Finite Group Databasebeta

← C43×#28493 #24948510

Subgroups — C43×#28493 #24948510

Order 11008.

1278 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#496C211yesmaximal, characteristic, complemented
2C2×C43×#469C211yesmaximal, characteristic, complemented
3C2×C43×#468C211yesmaximal, characteristic, complemented
4C2×C43×#466C211yesmaximal, characteristic, complemented
5C2×C43×#465C211yesmaximal, characteristic, complemented
6C2×C43×#435C211yesmaximal, characteristic, complemented
7C43×#2541C211yesmaximal, characteristic, complemented
8C43×#2540C211yesmaximal, characteristic, complemented
9C43×#2000C211yesmaximal, characteristic, complemented
10C43×#2000C211yesmaximal, characteristic, complemented
11C43×#1999C211yesmaximal, characteristic, complemented
12C43×#1999C211yesmaximal, characteristic, complemented
13C43×#1983C211yesmaximal, characteristic, complemented
14C43×#1982C211yesmaximal, characteristic, complemented
15C43×#1776C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C22×D8×C43C2211yescharacteristic
20C22×M16×C43C2211yescharacteristic
21C23×C8×C43C2211yescharacteristic
22C2×#127×C43—21no—
23C2×#127×C43C2211yescharacteristic
24C2×#124×C43C2211yescharacteristic
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×C22⋊Q8×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×#121×C43C2211yescharacteristic
29C2×#121×C43C2211yescharacteristic
30C2×#121×C43C2211yescharacteristic
31C2×#121×C43C2211yescharacteristic
32C2×#121×C43C2211yescharacteristic
33C2×C4×D4×C43C2211yescharacteristic
34C43×#496—24no—
35C43×#469—24no—
36C43×#468—24no—
37C43×#466—24no—
38C43×#465—24no—
39C43×#435—24no—
40C2×#107×C43C2211yescharacteristic
41C2×#106×C43C2211yescharacteristic
42C2×C4⋊C8×C43C2211yescharacteristic
43C2×#103×C43C2211yescharacteristic
44C2×#103×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×#102×C43C2211yescharacteristic
48C2×#102×C43C2211yescharacteristic
49C2×#102×C43C2211yescharacteristic
50C2×#102×C43C2211yescharacteristic
51C2×C22⋊C8×C43C2211yescharacteristic
52C2×C22⋊C8×C43C2211yescharacteristic
53C2×#97×C43C2211yescharacteristic
54C43×#399—21no—
55C43×#392—21no—
56C43×#392—21no—
57C43×#392—21no—
58C43×#390—21no—
59C43×#390—21no—
60C43×#390—21no—
61C4×C4⋊C4×C43C2211yescharacteristic
62C4×C4⋊C4×C43C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C43×#340C2211yescharacteristic
65C22×Q8×C43C2311yescharacteristic
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43D411yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C22×D4×C43C2311yescharacteristic
77C22×D4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2311yescharacteristic
80C2×SD16×C43—22no—
81C2×SD16×C43—22no—
82C2×SD16×C43—22no—
83C2×SD16×C43—22no—
84C2×SD16×C43—41no—
85C2×SD16×C43—41no—
86C2×D8×C43—22no—
87C2×D8×C43—22no—
88C2×D8×C43—22no—
89C2×D8×C43—22no—
90C2×D8×C43—41no—
91C2×D8×C43—41no—
92C2×M16×C43—22no—
93C2×M16×C43—22no—
94C2×M16×C43—22no—
95C22×C8×C43—22no—
96C22×C8×C43—22no—
97C22×C8×C43—22no—
98C22×C8×C43C2311yescharacteristic
99C22×C8×C43C2311yescharacteristic
100C22×C8×C43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102#127×C43—22no—
103#127×C43—22no—
104#127×C43—44no—
105#124×C43—22no—
106#124×C43—22no—
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43—22no—
109C22⋊Q8×C43—41no—
110C22⋊Q8×C43—41no—
111#121×C43—22no—
112#121×C43—22no—
113#121×C43—22no—
114#121×C43—22no—
115#121×C43—22no—
116#121×C43—22no—
117#121×C43—41no—
118#121×C43—41no—
119#121×C43—41no—
120#121×C43—41no—
121#121×C43—41no—
122#121×C43—41no—
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
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×C43D411yescharacteristic
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C42×C43—21no—
145C2×C42×C43—21no—
146C2×C42×C43C2311yescharacteristic
147#107×C43D414yescomplemented
148#106×C43D414yescomplemented
149C4⋊C8×C43—22no—
150#103×C43—22no—
