic
1009C232−1+4×C4311yescharacteristic
1010D4—232no—
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—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—416no—
1048C2×C4—416no—
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—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4#120×C4314yes—
1102C2×C4#121×C4314yes—
1103C2×C4C22⋊Q8×C4314yes—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22C2×#120×C4311yescharacteristic
1135C22C2×#121×C4311yescharacteristic
1136C22C2×C22⋊Q8×C4311yescharacteristic
1137C22C2×C22⋊Q8×C4311yescharacteristic
1138C22C2×C22⋊Q8×C4311yescharacteristic
1139C22C43×#52511yescharacteristic
1140C22C43×#52511yescharacteristic
1141C22C43×#52511yescharacteristic
1142C22C43×#52511yescharacteristic
1143C22C43×#52511yescharacteristic
1144C22C43×#52911yescharacteristic
1145C22C43×#52911yescharacteristic
1146C22C43×#53211yescharacteristic
1147C22C43×#53411yescharacteristic
1148C22C43×#53711yescharacteristic
1149C22C43×#53811yescharacteristic
1150C22C43×#53911yescharacteristic
1151C22C43×#54011yescharacteristic
1152C22C43×#54211yescharacteristic
1153C22D42×C4311yescharacteristic
1154C22D42×C4311yescharacteristic
1155C22C43×#54611yescharacteristic
1156C22C43×#54611yescharacteristic
1157C22C43×#54611yescharacteristic
1158C22C43×#54611yescharacteristic
1159C22C43×#54711yescharacteristic
1160C22C43×#54811yescharacteristic
1161C22D4×Q8×C4311yescharacteristic
1162C22C43×#55011yescharacteristic
1163C22C43×#55211yescharacteristic
1164C22C43×#55311yescharacteristic
1165C22C43×#55311yescharacteristic
1166C22C43×#55411yescharacteristic
1167C22C43×#55411yescharacteristic
1168C22C43×#55411yescharacteristic
1169C4—24no—
1170C4—24no—
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C2—44no—
1183C2—44no—
1184C2C43×#239211yescharacteristic
1185C2C43×#240711yescharacteristic
1186C2C43×#241011yescharacteristic
1187C2C43×#241711yescharacteristic
1188C2C43×#244911yescharacteristic
1189C2C43×#245011yescharacteristic
1190C2C43×#245211yescharacteristic
1191C2C43×#245411yescharacteristic
1192C2C43×#245611yescharacteristic
1193C2C43×#246011yescharacteristic
1194C2C43×#246411yescharacteristic
1195C2C43×#246811yescharacteristic
1196C2C43×#257911yescharacteristic
1197C2C43×#263011yescharacteristic
1198C2C43×#284811yescharacteristic
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×#398C2semidirect
3. C2×C43×#396C2semidirect
4. C2×C43×#385C2semidirect
5. C2×C43×#385C2semidirect
6. C2×C43×#380C2semidirect
7. C43×#1441C2semidirect
8. C43×#1439C2semidirect
9. C43×#1439C2semidirect
10. C43×#1439C2semidirect
13. C43×#1436C2semidirect
14. C43×#1436C2semidirect
15. C43×C22⋊#95C2semidirect
163. #95×C43D4semidirect
504. #14733C43direct (N × H)
584. C2×#398C2×C43semidirect
585. C2×#396C2×C43semidirect
586. C2×#385C2×C43semidirect
587. C2×#385C2×C43semidirect
588. C2×#380C2×C43semidirect
589. #1441C2×C43semidirect
590. #1439C2×C43semidirect
591. #1439C2×C43semidirect
592. #1439C2×C43semidirect
595. #1436C2×C43semidirect
596. #1436C2×C43semidirect
597. C22⋊#95C2×C43semidirect
658. C43#14733direct (N × H)
763. #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×#3982
C2×C43×#3962
C2×C43×#3852
C2×C43×#3802
C43×#14412
C43×#14392
C43×#14382
C43×#14362
C43×C22⋊#952
#1473343