Finite Group Databasebeta

← C43×#16272 #24936289

Subgroups — C43×#16272 #24936289

Order 11008.

2122 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#397C211yesmaximal, characteristic, complemented
2C2×C43×#394C211yesmaximal, characteristic, complemented
3C2×C43×#392C211yesmaximal, characteristic
4C2×C43×#386C211yesmaximal, characteristic, complemented
5C2×C43×#386C211yesmaximal, characteristic, complemented
6C2×C43×#385C211yesmaximal, characteristic, complemented
7C43×#1443C211yesmaximal, characteristic, complemented
8C43×#1442C211yesmaximal, characteristic, complemented
9C43×#1439C211yesmaximal, characteristic, complemented
10C43×#1439C211yesmaximal, characteristic, complemented
11C43×#1439C211yesmaximal, characteristic, complemented
12C43×#1439C211yesmaximal, characteristic, complemented
13C43×#1438C211yesmaximal, characteristic, complemented
14C43×#1438C211yesmaximal, characteristic, complemented
15C43×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C23×D4×C43C2211yescharacteristic
19C24×C4×C43C2211yescharacteristic
20C22×C4⋊C4×C43C2211yescharacteristic
21C22×C4⋊C4×C43C2211yescharacteristic
22C22×C4⋊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×C22⋊C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2211yescharacteristic
37C43×#397—24no—
38C43×#394—24no—
39C43×#392—24no—
40C43×#386—24no—
41C43×#386—24no—
42C43×#385—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
57C25×C43C2311yescharacteristic
58C25×C43C2311yescharacteristic
59C25×C43C2311yescharacteristic
60C22×D4×C43—22no—
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×C43—22no—
68C22×D4×C43—22no—
69C22×D4×C43—22no—
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×C43—41no—
78C22×D4×C43—41no—
79C22×D4×C43—41no—
80C22×D4×C43D414yes—
81C23×C4×C43—22no—
82C23×C4×C43—22no—
83C23×C4×C43—22no—
84C23×C4×C43—41no—
85C23×C4×C43—41no—
86C23×C4×C43—41no—
87C23×C4×C43—41no—
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
99C23×C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—41no—
105C2×C4⋊C4×C43—41no—
106C2×C4⋊C4×C43—41no—
107C2×C4⋊C4×C43—41no—
108C2×C4⋊C4×C43—41no—
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—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—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×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×C43—41no—
147C2×C22⋊C4×C43—41no—
148C2×C22⋊C4×C43—41no—
149C2×C22⋊C4×C43—41no—
150C2×C22⋊C4×C43—41no—
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×C43—41no—
160#95×C43—41no—
161#95×C43—41no—
162#95×C43—41no—
163#95×C43D414yescomplemented
164#95×C43D414yescomplemented
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×C43—21no—
205C24×C43C2×D412yes—
206C24×C43C2×D412yes—
207C24×C43#4112yes—
208C24×C43#4112yes—
209C24×C43#4112yes—
210C24×C43C2411yescharacteristic
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—
231C2×D4×C43—44no—
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—21no—
304C22×C4×C43—21no—
305C22×C4×C43—21no—
306C22×C4×C43—21no—
307C22×C4×C43—21no—
308C22×C4×C43—44no—
309C22×C4×C43—44no—
310C22×C4×C43—44no—
311C22×C4×C43—44no—
312C22×C4×C43—44no—
313C22×C4×C43—44no—
314C22×C4×C43—44no—
315C22×C4×C43C2×D412yes—
316C22×C4×C43C2×D412yes—
317C22×C4×C43C2×D412yes—
318C22×C4×C43C2×D412yes—
319C22×C4×C43C2×D412yes—
320C22×C4×C43C2×D412yes—
321C22×C4×C43C2×D412yes—
322C22×C4×C43#4112yes—
323C4⋊C4×C43—44no—
324C4⋊C4×C43—44no—
325C4⋊C4×C43—44no—
326C22⋊C4×C43—28no—
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—
337C22⋊C4×C43—44no—
338C22⋊C4×C43—44no—
339C22⋊C4×C43—44no—
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—22no—
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×C43—41no—
444C23×C43#12314yes—
445C23×C43C22×D411yescharacteristic
446C23×C43C22×D411yescharacteristic
447C23×C43C22×D411yescharacteristic
448C23×C43C2×#4111yescharacteristic
449C23×C43C2×#4111yescharacteristic
450C23×C43C2×#4111yescharacteristic
451C23×C43C2×#4111yescharacteristic
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
459C23×C432−1+411yescharacteristic
460D4×C43—416no—
461D4×C43—416no—
462D4×C43—416no—
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—416no—
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—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×C43—41no—
547C2×C4×C43—41no—
548#16272C4311yesmaximal, characteristic, direct product factor, Sylow
549C22×C43—24no—
550C22×C43—24no—
551C22×C43—24no—
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—42no—
