Finite Group Databasebeta

← C43×#14112 #24934129

Subgroups — C43×#14112 #24934129

Order 11008.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#389C211yesmaximal, characteristic, complemented
2C2×C43×#388C211yesmaximal, characteristic
3C2×C43×#388C211yesmaximal, characteristic
4C2×C43×#385C211yesmaximal, characteristic
5C2×C43×#385C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C43C211yesmaximal, characteristic
8C43×#1444C211yesmaximal, characteristic, complemented
9C43×#1441C211yesmaximal, characteristic, complemented
10C43×#1439C211yesmaximal, characteristic
11C43×#1439C211yesmaximal, characteristic
12C43×#1436C211yesmaximal, characteristic, complemented
13C43×#1436C211yesmaximal, characteristic, complemented
14C43×#1436C211yesmaximal, characteristic, complemented
15C43×C4⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C43C2211yescharacteristic
17C22×C4⋊C4×C43C2211yescharacteristic
18C22×C4⋊C4×C43C2211yescharacteristic
19C22×C4⋊C4×C43C2211yescharacteristic
20C22×C4⋊C4×C43C2211yescharacteristic
21C22×C4⋊C4×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C4⋊C4×C43C2211yescharacteristic
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2211yescharacteristic
31C22×C42×C43C2211yescharacteristic
32C22×C42×C43C2211yescharacteristic
33C22×C42×C43C2211yescharacteristic
34C22×C42×C43C2211yescharacteristic
35C43×#389—24no—
36C43×#388—24no—
37C43×#388C418yescomplemented
38C43×#385—24no—
39C43×#385—24no—
40C4×C4⋊C4×C43—24no—
41C4×C22⋊C4×C43—24no—
42C2×#95×C43C2211yescharacteristic
43C2×#95×C43C2211yescharacteristic
44C2×#95×C43C2211yescharacteristic
45C2×#95×C43C2211yescharacteristic
46C2×#95×C43C2211yescharacteristic
47C2×#95×C43C2211yescharacteristic
48C2×#95×C43C2211yescharacteristic
49C2×#95×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C25×C43C2311yescharacteristic
59C23×C4×C43—22no—
60C23×C4×C43—22no—
61C23×C4×C43—22no—
62C23×C4×C43—22no—
63C23×C4×C43—22no—
64C23×C4×C43—41no—
65C23×C4×C43—41no—
66C23×C4×C43C2311yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C23×C4×C43C2311yescharacteristic
70C23×C4×C43C2311yescharacteristic
71C23×C4×C43C2311yescharacteristic
72C23×C4×C43C2311yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2311yescharacteristic
80C2×C4⋊C4×C43—22no—
81C2×C4⋊C4×C43—22no—
82C2×C4⋊C4×C43—22no—
83C2×C4⋊C4×C43—22no—
84C2×C4⋊C4×C43—22no—
85C2×C4⋊C4×C43—22no—
86C2×C4⋊C4×C43—22no—
87C2×C4⋊C4×C43—22no—
88C2×C4⋊C4×C43—22no—
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—41no—
99C2×C4⋊C4×C43—41no—
100C2×C4⋊C4×C43—41no—
101C2×C4⋊C4×C43—41no—
102C2×C4⋊C4×C43C2×C414yescomplemented
103C2×C4⋊C4×C43D414yes—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—22no—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43—22no—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—41no—
116C2×C22⋊C4×C43—41no—
117C2×C22⋊C4×C43C2×C414yes—
118C2×C22⋊C4×C43C2×C414yes—
119C2×C22⋊C4×C43C2×C414yes—
120C2×C22⋊C4×C43D414yes—
121C2×C22⋊C4×C43Q814yes—
122C2×C42×C43—22no—
123C2×C42×C43—22no—
124C2×C42×C43—22no—
125C2×C42×C43—22no—
126C2×C42×C43—22no—
127C2×C42×C43—22no—
128C2×C42×C43—22no—
129C2×C42×C43—22no—
130C2×C42×C43—41no—
131C2×C42×C43—41no—
132C2×C42×C43—41no—
133C2×C42×C43C2×C414yescomplemented
134#95×C43—22no—
135#95×C43—22no—
136#95×C43—22no—
137#95×C43—22no—
138#95×C43—22no—
