Finite Group Databasebeta

← C43×#25762 #24945779

Subgroups — C43×#25762 #24945779

Order 11008.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#546C211yesmaximal, characteristic, complemented
2C2×C43×#495C211yesmaximal, characteristic, complemented
3C2×C43×#463C211yesmaximal, characteristic, complemented
4C2×C43×#452C211yesmaximal, characteristic, complemented
5C2×C43×#449C211yesmaximal, characteristic, complemented
6C2×C43×#450C211yesmaximal, characteristic, complemented
7C2×C43×#447C211yesmaximal, characteristic, complemented
8C43×#2540C211yesmaximal, characteristic, complemented
9C43×#2001C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#2000C211yesmaximal, characteristic, complemented
12C43×#1999C211yesmaximal, characteristic, complemented
13C43×#1983C211yesmaximal, characteristic, complemented
14C43×#1954C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C22×Q16×C43C2211yescharacteristic, complemented
19C22×SD16×C43C2211yescharacteristic
20C22×SD16×C43C2211yescharacteristic
21C22×SD16×C43C2211yescharacteristic, complemented
22C22×D8×C43C2211yescharacteristic
23C22×D8×C43C2211yescharacteristic
24C43×#546—24no—
25C43×#546—24no—
26C2×#124×C43C2211yescharacteristic
27C2×#124×C43C2211yescharacteristic, complemented
28C2×#123×C43—21no—
29C2×C22⋊Q8×C43C2211yescharacteristic
30C2×C22⋊Q8×C43C2211yescharacteristic
31C2×C22⋊Q8×C43C2211yescharacteristic, complemented
32C2×#121×C43—21no—
33C2×#121×C43C2211yescharacteristic
34C2×#121×C43C2211yescharacteristic
35C2×#121×C43C2211yescharacteristic, complemented
36C2×#120×C43—21no—
37C2×C4×D4×C43C2211yescharacteristic
38C2×C4×D4×C43C2211yescharacteristic
39C22×C22⋊C4×C43—21no—
40C43×#495—24no—
41C43×#463—24no—
42C43×#452—24no—
43C43×#450—24no—
44C43×#449—24no—
45C43×#447—24no—
46C2×C4⋊C8×C43C2211yescharacteristic, complemented
47C2×#103×C43C2211yescharacteristic, complemented
48C2×#103×C43C2211yescharacteristic, complemented
49C2×#103×C43C2211yescharacteristic, complemented
50C2×#102×C43C2211yescharacteristic
51C2×#102×C43C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic, complemented
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic, complemented
58C2×C22⋊C8×C43C2211yescharacteristic, complemented
59C2×C4×C8×C43C2211yescharacteristic, complemented
60C43×#399—21no—
61C43×#392—21no—
62C43×#390—21no—
63C43×#390—21no—
64C4×C4⋊C4×C43C2211yescharacteristic, complemented
65C43×#340C2211yescharacteristic, complemented
66C43×#340C2211yescharacteristic, complemented
67C25×C43—21no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—22no—
71C2×#41×C43—22no—
72C2×#41×C43—41no—
73C2×#41×C43—41no—
74C22×Q8×C43C2311yescharacteristic
75C22×Q8×C43C2311yescharacteristic
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—22no—
79C22×D4×C43—22no—
80C22×D4×C43—22no—
81C22×D4×C43—22no—
82C22×D4×C43—21no—
83C22×D4×C43—21no—
84C22×D4×C43—21no—
85C22×D4×C43—41no—
86C22×D4×C43—41no—
87C22×D4×C43D411yescharacteristic
88C22×D4×C43C2311yescharacteristic
