Finite Group Databasebeta

← C43×#27222 #24947239

Subgroups — C43×#27222 #24947239

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#474C211yesmaximal, characteristic, complemented
2C2×C43×#447C211yesmaximal, characteristic
3C43×#2491C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
5C43×#2075C211yesmaximal, characteristic, complemented
6C43×#2054C211yesmaximal, characteristic, complemented
7C43×#2033C211yesmaximal, characteristic, complemented
8C43×#2023C211yesmaximal, characteristic, complemented
9C43×#1970C211yesmaximal, characteristic, complemented
10C43×#1925C211yesmaximal, characteristic, complemented
11C43×#1923C211yesmaximal, characteristic, complemented
12C43×#1879C211yesmaximal, characteristic, complemented
13C43×#1879C211yesmaximal, characteristic, complemented
14C43×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C2×C4⋊Q8×C43C2211yescharacteristic, complemented
20C2×#124×C43—21no—
21C2×#121×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C2×C4×D4×C43C2211yescharacteristic
24C22×C22⋊C4×C43—21no—
25C43×#474—24no—
26C43×#447—24no—
27C2×#107×C43C2211yescharacteristic, complemented
28C2×#107×C43C2211yescharacteristic, complemented
29C2×C4⋊C8×C43C2211yescharacteristic, complemented
30C2×#102×C43C2211yescharacteristic
31C2×#102×C43C2211yescharacteristic
32C2×#102×C43C2211yescharacteristic
33C2×#102×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic, complemented
37C2×#102×C43C2211yescharacteristic, complemented
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C2×C4×C8×C43C2211yescharacteristic, complemented
41C43×#394—21no—
42C43×#393—21no—
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic, complemented
46C43×#390C2211yescharacteristic, complemented
47C43×#388—21no—
48C43×#386—21no—
49C43×#386—21no—
50C43×#380C2211yescharacteristic
51C43×#380C2211yescharacteristic
52C43×#379—21no—
53C4×C4⋊C4×C43C2211yescharacteristic, complemented
54C4×C22⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic, complemented
56C43×#340C2211yescharacteristic, complemented
57C43×#340C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C43×#336C2211yescharacteristic, complemented
61C25×C43—21no—
62C22×Q8×C43—21no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—41no—
70C22×D4×C43—41no—
71C22×D4×C43C2311yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C22×D4×C43C2311yescharacteristic
74C23×C4×C43—21no—
75C23×C4×C43—21no—
76C23×C4×C43C2311yescharacteristic
77C2×D8×C43—22no—
78C2×D8×C43—22no—
79C2×D8×C43—22no—
80C2×D8×C43—22no—
81C2×D8×C43—22no—
82C2×D8×C43—41no—
83C22×C8×C43C2311yescharacteristic
84C22×C8×C43C2311yescharacteristic
85C22×C8×C43C2311yescharacteristic
86C22×C8×C43C2311yescharacteristic
87C4⋊Q8×C43—22no—
88C4⋊Q8×C43—41no—
89#124×C43—44no—
90#121×C43—22no—
91#121×C43—41no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43—41no—
95C4×D4×C43—41no—
96C2×C4⋊C4×C43—21no—
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×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—44no—
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C22⋊C4×C43D411yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#107×C43—22no—
123C4⋊C8×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128#102×C43—41no—
129#102×C43—41no—
130#102×C43—41no—
131#102×C43D414yes—
132C22⋊C8×C43—22no—
133C22⋊C8×C43—41no—
134C4×C8×C43—41no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43D411yescharacteristic
139#95×C43D411yescharacteristic
140C24×C43—21no—
141C24×C43—24no—
142C24×C43—21no—
143C24×C43—21no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—42no—
147C24×C43—42no—
148C24×C43—81no—
149C24×C43—81no—
150C24×C43C2×D411yescharacteristic
151C2×Q8×C43—42no—
152C2×Q8×C43—42no—
153C2×Q8×C43—81no—
154C2×D4×C43—24no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—44no—
173C2×D4×C43—44no—
174C2×D4×C43—44no—
175C2×D4×C43—44no—
