Finite Group Databasebeta

← C43×#60184 #24980201

Subgroups — C43×#60184 #24980201

Order 11008.

2604 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3584C211yesmaximal, characteristic
2C43×#3573C212yesmaximal, complemented
3C43×#2957C216yesmaximal, complemented
4C43×#2956C216yesmaximal, complemented
5C43×#2955C216yesmaximal, complemented
6C2×C43×#444C216yesmaximal, complemented
7C43×#2916C211yesmaximal, characteristic, complemented
8C43×#2901C212yesmaximal, complemented
9C43×#2875C211yesmaximal, characteristic, complemented
10C43×#585C2212yes—
11C43×#578C414yescomplemented
12C43×#577C418yescomplemented
13C43×#576C414yescomplemented
14C43×#575C2216yes—
15C2×#135×C43C2216yes—
16C43×#568—28no—
17C43×#568C2212yes—
18C43×#568C22112yescomplemented
19C2×#131×C43—28no—
20C2×#131×C43C2211yescharacteristic
21C2×#131×C43C2211yescharacteristic
22C2×#131×C43C22112yescomplemented
23C4×#41×C43C2211yescharacteristic
24C43×#444C2214yescomplemented
25C43×#444C22112yescomplemented
26C43×#444C22112yescomplemented
27C43×#444C22112yescomplemented
28C43×#443C22124yescomplemented
29C43×#430C2216yescomplemented
30C2×#108×C43C2216yescomplemented
31C43×#421C22112yescomplemented
32C2×#104×C43C22112yescomplemented
33C43×#405C2213yescomplemented
34C43×#405C2213yescomplemented
35C4×M16×C43C2213yescomplemented
36C2×#97×C43C2213yescomplemented
372−1+4×C43—22no—
382−1+4×C43C2×C418yes—
39H(5,𝔽2)×C43—26no—
40H(5,𝔽2)×C43C2×C418yes—
41C2×#41×C43—28no—
42C2×#41×C43C23112yes—
43C2×#41×C43C2311yescharacteristic
44#137×C43C2×C4124yescomplemented
45AGL(1,ℤ/8)×C43C2×C4124yescomplemented
46#135×C43C2×C4112yescomplemented
47#135×C43C2×C4112yescomplemented
48#135×C43C2314yes—
49#135×C43C23112yes—
50C2×Q16×C43C2×C416yescomplemented
51C2×SD16×C43C2×C4112yescomplemented
52C2×D8×C43C2×C416yescomplemented
53#131×C43—28no—
54#131×C43—224no—
55#131×C43—212no—
56#131×C43—212no—
57#131×C43C2×C414yes—
58#131×C43C2×C414yes—
59#131×C43D418yes—
60#131×C43C2318yes—
61#131×C43C23124yes—
62C2×M16×C43—224no—
63C2×M16×C43—212no—
64C2×M16×C43C23112yes—
65C2×M16×C43C2313yes—
66C2×M16×C43C2313yes—
67C22×C8×C43—212no—
68C22×C8×C43C2313yes—
69C22×C8×C43C2313yes—
70C4×Q8×C43—21no—
71C4×D4×C43—23no—
72#117×C43C2313yes—
73C2×C42×C43C2313yes—
74#108×C43C2314yes—
75#108×C43C23112yes—
76#104×C43C2318yes—
77#104×C43C23124yes—
78#97×C43C2311yescharacteristic
79#97×C43C2313yes—
80#97×C43C2313yes—
81#97×C43C2313yes—
82C4×C8×C43C2316yes—
83#41×C43—28no—
84#41×C43—224no—
85#41×C43—212no—
86#41×C43—212no—
87#41×C43C22×C4124yes—
88#41×C43C22×C414yes—
89#41×C43C2×D414yes—
90#41×C43C2418yes—
91C2×Q8×C43—28no—
92C2×Q8×C43C22×C4112yes—
93C2×Q8×C43#4111yescharacteristic
94C2×D4×C43—224no—
95C2×D4×C43—212no—
