Finite Group Databasebeta

← C43×#24394 #24944411

Subgroups — C43×#24394 #24944411

Order 11008.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#535C211yesmaximal, characteristic
2C2×C43×#468C211yesmaximal, characteristic, complemented
3C2×C43×#465C211yesmaximal, characteristic, complemented
4C2×C43×#450C211yesmaximal, characteristic, complemented
5C2×C43×#408C211yesmaximal, characteristic, complemented
6C43×#2616C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2000C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#1895C211yesmaximal, characteristic, complemented
12C43×#1893C211yesmaximal, characteristic, complemented
13C43×#1873C211yesmaximal, characteristic, complemented
14C43×#1854C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×SD16×C43C2211yescharacteristic
20C22×M16×C43C2211yescharacteristic, complemented
21C23×C8×C43C2211yescharacteristic, complemented
22C43×#535—24no—
23C43×#535—24no—
24C2×#127×C43—21no—
25C2×#124×C43—21no—
26C2×C22⋊Q8×C43C2211yescharacteristic
27C2×C22⋊Q8×C43C2211yescharacteristic, complemented
28C2×C22⋊Q8×C43C2211yescharacteristic, complemented
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×#121×C43C2211yescharacteristic
32C2×#121×C43C2211yescharacteristic
33C2×#120×C43—21no—
34C2×#120×C43—21no—
35C2×#117×C43C2211yescharacteristic
36C43×#468—24no—
37C43×#465—24no—
38C43×#450—24no—
39C2×#107×C43C2211yescharacteristic, complemented
40C2×#106×C43C2211yescharacteristic, complemented
41C2×#103×C43C2211yescharacteristic, complemented
42C2×#103×C43C2211yescharacteristic, complemented
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×#102×C43C2211yescharacteristic
48C2×#102×C43C2211yescharacteristic
49C43×#408—24no—
50C2×C22⋊C8×C43C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C2×C22⋊C8×C43C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic, complemented
54C43×#395—21no—
55C43×#394—21no—
56C43×#394—21no—
57C43×#394—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×Q8×C43C2311yescharacteristic
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—22no—
79C22×D4×C43—22no—
80C22×D4×C43—21no—
81C22×D4×C43—22no—
82C22×D4×C43—22no—
83C22×D4×C43—41no—
84C22×D4×C43—41no—
85C22×D4×C43D411yescharacteristic
86C22×D4×C43D411yescharacteristic
87C22×D4×C43D411yescharacteristic
88C22×D4×C43C2311yescharacteristic
89C22×D4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C2×SD16×C43—22no—
94C2×SD16×C43—22no—
95C2×SD16×C43—22no—
96C2×SD16×C43—22no—
97C2×SD16×C43—41no—
98C2×SD16×C43—41no—
99C2×M16×C43—22no—
100C2×M16×C43—22no—
101C2×M16×C43—41no—
102C22×C8×C43—22no—
103C22×C8×C43—22no—
104C22×C8×C43—41no—
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#127×C43—28no—
110#124×C43—28no—
111C22⋊Q8×C43—22no—
112C22⋊Q8×C43—22no—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43—41no—
116C22⋊Q8×C43—41no—
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×C43D414yes—
124#121×C43D414yes—
125#120×C43—28no—
126#120×C43—28no—
127#117×C43—22no—
128#117×C43—22no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
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#103×C43—22no—
152#103×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—42no—
170C24×C43—42no—
171C24×C43—81no—
172C24×C43—81no—
173C24×C43—81no—
174C24×C43—81no—
175C24×C43C2×D411yescharacteristic
176C24×C43C2×D411yescharacteristic
177C24×C43C2×D411yescharacteristic
178#41×C43—44no—
179#41×C43—44no—
180#41×C43—44no—
181#41×C43—44no—
182C2×Q8×C43—22no—
183C2×Q8×C43—22no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—41no—
191C2×D4×C43—24no—
192C2×D4×C43—24no—
