Finite Group Databasebeta

← C43×#26246 #24946263

Subgroups — C43×#26246 #24946263

Order 11008.

1006 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#481C211yesmaximal, characteristic, complemented
2C2×C43×#482C211yesmaximal, characteristic, complemented
3C43×#2541C211yesmaximal, characteristic
4C43×#2352C211yesmaximal, characteristic, complemented
5C43×#2034C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic, complemented
7C43×#2033C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#1982C211yesmaximal, characteristic, complemented
10C43×#1961C211yesmaximal, characteristic, complemented
11C43×#1955C211yesmaximal, characteristic, complemented
12C43×#1949C211yesmaximal, characteristic, complemented
13C43×#1875C211yesmaximal, characteristic, complemented
14C43×#1874C211yesmaximal, characteristic, complemented
15C43×#1776C211yesmaximal, characteristic, complemented
16C2×#127×C43—21no—
17C2×#127×C43C2211yescharacteristic
18C2×#121×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×#121×C43C2211yescharacteristic
21C2×#121×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C2×#117×C43C2211yescharacteristic
24C22×C4⋊C4×C43C2211yescharacteristic
25C43×#482—24no—
26C43×#481—24no—
27C2×#107×C43C2211yescharacteristic
28C2×#107×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C2×#106×C43C2211yescharacteristic
31C2×C4⋊C8×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×C22⋊C8×C43C2211yescharacteristic
41C2×C22⋊C8×C43C2211yescharacteristic
42C2×C22⋊C8×C43C2211yescharacteristic
43C2×C22⋊C8×C43C2211yescharacteristic
44C2×#97×C43C2211yescharacteristic
45C43×#392—21no—
46C43×#392—21no—
47C43×#390—21no—
48C43×#388—21no—
49C43×#387—21no—
50C43×#386—21no—
51C43×#382C2211yescharacteristic
52C43×#380C2211yescharacteristic
53C43×#380C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C4×C22⋊C4×C43—21no—
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43—21no—
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43—21no—
67C22×D4×C43D411yescharacteristic
68C22×D4×C43C2311yescharacteristic
69C22×D4×C43C2311yescharacteristic
70C23×C4×C43—21no—
71C23×C4×C43C2311yescharacteristic
72C23×C4×C43C2311yescharacteristic
73C22×C8×C43C2311yescharacteristic
74C22×C8×C43C2311yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C22×C8×C43C2311yescharacteristic
77#127×C43—22no—
78#127×C43—22no—
79#127×C43—44no—
80#121×C43—22no—
81#121×C43—22no—
82#121×C43—22no—
83#121×C43—22no—
84#121×C43—41no—
85#121×C43—41no—
86#121×C43—41no—
87#121×C43—41no—
88C4×D4×C43—22no—
89C4×D4×C43—22no—
90#117×C43—22no—
91#117×C43—41no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—41no—
95C2×C4⋊C4×C43D411yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43D411yescharacteristic
110C2×C22⋊C4×C43D411yescharacteristic
111C2×C42×C43—21no—
112C2×C42×C43—21no—
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#107×C43—22no—
116#107×C43—22no—
117#106×C43—22no—
118#106×C43D414yescomplemented
119C4⋊C8×C43—22no—
120#102×C43—22no—
121#102×C43—22no—
122#102×C43—22no—
123#102×C43—22no—
124#102×C43—41no—
125#102×C43—41no—
126#102×C43—41no—
127#102×C43—41no—
128C22⋊C8×C43—22no—
129C22⋊C8×C43—22no—
130C22⋊C8×C43—41no—
131C22⋊C8×C43—41no—
132#97×C43—22no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43C2×D411yescharacteristic
142C24×C43C2×D411yescharacteristic
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
172C2×D4×C43—81no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—42no—
195C22×C4×C43—42no—
196C22×C4×C43—81no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43C2×D412yes—
214C4⋊C4×C43—22no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—42no—
225C4⋊C4×C43C2×D412yes—
226C4⋊C4×C43C2×D412yes—
227C4⋊C4×C43#4112yes—
228C22⋊C4×C43—22no—
229C22⋊C4×C43—22no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—81no—
237C42×C43—42no—
238C42×C43—42no—
239C42×C43—81no—
240C42×C43#4112yes—
241C42×C43#4112yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43AGL(1,ℤ/8)12yes—
270C23×C43C22×D411yescharacteristic
271D4×C43—44no—
