Finite Group Databasebeta

← C43×#18447 #24938464

Subgroups — C43×#18447 #24938464

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3534C211yesmaximal, characteristic
2C43×#3193C211yesmaximal, characteristic, complemented
3C43×#3190C211yesmaximal, characteristic, complemented
4C43×#2814C211yesmaximal, characteristic, complemented
5C43×#1612C211yesmaximal, characteristic, complemented
6C43×#1610C211yesmaximal, characteristic, complemented
7C43×#1609C211yesmaximal, characteristic, complemented
8C43×#1607C211yesmaximal, characteristic, complemented
9C43×#1606C211yesmaximal, characteristic, complemented
10C43×#1604C211yesmaximal, characteristic, complemented
11C43×#1603C211yesmaximal, characteristic, complemented
12C43×#1601C211yesmaximal, characteristic, complemented
13C43×#1519C211yesmaximal, characteristic, complemented
14C43×#1513C211yesmaximal, characteristic, complemented
15C43×#1468C211yesmaximal, characteristic, complemented
16C43×#562—21no—
17C43×#560—21no—
18C43×#553—21no—
19C43×#551—21no—
20C43×#546—21no—
21C43×#546—21no—
22C43×#546—21no—
23D42×C43—21no—
24C43×#540—21no—
25C43×#539—21no—
26C43×#539C2211yescharacteristic
27C43×#538—21no—
28C43×#538C2211yescharacteristic
29C43×#537C2211yescharacteristic
30C43×#534—21no—
31C43×#534C2211yescharacteristic
32C43×#525C2211yescharacteristic
33C2×#123×C43C2211yescharacteristic
34C2×C22⋊Q8×C43C2211yescharacteristic, complemented
35C2×#121×C43C2211yescharacteristic
36C43×#485—21no—
37C43×#484—21no—
38C43×#483C2211yescharacteristic, complemented
39C43×#480C2211yescharacteristic
40C43×#480C2211yescharacteristic, complemented
41C43×#480C2211yescharacteristic, complemented
42C43×#468—21no—
43C43×#468—21no—
44C43×#467—21no—
45C43×#465—21no—
46C43×#452—21no—
47C43×#451C2211yescharacteristic, complemented
48C43×#450—21no—
49C43×#448C2211yescharacteristic
50C43×#448C2211yescharacteristic, complemented
51C43×#448C2211yescharacteristic, complemented
52C43×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic, complemented
54C43×#398—21no—
55C43×#398C2211yescharacteristic, complemented
56C43×#397—21no—
57C43×#397C2211yescharacteristic, complemented
58C43×#396—21no—
59C43×#395C2211yescharacteristic, complemented
60C43×#394—21no—
61C43×#393C2211yescharacteristic, complemented
62C43×#380C2211yescharacteristic, complemented
63C43×#328C2211yescharacteristic, complemented
64C43×#328C2211yescharacteristic, complemented
65C43×#327C2211yescharacteristic
66C43×#327C2211yescharacteristic
67C43×#327C2211yescharacteristic, complemented
68C43×#327C2211yescharacteristic, complemented
69C43×#327C2211yescharacteristic, complemented
70C43×#327C2211yescharacteristic, complemented
71C43×#324C2211yescharacteristic, complemented
72C43×#324C2211yescharacteristic, complemented
73C43×#323C2211yescharacteristic, complemented
74C43×#323C2211yescharacteristic, complemented
75C2×#41×C43—21no—
76C2×#41×C43D411yescharacteristic
77C22×Q8×C43C2311yescharacteristic
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43D411yescharacteristic
82C22×D4×C43D411yescharacteristic
83C23×C4×C43C2311yescharacteristic
84C2×Q16×C43—21no—
85C2×SD16×C43—21no—
86C2×SD16×C43—21no—
87C2×SD16×C43—21no—
88C2×M16×C43—21no—
89C22×C8×C43—21no—
90#127×C43—21no—
91#126×C43—21no—
92#126×C43—21no—
93#126×C43—21no—
94#126×C43—21no—
95#125×C43—21no—
96#125×C43—21no—
97#124×C43—21no—
98#124×C43—21no—
99#124×C43—21no—
100#123×C43—21no—
101#123×C43—21no—
102#123×C43—21no—
103#123×C43—21no—
104#123×C43—21no—
