Finite Group Databasebeta

← C43×#14520 #24934537

Subgroups — C43×#14520 #24934537

Order 11008.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#392C211yesmaximal, characteristic
2C2×C43×#390C211yesmaximal, characteristic, complemented
3C2×C43×#388C211yesmaximal, characteristic, complemented
4C2×C43×#386C211yesmaximal, characteristic, complemented
5C2×C43×#386C211yesmaximal, characteristic, complemented
6C43×#1442C211yesmaximal, characteristic, complemented
7C43×#1440C211yesmaximal, characteristic, complemented
8C43×#1438C211yesmaximal, characteristic, complemented
9C43×#1438C211yesmaximal, characteristic, complemented
10C43×#1438C211yesmaximal, characteristic, complemented
11C43×#1437C211yesmaximal, characteristic, complemented
12C43×#1437C211yesmaximal, characteristic, complemented
13C43×#1437C211yesmaximal, characteristic, complemented
14C43×#1434C211yesmaximal, characteristic, complemented
15C43×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C23×D4×C43C2211yescharacteristic
19C24×C4×C43C2211yescharacteristic
20C22×C4⋊C4×C43C2211yescharacteristic
21C22×C22⋊C4×C43C2211yescharacteristic
22C22×C22⋊C4×C43C2211yescharacteristic
23C22×C22⋊C4×C43C2211yescharacteristic
24C22×C22⋊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×C42×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C43×#392C418yescomplemented
38C43×#390—24no—
39C43×#388—24no—
40C43×#386—24no—
41C43×#386—24no—
42C2×#95×C43C2211yescharacteristic
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
56C25×C43C2311yescharacteristic
57C25×C43C2311yescharacteristic
58C25×C43C2311yescharacteristic
59C22×D4×C43—22no—
60C22×D4×C43—22no—
61C22×D4×C43—22no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43—41no—
66C22×D4×C43—41no—
67C22×D4×C43—41no—
68C22×D4×C43—41no—
69C22×D4×C43—41no—
70C22×D4×C43—41no—
71C22×D4×C43—41no—
72C22×D4×C43—41no—
73C22×D4×C43—41no—
74C22×D4×C43—41no—
75C22×D4×C43—41no—
76C22×D4×C43—41no—
77C22×D4×C43C2×C414yes—
78C22×D4×C43C2×C414yes—
79C22×D4×C43C2×C414yescomplemented
80C23×C4×C43—22no—
81C23×C4×C43—22no—
82C23×C4×C43—22no—
83C23×C4×C43—41no—
84C23×C4×C43—41no—
85C23×C4×C43—41no—
86C23×C4×C43—41no—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C23×C4×C43C2311yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—41no—
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—41no—
121C2×C22⋊C4×C43—41no—
122C2×C22⋊C4×C43—41no—
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×C43—41no—
130C2×C22⋊C4×C43—41no—
131C2×C22⋊C4×C43—41no—
132C2×C22⋊C4×C43—41no—
133C2×C22⋊C4×C43—41no—
134C2×C22⋊C4×C43—41no—
135C2×C22⋊C4×C43—41no—
136C2×C22⋊C4×C43—41no—
137C2×C22⋊C4×C43—41no—
138C2×C22⋊C4×C43—41no—
139C2×C22⋊C4×C43—41no—
140C2×C22⋊C4×C43C2×C414yes—
141C2×C22⋊C4×C43C2×C414yescomplemented
142C2×C22⋊C4×C43C2×C414yescomplemented
143C2×C22⋊C4×C43D414yescomplemented