176C2×D4×C43—42no—
177C2×D4×C43—81no—
178C2×D4×C43C2×D412yes—
179C2×D4×C43#4112yes—
180C2×D4×C43#4112yes—
181C2×D4×C43#4112yes—
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—42no—
194C22×C4×C43—42no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43—81no—
198C22×C4×C43—81no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2411yescharacteristic
205D8×C43—44no—
206D8×C43—44no—
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×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43C2×D412yes—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—42no—
229C4⋊C4×C43C2×D412yes—
230C22⋊C4×C43—41no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—42no—
239C22⋊C4×C43—42no—
240C22⋊C4×C43—42no—
241C22⋊C4×C43—81no—
242C22⋊C4×C43—81no—
243C22⋊C4×C43—81no—
244C22⋊C4×C43D814yescomplemented
245C42×C43—21no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—21no—
249C42×C43—42no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—21no—
254C23×C43—22no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—48no—
261C23×C43—48no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—84no—
280C23×C43—84no—
281C23×C43—84no—
282C23×C43—84no—
283C23×C43—84no—
284C23×C43C2×D812yes—
285C23×C43C22×D411yescharacteristic
286Q8×C43—84no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—48no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43—84no—
300D4×C43#12414yescomplemented
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
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—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—84no—
334C2×C4×C43—84no—
335C2×C4×C43C2×D812yes—
336C2×C4×C43C2×D812yes—
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C2×#4111yescharacteristic
339C2×C4×C43C2×#4111yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C8×C43—22no—
344C8×C43—41no—
345C8×C43—41no—
346C8×C43—41no—
347#27222C4311yesmaximal, characteristic, direct product factor, Sylow
348C22×C43—22no—
349C22×C43—24no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—42no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—816no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43—81no—
374C22×C43—81no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43#52511yescharacteristic
378C22×C43D4211yescharacteristic
379C22×C43#54611yescharacteristic
380C22×C43C22×D811yescharacteristic
381C22×C43#57511yescharacteristic
382C22×C43#57611yescharacteristic
383C22×C43#57711yescharacteristic
384C4×C43—22no—
385C4×C43—22no—
386C4×C43—41no—
387C4×C43—41no—
388C4×C43—42no—
389C4×C43—41no—
390C4×C43—81no—
391C4×C43—81no—
392C4×C43—81no—
393C4×C43—81no—
394C4×C43C2×#12411yescharacteristic
395C4×C43#53811yescharacteristic
396C4×C43#54611yescharacteristic
397C4×C43#55111yescharacteristic
398C2×#474C2×C4311yescharacteristic, complemented
399C2×#447C2×C4311yescharacteristic
400#2491C2×C4311yescharacteristic, complemented
401D4×C22⋊C4C2×C4311yescharacteristic, complemented
402#2075C2×C4311yescharacteristic, complemented
403#2054C2×C4311yescharacteristic, complemented
404#2033C2×C4311yescharacteristic, complemented
405#2023C2×C4311yescharacteristic, complemented
406#1970C2×C4311yescharacteristic, complemented
407#1925C2×C4311yescharacteristic, complemented
408#1923C2×C4311yescharacteristic, complemented
409#1879C2×C4311yescharacteristic, complemented
410#1879C2×C4311yescharacteristic, complemented
411#1786C2×C4311yescharacteristic, complemented
412C4×#102C2×C4311yescharacteristic, complemented
413C2×C43—42no—
414C2×C43—44no—
415C2×C43—82no—
416C2×C43—161no—
417C2×C43#247211yescharacteristic
418C2×C43#310011yescharacteristic
419C2×C43#311811yescharacteristic
420C2×C43#327511yescharacteristic
421C2×C43D4×D811yescharacteristic
422C2×C43#329411yescharacteristic
423C2×C43#331911yescharacteristic
424C23×D4C22×C4311yescharacteristic
425C22×D8C22×C4311yescharacteristic
