Finite Group Databasebeta

← C43×#25547 #24945564

Subgroups — C43×#25547 #24945564

Order 11008.

1340 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#547C211yesmaximal, characteristic
2C2×C43×#484C211yesmaximal, characteristic, complemented
3C2×C43×#468C211yesmaximal, characteristic, complemented
4C43×#2415C211yesmaximal, characteristic, complemented
5C43×#2057C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#2024C211yesmaximal, characteristic, complemented
8C43×#2000C211yesmaximal, characteristic, complemented
9C43×#1877C211yesmaximal, characteristic, complemented
10C43×#1875C211yesmaximal, characteristic, complemented
11C43×#1872C211yesmaximal, characteristic, complemented
12C43×#1870C211yesmaximal, characteristic, complemented
13C43×#1862C211yesmaximal, characteristic, complemented
14C43×#1852C211yesmaximal, characteristic, complemented
15C43×#1736C211yesmaximal, characteristic, complemented
16C22×#41×C43—21no—
17C22×SD16×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C43×#547—24no—
20C43×#547—24no—
21C2×C4⋊Q8×C43C2211yescharacteristic
22C2×#123×C43—21no—
23C2×#123×C43—21no—
24C2×C22⋊Q8×C43—21no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×C22⋊Q8×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C2×C4×D4×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C22×C4⋊C4×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C43×#484—24no—
35C43×#468—24no—
36C2×#107×C43C2211yescharacteristic
37C2×#107×C43C2211yescharacteristic
38C2×#107×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#103×C43C2211yescharacteristic
41C2×#103×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#397—21no—
49C43×#394—21no—
50C43×#391C2211yescharacteristic
51C43×#389—21no—
52C43×#389C2211yescharacteristic
53C43×#388—21no—
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#41×C43—28no—
64C2×#41×C43—44no—
65C2×#41×C43—44no—
66C22×Q8×C43—21no—
67C22×Q8×C43C2311yescharacteristic
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43D411yescharacteristic
71C22×D4×C43C2311yescharacteristic
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43—21no—
75C23×C4×C43C2311yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C2×SD16×C43—22no—
78C2×SD16×C43—22no—
79C2×SD16×C43—41no—
80C2×M16×C43—22no—
81C2×M16×C43—22no—
82C2×M16×C43—41no—
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85C22×C8×C43C2311yescharacteristic
86C22×C8×C43C2311yescharacteristic
87C4⋊Q8×C43—22no—
88C4⋊Q8×C43—22no—
89#123×C43—28no—
90#123×C43—28no—
91C22⋊Q8×C43—28no—
92C22⋊Q8×C43—22no—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—22no—
95C22⋊Q8×C43—41no—
96#121×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99#121×C43D414yes—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104#117×C43—22no—
105#117×C43—41no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43D414yes—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—22no—
135#107×C43—22no—
136#107×C43—22no—
137#103×C43—22no—
138#103×C43—22no—
139#103×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—41no—
143C22⋊C8×C43—22no—
144C22⋊C8×C43—22no—
145C22⋊C8×C43—41no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149#95×C43—21no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C24×C43C2×D411yescharacteristic
153#41×C43—432no—
154C2×Q8×C43—24no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—42no—
162C2×Q8×C43—42no—
163C2×D4×C43—24no—
164C2×D4×C43—22no—
165C2×D4×C43—21no—
166C2×D4×C43—22no—
167C2×D4×C43—24no—
168C2×D4×C43—22no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—42no—
174C2×D4×C43—42no—
175C2×D4×C43—42no—
176C2×D4×C43—42no—
177C2×D4×C43C2×D412yes—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—24no—
183C22×C4×C43—24no—
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—24no—
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—42no—
199C22×C4×C43—42no—
200C22×C4×C43—42no—
201C22×C4×C43—42no—
202C22×C4×C43—42no—
203C22×C4×C43—42no—
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2×D412yes—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2411yescharacteristic
211SD16×C43—44no—
212M16×C43—44no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
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#4112yescomplemented
225C4⋊C4×C43—24no—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—22no—
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—42no—
238C4⋊C4×C43—42no—
239C4⋊C4×C43—42no—
240C4⋊C4×C43C2×D412yes—
241C4⋊C4×C43C2×D412yes—
242C4⋊C4×C43C2×D412yes—
243C4⋊C4×C43#4112yescomplemented
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—42no—
250C22⋊C4×C43—42no—
251C22⋊C4×C43—42no—
252C22⋊C4×C43—42no—
253C42×C43—21no—
254C42×C43—21no—
255C42×C43—42no—
