Finite Group Databasebeta

← C43×#24470 #24944487

Subgroups — C43×#24470 #24944487

Order 11008.

1360 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3489C211yesmaximal, characteristic
2C43×#3056C211yesmaximal, characteristic, complemented
3C2×C43×#456C211yesmaximal, characteristic, complemented
4C43×#3007C211yesmaximal, characteristic, complemented
5C2×C43×#421C211yesmaximal, characteristic, complemented
6C43×#2621C211yesmaximal, characteristic, complemented
7C43×#2040C211yesmaximal, characteristic, complemented
8C43×#2038C211yesmaximal, characteristic, complemented
9C43×#2007C211yesmaximal, characteristic, complemented
10C43×#2005C211yesmaximal, characteristic, complemented
11C43×#1901C211yesmaximal, characteristic, complemented
12C43×#1897C211yesmaximal, characteristic, complemented
13C43×#1882C211yesmaximal, characteristic, complemented
14C43×#1860C211yesmaximal, characteristic, complemented
15C43×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C2×#137×C43C2211yescharacteristic
19C2×#137×C43C2211yescharacteristic
20C2×#137×C43C2211yescharacteristic, complemented
21C22×M16×C43C2211yescharacteristic
22D4×Q8×C43—21no—
23C43×#548—21no—
24C43×#547—21no—
25C43×#547—22no—
26C43×#546—21no—
27C43×#546—22no—
28C43×#537—21no—
29C43×#537C2211yescharacteristic
30C43×#536—21no—
31C43×#536C2211yescharacteristic
32C2×C4⋊Q8×C43C2211yescharacteristic, complemented
33C43×#525—21no—
34C43×#525C2211yescharacteristic
35C2×C22⋊Q8×C43—21no—
36C2×C22⋊Q8×C43C2211yescharacteristic
37C2×C22⋊Q8×C43C2211yescharacteristic
38C43×#520C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C43×#470—21no—
41C43×#468—21no—
42C43×#467—21no—
43C43×#465—21no—
44C43×#456—24no—
45C43×#452—21no—
46C43×#452—21no—
47C43×#451—21no—
48C43×#450—21no—
49C43×#428C2211yescharacteristic, complemented
50C43×#421—24no—
51C2×#104×C43C2211yescharacteristic
52C2×#104×C43C2211yescharacteristic
53C2×#104×C43C2211yescharacteristic
54C2×#104×C43C2211yescharacteristic
55C2×#104×C43C2211yescharacteristic, complemented
56C2×#104×C43C2211yescharacteristic, complemented
57C43×#419C2211yescharacteristic, complemented
58C43×#417C2211yescharacteristic
59C43×#417C2211yescharacteristic
60C43×#417C2211yescharacteristic, complemented
61C2×#101×C43C2211yescharacteristic, complemented
62C2×#101×C43C2211yescharacteristic, complemented
63C43×#407C2211yescharacteristic
64C43×#398—22no—
65C43×#397—22no—
66C43×#391C2211yescharacteristic, complemented
67C43×#391C2211yescharacteristic, complemented
68C43×#382C2211yescharacteristic, complemented
69C43×#343C2211yescharacteristic, complemented
70C43×#343C2211yescharacteristic, complemented
71C43×#339C2211yescharacteristic, complemented
72C43×#339C2211yescharacteristic, complemented
732−1+4×C43—22no—
742−1+4×C43—22no—
752−1+4×C43—41no—
762−1+4×C43—41no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—22no—
81C2×#41×C43—21no—
82C2×#41×C43—22no—
83C2×#41×C43—22no—
84C2×#41×C43—41no—
85C2×#41×C43—41no—
86C2×#41×C43D411yescharacteristic
87C2×#41×C43D411yescharacteristic
88C2×#41×C43C2311yescharacteristic
89C2×#41×C43C2311yescharacteristic
90C2×#41×C43C2311yescharacteristic
91C22×Q8×C43—21no—
92C22×Q8×C43—21no—
93C22×Q8×C43D411yescharacteristic
