Finite Group Databasebeta

← C43×#24034 #24944051

Subgroups — C43×#24034 #24944051

Order 11008.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#550C211yesmaximal, characteristic
2C2×C43×#482C211yesmaximal, characteristic, complemented
3C2×C43×#416C211yesmaximal, characteristic, complemented
4C43×#2485C211yesmaximal, characteristic, complemented
5C43×#2041C211yesmaximal, characteristic, complemented
6C43×#2041C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#1893C211yesmaximal, characteristic, complemented
10C43×#1869C211yesmaximal, characteristic, complemented
11C43×#1865C211yesmaximal, characteristic, complemented
12C43×#1863C211yesmaximal, characteristic, complemented
13C43×#1788C211yesmaximal, characteristic, complemented
14C43×#1788C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C23×C8×C43C2211yescharacteristic
19C43×#550—24no—
20C43×#550—24no—
21C2×#127×C43—21no—
22C2×#127×C43C2211yescharacteristic
23C2×#121×C43—21no—
24C2×#121×C43—21no—
25C2×#121×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×C4×Q8×C43C2211yescharacteristic
28C2×C4×D4×C43—21no—
29C2×C4×D4×C43C2211yescharacteristic
30C2×#117×C43C2211yescharacteristic
31C43×#482—24no—
32C2×#107×C43C2211yescharacteristic
33C2×#106×C43C2211yescharacteristic
34C43×#416—24no—
35C2×#103×C43C2211yescharacteristic
36C2×#103×C43C2211yescharacteristic
37C2×#103×C43C2211yescharacteristic
38C2×#103×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
49C2×C22⋊C8×C43C2211yescharacteristic
50C43×#397—21no—
51C43×#394—21no—
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#387—21no—
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#41×C43—22no—
64C2×#41×C43—22no—
65C2×#41×C43—22no—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—41no—
71C2×#41×C43—41no—
72C2×#41×C43—41no—
73C2×#41×C43—41no—
74C2×#41×C43D414yes—
75C22×Q8×C43C2311yescharacteristic
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—21no—
82C22×D4×C43D411yescharacteristic
83C22×D4×C43C2311yescharacteristic
84C22×D4×C43C2311yescharacteristic
85C23×C4×C43—21no—
86C23×C4×C43—21no—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C22×C8×C43—22no—
90C22×C8×C43—41no—
91C22×C8×C43—41no—
92C22×C8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96#127×C43—28no—
97#127×C43—22no—
98#127×C43—22no—
99#121×C43—28no—
100#121×C43—28no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—22no—
104#121×C43D414yes—
105C4×Q8×C43—22no—
106C4×Q8×C43—22no—
107C4×D4×C43—28no—
108C4×D4×C43—22no—
109C4×D4×C43—22no—
110#117×C43—22no—
111#117×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—22no—
133#106×C43—22no—
134#103×C43—22no—
135#103×C43—22no—
136#103×C43—22no—
137#103×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—41no—
143#102×C43—41no—
144#102×C43—41no—
145#102×C43—41no—
146C22⋊C8×C43—22no—
147C22⋊C8×C43—41no—
148C22⋊C8×C43—41no—
149#95×C43—21no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43C2×D411yescharacteristic
157C24×C43C2×D411yescharacteristic
158#41×C43—28no—
159#41×C43—44no—
160#41×C43—44no—
161#41×C43—44no—
162#41×C43—44no—
163#41×C43—44no—
164#41×C43—44no—
165#41×C43—44no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43C2×D412yes—
170C2×Q8×C43#4112yes—
171C2×Q8×C43#4112yes—
172C2×D4×C43—24no—
173C2×D4×C43—24no—
174C2×D4×C43—24no—
175C2×D4×C43—24no—
176C2×D4×C43—22no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—22no—
180C2×D4×C43—24no—
181C2×D4×C43—24no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—41no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43—42no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—81no—
198C2×D4×C43—81no—
199C2×D4×C43—81no—
200C2×D4×C43—81no—
201C2×D4×C43—81no—
202C2×D4×C43—81no—
203C2×D4×C43C2×D412yes—
204C2×D4×C43C2×D412yes—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—24no—
210C22×C4×C43—24no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—42no—
224C22×C4×C43—42no—
225C22×C4×C43—42no—
226C22×C4×C43—42no—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—44no—
247C4⋊C4×C43—24no—
248C4⋊C4×C43—22no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—42no—