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—22no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43#12012yes—
276C23×C43AGL(1,ℤ/8)12yes—
277C23×C43C22×D411yescharacteristic
278Q8×C43—48no—
279Q8×C43—41no—
280Q8×C43—41no—
281Q8×C43—41no—
282Q8×C43—41no—
283D4×C43—28no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—48no—
287D4×C43—48no—
288D4×C43—41no—
289D4×C43—41no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
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—21no—
307C2×C4×C43—21no—
308C2×C4×C43—48no—
309C2×C4×C43—48no—
310C2×C4×C43—48no—
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—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43#12012yes—
333C2×C4×C43AGL(1,ℤ/8)12yes—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C2×C4×C432−1+411yescharacteristic
340C8×C43—22no—
341C8×C43—41no—
342C8×C43—41no—
343C8×C43—41no—
344#25547C4311yesmaximal, characteristic, direct product factor, Sylow
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43C2×#12011yescharacteristic
367C22×C43#54611yescharacteristic
368C22×C43#54711yescharacteristic
369C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C43#57811yescharacteristic
372C22×C43#57811yescharacteristic
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—42no—
376C4×C43—41no—
377C4×C43—42no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43—41no—
381C4×C43—81no—
382C4×C43—81no—
383C4×C43—81no—
384C4×C43#53211yescharacteristic
385C4×C43#53711yescharacteristic
386C4×C43#54611yescharacteristic
387C4×C43#54711yescharacteristic
388C2×#547C2×C4311yescharacteristic
389C2×#484C2×C4311yescharacteristic, complemented
390C2×#468C2×C4311yescharacteristic, complemented
391#2415C2×C4311yescharacteristic, complemented
392#2057C2×C4311yescharacteristic, complemented
393#2033C2×C4311yescharacteristic, complemented
394#2024C2×C4311yescharacteristic, complemented
395#2000C2×C4311yescharacteristic, complemented
396#1877C2×C4311yescharacteristic, complemented
397#1875C2×C4311yescharacteristic, complemented
398#1872C2×C4311yescharacteristic, complemented
399#1870C2×C4311yescharacteristic, complemented
400#1862C2×C4311yescharacteristic, complemented
401#1852C2×C4311yescharacteristic, complemented
402#1736C2×C4311yescharacteristic, complemented
403C2×C43—42no—
404C2×C43—42no—
405C2×C43—82no—
406C2×C43#243011yescharacteristic
407C2×C43#300311yescharacteristic
408C2×C43#301111yescharacteristic
409C2×C43#330811yescharacteristic
410C2×C43#333011yescharacteristic
411C2×C43#334311yescharacteristic
412C2×C43#335311yescharacteristic
413C22×#41—21no—
414C22×SD16C22×C4311yescharacteristic
415C22×M16C22×C4311yescharacteristic
416#547—24no—
417#547—24no—
418C2×C4⋊Q8C22×C4311yescharacteristic
419C2×#123—21no—
420C2×#123—21no—
421C2×C22⋊Q8—21no—
422C2×C22⋊Q8C22×C4311yescharacteristic
423C2×C22⋊Q8C22×C4311yescharacteristic
424C2×#121C22×C4311yescharacteristic
425C2×#121C22×C4311yescharacteristic
426C2×C4×D4C22×C4311yescharacteristic
427C2×C4×D4C22×C4311yescharacteristic
428C2×#117C22×C4311yescharacteristic
429C22×C4⋊C4C22×C4311yescharacteristic
430C22×C4⋊C4C22×C4311yescharacteristic
431#484—24no—
432#468—24no—
433C2×#107C22×C4311yescharacteristic
434C2×#107C22×C4311yescharacteristic
435C2×#107C22×C4311yescharacteristic
436C2×#103C22×C4311yescharacteristic
437C2×#103C22×C4311yescharacteristic
438C2×#103C22×C4311yescharacteristic
439C2×#102C22×C4311yescharacteristic
440C2×#102C22×C4311yescharacteristic
441C2×#102C22×C4311yescharacteristic
442C2×C22⋊C8C22×C4311yescharacteristic
443C2×C22⋊C8C22×C4311yescharacteristic
444C2×C22⋊C8C22×C4311yescharacteristic
445#397—21no—
446#394—21no—
447#391C22×C4311yescharacteristic
448#389—21no—
449#389C22×C4311yescharacteristic
450#388—21no—
451#380C22×C4311yescharacteristic
452#340C22×C4311yescharacteristic
453#340C22×C4311yescharacteristic
454#340C22×C4311yescharacteristic
455#340C22×C4311yescharacteristic
456#340C22×C4311yescharacteristic
457#340C22×C4311yescharacteristic
458#336C22×C4311yescharacteristic
459#336C22×C4311yescharacteristic
460C43#2554711yescharacteristic, direct product factor, Sylow
461C2×#41—28no—
462C2×#41—44no—
463C2×#41—44no—
464C22×Q8—21no—
465C22×Q8C23×C4311yescharacteristic
466C22×D4—21no—
467C22×D4—21no—
468C22×D4D4×C4311yescharacteristic
469C22×D4C23×C4311yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4C23×C4311yescharacteristic
474C23×C4C23×C4311yescharacteristic
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—41no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16—41no—
481C22×C8C23×C4311yescharacteristic
482C22×C8C23×C4311yescharacteristic
483C22×C8C23×C4311yescharacteristic
484C22×C8C23×C4311yescharacteristic
485C4⋊Q8—22no—
486C4⋊Q8—22no—
487#123—28no—
488#123—28no—