96C2×D4×C43C22×C4112yes—
97C2×D4×C43#4113yes—
98C22×C4×C43—212no—
99C22×C4×C43—23no—
100C22×C4×C43C2413yes—
101Q16×C43C22×C414yes—
102Q16×C43C22×C4112yes—
103SD16×C43C22×C418yes—
104SD16×C43C22×C4124yes—
105D8×C43C22×C414yes—
106D8×C43C22×C4112yes—
107M16×C43—212no—
108M16×C43—28no—
109M16×C43—224no—
110M16×C43C22×C4112yes—
111M16×C43C2×D4112yes—
112M16×C43C2418yes—
113C2×C8×C43—212no—
114C2×C8×C43—28no—
115C2×C8×C43—224no—
116C2×C8×C43C22×C416yes—
117C2×C8×C43C22×C416yes—
118C2×C8×C43C2×D4112yes—
119C2×C8×C43C2413yes—
120C2×C8×C43C2411yescharacteristic
121C2×C8×C43C2413yes—
122C2×C8×C43C2411yescharacteristic
123C4⋊C4×C43—23no—
124C22⋊C4×C43—23no—
125C42×C43—23no—
126C42×C43C2413yes—
127C42×C43C2411yescharacteristic
128C23×C43—212no—
129C23×C43C2×#4113yes—
130Q8×C43—212no—
131Q8×C43C4×D414yes—
132Q8×C43C23×C418yes—
133D4×C43—224no—
134D4×C43—28no—
135D4×C43—212no—
136D4×C43C4×D4112yes—
137D4×C43C23×C418yes—
138C2×C4×C43—212no—
139C2×C4×C43—224no—
140C2×C4×C43—28no—
141C2×C4×C43—21no—
142C2×C4×C43—23no—
143C2×C4×C43—83no—
144C2×C4×C43C23×C416yes—
145C2×C4×C43C22×D416yes—
146C2×C4×C43C2×#4113yes—
147C2×C4×C43C2511yescharacteristic
148C8×C43—28no—
149C8×C43C23×C411yescharacteristic
150C8×C43C23×C411yescharacteristic
151C8×C43C23×C416yes—
152C8×C43C22×D412yes—
153C8×C43C22×D416yes—
154#60184C4311yesmaximal, characteristic, direct product factor, Sylow
155C22×C43—28no—
156C22×C43—43no—
157C22×C43—812no—
158C22×C43C2×C4×D416yes—
159C22×C43C22×#4111yescharacteristic
160C4×C43—28no—
161C4×C43—43no—
162C4×C43—41no—
163C4×C43C2×C4×D416yes—
164C4×C43C24×C411yescharacteristic
165C4×C43C23×D411yescharacteristic
166#3584C2×C4311yescharacteristic
167#3573C2×C4312yescomplemented
168#2957C2×C4316yescomplemented
169#2956C2×C4316yescomplemented
170#2955C2×C4316yescomplemented
171C2×#444C2×C4316yescomplemented
172#2916C2×C4311yescharacteristic, complemented
173#2901C2×C4312yescomplemented
174#2875C2×C4311yescharacteristic, complemented
175C2×C43—21no—
176C2×C43—26no—
177C2×C43—48no—
178C2×C43C22×C4×D411yescharacteristic
179#585C22×C4312yes—
180#578C4×C4314yescomplemented
181#577C4×C4318yescomplemented
182#576C4×C4314yescomplemented
183#575C22×C4316yes—
184C2×#135C22×C4316yes—
185#568—28no—
186#568C22×C4312yes—
187#568C22×C43112yescomplemented
188C2×#131—28no—
189C2×#131C22×C4311yescharacteristic
190C2×#131C22×C4311yescharacteristic
191C2×#131C22×C43112yescomplemented
192C4×#41C22×C4311yescharacteristic
193#444C22×C4314yescomplemented
194#444C22×C43112yescomplemented
195#444C22×C43112yescomplemented
196#444C22×C43112yescomplemented
197#443C22×C43124yescomplemented
198#430C22×C4316yescomplemented
199C2×#108C22×C4316yescomplemented
