Finite Group Databasebeta

← C43×#24438 #24944455

Subgroups — C43×#24438 #24944455

Order 11008.

1498 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#547C211yesmaximal, characteristic, complemented
2C2×C43×#465C211yesmaximal, characteristic, complemented
3C2×C43×#449C211yesmaximal, characteristic, complemented
4C2×C43×#449C211yesmaximal, characteristic, complemented
5C2×C43×#416C211yesmaximal, characteristic, complemented
6C43×#2414C211yesmaximal, characteristic, complemented
7C43×#2043C211yesmaximal, characteristic, complemented
8C43×#2035C211yesmaximal, characteristic, complemented
9C43×#2013C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#1879C211yesmaximal, characteristic, complemented
12C43×#1873C211yesmaximal, characteristic, complemented
13C43×#1869C211yesmaximal, characteristic, complemented
14C43×#1864C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×SD16×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C23×C8×C43C2211yescharacteristic
22C43×#547—24no—
23C43×#547—24no—
24C2×C4⋊Q8×C43C2211yescharacteristic
25C2×#123×C43—21no—
26C2×#123×C43—21no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C2×C22⋊Q8×C43C2211yescharacteristic
29C2×#121×C43—21no—
30C2×#121×C43C2211yescharacteristic
31C2×#121×C43C2211yescharacteristic
32C2×C4×D4×C43C2211yescharacteristic
33C2×C4×D4×C43C2211yescharacteristic
34C2×#117×C43C2211yescharacteristic
35C22×C4⋊C4×C43—21no—
36C43×#465—24no—
37C43×#449—24no—
38C43×#449—24no—
39C2×#106×C43C2211yescharacteristic
40C43×#416—24no—
41C2×#103×C43C2211yescharacteristic
42C2×#103×C43C2211yescharacteristic
43C2×#103×C43C2211yescharacteristic
44C2×#103×C43C2211yescharacteristic
45C2×#103×C43C2211yescharacteristic
46C2×#103×C43C2211yescharacteristic
47C2×#102×C43C2211yescharacteristic
48C2×#102×C43C2211yescharacteristic
49C2×#102×C43C2211yescharacteristic
50C2×#102×C43C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C2×C22⋊C8×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#394—21no—
55C43×#392—21no—
56C43×#390—21no—
57C43×#390C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#388—21no—
60C43×#380C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C43×#336C2211yescharacteristic
65C2×#41×C43—22no—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—22no—
71C2×#41×C43—22no—
72C2×#41×C43—41no—
73C2×#41×C43—41no—
74C2×#41×C43—41no—
75C2×#41×C43—41no—
76C2×#41×C43D414yescomplemented
77C22×Q8×C43C2311yescharacteristic
78C22×Q8×C43C2311yescharacteristic
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—21no—
82C22×D4×C43—21no—
83C22×D4×C43D411yescharacteristic
84C22×D4×C43C2311yescharacteristic
85C22×D4×C43C2311yescharacteristic
86C23×C4×C43—21no—
87C23×C4×C43—21no—
88C23×C4×C43—21no—
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C2×SD16×C43—22no—
92C2×SD16×C43—22no—
93C2×SD16×C43—22no—
94C2×SD16×C43—41no—
95C2×SD16×C43—41no—
96C2×SD16×C43—41no—
97C2×D8×C43—22no—
98C2×D8×C43—22no—
99C2×D8×C43—22no—
100C22×C8×C43—22no—
101C22×C8×C43—22no—
102C22×C8×C43—41no—
103C22×C8×C43C2311yescharacteristic
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C4⋊Q8×C43—22no—
108C4⋊Q8×C43—22no—
109#123×C43—28no—
110#123×C43—28no—
111C22⋊Q8×C43—22no—
112C22⋊Q8×C43—22no—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43D414yescomplemented
115#121×C43—28no—
116#121×C43—22no—
117#121×C43—22no—
118#121×C43—22no—
119#121×C43—41no—
120C4×D4×C43—22no—
121C4×D4×C43—22no—
122C4×D4×C43—22no—
123C4×D4×C43—22no—
124#117×C43—22no—
125#117×C43—41no—
126C2×C4⋊C4×C43—28no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C22⋊C4×C43D411yescharacteristic
148C2×C42×C43—21no—
149C2×C42×C43C2311yescharacteristic
150#106×C43—22no—
151#103×C43—22no—
152#103×C43—22no—
153#103×C43—22no—
154#103×C43—22no—
155#103×C43—22no—
156#103×C43—41no—
157#102×C43—22no—
158#102×C43—22no—
159#102×C43—22no—
160#102×C43D414yescomplemented
161C22⋊C8×C43—22no—
162C22⋊C8×C43—22no—
163C22⋊C8×C43—41no—
164#95×C43—21no—
