Finite Group Databasebeta

← C43×#22424 #24942441

Subgroups — C43×#22424 #24942441

Order 11008.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#546C211yesmaximal, characteristic
2C2×C43×#435C211yesmaximal, characteristic, complemented
3C2×C43×#418C211yesmaximal, characteristic, complemented
4C2×C43×#416C211yesmaximal, characteristic, complemented
5C43×#2354C211yesmaximal, characteristic, complemented
6C43×#1983C211yesmaximal, characteristic, complemented
7C43×#1959C211yesmaximal, characteristic, complemented
8C43×#1894C211yesmaximal, characteristic, complemented
9C43×#1893C211yesmaximal, characteristic, complemented
10C43×#1875C211yesmaximal, characteristic, complemented
11C43×#1873C211yesmaximal, characteristic, complemented
12C43×#1802C211yesmaximal, characteristic, complemented
13C43×#1788C211yesmaximal, characteristic, complemented
14C43×#1786C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C23×C8×C43C2211yescharacteristic, complemented
20C43×#546—24no—
21C43×#546C418yescomplemented
22C2×#124×C43C2211yescharacteristic
23C2×#123×C43—21no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C2×#121×C43—21no—
26C2×#121×C43C2211yescharacteristic
27C2×#120×C43—21no—
28C2×C4×D4×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C2×#117×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic, complemented
32C22×C22⋊C4×C43—21no—
33C43×#435—24no—
34C2×C4⋊C8×C43C2211yescharacteristic, complemented
35C43×#418—24no—
36C43×#416—24no—
37C2×#103×C43C2211yescharacteristic, complemented
38C2×#103×C43C2211yescharacteristic, complemented
39C2×#103×C43C2211yescharacteristic, complemented
40C2×#103×C43C2211yescharacteristic, complemented
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×#102×C43C2211yescharacteristic
46C2×#102×C43C2211yescharacteristic
47C2×#102×C43C2211yescharacteristic
48C2×#102×C43C2211yescharacteristic
49C2×C22⋊C8×C43C2211yescharacteristic
50C2×C22⋊C8×C43C2211yescharacteristic, complemented
51C2×#97×C43C2211yescharacteristic, complemented
52C43×#390—21no—
53C43×#388—21no—
54C43×#388—21no—
55C43×#384C2211yescharacteristic, complemented
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic, complemented
58C4×C4⋊C4×C43—21no—
59C4×C4⋊C4×C43C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C25×C43—21no—
65C2×#41×C43—22no—
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—41no—
69C2×#41×C43—41no—
70C2×#41×C43C2×C414yes—
71C22×Q8×C43C2311yescharacteristic
72C22×D4×C43—22no—
73C22×D4×C43—22no—
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—22no—
78C22×D4×C43—41no—
79C22×D4×C43—41no—
80C22×D4×C43C2×C414yes—
81C22×D4×C43D411yescharacteristic
82C22×D4×C43C2311yescharacteristic
83C22×D4×C43C2311yescharacteristic
84C23×C4×C43—21no—
85C23×C4×C43—21no—
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2311yescharacteristic
88C2×M16×C43—22no—
89C2×M16×C43—22no—
90C2×M16×C43—41no—
91C22×C8×C43—22no—
92C22×C8×C43—22no—
93C22×C8×C43—41no—
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98#124×C43—22no—
99#124×C43C2×C414yes—
100#123×C43—28no—
101C22⋊Q8×C43—22no—
102C22⋊Q8×C43C2×C414yes—
103#121×C43—22no—
104#121×C43—28no—
105#121×C43C2×C414yes—
106#120×C43—28no—
107C4×D4×C43—22no—
108C4×D4×C43C2×C414yes—
109C4×D4×C43C2×C414yes—
110C4×D4×C43D414yes—
111#117×C43—22no—
112#117×C43—22no—
113#117×C43—41no—
114#117×C43—41no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—28no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43—21no—
139C2×C42×C43C2311yescharacteristic
140C4⋊C8×C43—22no—
141#103×C43—22no—
142#103×C43—22no—
143#103×C43—41no—
144#103×C43—41no—
145#102×C43—22no—
146#102×C43—22no—
147#102×C43—22no—
148#102×C43—22no—
149#102×C43—22no—
150#102×C43—41no—
151#102×C43—41no—
152#102×C43D414yescomplemented
153C22⋊C8×C43—22no—
154C22⋊C8×C43—22no—
155#97×C43—22no—
156#95×C43—21no—
157#95×C43—21no—
158#95×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—24no—
162C24×C43—42no—
163C24×C43—42no—
164C24×C43—42no—
165C24×C43—42no—
166C24×C43—81no—
167C24×C43—81no—
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170#41×C43—28no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43C22×C412yes—