193C2×D4×C43—24no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—24no—
201C2×D4×C43—24no—
202C2×D4×C43—22no—
203C2×D4×C43—22no—
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—41no—
213C2×D4×C43—41no—
214C2×D4×C43—41no—
215C2×D4×C43—44no—
216C2×D4×C43—44no—
217C2×D4×C43—44no—
218C2×D4×C43—44no—
219C2×D4×C43—42no—
220C2×D4×C43—42no—
221C2×D4×C43—81no—
222C2×D4×C43—81no—
223C2×D4×C43—81no—
224C2×D4×C43—81no—
225C2×D4×C43—81no—
226C2×D4×C43—81no—
227C2×D4×C43—81no—
228C2×D4×C43—81no—
229C2×D4×C43C2×D412yes—
230C2×D4×C43C2×D412yes—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43C2×D412yes—
252C22×C4×C43C2×D412yes—
253C22×C4×C43C2×D412yes—
254C22×C4×C43C2×D411yescharacteristic
255C22×C4×C43C2×D411yescharacteristic
256C22×C4×C43C2×D411yescharacteristic
257C22×C4×C43#4112yes—
258C22×C4×C43C2411yescharacteristic
259SD16×C43—44no—
260SD16×C43—44no—
261M16×C43—44no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—44no—
273C2×C8×C43C2×D412yes—
274C2×C8×C43C2×D412yes—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—42no—
284C4⋊C4×C43—42no—
285C4⋊C4×C43—42no—
286C4⋊C4×C43C2×D412yes—
287C4⋊C4×C43C2×D412yes—
288C22⋊C4×C43—24no—
289C22⋊C4×C43—24no—
290C22⋊C4×C43—24no—
291C22⋊C4×C43—24no—
292C22⋊C4×C43—24no—
293C22⋊C4×C43—42no—
294C22⋊C4×C43—42no—
295C22⋊C4×C43—42no—
296C22⋊C4×C43—81no—
297C22⋊C4×C43—81no—
298C22⋊C4×C43—81no—
299C42×C43—24no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—48no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—84no—
335C23×C43—84no—
336C23×C43—84no—
337C23×C43—84no—
338C23×C43—84no—
339C23×C43—84no—
340C23×C43#12012yes—
341C23×C43#12112yes—
342C23×C43C22×D411yescharacteristic
343Q8×C43—44no—
344Q8×C43—41no—
345Q8×C43—41no—
346Q8×C43—41no—
347Q8×C43—41no—
348D4×C43—22no—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—44no—
353D4×C43—44no—
354D4×C43—48no—
355D4×C43—44no—
356D4×C43—41no—
357D4×C43—41no—
358D4×C43—41no—
359D4×C43—41no—
360D4×C43—84no—
361D4×C43—84no—
362D4×C43—84no—
363D4×C43—84no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—21no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43#12012yes—
402C2×C4×C43#12112yes—
403C2×C4×C43C22×D411yescharacteristic
404C2×C4×C43C22×D411yescharacteristic
405C2×C4×C43C22×D411yescharacteristic
406C2×C4×C43C2×#4111yescharacteristic
407C2×C4×C43H(5,𝔽2)11yescharacteristic
408C2×C4×C43H(5,𝔽2)11yescharacteristic
409C8×C43—22no—
410C8×C43—22no—
411C8×C43—41no—
412C8×C43—41no—
413#24394C4311yesmaximal, characteristic, direct product factor, Sylow
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—41no—
429C22×C43—42no—
430C22×C43—42no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—41no—
437C22×C43—42no—
438C22×C43—42no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—816no—
442C22×C43—81no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43—81no—
446C22×C43—81no—
447C22×C43—81no—
448C22×C43—81no—
449C22×C43—81no—
450C22×C43C2×#12011yescharacteristic
451C22×C43C2×#12111yescharacteristic
452C22×C43#53411yescharacteristic
453C22×C43#57611yescharacteristic
454C22×C43#57711yescharacteristic
455C22×C43#57711yescharacteristic
456C22×C43#57711yescharacteristic
457C4×C43—22no—
458C4×C43—22no—
459C4×C43—41no—
460C4×C43—42no—
461C4×C43—42no—
462C4×C43—81no—
463C4×C43—81no—
464C4×C43—81no—
465C4×C43—81no—
466C4×C43D4211yescharacteristic
467C4×C43D4211yescharacteristic
468C4×C43#54611yescharacteristic
469C4×C43#54611yescharacteristic
470C2×#535C2×C4311yescharacteristic
471C2×#468C2×C4311yescharacteristic, complemented
472C2×#465C2×C4311yescharacteristic, complemented
473C2×#450C2×C4311yescharacteristic, complemented
