Finite Group Databasebeta

← C101×#13122 #38795273

Subgroups — C101×#13122 #38795273

Order 25856.

326 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#364×C101C211yesmaximal, characteristic, complemented
2C2×#350×C101C211yesmaximal, characteristic
3C101×#2113C211yesmaximal, characteristic
4C101×#2108C211yesmaximal, characteristic, complemented
5C101×#1764C211yesmaximal, characteristic
6C101×#1379C211yesmaximal, characteristic, complemented
7C101×#1374C211yesmaximal, characteristic, complemented
8C2×#131×C101C2211yescharacteristic
9C2×M32×C101C2211yescharacteristic
10C2×M32×C101C2211yescharacteristic
11C22×C16×C101C2211yescharacteristic
12C22×C16×C101C2211yescharacteristic
13C2×#104×C101C411yescharacteristic
14#416×C101C411yescharacteristic
15#405×C101C2211yescharacteristic
16C2×C4×C8×C101C2211yescharacteristic
17#364×C101—22no—
18#350×C101—22no—
19C22⋊C16×C101—21no—
20C22⋊C16×C101—21no—
21#346×C101—21no—
22C4×C16×C101—21no—
23#341×C101C411yescharacteristic
24#339×C101C411yescharacteristic
25C2×#41×C101C2×C411yescharacteristic
26#131×C101—21no—
27#131×C101—21no—
28#131×C101—21no—
29#131×C101—21no—
30C2×M16×C101—21no—
31C2×M16×C101C2×C411yescharacteristic
32C2×M16×C101C2×C411yescharacteristic
33C22×C8×C101—21no—
34C22×C8×C101C2×C411yescharacteristic
35C22×C8×C101C2311yescharacteristic
36#117×C101C2×C411yescharacteristic
37C2×C42×C101C2×C411yescharacteristic
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×C101—21no—
48C2×C16×C101—21no—
49C2×C16×C101D411yescharacteristic
50C2×C16×C101D411yescharacteristic
51#104×C101—22no—
52#103×C101C811yescharacteristic
53#103×C101C811yescharacteristic
54#102×C101C811yescharacteristic
55#102×C101C811yescharacteristic
56#97×C101—21no—
57C4×C8×C101—21no—
58C4×C8×C101—21no—
59C4×C8×C101—21no—
60#41×C101—21no—
61#41×C101—21no—
62#41×C101—21no—
63#41×C101—21no—
64C2×Q8×C101C2×C811yescharacteristic
65C2×D4×C101—21no—
66C2×D4×C101C2×C811yescharacteristic
67C22×C4×C101—21no—
68C22×C4×C101—21no—
69C22×C4×C101C22×C411yescharacteristic
70M16×C101—21no—
71M16×C101—21no—
72M16×C101—21no—
73M16×C101—41no—
74M16×C101—41no—
75M16×C101M1612yes—
76C2×C8×C101—21no—
77C2×C8×C101—21no—
78C2×C8×C101—21no—
79C2×C8×C101—21no—
80C2×C8×C101—41no—
81C2×C8×C101—41no—
82C2×C8×C101C2×C811yescharacteristic
83C2×C8×C101C2×C811yescharacteristic
84C2×C8×C101C2×D411yescharacteristic
85C2×C8×C101C2×D411yescharacteristic
86C2×C8×C101#4111yescharacteristic
87C2×C8×C101#4111yescharacteristic
88C2×C8×C101#4111yescharacteristic
89C2×C8×C101#4111yescharacteristic
90C4⋊C4×C101C2×C811yescharacteristic
91C4⋊C4×C101C2×C811yescharacteristic
92C22⋊C4×C101—21no—
93C42×C101—21no—
94C42×C101—21no—
95C42×C101—21no—
96C16×C101—22no—
97C16×C101—21no—
98C16×C101—21no—
99C16×C101—41no—
100C16×C101—41no—
101C23×C101—21no—
102C23×C101#13111yescharacteristic
103Q8×C101—21no—
104Q8×C101—21no—
105D4×C101—21no—
106D4×C101—21no—
107D4×C101—41no—
108D4×C101—41no—
109C2×C4×C101—22no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—41no—
114C2×C4×C101—41no—
115C2×C4×C101—41no—
116C2×C4×C101—41no—
117C2×C4×C101#11711yescharacteristic
118C2×C4×C101C4×D411yescharacteristic
119C2×C4×C101C4×D411yescharacteristic
120C2×C4×C101C22×C811yescharacteristic
121C2×C4×C101C2×M1611yescharacteristic
122C2×C4×C101#13111yescharacteristic
123C8×C101—21no—
124C8×C101—21no—
125C8×C101—22no—
126C8×C101—41no—
127C8×C101#12111yescharacteristic
128C8×C101#12311yescharacteristic
129C8×C101#12411yescharacteristic
130C8×C101#12611yescharacteristic
131C22×C101—21no—
132C22×C101—21no—
133C22×C101—41no—
134C22×C101—41no—
135C22×C101—41no—
136C22×C101#43311yescharacteristic
137C22×C101C8×D411yescharacteristic
138C22×C101#43611yescharacteristic
139C4×C101—42no—
140C4×C101—41no—
141C4×C101—41no—
142C4×C101—41no—
143C4×C101#38811yescharacteristic
144C4×C101#43111yescharacteristic
145C4×C101C8×D411yescharacteristic
146C4×C101#43511yescharacteristic
147#13122C10111yesmaximal, characteristic, direct product factor, Sylow
148C2×C101—21no—
149C2×C101—21no—
150C2×C101—81no—
151C2×C101#192311yescharacteristic
152C2×C101#217011yescharacteristic
153C2×C101#217111yescharacteristic
154C2×#364C2×C10111yescharacteristic, complemented
155C2×#350C2×C10111yescharacteristic