94C22×Q8×C43C2311yescharacteristic
95C22×Q8×C43C2311yescharacteristic
96C22×D4×C43—21no—
97C22×D4×C43D411yescharacteristic
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100#137×C43—22no—
101#137×C43—22no—
102#137×C43—22no—
103#137×C43—41no—
104#137×C43—41no—
105#137×C43—41no—
106C2×Q16×C43—21no—
107C2×Q16×C43—21no—
108C2×Q16×C43—21no—
109C2×SD16×C43—21no—
110C2×SD16×C43—21no—
111C2×SD16×C43—21no—
112C2×M16×C43—21no—
113C2×M16×C43—22no—
114C2×M16×C43—41no—
115C2×M16×C43C2311yescharacteristic
116C2×M16×C43C2311yescharacteristic
117C2×M16×C43C2311yescharacteristic
118C2×M16×C43C2311yescharacteristic
119C22×C8×C43—21no—
120C4⋊Q8×C43—22no—
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43—22no—
123C4⋊Q8×C43—41no—
124#124×C43—22no—
125#124×C43—21no—
126#123×C43—22no—
127#123×C43—22no—
128#123×C43—22no—
129#123×C43—21no—
130#123×C43—22no—
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43—22no—
133C22⋊Q8×C43—22no—
134C22⋊Q8×C43—21no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43—21no—
137C22⋊Q8×C43—21no—
138C22⋊Q8×C43—21no—
139C22⋊Q8×C43—21no—
140C22⋊Q8×C43—21no—
141C22⋊Q8×C43—21no—
142C22⋊Q8×C43—21no—
143C22⋊Q8×C43—21no—
144C22⋊Q8×C43—21no—
145C22⋊Q8×C43—21no—
146C22⋊Q8×C43D411yescharacteristic
147C22⋊Q8×C43D411yescharacteristic
148#121×C43—22no—
149#121×C43—22no—
150#121×C43—22no—
151#121×C43—21no—
152#121×C43—21no—
153#121×C43—22no—
154#121×C43D411yescharacteristic
155#121×C43D411yescharacteristic
156#120×C43—22no—
157#120×C43—21no—
158C4×Q8×C43—21no—
159C4×D4×C43—22no—
160C4×D4×C43—22no—
161C4×D4×C43—21no—
162C4×D4×C43—22no—
163C4×D4×C43—21no—
164C4×D4×C43—21no—
165#117×C43—21no—
166#117×C43—22no—
167#117×C43—41no—
168#117×C43C2311yescharacteristic
169C2×C4⋊C4×C43—22no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43—22no—
174C2×C4⋊C4×C43D412yes—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—22no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43D412yes—
181C2×C42×C43C2311yescharacteristic
182C2×C42×C43C2311yescharacteristic
183#107×C43—21no—
184#106×C43—21no—
185#104×C43—22no—
186#104×C43—22no—
187#104×C43—22no—
188#104×C43—22no—
189#104×C43—41no—
190#104×C43D414yescomplemented
191#103×C43—21no—
192#103×C43—21no—
193#103×C43—21no—
194#103×C43—21no—
195#103×C43—21no—
196#102×C43—21no—
197#102×C43—21no—
198#102×C43—21no—
199#101×C43—22no—
200#101×C43—41no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43—21no—
203#95×C43—22no—
204#95×C43—22no—
205#95×C43—22no—
206C24×C43—21no—
207C24×C43C2×D411yescharacteristic
208#41×C43—21no—
209#41×C43—21no—
210#41×C43—22no—
211#41×C43—22no—
212#41×C43—21no—
213#41×C43—21no—
214#41×C43—21no—
215#41×C43—21no—
216#41×C43—21no—
217#41×C43—21no—
218#41×C43—21no—
219#41×C43—21no—
220#41×C43—42no—
221#41×C43—42no—
222#41×C43—41no—
223#41×C43—41no—
224#41×C43—42no—
225#41×C43—42no—
226#41×C43—42no—
227#41×C43—42no—
228#41×C43—44no—
229#41×C43—44no—
230#41×C43—42no—
231#41×C43—42no—
232#41×C43C2×D412yes—
233#41×C43#4112yes—
234C2×Q8×C43—22no—
235C2×Q8×C43—21no—
236C2×Q8×C43—21no—
237C2×Q8×C43—21no—
238C2×Q8×C43—21no—
239C2×Q8×C43—21no—
240C2×Q8×C43—21no—
241C2×Q8×C43—21no—
242C2×Q8×C43—22no—
243C2×Q8×C43—21no—
244C2×Q8×C43—21no—
245C2×Q8×C43—21no—
246C2×Q8×C43—21no—
