Finite Group Databasebeta

← C103×#13127 #39918402

Subgroups — C103×#13127 #39918402

Order 26368.

300 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2153C211yesmaximal, characteristic, complemented
2C103×#2117C211yesmaximal, characteristic
3C103×#2115C211yesmaximal, characteristic
4C2×#347×C103C211yesmaximal, characteristic, complemented
5C103×#1765C211yesmaximal, characteristic
6C103×#1378C211yesmaximal, characteristic, complemented
7C103×#1377C211yesmaximal, characteristic, complemented
8C2×#131×C103C2211yescharacteristic
9C2×M32×C103C2211yescharacteristic
10C2×M32×C103C2211yescharacteristic
11C2×M32×C103C2211yescharacteristic
12C2×M32×C103C2211yescharacteristic
13C2×#104×C103C411yescharacteristic
14#416×C103C411yescharacteristic
15#405×C103C2211yescharacteristic
16C2×#97×C103C2211yescharacteristic
17#364×C103—22no—
18#350×C103—22no—
19#349×C103—22no—
20#347×C103—22no—
21#341×C103C411yescharacteristic
22#339×C103C411yescharacteristic
23C2×#41×C103C2×C411yescharacteristic
24#131×C103—21no—
25#131×C103—21no—
26#131×C103—21no—
27#131×C103—21no—
28C2×M16×C103—21no—
29C2×M16×C103C2×C411yescharacteristic
30C2×M16×C103C2×C411yescharacteristic
31C22×C8×C103—21no—
32C22×C8×C103C2×C411yescharacteristic
33C22×C8×C103C2311yescharacteristic
34#117×C103C2×C411yescharacteristic
35C2×C42×C103C2×C411yescharacteristic
36M32×C103—21no—
37M32×C103—21no—
38M32×C103—21no—
39M32×C103—21no—
40M32×C103—21no—
41M32×C103—21no—
42M32×C103D412yes—
43M32×C103D412yes—
44C2×C16×C103—21no—
45C2×C16×C103—21no—
46C2×C16×C103—21no—
47C2×C16×C103—21no—
48#104×C103—22no—
49#103×C103—21no—
50#102×C103—21no—
51#97×C103—21no—
52#97×C103—21no—
53#97×C103—21no—
54C4×C8×C103—21no—
55#41×C103—21no—
56#41×C103—21no—
57#41×C103—21no—
58#41×C103—21no—
59C2×Q8×C103M1611yescharacteristic
60C2×D4×C103—21no—
61C2×D4×C103M1611yescharacteristic
62C22×C4×C103—21no—
63C22×C4×C103—21no—
64C22×C4×C103C22×C411yescharacteristic
65M16×C103—21no—
66M16×C103—21no—
67M16×C103—21no—
68M16×C103—41no—
69M16×C103—41no—
70M16×C103M1612yes—
71C2×C8×C103—21no—
72C2×C8×C103—21no—
73C2×C8×C103—21no—
74C2×C8×C103—21no—
75C2×C8×C103—21no—
76C2×C8×C103—41no—
77C2×C8×C103—41no—
78C2×C8×C103C2×D411yescharacteristic
79C2×C8×C103C2×D411yescharacteristic
80C2×C8×C103#4111yescharacteristic
81C2×C8×C103#4111yescharacteristic
82C2×C8×C103#4111yescharacteristic
83C2×C8×C103#4111yescharacteristic
84C4⋊C4×C103—21no—
85C22⋊C4×C103—21no—
86C42×C103—21no—
87C42×C103—21no—
88C42×C103—21no—
89C16×C103—22no—
90C16×C103—22no—
91C16×C103—41no—
92C16×C103—41no—
93C23×C103—21no—
94C23×C103#13111yescharacteristic
95Q8×C103—21no—
96Q8×C103—21no—
97D4×C103—21no—
98D4×C103—21no—
99D4×C103—41no—
100D4×C103—41no—
101C2×C4×C103—21no—
102C2×C4×C103—41no—
103C2×C4×C103—41no—
104C2×C4×C103—41no—
105C2×C4×C103—41no—
106C2×C4×C103—81no—
107C2×C4×C103#11711yescharacteristic
108C2×C4×C103C4×D411yescharacteristic
109C2×C4×C103C4×D411yescharacteristic
110C2×C4×C103C2×M1611yescharacteristic
111C2×C4×C103C2×M1611yescharacteristic
112C2×C4×C103#13111yescharacteristic
113C8×C103—22no—
114C8×C103—41no—
115C8×C103—41no—
116C8×C103#12111yescharacteristic
117C8×C103#12311yescharacteristic
118C8×C103#12411yescharacteristic
119C8×C103#12611yescharacteristic
120C22×C103—41no—
121C22×C103—41no—
122C22×C103—81no—
123C22×C103#43311yescharacteristic
124C22×C103#43511yescharacteristic
125C22×C103#43611yescharacteristic
126C4×C103—41no—
127C4×C103—81no—
128C4×C103—81no—
129C4×C103#38811yescharacteristic
130C4×C103#43211yescharacteristic
131C4×C103#43511yescharacteristic
132C4×C103#43511yescharacteristic
133#13127C10311yesmaximal, characteristic, direct product factor, Sylow
134C2×C103—21no—
135C2×C103—21no—
136C2×C103—21no—
137C2×C103—81no—
138C2×C103#192411yescharacteristic
