Finite Group Databasebeta

← C101×#13136 #38795287

Subgroups — C101×#13136 #38795287

Order 25856.

360 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2159C211yesmaximal, characteristic, complemented
2C2×#361×C101C211yesmaximal, characteristic
3C101×#2140C211yesmaximal, characteristic
4C101×#1970C211yesmaximal, characteristic
5C101×#1772C211yesmaximal, characteristic, complemented
6C101×#1387C211yesmaximal, characteristic, complemented
7C101×#1376C211yesmaximal, characteristic, complemented
8C22×D8×C101C2211yescharacteristic
9C2×M32×C101C2211yescharacteristic
10C2×M32×C101C2211yescharacteristic
11C2×#108×C101C2211yescharacteristic
12#427×C101C2211yescharacteristic
13C2×#107×C101C2211yescharacteristic
14C2×#102×C101—21no—
15#405×C101—21no—
16C2×C4×C8×C101C2211yescharacteristic
17#390×C101—21no—
18#367×C101—21no—
19#366×C101—21no—
20#361×C101C414yescomplemented
21#357×C101—21no—
22#357×C101—21no—
23#339×C101—21no—
24C22×D4×C101—21no—
25C2×D8×C101—21no—
26C2×D8×C101—21no—
27C2×D8×C101—21no—
28C2×D8×C101—21no—
29C2×D8×C101—21no—
30C2×D8×C101C2×C412yes—
31C2×M16×C101—21no—
32C22×C8×C101D411yescharacteristic
33C22×C8×C101C2311yescharacteristic
34#117×C101—21no—
35C2×C4⋊C4×C101—21no—
36C2×C22⋊C4×C101—42no—
37C2×C42×C101D411yescharacteristic
38M32×C101—21no—
39M32×C101—21no—
40M32×C101—21no—
41M32×C101C2×C412yes—
42C2×C16×C101—21no—
43C2×C16×C101—21no—
44#108×C101—21no—
45#108×C101C2×C412yes—
46#107×C101—21no—
47#107×C101—21no—
48#107×C101D411yescharacteristic
49#107×C101D411yescharacteristic
50#106×C101—21no—
51#102×C101—41no—
52#102×C101—41no—
53#97×C101—41no—
54C4×C8×C101—21no—
55C4×C8×C101—21no—
56C4×C8×C101—41no—
57C24×C101—41no—
58C2×D4×C101—22no—
59C2×D4×C101—41no—
60C2×D4×C101—41no—
61C2×D4×C101—41no—
62C2×D4×C101—41no—
63C2×D4×C101—41no—
64C22×C4×C101—21no—
65C22×C4×C101—41no—
66C22×C4×C101C2×D411yescharacteristic
67D8×C101—22no—
68D8×C101—22no—
69D8×C101—41no—
70D8×C101—41no—
71M16×C101—22no—
72M16×C101—41no—
73C2×C8×C101—21no—
74C2×C8×C101—21no—
75C2×C8×C101—41no—
76C2×C8×C101D811yescharacteristic
77C2×C8×C101D811yescharacteristic
78C2×C8×C101C22×C411yescharacteristic
79C2×C8×C101C2×D411yescharacteristic
80C2×C8×C101#4111yescharacteristic
81C2×C8×C101#4111yescharacteristic
82C2×C8×C101#4111yescharacteristic
83C2×C8×C101#4111yescharacteristic
84C4⋊C4×C101—21no—
85C4⋊C4×C101—21no—
86C4⋊C4×C101—41no—
87C4⋊C4×C101—41no—
88C22⋊C4×C101—41no—
89C22⋊C4×C101—84no—
90C42×C101—21no—
91C42×C101—21no—
92C42×C101—41no—
93C16×C101—22no—
94C16×C101—41no—
95C23×C101—42no—
96C23×C101—82no—
97C23×C101—82no—
98C23×C101—81no—
99C23×C101—81no—
100C23×C101AGL(1,ℤ/8)11yescharacteristic
101D4×C101—42no—
102D4×C101—42no—
103D4×C101—81no—
104D4×C101—81no—
105C2×C4×C101—22no—
106C2×C4×C101—41no—
107C2×C4×C101—41no—
108C2×C4×C101—41no—
109C2×C4×C101—41no—
110C2×C4×C101—82no—
111C2×C4×C101—81no—
112C2×C4×C101C4×D411yescharacteristic
113C2×C4×C101#12111yescharacteristic
114C2×C4×C101#12311yescharacteristic
115C2×C4×C101C2×D811yescharacteristic
116C2×C4×C101#13511yescharacteristic
117C2×C4×C101#13711yescharacteristic
118C8×C101—21no—
119C8×C101—21no—
120C8×C101—42no—
121C8×C101#11711yescharacteristic
122C8×C101C4×D411yescharacteristic
123C8×C101#12411yescharacteristic
124C8×C101#12611yescharacteristic
125C22×C101—21no—
126C22×C101—21no—
127C22×C101—84no—
128C22×C101—82no—
129C22×C101—162no—
130C22×C101—161no—
131C22×C101—161no—
132C22×C101#44011yescharacteristic
133C22×C101#45911yescharacteristic
134C22×C101#48211yescharacteristic
135C4×C101—42no—
136C4×C101—81no—
137C4×C101—81no—
138C4×C101—161no—
139C4×C101#38811yescharacteristic
140C4×C101C4×D811yescharacteristic
141C4×C101#46411yescharacteristic
142C4×C101#48011yescharacteristic
143#13136C10111yesmaximal, characteristic, direct product factor, Sylow
144C2×C101—21no—
145C2×C101—21no—
146C2×C101—162no—
147C2×C101#192511yescharacteristic
148C2×C101#221211yescharacteristic
149C2×C101#221311yescharacteristic