200#421C22×C43112yescomplemented
201C2×#104C22×C43112yescomplemented
202#405C22×C4313yescomplemented
203#405C22×C4313yescomplemented
204C4×M16C22×C4313yescomplemented
205C2×#97C22×C4313yescomplemented
206C43#6018411yescharacteristic, direct product factor, Sylow
2072−1+4—22no—
2082−1+4C2×C4×C4318yes—
209H(5,𝔽2)—26no—
210H(5,𝔽2)C2×C4×C4318yes—
211C2×#41—28no—
212C2×#41C23×C43112yes—
213C2×#41C23×C4311yescharacteristic
214#137C2×C4×C43124yescomplemented
215AGL(1,ℤ/8)C2×C4×C43124yescomplemented
216#135C2×C4×C43112yescomplemented
217#135C2×C4×C43112yescomplemented
218#135C23×C4314yes—
219#135C23×C43112yes—
220C2×Q16C2×C4×C4316yescomplemented
221C2×SD16C2×C4×C43112yescomplemented
222C2×D8C2×C4×C4316yescomplemented
223#131—28no—
224#131—224no—
225#131—212no—
226#131—212no—
227#131C2×C4×C4314yes—
228#131C2×C4×C4314yes—
229#131D4×C4318yes—
230#131C23×C4318yes—
231#131C23×C43124yes—
232C2×M16—224no—
233C2×M16—212no—
234C2×M16C23×C43112yes—
235C2×M16C23×C4313yes—
236C2×M16C23×C4313yes—
237C22×C8—212no—
238C22×C8C23×C4313yes—
239C22×C8C23×C4313yes—
240C4×Q8—21no—
241C4×D4—23no—
242#117C23×C4313yes—
243C2×C42C23×C4313yes—
244#108C23×C4314yes—
245#108C23×C43112yes—
246#104C23×C4318yes—
247#104C23×C43124yes—
248#97C23×C4311yescharacteristic
249#97C23×C4313yes—
250#97C23×C4313yes—
251#97C23×C4313yes—
252C4×C8C23×C4316yes—
253#41—28no—
254#41—224no—
255#41—212no—
256#41—212no—
257#41C22×C4×C43124yes—
258#41C22×C4×C4314yes—
259#41C2×D4×C4314yes—
260#41C24×C4318yes—
261C2×Q8—28no—
262C2×Q8C22×C4×C43112yes—
263C2×Q8#41×C4311yescharacteristic
264C2×D4—212no—
265C2×D4—224no—
266C2×D4C22×C4×C43112yes—
267C2×D4#41×C4313yes—
268C22×C4—212no—
269C22×C4—23no—
270C22×C4C24×C4313yes—
271Q16C22×C4×C4314yes—
272Q16C22×C4×C43112yes—
273SD16C22×C4×C4318yes—
274SD16C22×C4×C43124yes—
275D8C22×C4×C4314yes—
276D8C22×C4×C43112yes—
277M16—212no—
278M16—28no—
279M16—224no—
280M16C22×C4×C43112yes—
281M16C2×D4×C43112yes—
282M16C24×C4318yes—
283C2×C8—212no—
284C2×C8—28no—
285C2×C8—224no—
286C2×C8C22×C4×C4316yes—
287C2×C8C22×C4×C4316yes—
288C2×C8C2×D4×C43112yes—
289C2×C8C24×C4313yes—
290C2×C8C24×C4311yescharacteristic
291C2×C8C24×C4313yes—
292C2×C8C24×C4311yescharacteristic
293C4⋊C4—23no—
294C22⋊C4—23no—
295C42—23no—
296C42C24×C4313yes—
297C42C24×C4311yescharacteristic
298C23—212no—
299C23C2×#41×C4313yes—
300Q8—212no—
301Q8C4×D4×C4314yes—
302Q8C23×C4×C4318yes—
303D4—224no—
304D4—28no—
305D4—212no—
306D4C4×D4×C43112yes—
307D4C23×C4×C4318yes—
308C2×C4—212no—
309C2×C4—224no—
310C2×C4—28no—
311C2×C4—21no—
312C2×C4—23no—
313C2×C4—83no—
314C2×C4C23×C4×C4316yes—
315C2×C4C22×D4×C4316yes—
316C2×C4C2×#41×C4313yes—
317C2×C4C25×C4311yescharacteristic
318C8—28no—
319C8C23×C4×C4311yescharacteristic