144C2×C42×C43—22no—
145C2×C42×C43—22no—
146C2×C42×C43—22no—
147C2×C42×C43—41no—
148C2×C42×C43—41no—
149C2×C42×C43—41no—
150#95×C43—22no—
151#95×C43—22no—
152#95×C43—22no—
153#95×C43—22no—
154#95×C43—41no—
155#95×C43—41no—
156#95×C43—41no—
157#95×C43—41no—
158#95×C43—41no—
159#95×C43—41no—
160#95×C43—41no—
161#95×C43—41no—
162#95×C43C2×C414yescomplemented
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×C43—21no—
189C24×C43—21no—
190C24×C43—21no—
191C24×C43—21no—
192C24×C43—21no—
193C24×C43—21no—
194C24×C43—21no—
195C24×C43—21no—
196C24×C43—21no—
197C24×C43—21no—
198C24×C43—21no—
199C24×C43—21no—
200C24×C43—21no—
201C24×C43—21no—
202C24×C43—21no—
203C24×C43—21no—
204C24×C43C22×C412yes—
205C24×C43C22×C412yes—
206C24×C43C22×C412yes—
207C24×C43C2×D412yes—
208C24×C43#4112yes—
209C24×C43C2411yescharacteristic
210C2×D4×C43—28no—
211C2×D4×C43—28no—
212C2×D4×C43—28no—
213C2×D4×C43—44no—
214C2×D4×C43—44no—
215C2×D4×C43—44no—
216C2×D4×C43—44no—
217C2×D4×C43—44no—
218C2×D4×C43—44no—
219C2×D4×C43—44no—
220C2×D4×C43—44no—
221C2×D4×C43—44no—
222C2×D4×C43—44no—
223C2×D4×C43—44no—
224C2×D4×C43—44no—
225C2×D4×C43—44no—
226C2×D4×C43—44no—
227C2×D4×C43—44no—
228C2×D4×C43—44no—
229C2×D4×C43—44no—
230C2×D4×C43—44no—
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—21no—
282C22×C4×C43—21no—
283C22×C4×C43—21no—
284C22×C4×C43—21no—
285C22×C4×C43—21no—
286C22×C4×C43—21no—
287C22×C4×C43—21no—
288C22×C4×C43—21no—
289C22×C4×C43—21no—
290C22×C4×C43—21no—
291C22×C4×C43—21no—
292C22×C4×C43—21no—
293C22×C4×C43—21no—
294C22×C4×C43—21no—
295C22×C4×C43—21no—
296C22×C4×C43—21no—
297C22×C4×C43—21no—
298C22×C4×C43—21no—
299C22×C4×C43—21no—
300C22×C4×C43—21no—
301C22×C4×C43—21no—
302C22×C4×C43—21no—
303C22×C4×C43—44no—
304C22×C4×C43—44no—
305C22×C4×C43—44no—
306C22×C4×C43—44no—
307C22×C4×C43—44no—
308C22×C4×C43—44no—
309C22×C4×C43—44no—
310C22×C4×C43C22×C412yes—
311C22×C4×C43C22×C412yes—
312C22×C4×C43C22×C412yes—
313C22×C4×C43C22×C412yes—
314C22×C4×C43C2×D412yes—
315C22×C4×C43C2×D412yes—
316C22×C4×C43C2×D412yes—
317C22×C4×C43C2×D412yes—
318C22×C4×C43C2×D412yes—
319C22×C4×C43#4112yes—
320C22×C4×C43#4112yes—
321C22×C4×C43#4112yes—
322C4⋊C4×C43—44no—
323C22⋊C4×C43—28no—
324C22⋊C4×C43—44no—
325C22⋊C4×C43—44no—
326C22⋊C4×C43—44no—
327C22⋊C4×C43—44no—
328C22⋊C4×C43—44no—
329C22⋊C4×C43—44no—
330C22⋊C4×C43—44no—
331C22⋊C4×C43—44no—
332C22⋊C4×C43—44no—
333C22⋊C4×C43—44no—
334C22⋊C4×C43—44no—
335C22⋊C4×C43—44no—
336C22⋊C4×C43—44no—
337C42×C43—44no—
338C42×C43—44no—
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—22no—
362C23×C43—22no—
363C23×C43—22no—
364C23×C43—22no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—22no—
368C23×C43—22no—
369C23×C43—22no—
370C23×C43—22no—
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×C43—41no—
394C23×C43—41no—
395C23×C43—41no—
