Finite Group Databasebeta

← C43×#24403 #24944420

Subgroups — C43×#24403 #24944420

Order 11008.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#575C211yesmaximal, characteristic
2C2×C43×#473C211yesmaximal, characteristic, complemented
3C2×C43×#471C211yesmaximal, characteristic, complemented
4C43×#3007C211yesmaximal, characteristic, complemented
5C2×C43×#452C211yesmaximal, characteristic, complemented
6C43×#2880C211yesmaximal, characteristic, complemented
7C43×#2052C211yesmaximal, characteristic, complemented
8C43×#2051C211yesmaximal, characteristic, complemented
9C43×#2020C211yesmaximal, characteristic, complemented
10C43×#2019C211yesmaximal, characteristic, complemented
11C43×#1908C211yesmaximal, characteristic, complemented
12C43×#1907C211yesmaximal, characteristic, complemented
13C43×#1901C211yesmaximal, characteristic, complemented
14C43×#1855C211yesmaximal, characteristic, complemented
15C43×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×#41×C43C2211yescharacteristic
18C43×#575—24no—
19C43×#575—24no—
20C2×#137×C43—21no—
21C2×#137×C43C2211yescharacteristic
22C2×#137×C43C2211yescharacteristic
23C2×#137×C43C2211yescharacteristic
24C2×#137×C43C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C43—21no—
26C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
28C2×#135×C43—21no—
29C2×#135×C43—21no—
30C22×Q16×C43C2211yescharacteristic, complemented
31C22×SD16×C43C2211yescharacteristic, complemented
32C2×#131×C43C2211yescharacteristic
33C2×#131×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C2×C22⋊Q8×C43C2211yescharacteristic
36C43×#473—24no—
37C43×#471—24no—
38C43×#452—21no—
39C43×#452—21no—
40C43×#452—21no—
41C43×#452—21no—
42C43×#452—21no—
43C43×#452—21no—
44C43×#451—21no—
45C43×#450—21no—
46C2×#108×C43C2211yescharacteristic, complemented
47C2×#108×C43C2211yescharacteristic, complemented
48C43×#417C2211yescharacteristic
49C43×#417C2211yescharacteristic
50C2×#103×C43C2211yescharacteristic, complemented
51C2×#102×C43C2211yescharacteristic, complemented
52C2×#101×C43C2211yescharacteristic, complemented
53C2×#101×C43C2211yescharacteristic, complemented
54C2×#101×C43C2211yescharacteristic, complemented
55C2×#101×C43C2211yescharacteristic, complemented
56C2×#100×C43C2211yescharacteristic, complemented
57C2×#100×C43C2211yescharacteristic, complemented
58C43×#408—21no—
59C43×#408—21no—
60C43×#408C2211yescharacteristic
61C43×#408C2211yescharacteristic
62C43×#407—21no—
63C43×#407C2211yescharacteristic
64C43×#407C2211yescharacteristic
65C2×C22⋊C8×C43—21no—
66C2×C22⋊C8×C43C2211yescharacteristic
67C43×#343C2211yescharacteristic, complemented
68C43×#343C2211yescharacteristic, complemented
69C43×#341C2211yescharacteristic, complemented
70C43×#341C2211yescharacteristic, complemented
71C2×#41×C43—21no—
72C2×#41×C43—21no—
73C2×#41×C43—22no—
74C2×#41×C43—22no—
75C2×#41×C43—22no—
76C2×#41×C43—22no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—41no—
82C2×#41×C43—41no—
83C2×#41×C43—41no—
84C2×#41×C43—41no—
85C2×#41×C43D411yescharacteristic
86C2×#41×C43D411yescharacteristic
87C2×#41×C43C2311yescharacteristic
88C2×#41×C43C2311yescharacteristic
89C22×Q8×C43D411yescharacteristic
90C22×Q8×C43C2311yescharacteristic
91C22×Q8×C43C2311yescharacteristic
92C22×D4×C43—21no—
93C22×D4×C43—21no—
94C22×D4×C43D411yescharacteristic
95C22×D4×C43C2311yescharacteristic
96C23×C4×C43—21no—
97C23×C4×C43—21no—
98C23×C4×C43C2311yescharacteristic