165#95×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170#41×C43—28no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175#41×C43—44no—
176#41×C43—44no—
177#41×C43—44no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43C2×D412yes—
189C2×Q8×C43C2×D412yes—
190C2×D4×C43—24no—
191C2×D4×C43—22no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—22no—
196C2×D4×C43—24no—
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—41no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43—42no—
207C2×D4×C43—42no—
208C2×D4×C43—42no—
209C2×D4×C43—42no—
210C2×D4×C43—42no—
211C2×D4×C43—81no—
212C2×D4×C43—81no—
213C2×D4×C43—81no—
214C2×D4×C43C2×D412yes—
215C2×D4×C43C2×D412yes—
216C2×D4×C43#4112yes—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—24no—
222C22×C4×C43—24no—
223C22×C4×C43—24no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
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×C43C2×D412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43C2×D411yescharacteristic
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2411yescharacteristic
249SD16×C43—44no—
250SD16×C43—44no—
251D8×C43—44no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—44no—
264C2×C8×C43C2×D412yes—
265C4⋊C4×C43—24no—
266C4⋊C4×C43—24no—
267C4⋊C4×C43—24no—
268C4⋊C4×C43—22no—
269C4⋊C4×C43—24no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—81no—
277C4⋊C4×C43C2×D412yes—
278C4⋊C4×C43C2×D412yes—
279C22⋊C4×C43—24no—
280C22⋊C4×C43—24no—
281C22⋊C4×C43—22no—
282C22⋊C4×C43—24no—
283C22⋊C4×C43—22no—
284C22⋊C4×C43—42no—
285C22⋊C4×C43—42no—
286C22⋊C4×C43—42no—
287C22⋊C4×C43—42no—
288C22⋊C4×C43—81no—
289C22⋊C4×C43—81no—
290C42×C43—21no—
291C42×C43—21no—
292C42×C43—42no—
293C23×C43—22no—
294C23×C43—21no—
295C23×C43—22no—
296C23×C43—21no—
297C23×C43—22no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43#12012yes—
321C23×C43C22×D411yescharacteristic
322Q8×C43—22no—
323Q8×C43—22no—
324Q8×C43—22no—
325Q8×C43—22no—
326Q8×C43—41no—
327Q8×C43—41no—
328Q8×C43—41no—
329Q8×C43—41no—
330D4×C43—22no—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—44no—
334D4×C43—48no—
335D4×C43—48no—
336D4×C43—41no—
337D4×C43—41no—
338D4×C43—41no—
339D4×C43—41no—
340D4×C43—84no—
341D4×C43—84no—
342D4×C43#12114yes—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—21no—
352C2×C4×C43—22no—
353C2×C4×C43—21no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—48no—
362C2×C4×C43—48no—
363C2×C4×C43—48no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43#12012yes—
383C2×C4×C43#13512yes—
384C2×C4×C43C22×D411yescharacteristic
385C2×C4×C43C22×D411yescharacteristic
386C2×C4×C43C22×D411yescharacteristic
387C2×C4×C43C2×#4111yescharacteristic
388C2×C4×C43H(5,𝔽2)11yescharacteristic
389C2×C4×C43H(5,𝔽2)11yescharacteristic
390C8×C43—22no—
391C8×C43—41no—
392C8×C43—41no—
393C8×C43—41no—
394#24438C4311yesmaximal, characteristic, direct product factor, Sylow
395C22×C43—24no—
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—41no—
402C22×C43—42no—
403C22×C43—41no—
404C22×C43—42no—
405C22×C43—41no—
406C22×C43—42no—
407C22×C43—41no—
408C22×C43—42no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43—41no—
415C22×C43—41no—
416C22×C43—81no—
417C22×C43—81no—
418C22×C43—81no—
419C22×C43—81no—
420C22×C43—81no—
421C22×C43—81no—
422C22×C43—81no—
423C22×C43C2×#12011yescharacteristic
424C22×C43D4211yescharacteristic
425C22×C43#54611yescharacteristic
426C22×C43C2×#13511yescharacteristic
427C22×C43#57511yescharacteristic
428C22×C43#57711yescharacteristic
429C22×C43#57711yescharacteristic
430C4×C43—22no—
431C4×C43—22no—
432C4×C43—41no—
433C4×C43—42no—
434C4×C43—42no—
435C4×C43—42no—
436C4×C43—41no—
437C4×C43—42no—
438C4×C43—81no—
439C4×C43—81no—
440C4×C43C2×#12111yescharacteristic
441C4×C43#53411yescharacteristic
442C4×C43D4211yescharacteristic
443C4×C43#54611yescharacteristic
444C2×#547C2×C4311yescharacteristic, complemented
445C2×#465C2×C4311yescharacteristic, complemented
