Finite Group Databasebeta

← C43×#15611 #24935628

Subgroups — C43×#15611 #24935628

Order 11008.

2350 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C43C211yesmaximal, characteristic, complemented
2C2×C43×#397C211yesmaximal, characteristic, complemented
3C2×C43×#394C211yesmaximal, characteristic, complemented
4C2×C43×#392C211yesmaximal, characteristic
5C2×C43×#390C211yesmaximal, characteristic, complemented
6C2×C43×#386C211yesmaximal, characteristic, complemented
7C43×#1441C211yesmaximal, characteristic, complemented
8C43×#1439C211yesmaximal, characteristic, complemented
9C43×#1439C211yesmaximal, characteristic, complemented
10C43×#1439C211yesmaximal, characteristic, complemented
11C43×#1438C211yesmaximal, characteristic, complemented
12C43×#1438C211yesmaximal, characteristic, complemented
13C43×#1437C211yesmaximal, characteristic, complemented
14C43×C4⋊#95C211yesmaximal, characteristic, complemented
15C43×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C23×D4×C43C2211yescharacteristic
19C24×C4×C43C2211yescharacteristic
20C2×#123×C43—24no—
21C2×#123×C43—24no—
22C2×#123×C43—24no—
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×C22⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2211yescharacteristic
40C22×C22⋊C4×C43C2211yescharacteristic
41C22×C42×C43C2211yescharacteristic
42C43×#397—24no—
43C43×#394—24no—
44C43×#392—24no—
45C43×#390—24no—
46C43×#386—24no—
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
61C25×C43C2311yescharacteristic
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—22no—
71C22×D4×C43—22no—
72C22×D4×C43—22no—
73C22×D4×C43—22no—
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×C43—41no—
81C22×D4×C43—41no—
82C22×D4×C43D414yes—
83C23×C4×C43—22no—
84C23×C4×C43—22no—
85C23×C4×C43—22no—
86C23×C4×C43—22no—
87C23×C4×C43—22no—
88C23×C4×C43—41no—
89C23×C4×C43—41no—
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
100C23×C4×C43C2311yescharacteristic
101C23×C4×C43C2311yescharacteristic
102#123×C43—232no—
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×C43D414yescomplemented
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—22no—
137C2×C22⋊C4×C43—22no—
138C2×C22⋊C4×C43—22no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—22no—
141C2×C22⋊C4×C43—22no—
142C2×C22⋊C4×C43—22no—
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—
151C2×C22⋊C4×C43—41no—
152C2×C22⋊C4×C43—41no—
153C2×C22⋊C4×C43—41no—
154C2×C22⋊C4×C43—41no—
155C2×C22⋊C4×C43D414yescomplemented
156C2×C22⋊C4×C43D414yescomplemented
157C2×C42×C43—22no—
158C2×C42×C43—22no—
159C2×C42×C43—41no—
160#95×C43—22no—
161#95×C43—22no—
162#95×C43—22no—
163#95×C43—22no—
164#95×C43—22no—
165#95×C43—22no—
166#95×C43—22no—
167#95×C43—41no—
168#95×C43—41no—
169#95×C43—41no—
170#95×C43—41no—
171#95×C43—41no—
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×C43—21no—
206C24×C43—21no—
207C24×C43—21no—
208C24×C43—21no—
209C24×C43—21no—
210C24×C43—21no—
211C24×C43—21no—
212C24×C43C2×D412yes—
213C24×C43C2×D412yes—
214C24×C43C2×D412yes—
215C24×C43C2×D412yes—
216C24×C43#4112yes—
217C24×C43C2411yescharacteristic
218C2×D4×C43—28no—
219C2×D4×C43—28no—
220C2×D4×C43—28no—
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—
232C2×D4×C43—44no—
233C2×D4×C43—44no—
234C2×D4×C43—44no—
235C2×D4×C43—44no—
236C2×D4×C43—44no—
237C2×D4×C43—44no—
238C2×D4×C43—44no—
239C22×C4×C43—28no—
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—21no—