99#137×C43—28no—
100#137×C43—22no—
101#137×C43—22no—
102#137×C43—22no—
103#137×C43—22no—
104#137×C43—22no—
105#137×C43—41no—
106#137×C43—41no—
107#137×C43D414yes—
108AGL(1,ℤ/8)×C43—28no—
109AGL(1,ℤ/8)×C43—22no—
110AGL(1,ℤ/8)×C43—22no—
111AGL(1,ℤ/8)×C43—22no—
112AGL(1,ℤ/8)×C43D414yes—
113#135×C43—28no—
114#135×C43—28no—
115C2×Q16×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43—22no—
118C2×Q16×C43—21no—
119C2×Q16×C43—21no—
120C2×Q16×C43—21no—
121C2×Q16×C43—21no—
122C2×Q16×C43—41no—
123C2×SD16×C43—21no—
124C2×SD16×C43—21no—
125C2×SD16×C43—21no—
126C2×SD16×C43—21no—
127C2×SD16×C43—22no—
128C2×SD16×C43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—21no—
132C2×SD16×C43—41no—
133C2×D8×C43—21no—
134C2×D8×C43—21no—
135#131×C43—22no—
136#131×C43—22no—
137#131×C43—41no—
138#131×C43—41no—
139C2×M16×C43—21no—
140C2×M16×C43—22no—
141C2×M16×C43—22no—
142C2×M16×C43—21no—
143C2×M16×C43—21no—
144C2×M16×C43C2311yescharacteristic
145C2×M16×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C2×M16×C43C2311yescharacteristic
150C22×C8×C43—21no—
151C22×C8×C43—21no—
152C22×C8×C43—21no—
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22⋊Q8×C43—21no—
156C22⋊Q8×C43—21no—
157C22⋊Q8×C43—21no—
158C22⋊Q8×C43—21no—
159C2×C4⋊C4×C43—21no—
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C22⋊C4×C43—21no—
162#108×C43—22no—
163#108×C43—22no—
164#103×C43—21no—
165#103×C43—21no—
166#103×C43—21no—
167#103×C43—21no—
168#102×C43—21no—
169#102×C43—21no—
170#102×C43—21no—
171#102×C43—21no—
172#101×C43—22no—
173#101×C43—22no—
174#101×C43—22no—
175#101×C43—41no—
176#100×C43—22no—
177#100×C43—41no—
178C22⋊C8×C43—21no—
179C22⋊C8×C43—21no—
180C22⋊C8×C43—21no—
181C22⋊C8×C43—21no—
182C22⋊C8×C43—21no—
183C22⋊C8×C43—21no—
184C22⋊C8×C43—21no—
185C22⋊C8×C43—21no—
186C22⋊C8×C43D411yescharacteristic
187C22⋊C8×C43D411yescharacteristic
188C22⋊C8×C43D411yescharacteristic
189C22⋊C8×C43D411yescharacteristic
190C24×C43—21no—
191C24×C43—21no—
192C24×C43#4111yescharacteristic
193#41×C43—21no—
194#41×C43—21no—
195#41×C43—24no—
196#41×C43—24no—
197#41×C43—22no—
198#41×C43—22no—
199#41×C43—21no—
200#41×C43—21no—
201#41×C43—21no—
202#41×C43—21no—
203#41×C43—42no—
204#41×C43—42no—
205#41×C43—41no—
206#41×C43—41no—
207#41×C43—42no—
208#41×C43—42no—
209#41×C43—42no—
210#41×C43—42no—
211#41×C43—42no—
212#41×C43—42no—
213#41×C43—42no—
214#41×C43—42no—
215#41×C43C2×D412yes—
216#41×C43C2×D412yes—
217C2×Q8×C43—21no—
218C2×Q8×C43—21no—
219C2×Q8×C43—22no—
220C2×Q8×C43—21no—
221C2×Q8×C43—21no—
222C2×Q8×C43—21no—
223C2×Q8×C43—21no—
224C2×Q8×C43—21no—
225C2×Q8×C43—21no—
226C2×Q8×C43—21no—
227C2×Q8×C43—21no—
228C2×Q8×C43—21no—
229C2×Q8×C43—21no—
230C2×Q8×C43—41no—
231C2×Q8×C43C2×D412yes—
232C2×Q8×C43C2×D411yescharacteristic
233C2×Q8×C43C2×D411yescharacteristic
234C2×D4×C43—21no—
235C2×D4×C43—21no—
236C2×D4×C43—21no—
237C2×D4×C43—21no—
238C2×D4×C43—21no—
239C2×D4×C43—21no—
240C2×D4×C43—22no—
241C2×D4×C43—21no—
242C2×D4×C43—21no—
243C2×D4×C43—21no—
244C2×D4×C43—21no—
245C2×D4×C43—42no—
246C2×D4×C43—42no—
247C2×D4×C43—42no—
248C2×D4×C43—42no—
249C2×D4×C43—41no—
250C2×D4×C43—41no—
251C2×D4×C43—41no—
252C2×D4×C43C2×D412yes—
253C2×D4×C43C2×D411yescharacteristic
254C2×D4×C43C2×D411yescharacteristic
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43—42no—
268C22×C4×C43—42no—
269C22×C4×C43—42no—
270C22×C4×C43—42no—
271C22×C4×C43—41no—
272C22×C4×C43—41no—
