Finite Group Databasebeta

← C43×#9576 #24929593

Subgroups — C43×#9576 #24929593

Order 11008.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#1990C211yesmaximal, characteristic
2C43×#1987C211yesmaximal, characteristic
3C43×#1947C211yesmaximal, characteristic
4C43×#1770C211yesmaximal, characteristic
5C2×C43×#333C211yesmaximal, characteristic
6C43×#1296C211yesmaximal, characteristic
7C43×#1277C211yesmaximal, characteristic
8C2×C4⋊Q8×C43C2211yescharacteristic
9C2×#107×C43—21no—
10C2×C4⋊C8×C43C2211yescharacteristic
11C2×C4⋊C8×C43C2211yescharacteristic
12C2×C4⋊C8×C43C2211yescharacteristic
13C2×#97×C43—21no—
14C2×C4×C8×C43C2211yescharacteristic
15C43×#384C2211yescharacteristic
16C4×C4⋊C4×C43C2211yescharacteristic
17C43×#340—21no—
18C43×#340—21no—
19C43×#340—21no—
20C43×#340—21no—
21C43×#340—21no—
22C43×#336—21no—
23C43×#333C414yescomplemented
24C22×Q8×C43—21no—
25C22×C8×C43—21no—
26C22×C8×C43—21no—
27C22×C8×C43—21no—
28C22×C8×C43D411yescharacteristic
29C22×C8×C43D411yescharacteristic
30C4⋊Q8×C43—21no—
31C4⋊Q8×C43—21no—
32C4⋊Q8×C43—21no—
33C4⋊Q8×C43C2×C412yes—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—21no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C42×C43—21no—
42C2×C42×C43C2311yescharacteristic
43#107×C43—42no—
44C4⋊C8×C43—21no—
45C4⋊C8×C43—21no—
46C4⋊C8×C43—21no—
47C4⋊C8×C43—21no—
48C4⋊C8×C43C2×C412yes—
49C4⋊C8×C43C2×C412yes—
50#97×C43—42no—
51C4×C8×C43—21no—
52C4×C8×C43—21no—
53#95×C43—21no—
54C2×Q8×C43—22no—
55C2×Q8×C43—41no—
56C2×Q8×C43—81no—
57C2×Q8×C43—81no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43#4111yescharacteristic
65C2×C8×C43—21no—
66C2×C8×C43—21no—
67C2×C8×C43—22no—
68C2×C8×C43—22no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—21no—
72C2×C8×C43—41no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43Q1612yes—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—81no—
93C42×C43—41no—
94C42×C43—41no—
95C42×C43C22×C411yescharacteristic
96C42×C43#4111yescharacteristic
97C42×C43#4111yescharacteristic
98C42×C43#4111yescharacteristic
99C23×C43#12111yescharacteristic
100Q8×C43—82no—
101Q8×C43—82no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—42no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—81no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43—81no—
115C2×C4×C43—81no—
116C2×C4×C43#11711yescharacteristic
117C2×C4×C43C4×D411yescharacteristic
118C2×C4×C43C4×D411yescharacteristic
119C2×C4×C43#12311yescharacteristic
120C2×C4×C43#12411yescharacteristic
121C2×C4×C43#12611yescharacteristic
122C2×C4×C43C2×Q1611yescharacteristic
123C2×C4×C43#13511yescharacteristic
124C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C43#13711yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×C4×C43#13711yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C8×C43—22no—
131C8×C43—42no—
132C8×C43—42no—
133C8×C43—41no—
134C8×C43—81no—
135#9576C4311yesmaximal, characteristic, direct product factor, Sylow
136C22×C43#38811yescharacteristic
137C22×C43#46211yescharacteristic
138C22×C43#46311yescharacteristic
139C22×C43#46811yescharacteristic
140C22×C43#47011yescharacteristic
141C22×C43#47111yescharacteristic
142C22×C43#47211yescharacteristic
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—82no—
146C4×C43—81no—
147C4×C43—81no—
148C4×C43—161no—
149C4×C43C4×Q1611yescharacteristic
150C4×C43#44011yescharacteristic
151C4×C43#44011yescharacteristic
152C4×C43#44111yescharacteristic
153C4×C43#48411yescharacteristic
154C4×C43#48511yescharacteristic
155C4×C43#48911yescharacteristic
156C4×C43#49111yescharacteristic
157#1990C2×C4311yescharacteristic
158#1987C2×C4311yescharacteristic
159#1947C2×C4311yescharacteristic
160#1770C2×C4311yescharacteristic