259C4⋊C4×C43—81no—
260C4⋊C4×C43C2×D412yes—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—22no—
264C22⋊C4×C43—22no—
265C22⋊C4×C43—42no—
266C22⋊C4×C43—42no—
267C22⋊C4×C43—81no—
268C22⋊C4×C43—81no—
269C42×C43—24no—
270C42×C43—21no—
271C42×C43—21no—
272C42×C43—42no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43#12012yes—
301C23×C43C22×D411yescharacteristic
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43#12314yes—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—44no—
311D4×C43—48no—
312D4×C43—48no—
313D4×C43—48no—
314D4×C43—41no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—84no—
319D4×C43—84no—
320D4×C43—84no—
321C2×C4×C43—21no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—48no—
340C2×C4×C43—48no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43#12012yes—
360C2×C4×C43#13512yes—
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C2×C4×C43C2×#4111yescharacteristic
365C2×C4×C43H(5,𝔽2)11yescharacteristic
366C2×C4×C43H(5,𝔽2)11yescharacteristic
367C8×C43—41no—
368C8×C43—41no—
369C8×C43—41no—
370C8×C43—41no—
371#24034C4311yesmaximal, characteristic, direct product factor, Sylow
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43—41no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—41no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43—81no—
400C22×C43C2×#12011yescharacteristic
401C22×C43#54611yescharacteristic
402C22×C43#54611yescharacteristic
403C22×C43C2×#13511yescharacteristic
404C22×C43#57511yescharacteristic
405C22×C43#57611yescharacteristic
406C22×C43#57711yescharacteristic
407C4×C43—22no—
408C4×C43—24no—
409C4×C43—22no—
410C4×C43—41no—
411C4×C43—41no—
412C4×C43—42no—
413C4×C43—81no—
414C4×C43—81no—
415C4×C43—81no—
416C4×C43—81no—
417C4×C43C2×#12311yescharacteristic
418C4×C43#53411yescharacteristic
419C4×C43#54611yescharacteristic
420C4×C43#54611yescharacteristic
421C2×#550C2×C4311yescharacteristic
422C2×#482C2×C4311yescharacteristic, complemented
423C2×#416C2×C4311yescharacteristic, complemented
424#2485C2×C4311yescharacteristic, complemented
425#2041C2×C4311yescharacteristic, complemented
426#2041C2×C4311yescharacteristic, complemented
427#2034C2×C4311yescharacteristic, complemented
428#2033C2×C4311yescharacteristic, complemented
429#1893C2×C4311yescharacteristic, complemented
430#1869C2×C4311yescharacteristic, complemented
431#1865C2×C4311yescharacteristic, complemented
432#1863C2×C4311yescharacteristic, complemented
433#1788C2×C4311yescharacteristic, complemented
434#1788C2×C4311yescharacteristic, complemented
435#1788C2×C4311yescharacteristic, complemented
436C2×C43—42no—
437C2×C43—81no—
438C2×C43—82no—
439C2×C43—82no—
440C2×C43#240511yescharacteristic
441C2×C43#300211yescharacteristic
442C2×C43#301211yescharacteristic
443C2×C43#330411yescharacteristic
444C2×C43#330511yescharacteristic
445C2×C43#330911yescharacteristic
446C2×C43#331711yescharacteristic
447C22×#41C22×C4311yescharacteristic
448C22×#41C22×C4311yescharacteristic
449C23×C8C22×C4311yescharacteristic
450#550—24no—
451#550—24no—
452C2×#127—21no—
453C2×#127C22×C4311yescharacteristic
454C2×#121—21no—
455C2×#121—21no—
456C2×#121C22×C4311yescharacteristic
457C2×#121C22×C4311yescharacteristic
458C2×C4×Q8C22×C4311yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C22×C4311yescharacteristic
461C2×#117C22×C4311yescharacteristic
462#482—24no—
463C2×#107C22×C4311yescharacteristic
464C2×#106C22×C4311yescharacteristic
465#416—24no—
466C2×#103C22×C4311yescharacteristic
467C2×#103C22×C4311yescharacteristic
468C2×#103C22×C4311yescharacteristic
469C2×#103C22×C4311yescharacteristic
470C2×#102C22×C4311yescharacteristic
471C2×#102C22×C4311yescharacteristic
472C2×#102C22×C4311yescharacteristic
473C2×#102C22×C4311yescharacteristic
474C2×#102C22×C4311yescharacteristic
475C2×#102C22×C4311yescharacteristic
476C2×#102C22×C4311yescharacteristic
477C2×#102C22×C4311yescharacteristic
478C2×C22⋊C8C22×C4311yescharacteristic
479C2×C22⋊C8C22×C4311yescharacteristic
480C2×C22⋊C8C22×C4311yescharacteristic
481#397—21no—
482#394—21no—
483#389C22×C4311yescharacteristic
484#389C22×C4311yescharacteristic
