Finite Group Databasebeta

← C43×#24162 #24944179

Subgroups — C43×#24162 #24944179

Order 11008.

1206 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#540C211yesmaximal, characteristic, complemented
2C2×C43×#478C211yesmaximal, characteristic, complemented
3C2×C43×#459C211yesmaximal, characteristic, complemented
4C43×#2324C211yesmaximal, characteristic, complemented
5C43×#2034C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#1999C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1989C211yesmaximal, characteristic, complemented
10C43×#1982C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1879C211yesmaximal, characteristic, complemented
13C43×#1864C211yesmaximal, characteristic, complemented
14C43×#1862C211yesmaximal, characteristic, complemented
15C43×#1798C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C43×#540—24no—
19C43×#540—24no—
20C2×#127×C43C2211yescharacteristic
21C2×#125×C43C2211yescharacteristic
22C2×#123×C43—21no—
23C2×#123×C43—21no—
24C2×#121×C43—21no—
25C2×#121×C43—21no—
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C2×C4×D4×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C2×#117×C43C2211yescharacteristic
33C43×#478—24no—
34C43×#459—24no—
35C2×#107×C43C2211yescharacteristic
36C2×#106×C43C2211yescharacteristic
37C2×C4⋊C8×C43C2211yescharacteristic
38C2×C4⋊C8×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C43×#390—21no—
50C43×#390C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#388—21no—
53C43×#386—21no—
54C43×#385—21no—
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43C2311yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C22×D4×C43C2311yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43C2311yescharacteristic
75C2×D8×C43—22no—
76C2×D8×C43—22no—
77C2×D8×C43—22no—
78C2×D8×C43—22no—
79C2×D8×C43—41no—
80C2×D8×C43—41no—
81C22×C8×C43C2311yescharacteristic
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85#127×C43—22no—
86#127×C43D414yescomplemented
87#125×C43—22no—
88#125×C43D414yescomplemented
89#123×C43—28no—
90#123×C43—28no—
91#121×C43—28no—
92#121×C43—28no—
93#121×C43—22no—
94#121×C43—22no—
95#121×C43—22no—
96#121×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105#117×C43—22no—
106#117×C43—22no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131#107×C43—22no—
132#106×C43—22no—
133C4⋊C8×C43—22no—
134C4⋊C8×C43—22no—
135#102×C43—22no—
136#102×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—41no—
142#102×C43—41no—
143C22⋊C8×C43—41no—
144C22⋊C8×C43—41no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C2×D4×C43—24no—
153C2×D4×C43—24no—
154C2×D4×C43—24no—
155C2×D4×C43—24no—
156C2×D4×C43—24no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—81no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C2×D4×C43—81no—
177C2×D4×C43—81no—
178C2×D4×C43—81no—
179C2×D4×C43—81no—
180C2×D4×C43—81no—
181C2×D4×C43—81no—
182C2×D4×C43C2×D412yes—
183C2×D4×C43C2×D412yes—
184C2×D4×C43#4112yes—
185C22×C4×C43—24no—
186C22×C4×C43—24no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—42no—
199C22×C4×C43—81no—
200C22×C4×C43—81no—
201C22×C4×C43—81no—
202C22×C4×C43—81no—
203C22×C4×C43—81no—
204C22×C4×C43—81no—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2411yescharacteristic
211D8×C43—44no—
212D8×C43—44no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—22no—
228C4⋊C4×C43—22no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—81no—
237C4⋊C4×C43C2×D412yes—
238C4⋊C4×C43C2×D412yes—
239C4⋊C4×C43#4112yes—
240C22⋊C4×C43—24no—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—24no—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—42no—
248C22⋊C4×C43—81no—
249C22⋊C4×C43—81no—
250C22⋊C4×C43—81no—
251C42×C43—21no—
252C42×C43—21no—
253C42×C43—81no—
254C42×C43C2×D412yes—
255C42×C43C2×D412yes—
256C23×C43—21no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43C22×D411yescharacteristic
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—84no—
