Finite Group Databasebeta

← C43×#24762 #24944779

Subgroups — C43×#24762 #24944779

Order 11008.

1060 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#469C211yesmaximal, characteristic, complemented
2C2×C43×#466C211yesmaximal, characteristic, complemented
3C2×C43×#459C211yesmaximal, characteristic, complemented
4C2×C43×#424C211yesmaximal, characteristic, complemented
5C43×#2619C211yesmaximal, characteristic, complemented
6C43×#2324C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic, complemented
8C43×#2065C211yesmaximal, characteristic, complemented
9C43×#2054C211yesmaximal, characteristic, complemented
10C43×#2054C211yesmaximal, characteristic, complemented
11C43×#1982C211yesmaximal, characteristic, complemented
12C43×#1949C211yesmaximal, characteristic, complemented
13C43×#1895C211yesmaximal, characteristic, complemented
14C43×#1893C211yesmaximal, characteristic, complemented
15C43×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C23×C8×C43C2211yescharacteristic
20C2×#127×C43C2211yescharacteristic
21C2×#121×C43C2211yescharacteristic
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×C4×D4×C43C2211yescharacteristic
25C2×#117×C43C2211yescharacteristic
26C43×#469—24no—
27C43×#466—24no—
28C43×#459—24no—
29C2×#107×C43C2211yescharacteristic
30C2×#106×C43C2211yescharacteristic
31C43×#424—24no—
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×C4⋊C8×C43C2211yescharacteristic
34C2×C4⋊C8×C43C2211yescharacteristic
35C2×C4⋊C8×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C43×#394—21no—
45C43×#394—21no—
46C43×#392—21no—
47C43×#392—21no—
48C43×#390—21no—
49C43×#390C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#388—21no—
54C43×#386—21no—
55C43×#385—21no—
56C43×#382C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
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×C43C2311yescharacteristic
73C2×D8×C43—22no—
74C2×D8×C43—22no—
75C2×D8×C43—22no—
76C2×D8×C43—22no—
77C2×D8×C43—41no—
78C2×D8×C43—41no—
79C2×M16×C43—22no—
80C2×M16×C43—22no—
81C2×M16×C43—41no—
82C22×C8×C43—22no—
83C22×C8×C43—22no—
84C22×C8×C43—41no—
85C22×C8×C43C2311yescharacteristic
86C22×C8×C43C2311yescharacteristic
87C22×C8×C43C2311yescharacteristic
88C22×C8×C43C2311yescharacteristic
89#127×C43—22no—
90#127×C43—22no—
91#121×C43—22no—
92#121×C43—22no—
93#121×C43—22no—
94#121×C43—22no—
95#121×C43—22no—
96#121×C43D414yescomplemented
97C4×D4×C43—22no—
98C4×D4×C43—22no—
99#117×C43—22no—
100#117×C43—22no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
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×C43D411yescharacteristic
121C2×C22⋊C4×C43D411yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125#107×C43—22no—
126#106×C43—22no—
127C4⋊C8×C43—22no—
128C4⋊C8×C43—22no—
129C4⋊C8×C43—22no—
130C4⋊C8×C43D414yescomplemented
131#102×C43—22no—
132#102×C43—22no—
133#102×C43—22no—
134#102×C43—22no—
135#102×C43—22no—
136#102×C43—22no—
137#102×C43—41no—
138#102×C43—41no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43—21no—
142#95×C43—21no—
143#95×C43—21no—
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—24no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
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—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
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×C43C2×D412yes—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—42no—
191C22×C4×C43—81no—
192C22×C4×C43—81no—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43#4112yes—
200C22×C4×C43C2411yescharacteristic
201D8×C43—44no—
202D8×C43—44no—
203M16×C43—44no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—44no—
215C2×C8×C43C2×D412yes—
216C2×C8×C43C2×D412yes—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—81no—
229C4⋊C4×C43C2×D412yes—
230C22⋊C4×C43—24no—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—81no—
237C22⋊C4×C43—81no—
238C22⋊C4×C43—81no—
239C22⋊C4×C43—81no—
240C22⋊C4×C43—81no—
241C22⋊C4×C43—81no—
242C22⋊C4×C43—81no—
243C42×C43—21no—
244C42×C43—21no—
245C42×C43—81no—
246C42×C43C2×D412yes—
247C42×C43#4112yes—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—22no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
