Finite Group Databasebeta

← C103×#8769 #39914044

Subgroups — C103×#8769 #39914044

Order 26368.

378 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2356C211yesmaximal, characteristic
2C103×#1801C211yesmaximal, characteristic
3C103×#1461C211yesmaximal, characteristic
4C103×#1303C212yesmaximal
5C103×#1286C212yesmaximal
6C2×C4×Q8×C103C2211yescharacteristic
7#431×C103C2212yes—
8#423×C103C2212yes—
9C2×#101×C103—21no—
10#391×C103—21no—
11#387×C103—22no—
12#383×C103C412yes—
13#382×C103C2211yescharacteristic
14C4×C4⋊C4×C103—21no—
15C4×C4⋊C4×C103C2211yescharacteristic
16#376×C103C412yes—
17#343×C103—21no—
18#324×C103—22no—
19C22×Q8×C103D411yescharacteristic
20C2×M16×C103—22no—
21C4×Q8×C103—22no—
22C4×Q8×C103—22no—
23C2×C4⋊C4×C103—21no—
24C2×C4⋊C4×C103—21no—
25C2×C4⋊C4×C103D411yescharacteristic
26C2×C4⋊C4×C103D412yes—
27C2×C42×C103—22no—
28C2×C42×C103—21no—
29C2×C42×C103C2×C412yes—
30C2×C42×C103C2311yescharacteristic
31C4⋊C8×C103—22no—
32C4⋊C8×C103—22no—
33C4⋊C8×C103—22no—
34#101×C103—42no—
35C22⋊C8×C103—22no—
36C4×C8×C103—22no—
37#95×C103—22no—
38#95×C103—22no—
39#95×C103—22no—
40#95×C103—21no—
41#95×C103C2×C411yescharacteristic
42#95×C103C2×C412yes—
43#95×C103C2×C411yescharacteristic
44C2×Q8×C103—22no—
45C2×Q8×C103—22no—
46C2×Q8×C103—21no—
47C2×Q8×C103—21no—
48C22×C4×C103—21no—
49C22×C4×C103—22no—
50C22×C4×C103—21no—
51C22×C4×C103C22⋊C412yes—
52C22×C4×C103C22⋊C412yes—
53C22×C4×C103C22×C411yescharacteristic
54C22×C4×C103C2×D411yescharacteristic
55C22×C4×C103C2×D411yescharacteristic
56M16×C103—42no—
57M16×C103—42no—
58C2×C8×C103—42no—
59C2×C8×C103—42no—
60C4⋊C4×C103—22no—
61C4⋊C4×C103—24no—
62C4⋊C4×C103—42no—
63C4⋊C4×C103—41no—
64C4⋊C4×C103—41no—
65C42×C103—22no—
66C42×C103—22no—
67C42×C103—44no—
68C42×C103—42no—
69C42×C103#4112yes—
70C42×C103#4112yes—
71C23×C103C2×C22⋊C411yescharacteristic
72Q8×C103—42no—
73Q8×C103—42no—
74C2×C4×C103—22no—
75C2×C4×C103—22no—
76C2×C4×C103—22no—
77C2×C4×C103—22no—
78C2×C4×C103—22no—
79C2×C4×C103—41no—
80C2×C4×C103—41no—
81C2×C4×C103—41no—
82C2×C4×C103—41no—
83C2×C4×C103—42no—
84C2×C4×C103—42no—
85C2×C4×C103—41no—
86C2×C4×C103—41no—
87C2×C4×C103—42no—
88C2×C4×C103—41no—
89C2×C4×C103—42no—
90C2×C4×C103#11711yescharacteristic
91C2×C4×C103#11711yescharacteristic
92C2×C4×C103#12312yes—
93C2×C4×C103#12312yes—
94C2×C4×C103#13512yes—
95C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C103#13711yescharacteristic
97C8×C103—82no—
98C8×C103—82no—
99C22×C103—21no—
100C22×C103—21no—
101C22×C103#38111yescharacteristic
102C22×C103#41611yescharacteristic
103C22×C103#41711yescharacteristic
104C4×C103—22no—
105C4×C103—21no—
106C4×C103—21no—
107C4×C103—42no—
108C4×C103—42no—
109C4×C103—42no—
110C4×C103—81no—
111C4×C103—82no—
112C4×C103#48212yes—
113C4×C103#48512yes—
114#8769C10311yesmaximal, characteristic, direct product factor, Sylow
115C2×C103—21no—
116C2×C103—21no—
117C2×C103#182511yescharacteristic
118C2×C103#182711yescharacteristic
119C2×C103#183011yescharacteristic
120#2356C2×C10311yescharacteristic
121#1801C2×C10311yescharacteristic
122#1461C2×C10311yescharacteristic
123#1303C2×C10312yes—
124#1286C2×C10312yes—
125C103#876911yescharacteristic, direct product factor, Sylow
126C2×C4×Q8C22×C10311yescharacteristic
127#431C22×C10312yes—
128#423C22×C10312yes—
129C2×#101—21no—
130#391—21no—
131#387—22no—
132#383C4×C10312yes—
133#382C22×C10311yescharacteristic
134C4×C4⋊C4—21no—
135C4×C4⋊C4C22×C10311yescharacteristic
136#376C4×C10312yes—
137#343—21no—
138#324—22no—
139C22×Q8D4×C10311yescharacteristic
140C2×M16—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4D4×C10312yes—
146C2×C4⋊C4D4×C10311yescharacteristic
147C2×C42—22no—
148C2×C42—21no—
149C2×C42C2×C4×C10312yes—
150C2×C42C23×C10311yescharacteristic
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—22no—
154#101—42no—
155C22⋊C8—22no—
156C4×C8—22no—
157#95—22no—
158#95—22no—
159#95—22no—
160#95—21no—
161#95C2×C4×C10311yescharacteristic
162#95C2×C4×C10312yes—
163#95C2×C4×C10311yescharacteristic
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—21no—
167C2×Q8—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—21no—
171C22×C4C22⋊C4×C10312yes—
172C22×C4C22⋊C4×C10312yes—
173C22×C4C22×C4×C10311yescharacteristic
174C22×C4C2×D4×C10311yescharacteristic
175C22×C4C2×D4×C10311yescharacteristic
176M16—42no—
177M16—42no—
178C2×C8—42no—
179C2×C8—42no—
180C4⋊C4—22no—
181C4⋊C4—24no—
182C4⋊C4—42no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C42—22no—
186C42—22no—
187C42—44no—
188C42—42no—
189C42#41×C10312yes—
190C42#41×C10312yes—
191C23C2×C22⋊C4×C10311yescharacteristic
192Q8—42no—
193Q8—42no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4#117×C10311yescharacteristic
211C2×C4#117×C10311yescharacteristic
212C2×C4#123×C10312yes—
213C2×C4#123×C10312yes—
214C2×C4#135×C10312yes—
215C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
216C2×C4#137×C10311yescharacteristic
217C8—82no—
218C8—82no—
219C22—21no—
220C22—21no—
221C22#381×C10311yescharacteristic
222C22#416×C10311yescharacteristic
223C22#417×C10311yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—42no—
228C4—42no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4#482×C10312yes—
233C4#485×C10312yes—
234C2—21no—
235C2—21no—
236C2C103×#182511yescharacteristic
237C2C103×#182711yescharacteristic
238C2C103×#183011yescharacteristic
subgroupG/H
center, socleC22×C103#381
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC23×C103C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
114. #8769C103direct (N × H)
125. C103#8769direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#23562
C103×#18012
C103×#14612
C103×#13032
C103×#12862
#8769103