105#123×C43—21no—
106#123×C43—21no—
107#123×C43—21no—
108#123×C43—21no—
109#123×C43—21no—
110#123×C43—21no—
111#123×C43—21no—
112#123×C43—21no—
113#123×C43—21no—
114C22⋊Q8×C43—21no—
115C22⋊Q8×C43—21no—
116C22⋊Q8×C43—21no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—21no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43D411yescharacteristic
124C22⋊Q8×C43C2311yescharacteristic
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134#121×C43—21no—
135#121×C43—21no—
136#121×C43—21no—
137#121×C43—21no—
138#121×C43—21no—
139#121×C43—21no—
140#121×C43D411yescharacteristic
141#121×C43D411yescharacteristic
142#121×C43D411yescharacteristic
143#121×C43C2311yescharacteristic
144#121×C43C2311yescharacteristic
145#121×C43C2311yescharacteristic
146#120×C43—21no—
147#120×C43—21no—
148#120×C43—21no—
149#120×C43—21no—
150#120×C43—21no—
151#120×C43—21no—
152#120×C43—21no—
153#120×C43—21no—
154C4×D4×C43—21no—
155C4×D4×C43—21no—
156C4×D4×C43—21no—
157C4×D4×C43—21no—
158C4×D4×C43—21no—
159C4×D4×C43—21no—
160C4×D4×C43—21no—
161C4×D4×C43—21no—
162#117×C43—21no—
163#117×C43D411yescharacteristic
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43D411yescharacteristic
169C2×C4⋊C4×C43D411yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43D411yescharacteristic
180C2×C22⋊C4×C43D411yescharacteristic
181C2×C22⋊C4×C43C2311yescharacteristic
182#107×C43—21no—
183#107×C43—21no—
184#107×C43—21no—
185#106×C43—21no—
186#103×C43—21no—
187#103×C43—21no—
188#103×C43—21no—
189#103×C43—21no—
190#103×C43—21no—
191#102×C43—21no—
192#102×C43—21no—
193#102×C43—21no—
194C22⋊C8×C43—21no—
195C22⋊C8×C43—21no—
196C22⋊C8×C43C2311yescharacteristic
197C22⋊C8×C43C2311yescharacteristic
198C22⋊C8×C43C2311yescharacteristic
199C22⋊C8×C43C2311yescharacteristic
200#95×C43—21no—
201#95×C43—21no—
202#95×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43—21no—
207C24×C43—21no—
208C24×C43C2×D411yescharacteristic
209C24×C43C2×D411yescharacteristic
210#41×C43—81no—
211#41×C43—81no—
212#41×C43—81no—
213C2×Q8×C43—21no—
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43—81no—
217C2×Q8×C43C2×D411yescharacteristic
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—21no—
235C2×D4×C43—81no—
236C2×D4×C43—81no—
237C2×D4×C43—81no—
238C2×D4×C43—81no—
239C2×D4×C43—81no—
240C2×D4×C43—81no—
241C2×D4×C43—82no—
242C2×D4×C43C2×D411yescharacteristic
243C2×D4×C43C2×D411yescharacteristic
244C2×D4×C43C2×D411yescharacteristic
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—81no—
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2×D411yescharacteristic
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2411yescharacteristic
266Q16×C43—81no—
267SD16×C43—81no—
268SD16×C43—81no—
269SD16×C43—81no—
270M16×C43—81no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—21no—
275C2×C8×C43—81no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43—21no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43—21no—
289C4⋊C4×C43—21no—
290C4⋊C4×C43—21no—
291C4⋊C4×C43—41no—
292C4⋊C4×C43—41no—
293C4⋊C4×C43—81no—
294C4⋊C4×C43—81no—
295C4⋊C4×C43—81no—
296C4⋊C4×C43C2×D411yescharacteristic
297C4⋊C4×C43C2×D411yescharacteristic
298C4⋊C4×C43C2×D411yescharacteristic
299C4⋊C4×C43C2×D411yescharacteristic
300C22⋊C4×C43—21no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43—21no—
310C22⋊C4×C43—21no—
311C22⋊C4×C43—21no—
312C22⋊C4×C43—21no—
313C22⋊C4×C43—21no—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—21no—
316C22⋊C4×C43—21no—
317C22⋊C4×C43—21no—
