Finite Group Databasebeta

← C103×#7812 #39913087

Subgroups — C103×#7812 #39913087

Order 26368.

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

normal subgroups only

This group has 398 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×#2811C211yesmaximal, characteristic
2C103×#2096C211yesmaximal, characteristic
3C103×#2072C212yesmaximal
4C103×#1272C212yesmaximal
5C103×#1272C211yesmaximal, characteristic
6C2×#106×C103—21no—
7C2×#103×C103—22no—
8C2×#103×C103—21no—
9#395×C103—21no—
10#395×C103—22no—
11#391×C103—22no—
12#391×C103—21no—
13#391×C103C2212yes—
14#391×C103C2211yescharacteristic
15#384×C103C2211yescharacteristic
16#340×C103—22no—
17#336×C103C2212yes—
18#336×C103C2211yescharacteristic
19C22×Q8×C103—21no—
20C22×Q8×C103D412yes—
21C22×Q8×C103D411yescharacteristic
22C22×C8×C103—21no—
23C22×C8×C103—22no—
24C2×C4⋊C4×C103—21no—
25C2×C4⋊C4×C103—22no—
26C2×C4⋊C4×C103—21no—
27C2×C4⋊C4×C103—22no—
28C2×C4⋊C4×C103D411yescharacteristic
29C2×C4⋊C4×C103D412yes—
30C2×C42×C103—21no—
31C2×C42×C103C2311yescharacteristic
32#106×C103—42no—
33#103×C103—42no—
34#103×C103—44no—
35#95×C103—21no—
36#95×C103—22no—
37#95×C103—22no—
38#95×C103—22no—
39#95×C103—22no—
40C2×Q8×C103—22no—
41C2×Q8×C103—21no—
42C2×Q8×C103—41no—
43C2×Q8×C103—42no—
44C2×Q8×C103—42no—
45C2×Q8×C103—41no—
46C2×Q8×C103—81no—
47C2×Q8×C103—82no—
48C2×Q8×C103SD1614yes—
49C2×Q8×C103Q1612yes—
50C22×C4×C103—22no—
51C22×C4×C103—21no—
52C22×C4×C103—21no—
53C22×C4×C103—22no—
54C22×C4×C103—41no—
55C22×C4×C103C2×D412yes—
56C22×C4×C103C2×D411yescharacteristic
57C2×C8×C103—22no—
58C2×C8×C103—41no—
59C2×C8×C103—41no—
60C2×C8×C103—42no—
61C2×C8×C103—42no—
62C2×C8×C103—42no—
63C4⋊C4×C103—41no—
64C4⋊C4×C103—42no—
65C4⋊C4×C103—41no—
66C4⋊C4×C103—41no—
67C4⋊C4×C103—42no—
68C4⋊C4×C103—42no—
69C4⋊C4×C103—81no—
70C4⋊C4×C103—82no—
71C42×C103—41no—
72C42×C103—81no—
73C23×C103#12011yescharacteristic
74Q8×C103—44no—
75Q8×C103—42no—
76Q8×C103—82no—
77Q8×C103—81no—
78Q8×C103—84no—
79C2×C4×C103—21no—
80C2×C4×C103—22no—
81C2×C4×C103—22no—
82C2×C4×C103—21no—
83C2×C4×C103—24no—
84C2×C4×C103—22no—
85C2×C4×C103—41no—
86C2×C4×C103—42no—
87C2×C4×C103—42no—
88C2×C4×C103—41no—
89C2×C4×C103—41no—
90C2×C4×C103—42no—
91C2×C4×C103—42no—
92C2×C4×C103—42no—
93C2×C4×C103—42no—
94C2×C4×C103—82no—
95C2×C4×C103—81no—
96C2×C4×C103C2×SD1612yes—
97C2×C4×C103C2×Q1611yescharacteristic
98C2×C4×C103#13712yes—
99C2×C4×C103#13711yescharacteristic
100C8×C103—42no—
101C8×C103—82no—
102C22×C103#44812yes—
103C22×C103#45111yescharacteristic
104C22×C103#45311yescharacteristic
105C22×C103#45512yes—
106C22×C103#45811yescharacteristic
107C4×C103—22no—
108C4×C103—22no—
109C4×C103—21no—
110C4×C103—21no—
111C4×C103—44no—
112C4×C103—42no—
113C4×C103—81no—
114C4×C103—82no—
115C4×C103—161no—
116#7812C10311yesmaximal, characteristic, direct product factor, Sylow
117C2×C103#160812yes—
118C2×C103#161411yescharacteristic
119C2×C103#162311yescharacteristic
120C2×C103#164512yes—
121C2×C103#165911yescharacteristic
122#2811C2×C10311yescharacteristic
123#2096C2×C10311yescharacteristic
124#2072C2×C10312yes—
125#1272C2×C10311yescharacteristic
126#1272C2×C10312yes—
127C103#781211yescharacteristic, direct product factor, Sylow
128C2×#106—21no—
129C2×#103—22no—
130C2×#103—21no—
131#395—22no—
132#395—21no—
133#391—22no—
134#391—21no—
135#391C22×C10312yes—
136#391C22×C10311yescharacteristic
137#384C22×C10311yescharacteristic
138#340—22no—
139#336C22×C10312yes—
140#336C22×C10311yescharacteristic
141C22×Q8—21no—
142C22×Q8D4×C10312yes—
143C22×Q8D4×C10311yescharacteristic
144C22×C8—21no—
145C22×C8—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4D4×C10312yes—
151C2×C4⋊C4D4×C10311yescharacteristic
152C2×C42—21no—
153C2×C42C23×C10311yescharacteristic
154#106—42no—
155#103—42no—
156#103—44no—
157#95—21no—
158#95—22no—
159#95—22no—
160#95—22no—
161#95—22no—
162C2×Q8—22no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—41no—
168C2×Q8—81no—
169C2×Q8—82no—
170C2×Q8SD16×C10314yes—
171C2×Q8Q16×C10312yes—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—41no—
177C22×C4C2×D4×C10312yes—
178C22×C4C2×D4×C10311yescharacteristic
179C2×C8—22no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—81no—
192C4⋊C4—82no—
193C42—41no—
194C42—81no—
195C23#120×C10311yescharacteristic
196Q8—44no—
197Q8—42no—
198Q8—82no—
199Q8—81no—
200Q8—84no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—82no—
217C2×C4—81no—
218C2×C4C2×SD16×C10312yes—
219C2×C4C2×Q16×C10311yescharacteristic
220C2×C4#137×C10312yes—
221C2×C4#137×C10311yescharacteristic
222C8—42no—
223C8—82no—
224C22#448×C10312yes—
225C22#451×C10311yescharacteristic
226C22#453×C10311yescharacteristic
227C22#455×C10312yes—
228C22#458×C10311yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—44no—
234C4—42no—
235C4—81no—
236C4—82no—
237C4—161no—
238C2C103×#160812yes—
239C2C103×#161411yescharacteristic
240C2C103×#162311yescharacteristic
241C2C103×#164512yes—
242C2C103×#165911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103#120
commutator, Frattini, cosocleC2×C42C23×C103
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
116. #7812C103direct (N × H)
127. C103#7812direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#28112
C103×#20962
C103×#20722
C103×#12722
#7812103