89C22×D4×C43C2311yescharacteristic
90C22×D4×C43C2311yescharacteristic
91C23×C4×C43—21no—
92C23×C4×C43—21no—
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C2×Q16×C43—22no—
96C2×Q16×C43—22no—
97C2×Q16×C43—41no—
98C2×SD16×C43—22no—
99C2×SD16×C43—22no—
100C2×SD16×C43—22no—
101C2×SD16×C43—22no—
102C2×SD16×C43—22no—
103C2×SD16×C43—22no—
104C2×SD16×C43—22no—
105C2×SD16×C43—41no—
106C2×SD16×C43—41no—
107C2×D8×C43—22no—
108C2×D8×C43—22no—
109C2×D8×C43—22no—
110C2×D8×C43—22no—
111C2×D8×C43—22no—
112C2×D8×C43—41no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117#124×C43—22no—
118#124×C43—22no—
119#124×C43—22no—
120#124×C43D414yescomplemented
121#123×C43—28no—
122C22⋊Q8×C43—22no—
123C22⋊Q8×C43—22no—
124C22⋊Q8×C43—22no—
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—41no—
127C22⋊Q8×C43—41no—
128#121×C43—28no—
129#121×C43—22no—
130#121×C43—22no—
131#121×C43—22no—
132#121×C43—22no—
133#121×C43—41no—
134#121×C43—41no—
135#120×C43—28no—
136C4×D4×C43—22no—
137C4×D4×C43—22no—
138C4×D4×C43—22no—
139C4×D4×C43D414yescomplemented
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43D411yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C22⋊C4×C43—28no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151C2×C22⋊C4×C43—21no—
152C2×C22⋊C4×C43—21no—
153C2×C22⋊C4×C43—21no—
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156C2×C22⋊C4×C43—21no—
157C2×C22⋊C4×C43—21no—
158C2×C22⋊C4×C43—21no—
159C2×C22⋊C4×C43D411yescharacteristic
160C2×C22⋊C4×C43D411yescharacteristic
161C2×C42×C43—21no—
162C2×C42×C43C2311yescharacteristic
163C4⋊C8×C43—22no—
164#103×C43—22no—
165#103×C43—22no—
166#103×C43—22no—
167#102×C43—22no—
168#102×C43—22no—
169#102×C43—22no—
170#102×C43D414yescomplemented
171#102×C43D414yescomplemented
172C22⋊C8×C43—22no—
173C22⋊C8×C43—22no—
174C22⋊C8×C43—22no—
175C22⋊C8×C43—22no—
176C4×C8×C43—22no—
177#95×C43—21no—
178C24×C43—21no—
179C24×C43—24no—
180C24×C43—21no—
181C24×C43—21no—
182C24×C43—42no—
183C24×C43—42no—
184C24×C43—42no—
185C24×C43—42no—
186C24×C43—81no—
187C24×C43—81no—
188C24×C43C2×D411yescharacteristic
189C24×C43C2×D411yescharacteristic
190#41×C43—44no—
191#41×C43—44no—
192#41×C43—44no—
193#41×C43—44no—
194C2×Q8×C43—21no—
195C2×Q8×C43—21no—
196C2×Q8×C43—21no—
197C2×Q8×C43—21no—
198C2×Q8×C43—21no—
199C2×Q8×C43—21no—
200C2×Q8×C43—21no—
201C2×Q8×C43—21no—
202C2×Q8×C43—21no—
203C2×Q8×C43—21no—
204C2×Q8×C43—21no—
205C2×Q8×C43C2×D412yes—
206C2×D4×C43—24no—
207C2×D4×C43—24no—
208C2×D4×C43—24no—
209C2×D4×C43—22no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—22no—
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—41no—
226C2×D4×C43—42no—
227C2×D4×C43—42no—
228C2×D4×C43—42no—
229C2×D4×C43—42no—
230C2×D4×C43—42no—
231C2×D4×C43—42no—
232C2×D4×C43—42no—
233C2×D4×C43—44no—
234C2×D4×C43—44no—
235C2×D4×C43—44no—
236C2×D4×C43—44no—
237C2×D4×C43—42no—
238C2×D4×C43—81no—
239C2×D4×C43—81no—
240C2×D4×C43—81no—
241C2×D4×C43—81no—
242C2×D4×C43C2×D412yes—
243C2×D4×C43C2×D412yes—