139#95×C43—22no—
140#95×C43—22no—
141#95×C43—22no—
142#95×C43—22no—
143#95×C43—22no—
144#95×C43—22no—
145#95×C43—22no—
146#95×C43—41no—
147#95×C43C2×C414yescomplemented
148#95×C43C2×C414yescomplemented
149#95×C43D414yes—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43C22×C412yes—
163C24×C43C2×D412yes—
164C24×C43C2×Q812yes—
165C24×C43C2411yescharacteristic
166C22×C4×C43—28no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
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—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
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×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—44no—
244C22×C4×C43—44no—
245C22×C4×C43—44no—
246C22×C4×C43—44no—
247C22×C4×C43—44no—
248C22×C4×C43—44no—
249C22×C4×C43C22×C412yes—
250C22×C4×C43C22×C412yes—
251C22×C4×C43C22×C412yes—
252C22×C4×C43C22×C412yes—
253C22×C4×C43C22×C412yes—
254C22×C4×C43C22×C412yes—
255C22×C4×C43C2×D412yes—
256C22×C4×C43C2×D412yes—
257C22×C4×C43C2×D412yes—
258C22×C4×C43C2×D412yes—
259C22×C4×C43C2×D412yes—
260C22×C4×C43C2×D412yes—
261C22×C4×C43C2×D412yes—
262C22×C4×C43C2×D412yes—
263C22×C4×C43C2×Q812yes—
264C22×C4×C43C2×Q812yes—
265C22×C4×C43#4112yes—
266C22×C4×C43#4112yes—
267C22×C4×C43#4112yes—
268C22×C4×C43#4112yes—
269C22×C4×C43#4112yes—
270C22×C4×C43#4112yes—
271C4⋊C4×C43—28no—
272C4⋊C4×C43—28no—
273C4⋊C4×C43—28no—
274C4⋊C4×C43—44no—
275C4⋊C4×C43—44no—
276C4⋊C4×C43—44no—
277C4⋊C4×C43—44no—
278C4⋊C4×C43—44no—
279C22⋊C4×C43—28no—
280C22⋊C4×C43—28no—
281C22⋊C4×C43—28no—
282C22⋊C4×C43—44no—
283C22⋊C4×C43—44no—
284C22⋊C4×C43C4⋊C4116yescomplemented
285C42×C43—28no—
286C42×C43—44no—
287C42×C43—44no—
288C42×C43—44no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
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×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43C2×C4⋊C414yes—
324C23×C43C23×C411yescharacteristic
325C23×C43C22×D411yescharacteristic
326C23×C43C22×D411yescharacteristic
327C23×C43C22×D411yescharacteristic
328C23×C43C22×Q811yescharacteristic
329C23×C43C2×#4111yescharacteristic
330C23×C43C2×#4111yescharacteristic
331C23×C43C2×#4111yescharacteristic
332C23×C43C2×#4111yescharacteristic
333C23×C43C2×#4111yescharacteristic
334C23×C43C2×#4111yescharacteristic
335C23×C43H(5,𝔽2)11yescharacteristic
336C23×C43H(5,𝔽2)11yescharacteristic
337C23×C432−1+411yescharacteristic
338C23×C432−1+411yescharacteristic
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—416no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
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—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43C2×C4⋊C414yes—
434C2×C4×C43C2×C4⋊C414yes—
435C2×C4×C43C4×D414yes—
436C2×C4×C43C4×D414yes—
437C2×C4×C43#12114yes—
438#14112C4311yesmaximal, characteristic, direct product factor, Sylow
439C22×C43—24no—
440C22×C43—24no—
441C22×C43—24no—
442C22×C43—42no—
443C22×C43—42no—
444C22×C43—42no—
445C22×C43—42no—
446C22×C43—42no—
447C22×C43—42no—
448C22×C43—42no—
449C22×C43—42no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43—42no—
453C22×C43—42no—
454C22×C43C22×C4⋊C411yescharacteristic
455C22×C43C2×C4×D411yescharacteristic
456C22×C43C2×C4×D411yescharacteristic
457C22×C43C4×#4111yescharacteristic
458C22×C43C4×#4111yescharacteristic
459C22×C43#52011yescharacteristic