247C2×Q8×C43—21no—
248C2×Q8×C43—21no—
249C2×Q8×C43—41no—
250C2×Q8×C43—42no—
251C2×Q8×C43—42no—
252C2×Q8×C43—42no—
253C2×Q8×C43—42no—
254C2×Q8×C43C2×D411yescharacteristic
255C2×Q8×C43C2×D411yescharacteristic
256C2×Q8×C43C2×D411yescharacteristic
257C2×D4×C43—22no—
258C2×D4×C43—22no—
259C2×D4×C43—21no—
260C2×D4×C43—21no—
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—22no—
268C2×D4×C43—42no—
269C2×D4×C43—42no—
270C2×D4×C43—41no—
271C2×D4×C43C2×D411yescharacteristic
272C2×D4×C43C2×D411yescharacteristic
273C2×D4×C43C2×D411yescharacteristic
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—21no—
277C22×C4×C43—21no—
278C22×C4×C43—21no—
279C22×C4×C43—22no—
280C22×C4×C43—22no—
281C22×C4×C43—22no—
282C22×C4×C43—21no—
283C22×C4×C43—21no—
284C22×C4×C43—21no—
285C22×C4×C43—21no—
286C22×C4×C43—21no—
287C22×C4×C43—21no—
288C22×C4×C43—21no—
289C22×C4×C43—21no—
290C22×C4×C43—21no—
291C22×C4×C43—42no—
292C22×C4×C43—42no—
293C22×C4×C43C2×D411yescharacteristic
294C22×C4×C43C2×D411yescharacteristic
295C22×C4×C43C2×D411yescharacteristic
296C22×C4×C43C2×D411yescharacteristic
297C22×C4×C43C2×D412yes—
298C22×C4×C43C2×D411yescharacteristic
299C22×C4×C43C2×D412yes—
300C22×C4×C43C2411yescharacteristic
301Q16×C43—42no—
302Q16×C43—42no—
303Q16×C43—42no—
304SD16×C43—42no—
305SD16×C43—42no—
306SD16×C43—42no—
307M16×C43—21no—
308M16×C43—21no—
309M16×C43—21no—
310M16×C43—21no—
311M16×C43—21no—
312M16×C43—21no—
313M16×C43—21no—
314M16×C43—42no—
315M16×C43C2×D412yes—
316C2×C8×C43—21no—
317C2×C8×C43—21no—
318C2×C8×C43—21no—
319C2×C8×C43—21no—
320C2×C8×C43—42no—
321C4⋊C4×C43—22no—
322C4⋊C4×C43—22no—
323C4⋊C4×C43—22no—
324C4⋊C4×C43—22no—
325C4⋊C4×C43—21no—
326C4⋊C4×C43—22no—
327C4⋊C4×C43—22no—
328C4⋊C4×C43—21no—
329C4⋊C4×C43—21no—
330C4⋊C4×C43—21no—
331C4⋊C4×C43—21no—
332C4⋊C4×C43—21no—
333C4⋊C4×C43—42no—
334C4⋊C4×C43—44no—
335C4⋊C4×C43—41no—
336C4⋊C4×C43—41no—
337C4⋊C4×C43C2×D411yescharacteristic
338C4⋊C4×C43C2×D411yescharacteristic
339C22⋊C4×C43—22no—
340C22⋊C4×C43—22no—
341C22⋊C4×C43—22no—
342C22⋊C4×C43—22no—
343C22⋊C4×C43—22no—
344C22⋊C4×C43—21no—
345C22⋊C4×C43—21no—
346C22⋊C4×C43—21no—
347C22⋊C4×C43—22no—
348C22⋊C4×C43—22no—
349C22⋊C4×C43—21no—
350C22⋊C4×C43—21no—
351C22⋊C4×C43—42no—
352C22⋊C4×C43—41no—
353C22⋊C4×C43—41no—
354C42×C43—22no—
355C42×C43—21no—
356C42×C43—21no—
357C42×C43—21no—
358C42×C43—21no—
359C42×C43C2×D412yes—
360C23×C43—21no—
361C23×C43—21no—
362C23×C43—21no—
363C23×C43—21no—
364C23×C43—21no—
365C23×C43—41no—
366C23×C43—41no—
367C23×C43—42no—
368C23×C43—42no—
369C23×C43—81no—
370C23×C43#12011yescharacteristic
371C23×C43#12011yescharacteristic
372C23×C43C22×D411yescharacteristic
373Q8×C43—21no—
374Q8×C43—21no—
375Q8×C43—21no—
376Q8×C43—21no—
377Q8×C43—21no—
378Q8×C43—42no—
379Q8×C43—44no—
380Q8×C43—41no—
381Q8×C43—41no—
382Q8×C43—41no—
383Q8×C43—41no—
384Q8×C43—41no—
385Q8×C43—41no—
386Q8×C43—41no—
387Q8×C43—41no—
388Q8×C43#12112yes—
389D4×C43—22no—
390D4×C43—22no—
391D4×C43—21no—
392D4×C43—21no—
393D4×C43—21no—
394D4×C43—21no—
395D4×C43—21no—
396D4×C43—42no—
397D4×C43—42no—
398D4×C43—42no—
399D4×C43—42no—
400D4×C43—44no—
401D4×C43—41no—
402D4×C43—41no—
403D4×C43—41no—
404D4×C43—41no—
405D4×C43—81no—
406D4×C43—82no—
407D4×C43#12112yes—
