Finite Group Databasebeta

← C43×#29747 #24949764

Subgroups — C43×#29747 #24949764

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#468C211yesmaximal, characteristic, complemented
2C2×C43×#408C211yesmaximal, characteristic, complemented
3C43×#2616C211yesmaximal, characteristic, complemented
4C43×#2615C211yesmaximal, characteristic
5C43×#2076C211yesmaximal, characteristic, complemented
6C43×#2075C211yesmaximal, characteristic, complemented
7C43×#2036C211yesmaximal, characteristic, complemented
8C43×#2035C211yesmaximal, characteristic, complemented
9C43×#2034C211yesmaximal, characteristic, complemented
10C43×#2033C211yesmaximal, characteristic, complemented
11C43×#2000C211yesmaximal, characteristic, complemented
12C43×#2000C211yesmaximal, characteristic, complemented
13C43×#1893C211yesmaximal, characteristic, complemented
14C43×#1892C211yesmaximal, characteristic, complemented
15C43×#1809C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C23×C8×C43C2211yescharacteristic
20C2×C22⋊Q8×C43C2211yescharacteristic
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic
26C43×#468—24no—
27C2×#107×C43C2211yescharacteristic
28C2×#107×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C43×#408—24no—
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C2×C22⋊C8×C43C2211yescharacteristic
41C43×#395—21no—
42C43×#394—21no—
43C43×#394—21no—
44C43×#394—21no—
45C43×#393—21no—
46C43×#392—21no—
47C43×#392—21no—
48C43×#392—21no—
49C43×#380C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C43×#380C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C2×#41×C43—22no—
62C2×#41×C43—22no—
63C2×#41×C43—41no—
64C2×#41×C43—41no—
65C2×#41×C43—41no—
66C2×#41×C43—41no—
67C22×Q8×C43D411yescharacteristic
68C22×Q8×C43C2311yescharacteristic
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43D411yescharacteristic
73C22×D4×C43D411yescharacteristic
74C22×D4×C43D411yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C2×SD16×C43—22no—
80C2×SD16×C43—41no—
81C2×SD16×C43—41no—
82C2×M16×C43—41no—
83C2×M16×C43—41no—
84C2×M16×C43D414yescomplemented
85C22×C8×C43—22no—
86C22×C8×C43—41no—
87C22×C8×C43—41no—
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90C22×C8×C43C2311yescharacteristic
91C22×C8×C43C2311yescharacteristic
92C22⋊Q8×C43—22no—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—41no—
95C22⋊Q8×C43—41no—
96C22⋊Q8×C43—41no—
97C22⋊Q8×C43—41no—
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—41no—
101#121×C43—41no—
102#121×C43—41no—
103#121×C43—41no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
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—
125#107×C43—22no—
126#107×C43—41no—
127#106×C43—41no—
128#103×C43—22no—
129#103×C43—41no—
130#103×C43—41no—
131#102×C43—22no—
132#102×C43—41no—
133#102×C43—41no—
134C22⋊C8×C43—22no—
135C22⋊C8×C43—22no—
136C22⋊C8×C43—22no—
137C22⋊C8×C43—22no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43—21no—
142#95×C43—21no—
143#95×C43—21no—
144C24×C43—21no—
145C24×C43C2×D411yescharacteristic
146C24×C43C2×D411yescharacteristic
147C24×C43C2×D411yescharacteristic
148#41×C43—44no—
149#41×C43—44no—
150#41×C43—44no—
151#41×C43—44no—
152C2×Q8×C43—22no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—41no—
160C2×Q8×C43—41no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—22no—
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—41no—
171C2×D4×C43—41no—
172C2×D4×C43—41no—
173C2×D4×C43—41no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—81no—
180C2×D4×C43—81no—
181C2×D4×C43—81no—
182C2×D4×C43—81no—
183C2×D4×C43—81no—
184C2×D4×C43—81no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
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—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43#4112yes—
213C22×C4×C43C2411yescharacteristic
214SD16×C43—44no—
215M16×C43—44no—
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—
225C2×C8×C43—21no—
226C2×C8×C43—44no—
227C2×C8×C43C2×D412yes—
228C2×C8×C43C2×D412yes—
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—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—42no—
242C4⋊C4×C43—42no—
243C4⋊C4×C43—42no—
244C22⋊C4×C43—42no—
245C22⋊C4×C43—42no—
246C22⋊C4×C43—42no—
247C22⋊C4×C43—42no—
248C22⋊C4×C43—42no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—81no—
251C22⋊C4×C43—81no—
