Finite Group Databasebeta

← C2×C43×#2180 #24953483

Subgroups — C2×C43×#2180 #24953483

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#510C211yesmaximal, characteristic
2C2×C43×#444C211yesmaximal, characteristic
3C2×C43×#441C211yesmaximal, characteristic, complemented
4C43×#2180C218yesmaximal, direct product factor
5C2×C43×#365C211yesmaximal, characteristic, complemented
6C2×C43×#362C211yesmaximal, characteristic, complemented
7C2×C43×#360C211yesmaximal, characteristic
8C2×C43×#347C211yesmaximal, characteristic, complemented
9C2×#135×C43C2211yescharacteristic
10C22×Q16×C43C2211yescharacteristic
11C2×#131×C43—21no—
12C2×C4×Q8×C43—21no—
13C43×#510C414yescomplemented
14C43×#510C2214yes—
15C2×Q32×C43C412yescomplemented
16C2×SD32×C43C412yescomplemented
17C2×M32×C43C2211yescharacteristic
18C2×M32×C43C2211yescharacteristic
19C43×#444—22no—
20C43×#444C2214yes—
21C43×#441—22no—
22C43×#441C2214yescomplemented
23C2×#108×C43C2211yescharacteristic
24C2×#106×C43C2211yescharacteristic
25C2×#104×C43—21no—
26C2×#103×C43—21no—
27C2×#97×C43C2211yescharacteristic
28C43×#365C2214yescomplemented
29C43×#362C2214yescomplemented
30C43×#360C2214yes—
31C43×#347C2214yescomplemented
32C2×#41×C43—21no—
33C22×Q8×C43—21no—
34#135×C43—21no—
35#135×C43—21no—
36#135×C43C2×C412yes—
37#135×C43C2312yes—
38C2×Q16×C43—21no—
39C2×Q16×C43—21no—
40C2×Q16×C43—21no—
41C2×Q16×C43C2×C412yes—
42C2×Q16×C43C2×C411yescharacteristic
43C2×Q16×C43C2×C412yes—
44C2×Q16×C43C2312yes—
45C2×SD16×C43—21no—
46C2×D8×C43C2×C411yescharacteristic
47#131×C43—24no—
48#131×C43—42no—
49C2×M16×C43—21no—
50C2×M16×C43—41no—
51C22×C8×C43—41no—
52C22×C8×C43D411yescharacteristic
53C22×C8×C43C2311yescharacteristic
54C4×Q8×C43—24no—
55C4×Q8×C43—42no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—41no—
58C2×C42×C43—41no—
59C2×C42×C43D411yescharacteristic
60Q32×C43C2×C418yescomplemented
61SD32×C43C2×C418yescomplemented
62M32×C43—21no—
63M32×C43C2×C412yes—
64M32×C43C2312yes—
65M32×C43C2312yes—
66C2×C16×C43—21no—
67C2×C16×C43C2×C412yes—
68#108×C43—21no—
69#108×C43C2312yes—
70#106×C43—21no—
71#106×C43C2312yes—
72#104×C43—24no—
73#103×C43—24no—
74#97×C43D412yes—
75#97×C43C2312yes—
76#41×C43—22no—
77#41×C43—22no—
78#41×C43—41no—
79#41×C43—41no—
80C2×Q8×C43—21no—
81C2×Q8×C43—22no—
82C2×Q8×C43—22no—
83C2×Q8×C43—22no—
84C2×Q8×C43—41no—
85C2×Q8×C43—41no—
86C2×Q8×C43—41no—
87C2×D4×C43—21no—
88C2×D4×C43—41no—
89C22×C4×C43—21no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43C2×D411yescharacteristic
94Q16×C43—22no—
95Q16×C43—22no—
96Q16×C43—21no—
97Q16×C43—22no—
98Q16×C43C22×C414yes—
99Q16×C43C22×C412yes—
100SD16×C43—22no—
101SD16×C43—22no—
102D8×C43—21no—
103D8×C43C22×C412yes—
104M16×C43—22no—
105M16×C43—44no—
106M16×C43—41no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—44no—
110C2×C8×C43—41no—
111C2×C8×C43C22×C411yescharacteristic
112C2×C8×C43C22×C411yescharacteristic
113C2×C8×C43C2×D412yes—
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43#4111yescharacteristic
116C2×C8×C43#4111yescharacteristic
117C2×C8×C43C2411yescharacteristic
118C4⋊C4×C43—22no—
119C4⋊C4×C43—44no—
120C4⋊C4×C43—41no—
121C42×C43—21no—
122C42×C43—44no—
123C42×C43C2×D412yes—
124C16×C43—22no—
125C16×C43C22×C414yes—