318C22⋊C4×C43—21no—
319C22⋊C4×C43—21no—
320C22⋊C4×C43—21no—
321C22⋊C4×C43—21no—
322C22⋊C4×C43—21no—
323C22⋊C4×C43—21no—
324C22⋊C4×C43—21no—
325C22⋊C4×C43—41no—
326C22⋊C4×C43—41no—
327C22⋊C4×C43—81no—
328C22⋊C4×C43—81no—
329C22⋊C4×C43—81no—
330C42×C43—21no—
331C42×C43—21no—
332C42×C43—21no—
333C23×C43—21no—
334C23×C43—21no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—21no—
339C23×C43—21no—
340C23×C43—21no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—42no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—81no—
347C23×C43—81no—
348C23×C43—81no—
349C23×C43—81no—
350C23×C43—81no—
351C23×C43#12011yescharacteristic
352C23×C43#12011yescharacteristic
353C23×C43C22×D411yescharacteristic
354Q8×C43—41no—
355Q8×C43—41no—
356Q8×C43—41no—
357Q8×C43—41no—
358Q8×C43—41no—
359Q8×C43—81no—
360D4×C43—41no—
361D4×C43—41no—
362D4×C43—41no—
363D4×C43—42no—
364D4×C43—42no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—81no—
372D4×C43—81no—
373D4×C43—81no—
374D4×C43—81no—
375D4×C43—81no—
376D4×C43—81no—
377D4×C43—81no—
378D4×C43—81no—
379D4×C43—81no—
380D4×C43—81no—
381D4×C43—81no—
382D4×C43—81no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—21no—
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43—41no—
402C2×C4×C43—41no—
403C2×C4×C43—41no—
404C2×C4×C43—41no—
405C2×C4×C43—41no—
406C2×C4×C43—41no—
407C2×C4×C43—41no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—81no—
414C2×C4×C43—81no—
415C2×C4×C43—81no—
416C2×C4×C43—81no—
417C2×C4×C43—81no—
418C2×C4×C43—81no—
419C2×C4×C43—81no—
420C2×C4×C43#12011yescharacteristic
421C2×C4×C43#12011yescharacteristic
422C2×C4×C43C22×D411yescharacteristic
423C2×C4×C43C22×D411yescharacteristic
424C8×C43—41no—
425C8×C43—41no—
426C8×C43—41no—
427C8×C43—41no—
428#18447C4311yesmaximal, characteristic, direct product factor, Sylow
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—41no—
442C22×C43—41no—
443C22×C43—41no—
444C22×C43—41no—
445C22×C43—41no—
446C22×C43—41no—
447C22×C43—41no—
448C22×C43—41no—
449C22×C43—81no—
450C22×C43—81no—
451C22×C43—81no—
452C22×C43—81no—
453C22×C43—162no—
454C22×C43—162no—
455C22×C43C2×#12011yescharacteristic
456C22×C43#57611yescharacteristic
457C22×C43#57711yescharacteristic
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—21no—
462C4×C43—41no—
463C4×C43—41no—
464C4×C43—41no—
465C4×C43—41no—
466C4×C43—41no—
467C4×C43—41no—
468C4×C43—41no—
469C4×C43—41no—
470C4×C43—81no—
471C4×C43—81no—
472C4×C43—81no—
473C4×C43—81no—
474#3534C2×C4311yescharacteristic
475#3193C2×C4311yescharacteristic, complemented
476#3190C2×C4311yescharacteristic, complemented
477#2814C2×C4311yescharacteristic, complemented
478#1612C2×C4311yescharacteristic, complemented
479#1610C2×C4311yescharacteristic, complemented
480#1609C2×C4311yescharacteristic, complemented
481#1607C2×C4311yescharacteristic, complemented
482#1606C2×C4311yescharacteristic, complemented
483#1604C2×C4311yescharacteristic, complemented
484#1603C2×C4311yescharacteristic, complemented
485#1601C2×C4311yescharacteristic, complemented
486#1519C2×C4311yescharacteristic, complemented
487#1513C2×C4311yescharacteristic, complemented
488#1468C2×C4311yescharacteristic, complemented
489C2×C43—21no—
490C2×C43—21no—
491C2×C43—41no—
492C2×C43—41no—
493C2×C43—81no—
494C2×C43—81no—
495C2×C43—81no—
496C2×C43—81no—
497C2×C43#301211yescharacteristic
498C2×C43#302211yescharacteristic
499C2×C43#302611yescharacteristic
500#562—21no—
501#560—21no—
502#553—21no—
503#551—21no—
504#546—21no—
505#546—21no—
