Finite Group Databasebeta

← C101×#13113 #38795264

Subgroups — C101×#13113 #38795264

Order 25856.

262 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2158C211yesmaximal, characteristic
2C101×#1945C211yesmaximal, characteristic
3C101×#1772C211yesmaximal, characteristic
4C101×#1382C211yesmaximal, characteristic
5C101×#1382C211yesmaximal, characteristic
6C101×#1381C211yesmaximal, characteristic
7C101×#1374C211yesmaximal, characteristic
8C22×C16×C101C2211yescharacteristic
9C22×C16×C101C2211yescharacteristic
10C2×#108×C101C2211yescharacteristic
11C2×#108×C101C2211yescharacteristic
12#427×C101C2211yescharacteristic
13#427×C101C2211yescharacteristic
14#424×C101—21no—
15#405×C101—21no—
16C2×C4×C8×C101C2211yescharacteristic
17#367×C101C411yescharacteristic, complemented
18#367×C101C411yescharacteristic, complemented
19#366×C101C411yescharacteristic, complemented
20#366×C101C411yescharacteristic, complemented
21#339×C101—21no—
22#339×C101—21no—
23C2×M16×C101—21no—
24C2×M16×C101—21no—
25C22×C8×C101D411yescharacteristic
26C22×C8×C101C2311yescharacteristic
27#117×C101—21no—
28#117×C101—21no—
29C2×C42×C101D411yescharacteristic
30C2×C16×C101—21no—
31C2×C16×C101—21no—
32C2×C16×C101—21no—
33C2×C16×C101—21no—
34C2×C16×C101—21no—
35C2×C16×C101C2×C411yescharacteristic
36C2×C16×C101C2×C411yescharacteristic
37#108×C101—21no—
38#108×C101—21no—
39#108×C101—21no—
40#108×C101Q812yes—
41#107×C101C2×C411yescharacteristic
42#107×C101C2×C411yescharacteristic
43#107×C101C2×C411yescharacteristic
44#107×C101C2×C411yescharacteristic
45#106×C101—21no—
46#106×C101—21no—
47C4⋊C8×C101—41no—
48C4⋊C8×C101—41no—
49#97×C101—41no—
50C4×C8×C101—21no—
51C4×C8×C101—21no—
52C4×C8×C101—41no—
53C22×C4×C101—21no—
54C22×C4×C101C2×D411yescharacteristic
55M16×C101—22no—
56M16×C101—41no—
57M16×C101—41no—
58M16×C101—41no—
59C2×C8×C101—21no—
60C2×C8×C101—21no—
61C2×C8×C101—41no—
62C2×C8×C101—41no—
63C2×C8×C101D811yescharacteristic
64C2×C8×C101D811yescharacteristic
65C2×C8×C101C22×C411yescharacteristic
66C2×C8×C101C2×Q811yescharacteristic
67C2×C8×C101#4111yescharacteristic
68C2×C8×C101#4111yescharacteristic
69C2×C8×C101#4111yescharacteristic
70C2×C8×C101#4111yescharacteristic
71C4⋊C4×C101—21no—
72C4⋊C4×C101—21no—
73C4⋊C4×C101—21no—
74C4⋊C4×C101—21no—
75C22⋊C4×C101—41no—
76C22⋊C4×C101—41no—
77C42×C101—21no—
78C42×C101—21no—
79C42×C101—41no—
80C42×C101—41no—
81C16×C101—21no—
82C16×C101—21no—
83C16×C101—41no—
84C23×C101#13511yescharacteristic
85C2×C4×C101—22no—
86C2×C4×C101—41no—
87C2×C4×C101—41no—
88C2×C4×C101—41no—
89C2×C4×C101—41no—
90C2×C4×C101—41no—
91C2×C4×C101—41no—
92C2×C4×C101C4×D411yescharacteristic
93C2×C4×C101C22⋊Q811yescharacteristic
94C2×C4×C101#12311yescharacteristic
95C2×C4×C101C2×D811yescharacteristic
96C2×C4×C101#13711yescharacteristic
97C2×C4×C101#13711yescharacteristic
98C8×C101—21no—
99C8×C101—21no—
100C8×C101—42no—
101C8×C101—81no—
102C8×C101#11711yescharacteristic
103C8×C101C4×Q811yescharacteristic
104C8×C101#12511yescharacteristic
105C8×C101#12611yescharacteristic
106C22×C101—21no—
107C22×C101—21no—
108C22×C101C4×D811yescharacteristic
109C22×C101#47911yescharacteristic
110C22×C101#48511yescharacteristic
111C4×C101—42no—
112C4×C101—81no—
113C4×C101—81no—
114C4×C101—81no—
115C4×C101—81no—
116C4×C101#38711yescharacteristic
117C4×C101#44111yescharacteristic
118C4×C101#47411yescharacteristic
119C4×C101#48011yescharacteristic
120#13113C10111yesmaximal, characteristic, direct product factor, Sylow
121C2×C101—21no—
122C2×C101—21no—
123C2×C101#191811yescharacteristic
124C2×C101#217811yescharacteristic
125C2×C101#217911yescharacteristic
126#2158C2×C10111yescharacteristic
127#1945C2×C10111yescharacteristic
