Finite Group Databasebeta

← C101×#13126 #38795277

Subgroups — C101×#13126 #38795277

Order 25856.

300 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
1C101×#2151C211yesmaximal, characteristic, complemented
2C101×#2117C211yesmaximal, characteristic
3C2×#350×C101C211yesmaximal, characteristic
4C101×#2110C211yesmaximal, characteristic, complemented
5C101×#1757C211yesmaximal, characteristic
6C101×#1379C211yesmaximal, characteristic, complemented
7C101×#1378C211yesmaximal, characteristic, complemented
8C2×#131×C101C2211yescharacteristic
9C2×M32×C101C2211yescharacteristic
10C2×M32×C101C2211yescharacteristic
11C2×M32×C101C2211yescharacteristic
12C22×C16×C101C2211yescharacteristic
13#413×C101C411yescharacteristic
14#410×C101C411yescharacteristic
15#405×C101C2211yescharacteristic
16#405×C101C2211yescharacteristic
17C4⋊C16×C101—22no—
18#350×C101—22no—
19#350×C101—22no—
20#347×C101—22no—
21#344×C101C411yescharacteristic
22#344×C101C411yescharacteristic
23C2×#41×C101C2×C411yescharacteristic
24#131×C101—21no—
25#131×C101—21no—
26#131×C101—21no—
27#131×C101—21no—
28C2×M16×C101—21no—
29C2×M16×C101C2×C411yescharacteristic
30C2×M16×C101C2×C411yescharacteristic
31C2×M16×C101C2×C411yescharacteristic
32C22×C8×C101—21no—
33C22×C8×C101C2311yescharacteristic
34#117×C101C2×C411yescharacteristic
35#117×C101C2×C411yescharacteristic
36M32×C101—21no—
37M32×C101—21no—
38M32×C101—21no—
39M32×C101—21no—
40M32×C101—21no—
41M32×C101D412yes—
42C2×C16×C101—21no—
43C2×C16×C101—21no—
44C2×C16×C101—21no—
45C2×C16×C101—21no—
46C2×C16×C101—21no—
47C2×C16×C101D412yes—
48#101×C101—21no—
49#100×C101—21no—
50#99×C101—22no—
51#97×C101—21no—
52#97×C101—21no—
53C4×C8×C101—21no—
54C4×C8×C101—21no—
55#41×C101—21no—
56#41×C101—21no—
57#41×C101—21no—
58#41×C101—21no—
59C2×Q8×C101M1611yescharacteristic
60C2×D4×C101—21no—
61C2×D4×C101M1611yescharacteristic
62C22×C4×C101—21no—
63C22×C4×C101C22×C411yescharacteristic
64M16×C101—21no—
65M16×C101—21no—
66M16×C101—21no—
67M16×C101—21no—
68M16×C101—21no—
69M16×C101—21no—
70M16×C101—41no—
71M16×C101—41no—
72C2×C8×C101—21no—
73C2×C8×C101—21no—
74C2×C8×C101—21no—
75C2×C8×C101—41no—
76C2×C8×C101—41no—
77C2×C8×C101C2×D411yescharacteristic
78C2×C8×C101C2×D411yescharacteristic
79C2×C8×C101#4111yescharacteristic
80C2×C8×C101#4111yescharacteristic
81C2×C8×C101#4111yescharacteristic
82C2×C8×C101#4111yescharacteristic
83C4⋊C4×C101—21no—
84C4⋊C4×C101—21no—
85C22⋊C4×C101—21no—
86C22⋊C4×C101M1612yes—
87C42×C101—21no—
88C42×C101—21no—
89C16×C101—22no—
90C16×C101—22no—
91C16×C101—41no—
92C16×C101—41no—
93C23×C101—21no—
94C23×C101C2×M1611yescharacteristic
95Q8×C101—21no—
96Q8×C101—21no—
97D4×C101—21no—
98D4×C101—21no—
99D4×C101—41no—
100D4×C101—41no—
101C2×C4×C101—21no—
102C2×C4×C101—22no—
103C2×C4×C101—41no—
104C2×C4×C101—41no—
105C2×C4×C101—41no—
106C2×C4×C101#11711yescharacteristic
107C2×C4×C101C4×D411yescharacteristic
108C2×C4×C101C4×D411yescharacteristic
109C2×C4×C101C2×M1611yescharacteristic
110C2×C4×C101#13111yescharacteristic
111C2×C4×C101#13111yescharacteristic
112C8×C101—41no—
113C8×C101—41no—
114C8×C101—41no—
115C8×C101#12111yescharacteristic
116C8×C101#12311yescharacteristic
117C8×C101#12411yescharacteristic
118C8×C101#12611yescharacteristic
119C22×C101—41no—
120C22×C101—41no—
121C22×C101—81no—
122C22×C101#43211yescharacteristic
123C22×C101#43511yescharacteristic
124C22×C101#43611yescharacteristic
125C4×C101—42no—
126C4×C101—41no—
127C4×C101—81no—
128C4×C101#38811yescharacteristic
129C4×C101#43311yescharacteristic
130C4×C101#43511yescharacteristic
131C4×C101#43511yescharacteristic
132#13126C10111yesmaximal, characteristic, direct product factor, Sylow
133C2×C101—21no—
134C2×C101—21no—
135C2×C101—21no—
136C2×C101—81no—
137C2×C101#192411yescharacteristic
138#2151C2×C10111yescharacteristic, complemented
