Finite Group Databasebeta

← C43×#24662 #24944679

Subgroups — C43×#24662 #24944679

Order 11008.

970 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#459C211yesmaximal, characteristic, complemented
2C2×C43×#433C211yesmaximal, characteristic, complemented
3C43×#2619C211yesmaximal, characteristic, complemented
4C43×#2324C211yesmaximal, characteristic, complemented
5C43×#2034C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#1999C211yesmaximal, characteristic, complemented
8C43×#1999C211yesmaximal, characteristic, complemented
9C43×#1982C211yesmaximal, characteristic, complemented
10C43×#1972C211yesmaximal, characteristic, complemented
11C43×#1970C211yesmaximal, characteristic, complemented
12C43×#1949C211yesmaximal, characteristic, complemented
13C43×#1936C211yesmaximal, characteristic, complemented
14C43×#1934C211yesmaximal, characteristic, complemented
15C43×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C2×#127×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×#121×C43C2211yescharacteristic
21C2×#121×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C2×#117×C43C2211yescharacteristic
24C43×#459—24no—
25C43×#433—24no—
26C2×#107×C43C2211yescharacteristic
27C2×#106×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×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
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C2×#97×C43C2211yescharacteristic
41C2×C4×C8×C43C2211yescharacteristic
42C43×#394—21no—
43C43×#394—21no—
44C43×#392—21no—
45C43×#392—21no—
46C43×#390—21no—
47C43×#390C2211yescharacteristic
48C43×#390C2211yescharacteristic
49C43×#390C2211yescharacteristic
50C43×#389C2211yescharacteristic
51C43×#388—21no—
52C43×#386—21no—
53C43×#385—21no—
54C43×#382C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
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—
77C22×C8×C43C2311yescharacteristic
78C22×C8×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81#127×C43—22no—
82#127×C43—22no—
83#121×C43—22no—
84#121×C43—22no—
85#121×C43—41no—
86#121×C43—41no—
87#121×C43—41no—
88#121×C43—41no—
89C4×D4×C43—22no—
90C4×D4×C43—22no—
91#117×C43—22no—
92#117×C43—22no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43D411yescharacteristic
95C2×C4⋊C4×C43D411yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
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×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117#107×C43—41no—
118#106×C43—41no—
119C4⋊C8×C43—22no—
120C4⋊C8×C43D414yescomplemented
121#102×C43—22no—
122#102×C43—22no—
123#102×C43—22no—
124#102×C43—22no—
125#102×C43—41no—
126#102×C43—41no—
127#102×C43—41no—
128#102×C43—41no—
129C22⋊C8×C43—22no—
130C22⋊C8×C43—22no—
131#97×C43—22no—
132C4×C8×C43—22no—
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—24no—
143C2×D4×C43—21no—
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×C43#4112yes—
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—21no—
185C22×C4×C43—21no—
186C22×C4×C43—42no—
187C22×C4×C43—81no—
188C22×C4×C43—81no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195D8×C43—44no—
196D8×C43—44no—
197C2×C8×C43—21no—
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×C43C2×D412yes—
208C2×C8×C43C2×D412yes—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—22no—
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—81no—
221C4⋊C4×C43#4112yes—
222C22⋊C4×C43—24no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—81no—
229C22⋊C4×C43—81no—
230C22⋊C4×C43—81no—
231C22⋊C4×C43—81no—
232C22⋊C4×C43—81no—
233C22⋊C4×C43—81no—
234C22⋊C4×C43—81no—
235C42×C43—21no—
236C42×C43—21no—
237C42×C43—81no—
238C42×C43C2×D412yes—
239C42×C43#4112yes—
240C23×C43—21no—
241C23×C43—22no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—41no—
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×C43C22×D411yescharacteristic
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—41no—
272D4×C43—41no—
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—84no—
282D4×C43—84no—
283D4×C43—84no—
284D4×C43—84no—
285D4×C43—84no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
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—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
