Finite Group Databasebeta

← C103×#9488 #39914763

Subgroups — C103×#9488 #39914763

Order 26368.

454 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2983C211yesmaximal, characteristic
2C103×#2581C211yesmaximal, characteristic
3C103×#1801C211yesmaximal, characteristic
4C103×#1487C212yesmaximal
5C103×#1286C212yesmaximal
6C2×C4×Q8×C103C2211yescharacteristic
7C2×C4×Q8×C103C2211yescharacteristic
8#446×C103—24no—
9#432×C103—22no—
10#431×C103C2212yes—
11#423×C103C2212yes—
12C2×#101×C103—21no—
13#400×C103C412yes—
14#395×C103C412yes—
15#391×C103—21no—
16#389×C103—21no—
17#387×C103—22no—
18#382×C103C2211yescharacteristic
19#343×C103—21no—
20Q8⋊C8×C103—24no—
21C22×Q8×C103C2×C411yescharacteristic
22C22×Q8×C103D411yescharacteristic
23C2×M16×C103—22no—
24C4×Q8×C103—22no—
25C4×Q8×C103—22no—
26C4×Q8×C103—22no—
27C4×Q8×C103—22no—
28C2×C4⋊C4×C103—22no—
29C2×C4⋊C4×C103—21no—
30C2×C4⋊C4×C103—21no—
31C2×C4⋊C4×C103C2×C411yescharacteristic
32C2×C4⋊C4×C103C2×C412yes—
33C2×C4⋊C4×C103D411yescharacteristic
34C2×C42×C103—21no—
35C2×C42×C103D412yes—
36C2×C42×C103C2311yescharacteristic
37C4⋊C8×C103—24no—
38C4⋊C8×C103—22no—
39C4⋊C8×C103—22no—
40C4⋊C8×C103—22no—
41#101×C103—42no—
42C22⋊C8×C103—22no—
43#97×C103—24no—
44C4×C8×C103D414yes—
45#95×C103—22no—
46#95×C103—22no—
47#95×C103—22no—
48#95×C103—21no—
49#95×C103C2×C412yes—
50C2×Q8×C103—22no—
51C2×Q8×C103—21no—
52C2×Q8×C103—21no—
53C2×Q8×C103—22no—
54C2×Q8×C103—22no—
55C2×Q8×C103—42no—
56C22×C4×C103—21no—
57C22×C4×C103—22no—
58C22×C4×C103—21no—
59C22×C4×C103C22⋊C412yes—
60C22×C4×C103C22⋊C412yes—
61C22×C4×C103C22×C411yescharacteristic
62C22×C4×C103C2×D411yescharacteristic
63C22×C4×C103C2×D411yescharacteristic
64M16×C103—42no—
65M16×C103—42no—
66C2×C8×C103—24no—
67C2×C8×C103—42no—
68C4⋊C4×C103—24no—
69C4⋊C4×C103—22no—
70C4⋊C4×C103—22no—
71C4⋊C4×C103—44no—
72C4⋊C4×C103—41no—
73C4⋊C4×C103—41no—
74C4⋊C4×C103—41no—
75C4⋊C4×C103—41no—
76C42×C103—22no—
77C42×C103—22no—
78C42×C103—42no—
79C42×C103C2×D412yes—
80C42×C103#4112yes—
81C23×C103C2×C22⋊C411yescharacteristic
82Q8×C103—24no—
83Q8×C103—42no—
84Q8×C103—42no—
85Q8×C103—42no—
86C2×C4×C103—22no—
87C2×C4×C103—22no—
88C2×C4×C103—22no—
89C2×C4×C103—22no—
90C2×C4×C103—22no—
91C2×C4×C103—41no—
92C2×C4×C103—41no—
93C2×C4×C103—41no—
94C2×C4×C103—41no—
95C2×C4×C103—42no—
96C2×C4×C103—42no—
97C2×C4×C103—42no—
98C2×C4×C103—42no—
99C2×C4×C103—41no—
100C2×C4×C103—42no—
101C2×C4×C103C4×D412yes—
102C2×C4×C103#12011yescharacteristic
103C2×C4×C103#12112yes—
104C2×C4×C103#12311yescharacteristic
105C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C103#13712yes—
107C2×C4×C103#13711yescharacteristic
108C8×C103—44no—
109C8×C103—82no—
110C22×C103—21no—
111C22×C103—21no—
112C22×C103#38611yescharacteristic
113C22×C103#41711yescharacteristic
114C22×C103#41911yescharacteristic
115C4×C103—22no—
116C4×C103—21no—
117C4×C103—21no—
118C4×C103—42no—
119C4×C103—42no—
120C4×C103—42no—