272D4×C43—41no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—84no—
281D4×C43—84no—
282D4×C43—84no—
283D4×C43—84no—
284D4×C43—84no—
285D4×C43—84no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—21no—
296C2×C4×C43—22no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—84no—
323C2×C4×C43#12312yes—
324C2×C4×C43#12312yes—
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43C2×#4111yescharacteristic
329C2×C4×C43H(5,𝔽2)11yescharacteristic
330C2×C4×C43H(5,𝔽2)11yescharacteristic
331C8×C43—22no—
332C8×C43—41no—
333C8×C43—41no—
334C8×C43—41no—
335#26246C4311yesmaximal, characteristic, direct product factor, Sylow
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43C2×#12311yescharacteristic
365C22×C43D4211yescharacteristic
366C22×C43#54611yescharacteristic
367C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C43#57511yescharacteristic
369C22×C43#57611yescharacteristic
370C22×C43#57711yescharacteristic
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—41no—
374C4×C43—41no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43—81no—
379C4×C43—81no—
380C4×C43—81no—
381C4×C43#53211yescharacteristic
382C4×C43#54011yescharacteristic
383C4×C43#55011yescharacteristic
384C4×C43#55911yescharacteristic
385C2×#481C2×C4311yescharacteristic, complemented
386C2×#482C2×C4311yescharacteristic, complemented
387#2541C2×C4311yescharacteristic
388#2352C2×C4311yescharacteristic, complemented
389#2034C2×C4311yescharacteristic, complemented
390#2033C2×C4311yescharacteristic, complemented
391#2033C2×C4311yescharacteristic, complemented
392#2033C2×C4311yescharacteristic, complemented
393#1982C2×C4311yescharacteristic, complemented
394#1961C2×C4311yescharacteristic, complemented
395#1955C2×C4311yescharacteristic, complemented
396#1949C2×C4311yescharacteristic, complemented
397#1875C2×C4311yescharacteristic, complemented
398#1874C2×C4311yescharacteristic, complemented
399#1776C2×C4311yescharacteristic, complemented
400C2×C43—42no—
401C2×C43—81no—
402C2×C43—161no—
403C2×C43—161no—
404C2×C43#244511yescharacteristic
405C2×C43#309411yescharacteristic
406C2×C43#309611yescharacteristic
407C2×C43#326511yescharacteristic
408C2×C43#326811yescharacteristic
409C2×C43#331711yescharacteristic
410C2×C43#331811yescharacteristic
411C2×#127—21no—
412C2×#127C22×C4311yescharacteristic
413C2×#121C22×C4311yescharacteristic
414C2×#121C22×C4311yescharacteristic
415C2×#121C22×C4311yescharacteristic
416C2×#121C22×C4311yescharacteristic
417C2×C4×D4C22×C4311yescharacteristic
418C2×#117C22×C4311yescharacteristic
419C22×C4⋊C4C22×C4311yescharacteristic
420#482—24no—
421#481—24no—
422C2×#107C22×C4311yescharacteristic
423C2×#107C22×C4311yescharacteristic
424C2×#106C22×C4311yescharacteristic
425C2×#106C22×C4311yescharacteristic
426C2×C4⋊C8C22×C4311yescharacteristic
427C2×#102C22×C4311yescharacteristic
428C2×#102C22×C4311yescharacteristic
429C2×#102C22×C4311yescharacteristic
430C2×#102C22×C4311yescharacteristic
431C2×#102C22×C4311yescharacteristic
432C2×#102C22×C4311yescharacteristic
433C2×#102C22×C4311yescharacteristic
434C2×#102C22×C4311yescharacteristic
435C2×C22⋊C8C22×C4311yescharacteristic
436C2×C22⋊C8C22×C4311yescharacteristic
437C2×C22⋊C8C22×C4311yescharacteristic
438C2×C22⋊C8C22×C4311yescharacteristic
439C2×#97C22×C4311yescharacteristic
440#392—21no—
441#392—21no—
442#390—21no—
443#388—21no—
444#387—21no—
445#386—21no—
446#382C22×C4311yescharacteristic
447#380C22×C4311yescharacteristic
448#380C22×C4311yescharacteristic
449C4×C4⋊C4C22×C4311yescharacteristic
450C4×C4⋊C4C22×C4311yescharacteristic
451C4×C22⋊C4—21no—
452#340C22×C4311yescharacteristic
453#340C22×C4311yescharacteristic
454#340C22×C4311yescharacteristic
455#340C22×C4311yescharacteristic
456C43#2624611yescharacteristic, direct product factor, Sylow
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4D4×C4311yescharacteristic
464C22×D4C23×C4311yescharacteristic
465C22×D4C23×C4311yescharacteristic
466C23×C4—21no—
467C23×C4C23×C4311yescharacteristic
468C23×C4C23×C4311yescharacteristic
469C22×C8C23×C4311yescharacteristic
470C22×C8C23×C4311yescharacteristic