244C2×D4×C43C2×D412yes—
245C2×D4×C43C2×D412yes—
246C22×C4×C43—24no—
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—24no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—42no—
266C22×C4×C43—42no—
267C22×C4×C43—81no—
268C22×C4×C43—81no—
269C22×C4×C43C2×D411yescharacteristic
270C22×C4×C43C2×D411yescharacteristic
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2×D411yescharacteristic
273C22×C4×C43C2411yescharacteristic
274Q16×C43—44no—
275SD16×C43—44no—
276SD16×C43—44no—
277SD16×C43—44no—
278D8×C43—44no—
279D8×C43—44no—
280C2×C8×C43—21no—
281C2×C8×C43—21no—
282C2×C8×C43—21no—
283C2×C8×C43—21no—
284C2×C8×C43—21no—
285C2×C8×C43—21no—
286C2×C8×C43—21no—
287C2×C8×C43—21no—
288C2×C8×C43—21no—
289C2×C8×C43—21no—
290C2×C8×C43C2×D412yes—
291C2×C8×C43C2×D412yes—
292C4⋊C4×C43—24no—
293C4⋊C4×C43—22no—
294C4⋊C4×C43—21no—
295C4⋊C4×C43—21no—
296C4⋊C4×C43—21no—
297C4⋊C4×C43—42no—
298C4⋊C4×C43—42no—
299C4⋊C4×C43C2×D412yes—
300C4⋊C4×C43C2×D412yes—
301C4⋊C4×C43C2×D412yes—
302C22⋊C4×C43—24no—
303C22⋊C4×C43—24no—
304C22⋊C4×C43—22no—
305C22⋊C4×C43—24no—
306C22⋊C4×C43—24no—
307C22⋊C4×C43—24no—
308C22⋊C4×C43—22no—
309C22⋊C4×C43—42no—
310C22⋊C4×C43—42no—
311C22⋊C4×C43—42no—
312C22⋊C4×C43—42no—
313C22⋊C4×C43—42no—
314C22⋊C4×C43—42no—
315C42×C43—81no—
316C42×C43C2×D412yes—
317C42×C43C2×D412yes—
318C23×C43—21no—
319C23×C43—22no—
320C23×C43—21no—
321C23×C43—21no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—21no—
325C23×C43—21no—
326C23×C43—21no—
327C23×C43—22no—
328C23×C43—21no—
329C23×C43—21no—
330C23×C43—21no—
331C23×C43—21no—
332C23×C43—21no—
333C23×C43—21no—
334C23×C43—21no—
335C23×C43—48no—
336C23×C43—48no—
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—41no—
348C23×C43—41no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—41no—
354C23×C43—84no—
355C23×C43—84no—
356C23×C43—84no—
357C23×C43—84no—
358C23×C43—84no—
359C23×C43#13512yes—
360C23×C43C22×D411yescharacteristic
361Q8×C43—22no—
362Q8×C43—22no—
363Q8×C43—41no—
364Q8×C43—41no—
365Q8×C43—41no—
366Q8×C43—41no—
367Q8×C43—41no—
368Q8×C43—41no—
369D4×C43—22no—
370D4×C43—22no—
371D4×C43—22no—
372D4×C43—22no—
373D4×C43—22no—
374D4×C43—44no—
375D4×C43—48no—
376D4×C43—48no—
377D4×C43—41no—
378D4×C43—41no—
379D4×C43—41no—
380D4×C43—41no—
381D4×C43—41no—
382D4×C43—41no—
383D4×C43—84no—
384D4×C43—84no—
385D4×C43—84no—
386D4×C43#12714yes—
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—22no—
392C2×C4×C43—21no—
393C2×C4×C43—22no—
394C2×C4×C43—21no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—48no—
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—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—84no—
422C2×C4×C43#12012yes—
423C2×C4×C43#12012yes—
424C2×C4×C43C22×D411yescharacteristic
425C2×C4×C43C22×D411yescharacteristic
426C2×C4×C43C22×D411yescharacteristic
427C2×C4×C43C22×D411yescharacteristic
428C2×C4×C43H(5,𝔽2)11yescharacteristic
429C2×C4×C43H(5,𝔽2)11yescharacteristic
430C8×C43—22no—
431C8×C43—22no—
432C8×C43—41no—
433C8×C43—41no—