446C2×#449C2×C4311yescharacteristic, complemented
447C2×#449C2×C4311yescharacteristic, complemented
448C2×#416C2×C4311yescharacteristic, complemented
449#2414C2×C4311yescharacteristic, complemented
450#2043C2×C4311yescharacteristic, complemented
451#2035C2×C4311yescharacteristic, complemented
452#2013C2×C4311yescharacteristic, complemented
453#2000C2×C4311yescharacteristic, complemented
454#1879C2×C4311yescharacteristic, complemented
455#1873C2×C4311yescharacteristic, complemented
456#1869C2×C4311yescharacteristic, complemented
457#1864C2×C4311yescharacteristic, complemented
458#1788C2×C4311yescharacteristic, complemented
459C2×C43—42no—
460C2×C43—44no—
461C2×C43—81no—
462C2×C43—161no—
463C2×C43#241011yescharacteristic
464C2×C43#300211yescharacteristic
465C2×C43#301011yescharacteristic
466C2×C43#326711yescharacteristic
467C2×C43#328411yescharacteristic
468C2×C43#330311yescharacteristic
469C2×C43#330711yescharacteristic
470C22×#41C22×C4311yescharacteristic
471C22×#41C22×C4311yescharacteristic
472C22×SD16C22×C4311yescharacteristic
473C22×SD16C22×C4311yescharacteristic
474C22×D8C22×C4311yescharacteristic
475C23×C8C22×C4311yescharacteristic
476#547—24no—
477#547—24no—
478C2×C4⋊Q8C22×C4311yescharacteristic
479C2×#123—21no—
480C2×#123—21no—
481C2×C22⋊Q8C22×C4311yescharacteristic
482C2×C22⋊Q8C22×C4311yescharacteristic
483C2×#121—21no—
484C2×#121C22×C4311yescharacteristic
485C2×#121C22×C4311yescharacteristic
486C2×C4×D4C22×C4311yescharacteristic
487C2×C4×D4C22×C4311yescharacteristic
488C2×#117C22×C4311yescharacteristic
489C22×C4⋊C4—21no—
490#465—24no—
491#449—24no—
492#449—24no—
493C2×#106C22×C4311yescharacteristic
494#416—24no—
495C2×#103C22×C4311yescharacteristic
496C2×#103C22×C4311yescharacteristic
497C2×#103C22×C4311yescharacteristic
498C2×#103C22×C4311yescharacteristic
499C2×#103C22×C4311yescharacteristic
500C2×#103C22×C4311yescharacteristic
501C2×#102C22×C4311yescharacteristic
502C2×#102C22×C4311yescharacteristic
503C2×#102C22×C4311yescharacteristic
504C2×#102C22×C4311yescharacteristic
505C2×C22⋊C8C22×C4311yescharacteristic
506C2×C22⋊C8C22×C4311yescharacteristic
507C2×C22⋊C8C22×C4311yescharacteristic
508#394—21no—
509#392—21no—
510#390—21no—
511#390C22×C4311yescharacteristic
512#389C22×C4311yescharacteristic
513#388—21no—
514#380C22×C4311yescharacteristic
515#340C22×C4311yescharacteristic
516#340C22×C4311yescharacteristic
517#336C22×C4311yescharacteristic
518#336C22×C4311yescharacteristic
519C43#2443811yescharacteristic, direct product factor, Sylow
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41D4×C4314yescomplemented
532C22×Q8C23×C4311yescharacteristic
533C22×Q8C23×C4311yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4D4×C4311yescharacteristic
539C22×D4C23×C4311yescharacteristic
540C22×D4C23×C4311yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C23×C4311yescharacteristic
545C23×C4C23×C4311yescharacteristic
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8C23×C4311yescharacteristic
559C22×C8C23×C4311yescharacteristic
560C22×C8C23×C4311yescharacteristic
561C22×C8C23×C4311yescharacteristic
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564#123—28no—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8D4×C4314yescomplemented
570#121—28no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579#117—22no—
580#117—41no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4D4×C4311yescharacteristic
588C2×C4⋊C4C23×C4311yescharacteristic
589C2×C4⋊C4C23×C4311yescharacteristic
590C2×C4⋊C4C23×C4311yescharacteristic
591C2×C4⋊C4C23×C4311yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C4311yescharacteristic
602C2×C22⋊C4D4×C4311yescharacteristic
603C2×C42—21no—
604C2×C42C23×C4311yescharacteristic
605#106—22no—
606#103—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—41no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102D4×C4314yescomplemented
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—41no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C4311yescharacteristic
