Finite Group Databasebeta

← C101×#13137 #38795288

Subgroups — C101×#13137 #38795288

Order 25856.

316 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2161C211yesmaximal, characteristic, complemented
2C101×#2148C211yesmaximal, characteristic
3C101×#2143C211yesmaximal, characteristic
4C101×#1974C211yesmaximal, characteristic
5C4×#108×C101C211yesmaximal, characteristic, complemented
6C101×#1388C211yesmaximal, characteristic, complemented
7C101×#1376C211yesmaximal, characteristic, complemented
8C2×#135×C101C2211yescharacteristic
9C2×M32×C101C2211yescharacteristic
10C2×M32×C101C2211yescharacteristic
11C2×#108×C101C2211yescharacteristic
12C2×#108×C101C2211yescharacteristic
13C2×#108×C101C2211yescharacteristic
14C2×#104×C101—21no—
15#408×C101—21no—
16C4×M16×C101—21no—
17C2×C4×C8×C101C2211yescharacteristic
18#368×C101—22no—
19#362×C101C412yescomplemented
20#361×C101C412yescomplemented
21#359×C101—22no—
22#341×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—
33C2×M16×C101—21no—
34C22×C8×C101D411yescharacteristic
35C22×C8×C101C2311yescharacteristic
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×C101—21no—
47#108×C101C2×C412yes—
48#108×C101D412yes—
49#104×C101—41no—
50#104×C101—41no—
51C22⋊C8×C101—42no—
52#97×C101—41no—
53C4×C8×C101—21no—
54C4×C8×C101—21no—
55C4×C8×C101—41no—
56#41×C101—41no—
57#41×C101—41no—
58#41×C101—41no—
59#41×C101—41no—
60C2×Q8×C101—21no—
61C2×D4×C101—21no—
62C2×D4×C101—41no—
63C22×C4×C101—21no—
64C22×C4×C101—41no—
65C22×C4×C101C2×D411yescharacteristic
66Q16×C101—21no—
67Q16×C101—21no—
68SD16×C101—41no—
69SD16×C101—41no—
70D8×C101—21no—
71D8×C101—21no—
72M16×C101—22no—
73M16×C101—22no—
74M16×C101—41no—
75M16×C101—41no—
76M16×C101—41no—
77M16×C101—41no—
78C2×C8×C101—21no—
79C2×C8×C101—21no—
80C2×C8×C101—21no—
81C2×C8×C101—41no—
82C2×C8×C101—41no—
83C2×C8×C101—41no—
84C2×C8×C101C22×C411yescharacteristic
85C2×C8×C101C2×D411yescharacteristic
86C2×C8×C101#4111yescharacteristic
87C2×C8×C101#4111yescharacteristic
88C2×C8×C101#4111yescharacteristic
89C2×C8×C101#4111yescharacteristic
90C42×C101—21no—
91C42×C101D811yescharacteristic
92C42×C101D811yescharacteristic
93C16×C101—22no—
94C16×C101—41no—
95C23×C101—41no—
96C23×C101#13711yescharacteristic
97Q8×C101—41no—
98Q8×C101—41no—
99D4×C101—41no—
100D4×C101—41no—
101D4×C101—81no—
102D4×C101—81no—
103C2×C4×C101—21no—
104C2×C4×C101—21no—
105C2×C4×C101—42no—
106C2×C4×C101—41no—
107C2×C4×C101—81no—
108C2×C4×C101—81no—
109C2×C4×C101C4×D411yescharacteristic
110C2×C4×C101#12111yescharacteristic
111C2×C4×C101#12311yescharacteristic
112C2×C4×C101C2×D811yescharacteristic
113C2×C4×C101#13511yescharacteristic
114C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
115C8×C101—42no—
116C8×C101—42no—
117C8×C101—41no—
118C8×C101—81no—
119C8×C101#11711yescharacteristic
120C8×C101C4×D411yescharacteristic
121C8×C101#12411yescharacteristic
122C8×C101#12611yescharacteristic
123C22×C101—41no—
124C22×C101—82no—
125C22×C101—81no—
126C22×C101#44011yescharacteristic
127C22×C101#46411yescharacteristic
128C22×C101#48011yescharacteristic
129C4×C101—22no—
130C4×C101—41no—
131C4×C101—81no—
132C4×C101#38811yescharacteristic
133C4×C101C4×D811yescharacteristic
134C4×C101#45911yescharacteristic
135C4×C101#48211yescharacteristic
136#13137C10111yesmaximal, characteristic, direct product factor, Sylow
137C2×C101—21no—
138C2×C101—21no—
139C2×C101—21no—
140C2×C101—161no—
141C2×C101#192511yescharacteristic
142#2161C2×C10111yescharacteristic, complemented
143#2148C2×C10111yescharacteristic
144#2143C2×C10111yescharacteristic
145#1974C2×C10111yescharacteristic
146C4×#108C2×C10111yescharacteristic, complemented
147#1388C2×C10111yescharacteristic, complemented
