Finite Group Databasebeta

← C43×#13875 #24933892

Subgroups — C43×#13875 #24933892

Order 11008.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#382C211yesmaximal, characteristic, complemented
2C2×C43×#380C211yesmaximal, characteristic
3C2×C43×#380C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C43C211yesmaximal, characteristic
6C43×#1443C212yesmaximal, complemented
7C43×#1440C212yesmaximal
8C43×#1437C212yesmaximal
9C43×C4⋊#95C211yesmaximal, characteristic, complemented
10C43×C4⋊#95C211yesmaximal, characteristic, complemented
11C43×#1434C212yesmaximal, complemented
12C24×C4×C43C2211yescharacteristic
13C22×C4⋊C4×C43C2211yescharacteristic
14C22×C4⋊C4×C43C2211yescharacteristic
15C22×C4⋊C4×C43C2211yescharacteristic
16C22×C4⋊C4×C43C2211yescharacteristic
17C22×C22⋊C4×C43C2212yes—
18C22×C22⋊C4×C43C2212yes—
19C22×C22⋊C4×C43C2211yescharacteristic
20C22×C22⋊C4×C43C2211yescharacteristic
21C22×C42×C43C2212yes—
22C22×C42×C43C2211yescharacteristic
23C22×C42×C43C2211yescharacteristic
24C43×#382—24no—
25C43×#380—24no—
26C43×#380—24no—
27C4×C4⋊C4×C43—24no—
28C4×C22⋊C4×C43C418yescomplemented
29C2×#95×C43C2212yes—
30C2×#95×C43C2212yes—
31C2×#95×C43C2212yes—
32C2×#95×C43C2212yes—
33C2×#95×C43C2212yes—
34C2×#95×C43C2212yes—
35C2×#95×C43C2212yes—
36C2×#95×C43C2212yes—
37C2×#95×C43C2212yes—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C25×C43C2311yescharacteristic
41C23×C4×C43—22no—
42C23×C4×C43—22no—
43C23×C4×C43—22no—
44C23×C4×C43—22no—
45C23×C4×C43—22no—
46C23×C4×C43—22no—
47C23×C4×C43C2×C414yes—
48C23×C4×C43C2312yes—
49C23×C4×C43C2312yes—
50C23×C4×C43C2311yescharacteristic
51C23×C4×C43C2311yescharacteristic
52C23×C4×C43C2311yescharacteristic
53C23×C4×C43C2311yescharacteristic
54C23×C4×C43C2312yes—
55C23×C4×C43C2312yes—
56C23×C4×C43C2311yescharacteristic
57C23×C4×C43C2311yescharacteristic
58C2×C4⋊C4×C43—22no—
59C2×C4⋊C4×C43—22no—
60C2×C4⋊C4×C43—22no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43—22no—
63C2×C4⋊C4×C43—22no—
64C2×C4⋊C4×C43—22no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×C43—22no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43D414yes—
69C2×C4⋊C4×C43D414yes—
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43—22no—
72C2×C22⋊C4×C43—22no—
73C2×C22⋊C4×C43—22no—
74C2×C22⋊C4×C43—24no—
75C2×C22⋊C4×C43—24no—
76C2×C22⋊C4×C43—24no—
77C2×C22⋊C4×C43—24no—
78C2×C22⋊C4×C43—42no—
79C2×C22⋊C4×C43—42no—
80C2×C22⋊C4×C43C2×C414yes—
81C2×C22⋊C4×C43C2×C414yes—
82C2×C42×C43—22no—
83C2×C42×C43—22no—
84C2×C42×C43—22no—
85C2×C42×C43—22no—
86C2×C42×C43—24no—
87C2×C42×C43—24no—
88C2×C42×C43—42no—
89C2×C42×C43C2×C414yes—
90C2×C42×C43C2×C414yes—
91#95×C43—24no—
92#95×C43—24no—
93#95×C43—24no—
94#95×C43—24no—
95#95×C43—24no—
96#95×C43—24no—
97#95×C43—42no—
98#95×C43—42no—
99#95×C43—42no—
100#95×C43C2×C414yes—
101#95×C43C2×C414yes—
102C24×C43—21no—
103C24×C43—21no—
104C24×C43—21no—
105C24×C43—21no—
106C24×C43—21no—
107C24×C43—21no—
108C24×C43—21no—
109C24×C43—21no—
110C24×C43—21no—
111C24×C43—21no—
112C24×C43—21no—
113C24×C43—21no—
114C24×C43C22×C412yes—
115C24×C43#4112yes—
116C24×C43#4112yes—
117C24×C43C2411yescharacteristic
118C22×C4×C43—28no—
119C22×C4×C43—28no—
120C22×C4×C43—28no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—21no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—22no—
173C22×C4×C43—21no—
174C22×C4×C43—22no—
175C22×C4×C43—44no—
176C22×C4×C43—44no—
177C22×C4×C43—44no—
178C22×C4×C43—44no—
179C22×C4×C43C22×C412yes—
180C22×C4×C43C22×C412yes—