151#103×C43—22no—
152#102×C43—22no—
153#102×C43—22no—
154#102×C43—22no—
155#102×C43—22no—
156#102×C43—22no—
157#102×C43—22no—
158C22⋊C8×C43—22no—
159C22⋊C8×C43—22no—
160#97×C43D414yescomplemented
161#95×C43—21no—
162#95×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43C2×D411yescharacteristic
167C24×C43C2×D411yescharacteristic
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×D4×C43—22no—
175C2×D4×C43—22no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—41no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—42no—
199C2×D4×C43—42no—
200C2×D4×C43—42no—
201C2×D4×C43—42no—
202C2×D4×C43—42no—
203C2×D4×C43—42no—
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×C43—81no—
215C2×D4×C43—81no—
216C2×D4×C43—81no—
217C2×D4×C43—81no—
218C2×D4×C43—81no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2411yescharacteristic
241SD16×C43—44no—
242SD16×C43—44no—
243D8×C43—44no—
244D8×C43—44no—
245M16×C43—44no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—44no—
255C2×C8×C43C2×D412yes—
256C2×C8×C43C2×D412yes—
257C2×C8×C43C2×D412yes—
258C2×C8×C43C2×D412yes—
259C4⋊C4×C43—22no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—42no—
265C4⋊C4×C43—42no—
266C4⋊C4×C43C2×D412yes—
267C4⋊C4×C43C2×D412yes—
268C4⋊C4×C43C2×D412yes—
269C4⋊C4×C43C2×D412yes—
270C22⋊C4×C43—22no—
271C22⋊C4×C43—22no—
272C22⋊C4×C43—42no—
273C22⋊C4×C43—42no—
274C22⋊C4×C43—42no—
275C22⋊C4×C43—42no—
276C22⋊C4×C43—42no—
277C22⋊C4×C43—42no—
278C22⋊C4×C43—42no—
279C22⋊C4×C43—42no—
280C22⋊C4×C43—42no—
281C22⋊C4×C43—42no—
282C42×C43—42no—
283C42×C43—81no—
284C42×C43C2×D412yes—
285C42×C43#4112yes—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
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×C43AGL(1,ℤ/8)12yes—
321C23×C43C22×D411yescharacteristic
322Q8×C43—41no—
323Q8×C43—41no—
324Q8×C43—41no—
325Q8×C43—41no—
326D4×C43—44no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—41no—
332D4×C43—41no—
333D4×C43—41no—
334D4×C43—41no—
335D4×C43—41no—
336D4×C43—41no—
337D4×C43—41no—
338D4×C43—41no—
339D4×C43—84no—
340D4×C43—84no—
341D4×C43—84no—
342D4×C43—84no—
343D4×C43—84no—
344D4×C43—84no—
345D4×C43—84no—
346D4×C43—84no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
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#12112yes—
381C2×C4×C43#12112yes—
382C2×C4×C43C22×D411yescharacteristic
383C2×C4×C43C22×D411yescharacteristic
384C2×C4×C43C22×D411yescharacteristic
385C2×C4×C43C2×#4111yescharacteristic
386C2×C4×C43H(5,𝔽2)11yescharacteristic
387C2×C4×C43H(5,𝔽2)11yescharacteristic
388C8×C43—22no—
389C8×C43—41no—
390C8×C43—41no—
391C8×C43#12714yescomplemented
392#28493C4311yesmaximal, characteristic, direct product factor, Sylow
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43—81no—
408C22×C43—81no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43—81no—
413C22×C43—81no—
414C22×C43—81no—
415C22×C43—81no—
416C22×C43—81no—
417C22×C43—81no—
418C22×C43—81no—
419C22×C43—81no—
420C22×C43—81no—
421C22×C43—81no—
422C22×C43—81no—
423C22×C43—81no—
424C22×C43—81no—
425C22×C43—81no—
426C22×C43—81no—
427C22×C43—81no—
428C22×C43C2×#12111yescharacteristic
429C22×C43D4211yescharacteristic
430C22×C43D4211yescharacteristic
431C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
432C22×C43#57511yescharacteristic
433C22×C43#57611yescharacteristic
434C22×C43#57711yescharacteristic
435C4×C43—22no—
436C4×C43—22no—
437C4×C43—42no—
438C4×C43—42no—
439C4×C43—42no—
440C4×C43—42no—
441C4×C43—41no—
442C4×C43—41no—
443C4×C43—81no—
444C4×C43C2×#12711yescharacteristic
445C4×C43#53511yescharacteristic
446C4×C43#55011yescharacteristic
447C4×C43#55011yescharacteristic
448C2×#496C2×C4311yescharacteristic, complemented
449C2×#469C2×C4311yescharacteristic, complemented
450C2×#468C2×C4311yescharacteristic, complemented
451C2×#466C2×C4311yescharacteristic, complemented
452C2×#465C2×C4311yescharacteristic, complemented