624C24C2×D4×C4311yescharacteristic
625#41—28no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C4312yes—
644C2×Q8C2×D4×C4312yes—
645C2×D4—24no—
646C2×D4—22no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—41no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—81no—
667C2×D4—81no—
668C2×D4—81no—
669C2×D4C2×D4×C4312yes—
670C2×D4C2×D4×C4312yes—
671C2×D4#41×C4312yes—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4C2×D4×C4311yescharacteristic
698C22×C4C2×D4×C4311yescharacteristic
699C22×C4C2×D4×C4311yescharacteristic
700C22×C4C2×D4×C4312yes—
701C22×C4C2×D4×C4312yes—
702C22×C4C2×D4×C4311yescharacteristic
703C22×C4C24×C4311yescharacteristic
704SD16—44no—
705SD16—44no—
706D8—44no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—44no—
719C2×C8C2×D4×C4312yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—22no—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—81no—
732C4⋊C4C2×D4×C4312yes—
733C4⋊C4C2×D4×C4312yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C42—21no—
746C42—21no—
747C42—42no—
748C23—22no—
749C23—21no—
750C23—22no—
751C23—21no—
752C23—22no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23#120×C4312yes—
776C23C22×D4×C4311yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—48no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4#121×C4314yes—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—48no—
817C2×C4—48no—
818C2×C4—48no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4#120×C4312yes—
838C2×C4#135×C4312yes—
839C2×C4C22×D4×C4311yescharacteristic
840C2×C4C22×D4×C4311yescharacteristic
841C2×C4C22×D4×C4311yescharacteristic
842C2×C4C2×#41×C4311yescharacteristic
843C2×C4H(5,𝔽2)×C4311yescharacteristic
844C2×C4H(5,𝔽2)×C4311yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—24no—
851C22—22no—
852C22—22no—
853C22—42no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C4311yescharacteristic
878C22D42×C4311yescharacteristic
879C22C43×#54611yescharacteristic
880C22C2×#135×C4311yescharacteristic
881C22C43×#57511yescharacteristic
882C22C43×#57711yescharacteristic
883C22C43×#57711yescharacteristic
884C4—22no—
885C4—22no—
886C4—41no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×#121×C4311yescharacteristic
895C4C43×#53411yescharacteristic
896C4D42×C4311yescharacteristic
897C4C43×#54611yescharacteristic
898C2—42no—
899C2—44no—
900C2—81no—
901C2—161no—
902C2C43×#241011yescharacteristic
903C2C43×#300211yescharacteristic
904C2C43×#301011yescharacteristic
905C2C43×#326711yescharacteristic
906C2C43×#328411yescharacteristic
907C2C43×#330311yescharacteristic
908C2C43×#330711yescharacteristic
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×#547C2semidirect
2. C2×C43×#465C2semidirect
3. C2×C43×#449C2semidirect
4. C2×C43×#449C2semidirect
5. C2×C43×#416C2semidirect
6. C43×#2414C2semidirect
7. C43×#2043C2semidirect
8. C43×#2035C2semidirect
9. C43×#2013C2semidirect
10. C43×#2000C2semidirect
11. C43×#1879C2semidirect
12. C43×#1873C2semidirect
13. C43×#1869C2semidirect
14. C43×#1864C2semidirect
15. C43×#1788C2semidirect
76. C2×#41×C43D4semidirect
114. C22⋊Q8×C43D4semidirect
160. #102×C43D4semidirect
394. #24438C43direct (N × H)
444. C2×#547C2×C43semidirect
445. C2×#465C2×C43semidirect
446. C2×#449C2×C43semidirect
447. C2×#449C2×C43semidirect
448. C2×#416C2×C43semidirect
449. #2414C2×C43semidirect
450. #2043C2×C43semidirect
451. #2035C2×C43semidirect
452. #2013C2×C43semidirect
453. #2000C2×C43semidirect
454. #1879C2×C43semidirect
455. #1873C2×C43semidirect
456. #1869C2×C43semidirect
457. #1864C2×C43semidirect
458. #1788C2×C43semidirect
519. C43#24438direct (N × H)
531. C2×#41D4×C43semidirect
569. C22⋊Q8D4×C43semidirect
615. #102D4×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×#4652
C2×C43×#4492
C2×C43×#4162
C43×#24142
C43×#20432
C43×#20352
C43×#20132
C43×#20002
C43×#18792
C43×#18732
C43×#18692
C43×#18642
C43×#17882
#2443843