309C22×C4×C43—21no—
310C22×C4×C43—21no—
311C22×C4×C43—21no—
312C22×C4×C43—44no—
313C22×C4×C43—44no—
314C22×C4×C43—44no—
315C22×C4×C43—44no—
316C22×C4×C43—44no—
317C22×C4×C43—44no—
318C22×C4×C43C2×D412yes—
319C22×C4×C43C2×D412yes—
320C22×C4×C43C2×D412yes—
321C22×C4×C43C2×D412yes—
322C22×C4×C43C2×D412yes—
323C22×C4×C43C2×D412yes—
324C22×C4×C43C2×D412yes—
325C22×C4×C43C2×D412yes—
326C22×C4×C43#4112yes—
327C22×C4×C43#4112yes—
328C22×C4×C43#4112yes—
329C22×C4×C43#4112yes—
330C4⋊C4×C43—28no—
331C4⋊C4×C43—28no—
332C4⋊C4×C43—44no—
333C4⋊C4×C43—44no—
334C22⋊C4×C43—28no—
335C22⋊C4×C43—28no—
336C22⋊C4×C43—28no—
337C22⋊C4×C43—44no—
338C22⋊C4×C43—44no—
339C22⋊C4×C43—44no—
340C22⋊C4×C43—44no—
341C22⋊C4×C43—44no—
342C22⋊C4×C43—44no—
343C22⋊C4×C43—44no—
344C22⋊C4×C43—44no—
345C22⋊C4×C43—44no—
346C22⋊C4×C43—44no—
347C22⋊C4×C43—44no—
348C42×C43—44no—
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—22no—
373C23×C43—22no—
374C23×C43—22no—
375C23×C43—22no—
376C23×C43—22no—
377C23×C43—22no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
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—41no—
445C23×C43—41no—
446C23×C43—41no—
447C23×C43—41no—
448C23×C43—41no—
449C23×C43—41no—
450C23×C43—41no—
451C23×C43—41no—
452C23×C43—41no—
453C23×C43#12114yes—
454C23×C43C22×D411yescharacteristic
455C23×C43C22×D411yescharacteristic
456C23×C43C22×D411yescharacteristic
457C23×C43C22×D411yescharacteristic
458C23×C43C2×#4111yescharacteristic
459C23×C43C2×#4111yescharacteristic
460C23×C43C2×#4111yescharacteristic
461C23×C43C2×#4111yescharacteristic
462C23×C43C2×#4111yescharacteristic
463C23×C43H(5,𝔽2)11yescharacteristic
464C23×C43H(5,𝔽2)11yescharacteristic
465C23×C43H(5,𝔽2)11yescharacteristic
466C23×C43H(5,𝔽2)11yescharacteristic
467C23×C43H(5,𝔽2)11yescharacteristic
468C23×C432−1+411yescharacteristic
469D4×C43—416no—
470D4×C43—416no—
471D4×C43—416no—
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—22no—
496C2×C4×C43—22no—
497C2×C4×C43—22no—
498C2×C4×C43—22no—
499C2×C4×C43—22no—
500C2×C4×C43—22no—
501C2×C4×C43—22no—
502C2×C4×C43—416no—
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—
548C2×C4×C43—41no—
549C2×C4×C43—41no—
550C2×C4×C43—41no—
551C2×C4×C43—41no—
552C2×C4×C43—41no—
553C2×C4×C43—41no—
554C2×C4×C43—41no—
555C2×C4×C43#12014yes—
556C2×C4×C43#12314yescomplemented
557#15611C4311yesmaximal, characteristic, direct product factor, Sylow
558C22×C43—24no—
559C22×C43—24no—
560C22×C43—24no—
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—42no—
579C22×C43—42no—
580C22×C43—42no—
581C22×C43—42no—
582C22×C43—42no—
583C22×C43—42no—
584C22×C43—42no—
585C22×C43—42no—
586C22×C43—42no—
587C22×C43—81no—
588C22×C43—81no—
589C22×C43—81no—
590C22×C43—81no—
591C22×C43—81no—
592C22×C43—81no—
593C22×C43—81no—
594C22×C43—81no—
595C22×C43—81no—
596C22×C43—81no—
597C22×C43—81no—
598C22×C43—81no—
599C22×C43—81no—
600C22×C43—81no—
601C22×C43—81no—
602C22×C43—81no—
603C22×C43C2×#12011yescharacteristic
604C22×C43C2×#12111yescharacteristic
605C22×C43C2×#12311yescharacteristic
606C22×C43#52911yescharacteristic
607C22×C43#53211yescharacteristic
608C22×C43#53211yescharacteristic
609C22×C43#53411yescharacteristic
610C22×C43#53511yescharacteristic
611C22×C43#53511yescharacteristic
612C22×C43#53711yescharacteristic
613C22×C43#53811yescharacteristic
614C22×C43#53811yescharacteristic
615C22×C43#53911yescharacteristic