474C2×#408C2×C4311yescharacteristic, complemented
475#2616C2×C4311yescharacteristic, complemented
476#2034C2×C4311yescharacteristic, complemented
477#2033C2×C4311yescharacteristic, complemented
478#2000C2×C4311yescharacteristic, complemented
479#2000C2×C4311yescharacteristic, complemented
480#1895C2×C4311yescharacteristic, complemented
481#1893C2×C4311yescharacteristic, complemented
482#1873C2×C4311yescharacteristic, complemented
483#1854C2×C4311yescharacteristic, complemented
484#1786C2×C4311yescharacteristic, complemented
485C2×C43—42no—
486C2×C43—42no—
487C2×C43—81no—
488C2×C43—82no—
489C2×C43—82no—
490C2×C43#241011yescharacteristic
491C2×C43#300911yescharacteristic
492C2×C43#301211yescharacteristic
493C2×C43#305711yescharacteristic
494C2×C43#306211yescharacteristic
495C2×C43#319811yescharacteristic
496C2×C43#320011yescharacteristic
497C22×#41C22×C4311yescharacteristic
498C23×D4C22×C4311yescharacteristic
499C22×SD16C22×C4311yescharacteristic
500C22×SD16C22×C4311yescharacteristic
501C22×M16C22×C4311yescharacteristic, complemented
502C23×C8C22×C4311yescharacteristic, complemented
503#535—24no—
504#535—24no—
505C2×#127—21no—
506C2×#124—21no—
507C2×C22⋊Q8C22×C4311yescharacteristic
508C2×C22⋊Q8C22×C4311yescharacteristic, complemented
509C2×C22⋊Q8C22×C4311yescharacteristic, complemented
510C2×#121C22×C4311yescharacteristic
511C2×#121C22×C4311yescharacteristic
512C2×#121C22×C4311yescharacteristic
513C2×#121C22×C4311yescharacteristic
514C2×#120—21no—
515C2×#120—21no—
516C2×#117C22×C4311yescharacteristic
517#468—24no—
518#465—24no—
519#450—24no—
520C2×#107C22×C4311yescharacteristic, complemented
521C2×#106C22×C4311yescharacteristic, complemented
522C2×#103C22×C4311yescharacteristic, complemented
523C2×#103C22×C4311yescharacteristic, complemented
524C2×#102C22×C4311yescharacteristic
525C2×#102C22×C4311yescharacteristic
526C2×#102C22×C4311yescharacteristic
527C2×#102C22×C4311yescharacteristic
528C2×#102C22×C4311yescharacteristic
529C2×#102C22×C4311yescharacteristic
530#408—24no—
531C2×C22⋊C8C22×C4311yescharacteristic
532C2×C22⋊C8C22×C4311yescharacteristic
533C2×C22⋊C8C22×C4311yescharacteristic, complemented
534C2×C22⋊C8C22×C4311yescharacteristic, complemented
535#395—21no—
536#394—21no—
537#394—21no—
538#394—21no—
539#380C22×C4311yescharacteristic
540#380C22×C4311yescharacteristic, complemented
541#380C22×C4311yescharacteristic, complemented
542#340C22×C4311yescharacteristic, complemented
543#340C22×C4311yescharacteristic, complemented
544#340C22×C4311yescharacteristic, complemented
545#340C22×C4311yescharacteristic, complemented
546C43#2439411yescharacteristic, direct product factor, Sylow
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C4311yescharacteristic
555C22×Q8C23×C4311yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C4311yescharacteristic
568C22×D4D4×C4311yescharacteristic
569C22×D4D4×C4311yescharacteristic
570C22×D4C23×C4311yescharacteristic
571C22×D4C23×C4311yescharacteristic
572C23×C4C23×C4311yescharacteristic
573C23×C4C23×C4311yescharacteristic
574C23×C4C23×C4311yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C4311yescharacteristic
588C22×C8C23×C4311yescharacteristic
589C22×C8C23×C4311yescharacteristic
590C22×C8C23×C4311yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C4314yes—
606#121D4×C4314yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C4311yescharacteristic
615C2×C4⋊C4C23×C4311yescharacteristic
616C2×C4⋊C4C23×C4311yescharacteristic
617C2×C4⋊C4C23×C4311yescharacteristic
618C2×C4⋊C4C23×C4311yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C4314yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C4311yescharacteristic
