Finite Group Databasebeta

← C43×#14722 #24934739

Subgroups — C43×#14722 #24934739

Order 11008.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C43C211yesmaximal, characteristic, complemented
2C22×C4×D4×C43C211yesmaximal, characteristic, complemented
3C2×C43×#394C211yesmaximal, characteristic, complemented
4C2×C43×#392C212yesmaximal, complemented
5C2×C43×#392C211yesmaximal, characteristic, complemented
6C2×C43×#386C212yesmaximal, complemented
7C43×#1441C211yesmaximal, characteristic, complemented
8C43×#1439C211yesmaximal, characteristic, complemented
9C43×#1438C212yesmaximal, complemented
10C43×#1437C212yesmaximal, complemented
11C43×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C43C2211yescharacteristic
13C23×D4×C43C2212yes—
14C23×D4×C43C2211yescharacteristic
15C23×D4×C43C2212yes—
16C24×C4×C43C2211yescharacteristic
17C24×C4×C43C2211yescharacteristic
18C2×#121×C43—24no—
19C2×#121×C43—28no—
20C2×C4×D4×C43—24no—
21C2×C4×D4×C43—24no—
22C2×C4×D4×C43—24no—
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C4⋊C4×C43C2211yescharacteristic
25C22×C22⋊C4×C43C2212yes—
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2212yes—
28C22×C22⋊C4×C43C2212yes—
29C22×C22⋊C4×C43C2212yes—
30C22×C22⋊C4×C43C2212yes—
31C22×C22⋊C4×C43C2211yescharacteristic
32C22×C22⋊C4×C43C2212yes—
33C22×C42×C43C2211yescharacteristic
34C43×#394—24no—
35C43×#392—28no—
36C43×#392—24no—
37C43×#386—28no—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C2×#95×C43C2211yescharacteristic
41C2×#95×C43C2212yes—
42C2×#95×C43C2212yes—
43C2×#95×C43C2212yes—
44C25×C43C2312yes—
45C25×C43C2311yescharacteristic
46C25×C43C2311yescharacteristic
47C22×D4×C43—22no—
48C22×D4×C43—22no—
49C22×D4×C43—22no—
50C22×D4×C43—22no—
51C22×D4×C43—24no—
52C22×D4×C43—24no—
53C22×D4×C43—24no—
54C22×D4×C43—24no—
55C22×D4×C43—24no—
56C22×D4×C43—24no—
57C22×D4×C43—24no—
58C22×D4×C43—24no—
59C22×D4×C43—24no—
60C22×D4×C43—22no—
61C22×D4×C43—24no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43—22no—
66C22×D4×C43—24no—
67C22×D4×C43—42no—
68C22×D4×C43—42no—
69C22×D4×C43—42no—
70C22×D4×C43—42no—
71C22×D4×C43—42no—
72C22×D4×C43D414yescomplemented
73C23×C4×C43—22no—
74C23×C4×C43—22no—
75C23×C4×C43—22no—
76C23×C4×C43—22no—
77C23×C4×C43—22no—
78C23×C4×C43—24no—
79C23×C4×C43—24no—
80C23×C4×C43—42no—
81C23×C4×C43—42no—
82C23×C4×C43D414yescomplemented
83C23×C4×C43C2312yes—
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2312yes—
87C23×C4×C43C2312yes—
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91#121×C43—232no—
92C4×D4×C43—232no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—24no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43D414yescomplemented
98C2×C22⋊C4×C43—22no—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43—24no—
104C2×C22⋊C4×C43—24no—
105C2×C22⋊C4×C43—24no—
106C2×C22⋊C4×C43—24no—
107C2×C22⋊C4×C43—24no—
108C2×C22⋊C4×C43—24no—
109C2×C22⋊C4×C43—24no—
110C2×C22⋊C4×C43—24no—
111C2×C22⋊C4×C43—24no—
112C2×C22⋊C4×C43—24no—
113C2×C22⋊C4×C43—24no—
114C2×C22⋊C4×C43—24no—
115C2×C22⋊C4×C43—24no—
116C2×C22⋊C4×C43—42no—
