Finite Group Databasebeta

← C43×#14732 #24934749

Subgroups — C43×#14732 #24934749

Order 11008.

2662 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C43C211yesmaximal, characteristic, complemented
2C2×C43×#396C211yesmaximal, characteristic, complemented
3C2×C43×#394C211yesmaximal, characteristic, complemented
4C2×C43×#394C211yesmaximal, characteristic, complemented
5C2×C43×#392C211yesmaximal, characteristic
6C2×C43×#386C211yesmaximal, characteristic, complemented
7C2×C43×#386C211yesmaximal, characteristic, complemented
8C2×C43×#380C211yesmaximal, characteristic, complemented
9C43×#1441C211yesmaximal, characteristic, complemented
10C43×#1440C211yesmaximal, characteristic, complemented
11C43×#1439C211yesmaximal, characteristic, complemented
12C43×#1438C211yesmaximal, characteristic, complemented
13C43×#1437C211yesmaximal, characteristic, complemented
14C43×#1436C211yesmaximal, characteristic, complemented
15C43×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C23×D4×C43C2211yescharacteristic
19C24×C4×C43C2211yescharacteristic
20C24×C4×C43C2211yescharacteristic
21C2×C4×D4×C43—24no—
22C2×C4×D4×C43—24no—
23C2×C4×D4×C43—24no—
24C22×C4⋊C4×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C22×C4⋊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×#396—24no—
43C43×#394—24no—
44C43×#394—24no—
45C43×#392—24no—
46C43×#386—24no—
47C43×#386—24no—
48C43×#380—24no—
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
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C25×C43C2311yescharacteristic
62C25×C43C2311yescharacteristic
63C25×C43C2311yescharacteristic
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—22no—
75C22×D4×C43—22no—
76C22×D4×C43—22no—
77C22×D4×C43—22no—
78C22×D4×C43—22no—
79C22×D4×C43—22no—
80C22×D4×C43—41no—
81C22×D4×C43—41no—
82C22×D4×C43—41no—
83C22×D4×C43—41no—
84C22×D4×C43D414yes—
85C23×C4×C43—22no—
86C23×C4×C43—22no—
87C23×C4×C43—22no—
88C23×C4×C43—22no—
89C23×C4×C43—22no—
90C23×C4×C43—22no—
91C23×C4×C43—22no—
92C23×C4×C43—22no—
93C23×C4×C43—22no—
94C23×C4×C43—41no—
95C23×C4×C43—41no—
96C23×C4×C43—41no—
97C23×C4×C43—41no—
98C23×C4×C43D414yescomplemented
99C23×C4×C43C2311yescharacteristic
100C23×C4×C43C2311yescharacteristic
101C23×C4×C43C2311yescharacteristic
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C23×C4×C43C2311yescharacteristic
106C23×C4×C43C2311yescharacteristic
107C23×C4×C43C2311yescharacteristic
108C23×C4×C43C2311yescharacteristic
109C23×C4×C43C2311yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C4×D4×C43—232no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—22no—
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43—22no—
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43—22no—
118C2×C4⋊C4×C43—22no—
119C2×C4⋊C4×C43—22no—
120C2×C4⋊C4×C43—22no—
121C2×C4⋊C4×C43—41no—
122C2×C4⋊C4×C43—41no—
123C2×C4⋊C4×C43D414yescomplemented
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—22no—
144C2×C22⋊C4×C43—22no—
145C2×C22⋊C4×C43—22no—
146C2×C22⋊C4×C43—22no—
147C2×C22⋊C4×C43—22no—
148C2×C22⋊C4×C43—22no—
149C2×C22⋊C4×C43—22no—
150C2×C22⋊C4×C43—22no—
151C2×C22⋊C4×C43—22no—
152C2×C22⋊C4×C43—22no—
153C2×C22⋊C4×C43—22no—
154C2×C22⋊C4×C43—22no—
155C2×C22⋊C4×C43—22no—
156C2×C22⋊C4×C43—41no—