396C23×C43—41no—
397C23×C43—41no—
398C23×C43—41no—
399C23×C43—41no—
400C23×C43—41no—
401C23×C43—41no—
402C23×C43—41no—
403C23×C43—41no—
404C23×C43—41no—
405C23×C43—41no—
406C23×C43—41no—
407C23×C43—41no—
408C23×C43—41no—
409C23×C43—41no—
410C23×C43—41no—
411C23×C43—41no—
412C23×C43—41no—
413C23×C43—41no—
414C23×C43—41no—
415C23×C43—41no—
416C23×C43—41no—
417C23×C43—41no—
418C23×C43—41no—
419C23×C43—41no—
420C23×C43—41no—
421C23×C43—41no—
422C23×C43—41no—
423C23×C43—41no—
424C23×C43—41no—
425C23×C43—41no—
426C23×C43—41no—
427C23×C43—41no—
428C23×C43—41no—
429C23×C43—41no—
430C23×C43—41no—
431C23×C43—41no—
432C23×C43—41no—
433C23×C43—41no—
434C23×C43—41no—
435C23×C43—41no—
436C23×C43—41no—
437C23×C43—41no—
438C23×C43—41no—
439C23×C43—41no—
440C23×C43—41no—
441C23×C43—41no—
442C23×C43—41no—
443C23×C43C4×D414yes—
444C23×C43C23×C411yescharacteristic
445C23×C43C22×D411yescharacteristic
446C23×C43C22×D411yescharacteristic
447C23×C43C2×#4111yescharacteristic
448C23×C43C2×#4111yescharacteristic
449C23×C43C2×#4111yescharacteristic
450C23×C43C2×#4111yescharacteristic
451C23×C43H(5,𝔽2)11yescharacteristic
452C23×C43H(5,𝔽2)11yescharacteristic
453C23×C43H(5,𝔽2)11yescharacteristic
454C23×C43H(5,𝔽2)11yescharacteristic
455C23×C43H(5,𝔽2)11yescharacteristic
456C23×C43H(5,𝔽2)11yescharacteristic
457C23×C43H(5,𝔽2)11yescharacteristic
458C23×C43H(5,𝔽2)11yescharacteristic
459D4×C43—416no—
460D4×C43—416no—
461D4×C43—416no—
462C2×C4×C43—22no—
463C2×C4×C43—22no—
464C2×C4×C43—22no—
465C2×C4×C43—22no—
466C2×C4×C43—22no—
467C2×C4×C43—22no—
468C2×C4×C43—22no—
469C2×C4×C43—22no—
470C2×C4×C43—22no—
471C2×C4×C43—22no—
472C2×C4×C43—22no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—22no—
476C2×C4×C43—22no—
477C2×C4×C43—22no—
478C2×C4×C43—22no—
479C2×C4×C43—22no—
480C2×C4×C43—22no—
481C2×C4×C43—22no—
482C2×C4×C43—22no—
483C2×C4×C43—22no—
484C2×C4×C43—22no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—22no—
491C2×C4×C43—22no—
492C2×C4×C43—22no—
493C2×C4×C43—22no—
494C2×C4×C43—22no—
495C2×C4×C43—416no—
496C2×C4×C43—41no—
497C2×C4×C43—41no—
498C2×C4×C43—41no—
499C2×C4×C43—41no—
500C2×C4×C43—41no—
501C2×C4×C43—41no—
502C2×C4×C43—41no—
503C2×C4×C43—41no—
504C2×C4×C43—41no—
505C2×C4×C43—41no—
506C2×C4×C43—41no—
507C2×C4×C43—41no—
508C2×C4×C43—41no—
509C2×C4×C43—41no—
510C2×C4×C43—41no—
511C2×C4×C43—41no—
512C2×C4×C43—41no—
513C2×C4×C43—41no—
514C2×C4×C43—41no—
515C2×C4×C43—41no—
516C2×C4×C43—41no—
517C2×C4×C43—41no—
518C2×C4×C43—41no—
519C2×C4×C43—41no—
520C2×C4×C43—41no—
521C2×C4×C43—41no—
522C2×C4×C43—41no—
523C2×C4×C43—41no—
524C2×C4×C43—41no—
525C2×C4×C43—41no—
526C2×C4×C43—41no—
527C2×C4×C43—41no—
528C2×C4×C43—41no—
529C2×C4×C43—41no—
530C2×C4×C43—41no—
531C2×C4×C43—41no—
532C2×C4×C43—41no—
533C2×C4×C43—41no—
534C2×C4×C43—41no—
535C2×C4×C43—41no—
536C2×C4×C43—41no—