181C22×C4×C43C22×C412yes—
182C22×C4×C43C22×C412yes—
183C22×C4×C43C22×C412yes—
184C22×C4×C43C22×C412yes—
185C22×C4×C43C2×D414yes—
186C22×C4×C43C2×D414yes—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D412yes—
189C22×C4×C43#4112yes—
190C22×C4×C43#4112yes—
191C22×C4×C43#4112yes—
192C22×C4×C43#4112yes—
193C22×C4×C43#4112yes—
194C22×C4×C43#4112yes—
195C4⋊C4×C43—28no—
196C4⋊C4×C43—28no—
197C4⋊C4×C43—44no—
198C4⋊C4×C43—44no—
199C22⋊C4×C43—28no—
200C22⋊C4×C43—28no—
201C22⋊C4×C43—48no—
202C22⋊C4×C43—48no—
203C42×C43—28no—
204C42×C43—28no—
205C42×C43—48no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43#11714yes—
241C23×C43C23×C411yescharacteristic
242C23×C43C22×D411yescharacteristic
243C23×C43C22×D411yescharacteristic
244C23×C43C2×#4111yescharacteristic
245C23×C43C2×#4111yescharacteristic
246C23×C43C2×#4111yescharacteristic
247C23×C43C2×#4111yescharacteristic
248C23×C43C2×#4111yescharacteristic
249C23×C43C2×#4111yescharacteristic
250C23×C43C2×#4111yescharacteristic
251C23×C43C2×#4111yescharacteristic
252C23×C43H(5,𝔽2)11yescharacteristic
253C23×C43H(5,𝔽2)11yescharacteristic
254C23×C432−1+411yescharacteristic
255C23×C432−1+411yescharacteristic
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—24no—
275C2×C4×C43—24no—
276C2×C4×C43—24no—
277C2×C4×C43—24no—
278C2×C4×C43—24no—
279C2×C4×C43—24no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—42no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—41no—
302C2×C4×C43—42no—
303C2×C4×C43—41no—
304C2×C4×C43—416no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43#11714yes—
320C2×C4×C43#11714yes—
321C2×C4×C43C4×D414yes—
322C2×C4×C43C4×D414yes—
323C2×C4×C43#12114yes—
324C2×C4×C43#12314yes—
325C2×C4×C43#12414yes—
326C2×C4×C43#12614yes—
327#13875C4311yesmaximal, characteristic, direct product factor, Sylow
328C22×C43—24no—
329C22×C43—24no—
330C22×C43—24no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43C2×#11711yescharacteristic
344C22×C43C2×#11711yescharacteristic
345C22×C43C2×#11711yescharacteristic
346C22×C43C2×C4×D411yescharacteristic
347C22×C43C2×C4×D411yescharacteristic
348C22×C43#52011yescharacteristic
349C22×C43#52011yescharacteristic
350C22×C43C2×#12111yescharacteristic
351C22×C43C2×#12311yescharacteristic
352C22×C43C2×#12411yescharacteristic
353C22×C43C2×#12611yescharacteristic
354C22×C43#52911yescharacteristic
355C22×C43#52911yescharacteristic
356C22×C43#52911yescharacteristic
357C22×C43#52911yescharacteristic
358C22×C43#54011yescharacteristic
359C22×C43#54111yescharacteristic
360C22×C43#54211yescharacteristic
361C22×C43#54211yescharacteristic
362C22×C43#54611yescharacteristic
363C22×C43#54611yescharacteristic
364C22×C43#54611yescharacteristic
365C22×C43#54711yescharacteristic
366C22×C43#54811yescharacteristic
367C22×C43#54811yescharacteristic
368C22×C43#54811yescharacteristic
369C22×C43#55011yescharacteristic
370C22×C43#55211yescharacteristic
371C22×C43#55211yescharacteristic
372C22×C43#55211yescharacteristic
373C22×C43#55311yescharacteristic
374C22×C43#55311yescharacteristic
375C22×C43#55311yescharacteristic
376C22×C43#55511yescharacteristic
377C22×C43#55611yescharacteristic
378C4×C43—24no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43—44no—
383C4×C43—44no—
384C4×C43—42no—
385C4×C43—82no—
386C4×C43—82no—
387C4×C43#38818yes—
388C2×#382C2×C4311yescharacteristic, complemented
389C2×#380C2×C4311yescharacteristic
390C2×#380C2×C4311yescharacteristic
391C2×C4×C4⋊C4C2×C4311yescharacteristic, complemented