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—84no—
319C2×C4×C43#12112yes—
320C2×C4×C43#12112yes—
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C2×C4×C43H(5,𝔽2)11yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C8×C43—22no—
328C8×C43—22no—
329C8×C43—41no—
330C8×C43—41no—
331#24662C4311yesmaximal, characteristic, direct product factor, Sylow
332C22×C43—41no—
333C22×C43—42no—
334C22×C43—41no—
335C22×C43—42no—
336C22×C43—41no—
337C22×C43—42no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—81no—
343C22×C43—81no—
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×C43C2×#12111yescharacteristic
361C22×C43#52511yescharacteristic
362C22×C43#53511yescharacteristic
363C22×C43#57611yescharacteristic
364C22×C43#57611yescharacteristic
365C22×C43#57611yescharacteristic
366C22×C43#57711yescharacteristic
367C4×C43—22no—
368C4×C43—22no—
369C4×C43—42no—
370C4×C43—41no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43—81no—
374C4×C43—81no—
375C4×C43—81no—
376C4×C43—81no—
377C4×C43#54611yescharacteristic
378C4×C43#55011yescharacteristic
379C4×C43#55311yescharacteristic
380C4×C43#55511yescharacteristic
381C2×#459C2×C4311yescharacteristic, complemented
382C2×#433C2×C4311yescharacteristic, complemented
383#2619C2×C4311yescharacteristic, complemented
384#2324C2×C4311yescharacteristic, complemented
385#2034C2×C4311yescharacteristic, complemented
386#2033C2×C4311yescharacteristic, complemented
387#1999C2×C4311yescharacteristic, complemented
388#1999C2×C4311yescharacteristic, complemented
389#1982C2×C4311yescharacteristic, complemented
390#1972C2×C4311yescharacteristic, complemented
391#1970C2×C4311yescharacteristic, complemented
392#1949C2×C4311yescharacteristic, complemented
393#1936C2×C4311yescharacteristic, complemented
394#1934C2×C4311yescharacteristic, complemented
395#1804C2×C4311yescharacteristic, complemented
396C2×C43—81no—
397C2×C43—82no—
398C2×C43—161no—
399C2×C43—161no—
400C2×C43#241411yescharacteristic
401C2×C43#305811yescharacteristic
402C2×C43#306211yescharacteristic
403C2×C43#311911yescharacteristic
404C2×C43#312211yescharacteristic
405C2×C43#322011yescharacteristic
406C2×C43#322411yescharacteristic
407C22×D8C22×C4311yescharacteristic
408C22×D8C22×C4311yescharacteristic
409C2×#127C22×C4311yescharacteristic
410C2×#121C22×C4311yescharacteristic
411C2×#121C22×C4311yescharacteristic
412C2×#121C22×C4311yescharacteristic
413C2×C4×D4C22×C4311yescharacteristic
414C2×#117C22×C4311yescharacteristic
415#459—24no—
416#433—24no—
417C2×#107C22×C4311yescharacteristic
418C2×#106C22×C4311yescharacteristic
419C2×C4⋊C8C22×C4311yescharacteristic
420C2×C4⋊C8C22×C4311yescharacteristic
421C2×#102C22×C4311yescharacteristic
422C2×#102C22×C4311yescharacteristic
423C2×#102C22×C4311yescharacteristic
424C2×#102C22×C4311yescharacteristic
425C2×#102C22×C4311yescharacteristic
426C2×#102C22×C4311yescharacteristic
427C2×#102C22×C4311yescharacteristic
428C2×#102C22×C4311yescharacteristic
429C2×C22⋊C8C22×C4311yescharacteristic
430C2×C22⋊C8C22×C4311yescharacteristic
431C2×#97C22×C4311yescharacteristic
432C2×C4×C8C22×C4311yescharacteristic
433#394—21no—
434#394—21no—
435#392—21no—
436#392—21no—
437#390—21no—
438#390C22×C4311yescharacteristic
439#390C22×C4311yescharacteristic
440#390C22×C4311yescharacteristic
441#389C22×C4311yescharacteristic
442#388—21no—
443#386—21no—
444#385—21no—
445#382C22×C4311yescharacteristic
446#380C22×C4311yescharacteristic
447C4×C4⋊C4C22×C4311yescharacteristic
448#340C22×C4311yescharacteristic
449#340C22×C4311yescharacteristic
450#340C22×C4311yescharacteristic
451#340C22×C4311yescharacteristic
452C43#2466211yescharacteristic, direct product factor, Sylow
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C23×C4311yescharacteristic
459C22×D4C23×C4311yescharacteristic
460C22×D4C23×C4311yescharacteristic
461C23×C4—21no—
462C23×C4C23×C4311yescharacteristic
463C2×D8—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—41no—
468C2×D8—41no—
469C22×C8C23×C4311yescharacteristic
470C22×C8C23×C4311yescharacteristic
471C22×C8C23×C4311yescharacteristic
472C22×C8C23×C4311yescharacteristic
473#127—22no—
474#127—22no—
475#121—22no—
476#121—22no—
477#121—41no—
478#121—41no—
479#121—41no—
480#121—41no—
481C4×D4—22no—