139#2153C2×C10311yescharacteristic, complemented
140#2117C2×C10311yescharacteristic
141#2115C2×C10311yescharacteristic
142C2×#347C2×C10311yescharacteristic, complemented
143#1765C2×C10311yescharacteristic
144#1378C2×C10311yescharacteristic, complemented
145#1377C2×C10311yescharacteristic, complemented
146C103#1312711yescharacteristic, direct product factor, Sylow
147C2×#131C22×C10311yescharacteristic
148C2×M32C22×C10311yescharacteristic
149C2×M32C22×C10311yescharacteristic
150C2×M32C22×C10311yescharacteristic
151C2×M32C22×C10311yescharacteristic
152C2×#104C4×C10311yescharacteristic
153#416C4×C10311yescharacteristic
154#405C22×C10311yescharacteristic
155C2×#97C22×C10311yescharacteristic
156#364—22no—
157#350—22no—
158#349—22no—
159#347—22no—
160#341C4×C10311yescharacteristic
161#339C4×C10311yescharacteristic
162C2×#41C2×C4×C10311yescharacteristic
163#131—21no—
164#131—21no—
165#131—21no—
166#131—21no—
167C2×M16—21no—
168C2×M16C2×C4×C10311yescharacteristic
169C2×M16C2×C4×C10311yescharacteristic
170C22×C8—21no—
171C22×C8C2×C4×C10311yescharacteristic
172C22×C8C23×C10311yescharacteristic
173#117C2×C4×C10311yescharacteristic
174C2×C42C2×C4×C10311yescharacteristic
175M32—21no—
176M32—21no—
177M32—21no—
178M32—21no—
179M32—21no—
180M32—21no—
181M32D4×C10312yes—
182M32D4×C10312yes—
183C2×C16—21no—
184C2×C16—21no—
185C2×C16—21no—
186C2×C16—21no—
187#104—22no—
188#103—21no—
189#102—21no—
190#97—21no—
191#97—21no—
192#97—21no—
193C4×C8—21no—
194#41—21no—
195#41—21no—
196#41—21no—
197#41—21no—
198C2×Q8M16×C10311yescharacteristic
199C2×D4—21no—
200C2×D4M16×C10311yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4C22×C4×C10311yescharacteristic
204M16—21no—
205M16—21no—
206M16—21no—
207M16—41no—
208M16—41no—
209M16M16×C10312yes—
210C2×C8—21no—
211C2×C8—21no—
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8C2×D4×C10311yescharacteristic
218C2×C8C2×D4×C10311yescharacteristic
219C2×C8#41×C10311yescharacteristic
220C2×C8#41×C10311yescharacteristic
221C2×C8#41×C10311yescharacteristic
222C2×C8#41×C10311yescharacteristic
223C4⋊C4—21no—
224C22⋊C4—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C16—22no—
229C16—22no—
230C16—41no—
231C16—41no—
232C23—21no—
233C23#131×C10311yescharacteristic
234Q8—21no—
235Q8—21no—
236D4—21no—
237D4—21no—
238D4—41no—
239D4—41no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4#117×C10311yescharacteristic
247C2×C4C4×D4×C10311yescharacteristic
248C2×C4C4×D4×C10311yescharacteristic
249C2×C4C2×M16×C10311yescharacteristic
250C2×C4C2×M16×C10311yescharacteristic
251C2×C4#131×C10311yescharacteristic
252C8—22no—
253C8—41no—
254C8—41no—
255C8#121×C10311yescharacteristic
256C8#123×C10311yescharacteristic
257C8#124×C10311yescharacteristic
258C8#126×C10311yescharacteristic
259C22—41no—
260C22—41no—
261C22—81no—
262C22#433×C10311yescharacteristic
263C22#435×C10311yescharacteristic
264C22#436×C10311yescharacteristic
265C4—41no—
266C4—81no—
267C4—81no—
268C4#388×C10311yescharacteristic
269C4#432×C10311yescharacteristic
270C4#435×C10311yescharacteristic
271C4#435×C10311yescharacteristic
272C2—21no—
273C2—21no—
274C2—21no—
275C2—81no—
276C2C103×#192411yescharacteristic
subgroupG/H
centerC4×C103#388
commutatorC22×C4C22×C4×C103
Frattini, cosocleC22×C8C23×C103
socleC2×C103#1924
prime radicalC2×#41×C103C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#2153C2semidirect
4. C2×#347×C103C2semidirect
6. C103×#1378C2semidirect
7. C103×#1377C2semidirect
133. #13127C103direct (N × H)
139. #2153C2×C103semidirect
142. C2×#347C2×C103semidirect
144. #1378C2×C103semidirect
145. #1377C2×C103semidirect
146. C103#13127direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#21532
C103×#21172
C103×#21152
C2×#347×C1032
C103×#17652
C103×#13782
C103×#13772
#13127103