616C22×C43#54011yescharacteristic
617C22×C43#54211yescharacteristic
618C22×C43D4211yescharacteristic
619C22×C43D4211yescharacteristic
620C22×C43#54611yescharacteristic
621C22×C43#54611yescharacteristic
622C22×C43#54611yescharacteristic
623C22×C43#54611yescharacteristic
624C22×C43#54611yescharacteristic
625C22×C43#54611yescharacteristic
626C22×C43#54611yescharacteristic
627C22×C43#54711yescharacteristic
628C22×C43#54711yescharacteristic
629C22×C43#54711yescharacteristic
630C22×C43#55011yescharacteristic
631C22×C43#55011yescharacteristic
632C22×C43#55111yescharacteristic
633C22×C43#55111yescharacteristic
634C22×C43#55311yescharacteristic
635C22×C43#55911yescharacteristic
636C22×C43#56011yescharacteristic
637C22×C43#56211yescharacteristic
638C4×C43—24no—
639C4×C43—24no—
640C4×C43—42no—
641C4×C43—42no—
642C4×C43—42no—
643C4×C43—42no—
644C4×C43—42no—
645C4×C43—42no—
646C4×C43—81no—
647C4×C43—81no—
648C4×C43—81no—
649C4×C43—81no—
650C22×#123C2×C4311yescharacteristic, complemented
651C2×#397C2×C4311yescharacteristic, complemented
652C2×#394C2×C4311yescharacteristic, complemented
653C2×#392C2×C4311yescharacteristic
654C2×#390C2×C4311yescharacteristic, complemented
655C2×#386C2×C4311yescharacteristic, complemented
656#1441C2×C4311yescharacteristic, complemented
657#1439C2×C4311yescharacteristic, complemented
658#1439C2×C4311yescharacteristic, complemented
659#1439C2×C4311yescharacteristic, complemented
660#1438C2×C4311yescharacteristic, complemented
661#1438C2×C4311yescharacteristic, complemented
662#1437C2×C4311yescharacteristic, complemented
663C4⋊#95C2×C4311yescharacteristic, complemented
664C22⋊#95C2×C4311yescharacteristic, complemented
665C2×C43—44no—
666C2×C43—82no—
667C2×C43—82no—
668C2×C43#240811yescharacteristic
669C2×C43#241211yescharacteristic
670C2×C43#242211yescharacteristic
671C2×C43#242511yescharacteristic
672C2×C43#243011yescharacteristic
673C2×C43#243111yescharacteristic
674C2×C43#244511yescharacteristic
675C2×C43#255411yescharacteristic
676C2×C43#255711yescharacteristic
677C2×C43#267811yescharacteristic
678C2×C43#268211yescharacteristic
679C2×C43#270311yescharacteristic
680C2×C43#270511yescharacteristic
681C2×C43#270611yescharacteristic
682C2×C43#271011yescharacteristic
683C23×D4C22×C4311yescharacteristic
684C23×D4C22×C4311yescharacteristic
685C23×D4C22×C4311yescharacteristic
686C24×C4C22×C4311yescharacteristic
687C2×#123—24no—
688C2×#123—24no—
689C2×#123—24no—
690C22×C4⋊C4C22×C4311yescharacteristic
691C22×C4⋊C4C22×C4311yescharacteristic
692C22×C4⋊C4C22×C4311yescharacteristic
693C22×C4⋊C4C22×C4311yescharacteristic
694C22×C22⋊C4C22×C4311yescharacteristic
695C22×C22⋊C4C22×C4311yescharacteristic
696C22×C22⋊C4C22×C4311yescharacteristic
697C22×C22⋊C4C22×C4311yescharacteristic
698C22×C22⋊C4C22×C4311yescharacteristic
699C22×C22⋊C4C22×C4311yescharacteristic
700C22×C22⋊C4C22×C4311yescharacteristic
701C22×C22⋊C4C22×C4311yescharacteristic
702C22×C22⋊C4C22×C4311yescharacteristic
703C22×C22⋊C4C22×C4311yescharacteristic
704C22×C22⋊C4C22×C4311yescharacteristic
705C22×C22⋊C4C22×C4311yescharacteristic
706C22×C22⋊C4C22×C4311yescharacteristic
707C22×C22⋊C4C22×C4311yescharacteristic
708C22×C42C22×C4311yescharacteristic
709#397—24no—
710#394—24no—
711#392—24no—
712#390—24no—
713#386—24no—
714C2×#95C22×C4311yescharacteristic
715C2×#95C22×C4311yescharacteristic
716C2×#95C22×C4311yescharacteristic