157C2×C22⋊C4×C43—41no—
158C2×C22⋊C4×C43—41no—
159C2×C22⋊C4×C43—41no—
160C2×C22⋊C4×C43—41no—
161C2×C22⋊C4×C43—41no—
162C2×C22⋊C4×C43D414yescomplemented
163C2×C42×C43—22no—
164C2×C42×C43—22no—
165C2×C42×C43—22no—
166#95×C43—22no—
167#95×C43—22no—
168#95×C43—22no—
169#95×C43—22no—
170#95×C43—22no—
171#95×C43—22no—
172#95×C43—22no—
173#95×C43—22no—
174#95×C43—22no—
175#95×C43—41no—
176#95×C43—41no—
177#95×C43D414yescomplemented
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×C43—21no—
213C24×C43—21no—
214C24×C43—21no—
215C24×C43—21no—
216C24×C43C2×D412yes—
217C24×C43C2×D412yes—
218C24×C43C2×D412yes—
219C24×C43C2×D412yes—
220C24×C43#4112yes—
221C24×C43#4112yes—
222C24×C43#4112yes—
223C24×C43C2411yescharacteristic
224C2×D4×C43—28no—
225C2×D4×C43—28no—
226C2×D4×C43—28no—
227C2×D4×C43—28no—
228C2×D4×C43—28no—
229C2×D4×C43—28no—
230C2×D4×C43—28no—
231C2×D4×C43—28no—
232C2×D4×C43—28no—
233C2×D4×C43—44no—
234C2×D4×C43—44no—
235C2×D4×C43—44no—
236C2×D4×C43—44no—
237C2×D4×C43—44no—
238C2×D4×C43—44no—
239C2×D4×C43—44no—
240C2×D4×C43—44no—
241C2×D4×C43—44no—
242C2×D4×C43—44no—
243C2×D4×C43—44no—
244C2×D4×C43—44no—
245C22×C4×C43—28no—
246C22×C4×C43—28no—
247C22×C4×C43—28no—
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—21no—
313C22×C4×C43—21no—
314C22×C4×C43—21no—
315C22×C4×C43—21no—
316C22×C4×C43—21no—
317C22×C4×C43—21no—
318C22×C4×C43—44no—
319C22×C4×C43—44no—
320C22×C4×C43—44no—
321C22×C4×C43—44no—
322C22×C4×C43—44no—
323C22×C4×C43—44no—
324C22×C4×C43—44no—
325C22×C4×C43—44no—
326C22×C4×C43—44no—
327C22×C4×C43—44no—
328C22×C4×C43—44no—
329C22×C4×C43C2×D412yes—
330C22×C4×C43C2×D412yes—
331C22×C4×C43C2×D412yes—
332C22×C4×C43C2×D412yes—
333C22×C4×C43C2×D412yes—
334C22×C4×C43C2×D412yes—
335C22×C4×C43C2×D412yes—
336C22×C4×C43C2×D412yes—
337C22×C4×C43C2×D412yes—
338C22×C4×C43C2×D412yes—
339C22×C4×C43C2×D412yes—
340C22×C4×C43#4112yes—
341C22×C4×C43#4112yes—
342C22×C4×C43#4112yes—
343C4⋊C4×C43—28no—
344C4⋊C4×C43—44no—
345C4⋊C4×C43—44no—
346C4⋊C4×C43—44no—
347C22⋊C4×C43—28no—
348C22⋊C4×C43—28no—
349C22⋊C4×C43—44no—
350C22⋊C4×C43—44no—
351C22⋊C4×C43—44no—
352C22⋊C4×C43—44no—
353C22⋊C4×C43—44no—
354C22⋊C4×C43—44no—
355C22⋊C4×C43—44no—
356C22⋊C4×C43—44no—
357C22⋊C4×C43—44no—
358C22⋊C4×C43—44no—
359C22⋊C4×C43—44no—
360C42×C43—28no—
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—22no—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—22no—
393C23×C43—22no—
394C23×C43—22no—
395C23×C43—22no—
396C23×C43—22no—
397C23×C43—22no—
398C23×C43—22no—
399C23×C43—22no—
400C23×C43—22no—
401C23×C43—22no—
402C23×C43—22no—
403C23×C43—22no—
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—41no—
454C23×C43—41no—
455C23×C43—41no—
456C23×C43—41no—
457C23×C43—41no—
458C23×C43—41no—
459C23×C43—41no—
460C23×C43—41no—
461C23×C43—41no—
462C23×C43—41no—
463C23×C43—41no—
464C23×C43#12114yes—
465C23×C43#12114yes—
466C23×C43C22×D411yescharacteristic
467C23×C43C22×D411yescharacteristic
468C23×C43C22×D411yescharacteristic
469C23×C43C22×D411yescharacteristic
470C23×C43C22×D411yescharacteristic
471C23×C43C2×#4111yescharacteristic
472C23×C43C2×#4111yescharacteristic
473C23×C43C2×#4111yescharacteristic
474C23×C43C2×#4111yescharacteristic
475C23×C43C2×#4111yescharacteristic