537C2×C4×C43—41no—
538C2×C4×C43—41no—
539C2×C4×C43—41no—
540C2×C4×C43—41no—
541C2×C4×C43—41no—
542C2×C4×C43—41no—
543C2×C4×C43—41no—
544C2×C4×C43—41no—
545C2×C4×C43—41no—
546C2×C4×C43C4×D414yes—
547#14520C4311yesmaximal, characteristic, direct product factor, Sylow
548C22×C43—24no—
549C22×C43—24no—
550C22×C43—24no—
551C22×C43—42no—
552C22×C43—42no—
553C22×C43—42no—
554C22×C43—42no—
555C22×C43—42no—
556C22×C43—42no—
557C22×C43—42no—
558C22×C43—42no—
559C22×C43—42no—
560C22×C43—42no—
561C22×C43—42no—
562C22×C43—42no—
563C22×C43—42no—
564C22×C43—42no—
565C22×C43—42no—
566C22×C43—42no—
567C22×C43—42no—
568C22×C43—42no—
569C22×C43—42no—
570C22×C43—42no—
571C22×C43—42no—
572C22×C43—42no—
573C22×C43—42no—
574C22×C43—42no—
575C22×C43—42no—
576C22×C43—42no—
577C22×C43—81no—
578C22×C43—81no—
579C22×C43—81no—
580C22×C43—81no—
581C22×C43—81no—
582C22×C43—81no—
583C22×C43—81no—
584C22×C43—81no—
585C22×C43—81no—
586C22×C43—81no—
587C22×C43—81no—
588C22×C43—81no—
589C22×C43—81no—
590C22×C43—81no—
591C22×C43—81no—
592C22×C43—81no—
593C22×C43C2×C4×D411yescharacteristic
594C22×C43C2×C4×D411yescharacteristic
595C22×C43C4×#4111yescharacteristic
596C22×C43#51811yescharacteristic
597C22×C43#51811yescharacteristic
598C22×C43#51811yescharacteristic
599C22×C43#51811yescharacteristic
600C22×C43#53411yescharacteristic
601C22×C43#53511yescharacteristic
602C22×C43#53511yescharacteristic
603C22×C43#53511yescharacteristic
604C22×C43#53811yescharacteristic
605C22×C43#53811yescharacteristic
606C22×C43#53811yescharacteristic
607C22×C43#53811yescharacteristic
608C22×C43#54011yescharacteristic
609C22×C43#54011yescharacteristic
610C22×C43#54011yescharacteristic
611C22×C43#54011yescharacteristic
612C22×C43D4211yescharacteristic
613C22×C43#54611yescharacteristic
614C22×C43#54611yescharacteristic
615C22×C43#54611yescharacteristic
616C22×C43#54611yescharacteristic
617C22×C43#54611yescharacteristic
618C22×C43#55011yescharacteristic
619C22×C43#55111yescharacteristic
620C22×C43#55311yescharacteristic
621C22×C43#55311yescharacteristic
622C22×C43#55311yescharacteristic
623C22×C43#55511yescharacteristic
624C22×C43#56011yescharacteristic
625C22×C43#56011yescharacteristic
626C22×C43#56011yescharacteristic
627C22×C43H(3,𝔽4)11yescharacteristic
628C4×C43—24no—
629C4×C43—42no—
630C4×C43—42no—
631C4×C43—42no—
632C4×C43—42no—
633C4×C43—42no—
634C4×C43—42no—
635C4×C43—42no—
636C4×C43—42no—
637C4×C43—42no—
638C4×C43—81no—
639C4×C43—81no—
640C2×#392C2×C4311yescharacteristic
641C2×#390C2×C4311yescharacteristic, complemented
642C2×#388C2×C4311yescharacteristic, complemented
643C2×#386C2×C4311yescharacteristic, complemented
644C2×#386C2×C4311yescharacteristic, complemented
645#1442C2×C4311yescharacteristic, complemented
646#1440C2×C4311yescharacteristic, complemented
647#1438C2×C4311yescharacteristic, complemented
