Finite Group Databasebeta

← C103×#12618 #39917893

Subgroups — C103×#12618 #39917893

Order 26368.

382 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3407C211yesmaximal, characteristic
2C103×#2117C211yesmaximal, characteristic
3C103×#2110C211yesmaximal, characteristic, complemented
4C2×#347×C103C211yesmaximal, characteristic, complemented
5C103×#1765C211yesmaximal, characteristic
6C103×#1378C211yesmaximal, characteristic, complemented
7C103×#1377C211yesmaximal, characteristic, complemented
8C2×#131×C103C2211yescharacteristic
9#504×C103—22no—
10#504×C103C414yescomplemented
11C2×M32×C103—22no—
12C2×M32×C103C2211yescharacteristic
13C2×M32×C103C2211yescharacteristic
14C2×M32×C103C2211yescharacteristic
15C2×M32×C103C2211yescharacteristic
16C2×#104×C103C411yescharacteristic
17#416×C103C411yescharacteristic
18#405×C103C2211yescharacteristic
19C2×#97×C103C2211yescharacteristic
20#350×C103C414yescomplemented
21#347×C103—22no—
22#347×C103—22no—
23#341×C103C411yescharacteristic
24#339×C103C411yescharacteristic
25C2×#41×C103C2×C411yescharacteristic
26#131×C103—21no—
27#131×C103—21no—
28#131×C103C2×C412yes—
29#131×C103C2×C412yes—
30C2×M16×C103—21no—
31C2×M16×C103C2×C411yescharacteristic
32C2×M16×C103C2×C411yescharacteristic
33C22×C8×C103—21no—
34C22×C8×C103C2×C411yescharacteristic
35C22×C8×C103C2311yescharacteristic
36#117×C103C2×C411yescharacteristic
37C2×C42×C103C2×C411yescharacteristic
38M32×C103—21no—
39M32×C103—21no—
40M32×C103—21no—
41M32×C103—21no—
42M32×C103—24no—
43M32×C103C2×C412yes—
44M32×C103C2×C412yes—
45M32×C103D412yes—
46M32×C103D412yes—
47C2×C16×C103—21no—
48C2×C16×C103—21no—
49C2×C16×C103—24no—
50C2×C16×C103C2×C412yes—
51C2×C16×C103C2×C412yes—
52#104×C103—22no—
53#103×C103—21no—
54#102×C103—21no—
55#97×C103—21no—
56#97×C103—21no—
57#97×C103—21no—
58C4×C8×C103—21no—
59#41×C103—21no—
60#41×C103—21no—
61#41×C103C4212yes—
62#41×C103M1612yes—
63C2×Q8×C103M1611yescharacteristic
64C2×D4×C103—21no—
65C2×D4×C103M1611yescharacteristic
66C22×C4×C103—21no—
67C22×C4×C103—21no—
68C22×C4×C103C22×C411yescharacteristic
69M16×C103—21no—
70M16×C103—22no—
71M16×C103—22no—
72M16×C103—21no—
73M16×C103—21no—
74M16×C103C4212yes—
75C2×C8×C103—21no—
76C2×C8×C103—22no—
77C2×C8×C103—22no—
78C2×C8×C103—21no—
79C2×C8×C103—21no—
80C2×C8×C103—21no—
81C2×C8×C103—21no—
82C2×C8×C103C22×C411yescharacteristic
83C2×C8×C103C22×C411yescharacteristic
84C2×C8×C103C2×D411yescharacteristic
85C2×C8×C103C2×D411yescharacteristic
86C2×C8×C103#4111yescharacteristic
87C2×C8×C103#4111yescharacteristic
88C4⋊C4×C103—21no—
89C22⋊C4×C103—21no—
90C42×C103—21no—
91C42×C103—21no—
92C42×C103—21no—
93C16×C103—22no—
94C16×C103—22no—
95C16×C103—22no—
96C16×C103C22⋊C414yes—
97C23×C103—21no—
98C23×C103#13111yescharacteristic
99Q8×C103—21no—
100Q8×C103#9712yes—
101D4×C103—22no—
102D4×C103—22no—
103D4×C103—21no—
104D4×C103#9712yes—
105C2×C4×C103—21no—
106C2×C4×C103—22no—
107C2×C4×C103—22no—
108C2×C4×C103—41no—
109C2×C4×C103—41no—
110C2×C4×C103—81no—
111C2×C4×C103C2×C4211yescharacteristic
112C2×C4×C103C4×D411yescharacteristic
113C2×C4×C103C4×D411yescharacteristic
114C2×C4×C103C2×M1611yescharacteristic
115C2×C4×C103C2×M1611yescharacteristic
116C2×C4×C103#13111yescharacteristic
117C8×C103—22no—
118C8×C103—41no—
119C8×C103—41no—
120C8×C103C2×C22⋊C411yescharacteristic
121C8×C103#11711yescharacteristic
122C8×C103C4×D411yescharacteristic
123C8×C103C4×D411yescharacteristic
124C22×C103—22no—
125C22×C103—41no—
126C22×C103—81no—
127C22×C103#40511yescharacteristic
128C22×C103#43511yescharacteristic
129C22×C103#43511yescharacteristic
130C4×C103—22no—
131C4×C103—81no—
132C4×C103—81no—
133C4×C103C4×C22⋊C411yescharacteristic
134C4×C103C2×#9711yescharacteristic
135C4×C103#43511yescharacteristic
136C4×C103#43511yescharacteristic
137#12618C10311yesmaximal, characteristic, direct product factor, Sylow
138C2×C103—21no—
139C2×C103—21no—
140C2×C103—21no—
141C2×C103—42no—
142C2×C103#175211yescharacteristic
143#3407C2×C10311yescharacteristic
144#2117C2×C10311yescharacteristic
145#2110C2×C10311yescharacteristic, complemented