434#25762C4311yesmaximal, characteristic, direct product factor, Sylow
435C22×C43—24no—
436C22×C43—22no—
437C22×C43—22no—
438C22×C43—22no—
439C22×C43—41no—
440C22×C43—42no—
441C22×C43—41no—
442C22×C43—42no—
443C22×C43—41no—
444C22×C43—42no—
445C22×C43—41no—
446C22×C43—42no—
447C22×C43—42no—
448C22×C43—42no—
449C22×C43—41no—
450C22×C43—42no—
451C22×C43—41no—
452C22×C43—42no—
453C22×C43—41no—
454C22×C43—42no—
455C22×C43—41no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43—816no—
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×C43—81no—
471C22×C43C2×#12011yescharacteristic
472C22×C43D4211yescharacteristic
473C22×C43D4211yescharacteristic
474C22×C43C2×#13511yescharacteristic
475C22×C43#57511yescharacteristic
476C22×C43#57611yescharacteristic
477C22×C43#57711yescharacteristic
478C4×C43—22no—
479C4×C43—22no—
480C4×C43—41no—
481C4×C43—41no—
482C4×C43—42no—
483C4×C43—42no—
484C4×C43—42no—
485C4×C43—42no—
486C4×C43—81no—
487C4×C43C2×#12711yescharacteristic
488C4×C43#53511yescharacteristic
489C4×C43D4211yescharacteristic
490C4×C43D4211yescharacteristic
491C2×#546C2×C4311yescharacteristic, complemented
492C2×#495C2×C4311yescharacteristic, complemented
493C2×#463C2×C4311yescharacteristic, complemented
494C2×#452C2×C4311yescharacteristic, complemented
495C2×#449C2×C4311yescharacteristic, complemented
496C2×#450C2×C4311yescharacteristic, complemented
497C2×#447C2×C4311yescharacteristic, complemented
498#2540C2×C4311yescharacteristic, complemented
499#2001C2×C4311yescharacteristic, complemented
500#2000C2×C4311yescharacteristic, complemented
501#2000C2×C4311yescharacteristic, complemented
502#1999C2×C4311yescharacteristic, complemented
503#1983C2×C4311yescharacteristic, complemented
504#1954C2×C4311yescharacteristic, complemented
505C4×#102C2×C4311yescharacteristic, complemented
506C2×C43—42no—
507C2×C43—44no—
508C2×C43—81no—
509C2×C43—82no—
510C2×C43—161no—
511C2×C43#243311yescharacteristic
512C2×C43#300211yescharacteristic
513C2×C43#301211yescharacteristic
514C2×C43#327311yescharacteristic
515C2×C43#327511yescharacteristic
516C2×C43#328011yescharacteristic
517C2×C43#328211yescharacteristic
518C22×#41C22×C4311yescharacteristic
519C23×D4C22×C4311yescharacteristic
520C22×Q16C22×C4311yescharacteristic, complemented
521C22×SD16C22×C4311yescharacteristic
522C22×SD16C22×C4311yescharacteristic
523C22×SD16C22×C4311yescharacteristic, complemented
524C22×D8C22×C4311yescharacteristic
525C22×D8C22×C4311yescharacteristic
526#546—24no—
527#546—24no—
528C2×#124C22×C4311yescharacteristic
529C2×#124C22×C4311yescharacteristic, complemented
530C2×#123—21no—
531C2×C22⋊Q8C22×C4311yescharacteristic
532C2×C22⋊Q8C22×C4311yescharacteristic
533C2×C22⋊Q8C22×C4311yescharacteristic, complemented
534C2×#121—21no—
535C2×#121C22×C4311yescharacteristic
536C2×#121C22×C4311yescharacteristic
537C2×#121C22×C4311yescharacteristic, complemented
538C2×#120—21no—
539C2×C4×D4C22×C4311yescharacteristic
540C2×C4×D4C22×C4311yescharacteristic