460C22×C43#52011yescharacteristic
461C22×C43C2×#12111yescharacteristic
462C22×C43#52511yescharacteristic
463C22×C43#52511yescharacteristic
464C22×C43#52511yescharacteristic
465C22×C43#52911yescharacteristic
466C22×C43#53211yescharacteristic
467C22×C43#53311yescharacteristic
468C22×C43#53311yescharacteristic
469C22×C43#53811yescharacteristic
470C22×C43#53911yescharacteristic
471C22×C43#54111yescharacteristic
472C22×C43#54211yescharacteristic
473C22×C43D4211yescharacteristic
474C22×C43D4211yescharacteristic
475C22×C43#54611yescharacteristic
476C22×C43#54611yescharacteristic
477C22×C43#54711yescharacteristic
478C22×C43#54711yescharacteristic
479C22×C43#54711yescharacteristic
480C22×C43#54811yescharacteristic
481C22×C43D4×Q811yescharacteristic
482C22×C43D4×Q811yescharacteristic
483C22×C43#55111yescharacteristic
484C22×C43#55211yescharacteristic
485C22×C43#55411yescharacteristic
486C22×C43#55411yescharacteristic
487C22×C43#55611yescharacteristic
488C22×C43#55911yescharacteristic
489C4×C43—24no—
490C4×C43—24no—
491C4×C43—24no—
492C4×C43—24no—
493C4×C43—24no—
494C4×C43—42no—
495C4×C43—42no—
496C4×C43—42no—
497C4×C43—42no—
498C4×C43—42no—
499C4×C43—42no—
500C4×C43—42no—
501C4×C43—81no—
502C4×C43—81no—
503C2×#389C2×C4311yescharacteristic, complemented
504C2×#388C2×C4311yescharacteristic
505C2×#388C2×C4311yescharacteristic
506C2×#385C2×C4311yescharacteristic
507C2×#385C2×C4311yescharacteristic
508C2×C4×C4⋊C4C2×C4311yescharacteristic, complemented
509C2×C4×C22⋊C4C2×C4311yescharacteristic
510#1444C2×C4311yescharacteristic, complemented
511#1441C2×C4311yescharacteristic, complemented
512#1439C2×C4311yescharacteristic
513#1439C2×C4311yescharacteristic
514#1436C2×C4311yescharacteristic, complemented
515#1436C2×C4311yescharacteristic, complemented
516#1436C2×C4311yescharacteristic, complemented
517C4⋊#95C2×C4311yescharacteristic, complemented
518C2×C43—44no—
519C2×C43#229611yescharacteristic
520C2×C43C4×#12111yescharacteristic
521C2×C43#233411yescharacteristic
522C2×C43D4×C4⋊C411yescharacteristic
523C2×C43D4×C4⋊C411yescharacteristic
524C2×C43#235911yescharacteristic
525C2×C43#236711yescharacteristic
526C2×C43#242411yescharacteristic
527C2×C43#242911yescharacteristic
528C2×C43#245511yescharacteristic
529C2×C43#246111yescharacteristic
530C2×C43#246511yescharacteristic
531C2×C43#247811yescharacteristic
532C2×C43#255611yescharacteristic
533C2×C43#258911yescharacteristic
534C24×C4C22×C4311yescharacteristic
535C22×C4⋊C4C22×C4311yescharacteristic
536C22×C4⋊C4C22×C4311yescharacteristic
537C22×C4⋊C4C22×C4311yescharacteristic
538C22×C4⋊C4C22×C4311yescharacteristic
539C22×C4⋊C4C22×C4311yescharacteristic
540C22×C4⋊C4C22×C4311yescharacteristic
541C22×C4⋊C4C22×C4311yescharacteristic
542C22×C4⋊C4C22×C4311yescharacteristic
543C22×C22⋊C4C22×C4311yescharacteristic
544C22×C22⋊C4C22×C4311yescharacteristic
545C22×C22⋊C4C22×C4311yescharacteristic
546C22×C22⋊C4C22×C4311yescharacteristic
547C22×C22⋊C4C22×C4311yescharacteristic
548C22×C22⋊C4C22×C4311yescharacteristic
549C22×C42C22×C4311yescharacteristic
550C22×C42C22×C4311yescharacteristic
551C22×C42C22×C4311yescharacteristic
552C22×C42C22×C4311yescharacteristic
553#389—24no—
554#388—24no—
555#388C4×C4318yescomplemented
556#385—24no—
557#385—24no—
558C4×C4⋊C4—24no—
559C4×C22⋊C4—24no—