471C22×C8C23×C4311yescharacteristic
472C22×C8C23×C4311yescharacteristic
473#127—22no—
474#127—22no—
475#127—44no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—41no—
481#121—41no—
482#121—41no—
483#121—41no—
484C4×D4—22no—
485C4×D4—22no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4D4×C4311yescharacteristic
492C2×C4⋊C4C23×C4311yescharacteristic
493C2×C4⋊C4C23×C4311yescharacteristic
494C2×C4⋊C4C23×C4311yescharacteristic
495C2×C4⋊C4C23×C4311yescharacteristic
496C2×C4⋊C4C23×C4311yescharacteristic
497C2×C4⋊C4C23×C4311yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C4311yescharacteristic
506C2×C22⋊C4D4×C4311yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42C23×C4311yescharacteristic
511#107—22no—
512#107—22no—
513#106—22no—
514#106D4×C4314yescomplemented
515C4⋊C8—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102—41no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528#97—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C4311yescharacteristic
538C24C2×D4×C4311yescharacteristic
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—81no—
593C22×C4C2×D4×C4311yescharacteristic
594C22×C4C2×D4×C4311yescharacteristic
595C22×C4C2×D4×C4311yescharacteristic
596C22×C4C2×D4×C4311yescharacteristic
597C22×C4C24×C4311yescharacteristic
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8C2×D4×C4312yes—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4C2×D4×C4312yes—
622C4⋊C4C2×D4×C4312yes—
623C4⋊C4#41×C4312yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C42—42no—
634C42—42no—
635C42—81no—
636C42#41×C4312yes—
637C42#41×C4312yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23AGL(1,ℤ/8)×C4312yes—
666C23C22×D4×C4311yescharacteristic
667D4—44no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—84no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4#123×C4312yes—
720C2×C4#123×C4312yes—
721C2×C4C22×D4×C4311yescharacteristic
722C2×C4C2×#41×C4311yescharacteristic
723C2×C4C2×#41×C4311yescharacteristic
724C2×C4C2×#41×C4311yescharacteristic
725C2×C4H(5,𝔽2)×C4311yescharacteristic
726C2×C4H(5,𝔽2)×C4311yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C2×#123×C4311yescharacteristic
760C22D42×C4311yescharacteristic
761C22C43×#54611yescharacteristic
762C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
763C22C43×#57511yescharacteristic
764C22C43×#57611yescharacteristic
765C22C43×#57711yescharacteristic
766C4—22no—
767C4—22no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—81no—
774C4—81no—
775C4—81no—
776C4C43×#53211yescharacteristic
777C4C43×#54011yescharacteristic
778C4C43×#55011yescharacteristic
779C4C43×#55911yescharacteristic
780C2—42no—
781C2—81no—
782C2—161no—
783C2—161no—
784C2C43×#244511yescharacteristic
785C2C43×#309411yescharacteristic
786C2C43×#309611yescharacteristic
787C2C43×#326511yescharacteristic
788C2C43×#326811yescharacteristic
789C2C43×#331711yescharacteristic
790C2C43×#331811yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2541C2
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×#481C2semidirect
2. C2×C43×#482C2semidirect
4. C43×#2352C2semidirect
5. C43×#2034C2semidirect
6. C43×#2033C2semidirect
7. C43×#2033C2semidirect
8. C43×#2033C2semidirect
9. C43×#1982C2semidirect
10. C43×#1961C2semidirect
11. C43×#1955C2semidirect
12. C43×#1949C2semidirect
13. C43×#1875C2semidirect
14. C43×#1874C2semidirect
15. C43×#1776C2semidirect
118. #106×C43D4semidirect
335. #26246C43direct (N × H)
385. C2×#481C2×C43semidirect
386. C2×#482C2×C43semidirect
388. #2352C2×C43semidirect
389. #2034C2×C43semidirect
390. #2033C2×C43semidirect
391. #2033C2×C43semidirect
392. #2033C2×C43semidirect
393. #1982C2×C43semidirect
394. #1961C2×C43semidirect
395. #1955C2×C43semidirect
396. #1949C2×C43semidirect
397. #1875C2×C43semidirect
398. #1874C2×C43semidirect
399. #1776C2×C43semidirect
456. C43#26246direct (N × H)
514. #106D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4812
C2×C43×#4822
C43×#25412
C43×#23522
C43×#20342
C43×#20332
C43×#19822
C43×#19612
C43×#19552
C43×#19492
C43×#18752
C43×#18742
C43×#17762
#2624643