Finite Group Databasebeta

← C101×#13140 #38795291

Subgroups — C101×#13140 #38795291

Order 25856.

314 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
1C101×#2155C211yesmaximal, characteristic, complemented
2C101×#2148C211yesmaximal, characteristic
3C101×#2145C211yesmaximal, characteristic
4C101×#1975C211yesmaximal, characteristic
5C101×#1773C211yesmaximal, characteristic, complemented
6C101×#1385C211yesmaximal, characteristic, complemented
7C101×#1377C211yesmaximal, characteristic, complemented
8C2×#135×C101C2211yescharacteristic
9C2×M32×C101C2211yescharacteristic
10C2×M32×C101C2211yescharacteristic
11C2×#108×C101C2211yescharacteristic
12C2×#108×C101C2211yescharacteristic
13#427×C101C2211yescharacteristic
14C2×#104×C101—21no—
15#408×C101—21no—
16#405×C101—21no—
17C2×#97×C101C2211yescharacteristic
18#365×C101—22no—
19#362×C101C412yescomplemented
20#361×C101C412yescomplemented
21#360×C101—22no—
22#339×C101—21no—
23C2×#41×C101—21no—
24#135×C101—21no—
25#135×C101—21no—
26#135×C101—21no—
27#135×C101—21no—
28C2×Q16×C101C2×C411yescharacteristic
29C2×SD16×C101—21no—
30C2×D8×C101C2×C411yescharacteristic
31C2×M16×C101—21no—
32C2×M16×C101—21no—
33C22×C8×C101D411yescharacteristic
34C22×C8×C101C2311yescharacteristic
35#117×C101—21no—
36C2×C42×C101D411yescharacteristic
37M32×C101—21no—
38M32×C101—21no—
39M32×C101—21no—
40M32×C101C2×C412yes—
41C2×C16×C101—21no—
42C2×C16×C101—21no—
43#108×C101—21no—
44#108×C101—21no—
45#108×C101—21no—
46#108×C101C2×C412yes—
47#107×C101—21no—
48#106×C101D412yes—
49#104×C101—42no—
50C22⋊C8×C101—42no—
51#97×C101—21no—
52#97×C101—21no—
53#97×C101—41no—
54C4×C8×C101—41no—
55#41×C101—41no—
56#41×C101—41no—
57#41×C101—41no—
58#41×C101—41no—
59C2×Q8×C101—21no—
60C2×D4×C101—21no—
61C2×D4×C101—41no—
62C22×C4×C101—21no—
63C22×C4×C101—41no—
64C22×C4×C101C2×D411yescharacteristic
65Q16×C101—21no—
66Q16×C101—21no—
67SD16×C101—41no—
68SD16×C101—41no—
69D8×C101—21no—
70D8×C101—21no—
71M16×C101—22no—
72M16×C101—41no—
73M16×C101—41no—
74M16×C101—41no—
75C2×C8×C101—21no—
76C2×C8×C101—21no—
77C2×C8×C101—41no—
78C2×C8×C101—41no—
79C2×C8×C101SD1612yes—
80C2×C8×C101C22×C411yescharacteristic
81C2×C8×C101C2×D411yescharacteristic
82C2×C8×C101#4111yescharacteristic
83C2×C8×C101#4111yescharacteristic
84C2×C8×C101#4111yescharacteristic
85C2×C8×C101#4111yescharacteristic
86C4⋊C4×C101—22no—
87C22⋊C4×C101—41no—
88C42×C101—21no—
89C42×C101—21no—
90C42×C101—41no—
91C16×C101—22no—
92C16×C101—41no—
93C23×C101—41no—
94C23×C101#13511yescharacteristic
95Q8×C101—41no—
96Q8×C101—41no—
97D4×C101—41no—
98D4×C101—41no—
99D4×C101—81no—
100D4×C101—81no—
101C2×C4×C101—41no—
102C2×C4×C101—42no—
103C2×C4×C101—41no—
104C2×C4×C101—81no—
105C2×C4×C101—81no—
106C2×C4×C101—81no—
107C2×C4×C101C4×D411yescharacteristic
108C2×C4×C101#12111yescharacteristic
109C2×C4×C101#12311yescharacteristic
110C2×C4×C101C2×SD1611yescharacteristic
111C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
113C8×C101—22no—
114C8×C101—42no—
115C8×C101—81no—
116C8×C101#11711yescharacteristic
117C8×C101C4×D411yescharacteristic
118C8×C101#12411yescharacteristic
119C8×C101#12611yescharacteristic
120C22×C101—41no—
121C22×C101—82no—
122C22×C101—81no—
123C22×C101C4×SD1611yescharacteristic
124C22×C101#46311yescharacteristic
125C22×C101#48211yescharacteristic
126C4×C101—82no—
127C4×C101—81no—
128C4×C101—81no—
129C4×C101#38811yescharacteristic
130C4×C101#44211yescharacteristic
131C4×C101#46011yescharacteristic
132C4×C101#48111yescharacteristic
133#13140C10111yesmaximal, characteristic, direct product factor, Sylow
134C2×C101—21no—
135C2×C101—21no—
136C2×C101—21no—
137C2×C101—161no—
138C2×C101#192611yescharacteristic
139#2155C2×C10111yescharacteristic, complemented
140#2148C2×C10111yescharacteristic
141#2145C2×C10111yescharacteristic
