Finite Group Databasebeta

← C43×#24790 #24944807

Subgroups — C43×#24790 #24944807

Order 11008.

1082 conjugacy classes of subgroups.

The subgroup lattice has 802 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×#435C211yesmaximal, characteristic, complemented
4C2×C43×#428C211yesmaximal, characteristic, complemented
5C43×#2416C211yesmaximal, characteristic, complemented
6C43×#2414C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic, complemented
8C43×#2065C211yesmaximal, characteristic, complemented
9C43×#2034C211yesmaximal, characteristic, complemented
10C43×#2033C211yesmaximal, characteristic, complemented
11C43×#1972C211yesmaximal, characteristic, complemented
12C43×#1943C211yesmaximal, characteristic, complemented
13C43×#1875C211yesmaximal, characteristic, complemented
14C43×#1874C211yesmaximal, characteristic, complemented
15C43×#1807C211yesmaximal, characteristic, complemented
16C22×D8×C43C2211yescharacteristic
17C22×M16×C43C2211yescharacteristic
18C23×C8×C43C2211yescharacteristic
19C2×#121×C43—21no—
20C2×#121×C43C2211yescharacteristic
21C2×#121×C43C2211yescharacteristic
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×C4×D4×C43C2211yescharacteristic
25C2×#117×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#469—24no—
28C43×#466—24no—
29C43×#435—24no—
30C43×#428—24no—
31C2×#107×C43C2211yescharacteristic
32C2×#107×C43C2211yescharacteristic
33C2×#106×C43C2211yescharacteristic
34C2×#106×C43C2211yescharacteristic
35C2×#106×C43C2211yescharacteristic
36C2×C4⋊C8×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×C22⋊C8×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic
45C2×#97×C43C2211yescharacteristic
46C43×#396—21no—
47C43×#394—21no—
48C43×#394—21no—
49C43×#392—21no—
50C43×#390—21no—
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#388—21no—
56C43×#386—21no—
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
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×C43D411yescharacteristic
68C22×D4×C43C2311yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C23×C4×C43—21no—
71C23×C4×C43C2311yescharacteristic
72C23×C4×C43C2311yescharacteristic
73C2×D8×C43—22no—
74C2×D8×C43—22no—
75C2×D8×C43—22no—
76C2×M16×C43—22no—
77C2×M16×C43—22no—
78C2×M16×C43D414yescomplemented
79C22×C8×C43—22no—
80C22×C8×C43—22no—
81C22×C8×C43—22no—
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85C22×C8×C43C2311yescharacteristic
86#121×C43—22no—
87#121×C43—22no—
88#121×C43—22no—
89#121×C43—22no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—41no—
93#121×C43—41no—
94#121×C43—44no—
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97#117×C43—22no—
98#117×C43—41no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—41no—
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43D411yescharacteristic
123C2×C22⋊C4×C43D411yescharacteristic
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#107×C43—22no—
127#107×C43D414yescomplemented
128#106×C43—22no—
129#106×C43—22no—
130#106×C43—22no—
131C4⋊C8×C43—22no—
132#102×C43—22no—
133#102×C43—22no—
134#102×C43—22no—
135#102×C43—22no—
136#102×C43—41no—
137#102×C43—41no—
138C22⋊C8×C43—22no—
139C22⋊C8×C43—22no—
140#97×C43—22no—
141#95×C43—21no—
142#95×C43—21no—
143#95×C43—21no—
144#95×C43—21no—
145C24×C43—21no—
146C24×C43—21no—
147C24×C43C2×D411yescharacteristic
148C24×C43C2×D411yescharacteristic
149C2×D4×C43—22no—
150C2×D4×C43—22no—
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—41no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—81no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
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—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—42no—
193C22×C4×C43—42no—
194C22×C4×C43—81no—
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43#4112yes—
201C22×C4×C43C2411yescharacteristic
202D8×C43—44no—
203M16×C43—28no—
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—44no—
213C2×C8×C43C2×D412yes—
214C2×C8×C43C2×D412yes—
215C2×C8×C43C2×D412yes—
216C2×C8×C43#4112yes—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—21no—
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—42no—
229C4⋊C4×C43—42no—
230C4⋊C4×C43—81no—
231C4⋊C4×C43C2×D412yes—
232C4⋊C4×C43C2×D412yes—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—42no—
239C22⋊C4×C43—42no—
240C22⋊C4×C43—42no—
241C22⋊C4×C43—42no—
242C22⋊C4×C43—42no—
243C22⋊C4×C43—81no—
244C22⋊C4×C43—81no—
245C22⋊C4×C43—81no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—42no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
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×C43AGL(1,ℤ/8)12yes—