161C2×#333C2×C4311yescharacteristic
162#1296C2×C4311yescharacteristic
163#1277C2×C4311yescharacteristic
164C2×C43#169211yescharacteristic
165C2×C43#169611yescharacteristic
166C2×C43#169711yescharacteristic
167C2×C43#170311yescharacteristic
168C2×C43#192811yescharacteristic
169C2×C43#193111yescharacteristic
170C2×C43#193511yescharacteristic
171C2×C4⋊Q8C22×C4311yescharacteristic
172C2×#107—21no—
173C2×C4⋊C8C22×C4311yescharacteristic
174C2×C4⋊C8C22×C4311yescharacteristic
175C2×C4⋊C8C22×C4311yescharacteristic
176C2×#97—21no—
177C2×C4×C8C22×C4311yescharacteristic
178#384C22×C4311yescharacteristic
179C4×C4⋊C4C22×C4311yescharacteristic
180#340—21no—
181#340—21no—
182#340—21no—
183#340—21no—
184#340—21no—
185#336—21no—
186#333C4×C4314yescomplemented
187C43#957611yescharacteristic, direct product factor, Sylow
188C22×Q8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8D4×C4311yescharacteristic
193C22×C8D4×C4311yescharacteristic
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C2×C4×C4312yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4D4×C4311yescharacteristic
204C2×C4⋊C4D4×C4311yescharacteristic
205C2×C42—21no—
206C2×C42C23×C4311yescharacteristic
207#107—42no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8C2×C4×C4312yes—
213C4⋊C8C2×C4×C4312yes—
214#97—42no—
215C4×C8—21no—
216C4×C8—21no—
217#95—21no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4C2×D4×C4311yescharacteristic
227C22×C4C2×D4×C4311yescharacteristic
228C22×C4#41×C4311yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8Q16×C4312yes—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C42—41no—
258C42—41no—
259C42C22×C4×C4311yescharacteristic
260C42#41×C4311yescharacteristic
261C42#41×C4311yescharacteristic
262C42#41×C4311yescharacteristic
263C23#121×C4311yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4#117×C4311yescharacteristic
281C2×C4C4×D4×C4311yescharacteristic
282C2×C4C4×D4×C4311yescharacteristic
283C2×C4#123×C4311yescharacteristic
284C2×C4#124×C4311yescharacteristic
285C2×C4#126×C4311yescharacteristic
286C2×C4C2×Q16×C4311yescharacteristic
287C2×C4#135×C4311yescharacteristic
288C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
289C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
290C2×C4#137×C4311yescharacteristic
291C2×C4#137×C4311yescharacteristic
292C2×C4#137×C4311yescharacteristic
293C2×C4#137×C4311yescharacteristic
294C8—22no—
295C8—42no—
296C8—42no—
297C8—41no—
298C8—81no—
299C22C43×#38811yescharacteristic
300C22C43×#46211yescharacteristic
301C22C43×#46311yescharacteristic
302C22C43×#46811yescharacteristic
303C22C43×#47011yescharacteristic
304C22C43×#47111yescharacteristic
305C22C43×#47211yescharacteristic
306C4—21no—
307C4—21no—
308C4—82no—
309C4—81no—
310C4—81no—
311C4—161no—
312C4C4×Q16×C4311yescharacteristic
313C4C43×#44011yescharacteristic
314C4C43×#44011yescharacteristic
315C4C43×#44111yescharacteristic
316C4C43×#48411yescharacteristic
317C4C43×#48511yescharacteristic
318C4C43×#48911yescharacteristic
319C4C43×#49111yescharacteristic
320C2C43×#169211yescharacteristic
321C2C43×#169611yescharacteristic
322C2C43×#169711yescharacteristic
323C2C43×#170311yescharacteristic
324C2C43×#192811yescharacteristic
325C2C43×#193111yescharacteristic
326C2C43×#193511yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C43#121
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
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
23. C43×#333C4semidirect
135. #9576C43direct (N × H)
186. #333C4×C43semidirect
187. C43#9576direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#19902
C43×#19872
C43×#19472
C43×#17702
C2×C43×#3332
C43×#12962
C43×#12772
#957643