408C2×C4×C43—21no—
409C2×C4×C43—21no—
410C2×C4×C43—21no—
411C2×C4×C43—21no—
412C2×C4×C43—21no—
413C2×C4×C43—21no—
414C2×C4×C43—21no—
415C2×C4×C43—21no—
416C2×C4×C43—21no—
417C2×C4×C43—22no—
418C2×C4×C43—21no—
419C2×C4×C43—21no—
420C2×C4×C43—22no—
421C2×C4×C43—21no—
422C2×C4×C43—22no—
423C2×C4×C43—21no—
424C2×C4×C43—21no—
425C2×C4×C43—22no—
426C2×C4×C43—21no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—42no—
431C2×C4×C43—42no—
432C2×C4×C43—42no—
433C2×C4×C43—44no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—44no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—42no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—42no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—82no—
451C2×C4×C43#12011yescharacteristic
452C2×C4×C43#12011yescharacteristic
453C2×C4×C43C22×D411yescharacteristic
454C2×C4×C43C22×D411yescharacteristic
455C2×C4×C43C22×D411yescharacteristic
456C2×C4×C43C2×#4111yescharacteristic
457C2×C4×C43H(5,𝔽2)11yescharacteristic
458C2×C4×C43H(5,𝔽2)11yescharacteristic
459C8×C43—22no—
460C8×C43—41no—
461C8×C43—41no—
462C8×C43—41no—
463#24470C4311yesmaximal, characteristic, direct product factor, Sylow
464C22×C43—21no—
465C22×C43—21no—
466C22×C43—21no—
467C22×C43—21no—
468C22×C43—22no—
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—41no—
474C22×C43—41no—
475C22×C43—41no—
476C22×C43—41no—
477C22×C43—41no—
478C22×C43—41no—
479C22×C43—41no—
480C22×C43—41no—
481C22×C43—81no—
482C22×C43—81no—
483C22×C43—84no—
484C22×C43C2×#12011yescharacteristic
485C22×C43D4211yescharacteristic
486C22×C43#54611yescharacteristic
487C4×C43—21no—
488C4×C43—21no—
489C4×C43—22no—
490C4×C43—42no—
491C4×C43—42no—
492C4×C43—41no—
493C4×C43—41no—
494C4×C43—41no—
495C4×C43—42no—
496C4×C43—41no—
497C4×C43—81no—
498C4×C43—81no—
499C4×C43—81no—
500C4×C43C2×#12111yescharacteristic
501C4×C43#53411yescharacteristic
502C4×C43D4211yescharacteristic
503C4×C43#54611yescharacteristic
504#3489C2×C4311yescharacteristic
505#3056C2×C4311yescharacteristic, complemented
506C2×#456C2×C4311yescharacteristic, complemented
507#3007C2×C4311yescharacteristic, complemented
508C2×#421C2×C4311yescharacteristic, complemented
509#2621C2×C4311yescharacteristic, complemented
510#2040C2×C4311yescharacteristic, complemented
511#2038C2×C4311yescharacteristic, complemented
512#2007C2×C4311yescharacteristic, complemented
513#2005C2×C4311yescharacteristic, complemented
514#1901C2×C4311yescharacteristic, complemented
515#1897C2×C4311yescharacteristic, complemented
516#1882C2×C4311yescharacteristic, complemented
517#1860C2×C4311yescharacteristic, complemented
518#1793C2×C4311yescharacteristic, complemented
519C2×C43—21no—
520C2×C43—21no—
521C2×C43—41no—
522C2×C43—41no—
523C2×C43—42no—
524C2×C43—81no—
525C2×C43—81no—
526C2×C43#241011yescharacteristic
527C2×C43#302011yescharacteristic
528C2×C43#302211yescharacteristic
529C2×2−1+4C22×C4311yescharacteristic
530C22×#41C22×C4311yescharacteristic
531C2×#137C22×C4311yescharacteristic
532C2×#137C22×C4311yescharacteristic
533C2×#137C22×C4311yescharacteristic, complemented
534C22×M16C22×C4311yescharacteristic
535D4×Q8—21no—
536#548—21no—
537#547—21no—
538#547—22no—
539#546—21no—
540#546—22no—
541#537—21no—
