Finite Group Databasebeta

← C43×#24390 #24944407

Subgroups — C43×#24390 #24944407

Order 11008.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#535C211yesmaximal, characteristic, complemented
2C2×C43×#469C211yesmaximal, characteristic, complemented
3C2×C43×#466C211yesmaximal, characteristic, complemented
4C2×C43×#447C211yesmaximal, characteristic, complemented
5C2×C43×#408C211yesmaximal, characteristic, complemented
6C43×#2615C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#1999C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1895C211yesmaximal, characteristic, complemented
12C43×#1893C211yesmaximal, characteristic, complemented
13C43×#1875C211yesmaximal, characteristic, complemented
14C43×#1854C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×M16×C43C2211yescharacteristic, complemented
21C23×C8×C43C2211yescharacteristic, complemented
22C43×#535—24no—
23C43×#535—24no—
24C2×#127×C43—21no—
25C2×#124×C43—21no—
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×#121×C43C2211yescharacteristic, complemented
32C2×#121×C43C2211yescharacteristic, complemented
33C2×#120×C43—21no—
34C2×#120×C43—21no—
35C2×#117×C43C2211yescharacteristic
36C43×#469—24no—
37C43×#466—24no—
38C43×#447—24no—
39C2×#107×C43C2211yescharacteristic, complemented
40C2×#106×C43C2211yescharacteristic, complemented
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×#102×C43C2211yescharacteristic, complemented
48C2×#102×C43C2211yescharacteristic, complemented
49C43×#408—24no—
50C2×C22⋊C8×C43C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C2×C22⋊C8×C43C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic, complemented
54C43×#393—21no—
55C43×#392—21no—
56C43×#392—21no—
57C43×#392—21no—
58C43×#380C2211yescharacteristic
59C43×#380C2211yescharacteristic, complemented
60C43×#380C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C43×#340C2211yescharacteristic, complemented
65C25×C43—21no—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—41no—
71C2×#41×C43—41no—
72C22×Q8×C43D411yescharacteristic
73C22×D4×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—22no—
78C22×D4×C43—22no—
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—21no—
82C22×D4×C43—21no—
83C22×D4×C43—22no—
84C22×D4×C43—22no—
85C22×D4×C43—41no—
86C22×D4×C43—41no—
87C22×D4×C43D411yescharacteristic
88C22×D4×C43D411yescharacteristic
89C22×D4×C43D411yescharacteristic
90C22×D4×C43C2311yescharacteristic
91C22×D4×C43C2311yescharacteristic
92C22×D4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2311yescharacteristic
96C2×D8×C43—22no—
97C2×D8×C43—22no—
98C2×D8×C43—22no—
99C2×D8×C43—22no—
100C2×D8×C43—41no—
101C2×D8×C43—41no—
102C2×M16×C43—22no—
103C2×M16×C43—22no—
104C2×M16×C43—41no—
105C22×C8×C43—22no—
106C22×C8×C43—22no—
107C22×C8×C43—41no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112#127×C43—28no—
113#124×C43—28no—
114#121×C43—22no—
115#121×C43—22no—
116#121×C43—22no—
117#121×C43—22no—
118#121×C43—22no—
119#121×C43—22no—
120#121×C43—22no—
121#121×C43—22no—
122#121×C43—22no—
123#121×C43—22no—
124#121×C43—41no—
125#121×C43—41no—
126#121×C43D414yescomplemented
127#121×C43D414yescomplemented
128#120×C43—28no—
129#120×C43—28no—
130#117×C43—22no—
131#117×C43—22no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C42×C43—21no—
149#107×C43—22no—
150#106×C43—22no—
151#102×C43—22no—
152#102×C43—22no—
153#102×C43—22no—
154#102×C43—22no—