506#546—21no—
507D42—21no—
508#540—21no—
509#539—21no—
510#539C22×C4311yescharacteristic
511#538—21no—
512#538C22×C4311yescharacteristic
513#537C22×C4311yescharacteristic
514#534—21no—
515#534C22×C4311yescharacteristic
516#525C22×C4311yescharacteristic
517C2×#123C22×C4311yescharacteristic
518C2×C22⋊Q8C22×C4311yescharacteristic, complemented
519C2×#121C22×C4311yescharacteristic
520#485—21no—
521#484—21no—
522#483C22×C4311yescharacteristic, complemented
523#480C22×C4311yescharacteristic
524#480C22×C4311yescharacteristic, complemented
525#480C22×C4311yescharacteristic, complemented
526#468—21no—
527#468—21no—
528#467—21no—
529#465—21no—
530#452—21no—
531#451C22×C4311yescharacteristic, complemented
532#450—21no—
533#448C22×C4311yescharacteristic
534#448C22×C4311yescharacteristic, complemented
535#448C22×C4311yescharacteristic, complemented
536#407C22×C4311yescharacteristic, complemented
537C2×C22⋊C8C22×C4311yescharacteristic, complemented
538#398—21no—
539#398C22×C4311yescharacteristic, complemented
540#397—21no—
541#397C22×C4311yescharacteristic, complemented
542#396—21no—
543#395C22×C4311yescharacteristic, complemented
544#394—21no—
545#393C22×C4311yescharacteristic, complemented
546#380C22×C4311yescharacteristic, complemented
547#328C22×C4311yescharacteristic, complemented
548#328C22×C4311yescharacteristic, complemented
549#327C22×C4311yescharacteristic
550#327C22×C4311yescharacteristic
551#327C22×C4311yescharacteristic, complemented
552#327C22×C4311yescharacteristic, complemented
553#327C22×C4311yescharacteristic, complemented
554#327C22×C4311yescharacteristic, complemented
555#324C22×C4311yescharacteristic, complemented
556#324C22×C4311yescharacteristic, complemented
557#323C22×C4311yescharacteristic, complemented
558#323C22×C4311yescharacteristic, complemented
559C43#1844711yescharacteristic, direct product factor, Sylow
560C2×#41—21no—
561C2×#41D4×C4311yescharacteristic
562C22×Q8C23×C4311yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C4311yescharacteristic
567C22×D4D4×C4311yescharacteristic
568C23×C4C23×C4311yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C4311yescharacteristic
609C22⋊Q8C23×C4311yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C4311yescharacteristic
626#121D4×C4311yescharacteristic
627#121D4×C4311yescharacteristic
628#121C23×C4311yescharacteristic
629#121C23×C4311yescharacteristic
630#121C23×C4311yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C4311yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4D4×C4311yescharacteristic
654C2×C4⋊C4D4×C4311yescharacteristic
655C2×C4⋊C4C23×C4311yescharacteristic
656C2×C4⋊C4C23×C4311yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4D4×C4311yescharacteristic
665C2×C22⋊C4D4×C4311yescharacteristic
666C2×C22⋊C4C23×C4311yescharacteristic
667#107—21no—
668#107—21no—
669#107—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C4311yescharacteristic
682C22⋊C8C23×C4311yescharacteristic
683C22⋊C8C23×C4311yescharacteristic
684C22⋊C8C23×C4311yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C4311yescharacteristic
690#95C23×C4311yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C4311yescharacteristic
694C24C2×D4×C4311yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C4311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C4311yescharacteristic
728C2×D4C2×D4×C4311yescharacteristic
729C2×D4C2×D4×C4311yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C4311yescharacteristic
743C22×C4C2×D4×C4311yescharacteristic
