Finite Group Databasebeta

← C103×#10425 #39915700

Subgroups — C103×#10425 #39915700

Order 26368.

518 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2819C211yesmaximal, characteristic
2C103×#1959C212yesmaximal, complemented
3C103×#1836C211yesmaximal, characteristic, complemented
4C2×#329×C103C212yesmaximal, complemented
5C103×#1295C211yesmaximal, characteristic, complemented
6C2×#124×C103C2212yes—
7C2×#103×C103—22no—
8C2×#102×C103—22no—
9C2×#97×C103C2212yes—
10C2×#97×C103C2211yescharacteristic
11#394×C103—22no—
12#393×C103—22no—
13#392×C103—22no—
14#384×C103C2211yescharacteristic
15#382×C103C2211yescharacteristic
16#340×C103—22no—
17#329×C103—24no—
18C22×Q8×C103D412yes—
19C22×D4×C103—22no—
20C22×D4×C103D412yes—
21C22×C8×C103—22no—
22C22×C8×C103—21no—
23#124×C103—22no—
24#124×C103—22no—
25#124×C103—22no—
26#124×C103—22no—
27C2×C4⋊C4×C103—22no—
28C2×C4⋊C4×C103—21no—
29C2×C4⋊C4×C103D412yes—
30C2×C22⋊C4×C103—22no—
31C2×C22⋊C4×C103—22no—
32C2×C22⋊C4×C103—22no—
33C2×C22⋊C4×C103—22no—
34C2×C42×C103C2311yescharacteristic
35#103×C103—44no—
36#102×C103—44no—
37#97×C103—22no—
38#97×C103—21no—
39#97×C103—22no—
40#97×C103D412yescomplemented
41#95×C103—22no—
42#95×C103—22no—
43C24×C103—22no—
44C2×Q8×C103—22no—
45C2×Q8×C103—22no—
46C2×Q8×C103—42no—
47C2×Q8×C103—42no—
48C2×D4×C103—22no—
49C2×D4×C103—22no—
50C2×D4×C103—42no—
51C2×D4×C103—42no—
52C2×D4×C103—82no—
53C2×D4×C103—82no—
54C2×D4×C103—82no—
55C22×C4×C103—22no—
56C22×C4×C103—22no—
57C22×C4×C103—41no—
58C22×C4×C103C2×D412yes—
59C22×C4×C103C2×D411yescharacteristic
60C2×C8×C103—24no—
61C2×C8×C103—22no—
62C2×C8×C103—41no—
63C2×C8×C103—41no—
64C2×C8×C103—42no—
65C2×C8×C103—42no—
66C4⋊C4×C103—42no—
67C4⋊C4×C103—42no—
68C4⋊C4×C103—42no—
69C4⋊C4×C103—42no—
70C22⋊C4×C103—42no—
71C22⋊C4×C103—42no—
72C22⋊C4×C103—42no—
73C22⋊C4×C103—42no—
74C22⋊C4×C103—82no—
75C22⋊C4×C103—82no—
76C42×C103C2×D411yescharacteristic
77C42×C103#4111yescharacteristic
78C42×C103#4112yes—
79C23×C103—42no—
80C23×C103—42no—
81C23×C103—42no—
82C23×C103—42no—
83C23×C103—42no—
84C23×C103—42no—
85C23×C103—42no—
86C23×C103#12011yescharacteristic
87Q8×C103—44no—
88Q8×C103—82no—
89D4×C103—44no—
90D4×C103—82no—
91D4×C103—88no—
92C2×C4×C103—22no—
93C2×C4×C103—21no—
94C2×C4×C103—21no—
95C2×C4×C103—22no—
96C2×C4×C103—42no—
97C2×C4×C103—42no—
98C2×C4×C103—42no—
99C2×C4×C103—42no—
100C2×C4×C103—42no—
101C2×C4×C103—42no—
102C2×C4×C103—82no—
103C2×C4×C103—81no—
104C2×C4×C103#12111yescharacteristic
105C2×C4×C103#12112yes—
106C2×C4×C103#12312yes—
107C2×C4×C103#12411yescharacteristic
108C8×C103—44no—
109C8×C103—42no—
110C22×C103—82no—
111C22×C103—82no—
112C22×C103—82no—
113C22×C103—82no—
114C22×C103—82no—
115C22×C103—82no—
116C22×C103—82no—
117C22×C103#39411yescharacteristic
118C22×C103#45312yes—
119C22×C103#45411yescharacteristic
120C22×C103#45511yescharacteristic
121C22×C103#45512yes—
122C4×C103—22no—
123C4×C103—22no—
124C4×C103—21no—
125C4×C103—21no—
126C4×C103—82no—
127C4×C103—82no—
128C4×C103—161no—
129#10425C10311yesmaximal, characteristic, direct product factor, Sylow
130C2×C103—162no—
131C2×C103#165611yescharacteristic