121C4×C103—82no—
122C4×C103—81no—
123C4×C103#46812yes—
124C4×C103#47012yes—
125#9488C10311yesmaximal, characteristic, direct product factor, Sylow
126C2×C103—21no—
127C2×C103—21no—
128C2×C103#189111yescharacteristic
129C2×C103#189411yescharacteristic
130C2×C103#191211yescharacteristic
131#2983C2×C10311yescharacteristic
132#2581C2×C10311yescharacteristic
133#1801C2×C10311yescharacteristic
134#1487C2×C10312yes—
135#1286C2×C10312yes—
136C103#948811yescharacteristic, direct product factor, Sylow
137C2×C4×Q8C22×C10311yescharacteristic
138C2×C4×Q8C22×C10311yescharacteristic
139#446—24no—
140#432—22no—
141#431C22×C10312yes—
142#423C22×C10312yes—
143C2×#101—21no—
144#400C4×C10312yes—
145#395C4×C10312yes—
146#391—21no—
147#389—21no—
148#387—22no—
149#382C22×C10311yescharacteristic
150#343—21no—
151Q8⋊C8—24no—
152C22×Q8C2×C4×C10311yescharacteristic
153C22×Q8D4×C10311yescharacteristic
154C2×M16—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×C4×C10311yescharacteristic
163C2×C4⋊C4C2×C4×C10312yes—
164C2×C4⋊C4D4×C10311yescharacteristic
165C2×C42—21no—
166C2×C42D4×C10312yes—
167C2×C42C23×C10311yescharacteristic
168C4⋊C8—24no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172#101—42no—
173C22⋊C8—22no—
174#97—24no—
175C4×C8D4×C10314yes—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—21no—
180#95C2×C4×C10312yes—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—42no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4C22⋊C4×C10312yes—
191C22×C4C22⋊C4×C10312yes—
192C22×C4C22×C4×C10311yescharacteristic
193C22×C4C2×D4×C10311yescharacteristic
194C22×C4C2×D4×C10311yescharacteristic
195M16—42no—
196M16—42no—
197C2×C8—24no—
198C2×C8—42no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—44no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C42—22no—
208C42—22no—
209C42—42no—
210C42C2×D4×C10312yes—
211C42#41×C10312yes—
212C23C2×C22⋊C4×C10311yescharacteristic
213Q8—24no—
214Q8—42no—
215Q8—42no—
216Q8—42no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4C4×D4×C10312yes—
233C2×C4#120×C10311yescharacteristic
234C2×C4#121×C10312yes—
235C2×C4#123×C10311yescharacteristic
236C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
237C2×C4#137×C10312yes—
238C2×C4#137×C10311yescharacteristic
239C8—44no—
240C8—82no—
241C22—21no—
242C22—21no—
243C22#386×C10311yescharacteristic
244C22#417×C10311yescharacteristic
245C22#419×C10311yescharacteristic
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—42no—
252C4—82no—
253C4—81no—
254C4#468×C10312yes—
255C4#470×C10312yes—
256C2—21no—
257C2—21no—
258C2C103×#189111yescharacteristic
259C2C103×#189411yescharacteristic
260C2C103×#191211yescharacteristic
subgroupG/H
center, socleC22×C103#386
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
125. #9488C103direct (N × H)
136. C103#9488direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#29832
C103×#25812
C103×#18012
C103×#14872
C103×#12862
#9488103