252C22⋊C4×C43—81no—
253C22⋊C4×C43—81no—
254C22⋊C4×C43—81no—
255C22⋊C4×C43—81no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43#12112yes—
284C23×C43C22×D411yescharacteristic
285Q8×C43—44no—
286Q8×C43—41no—
287Q8×C43—41no—
288Q8×C43—41no—
289Q8×C43—41no—
290D4×C43—44no—
291D4×C43—44no—
292D4×C43—44no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—84no—
298D4×C43—84no—
299D4×C43—84no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
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—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43#12112yes—
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43H(5,𝔽2)11yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C8×C43—22no—
349C8×C43—22no—
350C8×C43—41no—
351C8×C43—41no—
352#29747C4311yesmaximal, characteristic, direct product factor, Sylow
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43—81no—
381C22×C43C2×#12111yescharacteristic
382C22×C43#53411yescharacteristic
383C22×C43#53411yescharacteristic
384C22×C43#57611yescharacteristic
385C22×C43#57711yescharacteristic
386C22×C43#57711yescharacteristic
387C22×C43#57811yescharacteristic
388C4×C43—22no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—81no—
392C4×C43—81no—
393C4×C43—81no—
394C4×C43—81no—
395C4×C43—81no—
396C4×C43—81no—
397C4×C43—81no—
398C4×C43#53411yescharacteristic
399C4×C43#53511yescharacteristic
400C4×C43#53811yescharacteristic
401C4×C43#53811yescharacteristic
402C2×#468C2×C4311yescharacteristic, complemented
403C2×#408C2×C4311yescharacteristic, complemented
404#2616C2×C4311yescharacteristic, complemented
405#2615C2×C4311yescharacteristic
406#2076C2×C4311yescharacteristic, complemented
407#2075C2×C4311yescharacteristic, complemented
408#2036C2×C4311yescharacteristic, complemented
409#2035C2×C4311yescharacteristic, complemented
410#2034C2×C4311yescharacteristic, complemented
411#2033C2×C4311yescharacteristic, complemented
412#2000C2×C4311yescharacteristic, complemented
413#2000C2×C4311yescharacteristic, complemented
414#1893C2×C4311yescharacteristic, complemented
415#1892C2×C4311yescharacteristic, complemented
416#1809C2×C4311yescharacteristic, complemented
417C2×C43—42no—
418C2×C43—81no—
419C2×C43—81no—
420C2×C43—161no—
421C2×C43#261711yescharacteristic
422C2×C43#306211yescharacteristic
423C2×C43#306311yescharacteristic
424C2×C43#319811yescharacteristic
425C2×C43#320011yescharacteristic
426C2×C43#320111yescharacteristic
427C2×C43#320311yescharacteristic
428C22×#41C22×C4311yescharacteristic
429C22×SD16C22×C4311yescharacteristic
430C22×M16C22×C4311yescharacteristic
431C23×C8C22×C4311yescharacteristic
432C2×C22⋊Q8C22×C4311yescharacteristic
433C2×C22⋊Q8C22×C4311yescharacteristic
434C2×C22⋊Q8C22×C4311yescharacteristic
435C2×#121C22×C4311yescharacteristic
436C2×#121C22×C4311yescharacteristic
437C2×#121C22×C4311yescharacteristic
438#468—24no—
439C2×#107C22×C4311yescharacteristic
440C2×#107C22×C4311yescharacteristic
441C2×#106C22×C4311yescharacteristic
442C2×#103C22×C4311yescharacteristic
443C2×#103C22×C4311yescharacteristic
444C2×#103C22×C4311yescharacteristic
445C2×#102C22×C4311yescharacteristic
446C2×#102C22×C4311yescharacteristic
447C2×#102C22×C4311yescharacteristic
448#408—24no—
449C2×C22⋊C8C22×C4311yescharacteristic
450C2×C22⋊C8C22×C4311yescharacteristic
451C2×C22⋊C8C22×C4311yescharacteristic
452C2×C22⋊C8C22×C4311yescharacteristic
453#395—21no—
454#394—21no—
455#394—21no—
456#394—21no—
457#393—21no—
458#392—21no—
459#392—21no—
460#392—21no—
461#380C22×C4311yescharacteristic
462#380C22×C4311yescharacteristic
463#380C22×C4311yescharacteristic
464#380C22×C4311yescharacteristic
465#380C22×C4311yescharacteristic
466#380C22×C4311yescharacteristic
467#340C22×C4311yescharacteristic
468#340C22×C4311yescharacteristic
469#340C22×C4311yescharacteristic
470#340C22×C4311yescharacteristic
471#340C22×C4311yescharacteristic
472#340C22×C4311yescharacteristic
473C43#2974711yescharacteristic, direct product factor, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8D4×C4311yescharacteristic
481C22×Q8C23×C4311yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C4311yescharacteristic
486C22×D4D4×C4311yescharacteristic
487C22×D4D4×C4311yescharacteristic
488C22×D4C23×C4311yescharacteristic
489C23×C4C23×C4311yescharacteristic
490C23×C4C23×C4311yescharacteristic