658C24C2×D4×C4311yescharacteristic
659C24C2×D4×C4311yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C4312yes—
712C2×D4C2×D4×C4312yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C4311yescharacteristic
734C22×C4C2×D4×C4311yescharacteristic
735C22×C4C2×D4×C4312yes—
736C22×C4C2×D4×C4312yes—
737C22×C4C2×D4×C4311yescharacteristic
738C22×C4C2×D4×C4312yes—
739C22×C4#41×C4312yes—
740C22×C4C24×C4311yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C4312yes—
756C2×C8C2×D4×C4312yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C4312yes—
769C4⋊C4C2×D4×C4312yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C4312yes—
823C23#121×C4312yes—
824C23C22×D4×C4311yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4#120×C4312yes—
884C2×C4#121×C4312yes—
885C2×C4C22×D4×C4311yescharacteristic
886C2×C4C22×D4×C4311yescharacteristic
887C2×C4C22×D4×C4311yescharacteristic
888C2×C4C2×#41×C4311yescharacteristic
889C2×C4H(5,𝔽2)×C4311yescharacteristic
890C2×C4H(5,𝔽2)×C4311yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C4311yescharacteristic
932C22C2×#121×C4311yescharacteristic
933C22C43×#53411yescharacteristic
934C22C43×#57611yescharacteristic
935C22C43×#57711yescharacteristic
936C22C43×#57711yescharacteristic
937C22C43×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C4311yescharacteristic
948C4D42×C4311yescharacteristic
949C4C43×#54611yescharacteristic
950C4C43×#54611yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C43×#241011yescharacteristic
957C2C43×#300911yescharacteristic
958C2C43×#301211yescharacteristic
959C2C43×#305711yescharacteristic
960C2C43×#306211yescharacteristic
961C2C43×#319811yescharacteristic
962C2C43×#320011yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#535C2
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
2. C2×C43×#468C2semidirect
3. C2×C43×#465C2semidirect
4. C2×C43×#450C2semidirect
5. C2×C43×#408C2semidirect
6. C43×#2616C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#2000C2semidirect
10. C43×#2000C2semidirect
11. C43×#1895C2semidirect
12. C43×#1893C2semidirect
13. C43×#1873C2semidirect
14. C43×#1854C2semidirect
15. C43×#1786C2semidirect
20. C22×M16×C43C22semidirect
21. C23×C8×C43C22semidirect
27. C2×C22⋊Q8×C43C22semidirect
28. C2×C22⋊Q8×C43C22semidirect
39. C2×#107×C43C22semidirect
40. C2×#106×C43C22semidirect
41. C2×#103×C43C22semidirect
42. C2×#103×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
162. C22⋊C8×C43D4semidirect
413. #24394C43direct (N × H)
471. C2×#468C2×C43semidirect
472. C2×#465C2×C43semidirect
473. C2×#450C2×C43semidirect
474. C2×#408C2×C43semidirect
475. #2616C2×C43semidirect
476. #2034C2×C43semidirect
477. #2033C2×C43semidirect
478. #2000C2×C43semidirect
479. #2000C2×C43semidirect
480. #1895C2×C43semidirect
481. #1893C2×C43semidirect
482. #1873C2×C43semidirect
483. #1854C2×C43semidirect
484. #1786C2×C43semidirect
501. C22×M16C22×C43semidirect
502. C23×C8C22×C43semidirect
508. C2×C22⋊Q8C22×C43semidirect
509. C2×C22⋊Q8C22×C43semidirect
520. C2×#107C22×C43semidirect
521. C2×#106C22×C43semidirect
522. C2×#103C22×C43semidirect
523. C2×#103C22×C43semidirect
533. C2×C22⋊C8C22×C43semidirect
534. C2×C22⋊C8C22×C43semidirect
540. #380C22×C43semidirect
541. #380C22×C43semidirect
542. #340C22×C43semidirect
543. #340C22×C43semidirect
544. #340C22×C43semidirect
545. #340C22×C43semidirect
546. C43#24394direct (N × H)
644. 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×#4682
C2×C43×#4652
C2×C43×#4502
C2×C43×#4082
C43×#26162
C43×#20342
C43×#20332
C43×#20002
C43×#18952
C43×#18932
C43×#18732
C43×#18542
C43×#17862
#2439443