392C2×C4×C22⋊C4C2×C4311yescharacteristic
393#1443C2×C4312yescomplemented
394#1440C2×C4312yes—
395#1437C2×C4312yes—
396C4⋊#95C2×C4311yescharacteristic, complemented
397C4⋊#95C2×C4311yescharacteristic, complemented
398#1434C2×C4312yescomplemented
399C2×C43—44no—
400C2×C43#228311yescharacteristic
401C2×C43C2×#38811yescharacteristic
402C2×C43#231411yescharacteristic
403C2×C43#235211yescharacteristic
404C2×C43#235211yescharacteristic
405C2×C43#235211yescharacteristic
406C2×C43#235411yescharacteristic
407C2×C43#242011yescharacteristic
408C2×C43#242111yescharacteristic
409C2×C43#242611yescharacteristic
410C2×C43#242711yescharacteristic
411C2×C43#248911yescharacteristic
412C2×C43#249011yescharacteristic
413C2×C43#249411yescharacteristic
414C2×C43#249511yescharacteristic
415C24×C4C22×C4311yescharacteristic
416C22×C4⋊C4C22×C4311yescharacteristic
417C22×C4⋊C4C22×C4311yescharacteristic
418C22×C4⋊C4C22×C4311yescharacteristic
419C22×C4⋊C4C22×C4311yescharacteristic
420C22×C22⋊C4C22×C4312yes—
421C22×C22⋊C4C22×C4312yes—
422C22×C22⋊C4C22×C4311yescharacteristic
423C22×C22⋊C4C22×C4311yescharacteristic
424C22×C42C22×C4312yes—
425C22×C42C22×C4311yescharacteristic
426C22×C42C22×C4311yescharacteristic
427#382—24no—
428#380—24no—
429#380—24no—
430C4×C4⋊C4—24no—
431C4×C22⋊C4C4×C4318yescomplemented
432C2×#95C22×C4312yes—
433C2×#95C22×C4312yes—
434C2×#95C22×C4312yes—
435C2×#95C22×C4312yes—
436C2×#95C22×C4312yes—
437C2×#95C22×C4312yes—
438C2×#95C22×C4312yes—
439C2×#95C22×C4312yes—
440C2×#95C22×C4312yes—
441C2×#95C22×C4311yescharacteristic
442C2×#95C22×C4311yescharacteristic
443C43#1387511yescharacteristic, direct product factor, Sylow
444C25C23×C4311yescharacteristic
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4C2×C4×C4314yes—
452C23×C4C23×C4312yes—
453C23×C4C23×C4312yes—
454C23×C4C23×C4311yescharacteristic
455C23×C4C23×C4311yescharacteristic
456C23×C4C23×C4311yescharacteristic
457C23×C4C23×C4311yescharacteristic
458C23×C4C23×C4312yes—
459C23×C4C23×C4312yes—
460C23×C4C23×C4311yescharacteristic
461C23×C4C23×C4311yescharacteristic
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4D4×C4314yes—
473C2×C4⋊C4D4×C4314yes—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4C2×C4×C4314yes—
485C2×C22⋊C4C2×C4×C4314yes—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—24no—
491C2×C42—24no—
492C2×C42—42no—
493C2×C42C2×C4×C4314yes—
494C2×C42C2×C4×C4314yes—
495#95—24no—
496#95—24no—
497#95—24no—
498#95—24no—
499#95—24no—
500#95—24no—
501#95—42no—
502#95—42no—
503#95—42no—
504#95C2×C4×C4314yes—
505#95C2×C4×C4314yes—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24C22×C4×C4312yes—
519C24#41×C4312yes—
520C24#41×C4312yes—
521C24C24×C4311yescharacteristic
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4C22×C4×C4312yes—
584C22×C4C22×C4×C4312yes—
585C22×C4C22×C4×C4312yes—
586C22×C4C22×C4×C4312yes—
587C22×C4C22×C4×C4312yes—
588C22×C4C22×C4×C4312yes—
589C22×C4C2×D4×C4314yes—
590C22×C4C2×D4×C4314yes—
591C22×C4C2×D4×C4312yes—
592C22×C4C2×D4×C4312yes—
593C22×C4#41×C4312yes—
594C22×C4#41×C4312yes—
595C22×C4#41×C4312yes—
596C22×C4#41×C4312yes—
597C22×C4#41×C4312yes—
598C22×C4#41×C4312yes—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C22⋊C4—28no—
604C22⋊C4—28no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C42—28no—
608C42—28no—
609C42—48no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#117×C4314yes—
645C23C23×C4×C4311yescharacteristic
646C23C22×D4×C4311yescharacteristic