717C2×#95C22×C4311yescharacteristic
718C2×#95C22×C4311yescharacteristic
719C2×#95C22×C4311yescharacteristic
720C2×#95C22×C4311yescharacteristic
721C2×#95C22×C4311yescharacteristic
722C2×#95C22×C4311yescharacteristic
723C2×#95C22×C4311yescharacteristic
724C2×#95C22×C4311yescharacteristic
725C2×#95C22×C4311yescharacteristic
726C43#1561111yescharacteristic, direct product factor, Sylow
727C25C23×C4311yescharacteristic
728C25C23×C4311yescharacteristic
729C25C23×C4311yescharacteristic
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4D4×C4314yes—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—41no—
757C23×C4—41no—
758C23×C4C23×C4311yescharacteristic
759C23×C4C23×C4311yescharacteristic
760C23×C4C23×C4311yescharacteristic
761C23×C4C23×C4311yescharacteristic
762C23×C4C23×C4311yescharacteristic
763C23×C4C23×C4311yescharacteristic
764C23×C4C23×C4311yescharacteristic
765C23×C4C23×C4311yescharacteristic
766C23×C4C23×C4311yescharacteristic
767C23×C4C23×C4311yescharacteristic
768C23×C4C23×C4311yescharacteristic
769C23×C4C23×C4311yescharacteristic
770#123—232no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—22no—
777C2×C4⋊C4—22no—
778C2×C4⋊C4—22no—
779C2×C4⋊C4—22no—
780C2×C4⋊C4—41no—
781C2×C4⋊C4—41no—
782C2×C4⋊C4D4×C4314yescomplemented
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—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4D4×C4314yescomplemented
824C2×C22⋊C4D4×C4314yescomplemented
825C2×C42—22no—
826C2×C42—22no—
827C2×C42—41no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—41no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95—41no—
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—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24C2×D4×C4312yes—
881C24C2×D4×C4312yes—
882C24C2×D4×C4312yes—
883C24C2×D4×C4312yes—
884C24#41×C4312yes—
885C24C24×C4311yescharacteristic
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
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—28no—
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—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4C2×D4×C4312yes—
987C22×C4C2×D4×C4312yes—
988C22×C4C2×D4×C4312yes—
989C22×C4C2×D4×C4312yes—
990C22×C4C2×D4×C4312yes—
991C22×C4C2×D4×C4312yes—
992C22×C4C2×D4×C4312yes—
993C22×C4C2×D4×C4312yes—
994C22×C4#41×C4312yes—
995C22×C4#41×C4312yes—
996C22×C4#41×C4312yes—
997C22×C4#41×C4312yes—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C42—44no—
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—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
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—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23#121×C4314yes—
1122C23C22×D4×C4311yescharacteristic
1123C23C22×D4×C4311yescharacteristic
1124C23C22×D4×C4311yescharacteristic
1125C23C22×D4×C4311yescharacteristic
1126C23C2×#41×C4311yescharacteristic
1127C23C2×#41×C4311yescharacteristic
1128C23C2×#41×C4311yescharacteristic
1129C23C2×#41×C4311yescharacteristic
1130C23C2×#41×C4311yescharacteristic
1131C23H(5,𝔽2)×C4311yescharacteristic
1132C23H(5,𝔽2)×C4311yescharacteristic
1133C23H(5,𝔽2)×C4311yescharacteristic
1134C23H(5,𝔽2)×C4311yescharacteristic
1135C23H(5,𝔽2)×C4311yescharacteristic
1136C232−1+4×C4311yescharacteristic
1137D4—416no—
1138D4—416no—
1139D4—416no—
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—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—416no—