482C4×D4—22no—
483#117—22no—
484#117—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4D4×C4311yescharacteristic
487C2×C4⋊C4D4×C4311yescharacteristic
488C2×C4⋊C4C23×C4311yescharacteristic
489C2×C4⋊C4C23×C4311yescharacteristic
490C2×C4⋊C4C23×C4311yescharacteristic
491C2×C4⋊C4C23×C4311yescharacteristic
492C2×C4⋊C4C23×C4311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C4311yescharacteristic
505C2×C22⋊C4D4×C4311yescharacteristic
506C2×C42—21no—
507C2×C42C23×C4311yescharacteristic
508C2×C42C23×C4311yescharacteristic
509#107—41no—
510#106—41no—
511C4⋊C8—22no—
512C4⋊C8D4×C4314yescomplemented
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518#102—41no—
519#102—41no—
520#102—41no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523#97—22no—
524C4×C8—22no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24C2×D4×C4311yescharacteristic
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
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—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
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#41×C4312yes—
567C22×C4—21no—
568C22×C4—21no—
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×C4C24×C4311yescharacteristic
587D8—44no—
588D8—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8C2×D4×C4312yes—
600C2×C8C2×D4×C4312yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—81no—
613C4⋊C4#41×C4312yes—
614C22⋊C4—24no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C42—21no—
628C42—21no—
629C42—81no—
630C42C2×D4×C4312yes—
631C42#41×C4312yes—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—41no—
641C23—41no—
642C23—41no—
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—
660C23C22×D4×C4311yescharacteristic
661D4—22no—
662D4—22no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—84no—
674D4—84no—
675D4—84no—
676D4—84no—
677D4—84no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
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—84no—
711C2×C4#121×C4312yes—
712C2×C4#121×C4312yes—
713C2×C4C22×D4×C4311yescharacteristic
714C2×C4C2×#41×C4311yescharacteristic
715C2×C4C2×#41×C4311yescharacteristic
716C2×C4C2×#41×C4311yescharacteristic
717C2×C4H(5,𝔽2)×C4311yescharacteristic
718C2×C4H(5,𝔽2)×C4311yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
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—
751C22C2×#121×C4311yescharacteristic
752C22C43×#52511yescharacteristic
753C22C43×#53511yescharacteristic
754C22C43×#57611yescharacteristic
755C22C43×#57611yescharacteristic
756C22C43×#57611yescharacteristic
757C22C43×#57711yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4C43×#54611yescharacteristic
769C4C43×#55011yescharacteristic
770C4C43×#55311yescharacteristic
771C4C43×#55511yescharacteristic
772C2—81no—
773C2—82no—
774C2—161no—
775C2—161no—
776C2C43×#241411yescharacteristic
777C2C43×#305811yescharacteristic
778C2C43×#306211yescharacteristic
779C2C43×#311911yescharacteristic
780C2C43×#312211yescharacteristic
781C2C43×#322011yescharacteristic
782C2C43×#322411yescharacteristic
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×#459C2semidirect
2. C2×C43×#433C2semidirect
3. C43×#2619C2semidirect
4. C43×#2324C2semidirect
5. C43×#2034C2semidirect
6. C43×#2033C2semidirect
7. C43×#1999C2semidirect
8. C43×#1999C2semidirect
9. C43×#1982C2semidirect
10. C43×#1972C2semidirect
11. C43×#1970C2semidirect
12. C43×#1949C2semidirect
13. C43×#1936C2semidirect
14. C43×#1934C2semidirect
15. C43×#1804C2semidirect
120. C4⋊C8×C43D4semidirect
331. #24662C43direct (N × H)
381. C2×#459C2×C43semidirect
382. C2×#433C2×C43semidirect
383. #2619C2×C43semidirect
384. #2324C2×C43semidirect
385. #2034C2×C43semidirect
386. #2033C2×C43semidirect
387. #1999C2×C43semidirect
388. #1999C2×C43semidirect
389. #1982C2×C43semidirect
390. #1972C2×C43semidirect
391. #1970C2×C43semidirect
392. #1949C2×C43semidirect
393. #1936C2×C43semidirect
394. #1934C2×C43semidirect
395. #1804C2×C43semidirect
452. C43#24662direct (N × H)
512. 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×#4592
C2×C43×#4332
C43×#26192
C43×#23242
C43×#20342
C43×#20332
C43×#19992
C43×#19822
C43×#19722
C43×#19702
C43×#19492
C43×#19362
C43×#19342
C43×#18042
#2466243