Finite Group Databasebeta

← C2×C43×#1664 #24939003

Subgroups — C2×C43×#1664 #24939003

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#563C211yesmaximal, characteristic
2C2×C43×#501C211yesmaximal, characteristic, complemented
3C2×C43×#491C211yesmaximal, characteristic, complemented
4C2×C43×#489C211yesmaximal, characteristic
5C43×#1664C218yesmaximal, direct product factor
6C2×C43×#330C211yesmaximal, characteristic, complemented
7C2×C43×#330C211yesmaximal, characteristic, complemented
8C2×C43×#329C211yesmaximal, characteristic
9C43×#563—22no—
10C43×#563—22no—
11C43×#563—22no—
12C43×#563C2214yes—
13C2×C4⋊Q8×C43—21no—
14C2×C4⋊Q8×C43C2211yescharacteristic
15C2×#126×C43—21no—
16C2×#126×C43—21no—
17C2×#125×C43C2211yescharacteristic
18C2×#125×C43C2211yescharacteristic
19C2×#124×C43C2211yescharacteristic
20C2×#123×C43—21no—
21C2×C22⋊Q8×C43—21no—
22C2×C22⋊Q8×C43—21no—
23C43×#501—22no—
24C43×#501C2214yescomplemented
25C43×#491—22no—
26C43×#491C2214yescomplemented
27C43×#489—22no—
28C43×#489C2214yes—
29C2×#107×C43—21no—
30C2×#106×C43—21no—
31C2×#103×C43—21no—
32C2×#103×C43—21no—
33C2×#103×C43—21no—
34C2×#102×C43—21no—
35C2×#97×C43C2211yescharacteristic
36C2×#97×C43C2211yescharacteristic
37C2×#97×C43C2211yescharacteristic
38C43×#330C2214yescomplemented
39C43×#330C2214yescomplemented
40C43×#329C2214yes—
41C22×Q8×C43—21no—
42C22×Q8×C43—21no—
43C22×Q8×C43D411yescharacteristic
44C22×D4×C43D411yescharacteristic
45C23×C4×C43—21no—
46C22×C8×C43—21no—
47C22×C8×C43—21no—
48C22×C8×C43—21no—
49C4⋊Q8×C43—24no—
50C4⋊Q8×C43—24no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43C2312yes—
55#126×C43—24no—
56#126×C43—24no—
57#126×C43—24no—
58#126×C43—24no—
59#125×C43—21no—
60#125×C43—21no—
61#125×C43—21no—
62#125×C43—21no—
63#125×C43D412yes—
64#125×C43D412yes—
65#125×C43C2312yes—
66#125×C43C2312yes—
67#124×C43—21no—
68#124×C43—21no—
69#124×C43D412yes—
70#124×C43C2312yes—
71#123×C43—24no—
72#123×C43—24no—
73C22⋊Q8×C43—24no—
74C22⋊Q8×C43—24no—
75C22⋊Q8×C43—24no—
76C22⋊Q8×C43—24no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43D411yescharacteristic
86C2×C4⋊C4×C43D411yescharacteristic
87C2×C4⋊C4×C43D411yescharacteristic
88C2×C4⋊C4×C43D411yescharacteristic
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C42×C43—21no—
95C2×C42×C43C2311yescharacteristic
96#107×C43—24no—
97#106×C43—24no—
98#103×C43—24no—
99#103×C43—24no—
100#103×C43—24no—
101#102×C43—24no—
102#97×C43—21no—
103#97×C43—21no—
104#97×C43—21no—
105#97×C43C2312yes—
106#97×C43C2312yes—
107#97×C43C2312yes—
108C24×C43—21no—
109C2×Q8×C43—24no—
110C2×Q8×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—42no—
113C2×Q8×C43—44no—
114C2×Q8×C43—41no—
115C2×Q8×C43—82no—
116C2×Q8×C43C2×D412yes—
117C2×D4×C43—21no—
118C2×D4×C43—42no—
119C2×D4×C43C2×D412yes—
120C22×C4×C43—24no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—41no—
127C22×C4×C43—82no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C2×C8×C43—24no—
132C2×C8×C43—22no—
133C2×C8×C43—22no—
134C2×C8×C43—22no—
135C2×C8×C43—42no—
136C2×C8×C43—42no—
137C4⋊C4×C43—24no—
138C4⋊C4×C43—24no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43C2×D412yes—
156C4⋊C4×C43C2×D412yes—