180C2×D4×C43—24no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—24no—
186C2×D4×C43—24no—
187C2×D4×C43—28no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—41no—
193C2×D4×C43—41no—
194C2×D4×C43—42no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—44no—
199C2×D4×C43—44no—
200C2×D4×C43—44no—
201C2×D4×C43—81no—
202C2×D4×C43—81no—
203C2×D4×C43C22⋊C414yes—
204C2×D4×C43C22×C412yes—
205C2×D4×C43C22×C412yes—
206C2×D4×C43C2×D412yes—
207C2×D4×C43#4112yes—
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—24no—
217C22×C4×C43—24no—
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—42no—
225C22×C4×C43—42no—
226C22×C4×C43—81no—
227C22×C4×C43—81no—
228C22×C4×C43C22×C412yes—
229C22×C4×C43C22×C412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2×D412yes—
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2411yescharacteristic
237M16×C43—44no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—44no—
250C2×C8×C43C2×D412yes—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—42no—
261C4⋊C4×C43—81no—
262C4⋊C4×C43C22⋊C414yes—
263C4⋊C4×C43C22×C412yes—
264C4⋊C4×C43C2×D412yes—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—24no—
267C22⋊C4×C43—24no—
268C22⋊C4×C43—24no—
269C22⋊C4×C43—24no—
270C22⋊C4×C43—42no—
271C22⋊C4×C43—42no—
272C22⋊C4×C43—81no—
273C22⋊C4×C43—81no—
274C22⋊C4×C43C22⋊C414yes—
275C22⋊C4×C43C22⋊C414yes—
276C42×C43—42no—
277C42×C43—42no—
278C42×C43—42no—
279C42×C43C22×C412yes—
280C42×C43C2×D412yes—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—22no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—22no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—22no—
297C23×C43—48no—
298C23×C43—48no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—84no—
310C23×C43—84no—
311C23×C43—84no—
312C23×C43—84no—
313C23×C43—84no—
314C23×C43C2×C22⋊C412yes—
315C23×C43C2×C22⋊C412yes—
316C23×C43C22×D411yescharacteristic
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—41no—
320Q8×C43—41no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—22no—
325D4×C43—22no—
326D4×C43—44no—
327D4×C43—48no—
328D4×C43—48no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—84no—
332D4×C43C4×D414yes—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
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—48no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—84no—
369C2×C4×C43C2×C22⋊C412yes—
370C2×C4×C43C2×C22⋊C412yes—
371C2×C4×C43C2×C22⋊C412yes—
372C2×C4×C43C2×C22⋊C412yes—
373C2×C4×C43C23×C411yescharacteristic
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C2×#4111yescharacteristic
377C2×C4×C43H(5,𝔽2)11yescharacteristic
378C2×C4×C43H(5,𝔽2)11yescharacteristic
379C8×C43—22no—
380C8×C43—41no—
381C8×C43—41no—
382C8×C43—41no—
383#22424C4311yesmaximal, characteristic, direct product factor, Sylow
384C22×C43—24no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—42no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—42no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—42no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43—816no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43—81no—
413C22×C43C22×C22⋊C411yescharacteristic
414C22×C43D4211yescharacteristic
415C22×C43#54611yescharacteristic
416C22×C43#57511yescharacteristic
417C22×C43#57511yescharacteristic
418C22×C43#57611yescharacteristic
419C22×C43#57711yescharacteristic
420C4×C43—22no—
421C4×C43—22no—
422C4×C43—22no—
423C4×C43—22no—
424C4×C43—42no—
425C4×C43—42no—
426C4×C43—42no—
427C4×C43—81no—
428C4×C43—81no—
429C4×C43—81no—
430C4×C43C2×C4×D411yescharacteristic
431C4×C43#51811yescharacteristic
432C4×C43D4211yescharacteristic
433C4×C43#54611yescharacteristic
434C2×#546C2×C4311yescharacteristic
435C2×#435C2×C4311yescharacteristic, complemented
436C2×#418C2×C4311yescharacteristic, complemented
437C2×#416C2×C4311yescharacteristic, complemented
438#2354C2×C4311yescharacteristic, complemented
439#1983C2×C4311yescharacteristic, complemented
440#1959C2×C4311yescharacteristic, complemented
441#1894C2×C4311yescharacteristic, complemented
442#1893C2×C4311yescharacteristic, complemented
