Finite Group Databasebeta

← C2×C103×#2138 #39938651

Subgroups — C2×C103×#2138 #39938651

Order 26368.

1190 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
1C22×#135×C103C211yesmaximal, characteristic
2C23×C16×C103C211yesmaximal, characteristic, complemented
3C2×#427×C103C211yesmaximal, characteristic, complemented
4C103×#2138C218yesmaximal, direct product factor
5C2×#358×C103C212yesmaximal, complemented
6C2×#357×C103C212yesmaximal, complemented
7C22×#41×C103—21no—
8C2×#135×C103—22no—
9C2×#135×C103—24no—
10C2×#135×C103C418yescomplemented
11C2×#135×C103C2214yes—
12C22×Q16×C103C2211yescharacteristic
13C22×SD16×C103—21no—
14C22×D8×C103C2211yescharacteristic
15C23×C8×C103C2211yescharacteristic
16C2×#117×C103—21no—
17C22×C16×C103—24no—
18C22×C16×C103C2212yes—
19C22×C16×C103C2214yescomplemented
20#427×C103—22no—
21#427×C103C2214yescomplemented
22C2×#107×C103C2212yes—
23C2×#106×C103—21no—
24#358×C103C2218yescomplemented
25#357×C103C2218yescomplemented
26C2×#41×C103—28no—
27C2×#41×C103—24no—
28C2×#41×C103—42no—
29C2×#41×C103—44no—
30C22×Q8×C103—21no—
31C22×D4×C103—21no—
32C22×D4×C103—41no—
33C23×C4×C103—41no—
34C23×C4×C103D411yescharacteristic
35#135×C103—216no—
36#135×C103—28no—
37#135×C103C2×C4116yescomplemented
38C2×Q16×C103—21no—
39C2×Q16×C103—22no—
40C2×Q16×C103C2×C414yes—
41C2×Q16×C103C2312yes—
42C2×SD16×C103—28no—
43C2×SD16×C103—24no—
44C2×D8×C103—21no—
45C2×D8×C103—22no—
46C2×D8×C103C2×C414yes—
47C2×D8×C103C2312yes—
48C22×C8×C103C2×C414yes—
49C22×C8×C103D411yescharacteristic
50C22×C8×C103D412yes—
51C22×C8×C103D414yes—
52C22×C8×C103C2311yescharacteristic
53C22×C8×C103C2312yes—
54#117×C103—24no—
55#117×C103—42no—
56C2×C4⋊C4×C103—22no—
57C2×C22⋊C4×C103—41no—
58C2×C42×C103—41no—
59C2×C16×C103—24no—
60C2×C16×C103—28no—
61C2×C16×C103C2314yes—
62#107×C103—22no—
63#107×C103C2314yes—
64#106×C103—24no—
65C24×C103—41no—
66C24×C103D811yescharacteristic
67#41×C103—216no—
68#41×C103—416no—
69#41×C103—48no—
70C2×Q8×C103—24no—
71C2×Q8×C103—22no—
72C2×Q8×C103—41no—
73C2×Q8×C103—42no—
74C2×D4×C103—24no—
75C2×D4×C103—22no—
76C2×D4×C103—48no—
77C2×D4×C103—44no—
78C2×D4×C103—41no—
79C2×D4×C103—42no—
80C22×C4×C103—41no—
81C22×C4×C103—48no—
82C22×C4×C103—44no—
83C22×C4×C103—42no—
84C22×C4×C103C22⋊C414yes—
85C22×C4×C103D812yes—
86C22×C4×C103D811yescharacteristic
87C22×C4×C103SD1614yes—
88C22×C4×C103C2×D411yescharacteristic
89C22×C4×C103C2×D412yes—
90Q16×C103—24no—
91Q16×C103—22no—
92Q16×C103C22×C414yes—
93SD16×C103—216no—
94D8×C103—24no—
95D8×C103—22no—
96D8×C103C22×C414yes—
97C2×C8×C103C22⋊C414yes—
98C2×C8×C103C22⋊C418yes—
99C2×C8×C103C22×C412yes—
100C2×C8×C103C22×C414yes—
101C2×C8×C103C2×D412yes—
102C2×C8×C103C2×D411yescharacteristic
103C2×C8×C103C2×D412yes—
104C2×C8×C103C2×D414yes—
105C2×C8×C103C2411yescharacteristic
106C4⋊C4×C103—24no—
107C4⋊C4×C103—42no—
108C22⋊C4×C103—44no—
109C42×C103—44no—
110C16×C103—24no—
111C23×C103—24no—
112C23×C103—42no—
113C23×C103—44no—
114C23×C103—84no—
115C23×C103#10214yes—
116C23×C103C2×D812yes—
117C23×C103C2×D811yescharacteristic
