Finite Group Databasebeta

← C103×#33382 #39938657

Subgroups — C103×#33382 #39938657

Order 26368.

1124 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C103C211yesmaximal, characteristic
2C2×#504×C103C211yesmaximal, characteristic, complemented
3C103×#2913C211yesmaximal, characteristic, complemented
4C103×#2141C213yesmaximal, complemented
5C103×#2139C213yesmaximal, complemented
6C103×#2138C213yesmaximal, complemented
7C2×#358×C103C213yesmaximal, complemented
8C2×2−1+4×C103—21no—
9#578×C103—24no—
10#578×C103C418yescomplemented
11C2×#137×C103—23no—
12C2×#135×C103C2213yes—
13C22×Q16×C103C2213yes—
14C2×#131×C103C2211yescharacteristic
15#520×C103—21no—
16#504×C103—24no—
17C2×M32×C103C2213yes—
18C22×C16×C103C2213yes—
19#428×C103—23no—
20#427×C103C2213yes—
21C2×#107×C103C2213yes—
22#358×C103C2213yes—
23#358×C103C2216yes—
24#358×C103C2213yes—
25#357×C103C2211yescharacteristic
26#357×C103C2213yes—
272−1+4×C103—28no—
282−1+4×C103—44no—
29C2×#41×C103—23no—
30C2×#41×C103—43no—
31C2×#41×C103D411yescharacteristic
32C22×Q8×C103—23no—
33C22×Q8×C103—41no—
34#137×C103—224no—
35#135×C103—26no—
36#135×C103C2×C4112yescomplemented
37C2×Q16×C103—23no—
38C2×Q16×C103—26no—
39C2×Q16×C103C2×C4112yescomplemented
40C2×Q16×C103C2313yes—
41C2×SD16×C103—23no—
42C2×D8×C103C2311yescharacteristic
43#131×C103C2×C414yes—
44#131×C103D414yes—
45C2×M16×C103D413yes—
46C22×C8×C103C2313yes—
47C4×Q8×C103—41no—
48C4×D4×C103—43no—
49#117×C103—23no—
50C2×C4⋊C4×C103—23no—
51M32×C103—26no—
52C2×C16×C103—26no—
53C2×C16×C103C2311yescharacteristic
54C2×C16×C103C2313yes—
55#107×C103—23no—
56#107×C103C2313yes—
57#107×C103C2311yescharacteristic
58#106×C103—23no—
59#41×C103—212no—
60#41×C103—424no—
61#41×C103—46no—
62#41×C103C22⋊C414yes—
63#41×C103SD1614yes—
64C2×Q8×C103—212no—
65C2×Q8×C103—23no—
66C2×Q8×C103—48no—
67C2×Q8×C103—43no—
68C2×Q8×C103—46no—
69C2×Q8×C103D811yescharacteristic
70C2×D4×C103—21no—
71C2×D4×C103—43no—
72C2×D4×C103D813yes—
73C22×C4×C103—43no—
74C22×C4×C103—43no—
75C22×C4×C103—43no—
76C22×C4×C103C2×D413yes—
77Q16×C103—212no—
78Q16×C103—23no—
79Q16×C103C22×C416yes—
80SD16×C103—212no—
81D8×C103—21no—
82D8×C103C22×C412yes—
83M16×C103C22⋊C4112yes—
84C2×C8×C103C22×C416yes—
85C2×C8×C103C2×D413yes—
86C2×C8×C103C2×D416yes—
87C2×C8×C103C2411yescharacteristic
88C4⋊C4×C103—21no—
89C4⋊C4×C103—23no—
90C4⋊C4×C103—43no—
91C22⋊C4×C103—43no—
92C42×C103—43no—
93C16×C103—21no—
94C16×C103—23no—
95C23×C103—41no—
96C23×C103C2×D813yes—
97Q8×C103—26no—
98Q8×C103—43no—
99Q8×C103—412no—
100Q8×C103#10214yes—
101D4×C103—22no—
102D4×C103—412no—
103D4×C103—41no—
104D4×C103#102112yes—
105C2×C4×C103—43no—
106C2×C4×C103—412no—
107C2×C4×C103—412no—
108C2×C4×C103—41no—
109C2×C4×C103—43no—
110C2×C4×C103—163no—
111C2×C4×C103C2×C22⋊C416yes—
112C2×C4×C103C2×D813yes—
113C2×C4×C103C2×SD1616yes—
114C2×C4×C103C22×D411yescharacteristic
115C8×C103C2×C22⋊C416yes—
116C8×C103C23×C411yescharacteristic
117C8×C103C22×D411yescharacteristic
118C22×C103—23no—
119C22×C103—23no—
120C22×C103—42no—
121C22×C103—81no—
122C22×C103—81no—
123C22×C103C2×#10216yes—
124C22×C103C22×D811yescharacteristic
125C4×C103—46no—
126C4×C103—83no—
127C4×C103—81no—
128C4×C103C2×#10216yes—
129C4×C103C22×C22⋊C411yescharacteristic
130C4×C103C22×SD1611yescharacteristic
131#33382C10311yesmaximal, characteristic, direct product factor, Sylow
132C2×C103—26no—
133C2×C103—82no—
134C2×C103C22×#10211yescharacteristic
135C2×C103#341611yescharacteristic
136C2×C103#341711yescharacteristic
137C2×#578C2×C10311yescharacteristic
138C2×#504C2×C10311yescharacteristic, complemented
139#2913C2×C10311yescharacteristic, complemented
140#2141C2×C10313yescomplemented
141#2139C2×C10313yescomplemented
142#2138C2×C10313yescomplemented