156#2113C2×C10111yescharacteristic
157#2108C2×C10111yescharacteristic, complemented
158#1764C2×C10111yescharacteristic
159#1379C2×C10111yescharacteristic, complemented
160#1374C2×C10111yescharacteristic, complemented
161C101#1312211yescharacteristic, direct product factor, Sylow
162C2×#131C22×C10111yescharacteristic
163C2×M32C22×C10111yescharacteristic
164C2×M32C22×C10111yescharacteristic
165C22×C16C22×C10111yescharacteristic
166C22×C16C22×C10111yescharacteristic
167C2×#104C4×C10111yescharacteristic
168#416C4×C10111yescharacteristic
169#405C22×C10111yescharacteristic
170C2×C4×C8C22×C10111yescharacteristic
171#364—22no—
172#350—22no—
173C22⋊C16—21no—
174C22⋊C16—21no—
175#346—21no—
176C4×C16—21no—
177#341C4×C10111yescharacteristic
178#339C4×C10111yescharacteristic
179C2×#41C2×C4×C10111yescharacteristic
180#131—21no—
181#131—21no—
182#131—21no—
183#131—21no—
184C2×M16—21no—
185C2×M16C2×C4×C10111yescharacteristic
186C2×M16C2×C4×C10111yescharacteristic
187C22×C8—21no—
188C22×C8C2×C4×C10111yescharacteristic
189C22×C8C23×C10111yescharacteristic
190#117C2×C4×C10111yescharacteristic
191C2×C42C2×C4×C10111yescharacteristic
192M32—21no—
193M32—21no—
194M32—21no—
195M32D4×C10112yes—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—21no—
199C2×C16—21no—
200C2×C16—21no—
201C2×C16—21no—
202C2×C16—21no—
203C2×C16D4×C10111yescharacteristic
204C2×C16D4×C10111yescharacteristic
205#104—22no—
206#103C8×C10111yescharacteristic
207#103C8×C10111yescharacteristic
208#102C8×C10111yescharacteristic
209#102C8×C10111yescharacteristic
210#97—21no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—21no—
214#41—21no—
215#41—21no—
216#41—21no—
217#41—21no—
218C2×Q8C2×C8×C10111yescharacteristic
219C2×D4—21no—
220C2×D4C2×C8×C10111yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4C22×C4×C10111yescharacteristic
224M16—21no—
225M16—21no—
226M16—21no—
227M16—41no—
228M16—41no—
229M16M16×C10112yes—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8C2×C8×C10111yescharacteristic
237C2×C8C2×C8×C10111yescharacteristic
238C2×C8C2×D4×C10111yescharacteristic
239C2×C8C2×D4×C10111yescharacteristic
240C2×C8#41×C10111yescharacteristic
241C2×C8#41×C10111yescharacteristic
242C2×C8#41×C10111yescharacteristic
243C2×C8#41×C10111yescharacteristic
244C4⋊C4C2×C8×C10111yescharacteristic
245C4⋊C4C2×C8×C10111yescharacteristic
246C22⋊C4—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C16—22no—
251C16—21no—
252C16—21no—
253C16—41no—
254C16—41no—
255C23—21no—
256C23#131×C10111yescharacteristic
257Q8—21no—
258Q8—21no—
259D4—21no—
260D4—21no—
261D4—41no—
262D4—41no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4#117×C10111yescharacteristic
272C2×C4C4×D4×C10111yescharacteristic
273C2×C4C4×D4×C10111yescharacteristic
274C2×C4C22×C8×C10111yescharacteristic
275C2×C4C2×M16×C10111yescharacteristic
276C2×C4#131×C10111yescharacteristic
277C8—21no—
278C8—21no—
279C8—22no—
280C8—41no—
281C8#121×C10111yescharacteristic
282C8#123×C10111yescharacteristic
283C8#124×C10111yescharacteristic
284C8#126×C10111yescharacteristic
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22#433×C10111yescharacteristic
291C22C8×D4×C10111yescharacteristic
292C22#436×C10111yescharacteristic
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4#388×C10111yescharacteristic
298C4#431×C10111yescharacteristic
299C4C8×D4×C10111yescharacteristic
300C4#435×C10111yescharacteristic
301C2—21no—
302C2—21no—
303C2—81no—
304C2C101×#192311yescharacteristic
305C2C101×#217011yescharacteristic
306C2C101×#217111yescharacteristic
subgroupG/H
centerC2×C8×C101C2×D4
commutatorC2×C4C22×C8×C101
Frattini, cosocleC22×C8C23×C101
socleC22×C101C8×D4
prime radicalC2×#41×C101C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8×C101 ◁ C22×C16×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#364×C101C2semidirect
4. C101×#2108C2semidirect
6. C101×#1379C2semidirect
7. C101×#1374C2semidirect
147. #13122C101direct (N × H)
154. C2×#364C2×C101semidirect
157. #2108C2×C101semidirect
159. #1379C2×C101semidirect
160. #1374C2×C101semidirect
161. C101#13122direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#364×C1012
C2×#350×C1012
C101×#21132
C101×#21082
C101×#17642
C101×#13792
C101×#13742
#13122101