117C2×C22⋊C4×C43—42no—
118C2×C22⋊C4×C43—42no—
119C2×C22⋊C4×C43—42no—
120C2×C22⋊C4×C43D414yescomplemented
121C2×C22⋊C4×C43D418yescomplemented
122C2×C42×C43—22no—
123C2×C42×C43—22no—
124C2×C42×C43—22no—
125#95×C43—24no—
126#95×C43—24no—
127#95×C43—22no—
128#95×C43—24no—
129#95×C43—22no—
130#95×C43—42no—
131C24×C43—21no—
132C24×C43—21no—
133C24×C43—21no—
134C24×C43—21no—
135C24×C43—22no—
136C24×C43—22no—
137C24×C43—22no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—22no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43—22no—
149C24×C43—22no—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43C2×D414yes—
162C24×C43C2×D412yes—
163C24×C43C2×D412yes—
164C24×C43C2×D412yes—
165C24×C43C2×D412yes—
166C24×C43#4112yes—
167C24×C43#4112yes—
168C24×C43C2411yescharacteristic
169C2×D4×C43—28no—
170C2×D4×C43—28no—
171C2×D4×C43—28no—
172C2×D4×C43—28no—
173C2×D4×C43—216no—
174C2×D4×C43—28no—
175C2×D4×C43—216no—
176C2×D4×C43—28no—
177C2×D4×C43—28no—
178C2×D4×C43—28no—
179C2×D4×C43—48no—
180C2×D4×C43—48no—
181C2×D4×C43—48no—
182C2×D4×C43—48no—
183C2×D4×C43—48no—
184C2×D4×C43—48no—
185C2×D4×C43—48no—
186C2×D4×C43—48no—
187C2×D4×C43—48no—
188C2×D4×C43—48no—
189C2×D4×C43—48no—
190C2×D4×C43—48no—
191C2×D4×C43—44no—
192C2×D4×C43—44no—
193C2×D4×C43—48no—
194C2×D4×C43—48no—
195C22×C4×C43—28no—
196C22×C4×C43—28no—
197C22×C4×C43—28no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—22no—
220C22×C4×C43—22no—
221C22×C4×C43—22no—
222C22×C4×C43—22no—
223C22×C4×C43—22no—
224C22×C4×C43—22no—
225C22×C4×C43—22no—
226C22×C4×C43—22no—
227C22×C4×C43—22no—
228C22×C4×C43—22no—
229C22×C4×C43—22no—
230C22×C4×C43—22no—
231C22×C4×C43—22no—
232C22×C4×C43—22no—
233C22×C4×C43—22no—
234C22×C4×C43—44no—
235C22×C4×C43—48no—
236C22×C4×C43—48no—
237C22×C4×C43—48no—
238C22×C4×C43—48no—
239C22×C4×C43—44no—
240C22×C4×C43—44no—
241C22×C4×C43C2×D414yes—
242C22×C4×C43C2×D412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43C2×D414yes—
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2×D412yes—
247C22×C4×C43C2×D412yes—
248C22×C4×C43C2×D412yes—
249C22×C4×C43C2×D412yes—
250C22×C4×C43C2×D412yes—
251C22×C4×C43#4114yes—
252C22×C4×C43#4112yes—
253C4⋊C4×C43—28no—
254C4⋊C4×C43—28no—
255C22⋊C4×C43—28no—
256C22⋊C4×C43—28no—
257C22⋊C4×C43—216no—
258C22⋊C4×C43—48no—
259C22⋊C4×C43—48no—
260C22⋊C4×C43—48no—
261C22⋊C4×C43—48no—
262C22⋊C4×C43—48no—
263C42×C43—28no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—24no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—24no—
282C23×C43—24no—
283C23×C43—24no—
284C23×C43—24no—
285C23×C43—24no—
286C23×C43—24no—
287C23×C43—24no—
288C23×C43—24no—
289C23×C43—24no—
290C23×C43—24no—
291C23×C43—24no—
292C23×C43—24no—
293C23×C43—24no—
294C23×C43—24no—
295C23×C43—24no—
296C23×C43—24no—
297C23×C43—41no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—42no—
305C23×C43—42no—
306C23×C43—42no—
307C23×C43—42no—
308C23×C43—42no—
309C23×C43—42no—
310C23×C43—42no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43—42no—
319C23×C43—42no—
320C23×C43—42no—
321C23×C43—42no—