476C23×C43C2×#4111yescharacteristic
477C23×C43H(5,𝔽2)11yescharacteristic
478C23×C43H(5,𝔽2)11yescharacteristic
479C23×C43H(5,𝔽2)11yescharacteristic
480C23×C432−1+411yescharacteristic
481D4×C43—232no—
482D4×C43—416no—
483D4×C43—416no—
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—22no—
503C2×C4×C43—22no—
504C2×C4×C43—22no—
505C2×C4×C43—22no—
506C2×C4×C43—22no—
507C2×C4×C43—22no—
508C2×C4×C43—22no—
509C2×C4×C43—22no—
510C2×C4×C43—22no—
511C2×C4×C43—22no—
512C2×C4×C43—22no—
513C2×C4×C43—22no—
514C2×C4×C43—22no—
515C2×C4×C43—22no—
516C2×C4×C43—22no—
517C2×C4×C43—416no—
518C2×C4×C43—416no—
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—41no—
556C2×C4×C43—41no—
557C2×C4×C43—41no—
558C2×C4×C43—41no—
559C2×C4×C43—41no—
560C2×C4×C43—41no—
561C2×C4×C43—41no—
562C2×C4×C43—41no—
563C2×C4×C43—41no—
564C2×C4×C43—41no—
565C2×C4×C43—41no—
566C2×C4×C43—41no—
567C2×C4×C43#12014yes—
568C2×C4×C43#12114yes—
569C2×C4×C43#12114yes—
570#14732C4311yesmaximal, characteristic, direct product factor, Sylow
571C22×C43—24no—
572C22×C43—24no—
573C22×C43—24no—
574C22×C43—24no—
575C22×C43—24no—
576C22×C43—24no—
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—42no—
588C22×C43—42no—
589C22×C43—42no—
590C22×C43—42no—
591C22×C43—42no—
592C22×C43—42no—
593C22×C43—42no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—42no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43—42no—
600C22×C43—42no—
601C22×C43—42no—
602C22×C43—42no—
603C22×C43—42no—
604C22×C43—42no—
605C22×C43—42no—
606C22×C43—42no—
607C22×C43—42no—
608C22×C43—81no—
609C22×C43—81no—
610C22×C43—81no—
611C22×C43—81no—
612C22×C43—81no—
613C22×C43—81no—
614C22×C43—81no—
615C22×C43—81no—
616C22×C43C2×#12011yescharacteristic
617C22×C43C2×#12111yescharacteristic
618C22×C43C2×#12111yescharacteristic
619C22×C43C2×#12111yescharacteristic
620C22×C43C2×#12111yescharacteristic
621C22×C43#52511yescharacteristic
622C22×C43#52511yescharacteristic
623C22×C43#52511yescharacteristic
624C22×C43#52511yescharacteristic
625C22×C43#52511yescharacteristic
626C22×C43#52911yescharacteristic
627C22×C43#52911yescharacteristic
628C22×C43#53211yescharacteristic
629C22×C43#53411yescharacteristic
630C22×C43#53711yescharacteristic
631C22×C43#53811yescharacteristic
632C22×C43#53911yescharacteristic
633C22×C43#54011yescharacteristic
634C22×C43#54211yescharacteristic
635C22×C43D4211yescharacteristic
636C22×C43D4211yescharacteristic
637C22×C43D4211yescharacteristic
638C22×C43#54611yescharacteristic
639C22×C43#54611yescharacteristic
640C22×C43#54611yescharacteristic
641C22×C43#54611yescharacteristic
642C22×C43#54611yescharacteristic
643C22×C43#54711yescharacteristic
644C22×C43#54711yescharacteristic
645C22×C43#54811yescharacteristic
646C22×C43#54811yescharacteristic
647C22×C43#55011yescharacteristic
648C22×C43#55111yescharacteristic
649C22×C43#55111yescharacteristic
650C22×C43#55311yescharacteristic
651C4×C43—24no—
652C4×C43—24no—
653C4×C43—24no—
654C4×C43—42no—
655C4×C43—42no—
656C4×C43—42no—
657C4×C43—42no—
658C4×C43—42no—
659C4×C43—81no—
660C4×C43—81no—
661C4×C43—81no—
662C4×C43—81no—
663C22×C4×D4C2×C4311yescharacteristic, complemented
664C2×#396C2×C4311yescharacteristic, complemented