485#388—21no—
486#387—21no—
487#380C22×C4311yescharacteristic
488#380C22×C4311yescharacteristic
489#380C22×C4311yescharacteristic
490#340C22×C4311yescharacteristic
491#340C22×C4311yescharacteristic
492#336C22×C4311yescharacteristic
493#336C22×C4311yescharacteristic
494C43#2403411yescharacteristic, direct product factor, Sylow
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C4314yes—
507C22×Q8C23×C4311yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C4311yescharacteristic
515C22×D4C23×C4311yescharacteristic
516C22×D4C23×C4311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C4311yescharacteristic
520C23×C4C23×C4311yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C4311yescharacteristic
525C22×C8C23×C4311yescharacteristic
526C22×C8C23×C4311yescharacteristic
527C22×C8C23×C4311yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C4314yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C4311yescharacteristic
548C2×C4⋊C4C23×C4311yescharacteristic
549C2×C4⋊C4C23×C4311yescharacteristic
550C2×C4⋊C4C23×C4311yescharacteristic
551C2×C4⋊C4C23×C4311yescharacteristic
552C2×C4⋊C4C23×C4311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C4311yescharacteristic
560C2×C22⋊C4D4×C4311yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C4311yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C4311yescharacteristic
589C24C2×D4×C4311yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C4312yes—
602C2×Q8#41×C4312yes—
603C2×Q8#41×C4312yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C4312yes—
636C2×D4C2×D4×C4312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C4311yescharacteristic
660C22×C4C2×D4×C4311yescharacteristic
661C22×C4C2×D4×C4311yescharacteristic
662C22×C4C2×D4×C4312yes—
663C22×C4C2×D4×C4312yes—
664C22×C4C2×D4×C4311yescharacteristic
665C22×C4C24×C4311yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C4312yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C4312yes—
733C23C22×D4×C4311yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C4314yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#120×C4312yes—
792C2×C4#135×C4312yes—
793C2×C4C22×D4×C4311yescharacteristic
794C2×C4C22×D4×C4311yescharacteristic
795C2×C4C2×#41×C4311yescharacteristic
796C2×C4C2×#41×C4311yescharacteristic
797C2×C4H(5,𝔽2)×C4311yescharacteristic
798C2×C4H(5,𝔽2)×C4311yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C4311yescharacteristic
832C22C43×#54611yescharacteristic
833C22C43×#54611yescharacteristic
834C22C2×#135×C4311yescharacteristic
835C22C43×#57511yescharacteristic
836C22C43×#57611yescharacteristic
837C22C43×#57711yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C4311yescharacteristic
849C4C43×#53411yescharacteristic
850C4C43×#54611yescharacteristic
851C4C43×#54611yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C43×#240511yescharacteristic
857C2C43×#300211yescharacteristic
858C2C43×#301211yescharacteristic
859C2C43×#330411yescharacteristic
860C2C43×#330511yescharacteristic
861C2C43×#330911yescharacteristic
862C2C43×#331711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#550C2
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
2. C2×C43×#482C2semidirect
3. C2×C43×#416C2semidirect
4. C43×#2485C2semidirect
5. C43×#2041C2semidirect
6. C43×#2041C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#1893C2semidirect
10. C43×#1869C2semidirect
11. C43×#1865C2semidirect
12. C43×#1863C2semidirect
13. C43×#1788C2semidirect
14. C43×#1788C2semidirect
15. C43×#1788C2semidirect
371. #24034C43direct (N × H)
422. C2×#482C2×C43semidirect
423. C2×#416C2×C43semidirect
424. #2485C2×C43semidirect
425. #2041C2×C43semidirect
426. #2041C2×C43semidirect
427. #2034C2×C43semidirect
428. #2033C2×C43semidirect
429. #1893C2×C43semidirect
430. #1869C2×C43semidirect
431. #1865C2×C43semidirect
432. #1863C2×C43semidirect
433. #1788C2×C43semidirect
434. #1788C2×C43semidirect
435. #1788C2×C43semidirect
494. C43#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5502
C2×C43×#4822
C2×C43×#4162
C43×#24852
C43×#20412
C43×#20342
C43×#20332
C43×#18932
C43×#18692
C43×#18652
C43×#18632
C43×#17882
#2403443