320C8C23×C4×C4311yescharacteristic
321C8C23×C4×C4316yes—
322C8C22×D4×C4312yes—
323C8C22×D4×C4316yes—
324C22—28no—
325C22—43no—
326C22—812no—
327C22C2×C4×D4×C4316yes—
328C22C22×#41×C4311yescharacteristic
329C4—28no—
330C4—41no—
331C4—43no—
332C4C2×C4×D4×C4316yes—
333C4C24×C4×C4311yescharacteristic
334C4C23×D4×C4311yescharacteristic
335C2—21no—
336C2—26no—
337C2—48no—
338C2C22×C4×D4×C4311yescharacteristic
subgroupG/H
centerC4×C43C23×D4
commutatorC4C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC2×C43C22×C4×D4
prime radicalC43×#3584C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C43 ◁ C2×#131×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3573C2semidirect
3. C43×#2957C2semidirect
4. C43×#2956C2semidirect
5. C43×#2955C2semidirect
6. C2×C43×#444C2semidirect
7. C43×#2916C2semidirect
8. C43×#2901C2semidirect
9. C43×#2875C2semidirect
11. C43×#578C4semidirect
12. C43×#577C4semidirect
13. C43×#576C4semidirect
18. C43×#568C22semidirect
22. C2×#131×C43C22semidirect
24. C43×#444C22semidirect
25. C43×#444C22semidirect
26. C43×#444C22semidirect
27. C43×#444C22semidirect
28. C43×#443C22semidirect
29. C43×#430C22semidirect
30. C2×#108×C43C22semidirect
31. C43×#421C22semidirect
32. C2×#104×C43C22semidirect
33. C43×#405C22semidirect
34. C43×#405C22semidirect
35. C4×M16×C43C22semidirect
36. C2×#97×C43C22semidirect
44. #137×C43C2×C4semidirect
45. AGL(1,ℤ/8)×C43C2×C4semidirect
46. #135×C43C2×C4semidirect
47. #135×C43C2×C4semidirect
50. C2×Q16×C43C2×C4semidirect
51. C2×SD16×C43C2×C4semidirect
52. C2×D8×C43C2×C4semidirect
154. #60184C43direct (N × H)
167. #3573C2×C43semidirect
168. #2957C2×C43semidirect
169. #2956C2×C43semidirect
170. #2955C2×C43semidirect
171. C2×#444C2×C43semidirect
172. #2916C2×C43semidirect
173. #2901C2×C43semidirect
174. #2875C2×C43semidirect
180. #578C4×C43semidirect
181. #577C4×C43semidirect
182. #576C4×C43semidirect
187. #568C22×C43semidirect
191. C2×#131C22×C43semidirect
193. #444C22×C43semidirect
194. #444C22×C43semidirect
195. #444C22×C43semidirect
196. #444C22×C43semidirect
197. #443C22×C43semidirect
198. #430C22×C43semidirect
199. C2×#108C22×C43semidirect
200. #421C22×C43semidirect
201. C2×#104C22×C43semidirect
202. #405C22×C43semidirect
203. #405C22×C43semidirect
204. C4×M16C22×C43semidirect
205. C2×#97C22×C43semidirect
206. C43#60184direct (N × H)
214. #137C2×C4×C43semidirect
215. AGL(1,ℤ/8)C2×C4×C43semidirect
216. #135C2×C4×C43semidirect
217. #135C2×C4×C43semidirect
220. C2×Q16C2×C4×C43semidirect
221. C2×SD16C2×C4×C43semidirect
222. C2×D8C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35842
C43×#35732
C43×#29572
C43×#29562
C43×#29552
C2×C43×#4442
C43×#29162
C43×#29012
C43×#28752
#6018443