Finite Group Databasebeta

← C103×#12927 #39918202

Subgroups — C103×#12927 #39918202

Order 26368.

378 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2916C211yesmaximal, characteristic
2C103×#2161C211yesmaximal, characteristic, complemented
3C2×#368×C103C211yesmaximal, characteristic, complemented
4C2×#350×C103C211yesmaximal, characteristic
5C103×#1814C211yesmaximal, characteristic
6C103×#1389C211yesmaximal, characteristic, complemented
7C103×#1382C211yesmaximal, characteristic, complemented
8#568×C103—21no—
9C2×#131×C103C2211yescharacteristic
10C2×M32×C103C2211yescharacteristic
11C22×C16×C103C2211yescharacteristic
12#430×C103—21no—
13#430×C103—22no—
14C2×#108×C103—22no—
15C2×#108×C103C2211yescharacteristic
16C2×#108×C103C2211yescharacteristic
17C2×#108×C103C2211yescharacteristic
18#427×C103C2211yescharacteristic
19#421×C103—21no—
20#368×C103—22no—
21#368×C103—22no—
22#350×C103C414yescomplemented
23#344×C103—21no—
24C2×#41×C103D411yescharacteristic
25#131×C103—21no—
26#131×C103—21no—
27#131×C103—42no—
28#131×C103—42no—
29#131×C103C2×C412yes—
30#131×C103Q812yes—
31C2×M16×C103—21no—
32C2×M16×C103—24no—
33C2×M16×C103—21no—
34C2×M16×C103—21no—
35C2×M16×C103—21no—
36C2×M16×C103D411yescharacteristic
37C22×C8×C103—21no—
38C22×C8×C103C2311yescharacteristic
39#117×C103—21no—
40M32×C103—21no—
41M32×C103C2×C412yes—
42C2×C16×C103—21no—
43C2×C16×C103—21no—
44C2×C16×C103—21no—
45C2×C16×C103C2×C412yes—
46#108×C103—24no—
47#108×C103—21no—
48#108×C103—21no—
49#108×C103—21no—
50#108×C103—21no—
51#108×C103D412yes—
52#108×C103D412yes—
53#107×C103—21no—
54#106×C103—21no—
55#104×C103—42no—
56#41×C103—21no—
57#41×C103—21no—
58#41×C103C4⋊C412yes—
59#41×C103D812yes—
60C2×Q8×C103Q1611yescharacteristic
61C2×D4×C103—21no—
62C2×D4×C103Q1611yescharacteristic
63C22×C4×C103—21no—
64C22×C4×C103C2×D411yescharacteristic
65M16×C103—21no—
66M16×C103—22no—
67M16×C103—22no—
68M16×C103—22no—
69M16×C103—22no—
70M16×C103—44no—
71M16×C103—41no—
72M16×C103—41no—
73M16×C103—41no—
74M16×C103—41no—
75M16×C103C4⋊C412yes—
76C2×C8×C103—21no—
77C2×C8×C103—22no—
78C2×C8×C103—22no—
79C2×C8×C103—44no—
80C2×C8×C103—41no—
81C2×C8×C103—41no—
82C2×C8×C103—41no—
83C2×C8×C103C22×C411yescharacteristic
84C2×C8×C103C2×D411yescharacteristic
85C2×C8×C103C2×D411yescharacteristic
86C2×C8×C103C2×Q811yescharacteristic
87C2×C8×C103#4111yescharacteristic
88C2×C8×C103#4111yescharacteristic
89C4⋊C4×C103—41no—
90C22⋊C4×C103—41no—
91C42×C103—41no—
92C16×C103—22no—
93C16×C103—22no—
94C23×C103—21no—
95C23×C103#13711yescharacteristic
96Q8×C103—21no—
97Q8×C103#10712yes—
98D4×C103—22no—
99D4×C103—22no—
100D4×C103—21no—
101D4×C103#10712yes—
102C2×C4×C103—21no—
103C2×C4×C103—22no—
104C2×C4×C103—22no—
105C2×C4×C103—81no—
106C2×C4×C103C2×C4⋊C411yescharacteristic
107C2×C4×C103#12011yescharacteristic
108C2×C4×C103#12311yescharacteristic
109C2×C4×C103C2×D811yescharacteristic
110C2×C4×C103C2×Q1611yescharacteristic
111C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
112C8×C103—22no—
113C8×C103—42no—
114C8×C103—42no—
115C8×C103—81no—
116C8×C103C4×D411yescharacteristic
117C8×C103C4×D411yescharacteristic
118C8×C103C22⋊Q811yescharacteristic
119C8×C103C22⋊Q811yescharacteristic
120C22×C103—22no—
121C22×C103—41no—
122C22×C103—81no—
123C22×C103#42811yescharacteristic
124C22×C103#45111yescharacteristic
125C22×C103#48011yescharacteristic
126C4×C103—22no—
127C4×C103—161no—
128C4×C103#38511yescharacteristic
129C4×C103C2×#10711yescharacteristic
130C4×C103#44711yescharacteristic
131C4×C103#48411yescharacteristic
132#12927C10311yesmaximal, characteristic, direct product factor, Sylow
133C2×C103—21no—
134C2×C103—21no—
135C2×C103—21no—
136C2×C103—42no—
137C2×C103#185211yescharacteristic
138#2916C2×C10311yescharacteristic
139#2161C2×C10311yescharacteristic, complemented