560C2×#95C22×C4311yescharacteristic
561C2×#95C22×C4311yescharacteristic
562C2×#95C22×C4311yescharacteristic
563C2×#95C22×C4311yescharacteristic
564C2×#95C22×C4311yescharacteristic
565C2×#95C22×C4311yescharacteristic
566C2×#95C22×C4311yescharacteristic
567C2×#95C22×C4311yescharacteristic
568C2×#95C22×C4311yescharacteristic
569C2×#95C22×C4311yescharacteristic
570C2×#95C22×C4311yescharacteristic
571C2×#95C22×C4311yescharacteristic
572C2×#95C22×C4311yescharacteristic
573C2×#95C22×C4311yescharacteristic
574C2×#95C22×C4311yescharacteristic
575C2×#95C22×C4311yescharacteristic
576C43#1411211yescharacteristic, direct product factor, Sylow
577C25C23×C4311yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C4311yescharacteristic
586C23×C4C23×C4311yescharacteristic
587C23×C4C23×C4311yescharacteristic
588C23×C4C23×C4311yescharacteristic
589C23×C4C23×C4311yescharacteristic
590C23×C4C23×C4311yescharacteristic
591C23×C4C23×C4311yescharacteristic
592C23×C4C23×C4311yescharacteristic
593C23×C4C23×C4311yescharacteristic
594C23×C4C23×C4311yescharacteristic
595C23×C4C23×C4311yescharacteristic
596C23×C4C23×C4311yescharacteristic
597C23×C4C23×C4311yescharacteristic
598C23×C4C23×C4311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4C2×C4×C4314yescomplemented
622C2×C4⋊C4D4×C4314yes—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4C2×C4×C4314yes—
637C2×C22⋊C4C2×C4×C4314yes—
638C2×C22⋊C4C2×C4×C4314yes—
639C2×C22⋊C4D4×C4314yes—
640C2×C22⋊C4Q8×C4314yes—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42—22no—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—41no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42C2×C4×C4314yescomplemented
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—41no—
666#95C2×C4×C4314yescomplemented
667#95C2×C4×C4314yescomplemented
668#95D4×C4314yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C4312yes—
682C24C2×D4×C4312yes—
683C24C2×Q8×C4312yes—
684C24C24×C4311yescharacteristic
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×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—28no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
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—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4C22×C4×C4312yes—
769C22×C4C22×C4×C4312yes—
770C22×C4C22×C4×C4312yes—
771C22×C4C22×C4×C4312yes—
772C22×C4C22×C4×C4312yes—
773C22×C4C22×C4×C4312yes—
774C22×C4C2×D4×C4312yes—
775C22×C4C2×D4×C4312yes—
776C22×C4C2×D4×C4312yes—
777C22×C4C2×D4×C4312yes—
778C22×C4C2×D4×C4312yes—
779C22×C4C2×D4×C4312yes—
780C22×C4C2×D4×C4312yes—
781C22×C4C2×D4×C4312yes—
782C22×C4C2×Q8×C4312yes—
783C22×C4C2×Q8×C4312yes—
784C22×C4#41×C4312yes—
785C22×C4#41×C4312yes—
786C22×C4#41×C4312yes—
787C22×C4#41×C4312yes—
788C22×C4#41×C4312yes—
789C22×C4#41×C4312yes—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4C4⋊C4×C43116yescomplemented
804C42—28no—
805C42—44no—
806C42—44no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C4314yes—
843C23C23×C4×C4311yescharacteristic
844C23C22×D4×C4311yescharacteristic
845C23C22×D4×C4311yescharacteristic
846C23C22×D4×C4311yescharacteristic
847C23C22×Q8×C4311yescharacteristic
848C23C2×#41×C4311yescharacteristic
849C23C2×#41×C4311yescharacteristic
850C23C2×#41×C4311yescharacteristic
851C23C2×#41×C4311yescharacteristic
852C23C2×#41×C4311yescharacteristic