453C2×#435C2×C4311yescharacteristic, complemented
454#2541C2×C4311yescharacteristic, complemented
455#2540C2×C4311yescharacteristic, complemented
456#2000C2×C4311yescharacteristic, complemented
457#2000C2×C4311yescharacteristic, complemented
458#1999C2×C4311yescharacteristic, complemented
459#1999C2×C4311yescharacteristic, complemented
460#1983C2×C4311yescharacteristic, complemented
461#1982C2×C4311yescharacteristic, complemented
462#1776C2×C4311yescharacteristic, complemented
463C2×C43—42no—
464C2×C43—81no—
465C2×C43—161no—
466C2×C43—161no—
467C2×C43—161no—
468C2×C43#254111yescharacteristic
469C2×C43#305511yescharacteristic
470C2×C43#306211yescharacteristic
471C2×C43#326411yescharacteristic
472C2×C43#326511yescharacteristic
473C2×C43#326811yescharacteristic
474C2×C43#327111yescharacteristic
475C22×SD16C22×C4311yescharacteristic
476C22×SD16C22×C4311yescharacteristic
477C22×D8C22×C4311yescharacteristic
478C22×D8C22×C4311yescharacteristic
479C22×M16C22×C4311yescharacteristic
480C23×C8C22×C4311yescharacteristic
481C2×#127—21no—
482C2×#127C22×C4311yescharacteristic
483C2×#124C22×C4311yescharacteristic
484C2×C22⋊Q8C22×C4311yescharacteristic
485C2×C22⋊Q8C22×C4311yescharacteristic
486C2×#121C22×C4311yescharacteristic
487C2×#121C22×C4311yescharacteristic
488C2×#121C22×C4311yescharacteristic
489C2×#121C22×C4311yescharacteristic
490C2×#121C22×C4311yescharacteristic
491C2×#121C22×C4311yescharacteristic
492C2×C4×D4C22×C4311yescharacteristic
493#496—24no—
494#469—24no—
495#468—24no—
496#466—24no—
497#465—24no—
498#435—24no—
499C2×#107C22×C4311yescharacteristic
500C2×#106C22×C4311yescharacteristic
501C2×C4⋊C8C22×C4311yescharacteristic
502C2×#103C22×C4311yescharacteristic
503C2×#103C22×C4311yescharacteristic
504C2×#102C22×C4311yescharacteristic
505C2×#102C22×C4311yescharacteristic
506C2×#102C22×C4311yescharacteristic
507C2×#102C22×C4311yescharacteristic
508C2×#102C22×C4311yescharacteristic
509C2×#102C22×C4311yescharacteristic
510C2×C22⋊C8C22×C4311yescharacteristic
511C2×C22⋊C8C22×C4311yescharacteristic
512C2×#97C22×C4311yescharacteristic
513#399—21no—
514#392—21no—
515#392—21no—
516#392—21no—
517#390—21no—
518#390—21no—
519#390—21no—
520C4×C4⋊C4C22×C4311yescharacteristic
521C4×C4⋊C4C22×C4311yescharacteristic
522#340C22×C4311yescharacteristic
523#340C22×C4311yescharacteristic
524C43#2849311yescharacteristic, direct product factor, Sylow
525C22×Q8C23×C4311yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4D4×C4311yescharacteristic
535C22×D4C23×C4311yescharacteristic
536C22×D4C23×C4311yescharacteristic
537C22×D4C23×C4311yescharacteristic
538C23×C4C23×C4311yescharacteristic
539C23×C4C23×C4311yescharacteristic
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—41no—
551C2×D8—41no—
552C2×M16—22no—
553C2×M16—22no—
554C2×M16—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8C23×C4311yescharacteristic
559C22×C8C23×C4311yescharacteristic
560C22×C8C23×C4311yescharacteristic
561C22×C8C23×C4311yescharacteristic
562#127—22no—
563#127—22no—
564#127—44no—
565#124—22no—
566#124—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583C4×D4—22no—
584C4×D4—22no—
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⋊C4—21no—
602C2×C22⋊C4D4×C4311yescharacteristic
603C2×C22⋊C4D4×C4311yescharacteristic
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C23×C4311yescharacteristic
607#107D4×C4314yescomplemented
608#106D4×C4314yescomplemented
609C4⋊C8—22no—
610#103—22no—
611#103—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620#97D4×C4314yescomplemented
621#95—21no—
622#95—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24C2×D4×C4311yescharacteristic
627C24C2×D4×C4311yescharacteristic
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—41no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4—81no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