298D4×C43—84no—
299D4×C43—84no—
300D4×C43—84no—
301D4×C43—84no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—21no—
312C2×C4×C43—22no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—84no—
335C2×C4×C43—84no—
336C2×C4×C43—84no—
337C2×C4×C43#12012yes—
338C2×C4×C43#12012yes—
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C2×C4×C432−1+411yescharacteristic
345C8×C43—41no—
346C8×C43—41no—
347C8×C43—41no—
348C8×C43—41no—
349#24162C4311yesmaximal, characteristic, direct product factor, Sylow
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—41no—
353C22×C43—42no—
354C22×C43—41no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—41no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43C2×#12011yescharacteristic
379C22×C43#52511yescharacteristic
380C22×C43#53711yescharacteristic
381C22×C43#57611yescharacteristic
382C22×C43#57611yescharacteristic
383C22×C43#57611yescharacteristic
384C22×C43#57711yescharacteristic
385C4×C43—22no—
386C4×C43—22no—
387C4×C43—42no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43—42no—
391C4×C43—41no—
392C4×C43—42no—
393C4×C43—81no—
394C4×C43—81no—
395C4×C43#54611yescharacteristic
396C4×C43#54711yescharacteristic
397C4×C43#54811yescharacteristic
398C4×C43#55011yescharacteristic
399C2×#540C2×C4311yescharacteristic, complemented
400C2×#478C2×C4311yescharacteristic, complemented
401C2×#459C2×C4311yescharacteristic, complemented
402#2324C2×C4311yescharacteristic, complemented
403#2034C2×C4311yescharacteristic, complemented
404#2033C2×C4311yescharacteristic, complemented
405#1999C2×C4311yescharacteristic, complemented
406#1999C2×C4311yescharacteristic, complemented
407#1989C2×C4311yescharacteristic, complemented
408#1982C2×C4311yescharacteristic, complemented
409#1879C2×C4311yescharacteristic, complemented
410#1879C2×C4311yescharacteristic, complemented
411#1864C2×C4311yescharacteristic, complemented
412#1862C2×C4311yescharacteristic, complemented
413#1798C2×C4311yescharacteristic, complemented
414C2×C43—81no—
415C2×C43—82no—
416C2×C43—82no—
417C2×C43—82no—
418C2×C43#240711yescharacteristic
419C2×C43#300811yescharacteristic
420C2×C43#301211yescharacteristic
421C2×C43#311911yescharacteristic
422C2×C43#312211yescharacteristic
423C2×C43#325711yescharacteristic
424C2×C43#325911yescharacteristic
425C22×D8C22×C4311yescharacteristic
426C22×D8C22×C4311yescharacteristic
427#540—24no—
428#540—24no—
429C2×#127C22×C4311yescharacteristic
430C2×#125C22×C4311yescharacteristic
431C2×#123—21no—
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C4311yescharacteristic
436C2×#121C22×C4311yescharacteristic
437C2×#121C22×C4311yescharacteristic
438C2×C4×D4C22×C4311yescharacteristic
439C2×C4×D4C22×C4311yescharacteristic
440C2×C4×D4C22×C4311yescharacteristic
441C2×#117C22×C4311yescharacteristic
442#478—24no—
443#459—24no—
444C2×#107C22×C4311yescharacteristic
445C2×#106C22×C4311yescharacteristic
446C2×C4⋊C8C22×C4311yescharacteristic
447C2×C4⋊C8C22×C4311yescharacteristic
448C2×#102C22×C4311yescharacteristic
449C2×#102C22×C4311yescharacteristic
450C2×#102C22×C4311yescharacteristic
451C2×#102C22×C4311yescharacteristic
452C2×#102C22×C4311yescharacteristic
453C2×#102C22×C4311yescharacteristic
454C2×#102C22×C4311yescharacteristic
455C2×#102C22×C4311yescharacteristic
456C2×C22⋊C8C22×C4311yescharacteristic
457C2×C22⋊C8C22×C4311yescharacteristic
458#390—21no—
459#390C22×C4311yescharacteristic
460#389C22×C4311yescharacteristic
461#388—21no—
462#386—21no—
463#385—21no—
464#380C22×C4311yescharacteristic
465C4×C4⋊C4C22×C4311yescharacteristic
466#340C22×C4311yescharacteristic
467#340C22×C4311yescharacteristic
468#340C22×C4311yescharacteristic
469#340C22×C4311yescharacteristic
470#336C22×C4311yescharacteristic
471#336C22×C4311yescharacteristic
472C43#2416211yescharacteristic, direct product factor, Sylow
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C4311yescharacteristic
479C22×D4C23×C4311yescharacteristic