273C22×C4×C43C2×D411yescharacteristic
274C22×C4×C43C2×D411yescharacteristic
275C22×C4×C43C2×D411yescharacteristic
276C22×C4×C43C2×D411yescharacteristic
277C22×C4×C43#4111yescharacteristic
278C22×C4×C43C2411yescharacteristic
279Q16×C43—24no—
280Q16×C43—24no—
281Q16×C43—42no—
282Q16×C43—42no—
283Q16×C43—42no—
284Q16×C43—42no—
285SD16×C43—24no—
286SD16×C43—24no—
287SD16×C43—24no—
288SD16×C43—24no—
289SD16×C43—42no—
290SD16×C43—42no—
291SD16×C43—42no—
292SD16×C43—42no—
293D8×C43—24no—
294D8×C43—24no—
295M16×C43—24no—
296M16×C43—21no—
297M16×C43—21no—
298M16×C43—21no—
299M16×C43—21no—
300M16×C43—21no—
301M16×C43—21no—
302M16×C43—21no—
303M16×C43—21no—
304M16×C43—21no—
305M16×C43—21no—
306M16×C43—42no—
307M16×C43—42no—
308M16×C43C2×D412yes—
309M16×C43C2×D412yes—
310C2×C8×C43—24no—
311C2×C8×C43—21no—
312C2×C8×C43—21no—
313C2×C8×C43—21no—
314C2×C8×C43—21no—
315C2×C8×C43—21no—
316C2×C8×C43—21no—
317C2×C8×C43—21no—
318C2×C8×C43—21no—
319C2×C8×C43—21no—
320C2×C8×C43—21no—
321C2×C8×C43—42no—
322C2×C8×C43—42no—
323C2×C8×C43C2×D411yescharacteristic
324C2×C8×C43C2×D411yescharacteristic
325C2×C8×C43C2×D411yescharacteristic
326C2×C8×C43C2×D411yescharacteristic
327C4⋊C4×C43—21no—
328C4⋊C4×C43—21no—
329C4⋊C4×C43—41no—
330C4⋊C4×C43—41no—
331C22⋊C4×C43—41no—
332C22⋊C4×C43—41no—
333C23×C43—21no—
334C23×C43—21no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—22no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—42no—
341C23×C43—42no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—81no—
345C23×C43—81no—
346C23×C43—81no—
347C23×C43#12111yescharacteristic
348C23×C43#12111yescharacteristic
349C23×C43C2×#4111yescharacteristic
350Q8×C43—21no—
351Q8×C43—21no—
352Q8×C43—22no—
353Q8×C43—21no—
354Q8×C43—22no—
355Q8×C43—42no—
356Q8×C43—41no—
357Q8×C43—41no—
358Q8×C43—41no—
359Q8×C43—41no—
360Q8×C43—41no—
361Q8×C43—41no—
362Q8×C43#12012yes—
363D4×C43—22no—
364D4×C43—22no—
365D4×C43—21no—
366D4×C43—22no—
367D4×C43—21no—
368D4×C43—21no—
369D4×C43—22no—
370D4×C43—42no—
371D4×C43—42no—
372D4×C43—42no—
373D4×C43—44no—
374D4×C43—44no—
375D4×C43—41no—
376D4×C43—41no—
377D4×C43—41no—
378D4×C43—41no—
379D4×C43#12012yes—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—21no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—22no—
395C2×C4×C43—42no—
396C2×C4×C43—42no—
397C2×C4×C43—42no—
398C2×C4×C43—44no—
399C2×C4×C43—44no—
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—81no—
409C2×C4×C43#12111yescharacteristic
410C2×C4×C43#12111yescharacteristic
411C2×C4×C43C22×D411yescharacteristic
412C2×C4×C43C22×D411yescharacteristic
413C2×C4×C43C22×D411yescharacteristic
414C2×C4×C43C22×D411yescharacteristic
415C2×C4×C43H(5,𝔽2)11yescharacteristic
416C2×C4×C43H(5,𝔽2)11yescharacteristic
417C8×C43—22no—
418C8×C43—22no—
419C8×C43—21no—
420C8×C43—21no—
421C8×C43—21no—
422C8×C43—21no—
423C8×C43—41no—
424C8×C43—41no—
425C8×C43—41no—
426C8×C43—41no—
427#24403C4311yesmaximal, characteristic, direct product factor, Sylow
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—22no—
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—42no—
441C22×C43—41no—
442C22×C43—41no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43—82no—
446C22×C43—82no—
447C22×C43—84no—
448C22×C43—81no—
449C22×C43—81no—
450C22×C43C2×#12111yescharacteristic
451C22×C43#54611yescharacteristic
452C22×C43#54611yescharacteristic
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—22no—
456C4×C43—41no—