155#102×C43—22no—
156#102×C43—22no—
157#102×C43—41no—
158#102×C43—41no—
159C22⋊C8×C43—22no—
160C22⋊C8×C43—22no—
161C22⋊C8×C43—22no—
162C22⋊C8×C43D414yescomplemented
163#95×C43—21no—
164#95×C43—21no—
165#95×C43—21no—
166C24×C43—24no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—42no—
171C24×C43—42no—
172C24×C43—81no—
173C24×C43—81no—
174C24×C43—81no—
175C24×C43—81no—
176C24×C43C2×D411yescharacteristic
177C24×C43C2×D411yescharacteristic
178C24×C43C2×D411yescharacteristic
179#41×C43—44no—
180#41×C43—44no—
181#41×C43—44no—
182#41×C43—44no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43—41no—
186C2×D4×C43—24no—
187C2×D4×C43—24no—
188C2×D4×C43—24no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—24no—
196C2×D4×C43—24no—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—41no—
214C2×D4×C43—41no—
215C2×D4×C43—41no—
216C2×D4×C43—42no—
217C2×D4×C43—44no—
218C2×D4×C43—44no—
219C2×D4×C43—44no—
220C2×D4×C43—44no—
221C2×D4×C43—42no—
222C2×D4×C43—42no—
223C2×D4×C43—42no—
224C2×D4×C43—42no—
225C2×D4×C43—81no—
226C2×D4×C43—81no—
227C2×D4×C43—81no—
228C2×D4×C43—81no—
229C2×D4×C43—81no—
230C2×D4×C43—81no—
231C2×D4×C43—81no—
232C2×D4×C43—81no—
233C2×D4×C43—81no—
234C2×D4×C43—81no—
235C2×D4×C43—81no—
236C2×D4×C43—81no—
237C2×D4×C43—81no—
238C2×D4×C43—81no—
239C2×D4×C43C2×D412yes—
240C2×D4×C43C2×D412yes—
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×C43C2×D412yes—
261C22×C4×C43C2×D412yes—
262C22×C4×C43C2×D412yes—
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2×D411yescharacteristic
266C22×C4×C43#4112yes—
267C22×C4×C43C2411yescharacteristic
268D8×C43—44no—
269D8×C43—44no—
270M16×C43—44no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—21no—
275C2×C8×C43—21no—
276C2×C8×C43—21no—
277C2×C8×C43—21no—
278C2×C8×C43—21no—
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C2×C8×C43—44no—
282C2×C8×C43C2×D412yes—
283C2×C8×C43C2×D412yes—
284C4⋊C4×C43—21no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43—21no—
290C4⋊C4×C43—21no—
291C4⋊C4×C43—21no—
292C4⋊C4×C43C2×D412yes—
293C4⋊C4×C43C2×D412yes—
294C22⋊C4×C43—24no—
295C22⋊C4×C43—24no—
296C22⋊C4×C43—24no—
297C22⋊C4×C43—24no—
298C22⋊C4×C43—24no—
299C22⋊C4×C43—42no—
300C22⋊C4×C43—42no—
301C22⋊C4×C43—42no—
302C22⋊C4×C43—81no—
303C22⋊C4×C43—81no—
304C22⋊C4×C43—81no—
305C42×C43—24no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—21no—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43—21no—
324C23×C43—21no—
325C23×C43—21no—
326C23×C43—21no—
327C23×C43—48no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—84no—
348C23×C43—84no—
349C23×C43—84no—
350C23×C43—84no—
351C23×C43—84no—
352C23×C43—84no—
353C23×C43#12012yes—
354C23×C43#12112yes—
355C23×C43C22×D411yescharacteristic
356Q8×C43—44no—
357D4×C43—22no—
358D4×C43—22no—
359D4×C43—22no—
360D4×C43—22no—
361D4×C43—44no—
362D4×C43—44no—
363D4×C43—48no—
364D4×C43—44no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—41no—
372D4×C43—41no—
373D4×C43—84no—
374D4×C43—84no—
375D4×C43—84no—
376D4×C43—84no—
377D4×C43—84no—
378D4×C43—84no—
379D4×C43—84no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—21no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
414C2×C4×C43#12012yes—
415C2×C4×C43#12112yes—
416C2×C4×C43C22×D411yescharacteristic
417C2×C4×C43C22×D411yescharacteristic
418C2×C4×C43C22×D411yescharacteristic
419C2×C4×C43C2×#4111yescharacteristic
420C2×C4×C43H(5,𝔽2)11yescharacteristic