480C22×D4C23×C4311yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C4311yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×D8—41no—
491C22×C8C23×C4311yescharacteristic
492C22×C8C23×C4311yescharacteristic
493C22×C8C23×C4311yescharacteristic
494C22×C8C23×C4311yescharacteristic
495#127—22no—
496#127D4×C4314yescomplemented
497#125—22no—
498#125D4×C4314yescomplemented
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C4311yescharacteristic
521C2×C4⋊C4D4×C4311yescharacteristic
522C2×C4⋊C4C23×C4311yescharacteristic
523C2×C4⋊C4C23×C4311yescharacteristic
524C2×C4⋊C4C23×C4311yescharacteristic
525C2×C4⋊C4C23×C4311yescharacteristic
526C2×C4⋊C4C23×C4311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C4311yescharacteristic
537C2×C22⋊C4D4×C4311yescharacteristic
538C2×C42—21no—
539C2×C42C23×C4311yescharacteristic
540C2×C42C23×C4311yescharacteristic
541#107—22no—
542#106—22no—
543C4⋊C8—22no—
544C4⋊C8—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—41no—
554C22⋊C8—41no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C4311yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C4312yes—
593C2×D4C2×D4×C4312yes—
594C2×D4#41×C4312yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C4311yescharacteristic
616C22×C4C2×D4×C4311yescharacteristic
617C22×C4C2×D4×C4311yescharacteristic
618C22×C4C2×D4×C4311yescharacteristic
619C22×C4C2×D4×C4311yescharacteristic
620C22×C4C24×C4311yescharacteristic
621D8—44no—
622D8—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C4312yes—
648C4⋊C4C2×D4×C4312yes—
649C4⋊C4#41×C4312yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C4312yes—
665C42C2×D4×C4312yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C4311yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C4312yes—
748C2×C4#120×C4312yes—
749C2×C4C22×D4×C4311yescharacteristic
750C2×C4C22×D4×C4311yescharacteristic
751C2×C4C2×#41×C4311yescharacteristic
752C2×C4C2×#41×C4311yescharacteristic
753C2×C4H(5,𝔽2)×C4311yescharacteristic
754C2×C42−1+4×C4311yescharacteristic
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C4311yescharacteristic
788C22C43×#52511yescharacteristic
789C22C43×#53711yescharacteristic
790C22C43×#57611yescharacteristic
791C22C43×#57611yescharacteristic
792C22C43×#57611yescharacteristic
793C22C43×#57711yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4C43×#54611yescharacteristic
805C4C43×#54711yescharacteristic
806C4C43×#54811yescharacteristic
807C4C43×#55011yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C43×#240711yescharacteristic
813C2C43×#300811yescharacteristic
814C2C43×#301211yescharacteristic
815C2C43×#311911yescharacteristic
816C2C43×#312211yescharacteristic
817C2C43×#325711yescharacteristic
818C2C43×#325911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#540C2semidirect
2. C2×C43×#478C2semidirect
3. C2×C43×#459C2semidirect
4. C43×#2324C2semidirect
5. C43×#2034C2semidirect
6. C43×#2033C2semidirect
7. C43×#1999C2semidirect
8. C43×#1999C2semidirect
9. C43×#1989C2semidirect
10. C43×#1982C2semidirect
11. C43×#1879C2semidirect
12. C43×#1879C2semidirect
13. C43×#1864C2semidirect
14. C43×#1862C2semidirect
15. C43×#1798C2semidirect
86. #127×C43D4semidirect
88. #125×C43D4semidirect
349. #24162C43direct (N × H)
399. C2×#540C2×C43semidirect
400. C2×#478C2×C43semidirect
401. C2×#459C2×C43semidirect
402. #2324C2×C43semidirect
403. #2034C2×C43semidirect
404. #2033C2×C43semidirect
405. #1999C2×C43semidirect
406. #1999C2×C43semidirect
407. #1989C2×C43semidirect
408. #1982C2×C43semidirect
409. #1879C2×C43semidirect
410. #1879C2×C43semidirect
411. #1864C2×C43semidirect
412. #1862C2×C43semidirect
413. #1798C2×C43semidirect
472. C43#24162direct (N × H)
496. #127D4×C43semidirect
498. #125D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5402
C2×C43×#4782
C2×C43×#4592
C43×#23242
C43×#20342
C43×#20332
C43×#19992
C43×#19892
C43×#19822
C43×#18792
C43×#18642
C43×#18622
C43×#17982
#2416243