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×C43—81no—
594C22×C43C2×#12311yescharacteristic
595C22×C43#52511yescharacteristic
596C22×C43#52511yescharacteristic
597C22×C43#53411yescharacteristic
598C22×C43#53411yescharacteristic
599C22×C43#53511yescharacteristic
600C22×C43#53511yescharacteristic
601C22×C43#53511yescharacteristic
602C22×C43#53711yescharacteristic
603C22×C43#53811yescharacteristic
604C22×C43#53811yescharacteristic
605C22×C43#53811yescharacteristic
606C22×C43#53811yescharacteristic
607C22×C43#53811yescharacteristic
608C22×C43#53811yescharacteristic
609C22×C43#53811yescharacteristic
610C22×C43#53811yescharacteristic
611C22×C43#53911yescharacteristic
612C22×C43#53911yescharacteristic
613C22×C43D4211yescharacteristic
614C22×C43D4211yescharacteristic
615C22×C43D4211yescharacteristic
616C22×C43#54611yescharacteristic
617C22×C43#54611yescharacteristic
618C22×C43#54611yescharacteristic
619C22×C43#54711yescharacteristic
620C22×C43#54811yescharacteristic
621C22×C43#55011yescharacteristic
622C22×C43#55111yescharacteristic
623C22×C43#55311yescharacteristic
624C22×C43#55311yescharacteristic
625C22×C43#56011yescharacteristic
626C22×C43#56011yescharacteristic
627C22×C43#56211yescharacteristic
628C22×C43#56211yescharacteristic
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—81no—
638C4×C43—81no—
639C4×C43—81no—
640C4×C43—81no—
641C2×#397C2×C4311yescharacteristic, complemented
642C2×#394C2×C4311yescharacteristic, complemented
643C2×#392C2×C4311yescharacteristic
644C2×#386C2×C4311yescharacteristic, complemented
645C2×#386C2×C4311yescharacteristic, complemented
646C2×#385C2×C4311yescharacteristic, complemented
647#1443C2×C4311yescharacteristic, complemented
648#1442C2×C4311yescharacteristic, complemented
649#1439C2×C4311yescharacteristic, complemented
650#1439C2×C4311yescharacteristic, complemented
651#1439C2×C4311yescharacteristic, complemented
652#1439C2×C4311yescharacteristic, complemented
653#1438C2×C4311yescharacteristic, complemented
654#1438C2×C4311yescharacteristic, complemented
655#1438C2×C4311yescharacteristic, complemented
656C2×C43—44no—
657C2×C43—82no—
658C2×C43—82no—
659C2×C43#241811yescharacteristic
660C2×C43#244311yescharacteristic
661C2×C43#245611yescharacteristic
662C2×C43#262211yescharacteristic
663C2×C43#263111yescharacteristic
664C2×C43#263611yescharacteristic
665C2×C43#266911yescharacteristic
666C2×C43#267611yescharacteristic
667C2×C43#267811yescharacteristic
668C2×C43#268211yescharacteristic
669C2×C43#269611yescharacteristic
670C2×C43#270811yescharacteristic
671C2×C43#271411yescharacteristic
672C2×C43#277811yescharacteristic
673C2×C43#282611yescharacteristic
674C23×D4C22×C4311yescharacteristic
675C23×D4C22×C4311yescharacteristic
676C23×D4C22×C4311yescharacteristic
677C24×C4C22×C4311yescharacteristic
678C22×C4⋊C4C22×C4311yescharacteristic
679C22×C4⋊C4C22×C4311yescharacteristic
680C22×C4⋊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×C22⋊C4C22×C4311yescharacteristic
693C22×C22⋊C4C22×C4311yescharacteristic
694C22×C22⋊C4C22×C4311yescharacteristic
695#397—24no—
696#394—24no—
697#392—24no—
698#386—24no—
699#386—24no—
700#385—24no—
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
713C2×#95C22×C4311yescharacteristic
714C2×#95C22×C4311yescharacteristic
715C43#1627211yescharacteristic, direct product factor, Sylow
716C25C23×C4311yescharacteristic
717C25C23×C4311yescharacteristic
718C25C23×C4311yescharacteristic
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4D4×C4314yes—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—22no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4—41no—
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
757C23×C4C23×C4311yescharacteristic
758C23×C4C23×C4311yescharacteristic
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C4⋊C4—41no—
766C2×C4⋊C4—41no—
767C2×C4⋊C4—41no—
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—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
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⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—41no—
818#95—41no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95D4×C4314yescomplemented
823#95D4×C4314yescomplemented
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—
862C24—21no—
863C24—21no—
864C24C2×D4×C4312yes—
865C24C2×D4×C4312yes—
866C24#41×C4312yes—
867C24#41×C4312yes—
868C24#41×C4312yes—
869C24C24×C4311yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
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—