421C2×C4×C43H(5,𝔽2)11yescharacteristic
422C8×C43—22no—
423C8×C43—22no—
424C8×C43—41no—
425C8×C43—41no—
426#24390C4311yesmaximal, characteristic, direct product factor, Sylow
427C22×C43—22no—
428C22×C43—22no—
429C22×C43—22no—
430C22×C43—22no—
431C22×C43—22no—
432C22×C43—22no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—41no—
442C22×C43—42no—
443C22×C43—42no—
444C22×C43—41no—
445C22×C43—41no—
446C22×C43—41no—
447C22×C43—42no—
448C22×C43—42no—
449C22×C43—41no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43—41no—
453C22×C43—41no—
454C22×C43—816no—
455C22×C43—81no—
456C22×C43—81no—
457C22×C43—81no—
458C22×C43—81no—
459C22×C43—81no—
460C22×C43—81no—
461C22×C43—81no—
462C22×C43—81no—
463C22×C43—81no—
464C22×C43—81no—
465C22×C43—81no—
466C22×C43—81no—
467C22×C43—81no—
468C22×C43—81no—
469C22×C43—81no—
470C22×C43C2×#12011yescharacteristic
471C22×C43C2×#12111yescharacteristic
472C22×C43#53411yescharacteristic
473C22×C43#57611yescharacteristic
474C22×C43#57611yescharacteristic
475C22×C43#57611yescharacteristic
476C22×C43#57711yescharacteristic
477C4×C43—22no—
478C4×C43—22no—
479C4×C43—41no—
480C4×C43—42no—
481C4×C43—42no—
482C4×C43—81no—
483C4×C43—81no—
484C4×C43—81no—
485C4×C43D4211yescharacteristic
486C4×C43D4211yescharacteristic
487C4×C43#54611yescharacteristic
488C4×C43#54611yescharacteristic
489C2×#535C2×C4311yescharacteristic, complemented
490C2×#469C2×C4311yescharacteristic, complemented
491C2×#466C2×C4311yescharacteristic, complemented
492C2×#447C2×C4311yescharacteristic, complemented
493C2×#408C2×C4311yescharacteristic, complemented
494#2615C2×C4311yescharacteristic, complemented
495#2034C2×C4311yescharacteristic, complemented
496#2033C2×C4311yescharacteristic, complemented
497#1999C2×C4311yescharacteristic, complemented
498#1999C2×C4311yescharacteristic, complemented
499#1895C2×C4311yescharacteristic, complemented
500#1893C2×C4311yescharacteristic, complemented
501#1875C2×C4311yescharacteristic, complemented
502#1854C2×C4311yescharacteristic, complemented
503#1786C2×C4311yescharacteristic, complemented
504C2×C43—42no—
505C2×C43—42no—
506C2×C43—81no—
507C2×C43—82no—
508C2×C43—82no—
509C2×C43—161no—
510C2×C43#241011yescharacteristic
511C2×C43#300811yescharacteristic
512C2×C43#301211yescharacteristic
513C2×C43#305811yescharacteristic
514C2×C43#306211yescharacteristic
515C2×C43#319811yescharacteristic
516C2×C43#319911yescharacteristic
517C22×#41C22×C4311yescharacteristic
518C23×D4C22×C4311yescharacteristic
519C22×D8C22×C4311yescharacteristic
520C22×D8C22×C4311yescharacteristic
521C22×M16C22×C4311yescharacteristic, complemented
522C23×C8C22×C4311yescharacteristic, complemented
523#535—24no—
524#535—24no—
525C2×#127—21no—
526C2×#124—21no—
527C2×#121C22×C4311yescharacteristic
528C2×#121C22×C4311yescharacteristic
529C2×#121C22×C4311yescharacteristic
530C2×#121C22×C4311yescharacteristic
531C2×#121C22×C4311yescharacteristic
532C2×#121C22×C4311yescharacteristic, complemented
533C2×#121C22×C4311yescharacteristic, complemented
534C2×#120—21no—
535C2×#120—21no—
536C2×#117C22×C4311yescharacteristic
537#469—24no—
538#466—24no—
539#447—24no—
540C2×#107C22×C4311yescharacteristic, complemented
541C2×#106C22×C4311yescharacteristic, complemented
542C2×#102C22×C4311yescharacteristic
543C2×#102C22×C4311yescharacteristic
544C2×#102C22×C4311yescharacteristic
545C2×#102C22×C4311yescharacteristic