491C23×C4C23×C4311yescharacteristic
492C2×SD16—22no—
493C2×SD16—41no—
494C2×SD16—41no—
495C2×M16—41no—
496C2×M16—41no—
497C2×M16D4×C4314yescomplemented
498C22×C8—22no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8C23×C4311yescharacteristic
502C22×C8C23×C4311yescharacteristic
503C22×C8C23×C4311yescharacteristic
504C22×C8C23×C4311yescharacteristic
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—41no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510C22⋊Q8—41no—
511#121—22no—
512#121—22no—
513#121—41no—
514#121—41no—
515#121—41no—
516#121—41no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4C23×C4311yescharacteristic
521C2×C4⋊C4C23×C4311yescharacteristic
522C2×C4⋊C4C23×C4311yescharacteristic
523C2×C4⋊C4C23×C4311yescharacteristic
524C2×C4⋊C4C23×C4311yescharacteristic
525C2×C4⋊C4C23×C4311yescharacteristic
526C2×C22⋊C4—21no—
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⋊C4—21no—
537C2×C22⋊C4—21no—
538#107—22no—
539#107—41no—
540#106—41no—
541#103—22no—
542#103—41no—
543#103—41no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24C2×D4×C4311yescharacteristic
559C24C2×D4×C4311yescharacteristic
560C24C2×D4×C4311yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—41no—
573C2×Q8—41no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C22×C4—21no—
599C22×C4—21no—
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—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4C2×D4×C4311yescharacteristic
622C22×C4C2×D4×C4311yescharacteristic
623C22×C4C2×D4×C4311yescharacteristic
624C22×C4C2×D4×C4312yes—
625C22×C4#41×C4312yes—
626C22×C4C24×C4311yescharacteristic
627SD16—44no—
628M16—44no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—44no—
640C2×C8C2×D4×C4312yes—
641C2×C8C2×D4×C4312yes—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23#121×C4312yes—
697C23C22×D4×C4311yescharacteristic
698Q8—44no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703D4—44no—
704D4—44no—
705D4—44no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
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—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4#121×C4312yes—
755C2×C4C22×D4×C4311yescharacteristic
756C2×C4C2×#41×C4311yescharacteristic
757C2×C4H(5,𝔽2)×C4311yescharacteristic
758C2×C4H(5,𝔽2)×C4311yescharacteristic
759C2×C4H(5,𝔽2)×C4311yescharacteristic
760C2×C4H(5,𝔽2)×C4311yescharacteristic
761C8—22no—
762C8—22no—
763C8—41no—
764C8—41no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22C2×#121×C4311yescharacteristic
794C22C43×#53411yescharacteristic
795C22C43×#53411yescharacteristic
796C22C43×#57611yescharacteristic
797C22C43×#57711yescharacteristic
798C22C43×#57711yescharacteristic
799C22C43×#57811yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4C43×#53411yescharacteristic
811C4C43×#53511yescharacteristic
812C4C43×#53811yescharacteristic
813C4C43×#53811yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—161no—
818C2C43×#261711yescharacteristic
819C2C43×#306211yescharacteristic
820C2C43×#306311yescharacteristic
821C2C43×#319811yescharacteristic
822C2C43×#320011yescharacteristic
823C2C43×#320111yescharacteristic
824C2C43×#320311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2615C2
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×#468C2semidirect
2. C2×C43×#408C2semidirect
3. C43×#2616C2semidirect
5. C43×#2076C2semidirect
6. C43×#2075C2semidirect
7. C43×#2036C2semidirect
8. C43×#2035C2semidirect
9. C43×#2034C2semidirect
10. C43×#2033C2semidirect
11. C43×#2000C2semidirect
12. C43×#2000C2semidirect
13. C43×#1893C2semidirect
14. C43×#1892C2semidirect
15. C43×#1809C2semidirect
84. C2×M16×C43D4semidirect
352. #29747C43direct (N × H)
402. C2×#468C2×C43semidirect
403. C2×#408C2×C43semidirect
404. #2616C2×C43semidirect
406. #2076C2×C43semidirect
407. #2075C2×C43semidirect
408. #2036C2×C43semidirect
409. #2035C2×C43semidirect
410. #2034C2×C43semidirect
411. #2033C2×C43semidirect
412. #2000C2×C43semidirect
413. #2000C2×C43semidirect
414. #1893C2×C43semidirect
415. #1892C2×C43semidirect
416. #1809C2×C43semidirect
473. C43#29747direct (N × H)
497. C2×M16D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4682
C2×C43×#4082
C43×#26162
C43×#26152
C43×#20762
C43×#20752
C43×#20362
C43×#20352
C43×#20342
C43×#20332
C43×#20002
C43×#18932
C43×#18922
C43×#18092
#2974743