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#12112yes—
276C23×C43C22×D411yescharacteristic
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—84no—
290D4×C43—84no—
291D4×C43—84no—
292D4×C43—84no—
293D4×C43—84no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—41no—
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—84no—
326C2×C4×C43#12112yes—
327C2×C4×C43#12112yes—
328C2×C4×C43#12112yes—
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C432−1+411yescharacteristic
335C8×C43—22no—
336C8×C43—22no—
337C8×C43—41no—
338C8×C43—41no—
339#24762C4311yesmaximal, characteristic, direct product factor, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43C2×#12111yescharacteristic
369C22×C43C2×#12111yescharacteristic
370C22×C43#53711yescharacteristic
371C22×C43#57611yescharacteristic
372C22×C43#57611yescharacteristic
373C22×C43#57611yescharacteristic
374C22×C43#57711yescharacteristic
375C4×C43—22no—
376C4×C43—22no—
377C4×C43—22no—
378C4×C43—42no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43—81no—
382C4×C43—81no—
383C4×C43—81no—
384C4×C43—81no—
385C4×C43D4211yescharacteristic
386C4×C43#54711yescharacteristic
387C4×C43#54811yescharacteristic
388C4×C43#55311yescharacteristic
389C2×#469C2×C4311yescharacteristic, complemented
390C2×#466C2×C4311yescharacteristic, complemented
391C2×#459C2×C4311yescharacteristic, complemented
392C2×#424C2×C4311yescharacteristic, complemented
393#2619C2×C4311yescharacteristic, complemented
394#2324C2×C4311yescharacteristic, complemented
395#2067C2×C4311yescharacteristic, complemented
396#2065C2×C4311yescharacteristic, complemented
397#2054C2×C4311yescharacteristic, complemented
398#2054C2×C4311yescharacteristic, complemented
399#1982C2×C4311yescharacteristic, complemented
400#1949C2×C4311yescharacteristic, complemented
401#1895C2×C4311yescharacteristic, complemented
402#1893C2×C4311yescharacteristic, complemented
403#1804C2×C4311yescharacteristic, complemented
404C2×C43—42no—
405C2×C43—82no—
406C2×C43—161no—
407C2×C43—161no—
408C2×C43#241611yescharacteristic
409C2×C43#304111yescharacteristic
410C2×C43#304511yescharacteristic
411C2×C43#305811yescharacteristic
412C2×C43#306211yescharacteristic
413C2×C43#325711yescharacteristic
414C2×C43#325911yescharacteristic
415C22×D8C22×C4311yescharacteristic
416C22×D8C22×C4311yescharacteristic
417C22×M16C22×C4311yescharacteristic
418C23×C8C22×C4311yescharacteristic
419C2×#127C22×C4311yescharacteristic
420C2×#121C22×C4311yescharacteristic
421C2×#121C22×C4311yescharacteristic
422C2×#121C22×C4311yescharacteristic
423C2×C4×D4C22×C4311yescharacteristic
424C2×#117C22×C4311yescharacteristic
425#469—24no—
426#466—24no—
427#459—24no—
428C2×#107C22×C4311yescharacteristic
429C2×#106C22×C4311yescharacteristic
430#424—24no—
431C2×C4⋊C8C22×C4311yescharacteristic
432C2×C4⋊C8C22×C4311yescharacteristic
433C2×C4⋊C8C22×C4311yescharacteristic
434C2×C4⋊C8C22×C4311yescharacteristic
435C2×#102C22×C4311yescharacteristic
436C2×#102C22×C4311yescharacteristic
437C2×#102C22×C4311yescharacteristic
438C2×#102C22×C4311yescharacteristic
439C2×#102C22×C4311yescharacteristic
440C2×#102C22×C4311yescharacteristic
441C2×#102C22×C4311yescharacteristic
442C2×#102C22×C4311yescharacteristic
443#394—21no—
444#394—21no—
445#392—21no—
446#392—21no—
447#390—21no—
448#390C22×C4311yescharacteristic
449#390C22×C4311yescharacteristic
450#390C22×C4311yescharacteristic
451#389C22×C4311yescharacteristic
452#388—21no—
453#386—21no—
454#385—21no—
455#382C22×C4311yescharacteristic
456#380C22×C4311yescharacteristic
457C4×C4⋊C4C22×C4311yescharacteristic
458#340C22×C4311yescharacteristic
459#340C22×C4311yescharacteristic
460#340C22×C4311yescharacteristic
461#340C22×C4311yescharacteristic
462C43#2476211yescharacteristic, direct product factor, Sylow
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4C23×C4311yescharacteristic
469C22×D4C23×C4311yescharacteristic
470C22×D4C23×C4311yescharacteristic
471C23×C4—21no—
472C23×C4C23×C4311yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C4311yescharacteristic
486C22×C8C23×C4311yescharacteristic