665C2×#394C2×C4311yescharacteristic, complemented
666C2×#394C2×C4311yescharacteristic, complemented
667C2×#392C2×C4311yescharacteristic
668C2×#386C2×C4311yescharacteristic, complemented
669C2×#386C2×C4311yescharacteristic, complemented
670C2×#380C2×C4311yescharacteristic, complemented
671#1441C2×C4311yescharacteristic, complemented
672#1440C2×C4311yescharacteristic, complemented
673#1439C2×C4311yescharacteristic, complemented
674#1438C2×C4311yescharacteristic, complemented
675#1437C2×C4311yescharacteristic, complemented
676#1436C2×C4311yescharacteristic, complemented
677C22⋊#95C2×C4311yescharacteristic, complemented
678C2×C43—44no—
679C2×C43—44no—
680C2×C43—82no—
681C2×C43#239211yescharacteristic
682C2×C43#240711yescharacteristic
683C2×C43#241011yescharacteristic
684C2×C43#241611yescharacteristic
685C2×C43#242411yescharacteristic
686C2×C43#242511yescharacteristic
687C2×C43#242711yescharacteristic
688C2×C43#242811yescharacteristic
689C2×C43#245711yescharacteristic
690C2×C43#246111yescharacteristic
691C2×C43#246311yescharacteristic
692C2×C43#246711yescharacteristic
693C2×C43#253411yescharacteristic
694C2×C43#263011yescharacteristic
695C2×C43#284711yescharacteristic
696C23×D4C22×C4311yescharacteristic
697C23×D4C22×C4311yescharacteristic
698C23×D4C22×C4311yescharacteristic
699C24×C4C22×C4311yescharacteristic
700C24×C4C22×C4311yescharacteristic
701C2×C4×D4—24no—
702C2×C4×D4—24no—
703C2×C4×D4—24no—
704C22×C4⋊C4C22×C4311yescharacteristic
705C22×C4⋊C4C22×C4311yescharacteristic
706C22×C4⋊C4C22×C4311yescharacteristic
707C22×C4⋊C4C22×C4311yescharacteristic
708C22×C22⋊C4C22×C4311yescharacteristic
709C22×C22⋊C4C22×C4311yescharacteristic
710C22×C22⋊C4C22×C4311yescharacteristic
711C22×C22⋊C4C22×C4311yescharacteristic
712C22×C22⋊C4C22×C4311yescharacteristic
713C22×C22⋊C4C22×C4311yescharacteristic
714C22×C22⋊C4C22×C4311yescharacteristic
715C22×C22⋊C4C22×C4311yescharacteristic
716C22×C22⋊C4C22×C4311yescharacteristic
717C22×C22⋊C4C22×C4311yescharacteristic
718C22×C22⋊C4C22×C4311yescharacteristic
719C22×C22⋊C4C22×C4311yescharacteristic
720C22×C22⋊C4C22×C4311yescharacteristic
721C22×C42C22×C4311yescharacteristic
722#396—24no—
723#394—24no—
724#394—24no—
725#392—24no—
726#386—24no—
727#386—24no—
728#380—24no—
729C2×#95C22×C4311yescharacteristic
730C2×#95C22×C4311yescharacteristic
731C2×#95C22×C4311yescharacteristic
732C2×#95C22×C4311yescharacteristic
733C2×#95C22×C4311yescharacteristic
734C2×#95C22×C4311yescharacteristic
735C2×#95C22×C4311yescharacteristic
736C2×#95C22×C4311yescharacteristic
737C2×#95C22×C4311yescharacteristic
738C2×#95C22×C4311yescharacteristic
739C2×#95C22×C4311yescharacteristic
740C2×#95C22×C4311yescharacteristic
741C43#1473211yescharacteristic, direct product factor, Sylow
742C25C23×C4311yescharacteristic
743C25C23×C4311yescharacteristic
744C25C23×C4311yescharacteristic
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—22no—
756C22×D4—22no—
757C22×D4—22no—
758C22×D4—22no—
759C22×D4—22no—
760C22×D4—22no—
761C22×D4—41no—
762C22×D4—41no—
763C22×D4—41no—
764C22×D4—41no—
765C22×D4D4×C4314yes—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—22no—
775C23×C4—41no—
776C23×C4—41no—
777C23×C4—41no—
778C23×C4—41no—
779C23×C4D4×C4314yescomplemented