744C22×C4C2×D4×C4311yescharacteristic
745C22×C4C2×D4×C4311yescharacteristic
746C22×C4C2×D4×C4311yescharacteristic
747C22×C4C2×D4×C4311yescharacteristic
748C22×C4C2×D4×C4311yescharacteristic
749C22×C4C2×D4×C4311yescharacteristic
750C22×C4C24×C4311yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4—81no—
781C4⋊C4C2×D4×C4311yescharacteristic
782C4⋊C4C2×D4×C4311yescharacteristic
783C4⋊C4C2×D4×C4311yescharacteristic
784C4⋊C4C2×D4×C4311yescharacteristic
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4—81no—
815C42—21no—
816C42—21no—
817C42—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C4311yescharacteristic
837C23#120×C4311yescharacteristic
838C23C22×D4×C4311yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C4311yescharacteristic
906C2×C4#120×C4311yescharacteristic
907C2×C4C22×D4×C4311yescharacteristic
908C2×C4C22×D4×C4311yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C4311yescharacteristic
940C22C43×#57611yescharacteristic
941C22C43×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C43×#301211yescharacteristic
967C2C43×#302211yescharacteristic
968C2C43×#302611yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3193C2semidirect
3. C43×#3190C2semidirect
4. C43×#2814C2semidirect
5. C43×#1612C2semidirect
6. C43×#1610C2semidirect
7. C43×#1609C2semidirect
8. C43×#1607C2semidirect
9. C43×#1606C2semidirect
10. C43×#1604C2semidirect
11. C43×#1603C2semidirect
12. C43×#1601C2semidirect
13. C43×#1519C2semidirect
14. C43×#1513C2semidirect
15. C43×#1468C2semidirect
34. C2×C22⋊Q8×C43C22semidirect
38. C43×#483C22semidirect
40. C43×#480C22semidirect
41. C43×#480C22semidirect
47. C43×#451C22semidirect
50. C43×#448C22semidirect
51. C43×#448C22semidirect
52. C43×#407C22semidirect
53. C2×C22⋊C8×C43C22semidirect
55. C43×#398C22semidirect
57. C43×#397C22semidirect
59. C43×#395C22semidirect
61. C43×#393C22semidirect
62. C43×#380C22semidirect
63. C43×#328C22semidirect
64. C43×#328C22semidirect
67. C43×#327C22semidirect
68. C43×#327C22semidirect
69. C43×#327C22semidirect
70. C43×#327C22semidirect
71. C43×#324C22semidirect
72. C43×#324C22semidirect
73. C43×#323C22semidirect
74. C43×#323C22semidirect
428. #18447C43direct (N × H)
475. #3193C2×C43semidirect
476. #3190C2×C43semidirect
477. #2814C2×C43semidirect
478. #1612C2×C43semidirect
479. #1610C2×C43semidirect
480. #1609C2×C43semidirect
481. #1607C2×C43semidirect
482. #1606C2×C43semidirect
483. #1604C2×C43semidirect
484. #1603C2×C43semidirect
485. #1601C2×C43semidirect
486. #1519C2×C43semidirect
487. #1513C2×C43semidirect
488. #1468C2×C43semidirect
518. C2×C22⋊Q8C22×C43semidirect
522. #483C22×C43semidirect
524. #480C22×C43semidirect
525. #480C22×C43semidirect
531. #451C22×C43semidirect
534. #448C22×C43semidirect
535. #448C22×C43semidirect
536. #407C22×C43semidirect
537. C2×C22⋊C8C22×C43semidirect
539. #398C22×C43semidirect
541. #397C22×C43semidirect
543. #395C22×C43semidirect
545. #393C22×C43semidirect
546. #380C22×C43semidirect
547. #328C22×C43semidirect
548. #328C22×C43semidirect
551. #327C22×C43semidirect
552. #327C22×C43semidirect
553. #327C22×C43semidirect
554. #327C22×C43semidirect
555. #324C22×C43semidirect
556. #324C22×C43semidirect
557. #323C22×C43semidirect
558. #323C22×C43semidirect
559. C43#18447direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35342
C43×#31932
C43×#31902
C43×#28142
C43×#16122
C43×#16102
C43×#16092
C43×#16072
C43×#16062
C43×#16042
C43×#16032
C43×#16012
C43×#15192
C43×#15132
C43×#14682
#1844743