143C2×#358C2×C10313yescomplemented
144C103#3338211yescharacteristic, direct product factor, Sylow
145C2×2−1+4—21no—
146#578—24no—
147#578C4×C10318yescomplemented
148C2×#137—23no—
149C2×#135C22×C10313yes—
150C22×Q16C22×C10313yes—
151C2×#131C22×C10311yescharacteristic
152#520—21no—
153#504—24no—
154C2×M32C22×C10313yes—
155C22×C16C22×C10313yes—
156#428—23no—
157#427C22×C10313yes—
158C2×#107C22×C10313yes—
159#358C22×C10313yes—
160#358C22×C10316yes—
161#358C22×C10313yes—
162#357C22×C10311yescharacteristic
163#357C22×C10313yes—
1642−1+4—28no—
1652−1+4—44no—
166C2×#41—23no—
167C2×#41—43no—
168C2×#41D4×C10311yescharacteristic
169C22×Q8—23no—
170C22×Q8—41no—
171#137—224no—
172#135—26no—
173#135C2×C4×C103112yescomplemented
174C2×Q16—23no—
175C2×Q16—26no—
176C2×Q16C2×C4×C103112yescomplemented
177C2×Q16C23×C10313yes—
178C2×SD16—23no—
179C2×D8C23×C10311yescharacteristic
180#131C2×C4×C10314yes—
181#131D4×C10314yes—
182C2×M16D4×C10313yes—
183C22×C8C23×C10313yes—
184C4×Q8—41no—
185C4×D4—43no—
186#117—23no—
187C2×C4⋊C4—23no—
188M32—26no—
189C2×C16—26no—
190C2×C16C23×C10311yescharacteristic
191C2×C16C23×C10313yes—
192#107—23no—
193#107C23×C10313yes—
194#107C23×C10311yescharacteristic
195#106—23no—
196#41—212no—
197#41—424no—
198#41—46no—
199#41C22⋊C4×C10314yes—
200#41SD16×C10314yes—
201C2×Q8—212no—
202C2×Q8—23no—
203C2×Q8—48no—
204C2×Q8—43no—
205C2×Q8—46no—
206C2×Q8D8×C10311yescharacteristic
207C2×D4—21no—
208C2×D4—43no—
209C2×D4D8×C10313yes—
210C22×C4—43no—
211C22×C4—43no—
212C22×C4—43no—
213C22×C4C2×D4×C10313yes—
214Q16—212no—
215Q16—23no—
216Q16C22×C4×C10316yes—
217SD16—212no—
218D8—21no—
219D8C22×C4×C10312yes—
220M16C22⋊C4×C103112yes—
221C2×C8C22×C4×C10316yes—
222C2×C8C2×D4×C10313yes—
223C2×C8C2×D4×C10316yes—
224C2×C8C24×C10311yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—23no—
227C4⋊C4—43no—
228C22⋊C4—43no—
229C42—43no—
230C16—21no—
231C16—23no—
232C23—41no—
233C23C2×D8×C10313yes—
234Q8—26no—
235Q8—412no—
236Q8—43no—
237Q8#102×C10314yes—
238D4—22no—
239D4—412no—
240D4—41no—
241D4#102×C103112yes—
242C2×C4—412no—
243C2×C4—43no—
244C2×C4—412no—
245C2×C4—41no—
246C2×C4—43no—
247C2×C4—163no—
248C2×C4C2×C22⋊C4×C10316yes—
249C2×C4C2×D8×C10313yes—
250C2×C4C2×SD16×C10316yes—
251C2×C4C22×D4×C10311yescharacteristic
252C8C2×C22⋊C4×C10316yes—
253C8C23×C4×C10311yescharacteristic
254C8C22×D4×C10311yescharacteristic
255C22—23no—
256C22—23no—
257C22—42no—
258C22—81no—
259C22—81no—
260C22C2×#102×C10316yes—
261C22C22×D8×C10311yescharacteristic
262C4—46no—
263C4—83no—
264C4—81no—
265C4C2×#102×C10316yes—
266C4C22×C22⋊C4×C10311yescharacteristic
267C4C22×SD16×C10311yescharacteristic
268C2—26no—
269C2—82no—
270C2C22×#102×C10311yescharacteristic
271C2C103×#341611yescharacteristic
272C2C103×#341711yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutatorC8C23×C4×C103
Frattini, cosocleC2×C8C24×C103
prime radicalC2×#578×C103C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×#41×C103 ◁ C2×#131×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#504×C103C2semidirect
3. C103×#2913C2semidirect
4. C103×#2141C2semidirect
5. C103×#2139C2semidirect
6. C103×#2138C2semidirect
7. C2×#358×C103C2semidirect
10. #578×C103C4semidirect
36. #135×C103C2×C4semidirect
39. C2×Q16×C103C2×C4semidirect
131. #33382C103direct (N × H)
138. C2×#504C2×C103semidirect
139. #2913C2×C103semidirect
140. #2141C2×C103semidirect
141. #2139C2×C103semidirect
142. #2138C2×C103semidirect
143. C2×#358C2×C103semidirect
144. C103#33382direct (N × H)
147. #578C4×C103semidirect
173. #135C2×C4×C103semidirect
176. C2×Q16C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#578×C1032
C2×#504×C1032
C103×#29132
C103×#21412
C103×#21392
C103×#21382
C2×#358×C1032
#33382103