647C23C22×D4×C4311yescharacteristic
648C23C2×#41×C4311yescharacteristic
649C23C2×#41×C4311yescharacteristic
650C23C2×#41×C4311yescharacteristic
651C23C2×#41×C4311yescharacteristic
652C23C2×#41×C4311yescharacteristic
653C23C2×#41×C4311yescharacteristic
654C23C2×#41×C4311yescharacteristic
655C23C2×#41×C4311yescharacteristic
656C23H(5,𝔽2)×C4311yescharacteristic
657C23H(5,𝔽2)×C4311yescharacteristic
658C232−1+4×C4311yescharacteristic
659C232−1+4×C4311yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—416no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4#117×C4314yes—
724C2×C4#117×C4314yes—
725C2×C4C4×D4×C4314yes—
726C2×C4C4×D4×C4314yes—
727C2×C4#121×C4314yes—
728C2×C4#123×C4314yes—
729C2×C4#124×C4314yes—
730C2×C4#126×C4314yes—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×#117×C4311yescharacteristic
747C22C2×#117×C4311yescharacteristic
748C22C2×#117×C4311yescharacteristic
749C22C2×C4×D4×C4311yescharacteristic
750C22C2×C4×D4×C4311yescharacteristic
751C22C43×#52011yescharacteristic
752C22C43×#52011yescharacteristic
753C22C2×#121×C4311yescharacteristic
754C22C2×#123×C4311yescharacteristic
755C22C2×#124×C4311yescharacteristic
756C22C2×#126×C4311yescharacteristic
757C22C43×#52911yescharacteristic
758C22C43×#52911yescharacteristic
759C22C43×#52911yescharacteristic
760C22C43×#52911yescharacteristic
761C22C43×#54011yescharacteristic
762C22C43×#54111yescharacteristic
763C22C43×#54211yescharacteristic
764C22C43×#54211yescharacteristic
765C22C43×#54611yescharacteristic
766C22C43×#54611yescharacteristic
767C22C43×#54611yescharacteristic
768C22C43×#54711yescharacteristic
769C22C43×#54811yescharacteristic
770C22C43×#54811yescharacteristic
771C22C43×#54811yescharacteristic
772C22C43×#55011yescharacteristic
773C22C43×#55211yescharacteristic
774C22C43×#55211yescharacteristic
775C22C43×#55211yescharacteristic
776C22C43×#55311yescharacteristic
777C22C43×#55311yescharacteristic
778C22C43×#55311yescharacteristic
779C22C43×#55511yescharacteristic
780C22C43×#55611yescharacteristic
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—44no—
786C4—44no—
787C4—42no—
788C4—82no—
789C4—82no—
790C4C43×#38818yes—
791C2—44no—
792C2C43×#228311yescharacteristic
793C2C2×C43×#38811yescharacteristic
794C2C43×#231411yescharacteristic
795C2C43×#235211yescharacteristic
796C2C43×#235211yescharacteristic
797C2C43×#235211yescharacteristic
798C2C43×#235411yescharacteristic
799C2C43×#242011yescharacteristic
800C2C43×#242111yescharacteristic
801C2C43×#242611yescharacteristic
802C2C43×#242711yescharacteristic
803C2C43×#248911yescharacteristic
804C2C43×#249011yescharacteristic
805C2C43×#249411yescharacteristic
806C2C43×#249511yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutatorC23C23×C4×C43
Frattini, cosocleC24C24×C43
prime radicalC25×C43C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#382C2semidirect
4. C2×C4×C4⋊C4×C43C2semidirect
6. C43×#1443C2semidirect
9. C43×C4⋊#95C2semidirect
10. C43×C4⋊#95C2semidirect
11. C43×#1434C2semidirect
28. C4×C22⋊C4×C43C4semidirect
327. #13875C43direct (N × H)
388. C2×#382C2×C43semidirect
391. C2×C4×C4⋊C4C2×C43semidirect
393. #1443C2×C43semidirect
396. C4⋊#95C2×C43semidirect
397. C4⋊#95C2×C43semidirect
398. #1434C2×C43semidirect
431. C4×C22⋊C4C4×C43semidirect
443. C43#13875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#3822
C2×C43×#3802
C2×C4×C4⋊C4×C432
C2×C4×C22⋊C4×C432
C43×#14432
C43×#14402
C43×#14372
C43×C4⋊#952
C43×#14342
#1387543