128#1772C2×C10111yescharacteristic
129#1382C2×C10111yescharacteristic
130#1382C2×C10111yescharacteristic
131#1381C2×C10111yescharacteristic
132#1374C2×C10111yescharacteristic
133C101#1311311yescharacteristic, direct product factor, Sylow
134C22×C16C22×C10111yescharacteristic
135C22×C16C22×C10111yescharacteristic
136C2×#108C22×C10111yescharacteristic
137C2×#108C22×C10111yescharacteristic
138#427C22×C10111yescharacteristic
139#427C22×C10111yescharacteristic
140#424—21no—
141#405—21no—
142C2×C4×C8C22×C10111yescharacteristic
143#367C4×C10111yescharacteristic, complemented
144#367C4×C10111yescharacteristic, complemented
145#366C4×C10111yescharacteristic, complemented
146#366C4×C10111yescharacteristic, complemented
147#339—21no—
148#339—21no—
149C2×M16—21no—
150C2×M16—21no—
151C22×C8D4×C10111yescharacteristic
152C22×C8C23×C10111yescharacteristic
153#117—21no—
154#117—21no—
155C2×C42D4×C10111yescharacteristic
156C2×C16—21no—
157C2×C16—21no—
158C2×C16—21no—
159C2×C16—21no—
160C2×C16—21no—
161C2×C16C2×C4×C10111yescharacteristic
162C2×C16C2×C4×C10111yescharacteristic
163#108—21no—
164#108—21no—
165#108—21no—
166#108Q8×C10112yes—
167#107C2×C4×C10111yescharacteristic
168#107C2×C4×C10111yescharacteristic
169#107C2×C4×C10111yescharacteristic
170#107C2×C4×C10111yescharacteristic
171#106—21no—
172#106—21no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175#97—41no—
176C4×C8—21no—
177C4×C8—21no—
178C4×C8—41no—
179C22×C4—21no—
180C22×C4C2×D4×C10111yescharacteristic
181M16—22no—
182M16—41no—
183M16—41no—
184M16—41no—
185C2×C8—21no—
186C2×C8—21no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8D8×C10111yescharacteristic
190C2×C8D8×C10111yescharacteristic
191C2×C8C22×C4×C10111yescharacteristic
192C2×C8C2×Q8×C10111yescharacteristic
193C2×C8#41×C10111yescharacteristic
194C2×C8#41×C10111yescharacteristic
195C2×C8#41×C10111yescharacteristic
196C2×C8#41×C10111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C22⋊C4—41no—
202C22⋊C4—41no—
203C42—21no—
204C42—21no—
205C42—41no—
206C42—41no—
207C16—21no—
208C16—21no—
209C16—41no—
210C23#135×C10111yescharacteristic
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4C4×D4×C10111yescharacteristic
219C2×C4C22⋊Q8×C10111yescharacteristic
220C2×C4#123×C10111yescharacteristic
221C2×C4C2×D8×C10111yescharacteristic
222C2×C4#137×C10111yescharacteristic
223C2×C4#137×C10111yescharacteristic
224C8—21no—
225C8—21no—
226C8—42no—
227C8—81no—
228C8#117×C10111yescharacteristic
229C8C4×Q8×C10111yescharacteristic
230C8#125×C10111yescharacteristic
231C8#126×C10111yescharacteristic
232C22—21no—
233C22—21no—
234C22C4×D8×C10111yescharacteristic
235C22#479×C10111yescharacteristic
236C22#485×C10111yescharacteristic
237C4—42no—
238C4—81no—
239C4—81no—
240C4—81no—
241C4—81no—
242C4#387×C10111yescharacteristic
243C4#441×C10111yescharacteristic
244C4#474×C10111yescharacteristic
245C4#480×C10111yescharacteristic
246C2—21no—
247C2—21no—
248C2C101×#191811yescharacteristic
249C2C101×#217811yescharacteristic
250C2C101×#217911yescharacteristic
subgroupG/H
centerC2×C4×C101C2×D8
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
socleC22×C101C4×D8
prime radicalC23×C101#135
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C22×C8×C101 ◁ C2×C4×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
17. #367×C101C4semidirect
18. #367×C101C4semidirect
19. #366×C101C4semidirect
20. #366×C101C4semidirect
120. #13113C101direct (N × H)
133. C101#13113direct (N × H)
143. #367C4×C101semidirect
144. #367C4×C101semidirect
145. #366C4×C101semidirect
146. #366C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#21582
C101×#19452
C101×#17722
C101×#13822
C101×#13812
C101×#13742
#13113101