Finite Group Databasebeta

← C43×#60276 #24980293

Subgroups — C43×#60276 #24980293

Order 11008.

2306 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C43C211yesmaximal, characteristic
2C43×#2988C218yesmaximal, complemented
3C43×#2982C212yesmaximal, complemented
4C43×#2972C216yesmaximal, complemented
5C8×#41×C43C218yesmaximal, complemented
6C2×C43×#431C216yesmaximal, complemented
7C22×#41×C43C411yescharacteristic
8C4×#41×C43C414yes—
9C4×#41×C43C414yes—
10C4×#41×C43C2214yes—
11C4×#41×C43C2214yes—
12C2×C4×Q8×C43C411yescharacteristic
13C2×C4×Q8×C43C2211yescharacteristic
14C2×C4×D4×C43C413yes—
15C2×C4×D4×C43C2213yes—
16C2×#117×C43C413yes—
17C22×C42×C43C2213yes—
18C8×Q8×C43C22116yescomplemented
19C8×D4×C43C22148yescomplemented
20C43×#431C2214yes—
21C43×#431C22112yes—
22C43×#431C22112yescomplemented
23C43×#431C22112yescomplemented
24C2×C4⋊C8×C43C22112yescomplemented
25C2×C22⋊C8×C43C22112yes—
26C2×C4×C8×C43C22112yescomplemented
27C2×#41×C43C8116yescomplemented
28C2×#41×C43C2×C414yes—
29C2×#41×C43C2×C414yes—
30C22×Q8×C43C2×C411yescharacteristic
31C22×D4×C43C2×C413yes—
32C23×C4×C43C2×C413yes—
33C23×C4×C43C2×C413yes—
34C23×C4×C43C2313yes—
35C22×C8×C43C23124yes—
36C4×Q8×C43C2×C414yes—
37C4×Q8×C43C2×C414yes—
38C4×Q8×C43C2×C414yes—
39C4×Q8×C43C2314yes—
40C4×D4×C43C2×C4112yes—
41C4×D4×C43C2×C4112yes—
42C4×D4×C43C2×C4112yes—
43C4×D4×C43C23112yes—
44#117×C43C2×C4112yes—
45#117×C43C2×C4112yes—
46C2×C4⋊C4×C43C2×C413yes—
47C2×C4⋊C4×C43C2×C413yes—
48C2×C22⋊C4×C43C2×C416yes—
49C2×C42×C43C2×C413yes—
50C2×C42×C43C2×C413yes—
51C2×C42×C43C2×C416yes—
52C2×C42×C43C2×C416yes—
53C2×C42×C43C2313yes—
54C2×C42×C43C2316yes—
55C2×C42×C43C2311yescharacteristic
56C2×C42×C43C2316yes—
57C4⋊C8×C43C2318yes—
58C4⋊C8×C43C23124yes—
59C22⋊C8×C43C2318yes—
60C22⋊C8×C43C23124yes—
61C4×C8×C43C23124yes—
62C4×C8×C43C2318yes—
63C24×C43C22×C413yes—
64#41×C43C2×C8132yescomplemented
65#41×C43C2×C8132yescomplemented
66C2×Q8×C43C2×C818yescomplemented
67C2×Q8×C43C22×C414yes—
68C2×D4×C43C2×C8124yescomplemented
69C2×D4×C43C22×C4112yes—
70C22×C4×C43—46no—
71C22×C4×C43—46no—
72C22×C4×C43C2×C8124yescomplemented
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C22×C416yes—
75C22×C4×C43C22×C413yes—
76C22×C4×C43C22×C416yes—
77C22×C4×C43C22×C413yes—
78C22×C4×C43C22×C416yes—
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C22×C413yes—
81C22×C4×C43C22×C416yes—
82C22×C4×C43C22×C416yes—
83C22×C4×C43C2411yescharacteristic
84C22×C4×C43C2416yes—
85C2×C8×C43—424no—
86C2×C8×C43C24116yes—
87C4⋊C4×C43C22×C4112yes—
88C4⋊C4×C43C22×C4112yes—
89C22⋊C4×C43C22×C4124yes—
90C42×C43C22×C411yescharacteristic
91C42×C43C22×C411yescharacteristic
92C42×C43C22×C416yes—
93C42×C43C22×C416yes—
94C42×C43C22×C416yes—
95C42×C43C22×C416yes—
96C42×C43C22×C416yes—
97C42×C43C2416yes—
98C42×C43C2411yescharacteristic
99C42×C43C2411yescharacteristic
100C23×C43—43no—
101C23×C43—43no—
102C23×C43C22×C8112yes—
103C23×C43C23×C416yes—
104C23×C43C23×C411yescharacteristic
105Q8×C43C22×C8116yes—
106D4×C43C22×C8148yes—
107C2×C4×C43—22no—
108C2×C4×C43—212no—
109C2×C4×C43—212no—
110C2×C4×C43—22no—
111C2×C4×C43—46no—
112C2×C4×C43—43no—