443#1875C2×C4311yescharacteristic, complemented
444#1873C2×C4311yescharacteristic, complemented
445#1802C2×C4311yescharacteristic, complemented
446#1788C2×C4311yescharacteristic, complemented
447#1786C2×C4311yescharacteristic, complemented
448#1762C2×C4311yescharacteristic, complemented
449C2×C43—42no—
450C2×C43—42no—
451C2×C43—44no—
452C2×C43—82no—
453C2×C43D4×C22⋊C411yescharacteristic
454C2×C43#289611yescharacteristic
455C2×C43#289711yescharacteristic
456C2×C43#326711yescharacteristic
457C2×C43#326811yescharacteristic
458C2×C43#331111yescharacteristic
459C2×C43#331911yescharacteristic
460C22×#41C22×C4311yescharacteristic
461C23×D4C22×C4311yescharacteristic
462C22×M16C22×C4311yescharacteristic
463C23×C8C22×C4311yescharacteristic, complemented
464#546—24no—
465#546C4×C4318yescomplemented
466C2×#124C22×C4311yescharacteristic
467C2×#123—21no—
468C2×C22⋊Q8C22×C4311yescharacteristic
469C2×#121—21no—
470C2×#121C22×C4311yescharacteristic
471C2×#120—21no—
472C2×C4×D4C22×C4311yescharacteristic
473C2×C4×D4C22×C4311yescharacteristic
474C2×#117C22×C4311yescharacteristic
475C2×#117C22×C4311yescharacteristic, complemented
476C22×C22⋊C4—21no—
477#435—24no—
478C2×C4⋊C8C22×C4311yescharacteristic, complemented
479#418—24no—
480#416—24no—
481C2×#103C22×C4311yescharacteristic, complemented
482C2×#103C22×C4311yescharacteristic, complemented
483C2×#103C22×C4311yescharacteristic, complemented
484C2×#103C22×C4311yescharacteristic, complemented
485C2×#102C22×C4311yescharacteristic
486C2×#102C22×C4311yescharacteristic
487C2×#102C22×C4311yescharacteristic
488C2×#102C22×C4311yescharacteristic
489C2×#102C22×C4311yescharacteristic
490C2×#102C22×C4311yescharacteristic
491C2×#102C22×C4311yescharacteristic
492C2×#102C22×C4311yescharacteristic
493C2×C22⋊C8C22×C4311yescharacteristic
494C2×C22⋊C8C22×C4311yescharacteristic, complemented
495C2×#97C22×C4311yescharacteristic, complemented
496#390—21no—
497#388—21no—
498#388—21no—
499#384C22×C4311yescharacteristic, complemented
500#380C22×C4311yescharacteristic
501#380C22×C4311yescharacteristic, complemented
502C4×C4⋊C4—21no—
503C4×C4⋊C4C22×C4311yescharacteristic, complemented
504#340C22×C4311yescharacteristic, complemented
505#340C22×C4311yescharacteristic, complemented
506#340C22×C4311yescharacteristic, complemented
507#340C22×C4311yescharacteristic, complemented
508C43#2242411yescharacteristic, direct product factor, Sylow
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C4314yes—
516C22×Q8C23×C4311yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×C4×C4314yes—
526C22×D4D4×C4311yescharacteristic
527C22×D4C23×C4311yescharacteristic
528C22×D4C23×C4311yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C23×C4311yescharacteristic
532C23×C4C23×C4311yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8C23×C4311yescharacteristic
540C22×C8C23×C4311yescharacteristic
541C22×C8C23×C4311yescharacteristic
542C22×C8C23×C4311yescharacteristic
543#124—22no—
544#124C2×C4×C4314yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×C4×C4314yes—
548#121—22no—
549#121—28no—
550#121C2×C4×C4314yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×C4×C4314yes—
554C4×D4C2×C4×C4314yes—
555C4×D4D4×C4314yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4D4×C4311yescharacteristic
564C2×C4⋊C4C23×C4311yescharacteristic
565C2×C4⋊C4C23×C4311yescharacteristic
566C2×C4⋊C4C23×C4311yescharacteristic
567C2×C4⋊C4C23×C4311yescharacteristic
568C2×C4⋊C4C23×C4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C4311yescharacteristic
580C2×C22⋊C4D4×C4311yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C4311yescharacteristic
585C4⋊C8—22no—
586#103—22no—
587#103—22no—
588#103—41no—
589#103—41no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102—41no—
597#102D4×C4314yescomplemented
598C22⋊C8—22no—
599C22⋊C8—22no—
600#97—22no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×D4×C4311yescharacteristic
614C24C2×D4×C4311yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×C4×C4312yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C4314yes—
649C2×D4C22×C4×C4312yes—
650C2×D4C22×C4×C4312yes—