648#1438C2×C4311yescharacteristic, complemented
649#1438C2×C4311yescharacteristic, complemented
650#1437C2×C4311yescharacteristic, complemented
651#1437C2×C4311yescharacteristic, complemented
652#1437C2×C4311yescharacteristic, complemented
653#1434C2×C4311yescharacteristic, complemented
654C22⋊#95C2×C4311yescharacteristic, complemented
655C2×C43—44no—
656C2×C43—82no—
657C2×C43—82no—
658C2×C43#232111yescharacteristic
659C2×C43#232811yescharacteristic
660C2×C43#233311yescharacteristic
661C2×C43#235811yescharacteristic
662C2×C43#236311yescharacteristic
663C2×C43#236411yescharacteristic
664C2×C43#237511yescharacteristic
665C2×C43#267011yescharacteristic
666C2×C43#267311yescharacteristic
667C2×C43#269911yescharacteristic
668C2×C43#270311yescharacteristic
669C2×C43#270311yescharacteristic
670C2×C43#271411yescharacteristic
671C2×C43#275311yescharacteristic
672C2×C43#275611yescharacteristic
673C23×D4C22×C4311yescharacteristic
674C23×D4C22×C4311yescharacteristic
675C23×D4C22×C4311yescharacteristic
676C24×C4C22×C4311yescharacteristic
677C22×C4⋊C4C22×C4311yescharacteristic
678C22×C22⋊C4C22×C4311yescharacteristic
679C22×C22⋊C4C22×C4311yescharacteristic
680C22×C22⋊C4C22×C4311yescharacteristic
681C22×C22⋊C4C22×C4311yescharacteristic
682C22×C22⋊C4C22×C4311yescharacteristic
683C22×C22⋊C4C22×C4311yescharacteristic
684C22×C22⋊C4C22×C4311yescharacteristic
685C22×C22⋊C4C22×C4311yescharacteristic
686C22×C22⋊C4C22×C4311yescharacteristic
687C22×C22⋊C4C22×C4311yescharacteristic
688C22×C22⋊C4C22×C4311yescharacteristic
689C22×C22⋊C4C22×C4311yescharacteristic
690C22×C22⋊C4C22×C4311yescharacteristic
691C22×C22⋊C4C22×C4311yescharacteristic
692C22×C42C22×C4311yescharacteristic
693C22×C42C22×C4311yescharacteristic
694#392C4×C4318yescomplemented
695#390—24no—
696#388—24no—
697#386—24no—
698#386—24no—
699C2×#95C22×C4311yescharacteristic
700C2×#95C22×C4311yescharacteristic
701C2×#95C22×C4311yescharacteristic
702C2×#95C22×C4311yescharacteristic
703C2×#95C22×C4311yescharacteristic
704C2×#95C22×C4311yescharacteristic
705C2×#95C22×C4311yescharacteristic
706C2×#95C22×C4311yescharacteristic
707C2×#95C22×C4311yescharacteristic
708C2×#95C22×C4311yescharacteristic
709C2×#95C22×C4311yescharacteristic
710C2×#95C22×C4311yescharacteristic
711C2×#95C22×C4311yescharacteristic
712C2×#95C22×C4311yescharacteristic
713C43#1452011yescharacteristic, direct product factor, Sylow
714C25C23×C4311yescharacteristic
715C25C23×C4311yescharacteristic
716C25C23×C4311yescharacteristic
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4C2×C4×C4314yes—
736C22×D4C2×C4×C4314yes—
737C22×D4C2×C4×C4314yescomplemented
738C23×C4—22no—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4C23×C4311yescharacteristic
746C23×C4C23×C4311yescharacteristic
747C23×C4C23×C4311yescharacteristic
748C23×C4C23×C4311yescharacteristic