457C4×C43—42no—
458C4×C43—81no—
459C4×C43—81no—
460C4×C43C2×#12011yescharacteristic
461C4×C43#53411yescharacteristic
462C4×C43D4211yescharacteristic
463C4×C43D4211yescharacteristic
464C2×#575C2×C4311yescharacteristic
465C2×#473C2×C4311yescharacteristic, complemented
466C2×#471C2×C4311yescharacteristic, complemented
467#3007C2×C4311yescharacteristic, complemented
468C2×#452C2×C4311yescharacteristic, complemented
469#2880C2×C4311yescharacteristic, complemented
470#2052C2×C4311yescharacteristic, complemented
471#2051C2×C4311yescharacteristic, complemented
472#2020C2×C4311yescharacteristic, complemented
473#2019C2×C4311yescharacteristic, complemented
474#1908C2×C4311yescharacteristic, complemented
475#1907C2×C4311yescharacteristic, complemented
476#1901C2×C4311yescharacteristic, complemented
477#1855C2×C4311yescharacteristic, complemented
478#1785C2×C4311yescharacteristic, complemented
479C2×C43—21no—
480C2×C43—21no—
481C2×C43—41no—
482C2×C43—41no—
483C2×C43—42no—
484C2×C43—81no—
485C2×C43—82no—
486C2×C43#241011yescharacteristic
487C2×C43#306711yescharacteristic
488C2×C43#306911yescharacteristic
489C22×#41C22×C4311yescharacteristic
490C22×#41C22×C4311yescharacteristic
491#575—24no—
492#575—24no—
493C2×#137—21no—
494C2×#137C22×C4311yescharacteristic
495C2×#137C22×C4311yescharacteristic
496C2×#137C22×C4311yescharacteristic
497C2×#137C22×C4311yescharacteristic
498C2×AGL(1,ℤ/8)—21no—
499C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
500C2×AGL(1,ℤ/8)C22×C4311yescharacteristic
501C2×#135—21no—
502C2×#135—21no—
503C22×Q16C22×C4311yescharacteristic, complemented
504C22×SD16C22×C4311yescharacteristic, complemented
505C2×#131C22×C4311yescharacteristic
506C2×#131C22×C4311yescharacteristic
507C22×M16C22×C4311yescharacteristic
508C2×C22⋊Q8C22×C4311yescharacteristic
509#473—24no—
510#471—24no—
511#452—21no—
512#452—21no—
513#452—21no—
514#452—21no—
515#452—21no—
516#452—21no—
517#451—21no—
518#450—21no—
519C2×#108C22×C4311yescharacteristic, complemented
520C2×#108C22×C4311yescharacteristic, complemented
521#417C22×C4311yescharacteristic
522#417C22×C4311yescharacteristic
523C2×#103C22×C4311yescharacteristic, complemented
524C2×#102C22×C4311yescharacteristic, complemented
525C2×#101C22×C4311yescharacteristic, complemented
526C2×#101C22×C4311yescharacteristic, complemented
527C2×#101C22×C4311yescharacteristic, complemented
528C2×#101C22×C4311yescharacteristic, complemented
529C2×#100C22×C4311yescharacteristic, complemented
530C2×#100C22×C4311yescharacteristic, complemented
531#408—21no—
532#408—21no—
533#408C22×C4311yescharacteristic
534#408C22×C4311yescharacteristic
535#407—21no—
536#407C22×C4311yescharacteristic
537#407C22×C4311yescharacteristic
538C2×C22⋊C8—21no—
539C2×C22⋊C8C22×C4311yescharacteristic
540#343C22×C4311yescharacteristic, complemented
541#343C22×C4311yescharacteristic, complemented
542#341C22×C4311yescharacteristic, complemented
543#341C22×C4311yescharacteristic, complemented
544C43#2440311yescharacteristic, direct product factor, Sylow
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41—41no—
559C2×#41D4×C4311yescharacteristic
560C2×#41D4×C4311yescharacteristic
561C2×#41C23×C4311yescharacteristic
562C2×#41C23×C4311yescharacteristic
563C22×Q8D4×C4311yescharacteristic
564C22×Q8C23×C4311yescharacteristic
565C22×Q8C23×C4311yescharacteristic
566C22×D4—21no—
567C22×D4—21no—
568C22×D4D4×C4311yescharacteristic
