Finite Group Databasebeta

← C43×#28584 #24948601

Subgroups — C43×#28584 #24948601

Order 11008.

992 conjugacy classes of subgroups.

The subgroup lattice has 788 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
3C43×#2619C211yesmaximal, characteristic, complemented
4C43×#2324C211yesmaximal, characteristic, complemented
5C43×#2085C211yesmaximal, characteristic, complemented
6C43×#2073C211yesmaximal, characteristic, complemented
7C43×#2041C211yesmaximal, characteristic, complemented
8C43×#2011C211yesmaximal, characteristic, complemented
9C43×#1926C211yesmaximal, characteristic, complemented
10C43×#1925C211yesmaximal, characteristic, complemented
11C43×#1895C211yesmaximal, characteristic, complemented
12C43×#1893C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1879C211yesmaximal, characteristic, complemented
15C43×#1729C211yesmaximal, 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—
28C2×#107×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C43×#394—21no—
39C43×#394—21no—
40C43×#392—21no—
41C43×#392—21no—
42C43×#390—21no—
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic
46C43×#389C2211yescharacteristic
47C43×#388—21no—
48C43×#386—21no—
49C43×#385—21no—
50C43×#382C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43C2311yescharacteristic
67C22×D4×C43C2311yescharacteristic
68C22×D4×C43C2311yescharacteristic
69C23×C4×C43—21no—
70C23×C4×C43C2311yescharacteristic
71C2×D8×C43—22no—
72C2×D8×C43—22no—
73C2×D8×C43—22no—
74C2×D8×C43—22no—
75C2×D8×C43—41no—
76C2×D8×C43—41no—
77C2×M16×C43—22no—
78C2×M16×C43—22no—
79C2×M16×C43—41no—
80C22×C8×C43—22no—
81C22×C8×C43—22no—
82C22×C8×C43—41no—
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85C22×C8×C43C2311yescharacteristic
86C22×C8×C43C2311yescharacteristic
87#127×C43—41no—
88#127×C43—41no—
89#121×C43—22no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—22no—
93#121×C43—22no—
94#121×C43D414yescomplemented
95C4×D4×C43—41no—
96C4×D4×C43—41no—
97#117×C43—41no—
98#117×C43—41no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
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×C43D411yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#107×C43—22no—
124#106×C43—22no—
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130#102×C43—22no—
131#102×C43—41no—
132#102×C43—41no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43C2×D411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43—24no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
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—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43—81no—
167C2×D4×C43—81no—
168C2×D4×C43—81no—
169C2×D4×C43—81no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
172C2×D4×C43—81no—
173C2×D4×C43—81no—
174C2×D4×C43C2×D412yes—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—42no—
185C22×C4×C43—81no—
186C22×C4×C43—81no—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43#4112yes—
194C22×C4×C43C2411yescharacteristic
195D8×C43—44no—
196D8×C43—44no—
197M16×C43—44no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—44no—
209C2×C8×C43#4112yes—
210C2×C8×C43#4112yes—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—41no—
221C4⋊C4×C43—41no—
222C4⋊C4×C43—81no—
223C4⋊C4×C43C2×D412yes—
224C22⋊C4×C43—24no—
225C22⋊C4×C43—41no—
226C22⋊C4×C43—41no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—81no—
231C22⋊C4×C43—81no—
232C22⋊C4×C43—81no—
233C22⋊C4×C43—81no—
234C22⋊C4×C43—81no—
235C22⋊C4×C43—81no—
236C22⋊C4×C43—81no—
237C42×C43—21no—
238C42×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—81no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—22no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
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#12112yes—
270C23×C43C22×D411yescharacteristic
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—41no—
283D4×C43—84no—
284D4×C43—84no—
285D4×C43—84no—
286D4×C43—84no—