542#537C22×C4311yescharacteristic
543#536—21no—
544#536C22×C4311yescharacteristic
545C2×C4⋊Q8C22×C4311yescharacteristic, complemented
546#525—21no—
547#525C22×C4311yescharacteristic
548C2×C22⋊Q8—21no—
549C2×C22⋊Q8C22×C4311yescharacteristic
550C2×C22⋊Q8C22×C4311yescharacteristic
551#520C22×C4311yescharacteristic
552C2×#117C22×C4311yescharacteristic
553#470—21no—
554#468—21no—
555#467—21no—
556#465—21no—
557#456—24no—
558#452—21no—
559#452—21no—
560#451—21no—
561#450—21no—
562#428C22×C4311yescharacteristic, complemented
563#421—24no—
564C2×#104C22×C4311yescharacteristic
565C2×#104C22×C4311yescharacteristic
566C2×#104C22×C4311yescharacteristic
567C2×#104C22×C4311yescharacteristic
568C2×#104C22×C4311yescharacteristic, complemented
569C2×#104C22×C4311yescharacteristic, complemented
570#419C22×C4311yescharacteristic, complemented
571#417C22×C4311yescharacteristic
572#417C22×C4311yescharacteristic
573#417C22×C4311yescharacteristic, complemented
574C2×#101C22×C4311yescharacteristic, complemented
575C2×#101C22×C4311yescharacteristic, complemented
576#407C22×C4311yescharacteristic
577#398—22no—
578#397—22no—
579#391C22×C4311yescharacteristic, complemented
580#391C22×C4311yescharacteristic, complemented
581#382C22×C4311yescharacteristic, complemented
582#343C22×C4311yescharacteristic, complemented
583#343C22×C4311yescharacteristic, complemented
584#339C22×C4311yescharacteristic, complemented
585#339C22×C4311yescharacteristic, complemented
586C43#2447011yescharacteristic, direct product factor, Sylow
5872−1+4—22no—
5882−1+4—22no—
5892−1+4—41no—
5902−1+4—41no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—22no—
595C2×#41—21no—
596C2×#41—22no—
597C2×#41—22no—
598C2×#41—41no—
599C2×#41—41no—
600C2×#41D4×C4311yescharacteristic
601C2×#41D4×C4311yescharacteristic
602C2×#41C23×C4311yescharacteristic
603C2×#41C23×C4311yescharacteristic
604C2×#41C23×C4311yescharacteristic
605C22×Q8—21no—
606C22×Q8—21no—
607C22×Q8D4×C4311yescharacteristic
608C22×Q8C23×C4311yescharacteristic
609C22×Q8C23×C4311yescharacteristic
610C22×D4—21no—
611C22×D4D4×C4311yescharacteristic
612C23×C4—21no—
613C23×C4C23×C4311yescharacteristic
614#137—22no—
615#137—22no—
616#137—22no—
617#137—41no—
618#137—41no—
619#137—41no—
620C2×Q16—21no—
621C2×Q16—21no—
622C2×Q16—21no—
623C2×SD16—21no—
624C2×SD16—21no—
625C2×SD16—21no—
626C2×M16—21no—
627C2×M16—22no—
628C2×M16—41no—
629C2×M16C23×C4311yescharacteristic
630C2×M16C23×C4311yescharacteristic
631C2×M16C23×C4311yescharacteristic
632C2×M16C23×C4311yescharacteristic
633C22×C8—21no—
634C4⋊Q8—22no—
635C4⋊Q8—21no—
636C4⋊Q8—22no—
637C4⋊Q8—41no—
638#124—22no—
639#124—21no—
640#123—22no—
641#123—22no—
642#123—22no—
643#123—21no—
644#123—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—21no—
649C22⋊Q8—21no—
650C22⋊Q8—21no—
651C22⋊Q8—21no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8—21no—
658C22⋊Q8—21no—
659C22⋊Q8—21no—
660C22⋊Q8D4×C4311yescharacteristic
661C22⋊Q8D4×C4311yescharacteristic
662#121—22no—
663#121—22no—
664#121—22no—
665#121—21no—
666#121—21no—
667#121—22no—
668#121D4×C4311yescharacteristic
669#121D4×C4311yescharacteristic
670#120—22no—
671#120—21no—
672C4×Q8—21no—
673C4×D4—22no—
674C4×D4—22no—
675C4×D4—21no—
676C4×D4—22no—