541C22×C22⋊C4—21no—
542#495—24no—
543#463—24no—
544#452—24no—
545#450—24no—
546#449—24no—
547#447—24no—
548C2×C4⋊C8C22×C4311yescharacteristic, complemented
549C2×#103C22×C4311yescharacteristic, complemented
550C2×#103C22×C4311yescharacteristic, complemented
551C2×#103C22×C4311yescharacteristic, complemented
552C2×#102C22×C4311yescharacteristic
553C2×#102C22×C4311yescharacteristic
554C2×#102C22×C4311yescharacteristic
555C2×#102C22×C4311yescharacteristic
556C2×#102C22×C4311yescharacteristic, complemented
557C2×C22⋊C8C22×C4311yescharacteristic
558C2×C22⋊C8C22×C4311yescharacteristic
559C2×C22⋊C8C22×C4311yescharacteristic, complemented
560C2×C22⋊C8C22×C4311yescharacteristic, complemented
561C2×C4×C8C22×C4311yescharacteristic, complemented
562#399—21no—
563#392—21no—
564#390—21no—
565#390—21no—
566C4×C4⋊C4C22×C4311yescharacteristic, complemented
567#340C22×C4311yescharacteristic, complemented
568#340C22×C4311yescharacteristic, complemented
569C43#2576211yescharacteristic, direct product factor, Sylow
570C25—21no—
571C2×#41—22no—
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—41no—
576C2×#41—41no—
577C22×Q8C23×C4311yescharacteristic
578C22×Q8C23×C4311yescharacteristic
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—41no—
589C22×D4—41no—
590C22×D4D4×C4311yescharacteristic
591C22×D4C23×C4311yescharacteristic
592C22×D4C23×C4311yescharacteristic
593C22×D4C23×C4311yescharacteristic
594C23×C4—21no—
595C23×C4—21no—
596C23×C4C23×C4311yescharacteristic
597C23×C4C23×C4311yescharacteristic
598C2×Q16—22no—
599C2×Q16—22no—
600C2×Q16—41no—
601C2×SD16—22no—
602C2×SD16—22no—
603C2×SD16—22no—
604C2×SD16—22no—
605C2×SD16—22no—
606C2×SD16—22no—
607C2×SD16—22no—
608C2×SD16—41no—
609C2×SD16—41no—
610C2×D8—22no—
611C2×D8—22no—
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—41no—
616C22×C8C23×C4311yescharacteristic
617C22×C8C23×C4311yescharacteristic
618C22×C8C23×C4311yescharacteristic
619C22×C8C23×C4311yescharacteristic
620#124—22no—
621#124—22no—
622#124—22no—
623#124D4×C4314yescomplemented
624#123—28no—
625C22⋊Q8—22no—
626C22⋊Q8—22no—
627C22⋊Q8—22no—
628C22⋊Q8—22no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631#121—28no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—41no—
637#121—41no—
638#120—28no—
639C4×D4—22no—
640C4×D4—22no—
641C4×D4—22no—
642C4×D4D4×C4314yescomplemented
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4D4×C4311yescharacteristic
647C2×C4⋊C4C23×C4311yescharacteristic
648C2×C4⋊C4C23×C4311yescharacteristic
649C2×C4⋊C4C23×C4311yescharacteristic
650C2×C22⋊C4—28no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C4311yescharacteristic
663C2×C22⋊C4D4×C4311yescharacteristic
664C2×C42—21no—
665C2×C42C23×C4311yescharacteristic
666C4⋊C8—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102D4×C4314yescomplemented
674#102D4×C4314yescomplemented
675C22⋊C8—22no—
676C22⋊C8—22no—
677C22⋊C8—22no—
678C22⋊C8—22no—
679C4×C8—22no—
680#95—21no—
681C24—21no—
682C24—24no—
683C24—21no—