140C2×#368C2×C10311yescharacteristic, complemented
141C2×#350C2×C10311yescharacteristic
142#1814C2×C10311yescharacteristic
143#1389C2×C10311yescharacteristic, complemented
144#1382C2×C10311yescharacteristic, complemented
145C103#1292711yescharacteristic, direct product factor, Sylow
146#568—21no—
147C2×#131C22×C10311yescharacteristic
148C2×M32C22×C10311yescharacteristic
149C22×C16C22×C10311yescharacteristic
150#430—21no—
151#430—22no—
152C2×#108—22no—
153C2×#108C22×C10311yescharacteristic
154C2×#108C22×C10311yescharacteristic
155C2×#108C22×C10311yescharacteristic
156#427C22×C10311yescharacteristic
157#421—21no—
158#368—22no—
159#368—22no—
160#350C4×C10314yescomplemented
161#344—21no—
162C2×#41D4×C10311yescharacteristic
163#131—21no—
164#131—21no—
165#131—42no—
166#131—42no—
167#131C2×C4×C10312yes—
168#131Q8×C10312yes—
169C2×M16—21no—
170C2×M16—24no—
171C2×M16—21no—
172C2×M16—21no—
173C2×M16—21no—
174C2×M16D4×C10311yescharacteristic
175C22×C8—21no—
176C22×C8C23×C10311yescharacteristic
177#117—21no—
178M32—21no—
179M32C2×C4×C10312yes—
180C2×C16—21no—
181C2×C16—21no—
182C2×C16—21no—
183C2×C16C2×C4×C10312yes—
184#108—24no—
185#108—21no—
186#108—21no—
187#108—21no—
188#108—21no—
189#108D4×C10312yes—
190#108D4×C10312yes—
191#107—21no—
192#106—21no—
193#104—42no—
194#41—21no—
195#41—21no—
196#41C4⋊C4×C10312yes—
197#41D8×C10312yes—
198C2×Q8Q16×C10311yescharacteristic
199C2×D4—21no—
200C2×D4Q16×C10311yescharacteristic
201C22×C4—21no—
202C22×C4C2×D4×C10311yescharacteristic
203M16—21no—
204M16—22no—
205M16—22no—
206M16—22no—
207M16—22no—
208M16—44no—
209M16—41no—
210M16—41no—
211M16—41no—
212M16—41no—
213M16C4⋊C4×C10312yes—
214C2×C8—21no—
215C2×C8—22no—
216C2×C8—22no—
217C2×C8—44no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8C22×C4×C10311yescharacteristic
222C2×C8C2×D4×C10311yescharacteristic
223C2×C8C2×D4×C10311yescharacteristic
224C2×C8C2×Q8×C10311yescharacteristic
225C2×C8#41×C10311yescharacteristic
226C2×C8#41×C10311yescharacteristic
227C4⋊C4—41no—
228C22⋊C4—41no—
229C42—41no—
230C16—22no—
231C16—22no—
232C23—21no—
233C23#137×C10311yescharacteristic
234Q8—21no—
235Q8#107×C10312yes—
236D4—22no—
237D4—22no—
238D4—21no—
239D4#107×C10312yes—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—81no—
244C2×C4C2×C4⋊C4×C10311yescharacteristic
245C2×C4#120×C10311yescharacteristic
246C2×C4#123×C10311yescharacteristic
247C2×C4C2×D8×C10311yescharacteristic
248C2×C4C2×Q16×C10311yescharacteristic
249C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
250C8—22no—
251C8—42no—
252C8—42no—
253C8—81no—
254C8C4×D4×C10311yescharacteristic
255C8C4×D4×C10311yescharacteristic
256C8C22⋊Q8×C10311yescharacteristic
257C8C22⋊Q8×C10311yescharacteristic
258C22—22no—
259C22—41no—
260C22—81no—
261C22#428×C10311yescharacteristic
262C22#451×C10311yescharacteristic
263C22#480×C10311yescharacteristic
264C4—22no—
265C4—161no—
266C4#385×C10311yescharacteristic
267C4C2×#107×C10311yescharacteristic
268C4#447×C10311yescharacteristic
269C4#484×C10311yescharacteristic
270C2—21no—
271C2—21no—
272C2—21no—
273C2—42no—
274C2C103×#185211yescharacteristic
subgroupG/H
centerC4×C103#447
commutatorC2×C8C22×C4×C103
Frattini, cosocleC22×C8C23×C103
socleC2×C103#1852
prime radicalC2×#41×C103D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×C4×C103 ◁ C2×#131×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2161C2semidirect
3. C2×#368×C103C2semidirect
6. C103×#1389C2semidirect
7. C103×#1382C2semidirect
22. #350×C103C4semidirect
132. #12927C103direct (N × H)
139. #2161C2×C103semidirect
140. C2×#368C2×C103semidirect
143. #1389C2×C103semidirect
144. #1382C2×C103semidirect
145. C103#12927direct (N × H)
160. #350C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#29162
C103×#21612
C2×#368×C1032
C2×#350×C1032
C103×#18142
C103×#13892
C103×#13822
#12927103