489C22⋊Q8—28no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—41no—
494#121—22no—
495#121—22no—
496#121—22no—
497#121D4×C4314yes—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—22no—
503#117—41no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4D4×C4311yescharacteristic
514C2×C4⋊C4D4×C4314yes—
515C2×C4⋊C4C23×C4311yescharacteristic
516C2×C4⋊C4C23×C4311yescharacteristic
517C2×C4⋊C4C23×C4311yescharacteristic
518C2×C4⋊C4C23×C4311yescharacteristic
519C2×C4⋊C4C23×C4311yescharacteristic
520C2×C4⋊C4C23×C4311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4D4×C4311yescharacteristic
529C2×C22⋊C4D4×C4311yescharacteristic
530C2×C42—21no—
531C2×C42C23×C4311yescharacteristic
532#107—22no—
533#107—22no—
534#107—22no—
535#103—22no—
536#103—22no—
537#103—22no—
538#102—22no—
539#102—22no—
540#102—41no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—41no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548C24—21no—
549C24C2×D4×C4311yescharacteristic
550C24C2×D4×C4311yescharacteristic
551#41—432no—
552C2×Q8—24no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4C2×D4×C4312yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
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—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×D4×C4311yescharacteristic
603C22×C4C2×D4×C4311yescharacteristic
604C22×C4C2×D4×C4311yescharacteristic
605C22×C4C2×D4×C4312yes—
606C22×C4C2×D4×C4312yes—
607C22×C4C2×D4×C4311yescharacteristic
608C22×C4C24×C4311yescharacteristic
609SD16—44no—
610M16—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8#41×C4312yescomplemented
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4C2×D4×C4312yes—
639C4⋊C4C2×D4×C4312yes—
640C4⋊C4C2×D4×C4312yes—
641C4⋊C4#41×C4312yescomplemented
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—22no—
645C22⋊C4—24no—
646C22⋊C4—22no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C42—21no—
652C42—21no—
653C42—42no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—22no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23#120×C4312yes—
674C23AGL(1,ℤ/8)×C4312yes—
675C23C22×D4×C4311yescharacteristic
676Q8—48no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681D4—28no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—48no—
707C2×C4—48no—
708C2×C4—48no—
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—41no—
730C2×C4#120×C4312yes—
731C2×C4AGL(1,ℤ/8)×C4312yes—
732C2×C4C22×D4×C4311yescharacteristic
733C2×C4C22×D4×C4311yescharacteristic
734C2×C4C2×#41×C4311yescharacteristic
735C2×C4C2×#41×C4311yescharacteristic
736C2×C4H(5,𝔽2)×C4311yescharacteristic
737C2×C42−1+4×C4311yescharacteristic
738C8—22no—
739C8—41no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22C2×#120×C4311yescharacteristic
764C22C43×#54611yescharacteristic
765C22C43×#54711yescharacteristic
766C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
767C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
768C22C43×#57811yescharacteristic
769C22C43×#57811yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—41no—
777C4—42no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4C43×#53211yescharacteristic
782C4C43×#53711yescharacteristic
783C4C43×#54611yescharacteristic
784C4C43×#54711yescharacteristic
785C2—42no—
786C2—42no—
787C2—82no—
788C2C43×#243011yescharacteristic
789C2C43×#300311yescharacteristic
790C2C43×#301111yescharacteristic
791C2C43×#330811yescharacteristic
792C2C43×#333011yescharacteristic
793C2C43×#334311yescharacteristic
794C2C43×#335311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#547C2
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
2. C2×C43×#484C2semidirect
3. C2×C43×#468C2semidirect
4. C43×#2415C2semidirect
5. C43×#2057C2semidirect
6. C43×#2033C2semidirect
7. C43×#2024C2semidirect
8. C43×#2000C2semidirect
9. C43×#1877C2semidirect
10. C43×#1875C2semidirect
11. C43×#1872C2semidirect
12. C43×#1870C2semidirect
13. C43×#1862C2semidirect
14. C43×#1852C2semidirect
15. C43×#1736C2semidirect
224. C2×C8×C43#41semidirect
243. C4⋊C4×C43#41semidirect
344. #25547C43direct (N × H)
389. C2×#484C2×C43semidirect
390. C2×#468C2×C43semidirect
391. #2415C2×C43semidirect
392. #2057C2×C43semidirect
393. #2033C2×C43semidirect
394. #2024C2×C43semidirect
395. #2000C2×C43semidirect
396. #1877C2×C43semidirect
397. #1875C2×C43semidirect
398. #1872C2×C43semidirect
399. #1870C2×C43semidirect
400. #1862C2×C43semidirect
401. #1852C2×C43semidirect
402. #1736C2×C43semidirect
460. C43#25547direct (N × H)
622. C2×C8#41×C43semidirect
641. C4⋊C4#41×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5472
C2×C43×#4842
C2×C43×#4682
C43×#24152
C43×#20572
C43×#20332
C43×#20242
C43×#20002
C43×#18772
C43×#18752
C43×#18722
C43×#18702
C43×#18622
C43×#18522
C43×#17362
#2554743