322C23×C43—42no—
323C23×C43—42no—
324C23×C43—42no—
325C23×C43—42no—
326C23×C43—42no—
327C23×C43—42no—
328C23×C43—42no—
329C23×C43—42no—
330C23×C43—42no—
331C23×C43—42no—
332C23×C43—42no—
333C23×C43—42no—
334C23×C43—42no—
335C23×C43—42no—
336C23×C43—42no—
337C23×C43—42no—
338C23×C43—42no—
339C23×C43—42no—
340C23×C43—42no—
341C23×C43—42no—
342C23×C43—42no—
343C23×C43#12114yes—
344C23×C43#12114yescomplemented
345C23×C43C22×D411yescharacteristic
346C23×C43C22×D411yescharacteristic
347C23×C43C22×D411yescharacteristic
348C23×C43C22×D412yes—
349C23×C43C22×D411yescharacteristic
350C23×C43C2×#4111yescharacteristic
351C23×C43C2×#4111yescharacteristic
352C23×C43C2×#4111yescharacteristic
353C23×C43C2×#4112yes—
354C23×C43H(5,𝔽2)12yes—
355C23×C43H(5,𝔽2)12yes—
356D4×C43—232no—
357D4×C43—416no—
358D4×C43—432no—
359D4×C43—432no—
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—24no—
371C2×C4×C43—24no—
372C2×C4×C43—24no—
373C2×C4×C43—24no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—24no—
377C2×C4×C43—24no—
378C2×C4×C43—24no—
379C2×C4×C43—24no—
380C2×C4×C43—24no—
381C2×C4×C43—24no—
382C2×C4×C43—24no—
383C2×C4×C43—24no—
384C2×C4×C43—416no—
385C2×C4×C43—416no—
386C2×C4×C43—41no—
387C2×C4×C43—42no—
388C2×C4×C43—42no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—42no—
393C2×C4×C43—42no—
394C2×C4×C43—42no—
395C2×C4×C43—42no—
396C2×C4×C43—42no—
397C2×C4×C43—42no—
398C2×C4×C43—42no—
399C2×C4×C43—42no—
400C2×C4×C43—42no—
401C2×C4×C43—42no—
402C2×C4×C43—42no—
403C2×C4×C43—42no—
404C2×C4×C43—42no—
405C2×C4×C43—42no—
406C2×C4×C43—42no—
407C2×C4×C43#12014yes—
408C2×C4×C43#12014yes—
409C2×C4×C43#12114yescomplemented
410#14722C4311yesmaximal, characteristic, direct product factor, Sylow
411C22×C43—24no—
412C22×C43—24no—
413C22×C43—24no—
414C22×C43—28no—
415C22×C43—24no—
416C22×C43—42no—
417C22×C43—42no—
418C22×C43—42no—
419C22×C43—42no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—42no—
423C22×C43—44no—
424C22×C43—44no—
425C22×C43—44no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—44no—
429C22×C43—44no—
430C22×C43—44no—
431C22×C43—44no—
432C22×C43—42no—
433C22×C43—44no—
434C22×C43—44no—
435C22×C43—44no—
436C22×C43—44no—
437C22×C43—44no—
438C22×C43—44no—
439C22×C43—44no—
440C22×C43—82no—
441C22×C43—82no—
442C22×C43—82no—
443C22×C43—82no—
444C22×C43—82no—
445C22×C43—82no—
446C22×C43—82no—
447C22×C43—82no—
448C22×C43C2×#12011yescharacteristic
449C22×C43C2×#12011yescharacteristic
450C22×C43C2×#12111yescharacteristic
451C22×C43C2×#12111yescharacteristic
452C22×C43C2×#12111yescharacteristic
453C22×C43#52511yescharacteristic
454C22×C43#52511yescharacteristic
455C22×C43#52511yescharacteristic
456C22×C43#52512yes—
457C22×C43#53212yes—
458C22×C43#53211yescharacteristic
459C22×C43#53411yescharacteristic
460C22×C43#53511yescharacteristic
461C22×C43#53812yes—
462C22×C43#54012yes—
463C22×C43D4212yes—
464C22×C43D4212yes—
465C22×C43D4212yes—
466C22×C43#54612yes—
467C22×C43#54612yes—
468C22×C43#54612yes—
469C22×C43#55012yes—
470C22×C43#55312yes—
471C4×C43—24no—
472C4×C43—24no—
473C4×C43—24no—