142#1975C2×C10111yescharacteristic
143#1773C2×C10111yescharacteristic, complemented
144#1385C2×C10111yescharacteristic, complemented
145#1377C2×C10111yescharacteristic, complemented
146C101#1314011yescharacteristic, direct product factor, Sylow
147C2×#135C22×C10111yescharacteristic
148C2×M32C22×C10111yescharacteristic
149C2×M32C22×C10111yescharacteristic
150C2×#108C22×C10111yescharacteristic
151C2×#108C22×C10111yescharacteristic
152#427C22×C10111yescharacteristic
153C2×#104—21no—
154#408—21no—
155#405—21no—
156C2×#97C22×C10111yescharacteristic
157#365—22no—
158#362C4×C10112yescomplemented
159#361C4×C10112yescomplemented
160#360—22no—
161#339—21no—
162C2×#41—21no—
163#135—21no—
164#135—21no—
165#135—21no—
166#135—21no—
167C2×Q16C2×C4×C10111yescharacteristic
168C2×SD16—21no—
169C2×D8C2×C4×C10111yescharacteristic
170C2×M16—21no—
171C2×M16—21no—
172C22×C8D4×C10111yescharacteristic
173C22×C8C23×C10111yescharacteristic
174#117—21no—
175C2×C42D4×C10111yescharacteristic
176M32—21no—
177M32—21no—
178M32—21no—
179M32C2×C4×C10112yes—
180C2×C16—21no—
181C2×C16—21no—
182#108—21no—
183#108—21no—
184#108—21no—
185#108C2×C4×C10112yes—
186#107—21no—
187#106D4×C10112yes—
188#104—42no—
189C22⋊C8—42no—
190#97—21no—
191#97—21no—
192#97—41no—
193C4×C8—41no—
194#41—41no—
195#41—41no—
196#41—41no—
197#41—41no—
198C2×Q8—21no—
199C2×D4—21no—
200C2×D4—41no—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4C2×D4×C10111yescharacteristic
204Q16—21no—
205Q16—21no—
206SD16—41no—
207SD16—41no—
208D8—21no—
209D8—21no—
210M16—22no—
211M16—41no—
212M16—41no—
213M16—41no—
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8SD16×C10112yes—
219C2×C8C22×C4×C10111yescharacteristic
220C2×C8C2×D4×C10111yescharacteristic
221C2×C8#41×C10111yescharacteristic
222C2×C8#41×C10111yescharacteristic
223C2×C8#41×C10111yescharacteristic
224C2×C8#41×C10111yescharacteristic
225C4⋊C4—22no—
226C22⋊C4—41no—
227C42—21no—
228C42—21no—
229C42—41no—
230C16—22no—
231C16—41no—
232C23—41no—
233C23#135×C10111yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—41no—
238D4—81no—
239D4—81no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C4×D4×C10111yescharacteristic
247C2×C4#121×C10111yescharacteristic
248C2×C4#123×C10111yescharacteristic
249C2×C4C2×SD16×C10111yescharacteristic
250C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
251C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
252C8—22no—
253C8—42no—
254C8—81no—
255C8#117×C10111yescharacteristic
256C8C4×D4×C10111yescharacteristic
257C8#124×C10111yescharacteristic
258C8#126×C10111yescharacteristic
259C22—41no—
260C22—82no—
261C22—81no—
262C22C4×SD16×C10111yescharacteristic
263C22#463×C10111yescharacteristic
264C22#482×C10111yescharacteristic
265C4—81no—
266C4—82no—
267C4—81no—
268C4#388×C10111yescharacteristic
269C4#442×C10111yescharacteristic
270C4#460×C10111yescharacteristic
271C4#481×C10111yescharacteristic
272C2—21no—
273C2—21no—
274C2—21no—
275C2—161no—
276C2C101×#192611yescharacteristic
subgroupG/H
centerC4×C101#481
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
socleC2×C101#1926
prime radicalC2×#135×C101C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C101 ◁ C22×C4×C101 ◁ C2×#97×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#2155C2semidirect
5. C101×#1773C2semidirect
6. C101×#1385C2semidirect
7. C101×#1377C2semidirect
19. #362×C101C4semidirect
20. #361×C101C4semidirect
133. #13140C101direct (N × H)
139. #2155C2×C101semidirect
143. #1773C2×C101semidirect
144. #1385C2×C101semidirect
145. #1377C2×C101semidirect
146. C101#13140direct (N × H)
158. #362C4×C101semidirect
159. #361C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#21552
C101×#21482
C101×#21452
C101×#19752
C101×#17732
C101×#13852
C101×#13772
#13140101