157C4⋊C4×C43C2×D412yes—
158C4⋊C4×C43C2×D412yes—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C42×C43—24no—
167C42×C43C2×D411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43C2×D411yescharacteristic
170C42×C43C2411yescharacteristic
171C23×C43—22no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43#12011yescharacteristic
176Q8×C43—42no—
177Q8×C43—44no—
178Q8×C43—81no—
179Q8×C43—82no—
180Q8×C43—84no—
181D4×C43—42no—
182D4×C43—81no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—42no—
192C2×C4×C43—42no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—84no—
198C2×C4×C43—82no—
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#12011yescharacteristic
201C2×C4×C43#12011yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C8×C43—24no—
206C8×C43—42no—
207C8×C43—42no—
208C2×#1664C4311yesmaximal, characteristic, direct product factor, Sylow
209C22×C43—42no—
210C22×C43—42no—
211C22×C43—42no—
212C22×C43—84no—
213C22×C43#45412yes—
214C22×C43#45512yes—
215C22×C43#45612yes—
216C22×C43C2×#12011yescharacteristic
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—42no—
224C4×C43—42no—
225C4×C43—42no—
226C4×C43—42no—
227C4×C43—42no—
228C4×C43—82no—
229C2×#563C2×C4311yescharacteristic
230C2×#501C2×C4311yescharacteristic, complemented
231C2×#491C2×C4311yescharacteristic, complemented
232C2×#489C2×C4311yescharacteristic
233#1664C2×C4318yesdirect product factor
234C2×#330C2×C4311yescharacteristic, complemented
235C2×#330C2×C4311yescharacteristic, complemented
236C2×#329C2×C4311yescharacteristic
237C2×C43—82no—
238C2×C43#166414yesdirect product factor
239C2×C43C2×#45511yescharacteristic
240C2×C43C2×#45411yescharacteristic
241C2×C43C2×#45611yescharacteristic
242#563—22no—
243#563—22no—
244#563—22no—
245#563C22×C4314yes—
246C2×C4⋊Q8—21no—
247C2×C4⋊Q8C22×C4311yescharacteristic
248C2×#126—21no—
249C2×#126—21no—
250C2×#125C22×C4311yescharacteristic
251C2×#125C22×C4311yescharacteristic
252C2×#124C22×C4311yescharacteristic
253C2×#123—21no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—21no—
256#501—22no—
257#501C22×C4314yescomplemented
258#491—22no—
259#491C22×C4314yescomplemented
260#489—22no—
261#489C22×C4314yes—
262C2×#107—21no—
263C2×#106—21no—
264C2×#103—21no—
265C2×#103—21no—
266C2×#103—21no—
267C2×#102—21no—
268C2×#97C22×C4311yescharacteristic
269C2×#97C22×C4311yescharacteristic
270C2×#97C22×C4311yescharacteristic
271#330C22×C4314yescomplemented
272#330C22×C4314yescomplemented
273#329C22×C4314yes—
274C43C2×#166411yescharacteristic, direct product factor, Sylow
275C22×Q8—21no—
276C22×Q8—21no—
277C22×Q8D4×C4311yescharacteristic
278C22×D4D4×C4311yescharacteristic
279C23×C4—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C4⋊Q8—24no—
284C4⋊Q8—24no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8C23×C4312yes—
289#126—24no—
290#126—24no—
291#126—24no—
292#126—24no—
293#125—21no—
294#125—21no—
295#125—21no—
296#125—21no—
297#125D4×C4312yes—
298#125D4×C4312yes—
299#125C23×C4312yes—
300#125C23×C4312yes—
301#124—21no—
302#124—21no—
303#124D4×C4312yes—
304#124C23×C4312yes—
305#123—24no—
306#123—24no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—24no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4D4×C4311yescharacteristic