684C24—21no—
685C24—42no—
686C24—42no—
687C24—42no—
688C24—42no—
689C24—81no—
690C24—81no—
691C24C2×D4×C4311yescharacteristic
692C24C2×D4×C4311yescharacteristic
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8C2×D4×C4312yes—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—24no—
713C2×D4—22no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—41no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C2×D4×C4312yes—
746C2×D4C2×D4×C4312yes—
747C2×D4C2×D4×C4312yes—
748C2×D4C2×D4×C4312yes—
749C22×C4—24no—
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×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—81no—
771C22×C4—81no—
772C22×C4C2×D4×C4311yescharacteristic
773C22×C4C2×D4×C4311yescharacteristic
774C22×C4C2×D4×C4311yescharacteristic
775C22×C4C2×D4×C4311yescharacteristic
776C22×C4C24×C4311yescharacteristic
777Q16—44no—
778SD16—44no—
779SD16—44no—
780SD16—44no—
781D8—44no—
782D8—44no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8C2×D4×C4312yes—
794C2×C8C2×D4×C4312yes—
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—42no—
801C4⋊C4—42no—
802C4⋊C4C2×D4×C4312yes—
803C4⋊C4C2×D4×C4312yes—
804C4⋊C4C2×D4×C4312yes—
805C22⋊C4—24no—
806C22⋊C4—24no—
807C22⋊C4—22no—
808C22⋊C4—24no—
809C22⋊C4—24no—
810C22⋊C4—24no—
811C22⋊C4—22no—
812C22⋊C4—42no—
813C22⋊C4—42no—
814C22⋊C4—42no—
815C22⋊C4—42no—
816C22⋊C4—42no—
817C22⋊C4—42no—
818C42—81no—
819C42C2×D4×C4312yes—
820C42C2×D4×C4312yes—
821C23—21no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—22no—
826C23—22no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—48no—
839C23—48no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23—84no—
861C23—84no—
862C23#135×C4312yes—
863C23C22×D4×C4311yescharacteristic
864Q8—22no—
865Q8—22no—
866Q8—41no—
867Q8—41no—
868Q8—41no—
869Q8—41no—
870Q8—41no—
871Q8—41no—
872D4—22no—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—44no—
878D4—48no—
879D4—48no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—84no—
887D4—84no—
888D4—84no—
889D4#127×C4314yes—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—48no—
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—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—84no—
925C2×C4#120×C4312yes—
926C2×C4#120×C4312yes—
927C2×C4C22×D4×C4311yescharacteristic
928C2×C4C22×D4×C4311yescharacteristic
929C2×C4C22×D4×C4311yescharacteristic
930C2×C4C22×D4×C4311yescharacteristic
931C2×C4H(5,𝔽2)×C4311yescharacteristic
932C2×C4H(5,𝔽2)×C4311yescharacteristic
933C8—22no—
934C8—22no—
935C8—41no—
936C8—41no—
937C22—24no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—41no—
942C22—42no—
943C22—42no—
944C22—41no—
945C22—41no—
946C22—42no—
947C22—41no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—41no—
952C22—42no—
953C22—41no—
954C22—42no—
955C22—41no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—816no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22C2×#120×C4311yescharacteristic
974C22D42×C4311yescharacteristic
975C22D42×C4311yescharacteristic