426C22×D8C22×C4311yescharacteristic
427C2×C4⋊Q8C22×C4311yescharacteristic, complemented
428C2×#124—21no—
429C2×#121C22×C4311yescharacteristic
430C2×C4×D4C22×C4311yescharacteristic
431C2×C4×D4C22×C4311yescharacteristic
432C22×C22⋊C4—21no—
433#474—24no—
434#447—24no—
435C2×#107C22×C4311yescharacteristic, complemented
436C2×#107C22×C4311yescharacteristic, complemented
437C2×C4⋊C8C22×C4311yescharacteristic, complemented
438C2×#102C22×C4311yescharacteristic
439C2×#102C22×C4311yescharacteristic
440C2×#102C22×C4311yescharacteristic
441C2×#102C22×C4311yescharacteristic
442C2×#102C22×C4311yescharacteristic
443C2×#102C22×C4311yescharacteristic
444C2×#102C22×C4311yescharacteristic, complemented
445C2×#102C22×C4311yescharacteristic, complemented
446C2×C22⋊C8C22×C4311yescharacteristic
447C2×C22⋊C8C22×C4311yescharacteristic
448C2×C4×C8C22×C4311yescharacteristic, complemented
449#394—21no—
450#393—21no—
451#390C22×C4311yescharacteristic
452#390C22×C4311yescharacteristic
453#390C22×C4311yescharacteristic, complemented
454#390C22×C4311yescharacteristic, complemented
455#388—21no—
456#386—21no—
457#386—21no—
458#380C22×C4311yescharacteristic
459#380C22×C4311yescharacteristic
460#379—21no—
461C4×C4⋊C4C22×C4311yescharacteristic, complemented
462C4×C22⋊C4C22×C4311yescharacteristic
463#340C22×C4311yescharacteristic, complemented
464#340C22×C4311yescharacteristic, complemented
465#340C22×C4311yescharacteristic, complemented
466#340C22×C4311yescharacteristic, complemented
467#336C22×C4311yescharacteristic, complemented
468#336C22×C4311yescharacteristic, complemented
469C43#2722211yescharacteristic, direct product factor, Sylow
470C25—21no—
471C22×Q8—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—41no—
479C22×D4—41no—
480C22×D4C23×C4311yescharacteristic
481C22×D4C23×C4311yescharacteristic
482C22×D4C23×C4311yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C4311yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C2×D8—41no—
492C22×C8C23×C4311yescharacteristic
493C22×C8C23×C4311yescharacteristic
494C22×C8C23×C4311yescharacteristic
495C22×C8C23×C4311yescharacteristic
496C4⋊Q8—22no—
497C4⋊Q8—41no—
498#124—44no—
499#121—22no—
500#121—41no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—41no—
504C4×D4—41no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4C23×C4311yescharacteristic
507C2×C4⋊C4C23×C4311yescharacteristic
508C2×C4⋊C4C23×C4311yescharacteristic
509C2×C4⋊C4C23×C4311yescharacteristic
510C2×C4⋊C4C23×C4311yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—44no—
525C2×C22⋊C4D4×C4311yescharacteristic
526C2×C22⋊C4D4×C4311yescharacteristic
527C2×C42—21no—
528C2×C42C23×C4311yescharacteristic
529C2×C42C23×C4311yescharacteristic
530#107—22no—
531#107—22no—
532C4⋊C8—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539#102—41no—
540#102D4×C4314yes—
541C22⋊C8—22no—
542C22⋊C8—41no—
543C4×C8—41no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95D4×C4311yescharacteristic
548#95D4×C4311yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—21no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—81no—
558C24—81no—
559C24C2×D4×C4311yescharacteristic
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—81no—
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—44no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4C2×D4×C4312yes—
588C2×D4#41×C4312yes—
589C2×D4#41×C4312yes—
590C2×D4#41×C4312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C4311yescharacteristic
609C22×C4C2×D4×C4311yescharacteristic
610C22×C4C2×D4×C4311yescharacteristic
611C22×C4C2×D4×C4311yescharacteristic
612C22×C4C2×D4×C4311yescharacteristic
613C22×C4C24×C4311yescharacteristic
614D8—44no—
615D8—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×D4×C4312yes—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—42no—
638C4⋊C4C2×D4×C4312yes—