113C2×C4×C43—46no—
114C2×C4×C43—43no—
115C2×C4×C43C22×C814yes—
116C2×C4×C43C22×C8112yes—
117C2×C4×C43C22×C8124yes—
118C2×C4×C43C22×C8124yes—
119C2×C4×C43C23×C411yescharacteristic
120C2×C4×C43C23×C411yescharacteristic
121C2×C4×C43C23×C416yes—
122C2×C4×C43C23×C416yes—
123C2×C4×C43C23×C411yescharacteristic
124C2×C4×C43C23×C411yescharacteristic
125C2×C4×C43C23×C416yes—
126C2×C4×C43C23×C411yescharacteristic
127C2×C4×C43C2511yescharacteristic
128C8×C43—216no—
129#60276C4311yesmaximal, characteristic, direct product factor, Sylow
130C22×C43—21no—
131C22×C43—26no—
132C22×C43—21no—
133C22×C43—26no—
134C22×C43—412no—
135C22×C43C23×C812yes—
136C22×C43C23×C8112yes—
137C22×C43C24×C411yescharacteristic
138C4×C43—21no—
139C4×C43—26no—
140C4×C43—21no—
141C4×C43—26no—
142C4×C43C23×C812yes—
143C4×C43C23×C812yes—
144C4×C43C23×C8112yes—
145C4×C43#56812yes—
146C4×C43#58512yes—
147C2×C4×#41C2×C4311yescharacteristic
148#2988C2×C4318yescomplemented
149#2982C2×C4312yescomplemented
150#2972C2×C4316yescomplemented
151C8×#41C2×C4318yescomplemented
152C2×#431C2×C4316yescomplemented
153C2×C43—22no—
154C2×C43—212no—
155C2×C43#342811yescharacteristic
156C2×C43C24×C811yescharacteristic
157C2×C43C2×#56811yescharacteristic
158C22×#41C4×C4311yescharacteristic
159C4×#41C4×C4314yes—
160C4×#41C4×C4314yes—
161C4×#41C22×C4314yes—
162C4×#41C22×C4314yes—
163C2×C4×Q8C4×C4311yescharacteristic
164C2×C4×Q8C22×C4311yescharacteristic
165C2×C4×D4C4×C4313yes—
166C2×C4×D4C22×C4313yes—
167C2×#117C4×C4313yes—
168C22×C42C22×C4313yes—
169C8×Q8C22×C43116yescomplemented
170C8×D4C22×C43148yescomplemented
171#431C22×C4314yes—
172#431C22×C43112yes—
173#431C22×C43112yescomplemented
174#431C22×C43112yescomplemented
175C2×C4⋊C8C22×C43112yescomplemented
176C2×C22⋊C8C22×C43112yes—
177C2×C4×C8C22×C43112yescomplemented
178C43#6027611yescharacteristic, direct product factor, Sylow
179C2×#41C8×C43116yescomplemented
180C2×#41C2×C4×C4314yes—
181C2×#41C2×C4×C4314yes—
182C22×Q8C2×C4×C4311yescharacteristic
183C22×D4C2×C4×C4313yes—
184C23×C4C2×C4×C4313yes—
185C23×C4C2×C4×C4313yes—
186C23×C4C23×C4313yes—
187C22×C8C23×C43124yes—
188C4×Q8C2×C4×C4314yes—
189C4×Q8C2×C4×C4314yes—
190C4×Q8C2×C4×C4314yes—
191C4×Q8C23×C4314yes—
192C4×D4C2×C4×C43112yes—
193C4×D4C2×C4×C43112yes—
194C4×D4C2×C4×C43112yes—
195C4×D4C23×C43112yes—
196#117C2×C4×C43112yes—
197#117C2×C4×C43112yes—
198C2×C4⋊C4C2×C4×C4313yes—
199C2×C4⋊C4C2×C4×C4313yes—
200C2×C22⋊C4C2×C4×C4316yes—
201C2×C42C2×C4×C4313yes—
202C2×C42C2×C4×C4313yes—
203C2×C42C2×C4×C4316yes—
204C2×C42C2×C4×C4316yes—
205C2×C42C23×C4313yes—
206C2×C42C23×C4316yes—
207C2×C42C23×C4316yes—
208C2×C42C23×C4311yescharacteristic
209C4⋊C8C23×C4318yes—
210C4⋊C8C23×C43124yes—
211C22⋊C8C23×C4318yes—
212C22⋊C8C23×C43124yes—
213C4×C8C23×C4318yes—
214C4×C8C23×C43124yes—
215C24C22×C4×C4313yes—
216#41C2×C8×C43132yescomplemented
217#41C2×C8×C43132yescomplemented
218C2×Q8C2×C8×C4318yescomplemented
219C2×Q8C22×C4×C4314yes—
220C2×D4C2×C8×C43124yescomplemented
221C2×D4C22×C4×C43112yes—
222C22×C4—46no—
223C22×C4—46no—
224C22×C4C2×C8×C43124yescomplemented
225C22×C4C22×C4×C4311yescharacteristic
226C22×C4C22×C4×C4316yes—