150#2159C2×C10111yescharacteristic, complemented
151C2×#361C2×C10111yescharacteristic
152#2140C2×C10111yescharacteristic
153#1970C2×C10111yescharacteristic
154#1772C2×C10111yescharacteristic, complemented
155#1387C2×C10111yescharacteristic, complemented
156#1376C2×C10111yescharacteristic, complemented
157C101#1313611yescharacteristic, direct product factor, Sylow
158C22×D8C22×C10111yescharacteristic
159C2×M32C22×C10111yescharacteristic
160C2×M32C22×C10111yescharacteristic
161C2×#108C22×C10111yescharacteristic
162#427C22×C10111yescharacteristic
163C2×#107C22×C10111yescharacteristic
164C2×#102—21no—
165#405—21no—
166C2×C4×C8C22×C10111yescharacteristic
167#390—21no—
168#367—21no—
169#366—21no—
170#361C4×C10114yescomplemented
171#357—21no—
172#357—21no—
173#339—21no—
174C22×D4—21no—
175C2×D8—21no—
176C2×D8—21no—
177C2×D8—21no—
178C2×D8—21no—
179C2×D8—21no—
180C2×D8C2×C4×C10112yes—
181C2×M16—21no—
182C22×C8D4×C10111yescharacteristic
183C22×C8C23×C10111yescharacteristic
184#117—21no—
185C2×C4⋊C4—21no—
186C2×C22⋊C4—42no—
187C2×C42D4×C10111yescharacteristic
188M32—21no—
189M32—21no—
190M32—21no—
191M32C2×C4×C10112yes—
192C2×C16—21no—
193C2×C16—21no—
194#108—21no—
195#108C2×C4×C10112yes—
196#107—21no—
197#107—21no—
198#107D4×C10111yescharacteristic
199#107D4×C10111yescharacteristic
200#106—21no—
201#102—41no—
202#102—41no—
203#97—41no—
204C4×C8—21no—
205C4×C8—21no—
206C4×C8—41no—
207C24—41no—
208C2×D4—22no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—41no—
214C22×C4—21no—
215C22×C4—41no—
216C22×C4C2×D4×C10111yescharacteristic
217D8—22no—
218D8—22no—
219D8—41no—
220D8—41no—
221M16—22no—
222M16—41no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—41no—
226C2×C8D8×C10111yescharacteristic
227C2×C8D8×C10111yescharacteristic
228C2×C8C22×C4×C10111yescharacteristic
229C2×C8C2×D4×C10111yescharacteristic
230C2×C8#41×C10111yescharacteristic
231C2×C8#41×C10111yescharacteristic
232C2×C8#41×C10111yescharacteristic
233C2×C8#41×C10111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—84no—
240C42—21no—
241C42—21no—
242C42—41no—
243C16—22no—
244C16—41no—
245C23—42no—
246C23—82no—
247C23—82no—
248C23—81no—
249C23—81no—
250C23AGL(1,ℤ/8)×C10111yescharacteristic
251D4—42no—
252D4—42no—
253D4—81no—
254D4—81no—
255C2×C4—22no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—82no—
261C2×C4—81no—
262C2×C4C4×D4×C10111yescharacteristic
263C2×C4#121×C10111yescharacteristic
264C2×C4#123×C10111yescharacteristic
265C2×C4C2×D8×C10111yescharacteristic
266C2×C4#135×C10111yescharacteristic
267C2×C4#137×C10111yescharacteristic
268C8—21no—
269C8—21no—
270C8—42no—
271C8#117×C10111yescharacteristic
272C8C4×D4×C10111yescharacteristic
273C8#124×C10111yescharacteristic
274C8#126×C10111yescharacteristic
275C22—21no—
276C22—21no—
277C22—84no—
278C22—82no—
279C22—162no—
280C22—161no—
281C22—161no—
282C22#440×C10111yescharacteristic
283C22#459×C10111yescharacteristic
284C22#482×C10111yescharacteristic
285C4—42no—
286C4—81no—
287C4—81no—
288C4—161no—
289C4#388×C10111yescharacteristic
290C4C4×D8×C10111yescharacteristic
291C4#464×C10111yescharacteristic
292C4#480×C10111yescharacteristic
293C2—21no—
294C2—21no—
295C2—162no—
296C2C101×#192511yescharacteristic
297C2C101×#221211yescharacteristic
298C2C101×#221311yescharacteristic
subgroupG/H
center, socleC22×C101#459
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
prime radicalC22×D8×C101C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×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×#2159C2semidirect
5. C101×#1772C2semidirect
6. C101×#1387C2semidirect
7. C101×#1376C2semidirect
20. #361×C101C4semidirect
143. #13136C101direct (N × H)
150. #2159C2×C101semidirect
154. #1772C2×C101semidirect
155. #1387C2×C101semidirect
156. #1376C2×C101semidirect
157. C101#13136direct (N × H)
170. #361C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#21592
C2×#361×C1012
C101×#21402
C101×#19702
C101×#17722
C101×#13872
C101×#13762
#13136101