287D4×C43—84no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
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—84no—
322C2×C4×C43#12112yes—
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C8×C43—22no—
330C8×C43—22no—
331C8×C43—41no—
332C8×C43—41no—
333#28584C4311yesmaximal, characteristic, direct product factor, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
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×C43C2×#12111yescharacteristic
363C22×C43#53211yescharacteristic
364C22×C43#53411yescharacteristic
365C22×C43#57611yescharacteristic
366C22×C43#57611yescharacteristic
367C22×C43#57611yescharacteristic
368C22×C43#57711yescharacteristic
369C4×C43—22no—
370C4×C43—41no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43—41no—
374C4×C43—42no—
375C4×C43—81no—
376C4×C43—81no—
377C4×C43—81no—
378C4×C43—81no—
379C4×C43#54611yescharacteristic
380C4×C43#54611yescharacteristic
381C4×C43#55311yescharacteristic
382C4×C43#55311yescharacteristic
383C2×#469C2×C4311yescharacteristic, complemented
384C2×#466C2×C4311yescharacteristic, complemented
385#2619C2×C4311yescharacteristic, complemented
386#2324C2×C4311yescharacteristic, complemented
387#2085C2×C4311yescharacteristic, complemented
388#2073C2×C4311yescharacteristic, complemented
389#2041C2×C4311yescharacteristic, complemented
390#2011C2×C4311yescharacteristic, complemented
391#1926C2×C4311yescharacteristic, complemented
392#1925C2×C4311yescharacteristic, complemented
393#1895C2×C4311yescharacteristic, complemented
394#1893C2×C4311yescharacteristic, complemented
395#1879C2×C4311yescharacteristic, complemented
396#1879C2×C4311yescharacteristic, complemented
397#1729C2×C4311yescharacteristic, complemented
398C2×C43—42no—
399C2×C43—82no—
400C2×C43—161no—
401C2×C43—161no—
402C2×C43#254311yescharacteristic
403C2×C43#304111yescharacteristic
404C2×C43#304511yescharacteristic
405C2×C43#317611yescharacteristic
406C2×C43#317911yescharacteristic
407C2×C43#319811yescharacteristic
408C2×C43#319911yescharacteristic
409C22×D8C22×C4311yescharacteristic
410C22×D8C22×C4311yescharacteristic
411C22×M16C22×C4311yescharacteristic
412C23×C8C22×C4311yescharacteristic
413C2×#127C22×C4311yescharacteristic
414C2×#121C22×C4311yescharacteristic
415C2×#121C22×C4311yescharacteristic
416C2×#121C22×C4311yescharacteristic
417C2×C4×D4C22×C4311yescharacteristic
418C2×#117C22×C4311yescharacteristic
419#469—24no—
420#466—24no—
421C2×#107C22×C4311yescharacteristic
422C2×#106C22×C4311yescharacteristic
423C2×#102C22×C4311yescharacteristic
424C2×#102C22×C4311yescharacteristic
425C2×#102C22×C4311yescharacteristic
426C2×#102C22×C4311yescharacteristic
427C2×#102C22×C4311yescharacteristic
428C2×#102C22×C4311yescharacteristic
429C2×#102C22×C4311yescharacteristic
430C2×#102C22×C4311yescharacteristic
431#394—21no—
432#394—21no—
433#392—21no—
434#392—21no—
435#390—21no—
436#390C22×C4311yescharacteristic
437#390C22×C4311yescharacteristic
438#390C22×C4311yescharacteristic
439#389C22×C4311yescharacteristic
440#388—21no—
441#386—21no—
442#385—21no—
443#382C22×C4311yescharacteristic
444#380C22×C4311yescharacteristic
445C4×C4⋊C4C22×C4311yescharacteristic
446#340C22×C4311yescharacteristic
447#340C22×C4311yescharacteristic
448#340C22×C4311yescharacteristic
449#340C22×C4311yescharacteristic
450#336C22×C4311yescharacteristic
451#336C22×C4311yescharacteristic
452#336C22×C4311yescharacteristic
453#336C22×C4311yescharacteristic
454C43#2858411yescharacteristic, direct product factor, Sylow
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C23×C4311yescharacteristic
461C22×D4C23×C4311yescharacteristic
462C22×D4C23×C4311yescharacteristic
463C23×C4—21no—
464C23×C4C23×C4311yescharacteristic
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—22no—
468C2×D8—22no—
469C2×D8—41no—
470C2×D8—41no—
471C2×M16—22no—
472C2×M16—22no—
473C2×M16—41no—
474C22×C8—22no—
475C22×C8—22no—
476C22×C8—41no—
477C22×C8C23×C4311yescharacteristic