780C23×C4C23×C4311yescharacteristic
781C23×C4C23×C4311yescharacteristic
782C23×C4C23×C4311yescharacteristic
783C23×C4C23×C4311yescharacteristic
784C23×C4C23×C4311yescharacteristic
785C23×C4C23×C4311yescharacteristic
786C23×C4C23×C4311yescharacteristic
787C23×C4C23×C4311yescharacteristic
788C23×C4C23×C4311yescharacteristic
789C23×C4C23×C4311yescharacteristic
790C23×C4C23×C4311yescharacteristic
791C23×C4C23×C4311yescharacteristic
792C4×D4—232no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—22no—
799C2×C4⋊C4—22no—
800C2×C4⋊C4—22no—
801C2×C4⋊C4—22no—
802C2×C4⋊C4—41no—
803C2×C4⋊C4—41no—
804C2×C4⋊C4D4×C4314yescomplemented
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—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—22no—
830C2×C22⋊C4—22no—
831C2×C22⋊C4—22no—
832C2×C22⋊C4—22no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4—41no—
839C2×C22⋊C4—41no—
840C2×C22⋊C4—41no—
841C2×C22⋊C4—41no—
842C2×C22⋊C4—41no—
843C2×C22⋊C4D4×C4314yescomplemented
844C2×C42—22no—
845C2×C42—22no—
846C2×C42—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—41no—
857#95—41no—
858#95D4×C4314yescomplemented
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—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24C2×D4×C4312yes—
898C24C2×D4×C4312yes—
899C24C2×D4×C4312yes—
900C24C2×D4×C4312yes—
901C24#41×C4312yes—
902C24#41×C4312yes—
903C24#41×C4312yes—
904C24C24×C4311yescharacteristic
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
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—28no—
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—28no—
970C22×C4—28no—
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—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4C2×D4×C4312yes—
1011C22×C4C2×D4×C4312yes—
1012C22×C4C2×D4×C4312yes—
1013C22×C4C2×D4×C4312yes—
1014C22×C4C2×D4×C4312yes—
1015C22×C4C2×D4×C4312yes—
1016C22×C4C2×D4×C4312yes—
1017C22×C4C2×D4×C4312yes—
1018C22×C4C2×D4×C4312yes—
1019C22×C4C2×D4×C4312yes—
1020C22×C4C2×D4×C4312yes—
1021C22×C4#41×C4312yes—
1022C22×C4#41×C4312yes—
1023C22×C4#41×C4312yes—
1024C4⋊C4—28no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C42—28no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
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—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23#121×C4314yes—
1146C23#121×C4314yes—
1147C23C22×D4×C4311yescharacteristic
1148C23C22×D4×C4311yescharacteristic
1149C23C22×D4×C4311yescharacteristic
1150C23C22×D4×C4311yescharacteristic
1151C23C22×D4×C4311yescharacteristic
1152C23C2×#41×C4311yescharacteristic
1153C23C2×#41×C4311yescharacteristic
1154C23C2×#41×C4311yescharacteristic
1155C23C2×#41×C4311yescharacteristic
1156C23C2×#41×C4311yescharacteristic
1157C23C2×#41×C4311yescharacteristic
1158C23H(5,𝔽2)×C4311yescharacteristic
1159C23H(5,𝔽2)×C4311yescharacteristic
1160C23H(5,𝔽2)×C4311yescharacteristic
1161C232−1+4×C4311yescharacteristic
1162D4—232no—
1163D4—416no—
1164D4—416no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—416no—
1199C2×C4—416no—
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—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4#120×C4314yes—
1249C2×C4#121×C4314yes—