146C2×#347C2×C10311yescharacteristic, complemented
147#1765C2×C10311yescharacteristic
148#1378C2×C10311yescharacteristic, complemented
149#1377C2×C10311yescharacteristic, complemented
150C103#1261811yescharacteristic, direct product factor, Sylow
151C2×#131C22×C10311yescharacteristic
152#504—22no—
153#504C4×C10314yescomplemented
154C2×M32—22no—
155C2×M32C22×C10311yescharacteristic
156C2×M32C22×C10311yescharacteristic
157C2×M32C22×C10311yescharacteristic
158C2×M32C22×C10311yescharacteristic
159C2×#104C4×C10311yescharacteristic
160#416C4×C10311yescharacteristic
161#405C22×C10311yescharacteristic
162C2×#97C22×C10311yescharacteristic
163#350C4×C10314yescomplemented
164#347—22no—
165#347—22no—
166#341C4×C10311yescharacteristic
167#339C4×C10311yescharacteristic
168C2×#41C2×C4×C10311yescharacteristic
169#131—21no—
170#131—21no—
171#131C2×C4×C10312yes—
172#131C2×C4×C10312yes—
173C2×M16—21no—
174C2×M16C2×C4×C10311yescharacteristic
175C2×M16C2×C4×C10311yescharacteristic
176C22×C8—21no—
177C22×C8C2×C4×C10311yescharacteristic
178C22×C8C23×C10311yescharacteristic
179#117C2×C4×C10311yescharacteristic
180C2×C42C2×C4×C10311yescharacteristic
181M32—21no—
182M32—21no—
183M32—21no—
184M32—21no—
185M32—24no—
186M32C2×C4×C10312yes—
187M32C2×C4×C10312yes—
188M32D4×C10312yes—
189M32D4×C10312yes—
190C2×C16—21no—
191C2×C16—21no—
192C2×C16—24no—
193C2×C16C2×C4×C10312yes—
194C2×C16C2×C4×C10312yes—
195#104—22no—
196#103—21no—
197#102—21no—
198#97—21no—
199#97—21no—
200#97—21no—
201C4×C8—21no—
202#41—21no—
203#41—21no—
204#41C42×C10312yes—
205#41M16×C10312yes—
206C2×Q8M16×C10311yescharacteristic
207C2×D4—21no—
208C2×D4M16×C10311yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4C22×C4×C10311yescharacteristic
212M16—21no—
213M16—22no—
214M16—22no—
215M16—21no—
216M16—21no—
217M16C42×C10312yes—
218C2×C8—21no—
219C2×C8—22no—
220C2×C8—22no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8C22×C4×C10311yescharacteristic
226C2×C8C22×C4×C10311yescharacteristic
227C2×C8C2×D4×C10311yescharacteristic
228C2×C8C2×D4×C10311yescharacteristic
229C2×C8#41×C10311yescharacteristic
230C2×C8#41×C10311yescharacteristic
231C4⋊C4—21no—
232C22⋊C4—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C16—22no—
237C16—22no—
238C16—22no—
239C16C22⋊C4×C10314yes—
240C23—21no—
241C23#131×C10311yescharacteristic
242Q8—21no—
243Q8#97×C10312yes—
244D4—22no—
245D4—22no—
246D4—21no—
247D4#97×C10312yes—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4C2×C42×C10311yescharacteristic
255C2×C4C4×D4×C10311yescharacteristic
256C2×C4C4×D4×C10311yescharacteristic
257C2×C4C2×M16×C10311yescharacteristic
258C2×C4C2×M16×C10311yescharacteristic
259C2×C4#131×C10311yescharacteristic
260C8—22no—
261C8—41no—
262C8—41no—
263C8C2×C22⋊C4×C10311yescharacteristic
264C8#117×C10311yescharacteristic
265C8C4×D4×C10311yescharacteristic
266C8C4×D4×C10311yescharacteristic
267C22—22no—
268C22—41no—
269C22—81no—
270C22#405×C10311yescharacteristic
271C22#435×C10311yescharacteristic
272C22#435×C10311yescharacteristic
273C4—22no—
274C4—81no—
275C4—81no—
276C4C4×C22⋊C4×C10311yescharacteristic
277C4C2×#97×C10311yescharacteristic
278C4#435×C10311yescharacteristic
279C4#435×C10311yescharacteristic
280C2—21no—
281C2—21no—
282C2—21no—
283C2—42no—
284C2C103×#175211yescharacteristic
subgroupG/H
centerC4×C103C4×C22⋊C4
commutatorC2×C4C2×C42×C103
Frattini, cosocleC22×C8C23×C103
socleC2×C103#1752
prime radicalC2×#41×C103C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C2×M32×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#2110C2semidirect
4. C2×#347×C103C2semidirect
6. C103×#1378C2semidirect
7. C103×#1377C2semidirect
10. #504×C103C4semidirect
20. #350×C103C4semidirect
137. #12618C103direct (N × H)
145. #2110C2×C103semidirect
146. C2×#347C2×C103semidirect
148. #1378C2×C103semidirect
149. #1377C2×C103semidirect
150. C103#12618direct (N × H)
153. #504C4×C103semidirect
163. #350C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34072
C103×#21172
C103×#21102
C2×#347×C1032
C103×#17652
C103×#13782
C103×#13772
#12618103