651C2×D4C2×D4×C4312yes—
652C2×D4#41×C4312yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4C22×C4×C4312yes—
674C22×C4C22×C4×C4312yes—
675C22×C4C2×D4×C4311yescharacteristic
676C22×C4C2×D4×C4311yescharacteristic
677C22×C4C2×D4×C4311yescharacteristic
678C22×C4C2×D4×C4311yescharacteristic
679C22×C4C2×D4×C4312yes—
680C22×C4C2×D4×C4312yes—
681C22×C4C24×C4311yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8C2×D4×C4312yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—81no—
707C4⋊C4C22⋊C4×C4314yes—
708C4⋊C4C22×C4×C4312yes—
709C4⋊C4C2×D4×C4312yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4C22⋊C4×C4314yes—
720C22⋊C4C22⋊C4×C4314yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C22×C4×C4312yes—
725C42C2×D4×C4312yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊C4×C4312yes—
760C23C2×C22⋊C4×C4312yes—
761C23C22×D4×C4311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4C4×D4×C4314yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4C2×C22⋊C4×C4312yes—
815C2×C4C2×C22⋊C4×C4312yes—
816C2×C4C2×C22⋊C4×C4312yes—
817C2×C4C2×C22⋊C4×C4312yes—
818C2×C4C23×C4×C4311yescharacteristic
819C2×C4C22×D4×C4311yescharacteristic
820C2×C4C22×D4×C4311yescharacteristic
821C2×C4C2×#41×C4311yescharacteristic
822C2×C4H(5,𝔽2)×C4311yescharacteristic
823C2×C4H(5,𝔽2)×C4311yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊C4×C4311yescharacteristic
858C22D42×C4311yescharacteristic
859C22C43×#54611yescharacteristic
860C22C43×#57511yescharacteristic
861C22C43×#57511yescharacteristic
862C22C43×#57611yescharacteristic
863C22C43×#57711yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4C2×C4×D4×C4311yescharacteristic
875C4C43×#51811yescharacteristic
876C4D42×C4311yescharacteristic
877C4C43×#54611yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊C4×C4311yescharacteristic
883C2C43×#289611yescharacteristic
884C2C43×#289711yescharacteristic
885C2C43×#326711yescharacteristic
886C2C43×#326811yescharacteristic
887C2C43×#331111yescharacteristic
888C2C43×#331911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#546C2
LCSG ▷ C2×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
2. C2×C43×#435C2semidirect
3. C2×C43×#418C2semidirect
4. C2×C43×#416C2semidirect
5. C43×#2354C2semidirect
6. C43×#1983C2semidirect
7. C43×#1959C2semidirect
8. C43×#1894C2semidirect
9. C43×#1893C2semidirect
10. C43×#1875C2semidirect
11. C43×#1873C2semidirect
12. C43×#1802C2semidirect
13. C43×#1788C2semidirect
14. C43×#1786C2semidirect
15. C43×#1762C2semidirect
19. C23×C8×C43C22semidirect
21. C43×#546C4semidirect
31. C2×#117×C43C22semidirect
34. C2×C4⋊C8×C43C22semidirect
37. C2×#103×C43C22semidirect
38. C2×#103×C43C22semidirect
39. C2×#103×C43C22semidirect
40. C2×#103×C43C22semidirect
50. C2×C22⋊C8×C43C22semidirect
51. C2×#97×C43C22semidirect
55. C43×#384C22semidirect
57. C43×#380C22semidirect
59. C4×C4⋊C4×C43C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
152. #102×C43D4semidirect
383. #22424C43direct (N × H)
435. C2×#435C2×C43semidirect
436. C2×#418C2×C43semidirect
437. C2×#416C2×C43semidirect
438. #2354C2×C43semidirect
439. #1983C2×C43semidirect
440. #1959C2×C43semidirect
441. #1894C2×C43semidirect
442. #1893C2×C43semidirect
443. #1875C2×C43semidirect
444. #1873C2×C43semidirect
445. #1802C2×C43semidirect
446. #1788C2×C43semidirect
447. #1786C2×C43semidirect
448. #1762C2×C43semidirect
463. C23×C8C22×C43semidirect
465. #546C4×C43semidirect
475. C2×#117C22×C43semidirect
478. C2×C4⋊C8C22×C43semidirect
481. C2×#103C22×C43semidirect
482. C2×#103C22×C43semidirect
483. C2×#103C22×C43semidirect
484. C2×#103C22×C43semidirect
494. C2×C22⋊C8C22×C43semidirect
495. C2×#97C22×C43semidirect
499. #384C22×C43semidirect
501. #380C22×C43semidirect
503. C4×C4⋊C4C22×C43semidirect
504. #340C22×C43semidirect
505. #340C22×C43semidirect
506. #340C22×C43semidirect
507. #340C22×C43semidirect
508. C43#22424direct (N × H)
597. #102D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5462
C2×C43×#4352
C2×C43×#4182
C2×C43×#4162
C43×#23542
C43×#19832
C43×#19592
C43×#18942
C43×#18932
C43×#18752
C43×#18732
C43×#18022
C43×#17882
C43×#17862
C43×#17622
#2242443