1250C2×C4#121×C4314yes—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22C2×#120×C4311yescharacteristic
1297C22C2×#121×C4311yescharacteristic
1298C22C2×#121×C4311yescharacteristic
1299C22C2×#121×C4311yescharacteristic
1300C22C2×#121×C4311yescharacteristic
1301C22C43×#52511yescharacteristic
1302C22C43×#52511yescharacteristic
1303C22C43×#52511yescharacteristic
1304C22C43×#52511yescharacteristic
1305C22C43×#52511yescharacteristic
1306C22C43×#52911yescharacteristic
1307C22C43×#52911yescharacteristic
1308C22C43×#53211yescharacteristic
1309C22C43×#53411yescharacteristic
1310C22C43×#53711yescharacteristic
1311C22C43×#53811yescharacteristic
1312C22C43×#53911yescharacteristic
1313C22C43×#54011yescharacteristic
1314C22C43×#54211yescharacteristic
1315C22D42×C4311yescharacteristic
1316C22D42×C4311yescharacteristic
1317C22D42×C4311yescharacteristic
1318C22C43×#54611yescharacteristic
1319C22C43×#54611yescharacteristic
1320C22C43×#54611yescharacteristic
1321C22C43×#54611yescharacteristic
1322C22C43×#54611yescharacteristic
1323C22C43×#54711yescharacteristic
1324C22C43×#54711yescharacteristic
1325C22C43×#54811yescharacteristic
1326C22C43×#54811yescharacteristic
1327C22C43×#55011yescharacteristic
1328C22C43×#55111yescharacteristic
1329C22C43×#55111yescharacteristic
1330C22C43×#55311yescharacteristic
1331C4—24no—
1332C4—24no—
1333C4—24no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C2—44no—
1344C2—44no—
1345C2—82no—
1346C2C43×#239211yescharacteristic
1347C2C43×#240711yescharacteristic
1348C2C43×#241011yescharacteristic
1349C2C43×#241611yescharacteristic
1350C2C43×#242411yescharacteristic
1351C2C43×#242511yescharacteristic
1352C2C43×#242711yescharacteristic
1353C2C43×#242811yescharacteristic
1354C2C43×#245711yescharacteristic
1355C2C43×#246111yescharacteristic
1356C2C43×#246311yescharacteristic
1357C2C43×#246711yescharacteristic
1358C2C43×#253411yescharacteristic
1359C2C43×#263011yescharacteristic
1360C2C43×#284711yescharacteristic
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×C4×D4×C43C2semidirect
2. C2×C43×#396C2semidirect
3. C2×C43×#394C2semidirect
4. C2×C43×#394C2semidirect
6. C2×C43×#386C2semidirect
7. C2×C43×#386C2semidirect
8. C2×C43×#380C2semidirect
9. C43×#1441C2semidirect
10. C43×#1440C2semidirect
11. C43×#1439C2semidirect
12. C43×#1438C2semidirect
13. C43×#1437C2semidirect
14. C43×#1436C2semidirect
15. C43×C22⋊#95C2semidirect
98. C23×C4×C43D4semidirect
123. C2×C4⋊C4×C43D4semidirect
162. C2×C22⋊C4×C43D4semidirect
177. #95×C43D4semidirect
570. #14732C43direct (N × H)
663. C22×C4×D4C2×C43semidirect
664. C2×#396C2×C43semidirect
665. C2×#394C2×C43semidirect
666. C2×#394C2×C43semidirect
668. C2×#386C2×C43semidirect
669. C2×#386C2×C43semidirect
670. C2×#380C2×C43semidirect
671. #1441C2×C43semidirect
672. #1440C2×C43semidirect
673. #1439C2×C43semidirect
674. #1438C2×C43semidirect
675. #1437C2×C43semidirect
676. #1436C2×C43semidirect
677. C22⋊#95C2×C43semidirect
741. C43#14732direct (N × H)
779. C23×C4D4×C43semidirect
804. C2×C4⋊C4D4×C43semidirect
843. C2×C22⋊C4D4×C43semidirect
858. #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×#3962
C2×C43×#3942
C2×C43×#3922
C2×C43×#3862
C2×C43×#3802
C43×#14412
C43×#14402
C43×#14392
C43×#14382
C43×#14372
C43×#14362
C43×C22⋊#952
#1473243