320C2×C4⋊C4D4×C4311yescharacteristic
321C2×C4⋊C4D4×C4311yescharacteristic
322C2×C4⋊C4D4×C4311yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C42—21no—
329C2×C42C23×C4311yescharacteristic
330#107—24no—
331#106—24no—
332#103—24no—
333#103—24no—
334#103—24no—
335#102—24no—
336#97—21no—
337#97—21no—
338#97—21no—
339#97C23×C4312yes—
340#97C23×C4312yes—
341#97C23×C4312yes—
342C24—21no—
343C2×Q8—24no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—42no—
347C2×Q8—44no—
348C2×Q8—41no—
349C2×Q8—82no—
350C2×Q8C2×D4×C4312yes—
351C2×D4—21no—
352C2×D4—42no—
353C2×D4C2×D4×C4312yes—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—24no—
360C22×C4—41no—
361C22×C4—82no—
362C22×C4C2×D4×C4311yescharacteristic
363C22×C4C2×D4×C4311yescharacteristic
364C22×C4C2×D4×C4311yescharacteristic
365C2×C8—24no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—42no—
371C4⋊C4—24no—
372C4⋊C4—24no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4C2×D4×C4312yes—
390C4⋊C4C2×D4×C4312yes—
391C4⋊C4C2×D4×C4312yes—
392C4⋊C4C2×D4×C4312yes—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—24no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C42—24no—
401C42C2×D4×C4311yescharacteristic
402C42C2×D4×C4311yescharacteristic
403C42C2×D4×C4311yescharacteristic
404C42C24×C4311yescharacteristic
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23#120×C4311yescharacteristic
410Q8—42no—
411Q8—44no—
412Q8—81no—
413Q8—82no—
414Q8—84no—
415D4—42no—
416D4—81no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—84no—
432C2×C4—82no—
433C2×C4#120×C4311yescharacteristic
434C2×C4#120×C4311yescharacteristic
435C2×C4#120×C4311yescharacteristic
436C2×C4C22×D4×C4311yescharacteristic
437C2×C4C22×D4×C4311yescharacteristic
438C2×C4C22×D4×C4311yescharacteristic
439C8—24no—
440C8—42no—
441C8—42no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—84no—
446C22C43×#45412yes—
447C22C43×#45512yes—
448C22C43×#45612yes—
449C22C2×#120×C4311yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—42no—
461C4—82no—
462C2—82no—
463C2C43×#166414yesdirect product factor
464C2C2×C43×#45511yescharacteristic
465C2C2×C43×#45411yescharacteristic
466C2C2×C43×#45611yescharacteristic
subgroupG/H
center, socleC23×C43#120
commutator, Frattini, cosocleC42C24×C43
prime radicalC22×D4×C43D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C43×#501C2semidirect
3. C2×C43×#491C2semidirect
5. C43×#1664C2direct (N × H)
6. C2×C43×#330C2semidirect
7. C2×C43×#330C2semidirect
24. C43×#501C22semidirect
26. C43×#491C22semidirect
38. C43×#330C22semidirect
39. C43×#330C22semidirect
208. C2×#1664C43direct (N × H)
230. C2×#501C2×C43semidirect
231. C2×#491C2×C43semidirect
233. #1664C2×C43direct (N × H)
234. C2×#330C2×C43semidirect
235. C2×#330C2×C43semidirect
238. C2×C43#1664direct (N × H)
257. #501C22×C43semidirect
259. #491C22×C43semidirect
271. #330C22×C43semidirect
272. #330C22×C43semidirect
274. C43C2×#1664direct (N × H)
463. C2C43×#1664direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5632
C2×C43×#5012
C2×C43×#4912
C2×C43×#4892
C43×#16642
C2×C43×#3302
C2×C43×#3292
C2×#166443