749C23×C4C23×C4311yescharacteristic
750C23×C4C23×C4311yescharacteristic
751C23×C4C23×C4311yescharacteristic
752C23×C4C23×C4311yescharacteristic
753C23×C4C23×C4311yescharacteristic
754C23×C4C23×C4311yescharacteristic
755C23×C4C23×C4311yescharacteristic
756C23×C4C23×C4311yescharacteristic
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—41no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4C2×C4×C4314yes—
799C2×C22⋊C4C2×C4×C4314yescomplemented
800C2×C22⋊C4C2×C4×C4314yescomplemented
801C2×C22⋊C4D4×C4314yescomplemented
802C2×C42—22no—
803C2×C42—22no—
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807C2×C42—41no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—41no—
813#95—41no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95—41no—
819#95—41no—
820#95C2×C4×C4314yescomplemented
821#95D4×C4314yescomplemented
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24C22×C4×C4312yes—
863C24C22×C4×C4312yes—
864C24C22×C4×C4312yes—
865C24C2×D4×C4312yes—
866C24#41×C4312yes—
867C24C24×C4311yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4C22×C4×C4312yes—
969C22×C4C22×C4×C4312yes—
970C22×C4C22×C4×C4312yes—
971C22×C4C22×C4×C4312yes—
972C22×C4C2×D4×C4312yes—
973C22×C4C2×D4×C4312yes—
974C22×C4C2×D4×C4312yes—
975C22×C4C2×D4×C4312yes—
976C22×C4C2×D4×C4312yes—
977C22×C4#41×C4312yes—
978C22×C4#41×C4312yes—
979C22×C4#41×C4312yes—
980C4⋊C4—44no—
981C22⋊C4—28no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C42—44no—
996C42—44no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23C4×D4×C4314yes—
1102C23C23×C4×C4311yescharacteristic
1103C23C22×D4×C4311yescharacteristic
1104C23C22×D4×C4311yescharacteristic
1105C23C2×#41×C4311yescharacteristic
1106C23C2×#41×C4311yescharacteristic
1107C23C2×#41×C4311yescharacteristic
1108C23C2×#41×C4311yescharacteristic
1109C23H(5,𝔽2)×C4311yescharacteristic
1110C23H(5,𝔽2)×C4311yescharacteristic
1111C23H(5,𝔽2)×C4311yescharacteristic
1112C23H(5,𝔽2)×C4311yescharacteristic
1113C23H(5,𝔽2)×C4311yescharacteristic
1114C23H(5,𝔽2)×C4311yescharacteristic
1115C23H(5,𝔽2)×C4311yescharacteristic
1116C23H(5,𝔽2)×C4311yescharacteristic
1117D4—416no—
1118D4—416no—
1119D4—416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—416no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4C4×D4×C4314yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×C4×D4×C4311yescharacteristic
1251C22C2×C4×D4×C4311yescharacteristic
1252C22C4×#41×C4311yescharacteristic
1253C22C43×#51811yescharacteristic
1254C22C43×#51811yescharacteristic
1255C22C43×#51811yescharacteristic
1256C22C43×#51811yescharacteristic
1257C22C43×#53411yescharacteristic
1258C22C43×#53511yescharacteristic
1259C22C43×#53511yescharacteristic
1260C22C43×#53511yescharacteristic
1261C22C43×#53811yescharacteristic
1262C22C43×#53811yescharacteristic
