Finite Group Databasebeta

← C103×#13152 #39918427

Subgroups — C103×#13152 #39918427

Order 26368.

324 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
1C2×#359×C103C211yesmaximal, characteristic
2C103×#2138C211yesmaximal, characteristic
3C2×#346×C103C211yesmaximal, characteristic, complemented
4C103×#1974C211yesmaximal, characteristic
5C103×#1945C211yesmaximal, characteristic, complemented
6C103×#1382C211yesmaximal, characteristic, complemented
7C103×#1381C211yesmaximal, characteristic, complemented
8C2×#135×C103C2211yescharacteristic
9C22×C16×C103C2211yescharacteristic
10C22×C16×C103C2211yescharacteristic
11C2×#108×C103C2211yescharacteristic
12C2×#108×C103C2211yescharacteristic
13#427×C103C2211yescharacteristic
14#424×C103—21no—
15C2×#104×C103—21no—
16#408×C103—21no—
17C2×C4×C8×C103C2211yescharacteristic
18#359×C103—22no—
19#358×C103C412yescomplemented
20#357×C103C412yescomplemented
21#346×C103—22no—
22#339×C103—21no—
23C2×#41×C103—21no—
24#135×C103—21no—
25#135×C103—21no—
26#135×C103—21no—
27#135×C103—21no—
28C2×Q16×C103C2×C411yescharacteristic
29C2×SD16×C103—21no—
30C2×D8×C103C2×C411yescharacteristic
31C2×M16×C103—21no—
32C2×M16×C103—21no—
33C22×C8×C103D411yescharacteristic
34C22×C8×C103C2311yescharacteristic
35#117×C103—21no—
36C2×C42×C103D411yescharacteristic
37C2×C16×C103—21no—
38C2×C16×C103—21no—
39C2×C16×C103—21no—
40C2×C16×C103—21no—
41C2×C16×C103C2×C412yes—
42C2×C16×C103D412yes—
43#108×C103—21no—
44#108×C103—21no—
45#108×C103—21no—
46#108×C103—21no—
47#107×C103C2×C412yes—
48#106×C103—21no—
49C4⋊C8×C103—42no—
50#104×C103—42no—
51C22⋊C8×C103—42no—
52C4×C8×C103—21no—
53C4×C8×C103—21no—
54#41×C103—41no—
55#41×C103—41no—
56#41×C103—41no—
57#41×C103—41no—
58C2×Q8×C103—21no—
59C2×D4×C103—21no—
60C2×D4×C103—41no—
61C22×C4×C103—21no—
62C22×C4×C103—41no—
63C22×C4×C103C2×D411yescharacteristic
64Q16×C103—21no—
65Q16×C103—21no—
66SD16×C103—41no—
67SD16×C103—41no—
68D8×C103—21no—
69D8×C103—21no—
70M16×C103—41no—
71M16×C103—41no—
72M16×C103—41no—
73M16×C103—41no—
74C2×C8×C103—21no—
75C2×C8×C103—21no—
76C2×C8×C103—41no—
77C2×C8×C103—41no—
78C2×C8×C103D812yes—
79C2×C8×C103C22×C411yescharacteristic
80C2×C8×C103C2×D411yescharacteristic
81C2×C8×C103#4111yescharacteristic
82C2×C8×C103#4111yescharacteristic
83C2×C8×C103#4111yescharacteristic
84C2×C8×C103#4111yescharacteristic
85C4⋊C4×C103—22no—
86C22⋊C4×C103—41no—
87C42×C103—21no—
88C42×C103—41no—
89C42×C103SD1612yes—
90C16×C103—22no—
91C16×C103—22no—
92C23×C103—41no—
93C23×C103#13511yescharacteristic
94Q8×C103—41no—
95Q8×C103—41no—
96D4×C103—41no—
97D4×C103—41no—
98D4×C103—81no—
99D4×C103—81no—
100C2×C4×C103—22no—
101C2×C4×C103—42no—
102C2×C4×C103—42no—
103C2×C4×C103—41no—
104C2×C4×C103—81no—
105C2×C4×C103—81no—
106C2×C4×C103C4×D411yescharacteristic
107C2×C4×C103#12111yescharacteristic
108C2×C4×C103#12411yescharacteristic
109C2×C4×C103C2×D811yescharacteristic
110C2×C4×C103C2×SD1611yescharacteristic
111C2×C4×C103#13511yescharacteristic
112C8×C103—22no—
113C8×C103—81no—
114C8×C103—81no—
115C8×C103#11711yescharacteristic
116C8×C103C4×D411yescharacteristic
117C8×C103#12311yescharacteristic
118C8×C103#12611yescharacteristic
119C22×C103—22no—
120C22×C103—82no—
121C22×C103—81no—
122C22×C103C4×D811yescharacteristic
123C22×C103#46511yescharacteristic
124C22×C103#48811yescharacteristic
125C4×C103—42no—
126C4×C103—82no—
127C4×C103—81no—
128C4×C103#38811yescharacteristic
129C4×C103C4×SD1611yescharacteristic
130C4×C103#46611yescharacteristic
131C4×C103#48611yescharacteristic
132#13152C10311yesmaximal, characteristic, direct product factor, Sylow
133C2×C103—21no—
134C2×C103—21no—
135C2×C103—161no—
136C2×C103#193411yescharacteristic
137C2×C103#217912yes—
138C2×#359C2×C10311yescharacteristic
139#2138C2×C10311yescharacteristic