546C2×#102C22×C4311yescharacteristic
547C2×#102C22×C4311yescharacteristic
548C2×#102C22×C4311yescharacteristic, complemented
549C2×#102C22×C4311yescharacteristic, complemented
550#408—24no—
551C2×C22⋊C8C22×C4311yescharacteristic
552C2×C22⋊C8C22×C4311yescharacteristic
553C2×C22⋊C8C22×C4311yescharacteristic, complemented
554C2×C22⋊C8C22×C4311yescharacteristic, complemented
555#393—21no—
556#392—21no—
557#392—21no—
558#392—21no—
559#380C22×C4311yescharacteristic
560#380C22×C4311yescharacteristic, complemented
561#380C22×C4311yescharacteristic, complemented
562#340C22×C4311yescharacteristic, complemented
563#340C22×C4311yescharacteristic, complemented
564#340C22×C4311yescharacteristic, complemented
565#340C22×C4311yescharacteristic, complemented
566C43#2439011yescharacteristic, direct product factor, Sylow
567C25—21no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—22no—
572C2×#41—41no—
573C2×#41—41no—
574C22×Q8D4×C4311yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—41no—
588C22×D4—41no—
589C22×D4D4×C4311yescharacteristic
590C22×D4D4×C4311yescharacteristic
591C22×D4D4×C4311yescharacteristic
592C22×D4C23×C4311yescharacteristic
593C22×D4C23×C4311yescharacteristic
594C22×D4C23×C4311yescharacteristic
595C23×C4C23×C4311yescharacteristic
596C23×C4C23×C4311yescharacteristic
597C23×C4C23×C4311yescharacteristic
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×M16—22no—
605C2×M16—22no—
606C2×M16—41no—
607C22×C8—22no—
608C22×C8—22no—
609C22×C8—41no—
610C22×C8C23×C4311yescharacteristic
611C22×C8C23×C4311yescharacteristic
612C22×C8C23×C4311yescharacteristic
613C22×C8C23×C4311yescharacteristic
614#127—28no—
615#124—28no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—41no—
627#121—41no—
628#121D4×C4314yescomplemented
629#121D4×C4314yescomplemented
630#120—28no—
631#120—28no—
632#117—22no—
633#117—22no—
634C2×C4⋊C4C23×C4311yescharacteristic
635C2×C4⋊C4C23×C4311yescharacteristic
636C2×C4⋊C4C23×C4311yescharacteristic
637C2×C4⋊C4C23×C4311yescharacteristic
638C2×C4⋊C4C23×C4311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C42—21no—
651#107—22no—
652#106—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—41no—
660#102—41no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8—22no—
664C22⋊C8D4×C4314yescomplemented
665#95—21no—
666#95—21no—
667#95—21no—
668C24—24no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—42no—
673C24—42no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24C2×D4×C4311yescharacteristic
679C24C2×D4×C4311yescharacteristic
680C24C2×D4×C4311yescharacteristic
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—41no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4C2×D4×C4312yes—
742C2×D4C2×D4×C4312yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4C2×D4×C4311yescharacteristic
763C22×C4C2×D4×C4311yescharacteristic
764C22×C4C2×D4×C4312yes—
765C22×C4C2×D4×C4312yes—
766C22×C4C2×D4×C4311yescharacteristic
767C22×C4C2×D4×C4312yes—
768C22×C4#41×C4312yes—
769C22×C4C24×C4311yescharacteristic
770D8—44no—
771D8—44no—
772M16—44no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C4312yes—
785C2×C8C2×D4×C4312yes—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4C2×D4×C4312yes—
795C4⋊C4C2×D4×C4312yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C42—24no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23#120×C4312yes—
856C23#121×C4312yes—