1263C22C43×#53811yescharacteristic
1264C22C43×#53811yescharacteristic
1265C22C43×#54011yescharacteristic
1266C22C43×#54011yescharacteristic
1267C22C43×#54011yescharacteristic
1268C22C43×#54011yescharacteristic
1269C22D42×C4311yescharacteristic
1270C22C43×#54611yescharacteristic
1271C22C43×#54611yescharacteristic
1272C22C43×#54611yescharacteristic
1273C22C43×#54611yescharacteristic
1274C22C43×#54611yescharacteristic
1275C22C43×#55011yescharacteristic
1276C22C43×#55111yescharacteristic
1277C22C43×#55311yescharacteristic
1278C22C43×#55311yescharacteristic
1279C22C43×#55311yescharacteristic
1280C22C43×#55511yescharacteristic
1281C22C43×#56011yescharacteristic
1282C22C43×#56011yescharacteristic
1283C22C43×#56011yescharacteristic
1284C22C43×H(3,𝔽4)11yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2C43×#232111yescharacteristic
1301C2C43×#232811yescharacteristic
1302C2C43×#233311yescharacteristic
1303C2C43×#235811yescharacteristic
1304C2C43×#236311yescharacteristic
1305C2C43×#236411yescharacteristic
1306C2C43×#237511yescharacteristic
1307C2C43×#267011yescharacteristic
1308C2C43×#267311yescharacteristic
1309C2C43×#269911yescharacteristic
1310C2C43×#270311yescharacteristic
1311C2C43×#270311yescharacteristic
1312C2C43×#271411yescharacteristic
1313C2C43×#275311yescharacteristic
1314C2C43×#275611yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
prime radicalC2×C43×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#390C2semidirect
3. C2×C43×#388C2semidirect
4. C2×C43×#386C2semidirect
5. C2×C43×#386C2semidirect
6. C43×#1442C2semidirect
7. C43×#1440C2semidirect
8. C43×#1438C2semidirect
9. C43×#1438C2semidirect
10. C43×#1438C2semidirect
11. C43×#1437C2semidirect
12. C43×#1437C2semidirect
13. C43×#1437C2semidirect
14. C43×#1434C2semidirect
15. C43×C22⋊#95C2semidirect
37. C43×#392C4semidirect
79. C22×D4×C43C2×C4semidirect
141. C2×C22⋊C4×C43C2×C4semidirect
142. C2×C22⋊C4×C43C2×C4semidirect
143. C2×C22⋊C4×C43D4semidirect
162. #95×C43C2×C4semidirect
163. #95×C43D4semidirect
547. #14520C43direct (N × H)
641. C2×#390C2×C43semidirect
642. C2×#388C2×C43semidirect
643. C2×#386C2×C43semidirect
644. C2×#386C2×C43semidirect
645. #1442C2×C43semidirect
646. #1440C2×C43semidirect
647. #1438C2×C43semidirect
648. #1438C2×C43semidirect
649. #1438C2×C43semidirect
650. #1437C2×C43semidirect
651. #1437C2×C43semidirect
652. #1437C2×C43semidirect
653. #1434C2×C43semidirect
654. C22⋊#95C2×C43semidirect
694. #392C4×C43semidirect
713. C43#14520direct (N × H)
737. C22×D4C2×C4×C43semidirect
799. C2×C22⋊C4C2×C4×C43semidirect
800. C2×C22⋊C4C2×C4×C43semidirect
801. C2×C22⋊C4D4×C43semidirect
820. #95C2×C4×C43semidirect
821. #95D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3922
C2×C43×#3902
C2×C43×#3882
C2×C43×#3862
C43×#14422
C43×#14402
C43×#14382
C43×#14372
C43×#14342
C43×C22⋊#952
#1452043