126C23×C43—41no—
127C23×C43AGL(1,ℤ/8)11yescharacteristic
128Q8×C43—22no—
129Q8×C43—24no—
130Q8×C43—42no—
131Q8×C43—42no—
132Q8×C43—42no—
133Q8×C43—41no—
134D4×C43—22no—
135D4×C43—42no—
136D4×C43—42no—
137D4×C43—41no—
138C2×C4×C43—22no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—82no—
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C43C22×D411yescharacteristic
154C8×C43—22no—
155C8×C43—42no—
156C8×C43C4×D411yescharacteristic
157C8×C43C4×D411yescharacteristic
158C8×C43C23×C411yescharacteristic
159C8×C43C2×#4111yescharacteristic
160C2×#2180C4311yesmaximal, characteristic, direct product factor, Sylow
161C22×C43—22no—
162C22×C43—42no—
163C22×C43—82no—
164C22×C43#44211yescharacteristic
165C22×C43#44211yescharacteristic
166C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
167C4×C43—42no—
168C4×C43—42no—
169C4×C43—44no—
170C4×C43—82no—
171C4×C43#44211yescharacteristic
172C4×C43#44211yescharacteristic
173C4×C43C2×C4×D411yescharacteristic
174C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
175C2×#510C2×C4311yescharacteristic
176C2×#444C2×C4311yescharacteristic
177C2×#441C2×C4311yescharacteristic, complemented
178#2180C2×C4318yesdirect product factor
179C2×#365C2×C4311yescharacteristic, complemented
180C2×#362C2×C4311yescharacteristic, complemented
181C2×#360C2×C4311yescharacteristic
182C2×#347C2×C4311yescharacteristic, complemented
183C2×C43—21no—
184C2×C43—21no—
185C2×C43—82no—
186C2×C43#218012yesdirect product factor
187C2×C43C2×#44211yescharacteristic
188C2×#135C22×C4311yescharacteristic
189C22×Q16C22×C4311yescharacteristic
190C2×#131—21no—
191C2×C4×Q8—21no—
192#510C4×C4314yescomplemented
193#510C22×C4314yes—
194C2×Q32C4×C4312yescomplemented
195C2×SD32C4×C4312yescomplemented
196C2×M32C22×C4311yescharacteristic
197C2×M32C22×C4311yescharacteristic
198#444—22no—
199#444C22×C4314yes—
200#441—22no—
201#441C22×C4314yescomplemented
202C2×#108C22×C4311yescharacteristic
203C2×#106C22×C4311yescharacteristic
204C2×#104—21no—
205C2×#103—21no—
206C2×#97C22×C4311yescharacteristic
207#365C22×C4314yescomplemented
208#362C22×C4314yescomplemented
209#360C22×C4314yes—
210#347C22×C4314yescomplemented
211C43C2×#218011yescharacteristic, direct product factor, Sylow
212C2×#41—21no—
213C22×Q8—21no—
214#135—21no—
215#135—21no—
216#135C2×C4×C4312yes—
217#135C23×C4312yes—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16C2×C4×C4312yes—
222C2×Q16C2×C4×C4312yes—
223C2×Q16C2×C4×C4311yescharacteristic
224C2×Q16C23×C4312yes—
225C2×SD16—21no—
226C2×D8C2×C4×C4311yescharacteristic
227#131—24no—
228#131—42no—
229C2×M16—21no—
230C2×M16—41no—
231C22×C8—41no—
232C22×C8D4×C4311yescharacteristic
233C22×C8C23×C4311yescharacteristic
234C4×Q8—24no—
235C4×Q8—42no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—41no—
238C2×C42—41no—
239C2×C42D4×C4311yescharacteristic
240Q32C2×C4×C4318yescomplemented
241SD32C2×C4×C4318yescomplemented
242M32—21no—
243M32C2×C4×C4312yes—
244M32C23×C4312yes—
245M32C23×C4312yes—
246C2×C16—21no—
247C2×C16C2×C4×C4312yes—
248#108—21no—
249#108C23×C4312yes—
250#106—21no—
251#106C23×C4312yes—
252#104—24no—
253#103—24no—
254#97D4×C4312yes—
255#97C23×C4312yes—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—21no—