474C4×C43—42no—
475C4×C43—44no—
476C4×C43—44no—
477C4×C43—42no—
478C4×C43—82no—
479C22×#121C2×C4311yescharacteristic, complemented
480C22×C4×D4C2×C4311yescharacteristic, complemented
481C2×#394C2×C4311yescharacteristic, complemented
482C2×#392C2×C4312yescomplemented
483C2×#392C2×C4311yescharacteristic, complemented
484C2×#386C2×C4312yescomplemented
485#1441C2×C4311yescharacteristic, complemented
486#1439C2×C4311yescharacteristic, complemented
487#1438C2×C4312yescomplemented
488#1437C2×C4312yescomplemented
489C22⋊#95C2×C4311yescharacteristic, complemented
490C2×C43—44no—
491C2×C43—44no—
492C2×C43—84no—
493C2×C43#238811yescharacteristic
494C2×C43#240311yescharacteristic
495C2×C43#240811yescharacteristic
496C2×C43#242412yes—
497C2×C43#242812yes—
498C2×C43#243111yescharacteristic
499C2×C43#245612yes—
500C2×C43#246412yes—
501C2×C43#254311yescharacteristic
502C2×C43#263511yescharacteristic
503C2×C43#284711yescharacteristic
504C23×D4C22×C4311yescharacteristic
505C23×D4C22×C4312yes—
506C23×D4C22×C4311yescharacteristic
507C23×D4C22×C4312yes—
508C24×C4C22×C4311yescharacteristic
509C24×C4C22×C4311yescharacteristic
510C2×#121—24no—
511C2×#121—28no—
512C2×C4×D4—24no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C22×C4⋊C4C22×C4311yescharacteristic
516C22×C4⋊C4C22×C4311yescharacteristic
517C22×C22⋊C4C22×C4312yes—
518C22×C22⋊C4C22×C4311yescharacteristic
519C22×C22⋊C4C22×C4312yes—
520C22×C22⋊C4C22×C4312yes—
521C22×C22⋊C4C22×C4312yes—
522C22×C22⋊C4C22×C4312yes—
523C22×C22⋊C4C22×C4311yescharacteristic
524C22×C22⋊C4C22×C4312yes—
525C22×C42C22×C4311yescharacteristic
526#394—24no—
527#392—28no—
528#392—24no—
529#386—28no—
530C2×#95C22×C4311yescharacteristic
531C2×#95C22×C4312yes—
532C2×#95C22×C4311yescharacteristic
533C2×#95C22×C4312yes—
534C2×#95C22×C4312yes—
535C2×#95C22×C4312yes—
536C43#1472211yescharacteristic, direct product factor, Sylow
537C25C23×C4312yes—
538C25C23×C4311yescharacteristic
539C25C23×C4311yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C4314yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C4314yescomplemented
576C23×C4C23×C4312yes—
577C23×C4C23×C4311yescharacteristic
578C23×C4C23×C4311yescharacteristic
579C23×C4C23×C4312yes—
580C23×C4C23×C4312yes—
581C23×C4C23×C4311yescharacteristic
582C23×C4C23×C4311yescharacteristic
583C23×C4C23×C4311yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C4314yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C4314yescomplemented
614C2×C22⋊C4D4×C4318yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C4314yes—
655C24C2×D4×C4312yes—
656C24C2×D4×C4312yes—
657C24C2×D4×C4312yes—
658C24C2×D4×C4312yes—
659C24#41×C4312yes—
660C24#41×C4312yes—
661C24C24×C4311yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C4314yes—
735C22×C4C2×D4×C4312yes—
736C22×C4C2×D4×C4312yes—
737C22×C4C2×D4×C4314yes—
738C22×C4C2×D4×C4312yes—
739C22×C4C2×D4×C4312yes—
740C22×C4C2×D4×C4312yes—
741C22×C4C2×D4×C4312yes—
742C22×C4C2×D4×C4312yes—
743C22×C4C2×D4×C4312yes—
744C22×C4#41×C4314yes—
745C22×C4#41×C4312yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C4314yes—