227C22×C4C22×C4×C4313yes—
228C22×C4C22×C4×C4316yes—
229C22×C4C22×C4×C4313yes—
230C22×C4C22×C4×C4316yes—
231C22×C4C22×C4×C4311yescharacteristic
232C22×C4C22×C4×C4313yes—
233C22×C4C22×C4×C4316yes—
234C22×C4C22×C4×C4316yes—
235C22×C4C24×C4311yescharacteristic
236C22×C4C24×C4316yes—
237C2×C8—424no—
238C2×C8C24×C43116yes—
239C4⋊C4C22×C4×C43112yes—
240C4⋊C4C22×C4×C43112yes—
241C22⋊C4C22×C4×C43124yes—
242C42C22×C4×C4311yescharacteristic
243C42C22×C4×C4311yescharacteristic
244C42C22×C4×C4316yes—
245C42C22×C4×C4316yes—
246C42C22×C4×C4316yes—
247C42C22×C4×C4316yes—
248C42C22×C4×C4316yes—
249C42C24×C4311yescharacteristic
250C42C24×C4316yes—
251C42C24×C4311yescharacteristic
252C23—43no—
253C23—43no—
254C23C22×C8×C43112yes—
255C23C23×C4×C4316yes—
256C23C23×C4×C4311yescharacteristic
257Q8C22×C8×C43116yes—
258D4C22×C8×C43148yes—
259C2×C4—22no—
260C2×C4—212no—
261C2×C4—212no—
262C2×C4—22no—
263C2×C4—46no—
264C2×C4—43no—
265C2×C4—46no—
266C2×C4—43no—
267C2×C4C22×C8×C4314yes—
268C2×C4C22×C8×C43112yes—
269C2×C4C22×C8×C43124yes—
270C2×C4C22×C8×C43124yes—
271C2×C4C23×C4×C4311yescharacteristic
272C2×C4C23×C4×C4311yescharacteristic
273C2×C4C23×C4×C4316yes—
274C2×C4C23×C4×C4316yes—
275C2×C4C23×C4×C4311yescharacteristic
276C2×C4C23×C4×C4311yescharacteristic
277C2×C4C23×C4×C4316yes—
278C2×C4C23×C4×C4311yescharacteristic
279C2×C4C25×C4311yescharacteristic
280C8—216no—
281C22—21no—
282C22—26no—
283C22—21no—
284C22—26no—
285C22—412no—
286C22C23×C8×C4312yes—
287C22C23×C8×C43112yes—
288C22C24×C4×C4311yescharacteristic
289C4—21no—
290C4—26no—
291C4—21no—
292C4—26no—
293C4C23×C8×C4312yes—
294C4C23×C8×C4312yes—
295C4C23×C8×C43112yes—
296C4C43×#56812yes—
297C4C43×#58512yes—
298C2—22no—
299C2—212no—
300C2C43×#342811yescharacteristic
301C2C24×C8×C4311yescharacteristic
302C2C2×C43×#56811yescharacteristic
subgroupG/H
centerC42×C43C24
commutatorC2C24×C8×C43
Frattini, cosocleC2×C4C25×C43
socleC22×C43C24×C4
prime radicalC22×#41×C43C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2988C2semidirect
3. C43×#2982C2semidirect
4. C43×#2972C2semidirect
5. C8×#41×C43C2semidirect
6. C2×C43×#431C2semidirect
18. C8×Q8×C43C22semidirect
19. C8×D4×C43C22semidirect
22. C43×#431C22semidirect
23. C43×#431C22semidirect
24. C2×C4⋊C8×C43C22semidirect
26. C2×C4×C8×C43C22semidirect
27. C2×#41×C43C8semidirect
64. #41×C43C2×C8semidirect
65. #41×C43C2×C8semidirect
66. C2×Q8×C43C2×C8semidirect
68. C2×D4×C43C2×C8semidirect
72. C22×C4×C43C2×C8semidirect
129. #60276C43direct (N × H)
148. #2988C2×C43semidirect
149. #2982C2×C43semidirect
150. #2972C2×C43semidirect
151. C8×#41C2×C43semidirect
152. C2×#431C2×C43semidirect
169. C8×Q8C22×C43semidirect
170. C8×D4C22×C43semidirect
173. #431C22×C43semidirect
174. #431C22×C43semidirect
175. C2×C4⋊C8C22×C43semidirect
177. C2×C4×C8C22×C43semidirect
178. C43#60276direct (N × H)
179. C2×#41C8×C43semidirect
216. #41C2×C8×C43semidirect
217. #41C2×C8×C43semidirect
218. C2×Q8C2×C8×C43semidirect
220. C2×D4C2×C8×C43semidirect
224. C22×C4C2×C8×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C432
C43×#29882
C43×#29822
C43×#29722
C8×#41×C432
C2×C43×#4312
#6027643