268C2×D4—41no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C2×D4×C4311yescharacteristic
274Q16—22no—
275Q16—22no—
276Q16—21no—
277Q16—22no—
278Q16C22×C4×C4314yes—
279Q16C22×C4×C4312yes—
280SD16—22no—
281SD16—22no—
282D8—21no—
283D8C22×C4×C4312yes—
284M16—22no—
285M16—44no—
286M16—41no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—44no—
290C2×C8—41no—
291C2×C8C22×C4×C4311yescharacteristic
292C2×C8C22×C4×C4311yescharacteristic
293C2×C8C2×D4×C4312yes—
294C2×C8C2×D4×C4311yescharacteristic
295C2×C8#41×C4311yescharacteristic
296C2×C8#41×C4311yescharacteristic
297C2×C8C24×C4311yescharacteristic
298C4⋊C4—22no—
299C4⋊C4—44no—
300C4⋊C4—41no—
301C42—21no—
302C42—44no—
303C42C2×D4×C4312yes—
304C16—22no—
305C16C22×C4×C4314yes—
306C23—41no—
307C23AGL(1,ℤ/8)×C4311yescharacteristic
308Q8—22no—
309Q8—24no—
310Q8—42no—
311Q8—42no—
312Q8—42no—
313Q8—41no—
314D4—22no—
315D4—42no—
316D4—42no—
317D4—41no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4C4×D4×C4311yescharacteristic
329C2×C4C4×D4×C4311yescharacteristic
330C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
331C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
332C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
333C2×C4C22×D4×C4311yescharacteristic
334C8—22no—
335C8—42no—
336C8C4×D4×C4311yescharacteristic
337C8C4×D4×C4311yescharacteristic
338C8C23×C4×C4311yescharacteristic
339C8C2×#41×C4311yescharacteristic
340C22—22no—
341C22—42no—
342C22—82no—
343C22C43×#44211yescharacteristic
344C22C43×#44211yescharacteristic
345C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
346C4—42no—
347C4—42no—
348C4—44no—
349C4—82no—
350C4C43×#44211yescharacteristic
351C4C43×#44211yescharacteristic
352C4C2×C4×D4×C4311yescharacteristic
353C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
354C2—21no—
355C2—21no—
356C2—82no—
357C2C43×#218012yesdirect product factor
358C2C2×C43×#44211yescharacteristic
subgroupG/H
center, socleC22×C43#442
commutatorC8C23×C4×C43
Frattini, cosocleC2×C8C24×C43
prime radicalC2×#135×C43C22
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×#97×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C43×#441C2semidirect
4. C43×#2180C2direct (N × H)
5. C2×C43×#365C2semidirect
6. C2×C43×#362C2semidirect
8. C2×C43×#347C2semidirect
13. C43×#510C4semidirect
15. C2×Q32×C43C4semidirect
16. C2×SD32×C43C4semidirect
22. C43×#441C22semidirect
28. C43×#365C22semidirect
29. C43×#362C22semidirect
31. C43×#347C22semidirect
60. Q32×C43C2×C4semidirect
61. SD32×C43C2×C4semidirect
160. C2×#2180C43direct (N × H)
177. C2×#441C2×C43semidirect
178. #2180C2×C43direct (N × H)
179. C2×#365C2×C43semidirect
180. C2×#362C2×C43semidirect
182. C2×#347C2×C43semidirect
186. C2×C43#2180direct (N × H)
192. #510C4×C43semidirect
194. C2×Q32C4×C43semidirect
195. C2×SD32C4×C43semidirect
201. #441C22×C43semidirect
207. #365C22×C43semidirect
208. #362C22×C43semidirect
210. #347C22×C43semidirect
211. C43C2×#2180direct (N × H)
240. Q32C2×C4×C43semidirect
241. SD32C2×C4×C43semidirect
357. C2C43×#2180direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#5102
C2×C43×#4442
C2×C43×#4412
C43×#21802
C2×C43×#3652
C2×C43×#3622
C2×C43×#3602
C2×C43×#3472
C2×#218043