569C22×D4C23×C4311yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C4311yescharacteristic
573#137—28no—
574#137—22no—
575#137—22no—
576#137—22no—
577#137—22no—
578#137—22no—
579#137—41no—
580#137—41no—
581#137D4×C4314yes—
582AGL(1,ℤ/8)—28no—
583AGL(1,ℤ/8)—22no—
584AGL(1,ℤ/8)—22no—
585AGL(1,ℤ/8)—22no—
586AGL(1,ℤ/8)D4×C4314yes—
587#135—28no—
588#135—28no—
589C2×Q16—21no—
590C2×Q16—21no—
591C2×Q16—22no—
592C2×Q16—21no—
593C2×Q16—21no—
594C2×Q16—21no—
595C2×Q16—21no—
596C2×Q16—41no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×SD16—22no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—41no—
607C2×D8—21no—
608C2×D8—21no—
609#131—22no—
610#131—22no—
611#131—41no—
612#131—41no—
613C2×M16—21no—
614C2×M16—22no—
615C2×M16—22no—
616C2×M16—21no—
617C2×M16—21no—
618C2×M16C23×C4311yescharacteristic
619C2×M16C23×C4311yescharacteristic
620C2×M16C23×C4311yescharacteristic
621C2×M16C23×C4311yescharacteristic
622C2×M16C23×C4311yescharacteristic
623C2×M16C23×C4311yescharacteristic
624C22×C8—21no—
625C22×C8—21no—
626C22×C8—21no—
627C22×C8C23×C4311yescharacteristic
628C22×C8C23×C4311yescharacteristic
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4C23×C4311yescharacteristic
635C2×C22⋊C4—21no—
636#108—22no—
637#108—22no—
638#103—21no—
639#103—21no—
640#103—21no—
641#103—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645#102—21no—
646#101—22no—
647#101—22no—
648#101—22no—
649#101—41no—
650#100—22no—
651#100—41no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—21no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C22⋊C8—21no—
660C22⋊C8D4×C4311yescharacteristic
661C22⋊C8D4×C4311yescharacteristic
662C22⋊C8D4×C4311yescharacteristic
663C22⋊C8D4×C4311yescharacteristic
664C24—21no—
665C24—21no—
666C24#41×C4311yescharacteristic
667#41—21no—
668#41—21no—
669#41—24no—
670#41—24no—
671#41—22no—
672#41—22no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—21no—
677#41—42no—
678#41—42no—
679#41—41no—
680#41—41no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41C2×D4×C4312yes—
690#41C2×D4×C4312yes—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—41no—
705C2×Q8C2×D4×C4312yes—
706C2×Q8C2×D4×C4311yescharacteristic
707C2×Q8C2×D4×C4311yescharacteristic
708C2×D4—21no—
709C2×D4—22no—
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—41no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4C2×D4×C4312yes—
727C2×D4C2×D4×C4311yescharacteristic
728C2×D4C2×D4×C4311yescharacteristic
729C22×C4—21no—
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—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4C2×D4×C4311yescharacteristic
748C22×C4C2×D4×C4311yescharacteristic
749C22×C4C2×D4×C4311yescharacteristic
750C22×C4C2×D4×C4311yescharacteristic
751C22×C4#41×C4311yescharacteristic
752C22×C4C24×C4311yescharacteristic
753Q16—24no—
754Q16—24no—
755Q16—42no—
756Q16—42no—
757Q16—42no—
758Q16—42no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—24no—
763SD16—42no—
764SD16—42no—
765SD16—42no—
766SD16—42no—
767D8—24no—
768D8—24no—
769M16—24no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—21no—
779M16—21no—
780M16—42no—
781M16—42no—
782M16C2×D4×C4312yes—
783M16C2×D4×C4312yes—
784C2×C8—24no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—42no—
796C2×C8—42no—
797C2×C8C2×D4×C4311yescharacteristic
798C2×C8C2×D4×C4311yescharacteristic
799C2×C8C2×D4×C4311yescharacteristic
800C2×C8C2×D4×C4311yescharacteristic