132C2×C103#165912yes—
133C2×C103#166211yescharacteristic
134C2×C103#203712yes—
135C2×C103#204011yescharacteristic
136#2819C2×C10311yescharacteristic
137#1959C2×C10312yescomplemented
138#1836C2×C10311yescharacteristic, complemented
139C2×#329C2×C10312yescomplemented
140#1295C2×C10311yescharacteristic, complemented
141C103#1042511yescharacteristic, direct product factor, Sylow
142C2×#124C22×C10312yes—
143C2×#103—22no—
144C2×#102—22no—
145C2×#97C22×C10312yes—
146C2×#97C22×C10311yescharacteristic
147#394—22no—
148#393—22no—
149#392—22no—
150#384C22×C10311yescharacteristic
151#382C22×C10311yescharacteristic
152#340—22no—
153#329—24no—
154C22×Q8D4×C10312yes—
155C22×D4—22no—
156C22×D4D4×C10312yes—
157C22×C8—21no—
158C22×C8—22no—
159#124—22no—
160#124—22no—
161#124—22no—
162#124—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4D4×C10312yes—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C42C23×C10311yescharacteristic
171#103—44no—
172#102—44no—
173#97—22no—
174#97—21no—
175#97—22no—
176#97D4×C10312yescomplemented
177#95—22no—
178#95—22no—
179C24—22no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—42no—
183C2×Q8—42no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—42no—
188C2×D4—82no—
189C2×D4—82no—
190C2×D4—82no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4C2×D4×C10312yes—
195C22×C4C2×D4×C10311yescharacteristic
196C2×C8—24no—
197C2×C8—22no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—42no—
201C2×C8—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C22⋊C4—42no—
210C22⋊C4—82no—
211C22⋊C4—82no—
212C42C2×D4×C10311yescharacteristic
213C42#41×C10311yescharacteristic
214C42#41×C10312yes—
215C23—42no—
216C23—42no—
217C23—42no—
218C23—42no—
219C23—42no—
220C23—42no—
221C23—42no—
222C23#120×C10311yescharacteristic
223Q8—44no—
224Q8—82no—
225D4—44no—
226D4—82no—
227D4—88no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—81no—
240C2×C4#121×C10311yescharacteristic
241C2×C4#121×C10312yes—
242C2×C4#123×C10312yes—
243C2×C4#124×C10311yescharacteristic
244C8—44no—
245C8—42no—
246C22—82no—
247C22—82no—
248C22—82no—
249C22—82no—
250C22—82no—
251C22—82no—
252C22—82no—
253C22#394×C10311yescharacteristic
254C22#453×C10312yes—
255C22#454×C10311yescharacteristic
256C22#455×C10312yes—
257C22#455×C10311yescharacteristic
258C4—22no—
259C4—22no—
260C4—21no—
261C4—21no—
262C4—82no—
263C4—82no—
264C4—161no—
265C2—162no—
266C2C103×#165611yescharacteristic
267C2C103×#165912yes—
268C2C103×#166211yescharacteristic
269C2C103×#203712yes—
270C2C103×#204011yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutator, Frattini, cosocleC2×C42C23×C103
prime radicalC103×#2819C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#1959C2semidirect
3. C103×#1836C2semidirect
4. C2×#329×C103C2semidirect
5. C103×#1295C2semidirect
40. #97×C103D4semidirect
129. #10425C103direct (N × H)
137. #1959C2×C103semidirect
138. #1836C2×C103semidirect
139. C2×#329C2×C103semidirect
140. #1295C2×C103semidirect
141. C103#10425direct (N × H)
176. #97D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#28192
C103×#19592
C103×#18362
C2×#329×C1032
C103×#12952
#10425103