277C23×C43C22×D411yescharacteristic
278D4×C43—44no—
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—84no—
288D4×C43—84no—
289D4×C43—84no—
290D4×C43—84no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—22no—
301C2×C4×C43—21no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
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—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—84no—
329C2×C4×C43#12112yes—
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43C2×#4111yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C432−1+411yescharacteristic
336C8×C43—22no—
337C8×C43—41no—
338C8×C43—41no—
339C8×C43#12114yescomplemented
340#24790C4311yesmaximal, characteristic, direct product factor, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
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×C43—81no—
369C22×C43C2×#12111yescharacteristic
370C22×C43D4211yescharacteristic
371C22×C43#54711yescharacteristic
372C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C43#57511yescharacteristic
374C22×C43#57611yescharacteristic
375C22×C43#57711yescharacteristic
376C4×C43—22no—
377C4×C43—41no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43—41no—
381C4×C43—41no—
382C4×C43—81no—
383C4×C43—81no—
384C4×C43—81no—
385C4×C43—81no—
386C4×C43C2×#12111yescharacteristic
387C4×C43#53711yescharacteristic
388C4×C43#54811yescharacteristic
389C4×C43#55311yescharacteristic
390C2×#469C2×C4311yescharacteristic, complemented
391C2×#466C2×C4311yescharacteristic, complemented
392C2×#435C2×C4311yescharacteristic, complemented
393C2×#428C2×C4311yescharacteristic, complemented
394#2416C2×C4311yescharacteristic, complemented
395#2414C2×C4311yescharacteristic, complemented
396#2067C2×C4311yescharacteristic, complemented
397#2065C2×C4311yescharacteristic, complemented
398#2034C2×C4311yescharacteristic, complemented
399#2033C2×C4311yescharacteristic, complemented
400#1972C2×C4311yescharacteristic, complemented
401#1943C2×C4311yescharacteristic, complemented
402#1875C2×C4311yescharacteristic, complemented
403#1874C2×C4311yescharacteristic, complemented
404#1807C2×C4311yescharacteristic, complemented
405C2×C43—42no—
406C2×C43—42no—
407C2×C43—161no—
408C2×C43—161no—
409C2×C43#241611yescharacteristic
410C2×C43#305511yescharacteristic
411C2×C43#306211yescharacteristic
412C2×C43#326411yescharacteristic
413C2×C43#327111yescharacteristic
414C2×C43#334511yescharacteristic
415C2×C43#334711yescharacteristic
416C22×D8C22×C4311yescharacteristic
417C22×M16C22×C4311yescharacteristic
418C23×C8C22×C4311yescharacteristic
419C2×#121—21no—
420C2×#121C22×C4311yescharacteristic
421C2×#121C22×C4311yescharacteristic
422C2×#121C22×C4311yescharacteristic
423C2×#121C22×C4311yescharacteristic
424C2×C4×D4C22×C4311yescharacteristic
425C2×#117C22×C4311yescharacteristic
426C22×C4⋊C4C22×C4311yescharacteristic
427#469—24no—
428#466—24no—
429#435—24no—
430#428—24no—
431C2×#107C22×C4311yescharacteristic
432C2×#107C22×C4311yescharacteristic
433C2×#106C22×C4311yescharacteristic
434C2×#106C22×C4311yescharacteristic
435C2×#106C22×C4311yescharacteristic
436C2×C4⋊C8C22×C4311yescharacteristic
437C2×#102C22×C4311yescharacteristic
438C2×#102C22×C4311yescharacteristic
439C2×#102C22×C4311yescharacteristic
440C2×#102C22×C4311yescharacteristic
441C2×#102C22×C4311yescharacteristic
442C2×#102C22×C4311yescharacteristic
443C2×C22⋊C8C22×C4311yescharacteristic
444C2×C22⋊C8C22×C4311yescharacteristic
445C2×#97C22×C4311yescharacteristic
446#396—21no—
447#394—21no—
448#394—21no—
449#392—21no—
450#390—21no—
451#390C22×C4311yescharacteristic
452#390C22×C4311yescharacteristic
453#389C22×C4311yescharacteristic
454#389C22×C4311yescharacteristic
455#388—21no—
456#386—21no—
457#380C22×C4311yescharacteristic
458#380C22×C4311yescharacteristic
459#340C22×C4311yescharacteristic
460#340C22×C4311yescharacteristic
461#340C22×C4311yescharacteristic
462#340C22×C4311yescharacteristic
463C43#2479011yescharacteristic, direct product factor, Sylow
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4D4×C4311yescharacteristic
469C22×D4C23×C4311yescharacteristic
470C22×D4C23×C4311yescharacteristic
471C23×C4—21no—
472C23×C4C23×C4311yescharacteristic
473C23×C4C23×C4311yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16D4×C4314yescomplemented
480C22×C8—22no—
481C22×C8—22no—
482C22×C8—22no—
483C22×C8C23×C4311yescharacteristic
484C22×C8C23×C4311yescharacteristic
485C22×C8C23×C4311yescharacteristic
486C22×C8C23×C4311yescharacteristic
487#121—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495#121—44no—
496C4×D4—22no—