677C4×D4—21no—
678C4×D4—21no—
679#117—21no—
680#117—22no—
681#117—41no—
682#117C23×C4311yescharacteristic
683C2×C4⋊C4—22no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4D4×C4312yes—
689C2×C4⋊C4C23×C4311yescharacteristic
690C2×C4⋊C4C23×C4311yescharacteristic
691C2×C22⋊C4—22no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4D4×C4312yes—
695C2×C42C23×C4311yescharacteristic
696C2×C42C23×C4311yescharacteristic
697#107—21no—
698#106—21no—
699#104—22no—
700#104—22no—
701#104—22no—
702#104—22no—
703#104—41no—
704#104D4×C4314yescomplemented
705#103—21no—
706#103—21no—
707#103—21no—
708#103—21no—
709#103—21no—
710#102—21no—
711#102—21no—
712#102—21no—
713#101—22no—
714#101—41no—
715C22⋊C8—21no—
716C22⋊C8—21no—
717#95—22no—
718#95—22no—
719#95—22no—
720C24—21no—
721C24C2×D4×C4311yescharacteristic
722#41—21no—
723#41—21no—
724#41—22no—
725#41—22no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—42no—
735#41—42no—
736#41—41no—
737#41—41no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—44no—
744#41—42no—
745#41—42no—
746#41C2×D4×C4312yes—
747#41#41×C4312yes—
748C2×Q8—22no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—22no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—42no—
768C2×Q8C2×D4×C4311yescharacteristic
769C2×Q8C2×D4×C4311yescharacteristic
770C2×Q8C2×D4×C4311yescharacteristic
771C2×D4—21no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4C2×D4×C4311yescharacteristic
786C2×D4C2×D4×C4311yescharacteristic
787C2×D4C2×D4×C4311yescharacteristic
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4C2×D4×C4312yes—
808C22×C4C2×D4×C4311yescharacteristic
809C22×C4C2×D4×C4311yescharacteristic
810C22×C4C2×D4×C4311yescharacteristic
811C22×C4C2×D4×C4311yescharacteristic
812C22×C4C2×D4×C4311yescharacteristic
813C22×C4C2×D4×C4312yes—
814C22×C4C24×C4311yescharacteristic
815Q16—42no—
816Q16—42no—
817Q16—42no—
818SD16—42no—
819SD16—42no—
820SD16—42no—
821M16—21no—
822M16—21no—
823M16—21no—
824M16—21no—
825M16—21no—
826M16—21no—
827M16—21no—
828M16—42no—
829M16C2×D4×C4312yes—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—42no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—21no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—42no—
848C4⋊C4—44no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4C2×D4×C4311yescharacteristic
852C4⋊C4C2×D4×C4311yescharacteristic
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—21no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—42no—
866C22⋊C4—41no—
867C22⋊C4—41no—
868C42—22no—
869C42—21no—
870C42—21no—
871C42—21no—
872C42—21no—
873C42C2×D4×C4312yes—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—81no—
884C23#120×C4311yescharacteristic
885C23#120×C4311yescharacteristic
886C23C22×D4×C4311yescharacteristic
887Q8—21no—
888Q8—21no—
889Q8—21no—
890Q8—21no—
891Q8—21no—
892Q8—42no—
893Q8—44no—
894Q8—41no—
895Q8—41no—
896Q8—41no—
897Q8—41no—
898Q8—41no—
899Q8—41no—
900Q8—41no—
901Q8—41no—
902Q8#121×C4312yes—
903D4—22no—
904D4—22no—
905D4—21no—
906D4—21no—
907D4—21no—
908D4—21no—
909D4—21no—
910D4—42no—
911D4—42no—
912D4—42no—
913D4—44no—
914D4—42no—
915D4—41no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—81no—
920D4—82no—