148#1376C2×C10111yescharacteristic, complemented
149C101#1313711yescharacteristic, direct product factor, Sylow
150C2×#135C22×C10111yescharacteristic
151C2×M32C22×C10111yescharacteristic
152C2×M32C22×C10111yescharacteristic
153C2×#108C22×C10111yescharacteristic
154C2×#108C22×C10111yescharacteristic
155C2×#108C22×C10111yescharacteristic
156C2×#104—21no—
157#408—21no—
158C4×M16—21no—
159C2×C4×C8C22×C10111yescharacteristic
160#368—22no—
161#362C4×C10112yescomplemented
162#361C4×C10112yescomplemented
163#359—22no—
164#341—21no—
165C2×#41—21no—
166#135—21no—
167#135—21no—
168#135—21no—
169#135—21no—
170C2×Q16C2×C4×C10111yescharacteristic
171C2×SD16—21no—
172C2×D8C2×C4×C10111yescharacteristic
173C2×M16—21no—
174C2×M16—21no—
175C2×M16—21no—
176C22×C8D4×C10111yescharacteristic
177C22×C8C23×C10111yescharacteristic
178C2×C42D4×C10111yescharacteristic
179M32—21no—
180M32—21no—
181M32—21no—
182M32C2×C4×C10112yes—
183C2×C16—21no—
184C2×C16—21no—
185#108—21no—
186#108—21no—
187#108—21no—
188#108—21no—
189#108C2×C4×C10112yes—
190#108D4×C10112yes—
191#104—41no—
192#104—41no—
193C22⋊C8—42no—
194#97—41no—
195C4×C8—21no—
196C4×C8—21no—
197C4×C8—41no—
198#41—41no—
199#41—41no—
200#41—41no—
201#41—41no—
202C2×Q8—21no—
203C2×D4—21no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—41no—
207C22×C4C2×D4×C10111yescharacteristic
208Q16—21no—
209Q16—21no—
210SD16—41no—
211SD16—41no—
212D8—21no—
213D8—21no—
214M16—22no—
215M16—22no—
216M16—41no—
217M16—41no—
218M16—41no—
219M16—41no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8C22×C4×C10111yescharacteristic
227C2×C8C2×D4×C10111yescharacteristic
228C2×C8#41×C10111yescharacteristic
229C2×C8#41×C10111yescharacteristic
230C2×C8#41×C10111yescharacteristic
231C2×C8#41×C10111yescharacteristic
232C42—21no—
233C42D8×C10111yescharacteristic
234C42D8×C10111yescharacteristic
235C16—22no—
236C16—41no—
237C23—41no—
238C23#137×C10111yescharacteristic
239Q8—41no—
240Q8—41no—
241D4—41no—
242D4—41no—
243D4—81no—
244D4—81no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4C4×D4×C10111yescharacteristic
252C2×C4#121×C10111yescharacteristic
253C2×C4#123×C10111yescharacteristic
254C2×C4C2×D8×C10111yescharacteristic
255C2×C4#135×C10111yescharacteristic
256C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
257C8—42no—
258C8—42no—
259C8—41no—
260C8—81no—
261C8#117×C10111yescharacteristic
262C8C4×D4×C10111yescharacteristic
263C8#124×C10111yescharacteristic
264C8#126×C10111yescharacteristic
265C22—41no—
266C22—82no—
267C22—81no—
268C22#440×C10111yescharacteristic
269C22#464×C10111yescharacteristic
270C22#480×C10111yescharacteristic
271C4—22no—
272C4—41no—
273C4—81no—
274C4#388×C10111yescharacteristic
275C4C4×D8×C10111yescharacteristic
276C4#459×C10111yescharacteristic
277C4#482×C10111yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—161no—
282C2C101×#192511yescharacteristic
subgroupG/H
centerC4×C101#459
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
socleC2×C101#1925
prime radicalC2×#135×C101C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C101 ◁ C22×C4×C101 ◁ C2×C4×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#2161C2semidirect
5. C4×#108×C101C2semidirect
6. C101×#1388C2semidirect
7. C101×#1376C2semidirect
19. #362×C101C4semidirect
20. #361×C101C4semidirect
136. #13137C101direct (N × H)
142. #2161C2×C101semidirect
146. C4×#108C2×C101semidirect
147. #1388C2×C101semidirect
148. #1376C2×C101semidirect
149. C101#13137direct (N × H)
161. #362C4×C101semidirect
162. #361C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#21612
C101×#21482
C101×#21432
C101×#19742
C4×#108×C1012
C101×#13882
C101×#13762
#13137101