639C22⋊C4—41no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—81no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C22⋊C4D8×C4314yescomplemented
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—42no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—48no—
670C23—48no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23C2×D8×C4312yes—
694C23C22×D4×C4311yescharacteristic
695Q8—84no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—48no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—84no—
709D4#124×C4314yescomplemented
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4C2×D8×C4312yes—
745C2×C4C2×D8×C4312yes—
746C2×C4C22×D4×C4311yescharacteristic
747C2×C4C2×#41×C4311yescharacteristic
748C2×C4C2×#41×C4311yescharacteristic
749C2×C4C2×#41×C4311yescharacteristic
750C2×C4H(5,𝔽2)×C4311yescharacteristic
751C2×C4H(5,𝔽2)×C4311yescharacteristic
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—24no—
758C22—22no—
759C22—22no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—816no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C43×#52511yescharacteristic
786C22D42×C4311yescharacteristic
787C22C43×#54611yescharacteristic
788C22C22×D8×C4311yescharacteristic
789C22C43×#57511yescharacteristic
790C22C43×#57611yescharacteristic
791C22C43×#57711yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—42no—
797C4—41no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C2×#124×C4311yescharacteristic
803C4C43×#53811yescharacteristic
804C4C43×#54611yescharacteristic
805C4C43×#55111yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—161no—
810C2C43×#247211yescharacteristic
811C2C43×#310011yescharacteristic
812C2C43×#311811yescharacteristic
813C2C43×#327511yescharacteristic
814C2D4×D8×C4311yescharacteristic
815C2C43×#329411yescharacteristic
816C2C43×#331911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#474C2semidirect
3. C43×#2491C2semidirect
4. D4×C22⋊C4×C43C2semidirect
5. C43×#2075C2semidirect
6. C43×#2054C2semidirect
7. C43×#2033C2semidirect
8. C43×#2023C2semidirect
9. C43×#1970C2semidirect
10. C43×#1925C2semidirect
11. C43×#1923C2semidirect
12. C43×#1879C2semidirect
13. C43×#1879C2semidirect
14. C43×#1786C2semidirect
15. C4×#102×C43C2semidirect
19. C2×C4⋊Q8×C43C22semidirect
27. C2×#107×C43C22semidirect
28. C2×#107×C43C22semidirect
29. C2×C4⋊C8×C43C22semidirect
36. C2×#102×C43C22semidirect
37. C2×#102×C43C22semidirect
40. C2×C4×C8×C43C22semidirect
45. C43×#390C22semidirect
46. C43×#390C22semidirect
53. C4×C4⋊C4×C43C22semidirect
55. C43×#340C22semidirect
56. C43×#340C22semidirect
57. C43×#340C22semidirect
58. C43×#340C22semidirect
59. C43×#336C22semidirect
60. C43×#336C22semidirect
244. C22⋊C4×C43D8semidirect
300. D4×C43#124semidirect
347. #27222C43direct (N × H)
398. C2×#474C2×C43semidirect
400. #2491C2×C43semidirect
401. D4×C22⋊C4C2×C43semidirect
402. #2075C2×C43semidirect
403. #2054C2×C43semidirect
404. #2033C2×C43semidirect
405. #2023C2×C43semidirect
406. #1970C2×C43semidirect
407. #1925C2×C43semidirect
408. #1923C2×C43semidirect
409. #1879C2×C43semidirect
410. #1879C2×C43semidirect
411. #1786C2×C43semidirect
412. C4×#102C2×C43semidirect
427. C2×C4⋊Q8C22×C43semidirect
435. C2×#107C22×C43semidirect
436. C2×#107C22×C43semidirect
437. C2×C4⋊C8C22×C43semidirect
444. C2×#102C22×C43semidirect
445. C2×#102C22×C43semidirect
448. C2×C4×C8C22×C43semidirect
453. #390C22×C43semidirect
454. #390C22×C43semidirect
461. C4×C4⋊C4C22×C43semidirect
463. #340C22×C43semidirect
464. #340C22×C43semidirect
465. #340C22×C43semidirect
466. #340C22×C43semidirect
467. #336C22×C43semidirect
468. #336C22×C43semidirect
469. C43#27222direct (N × H)
653. C22⋊C4D8×C43semidirect
709. D4#124×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4742
C2×C43×#4472
C43×#24912
D4×C22⋊C4×C432
C43×#20752
C43×#20542
C43×#20332
C43×#20232
C43×#19702
C43×#19252
C43×#19232
C43×#18792
C43×#17862
C4×#102×C432
#2722243