837C23#121×C4314yescomplemented
838C23C22×D4×C4311yescharacteristic
839C23C22×D4×C4311yescharacteristic
840C23C22×D4×C4311yescharacteristic
841C23C22×D4×C4312yes—
842C23C22×D4×C4311yescharacteristic
843C23C2×#41×C4311yescharacteristic
844C23C2×#41×C4311yescharacteristic
845C23C2×#41×C4311yescharacteristic
846C23C2×#41×C4312yes—
847C23H(5,𝔽2)×C4312yes—
848C23H(5,𝔽2)×C4312yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C4314yes—
901C2×C4#120×C4314yes—
902C2×C4#121×C4314yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—28no—
907C22—24no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—42no—
919C22—42no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C4311yescharacteristic
941C22C2×#120×C4311yescharacteristic
942C22C2×#121×C4311yescharacteristic
943C22C2×#121×C4311yescharacteristic
944C22C2×#121×C4311yescharacteristic
945C22C43×#52511yescharacteristic
946C22C43×#52511yescharacteristic
947C22C43×#52511yescharacteristic
948C22C43×#52512yes—
949C22C43×#53212yes—
950C22C43×#53211yescharacteristic
951C22C43×#53411yescharacteristic
952C22C43×#53511yescharacteristic
953C22C43×#53812yes—
954C22C43×#54012yes—
955C22D42×C4312yes—
956C22D42×C4312yes—
957C22D42×C4312yes—
958C22C43×#54612yes—
959C22C43×#54612yes—
960C22C43×#54612yes—
961C22C43×#55012yes—
962C22C43×#55312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C43×#238811yescharacteristic
975C2C43×#240311yescharacteristic
976C2C43×#240811yescharacteristic
977C2C43×#242412yes—
978C2C43×#242812yes—
979C2C43×#243111yescharacteristic
980C2C43×#245612yes—
981C2C43×#246412yes—
982C2C43×#254311yescharacteristic
983C2C43×#263511yescharacteristic
984C2C43×#284711yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutator, Frattini, cosocleC24C24×C43
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C43C2semidirect
2. C22×C4×D4×C43C2semidirect
3. C2×C43×#394C2semidirect
4. C2×C43×#392C2semidirect
5. C2×C43×#392C2semidirect
6. C2×C43×#386C2semidirect
7. C43×#1441C2semidirect
8. C43×#1439C2semidirect
9. C43×#1438C2semidirect
10. C43×#1437C2semidirect
11. C43×C22⋊#95C2semidirect
72. C22×D4×C43D4semidirect
82. C23×C4×C43D4semidirect
97. C2×C4⋊C4×C43D4semidirect
120. C2×C22⋊C4×C43D4semidirect
121. C2×C22⋊C4×C43D4semidirect
344. C23×C43#121semidirect
409. C2×C4×C43#121semidirect
410. #14722C43direct (N × H)
479. C22×#121C2×C43semidirect
480. C22×C4×D4C2×C43semidirect
481. C2×#394C2×C43semidirect
482. C2×#392C2×C43semidirect
483. C2×#392C2×C43semidirect
484. C2×#386C2×C43semidirect
485. #1441C2×C43semidirect
486. #1439C2×C43semidirect
487. #1438C2×C43semidirect
488. #1437C2×C43semidirect
489. C22⋊#95C2×C43semidirect
536. C43#14722direct (N × H)
565. C22×D4D4×C43semidirect
575. C23×C4D4×C43semidirect
590. C2×C4⋊C4D4×C43semidirect
613. C2×C22⋊C4D4×C43semidirect
614. C2×C22⋊C4D4×C43semidirect
837. C23#121×C43semidirect
902. C2×C4#121×C43semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C432
C22×C4×D4×C432
C2×C43×#3942
C2×C43×#3922
C2×C43×#3862
C43×#14412
C43×#14392
C43×#14382
C43×#14372
C43×C22⋊#952
#1472243