Finite Group Databasebeta

← C103×#12830 #39918105

Subgroups — C103×#12830 #39918105

Order 26368.

378 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2957C211yesmaximal, characteristic
2C103×#2151C211yesmaximal, characteristic, complemented
3C103×#2145C211yesmaximal, characteristic
4C2×#359×C103C211yesmaximal, characteristic
5C103×#1833C211yesmaximal, characteristic, complemented
6C103×#1388C211yesmaximal, characteristic, complemented
7C103×#1382C211yesmaximal, characteristic, complemented
8C2×#135×C103C2211yescharacteristic
9#568×C103—21no—
10C2×M32×C103C2211yescharacteristic
11C22×C16×C103C2211yescharacteristic
12#444×C103C414yescomplemented
13#443×C103—22no—
14C2×#108×C103C2211yescharacteristic
15C2×#108×C103C2211yescharacteristic
16#427×C103C2211yescharacteristic
17#421×C103—21no—
18#405×C103C2211yescharacteristic
19C4⋊C16×C103—22no—
20#360×C103—22no—
21#359×C103—22no—
22#344×C103—21no—
23H(3,ℤ/4)×C103—21no—
24C2×#41×C103—21no—
25#135×C103—21no—
26#135×C103—21no—
27#135×C103C2×C412yes—
28#135×C103D412yes—
29C2×Q16×C103Q811yescharacteristic
30C2×SD16×C103—21no—
31C2×D8×C103Q811yescharacteristic
32#131×C103—24no—
33#131×C103—42no—
34C2×M16×C103—21no—
35C2×M16×C103—21no—
36C2×M16×C103—42no—
37C2×M16×C103D411yescharacteristic
38C22×C8×C103C2311yescharacteristic
39#117×C103—21no—
40#117×C103D411yescharacteristic
41M32×C103—21no—
42M32×C103—21no—
43C2×C16×C103—21no—
44C2×C16×C103—21no—
45C2×C16×C103—21no—
46C2×C16×C103—21no—
47#108×C103—21no—
48#108×C103—21no—
49#108×C103—21no—
50#108×C103C2×C412yes—
51#107×C103—21no—
52#106×C103—21no—
53#104×C103—24no—
54#97×C103C2×C412yes—
55C4×C8×C103D412yes—
56#41×C103—22no—
57#41×C103—22no—
58#41×C103—41no—
59#41×C103—41no—
60C2×Q8×C103—21no—
61C2×D4×C103—21no—
62C2×D4×C103—41no—
63C22×C4×C103—41no—
64C22×C4×C103C2×D411yescharacteristic
65Q16×C103—21no—
66Q16×C103C4⋊C412yes—
67SD16×C103—22no—
68SD16×C103—22no—
69D8×C103—21no—
70D8×C103C4⋊C412yes—
71M16×C103—21no—
72M16×C103—21no—
73M16×C103—22no—
74M16×C103—44no—
75M16×C103—41no—
76M16×C103—41no—
77M16×C103—41no—
78C2×C8×C103—44no—
79C2×C8×C103—41no—
80C2×C8×C103—41no—
81C2×C8×C103C22⋊C412yes—
82C2×C8×C103C22×C411yescharacteristic
83C2×C8×C103C2×D411yescharacteristic
84C2×C8×C103C2×D411yescharacteristic
85C2×C8×C103C2×Q811yescharacteristic
86C2×C8×C103#4111yescharacteristic
87C2×C8×C103#4111yescharacteristic
88C4⋊C4×C103—21no—
89C4⋊C4×C103—41no—
90C22⋊C4×C103—21no—
91C22⋊C4×C103—41no—
92C42×C103—41no—
93C42×C103C22⋊C412yes—
94C16×C103—41no—
95C16×C103—41no—
96C23×C103—41no—
97C23×C103#13511yescharacteristic
98Q8×C103—22no—
99Q8×C103—41no—
100D4×C103—22no—
101D4×C103—42no—
102D4×C103—42no—
103D4×C103—41no—
104C2×C4×C103—22no—
105C2×C4×C103—41no—
106C2×C4×C103—42no—
107C2×C4×C103—42no—
108C2×C4×C103—81no—
109C2×C4×C103C2×C22⋊C411yescharacteristic
110C2×C4×C103#12111yescharacteristic
111C2×C4×C103C22⋊Q811yescharacteristic
112C2×C4×C103#13511yescharacteristic
113C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
115C8×C103—22no—
116C8×C103—42no—
117C8×C103—81no—
118C8×C103C2×C4⋊C411yescharacteristic
119C8×C103#11711yescharacteristic
120C8×C103#12111yescharacteristic
121C8×C103C22⋊Q811yescharacteristic
122C22×C103—41no—
123C22×C103—42no—
124C22×C103—161no—
125C22×C103#41611yescharacteristic
126C22×C103#46311yescharacteristic
127C22×C103#47811yescharacteristic
128C4×C103—42no—
129C4×C103—42no—
130C4×C103—161no—
131C4×C103#38011yescharacteristic
132C4×C103#41811yescharacteristic
133C4×C103#46311yescharacteristic
134C4×C103#47811yescharacteristic
135#12830C10311yesmaximal, characteristic, direct product factor, Sylow
136C2×C103—21no—
137C2×C103—21no—
138C2×C103—21no—
139C2×C103—82no—
140C2×C103#180411yescharacteristic
141#2957C2×C10311yescharacteristic
142#2151C2×C10311yescharacteristic, complemented
143#2145C2×C10311yescharacteristic