140C2×#346C2×C10311yescharacteristic, complemented
141#1974C2×C10311yescharacteristic
142#1945C2×C10311yescharacteristic, complemented
143#1382C2×C10311yescharacteristic, complemented
144#1381C2×C10311yescharacteristic, complemented
145C103#1315211yescharacteristic, direct product factor, Sylow
146C2×#135C22×C10311yescharacteristic
147C22×C16C22×C10311yescharacteristic
148C22×C16C22×C10311yescharacteristic
149C2×#108C22×C10311yescharacteristic
150C2×#108C22×C10311yescharacteristic
151#427C22×C10311yescharacteristic
152#424—21no—
153C2×#104—21no—
154#408—21no—
155C2×C4×C8C22×C10311yescharacteristic
156#359—22no—
157#358C4×C10312yescomplemented
158#357C4×C10312yescomplemented
159#346—22no—
160#339—21no—
161C2×#41—21no—
162#135—21no—
163#135—21no—
164#135—21no—
165#135—21no—
166C2×Q16C2×C4×C10311yescharacteristic
167C2×SD16—21no—
168C2×D8C2×C4×C10311yescharacteristic
169C2×M16—21no—
170C2×M16—21no—
171C22×C8D4×C10311yescharacteristic
172C22×C8C23×C10311yescharacteristic
173#117—21no—
174C2×C42D4×C10311yescharacteristic
175C2×C16—21no—
176C2×C16—21no—
177C2×C16—21no—
178C2×C16—21no—
179C2×C16C2×C4×C10312yes—
180C2×C16D4×C10312yes—
181#108—21no—
182#108—21no—
183#108—21no—
184#108—21no—
185#107C2×C4×C10312yes—
186#106—21no—
187C4⋊C8—42no—
188#104—42no—
189C22⋊C8—42no—
190C4×C8—21no—
191C4×C8—21no—
192#41—41no—
193#41—41no—
194#41—41no—
195#41—41no—
196C2×Q8—21no—
197C2×D4—21no—
198C2×D4—41no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4C2×D4×C10311yescharacteristic
202Q16—21no—
203Q16—21no—
204SD16—41no—
205SD16—41no—
206D8—21no—
207D8—21no—
208M16—41no—
209M16—41no—
210M16—41no—
211M16—41no—
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8D8×C10312yes—
217C2×C8C22×C4×C10311yescharacteristic
218C2×C8C2×D4×C10311yescharacteristic
219C2×C8#41×C10311yescharacteristic
220C2×C8#41×C10311yescharacteristic
221C2×C8#41×C10311yescharacteristic
222C2×C8#41×C10311yescharacteristic
223C4⋊C4—22no—
224C22⋊C4—41no—
225C42—21no—
226C42—41no—
227C42SD16×C10312yes—
228C16—22no—
229C16—22no—
230C23—41no—
231C23#135×C10311yescharacteristic
232Q8—41no—
233Q8—41no—
234D4—41no—
235D4—41no—
236D4—81no—
237D4—81no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4C4×D4×C10311yescharacteristic
245C2×C4#121×C10311yescharacteristic
246C2×C4#124×C10311yescharacteristic
247C2×C4C2×D8×C10311yescharacteristic
248C2×C4C2×SD16×C10311yescharacteristic
249C2×C4#135×C10311yescharacteristic
250C8—22no—
251C8—81no—
252C8—81no—
253C8#117×C10311yescharacteristic
254C8C4×D4×C10311yescharacteristic
255C8#123×C10311yescharacteristic
256C8#126×C10311yescharacteristic
257C22—22no—
258C22—81no—
259C22—82no—
260C22C4×D8×C10311yescharacteristic
261C22#465×C10311yescharacteristic
262C22#488×C10311yescharacteristic
263C4—42no—
264C4—81no—
265C4—82no—
266C4#388×C10311yescharacteristic
267C4C4×SD16×C10311yescharacteristic
268C4#466×C10311yescharacteristic
269C4#486×C10311yescharacteristic
270C2—21no—
271C2—21no—
272C2—161no—
273C2C103×#193411yescharacteristic
274C2C103×#217912yes—
subgroupG/H
centerC2×C4×C103C2×D8
commutatorC2×C8C22×C4×C103
Frattini, cosocleC22×C8C23×C103
socleC22×C103C4×D8
prime radicalC2×#135×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C22×C8×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#346×C103C2semidirect
5. C103×#1945C2semidirect
6. C103×#1382C2semidirect
7. C103×#1381C2semidirect
19. #358×C103C4semidirect
20. #357×C103C4semidirect
132. #13152C103direct (N × H)
140. C2×#346C2×C103semidirect
142. #1945C2×C103semidirect
143. #1382C2×C103semidirect
144. #1381C2×C103semidirect
145. C103#13152direct (N × H)
157. #358C4×C103semidirect
158. #357C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#359×C1032
C103×#21382
C2×#346×C1032
C103×#19742
C103×#19452
C103×#13822
C103×#13812
#13152103