139#2117C2×C10111yescharacteristic
140C2×#350C2×C10111yescharacteristic
141#2110C2×C10111yescharacteristic, complemented
142#1757C2×C10111yescharacteristic
143#1379C2×C10111yescharacteristic, complemented
144#1378C2×C10111yescharacteristic, complemented
145C101#1312611yescharacteristic, direct product factor, Sylow
146C2×#131C22×C10111yescharacteristic
147C2×M32C22×C10111yescharacteristic
148C2×M32C22×C10111yescharacteristic
149C2×M32C22×C10111yescharacteristic
150C22×C16C22×C10111yescharacteristic
151#413C4×C10111yescharacteristic
152#410C4×C10111yescharacteristic
153#405C22×C10111yescharacteristic
154#405C22×C10111yescharacteristic
155C4⋊C16—22no—
156#350—22no—
157#350—22no—
158#347—22no—
159#344C4×C10111yescharacteristic
160#344C4×C10111yescharacteristic
161C2×#41C2×C4×C10111yescharacteristic
162#131—21no—
163#131—21no—
164#131—21no—
165#131—21no—
166C2×M16—21no—
167C2×M16C2×C4×C10111yescharacteristic
168C2×M16C2×C4×C10111yescharacteristic
169C2×M16C2×C4×C10111yescharacteristic
170C22×C8—21no—
171C22×C8C23×C10111yescharacteristic
172#117C2×C4×C10111yescharacteristic
173#117C2×C4×C10111yescharacteristic
174M32—21no—
175M32—21no—
176M32—21no—
177M32—21no—
178M32—21no—
179M32D4×C10112yes—
180C2×C16—21no—
181C2×C16—21no—
182C2×C16—21no—
183C2×C16—21no—
184C2×C16—21no—
185C2×C16D4×C10112yes—
186#101—21no—
187#100—21no—
188#99—22no—
189#97—21no—
190#97—21no—
191C4×C8—21no—
192C4×C8—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—21no—
197C2×Q8M16×C10111yescharacteristic
198C2×D4—21no—
199C2×D4M16×C10111yescharacteristic
200C22×C4—21no—
201C22×C4C22×C4×C10111yescharacteristic
202M16—21no—
203M16—21no—
204M16—21no—
205M16—21no—
206M16—21no—
207M16—21no—
208M16—41no—
209M16—41no—
210C2×C8—21no—
211C2×C8—21no—
212C2×C8—21no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8C2×D4×C10111yescharacteristic
216C2×C8C2×D4×C10111yescharacteristic
217C2×C8#41×C10111yescharacteristic
218C2×C8#41×C10111yescharacteristic
219C2×C8#41×C10111yescharacteristic
220C2×C8#41×C10111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—21no—
223C22⋊C4—21no—
224C22⋊C4M16×C10112yes—
225C42—21no—
226C42—21no—
227C16—22no—
228C16—22no—
229C16—41no—
230C16—41no—
231C23—21no—
232C23C2×M16×C10111yescharacteristic
233Q8—21no—
234Q8—21no—
235D4—21no—
236D4—21no—
237D4—41no—
238D4—41no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4#117×C10111yescharacteristic
245C2×C4C4×D4×C10111yescharacteristic
246C2×C4C4×D4×C10111yescharacteristic
247C2×C4C2×M16×C10111yescharacteristic
248C2×C4#131×C10111yescharacteristic
249C2×C4#131×C10111yescharacteristic
250C8—41no—
251C8—41no—
252C8—41no—
253C8#121×C10111yescharacteristic
254C8#123×C10111yescharacteristic
255C8#124×C10111yescharacteristic
256C8#126×C10111yescharacteristic
257C22—41no—
258C22—41no—
259C22—81no—
260C22#432×C10111yescharacteristic
261C22#435×C10111yescharacteristic
262C22#436×C10111yescharacteristic
263C4—42no—
264C4—41no—
265C4—81no—
266C4#388×C10111yescharacteristic
267C4#433×C10111yescharacteristic
268C4#435×C10111yescharacteristic
269C4#435×C10111yescharacteristic
270C2—21no—
271C2—21no—
272C2—21no—
273C2—81no—
274C2C101×#192411yescharacteristic
subgroupG/H
centerC8×C101#124
commutatorC22×C4C22×C4×C101
Frattini, cosocleC22×C8C23×C101
socleC2×C101#1924
prime radicalC2×#41×C101C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C101 ◁ C22×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#2151C2semidirect
4. C101×#2110C2semidirect
6. C101×#1379C2semidirect
7. C101×#1378C2semidirect
132. #13126C101direct (N × H)
138. #2151C2×C101semidirect
141. #2110C2×C101semidirect
143. #1379C2×C101semidirect
144. #1378C2×C101semidirect
145. C101#13126direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#21512
C101×#21172
C2×#350×C1012
C101×#21102
C101×#17572
C101×#13792
C101×#13782
#13126101