857C23C22×D4×C4311yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4#120×C4312yes—
917C2×C4#121×C4312yes—
918C2×C4C22×D4×C4311yescharacteristic
919C2×C4C22×D4×C4311yescharacteristic
920C2×C4C22×D4×C4311yescharacteristic
921C2×C4C2×#41×C4311yescharacteristic
922C2×C4H(5,𝔽2)×C4311yescharacteristic
923C2×C4H(5,𝔽2)×C4311yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—42no—
944C22—42no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—42no—
949C22—42no—
950C22—41no—
951C22—42no—
952C22—42no—
953C22—41no—
954C22—41no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×#120×C4311yescharacteristic
972C22C2×#121×C4311yescharacteristic
973C22C43×#53411yescharacteristic
974C22C43×#57611yescharacteristic
975C22C43×#57611yescharacteristic
976C22C43×#57611yescharacteristic
977C22C43×#57711yescharacteristic
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C4311yescharacteristic
987C4D42×C4311yescharacteristic
988C4C43×#54611yescharacteristic
989C4C43×#54611yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2C43×#241011yescharacteristic
997C2C43×#300811yescharacteristic
998C2C43×#301211yescharacteristic
999C2C43×#305811yescharacteristic
1000C2C43×#306211yescharacteristic
1001C2C43×#319811yescharacteristic
1002C2C43×#319911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#535C2semidirect
2. C2×C43×#469C2semidirect
3. C2×C43×#466C2semidirect
4. C2×C43×#447C2semidirect
5. C2×C43×#408C2semidirect
6. C43×#2615C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#1999C2semidirect
10. C43×#1999C2semidirect
11. C43×#1895C2semidirect
12. C43×#1893C2semidirect
13. C43×#1875C2semidirect
14. C43×#1854C2semidirect
15. C43×#1786C2semidirect
20. C22×M16×C43C22semidirect
21. C23×C8×C43C22semidirect
31. C2×#121×C43C22semidirect
32. C2×#121×C43C22semidirect
39. C2×#107×C43C22semidirect
40. C2×#106×C43C22semidirect
47. C2×#102×C43C22semidirect
48. C2×#102×C43C22semidirect
52. C2×C22⋊C8×C43C22semidirect
53. C2×C22⋊C8×C43C22semidirect
59. C43×#380C22semidirect
60. C43×#380C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
64. C43×#340C22semidirect
126. #121×C43D4semidirect
127. #121×C43D4semidirect
162. C22⋊C8×C43D4semidirect
426. #24390C43direct (N × H)
489. C2×#535C2×C43semidirect
490. C2×#469C2×C43semidirect
491. C2×#466C2×C43semidirect
492. C2×#447C2×C43semidirect
493. C2×#408C2×C43semidirect
494. #2615C2×C43semidirect
495. #2034C2×C43semidirect
496. #2033C2×C43semidirect
497. #1999C2×C43semidirect
498. #1999C2×C43semidirect
499. #1895C2×C43semidirect
500. #1893C2×C43semidirect
501. #1875C2×C43semidirect
502. #1854C2×C43semidirect
503. #1786C2×C43semidirect
521. C22×M16C22×C43semidirect
522. C23×C8C22×C43semidirect
532. C2×#121C22×C43semidirect
533. C2×#121C22×C43semidirect
540. C2×#107C22×C43semidirect
541. C2×#106C22×C43semidirect
548. C2×#102C22×C43semidirect
549. C2×#102C22×C43semidirect
553. C2×C22⋊C8C22×C43semidirect
554. C2×C22⋊C8C22×C43semidirect
560. #380C22×C43semidirect
561. #380C22×C43semidirect
562. #340C22×C43semidirect
563. #340C22×C43semidirect
564. #340C22×C43semidirect
565. #340C22×C43semidirect
566. C43#24390direct (N × H)
628. #121D4×C43semidirect
629. #121D4×C43semidirect
664. C22⋊C8D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5352
C2×C43×#4692
C2×C43×#4662
C2×C43×#4472
C2×C43×#4082
C43×#26152
C43×#20342
C43×#20332
C43×#19992
C43×#18952
C43×#18932
C43×#18752
C43×#18542
C43×#17862
#2439043