478C22×C8C23×C4311yescharacteristic
479C22×C8C23×C4311yescharacteristic
480C22×C8C23×C4311yescharacteristic
481#127—41no—
482#127—41no—
483#121—22no—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121D4×C4314yescomplemented
489C4×D4—41no—
490C4×D4—41no—
491#117—41no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4D4×C4311yescharacteristic
495C2×C4⋊C4D4×C4311yescharacteristic
496C2×C4⋊C4C23×C4311yescharacteristic
497C2×C4⋊C4C23×C4311yescharacteristic
498C2×C4⋊C4C23×C4311yescharacteristic
499C2×C4⋊C4C23×C4311yescharacteristic
500C2×C4⋊C4C23×C4311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4D4×C4311yescharacteristic
513C2×C22⋊C4D4×C4311yescharacteristic
514C2×C42—21no—
515C2×C42C23×C4311yescharacteristic
516C2×C42C23×C4311yescharacteristic
517#107—22no—
518#106—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24C2×D4×C4311yescharacteristic
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4C2×D4×C4312yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C4311yescharacteristic
582C22×C4C2×D4×C4311yescharacteristic
583C22×C4C2×D4×C4311yescharacteristic
584C22×C4C2×D4×C4311yescharacteristic
585C22×C4C2×D4×C4311yescharacteristic
586C22×C4C2×D4×C4312yes—
587C22×C4#41×C4312yes—
588C22×C4C24×C4311yescharacteristic
589D8—44no—
590D8—44no—
591M16—44no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—44no—
603C2×C8#41×C4312yes—
604C2×C8#41×C4312yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—81no—
617C4⋊C4C2×D4×C4312yes—
618C22⋊C4—24no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—81no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23#121×C4312yes—
664C23C22×D4×C4311yescharacteristic
665D4—22no—
666D4—22no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—84no—
716C2×C4#121×C4312yes—
717C2×C4C22×D4×C4311yescharacteristic
718C2×C4C2×#41×C4311yescharacteristic
719C2×C4C2×#41×C4311yescharacteristic
720C2×C4C2×#41×C4311yescharacteristic
721C2×C4H(5,𝔽2)×C4311yescharacteristic
722C2×C4H(5,𝔽2)×C4311yescharacteristic
723C8—22no—
724C8—22no—
725C8—41no—
726C8—41no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×#121×C4311yescharacteristic
756C22C43×#53211yescharacteristic
757C22C43×#53411yescharacteristic
758C22C43×#57611yescharacteristic
759C22C43×#57611yescharacteristic
760C22C43×#57611yescharacteristic
761C22C43×#57711yescharacteristic
762C4—22no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4C43×#54611yescharacteristic
773C4C43×#54611yescharacteristic
774C4C43×#55311yescharacteristic
775C4C43×#55311yescharacteristic
776C2—42no—
777C2—82no—
778C2—161no—
779C2—161no—
780C2C43×#254311yescharacteristic
781C2C43×#304111yescharacteristic
782C2C43×#304511yescharacteristic
783C2C43×#317611yescharacteristic
784C2C43×#317911yescharacteristic
785C2C43×#319811yescharacteristic
786C2C43×#319911yescharacteristic
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. C43×#2619C2semidirect
4. C43×#2324C2semidirect
5. C43×#2085C2semidirect
6. C43×#2073C2semidirect
7. C43×#2041C2semidirect
8. C43×#2011C2semidirect
9. C43×#1926C2semidirect
10. C43×#1925C2semidirect
11. C43×#1895C2semidirect
12. C43×#1893C2semidirect
13. C43×#1879C2semidirect
14. C43×#1879C2semidirect
15. C43×#1729C2semidirect
94. #121×C43D4semidirect
333. #28584C43direct (N × H)
383. C2×#469C2×C43semidirect
384. C2×#466C2×C43semidirect
385. #2619C2×C43semidirect
386. #2324C2×C43semidirect
387. #2085C2×C43semidirect
388. #2073C2×C43semidirect
389. #2041C2×C43semidirect
390. #2011C2×C43semidirect
391. #1926C2×C43semidirect
392. #1925C2×C43semidirect
393. #1895C2×C43semidirect
394. #1893C2×C43semidirect
395. #1879C2×C43semidirect
396. #1879C2×C43semidirect
397. #1729C2×C43semidirect
454. C43#28584direct (N × H)
488. #121D4×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
C43×#26192
C43×#23242
C43×#20852
C43×#20732
C43×#20412
C43×#20112
C43×#19262
C43×#19252
C43×#18952
C43×#18932
C43×#18792
C43×#17292
#2858443