118Q8×C103—24no—
119Q8×C103—42no—
120Q8×C103—44no—
121D4×C103—24no—
122D4×C103—416no—
123D4×C103—42no—
124D4×C103—44no—
125C2×C4×C103—42no—
126C2×C4×C103—44no—
127C2×C4×C103—416no—
128C2×C4×C103—44no—
129C2×C4×C103—84no—
130C2×C4×C103#10214yes—
131C2×C4×C103#10218yes—
132C2×C4×C103C2×C22⋊C412yes—
133C2×C4×C103C2×C22⋊C414yes—
134C2×C4×C103C2×D812yes—
135C2×C4×C103C2×D811yescharacteristic
136C2×C4×C103C2×SD1612yes—
137C2×C4×C103C2×SD1614yes—
138C2×C4×C103C22×D411yescharacteristic
139C8×C103C2×C22⋊C412yes—
140C8×C103C2×C22⋊C414yes—
141C8×C103C23×C411yescharacteristic
142C8×C103C22×D411yescharacteristic
143C22×C103—24no—
144C22×C103—28no—
145C22×C103—44no—
146C22×C103—84no—
147C22×C103—88no—
148C22×C103C2×#10214yes—
149C22×C103C2×#10212yes—
150C22×C103#50814yes—
151C22×C103C22×D811yescharacteristic
152C4×C103—44no—
153C4×C103—84no—
154C4×C103C2×#10214yes—
155C4×C103C2×#10212yes—
156C4×C103C22×C22⋊C411yescharacteristic
157C4×C103C22×SD1611yescharacteristic
158C2×#2138C10311yesmaximal, characteristic, direct product factor, Sylow
159C2×C103—24no—
160C2×C103—84no—
161C2×C103#213814yesdirect product factor
162C2×C103C22×#10211yescharacteristic
163C2×C103C2×#50812yes—
164C22×#135C2×C10311yescharacteristic
165C23×C16C2×C10311yescharacteristic, complemented
166C2×#427C2×C10311yescharacteristic, complemented
167#2138C2×C10318yesdirect product factor
168C2×#358C2×C10312yescomplemented
169C2×#357C2×C10312yescomplemented
170C103C2×#213811yescharacteristic, direct product factor, Sylow
171C22×#41—21no—
172C2×#135—22no—
173C2×#135—24no—
174C2×#135C4×C10318yescomplemented
175C2×#135C22×C10314yes—
176C22×Q16C22×C10311yescharacteristic
177C22×SD16—21no—
178C22×D8C22×C10311yescharacteristic
179C23×C8C22×C10311yescharacteristic
180C2×#117—21no—
181C22×C16—24no—
182C22×C16C22×C10312yes—
183C22×C16C22×C10314yescomplemented
184#427—22no—
185#427C22×C10314yescomplemented
186C2×#107C22×C10312yes—
187C2×#106—21no—
188#358C22×C10318yescomplemented
189#357C22×C10318yescomplemented
190C2×#41—28no—
191C2×#41—24no—
192C2×#41—42no—
193C2×#41—44no—
194C22×Q8—21no—
195C22×D4—21no—
196C22×D4—41no—
197C23×C4—41no—
198C23×C4D4×C10311yescharacteristic
199#135—216no—
200#135—28no—
201#135C2×C4×C103116yescomplemented
202C2×Q16—21no—
203C2×Q16—22no—
204C2×Q16C2×C4×C10314yes—
205C2×Q16C23×C10312yes—
206C2×SD16—28no—
207C2×SD16—24no—
208C2×D8—21no—
209C2×D8—22no—
210C2×D8C2×C4×C10314yes—
211C2×D8C23×C10312yes—
212C22×C8C2×C4×C10314yes—
213C22×C8D4×C10311yescharacteristic
214C22×C8D4×C10312yes—
215C22×C8D4×C10314yes—
216C22×C8C23×C10311yescharacteristic
217C22×C8C23×C10312yes—
218#117—24no—
219#117—42no—
220C2×C4⋊C4—22no—
221C2×C22⋊C4—41no—
222C2×C42—41no—
223C2×C16—24no—
224C2×C16—28no—
225C2×C16C23×C10314yes—
226#107—22no—
227#107C23×C10314yes—
228#106—24no—
229C24—41no—
230C24D8×C10311yescharacteristic
231#41—216no—
232#41—416no—
233#41—48no—
234C2×Q8—24no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—42no—
238C2×D4—24no—
239C2×D4—22no—
240C2×D4—48no—
241C2×D4—44no—