889C2×D4—44no—
890C2×D4—44no—
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—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4C2×D4×C4312yes—
975C22×C4C2×D4×C4312yes—
976C22×C4C2×D4×C4312yes—
977C22×C4C2×D4×C4312yes—
978C22×C4C2×D4×C4312yes—
979C22×C4C2×D4×C4312yes—
980C22×C4C2×D4×C4312yes—
981C22×C4#41×C4312yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C22⋊C4—28no—
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—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
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—22no—
1030C23—22no—
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—
1101C23—41no—
1102C23—41no—
1103C23#123×C4314yes—
1104C23C22×D4×C4311yescharacteristic
1105C23C22×D4×C4311yescharacteristic
1106C23C22×D4×C4311yescharacteristic
1107C23C2×#41×C4311yescharacteristic
1108C23C2×#41×C4311yescharacteristic
1109C23C2×#41×C4311yescharacteristic
1110C23C2×#41×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
1117C23H(5,𝔽2)×C4311yescharacteristic
1118C232−1+4×C4311yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
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—416no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
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×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
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—42no—
1235C22—42no—
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—
1250C22—81no—
1251C22—81no—
1252C22C2×#123×C4311yescharacteristic
1253C22C43×#52511yescharacteristic
1254C22C43×#52511yescharacteristic
1255C22C43×#53411yescharacteristic
1256C22C43×#53411yescharacteristic
1257C22C43×#53511yescharacteristic
1258C22C43×#53511yescharacteristic
1259C22C43×#53511yescharacteristic
1260C22C43×#53711yescharacteristic
1261C22C43×#53811yescharacteristic
1262C22C43×#53811yescharacteristic
1263C22C43×#53811yescharacteristic
1264C22C43×#53811yescharacteristic
1265C22C43×#53811yescharacteristic
1266C22C43×#53811yescharacteristic
1267C22C43×#53811yescharacteristic
1268C22C43×#53811yescharacteristic
1269C22C43×#53911yescharacteristic
1270C22C43×#53911yescharacteristic
1271C22D42×C4311yescharacteristic
1272C22D42×C4311yescharacteristic
1273C22D42×C4311yescharacteristic
1274C22C43×#54611yescharacteristic
1275C22C43×#54611yescharacteristic
1276C22C43×#54611yescharacteristic
1277C22C43×#54711yescharacteristic
1278C22C43×#54811yescharacteristic
1279C22C43×#55011yescharacteristic
1280C22C43×#55111yescharacteristic
1281C22C43×#55311yescharacteristic
1282C22C43×#55311yescharacteristic
1283C22C43×#56011yescharacteristic
1284C22C43×#56011yescharacteristic
1285C22C43×#56211yescharacteristic
1286C22C43×#56211yescharacteristic
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C43×#241811yescharacteristic
1303C2C43×#244311yescharacteristic
1304C2C43×#245611yescharacteristic
1305C2C43×#262211yescharacteristic
1306C2C43×#263111yescharacteristic
1307C2C43×#263611yescharacteristic
1308C2C43×#266911yescharacteristic
1309C2C43×#267611yescharacteristic
1310C2C43×#267811yescharacteristic
1311C2C43×#268211yescharacteristic
1312C2C43×#269611yescharacteristic
1313C2C43×#270811yescharacteristic
1314C2C43×#271411yescharacteristic
1315C2C43×#277811yescharacteristic
1316C2C43×#282611yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutator, Frattini, cosocleC24C24×C43
prime radicalC2×C43×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#397C2semidirect
2. C2×C43×#394C2semidirect
4. C2×C43×#386C2semidirect
5. C2×C43×#386C2semidirect
6. C2×C43×#385C2semidirect
7. C43×#1443C2semidirect
8. C43×#1442C2semidirect
9. C43×#1439C2semidirect
10. C43×#1439C2semidirect
11. C43×#1439C2semidirect
12. C43×#1439C2semidirect
13. C43×#1438C2semidirect
14. C43×#1438C2semidirect
15. C43×#1438C2semidirect
163. #95×C43D4semidirect
164. #95×C43D4semidirect
548. #16272C43direct (N × H)
641. C2×#397C2×C43semidirect
642. C2×#394C2×C43semidirect
644. C2×#386C2×C43semidirect
645. C2×#386C2×C43semidirect
646. C2×#385C2×C43semidirect
647. #1443C2×C43semidirect
648. #1442C2×C43semidirect
649. #1439C2×C43semidirect
650. #1439C2×C43semidirect
651. #1439C2×C43semidirect
652. #1439C2×C43semidirect
653. #1438C2×C43semidirect
654. #1438C2×C43semidirect
655. #1438C2×C43semidirect
715. C43#16272direct (N × H)
822. #95D4×C43semidirect
823. #95D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3972
C2×C43×#3942
C2×C43×#3922
C2×C43×#3862
C2×C43×#3852
C43×#14432
C43×#14422
C43×#14392
C43×#14382
#1627243