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—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4C2×D4×C4311yescharacteristic
697C22×C4C2×D4×C4311yescharacteristic
698C22×C4C2×D4×C4311yescharacteristic
699C22×C4C2×D4×C4311yescharacteristic
700C22×C4C24×C4311yescharacteristic
701SD16—44no—
702SD16—44no—
703D8—44no—
704D8—44no—
705M16—44no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—44no—
715C2×C8C2×D4×C4312yes—
716C2×C8C2×D4×C4312yes—
717C2×C8C2×D4×C4312yes—
718C2×C8C2×D4×C4312yes—
719C4⋊C4—22no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—42no—
725C4⋊C4—42no—
726C4⋊C4C2×D4×C4312yes—
727C4⋊C4C2×D4×C4312yes—
728C4⋊C4C2×D4×C4312yes—
729C4⋊C4C2×D4×C4312yes—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—42no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C42—42no—
743C42—81no—
744C42C2×D4×C4312yes—
745C42#41×C4312yes—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23AGL(1,ℤ/8)×C4312yes—
781C23C22×D4×C4311yescharacteristic
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786D4—44no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—84no—
800D4—84no—
801D4—84no—
802D4—84no—
803D4—84no—
804D4—84no—
805D4—84no—
806D4—84no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
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—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4#121×C4312yes—
841C2×C4#121×C4312yes—
842C2×C4C22×D4×C4311yescharacteristic
843C2×C4C22×D4×C4311yescharacteristic
844C2×C4C22×D4×C4311yescharacteristic
845C2×C4C2×#41×C4311yescharacteristic
846C2×C4H(5,𝔽2)×C4311yescharacteristic
847C2×C4H(5,𝔽2)×C4311yescharacteristic
848C8—22no—
849C8—41no—
850C8—41no—
851C8#127×C4314yescomplemented
852C22—22no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22C2×#121×C4311yescharacteristic
888C22D42×C4311yescharacteristic
889C22D42×C4311yescharacteristic
890C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
891C22C43×#57511yescharacteristic
892C22C43×#57611yescharacteristic
893C22C43×#57711yescharacteristic
894C4—22no—
895C4—22no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—42no—
900C4—41no—
901C4—41no—
902C4—81no—
903C4C2×#127×C4311yescharacteristic
904C4C43×#53511yescharacteristic
905C4C43×#55011yescharacteristic
906C4C43×#55011yescharacteristic
907C2—42no—
908C2—81no—
909C2—161no—
910C2—161no—
911C2—161no—
912C2C43×#254111yescharacteristic
913C2C43×#305511yescharacteristic
914C2C43×#306211yescharacteristic
915C2C43×#326411yescharacteristic
916C2C43×#326511yescharacteristic
917C2C43×#326811yescharacteristic
918C2C43×#327111yescharacteristic
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×#496C2semidirect
2. C2×C43×#469C2semidirect
3. C2×C43×#468C2semidirect
4. C2×C43×#466C2semidirect
5. C2×C43×#465C2semidirect
6. C2×C43×#435C2semidirect
7. C43×#2541C2semidirect
8. C43×#2540C2semidirect
9. C43×#2000C2semidirect
10. C43×#2000C2semidirect
11. C43×#1999C2semidirect
12. C43×#1999C2semidirect
13. C43×#1983C2semidirect
14. C43×#1982C2semidirect
15. C43×#1776C2semidirect
147. #107×C43D4semidirect
148. #106×C43D4semidirect
160. #97×C43D4semidirect
391. C8×C43#127semidirect
392. #28493C43direct (N × H)
448. C2×#496C2×C43semidirect
449. C2×#469C2×C43semidirect
450. C2×#468C2×C43semidirect
451. C2×#466C2×C43semidirect
452. C2×#465C2×C43semidirect
453. C2×#435C2×C43semidirect
454. #2541C2×C43semidirect
455. #2540C2×C43semidirect
456. #2000C2×C43semidirect
457. #2000C2×C43semidirect
458. #1999C2×C43semidirect
459. #1999C2×C43semidirect
460. #1983C2×C43semidirect
461. #1982C2×C43semidirect
462. #1776C2×C43semidirect
524. C43#28493direct (N × H)
607. #107D4×C43semidirect
608. #106D4×C43semidirect
620. #97D4×C43semidirect
851. C8#127×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4962
C2×C43×#4692
C2×C43×#4682
C2×C43×#4662
C2×C43×#4652
C2×C43×#4352
C43×#25412
C43×#25402
C43×#20002
C43×#19992
C43×#19832
C43×#19822
C43×#17762
#2849343