976C22C2×#135×C4311yescharacteristic
977C22C43×#57511yescharacteristic
978C22C43×#57611yescharacteristic
979C22C43×#57711yescharacteristic
980C4—22no—
981C4—22no—
982C4—41no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—81no—
989C4C2×#127×C4311yescharacteristic
990C4C43×#53511yescharacteristic
991C4D42×C4311yescharacteristic
992C4D42×C4311yescharacteristic
993C2—42no—
994C2—44no—
995C2—81no—
996C2—82no—
997C2—161no—
998C2C43×#243311yescharacteristic
999C2C43×#300211yescharacteristic
1000C2C43×#301211yescharacteristic
1001C2C43×#327311yescharacteristic
1002C2C43×#327511yescharacteristic
1003C2C43×#328011yescharacteristic
1004C2C43×#328211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#546C2semidirect
2. C2×C43×#495C2semidirect
3. C2×C43×#463C2semidirect
4. C2×C43×#452C2semidirect
5. C2×C43×#449C2semidirect
6. C2×C43×#450C2semidirect
7. C2×C43×#447C2semidirect
8. C43×#2540C2semidirect
9. C43×#2001C2semidirect
10. C43×#2000C2semidirect
11. C43×#2000C2semidirect
12. C43×#1999C2semidirect
13. C43×#1983C2semidirect
14. C43×#1954C2semidirect
15. C4×#102×C43C2semidirect
18. C22×Q16×C43C22semidirect
21. C22×SD16×C43C22semidirect
27. C2×#124×C43C22semidirect
31. C2×C22⋊Q8×C43C22semidirect
35. C2×#121×C43C22semidirect
46. C2×C4⋊C8×C43C22semidirect
47. C2×#103×C43C22semidirect
48. C2×#103×C43C22semidirect
49. C2×#103×C43C22semidirect
54. C2×#102×C43C22semidirect
57. C2×C22⋊C8×C43C22semidirect
58. C2×C22⋊C8×C43C22semidirect
59. C2×C4×C8×C43C22semidirect
64. C4×C4⋊C4×C43C22semidirect
65. C43×#340C22semidirect
66. C43×#340C22semidirect
120. #124×C43D4semidirect
139. C4×D4×C43D4semidirect
170. #102×C43D4semidirect
171. #102×C43D4semidirect
434. #25762C43direct (N × H)
491. C2×#546C2×C43semidirect
492. C2×#495C2×C43semidirect
493. C2×#463C2×C43semidirect
494. C2×#452C2×C43semidirect
495. C2×#449C2×C43semidirect
496. C2×#450C2×C43semidirect
497. C2×#447C2×C43semidirect
498. #2540C2×C43semidirect
499. #2001C2×C43semidirect
500. #2000C2×C43semidirect
501. #2000C2×C43semidirect
502. #1999C2×C43semidirect
503. #1983C2×C43semidirect
504. #1954C2×C43semidirect
505. C4×#102C2×C43semidirect
520. C22×Q16C22×C43semidirect
523. C22×SD16C22×C43semidirect
529. C2×#124C22×C43semidirect
533. C2×C22⋊Q8C22×C43semidirect
537. C2×#121C22×C43semidirect
548. C2×C4⋊C8C22×C43semidirect
549. C2×#103C22×C43semidirect
550. C2×#103C22×C43semidirect
551. C2×#103C22×C43semidirect
556. C2×#102C22×C43semidirect
559. C2×C22⋊C8C22×C43semidirect
560. C2×C22⋊C8C22×C43semidirect
561. C2×C4×C8C22×C43semidirect
566. C4×C4⋊C4C22×C43semidirect
567. #340C22×C43semidirect
568. #340C22×C43semidirect
569. C43#25762direct (N × H)
623. #124D4×C43semidirect
642. C4×D4D4×C43semidirect
673. #102D4×C43semidirect
674. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5462
C2×C43×#4952
C2×C43×#4632
C2×C43×#4522
C2×C43×#4492
C2×C43×#4502
C2×C43×#4472
C43×#25402
C43×#20012
C43×#20002
C43×#19992
C43×#19832
C43×#19542
C4×#102×C432
#2576243