487C22×C8C23×C4311yescharacteristic
488C22×C8C23×C4311yescharacteristic
489#127—22no—
490#127—22no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121—22no—
496#121D4×C4314yescomplemented
497C4×D4—22no—
498C4×D4—22no—
499#117—22no—
500#117—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4D4×C4311yescharacteristic
503C2×C4⋊C4D4×C4311yescharacteristic
504C2×C4⋊C4C23×C4311yescharacteristic
505C2×C4⋊C4C23×C4311yescharacteristic
506C2×C4⋊C4C23×C4311yescharacteristic
507C2×C4⋊C4C23×C4311yescharacteristic
508C2×C4⋊C4C23×C4311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4D4×C4311yescharacteristic
521C2×C22⋊C4D4×C4311yescharacteristic
522C2×C42—21no—
523C2×C42C23×C4311yescharacteristic
524C2×C42C23×C4311yescharacteristic
525#107—22no—
526#106—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—22no—
530C4⋊C8D4×C4314yescomplemented
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24C2×D4×C4311yescharacteristic
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C4312yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4C2×D4×C4311yescharacteristic
594C22×C4C2×D4×C4311yescharacteristic
595C22×C4C2×D4×C4311yescharacteristic
596C22×C4C2×D4×C4311yescharacteristic
597C22×C4C2×D4×C4311yescharacteristic
598C22×C4C2×D4×C4312yes—
599C22×C4#41×C4312yes—
600C22×C4C24×C4311yescharacteristic
601D8—44no—
602D8—44no—
603M16—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—44no—
615C2×C8C2×D4×C4312yes—
616C2×C8C2×D4×C4312yes—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—81no—
629C4⋊C4C2×D4×C4312yes—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C42—21no—
644C42—21no—
645C42—81no—
646C42C2×D4×C4312yes—
647C42#41×C4312yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23#121×C4312yes—
676C23C22×D4×C4311yescharacteristic
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—84no—
690D4—84no—
691D4—84no—
692D4—84no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4#121×C4312yes—
727C2×C4#121×C4312yes—
728C2×C4#121×C4312yes—
729C2×C4C22×D4×C4311yescharacteristic
730C2×C4C22×D4×C4311yescharacteristic
731C2×C4C2×#41×C4311yescharacteristic
732C2×C4C2×#41×C4311yescharacteristic
733C2×C4H(5,𝔽2)×C4311yescharacteristic
734C2×C42−1+4×C4311yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C4311yescharacteristic
768C22C2×#121×C4311yescharacteristic
769C22C43×#53711yescharacteristic
770C22C43×#57611yescharacteristic
771C22C43×#57611yescharacteristic
772C22C43×#57611yescharacteristic
773C22C43×#57711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4D42×C4311yescharacteristic
785C4C43×#54711yescharacteristic
786C4C43×#54811yescharacteristic
787C4C43×#55311yescharacteristic
788C2—42no—
789C2—82no—
790C2—161no—
791C2—161no—
792C2C43×#241611yescharacteristic
793C2C43×#304111yescharacteristic
794C2C43×#304511yescharacteristic
795C2C43×#305811yescharacteristic
796C2C43×#306211yescharacteristic
797C2C43×#325711yescharacteristic
798C2C43×#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×#469C2semidirect
2. C2×C43×#466C2semidirect
3. C2×C43×#459C2semidirect
4. C2×C43×#424C2semidirect
5. C43×#2619C2semidirect
6. C43×#2324C2semidirect
7. C43×#2067C2semidirect
8. C43×#2065C2semidirect
9. C43×#2054C2semidirect
10. C43×#2054C2semidirect
11. C43×#1982C2semidirect
12. C43×#1949C2semidirect
13. C43×#1895C2semidirect
14. C43×#1893C2semidirect
15. C43×#1804C2semidirect
96. #121×C43D4semidirect
130. C4⋊C8×C43D4semidirect
339. #24762C43direct (N × H)
389. C2×#469C2×C43semidirect
390. C2×#466C2×C43semidirect
391. C2×#459C2×C43semidirect
392. C2×#424C2×C43semidirect
393. #2619C2×C43semidirect
394. #2324C2×C43semidirect
395. #2067C2×C43semidirect
396. #2065C2×C43semidirect
397. #2054C2×C43semidirect
398. #2054C2×C43semidirect
399. #1982C2×C43semidirect
400. #1949C2×C43semidirect
401. #1895C2×C43semidirect
402. #1893C2×C43semidirect
403. #1804C2×C43semidirect
462. C43#24762direct (N × H)
496. #121D4×C43semidirect
530. C4⋊C8D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4692
C2×C43×#4662
C2×C43×#4592
C2×C43×#4242
C43×#26192
C43×#23242
C43×#20672
C43×#20652
C43×#20542
C43×#19822
C43×#19492
C43×#18952
C43×#18932
C43×#18042
#2476243