853C23C2×#41×C4311yescharacteristic
854C23H(5,𝔽2)×C4311yescharacteristic
855C23H(5,𝔽2)×C4311yescharacteristic
856C232−1+4×C4311yescharacteristic
857C232−1+4×C4311yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—416no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4C2×C4⋊C4×C4314yes—
953C2×C4C2×C4⋊C4×C4314yes—
954C2×C4C4×D4×C4314yes—
955C2×C4C4×D4×C4314yes—
956C2×C4#121×C4314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C4311yescharacteristic
973C22C2×C4×D4×C4311yescharacteristic
974C22C2×C4×D4×C4311yescharacteristic
975C22C4×#41×C4311yescharacteristic
976C22C4×#41×C4311yescharacteristic
977C22C43×#52011yescharacteristic
978C22C43×#52011yescharacteristic
979C22C2×#121×C4311yescharacteristic
980C22C43×#52511yescharacteristic
981C22C43×#52511yescharacteristic
982C22C43×#52511yescharacteristic
983C22C43×#52911yescharacteristic
984C22C43×#53211yescharacteristic
985C22C43×#53311yescharacteristic
986C22C43×#53311yescharacteristic
987C22C43×#53811yescharacteristic
988C22C43×#53911yescharacteristic
989C22C43×#54111yescharacteristic
990C22C43×#54211yescharacteristic
991C22D42×C4311yescharacteristic
992C22D42×C4311yescharacteristic
993C22C43×#54611yescharacteristic
994C22C43×#54611yescharacteristic
995C22C43×#54711yescharacteristic
996C22C43×#54711yescharacteristic
997C22C43×#54711yescharacteristic
998C22C43×#54811yescharacteristic
999C22D4×Q8×C4311yescharacteristic
1000C22D4×Q8×C4311yescharacteristic
1001C22C43×#55111yescharacteristic
1002C22C43×#55211yescharacteristic
1003C22C43×#55411yescharacteristic
1004C22C43×#55411yescharacteristic
1005C22C43×#55611yescharacteristic
1006C22C43×#55911yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C43×#229611yescharacteristic
1023C2C4×#121×C4311yescharacteristic
1024C2C43×#233411yescharacteristic
1025C2D4×C4⋊C4×C4311yescharacteristic
1026C2D4×C4⋊C4×C4311yescharacteristic
1027C2C43×#235911yescharacteristic
1028C2C43×#236711yescharacteristic
1029C2C43×#242411yescharacteristic
1030C2C43×#242911yescharacteristic
1031C2C43×#245511yescharacteristic
1032C2C43×#246111yescharacteristic
1033C2C43×#246511yescharacteristic
1034C2C43×#247811yescharacteristic
1035C2C43×#255611yescharacteristic
1036C2C43×#258911yescharacteristic
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×#389C2semidirect
6. C2×C4×C4⋊C4×C43C2semidirect
8. C43×#1444C2semidirect
9. C43×#1441C2semidirect
12. C43×#1436C2semidirect
13. C43×#1436C2semidirect
14. C43×#1436C2semidirect
15. C43×C4⋊#95C2semidirect
37. C43×#388C4semidirect
102. C2×C4⋊C4×C43C2×C4semidirect
133. C2×C42×C43C2×C4semidirect
147. #95×C43C2×C4semidirect
148. #95×C43C2×C4semidirect
284. C22⋊C4×C43C4⋊C4semidirect
438. #14112C43direct (N × H)
503. C2×#389C2×C43semidirect
508. C2×C4×C4⋊C4C2×C43semidirect
510. #1444C2×C43semidirect
511. #1441C2×C43semidirect
514. #1436C2×C43semidirect
515. #1436C2×C43semidirect
516. #1436C2×C43semidirect
517. C4⋊#95C2×C43semidirect
555. #388C4×C43semidirect
576. C43#14112direct (N × H)
621. C2×C4⋊C4C2×C4×C43semidirect
652. C2×C42C2×C4×C43semidirect
666. #95C2×C4×C43semidirect
667. #95C2×C4×C43semidirect
803. C22⋊C4C4⋊C4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3892
C2×C43×#3882
C2×C43×#3852
C2×C4×C4⋊C4×C432
C2×C4×C22⋊C4×C432
C43×#14442
C43×#14412
C43×#14392
C43×#14362
C43×C4⋊#952
#1411243