144C2×#359C2×C10311yescharacteristic
145#1833C2×C10311yescharacteristic, complemented
146#1388C2×C10311yescharacteristic, complemented
147#1382C2×C10311yescharacteristic, complemented
148C103#1283011yescharacteristic, direct product factor, Sylow
149C2×#135C22×C10311yescharacteristic
150#568—21no—
151C2×M32C22×C10311yescharacteristic
152C22×C16C22×C10311yescharacteristic
153#444C4×C10314yescomplemented
154#443—22no—
155C2×#108C22×C10311yescharacteristic
156C2×#108C22×C10311yescharacteristic
157#427C22×C10311yescharacteristic
158#421—21no—
159#405C22×C10311yescharacteristic
160C4⋊C16—22no—
161#360—22no—
162#359—22no—
163#344—21no—
164H(3,ℤ/4)—21no—
165C2×#41—21no—
166#135—21no—
167#135—21no—
168#135C2×C4×C10312yes—
169#135D4×C10312yes—
170C2×Q16Q8×C10311yescharacteristic
171C2×SD16—21no—
172C2×D8Q8×C10311yescharacteristic
173#131—24no—
174#131—42no—
175C2×M16—21no—
176C2×M16—21no—
177C2×M16—42no—
178C2×M16D4×C10311yescharacteristic
179C22×C8C23×C10311yescharacteristic
180#117—21no—
181#117D4×C10311yescharacteristic
182M32—21no—
183M32—21no—
184C2×C16—21no—
185C2×C16—21no—
186C2×C16—21no—
187C2×C16—21no—
188#108—21no—
189#108—21no—
190#108—21no—
191#108C2×C4×C10312yes—
192#107—21no—
193#106—21no—
194#104—24no—
195#97C2×C4×C10312yes—
196C4×C8D4×C10312yes—
197#41—22no—
198#41—22no—
199#41—41no—
200#41—41no—
201C2×Q8—21no—
202C2×D4—21no—
203C2×D4—41no—
204C22×C4—41no—
205C22×C4C2×D4×C10311yescharacteristic
206Q16—21no—
207Q16C4⋊C4×C10312yes—
208SD16—22no—
209SD16—22no—
210D8—21no—
211D8C4⋊C4×C10312yes—
212M16—21no—
213M16—21no—
214M16—22no—
215M16—44no—
216M16—41no—
217M16—41no—
218M16—41no—
219C2×C8—44no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C22⋊C4×C10312yes—
223C2×C8C22×C4×C10311yescharacteristic
224C2×C8C2×D4×C10311yescharacteristic
225C2×C8C2×D4×C10311yescharacteristic
226C2×C8C2×Q8×C10311yescharacteristic
227C2×C8#41×C10311yescharacteristic
228C2×C8#41×C10311yescharacteristic
229C4⋊C4—21no—
230C4⋊C4—41no—
231C22⋊C4—21no—
232C22⋊C4—41no—
233C42—41no—
234C42C22⋊C4×C10312yes—
235C16—41no—
236C16—41no—
237C23—41no—
238C23#135×C10311yescharacteristic
239Q8—22no—
240Q8—41no—
241D4—22no—
242D4—42no—
243D4—42no—
244D4—41no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4C2×C22⋊C4×C10311yescharacteristic
251C2×C4#121×C10311yescharacteristic
252C2×C4C22⋊Q8×C10311yescharacteristic
253C2×C4#135×C10311yescharacteristic
254C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
255C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
256C8—22no—
257C8—42no—
258C8—81no—
259C8C2×C4⋊C4×C10311yescharacteristic
260C8#117×C10311yescharacteristic
261C8#121×C10311yescharacteristic
262C8C22⋊Q8×C10311yescharacteristic
263C22—41no—
264C22—42no—
265C22—161no—
266C22#416×C10311yescharacteristic
267C22#463×C10311yescharacteristic
268C22#478×C10311yescharacteristic
269C4—42no—
270C4—42no—
271C4—161no—
272C4#380×C10311yescharacteristic
273C4#418×C10311yescharacteristic
274C4#463×C10311yescharacteristic
275C4#478×C10311yescharacteristic
276C2—21no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2C103×#180411yescharacteristic
subgroupG/H
centerC4×C103#418
commutatorC2×C8C22×C4×C103
Frattini, cosocleC22×C8C23×C103
socleC2×C103#1804
prime radicalC2×#135×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C103 ◁ C22×C4×C103 ◁ #405×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2151C2semidirect
5. C103×#1833C2semidirect
6. C103×#1388C2semidirect
7. C103×#1382C2semidirect
12. #444×C103C4semidirect
135. #12830C103direct (N × H)
142. #2151C2×C103semidirect
145. #1833C2×C103semidirect
146. #1388C2×C103semidirect
147. #1382C2×C103semidirect
148. C103#12830direct (N × H)
153. #444C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#29572
C103×#21512
C103×#21452
C2×#359×C1032
C103×#18332
C103×#13882
C103×#13822
#12830103