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—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4#120×C4314yes—
1224C2×C4#123×C4314yescomplemented
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C2×#120×C4311yescharacteristic
1271C22C2×#121×C4311yescharacteristic
1272C22C2×#123×C4311yescharacteristic
1273C22C43×#52911yescharacteristic
1274C22C43×#53211yescharacteristic
1275C22C43×#53211yescharacteristic
1276C22C43×#53411yescharacteristic
1277C22C43×#53511yescharacteristic
1278C22C43×#53511yescharacteristic
1279C22C43×#53711yescharacteristic
1280C22C43×#53811yescharacteristic
1281C22C43×#53811yescharacteristic
1282C22C43×#53911yescharacteristic
1283C22C43×#54011yescharacteristic
1284C22C43×#54211yescharacteristic
1285C22D42×C4311yescharacteristic
1286C22D42×C4311yescharacteristic
1287C22C43×#54611yescharacteristic
1288C22C43×#54611yescharacteristic
1289C22C43×#54611yescharacteristic
1290C22C43×#54611yescharacteristic
1291C22C43×#54611yescharacteristic
1292C22C43×#54611yescharacteristic
1293C22C43×#54611yescharacteristic
1294C22C43×#54711yescharacteristic
1295C22C43×#54711yescharacteristic
1296C22C43×#54711yescharacteristic
1297C22C43×#55011yescharacteristic
1298C22C43×#55011yescharacteristic
1299C22C43×#55111yescharacteristic
1300C22C43×#55111yescharacteristic
1301C22C43×#55311yescharacteristic
1302C22C43×#55911yescharacteristic
1303C22C43×#56011yescharacteristic
1304C22C43×#56211yescharacteristic
1305C4—24no—
1306C4—24no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C2—44no—
1318C2—82no—
1319C2—82no—
1320C2C43×#240811yescharacteristic
1321C2C43×#241211yescharacteristic
1322C2C43×#242211yescharacteristic
1323C2C43×#242511yescharacteristic
1324C2C43×#243011yescharacteristic
1325C2C43×#243111yescharacteristic
1326C2C43×#244511yescharacteristic
1327C2C43×#255411yescharacteristic
1328C2C43×#255711yescharacteristic
1329C2C43×#267811yescharacteristic
1330C2C43×#268211yescharacteristic
1331C2C43×#270311yescharacteristic
1332C2C43×#270511yescharacteristic
1333C2C43×#270611yescharacteristic
1334C2C43×#271011yescharacteristic
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. C22×#123×C43C2semidirect
2. C2×C43×#397C2semidirect
3. C2×C43×#394C2semidirect
5. C2×C43×#390C2semidirect
6. C2×C43×#386C2semidirect
7. C43×#1441C2semidirect
8. C43×#1439C2semidirect
9. C43×#1439C2semidirect
10. C43×#1439C2semidirect
11. C43×#1438C2semidirect
12. C43×#1438C2semidirect
13. C43×#1437C2semidirect
14. C43×C4⋊#95C2semidirect
15. C43×C22⋊#95C2semidirect
114. C2×C4⋊C4×C43D4semidirect
155. C2×C22⋊C4×C43D4semidirect
156. C2×C22⋊C4×C43D4semidirect
556. C2×C4×C43#123semidirect
557. #15611C43direct (N × H)
650. C22×#123C2×C43semidirect
651. C2×#397C2×C43semidirect
652. C2×#394C2×C43semidirect
654. C2×#390C2×C43semidirect
655. C2×#386C2×C43semidirect
656. #1441C2×C43semidirect
657. #1439C2×C43semidirect
658. #1439C2×C43semidirect
659. #1439C2×C43semidirect
660. #1438C2×C43semidirect
661. #1438C2×C43semidirect
662. #1437C2×C43semidirect
663. C4⋊#95C2×C43semidirect
664. C22⋊#95C2×C43semidirect
726. C43#15611direct (N × H)
782. C2×C4⋊C4D4×C43semidirect
823. C2×C22⋊C4D4×C43semidirect
824. C2×C22⋊C4D4×C43semidirect
1224. C2×C4#123×C43semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C432
C2×C43×#3972
C2×C43×#3942
C2×C43×#3922
C2×C43×#3902
C2×C43×#3862
C43×#14412
C43×#14392
C43×#14382
C43×#14372
C43×C4⋊#952
C43×C22⋊#952
#1561143