497C4×D4—22no—
498#117—22no—
499#117—41no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4D4×C4311yescharacteristic
506C2×C4⋊C4C23×C4311yescharacteristic
507C2×C4⋊C4C23×C4311yescharacteristic
508C2×C4⋊C4C23×C4311yescharacteristic
509C2×C4⋊C4C23×C4311yescharacteristic
510C2×C4⋊C4C23×C4311yescharacteristic
511C2×C4⋊C4C23×C4311yescharacteristic
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⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4D4×C4311yescharacteristic
524C2×C22⋊C4D4×C4311yescharacteristic
525C2×C42—21no—
526C2×C42C23×C4311yescharacteristic
527#107—22no—
528#107D4×C4314yescomplemented
529#106—22no—
530#106—22no—
531#106—22no—
532C4⋊C8—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541#97—22no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546C24—21no—
547C24—21no—
548C24C2×D4×C4311yescharacteristic
549C24C2×D4×C4311yescharacteristic
550C2×D4—22no—
551C2×D4—22no—
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—41no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
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—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4C2×D4×C4311yescharacteristic
597C22×C4C2×D4×C4311yescharacteristic
598C22×C4C2×D4×C4311yescharacteristic
599C22×C4C2×D4×C4311yescharacteristic
600C22×C4C2×D4×C4312yes—
601C22×C4#41×C4312yes—
602C22×C4C24×C4311yescharacteristic
603D8—44no—
604M16—28no—
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—44no—
614C2×C8C2×D4×C4312yes—
615C2×C8C2×D4×C4312yes—
616C2×C8C2×D4×C4312yes—
617C2×C8#41×C4312yes—
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—21no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—81no—
632C4⋊C4C2×D4×C4312yes—
633C4⋊C4C2×D4×C4312yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
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—41no—
676C23#121×C4312yes—
677C23AGL(1,ℤ/8)×C4312yes—
678C23C22×D4×C4311yescharacteristic
679D4—44no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
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—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—84no—
730C2×C4#121×C4312yes—
731C2×C4C22×D4×C4311yescharacteristic
732C2×C4C22×D4×C4311yescharacteristic
733C2×C4C2×#41×C4311yescharacteristic
734C2×C4C2×#41×C4311yescharacteristic
735C2×C4H(5,𝔽2)×C4311yescharacteristic
736C2×C42−1+4×C4311yescharacteristic
737C8—22no—
738C8—41no—
739C8—41no—
740C8#121×C4314yescomplemented
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C2×#121×C4311yescharacteristic
770C22D42×C4311yescharacteristic
771C22C43×#54711yescharacteristic
772C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
773C22C43×#57511yescharacteristic
774C22C43×#57611yescharacteristic
775C22C43×#57711yescharacteristic
776C4—22no—
777C4—41no—
778C4—42no—
779C4—42no—
780C4—41no—
781C4—41no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C2×#121×C4311yescharacteristic
787C4C43×#53711yescharacteristic
788C4C43×#54811yescharacteristic
789C4C43×#55311yescharacteristic
790C2—42no—
791C2—42no—
792C2—161no—
793C2—161no—
794C2C43×#241611yescharacteristic
795C2C43×#305511yescharacteristic
796C2C43×#306211yescharacteristic
797C2C43×#326411yescharacteristic
798C2C43×#327111yescharacteristic
799C2C43×#334511yescharacteristic
800C2C43×#334711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
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
1. C2×C43×#469C2semidirect
2. C2×C43×#466C2semidirect
3. C2×C43×#435C2semidirect
4. C2×C43×#428C2semidirect
5. C43×#2416C2semidirect
6. C43×#2414C2semidirect
7. C43×#2067C2semidirect
8. C43×#2065C2semidirect
9. C43×#2034C2semidirect
10. C43×#2033C2semidirect
11. C43×#1972C2semidirect
12. C43×#1943C2semidirect
13. C43×#1875C2semidirect
14. C43×#1874C2semidirect
15. C43×#1807C2semidirect
78. C2×M16×C43D4semidirect
127. #107×C43D4semidirect
339. C8×C43#121semidirect
340. #24790C43direct (N × H)
390. C2×#469C2×C43semidirect
391. C2×#466C2×C43semidirect
392. C2×#435C2×C43semidirect
393. C2×#428C2×C43semidirect
394. #2416C2×C43semidirect
395. #2414C2×C43semidirect
396. #2067C2×C43semidirect
397. #2065C2×C43semidirect
398. #2034C2×C43semidirect
399. #2033C2×C43semidirect
400. #1972C2×C43semidirect
401. #1943C2×C43semidirect
402. #1875C2×C43semidirect
403. #1874C2×C43semidirect
404. #1807C2×C43semidirect
463. C43#24790direct (N × H)
479. C2×M16D4×C43semidirect
528. #107D4×C43semidirect
740. C8#121×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×#4352
C2×C43×#4282
C43×#24162
C43×#24142
C43×#20672
C43×#20652
C43×#20342
C43×#20332
C43×#19722
C43×#19432
C43×#18752
C43×#18742
C43×#18072
#2479043