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—41no—
804C4⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23#121×C4311yescharacteristic
822C23#121×C4311yescharacteristic
823C23C2×#41×C4311yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—41no—
833Q8—41no—
834Q8—41no—
835Q8—41no—
836Q8#120×C4312yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4#120×C4312yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—81no—
883C2×C4#121×C4311yescharacteristic
884C2×C4#121×C4311yescharacteristic
885C2×C4C22×D4×C4311yescharacteristic
886C2×C4C22×D4×C4311yescharacteristic
887C2×C4C22×D4×C4311yescharacteristic
888C2×C4C22×D4×C4311yescharacteristic
889C2×C4H(5,𝔽2)×C4311yescharacteristic
890C2×C4H(5,𝔽2)×C4311yescharacteristic
891C8—22no—
892C8—22no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—41no—
898C8—41no—
899C8—41no—
900C8—41no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—22no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×#121×C4311yescharacteristic
924C22C43×#54611yescharacteristic
925C22C43×#54611yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×#120×C4311yescharacteristic
934C4C43×#53411yescharacteristic
935C4D42×C4311yescharacteristic
936C4D42×C4311yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C43×#241011yescharacteristic
945C2C43×#306711yescharacteristic
946C2C43×#306911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#575C2
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. C2×C43×#473C2semidirect
3. C2×C43×#471C2semidirect
4. C43×#3007C2semidirect
5. C2×C43×#452C2semidirect
6. C43×#2880C2semidirect
7. C43×#2052C2semidirect
8. C43×#2051C2semidirect
9. C43×#2020C2semidirect
10. C43×#2019C2semidirect
11. C43×#1908C2semidirect
12. C43×#1907C2semidirect
13. C43×#1901C2semidirect
14. C43×#1855C2semidirect
15. C43×#1785C2semidirect
30. C22×Q16×C43C22semidirect
31. C22×SD16×C43C22semidirect
46. C2×#108×C43C22semidirect
47. C2×#108×C43C22semidirect
50. C2×#103×C43C22semidirect
51. C2×#102×C43C22semidirect
52. C2×#101×C43C22semidirect
53. C2×#101×C43C22semidirect
54. C2×#101×C43C22semidirect
55. C2×#101×C43C22semidirect
56. C2×#100×C43C22semidirect
57. C2×#100×C43C22semidirect
67. C43×#343C22semidirect
68. C43×#343C22semidirect
69. C43×#341C22semidirect
70. C43×#341C22semidirect
427. #24403C43direct (N × H)
465. C2×#473C2×C43semidirect
466. C2×#471C2×C43semidirect
467. #3007C2×C43semidirect
468. C2×#452C2×C43semidirect
469. #2880C2×C43semidirect
470. #2052C2×C43semidirect
471. #2051C2×C43semidirect
472. #2020C2×C43semidirect
473. #2019C2×C43semidirect
474. #1908C2×C43semidirect
475. #1907C2×C43semidirect
476. #1901C2×C43semidirect
477. #1855C2×C43semidirect
478. #1785C2×C43semidirect
503. C22×Q16C22×C43semidirect
504. C22×SD16C22×C43semidirect
519. C2×#108C22×C43semidirect
520. C2×#108C22×C43semidirect
523. C2×#103C22×C43semidirect
524. C2×#102C22×C43semidirect
525. C2×#101C22×C43semidirect
526. C2×#101C22×C43semidirect
527. C2×#101C22×C43semidirect
528. C2×#101C22×C43semidirect
529. C2×#100C22×C43semidirect
530. C2×#100C22×C43semidirect
540. #343C22×C43semidirect
541. #343C22×C43semidirect
542. #341C22×C43semidirect
543. #341C22×C43semidirect
544. C43#24403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5752
C2×C43×#4732
C2×C43×#4712
C43×#30072
C2×C43×#4522
C43×#28802
C43×#20522
C43×#20512
C43×#20202
C43×#20192
C43×#19082
C43×#19072
C43×#19012
C43×#18552
C43×#17852
#2440343