242C2×D4—41no—
243C2×D4—42no—
244C22×C4—41no—
245C22×C4—48no—
246C22×C4—44no—
247C22×C4—42no—
248C22×C4C22⋊C4×C10314yes—
249C22×C4D8×C10312yes—
250C22×C4D8×C10311yescharacteristic
251C22×C4SD16×C10314yes—
252C22×C4C2×D4×C10311yescharacteristic
253C22×C4C2×D4×C10312yes—
254Q16—24no—
255Q16—22no—
256Q16C22×C4×C10314yes—
257SD16—216no—
258D8—24no—
259D8—22no—
260D8C22×C4×C10314yes—
261C2×C8C22⋊C4×C10314yes—
262C2×C8C22⋊C4×C10318yes—
263C2×C8C22×C4×C10312yes—
264C2×C8C22×C4×C10314yes—
265C2×C8C2×D4×C10312yes—
266C2×C8C2×D4×C10311yescharacteristic
267C2×C8C2×D4×C10312yes—
268C2×C8C2×D4×C10314yes—
269C2×C8C24×C10311yescharacteristic
270C4⋊C4—24no—
271C4⋊C4—42no—
272C22⋊C4—44no—
273C42—44no—
274C16—24no—
275C23—24no—
276C23—44no—
277C23—42no—
278C23—84no—
279C23#102×C10314yes—
280C23C2×D8×C10312yes—
281C23C2×D8×C10311yescharacteristic
282Q8—24no—
283Q8—44no—
284Q8—42no—
285D4—24no—
286D4—416no—
287D4—44no—
288D4—42no—
289C2×C4—44no—
290C2×C4—42no—
291C2×C4—416no—
292C2×C4—44no—
293C2×C4—84no—
294C2×C4#102×C10314yes—
295C2×C4#102×C10318yes—
296C2×C4C2×C22⋊C4×C10312yes—
297C2×C4C2×C22⋊C4×C10314yes—
298C2×C4C2×D8×C10312yes—
299C2×C4C2×D8×C10311yescharacteristic
300C2×C4C2×SD16×C10312yes—
301C2×C4C2×SD16×C10314yes—
302C2×C4C22×D4×C10311yescharacteristic
303C8C2×C22⋊C4×C10312yes—
304C8C2×C22⋊C4×C10314yes—
305C8C23×C4×C10311yescharacteristic
306C8C22×D4×C10311yescharacteristic
307C22—24no—
308C22—28no—
309C22—44no—
310C22—84no—
311C22—88no—
312C22C2×#102×C10314yes—
313C22C2×#102×C10312yes—
314C22#508×C10314yes—
315C22C22×D8×C10311yescharacteristic
316C4—44no—
317C4—84no—
318C4C2×#102×C10314yes—
319C4C2×#102×C10312yes—
320C4C22×C22⋊C4×C10311yescharacteristic
321C4C22×SD16×C10311yescharacteristic
322C2—24no—
323C2—84no—
324C2C103×#213814yesdirect product factor
325C2C22×#102×C10311yescharacteristic
326C2C2×#508×C10312yes—
subgroupG/H
centerC22×C4×C103D8
commutatorC8C23×C4×C103
Frattini, cosocleC2×C8C24×C103
socleC23×C103C2×D8
prime radicalC22×#135×C103C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ C23×C4×C103 ◁ C23×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C16×C103C2semidirect
3. C2×#427×C103C2semidirect
4. C103×#2138C2direct (N × H)
5. C2×#358×C103C2semidirect
6. C2×#357×C103C2semidirect
10. C2×#135×C103C4semidirect
19. C22×C16×C103C22semidirect
21. #427×C103C22semidirect
24. #358×C103C22semidirect
25. #357×C103C22semidirect
37. #135×C103C2×C4semidirect
158. C2×#2138C103direct (N × H)
161. C2×C103#2138direct (N × H)
165. C23×C16C2×C103semidirect
166. C2×#427C2×C103semidirect
167. #2138C2×C103direct (N × H)
168. C2×#358C2×C103semidirect
169. C2×#357C2×C103semidirect
170. C103C2×#2138direct (N × H)
174. C2×#135C4×C103semidirect
183. C22×C16C22×C103semidirect
185. #427C22×C103semidirect
188. #358C22×C103semidirect
189. #357C22×C103semidirect
201. #135C2×C4×C103semidirect
324. C2C103×#2138direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#135×C1032
C23×C16×C1032
C2×#427×C1032
C103×#21382
C2×#358×C1032
C2×#357×C1032
C2×#2138103