921D4#121×C4312yes—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—42no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—82no—
965C2×C4#120×C4311yescharacteristic
966C2×C4#120×C4311yescharacteristic
967C2×C4C22×D4×C4311yescharacteristic
968C2×C4C22×D4×C4311yescharacteristic
969C2×C4C22×D4×C4311yescharacteristic
970C2×C4C2×#41×C4311yescharacteristic
971C2×C4H(5,𝔽2)×C4311yescharacteristic
972C2×C4H(5,𝔽2)×C4311yescharacteristic
973C8—22no—
974C8—41no—
975C8—41no—
976C8—41no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—22no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—81no—
995C22—81no—
996C22—84no—
997C22C2×#120×C4311yescharacteristic
998C22D42×C4311yescharacteristic
999C22C43×#54611yescharacteristic
1000C4—21no—
1001C4—21no—
1002C4—22no—
1003C4—42no—
1004C4—42no—
1005C4—41no—
1006C4—41no—
1007C4—41no—
1008C4—42no—
1009C4—41no—
1010C4—81no—
1011C4—81no—
1012C4—81no—
1013C4C2×#121×C4311yescharacteristic
1014C4C43×#53411yescharacteristic
1015C4D42×C4311yescharacteristic
1016C4C43×#54611yescharacteristic
1017C2—21no—
1018C2—21no—
1019C2—41no—
1020C2—41no—
1021C2—42no—
1022C2—81no—
1023C2—81no—
1024C2C43×#241011yescharacteristic
1025C2C43×#302011yescharacteristic
1026C2C43×#302211yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C43×#3056C2semidirect
3. C2×C43×#456C2semidirect
4. C43×#3007C2semidirect
5. C2×C43×#421C2semidirect
6. C43×#2621C2semidirect
7. C43×#2040C2semidirect
8. C43×#2038C2semidirect
9. C43×#2007C2semidirect
10. C43×#2005C2semidirect
11. C43×#1901C2semidirect
12. C43×#1897C2semidirect
13. C43×#1882C2semidirect
14. C43×#1860C2semidirect
15. C43×#1793C2semidirect
20. C2×#137×C43C22semidirect
32. C2×C4⋊Q8×C43C22semidirect
49. C43×#428C22semidirect
55. C2×#104×C43C22semidirect
56. C2×#104×C43C22semidirect
57. C43×#419C22semidirect
60. C43×#417C22semidirect
61. C2×#101×C43C22semidirect
62. C2×#101×C43C22semidirect
66. C43×#391C22semidirect
67. C43×#391C22semidirect
68. C43×#382C22semidirect
69. C43×#343C22semidirect
70. C43×#343C22semidirect
71. C43×#339C22semidirect
72. C43×#339C22semidirect
190. #104×C43D4semidirect
463. #24470C43direct (N × H)
505. #3056C2×C43semidirect
506. C2×#456C2×C43semidirect
507. #3007C2×C43semidirect
508. C2×#421C2×C43semidirect
509. #2621C2×C43semidirect
510. #2040C2×C43semidirect
511. #2038C2×C43semidirect
512. #2007C2×C43semidirect
513. #2005C2×C43semidirect
514. #1901C2×C43semidirect
515. #1897C2×C43semidirect
516. #1882C2×C43semidirect
517. #1860C2×C43semidirect
518. #1793C2×C43semidirect
533. C2×#137C22×C43semidirect
545. C2×C4⋊Q8C22×C43semidirect
562. #428C22×C43semidirect
568. C2×#104C22×C43semidirect
569. C2×#104C22×C43semidirect
570. #419C22×C43semidirect
573. #417C22×C43semidirect
574. C2×#101C22×C43semidirect
575. C2×#101C22×C43semidirect
579. #391C22×C43semidirect
580. #391C22×C43semidirect
581. #382C22×C43semidirect
582. #343C22×C43semidirect
583. #343C22×C43semidirect
584. #339C22×C43semidirect
585. #339C22×C43semidirect
586. C43#24470direct (N × H)
704. #104D4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34892
C43×#30562
C2×C43×#4562
C43×#30072
C2×C43×#4212
C43×#26212
C43×#20402
C43×#20382
C43×#20072
C43×#20052
C43×#19012
C43×#18972
C43×#18822
C43×#18602
C43×#17932
#2447043