Finite Group Databasebeta

← C101×#9026 #38791177

Subgroups — C101×#9026 #38791177

Order 25856.

616 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C101C211yesmaximal, characteristic
2C101×#2313C211yesmaximal, characteristic
3C101×#1823C212yesmaximal
4C2×#324×C101C211yesmaximal, characteristic
5C101×#1294C212yesmaximal
6C22×C4⋊C4×C101—21no—
7C22×C4⋊C4×C101C2211yescharacteristic
8C22×C4⋊C4×C101C2211yescharacteristic
9C2×C22⋊C8×C101C2212yes—
10#398×C101—22no—
11#398×C101C414yescomplemented
12#387×C101—24no—
13#381×C101—21no—
14#380×C101C2212yes—
15C4×C22⋊C4×C101—21no—
16C2×#95×C101—21no—
17C2×#95×C101C2211yescharacteristic
18#340×C101—24no—
19#324×C101—22no—
20C23×C4×C101—21no—
21C23×C4×C101—21no—
22C23×C4×C101D411yescharacteristic
23C23×C4×C101D411yescharacteristic
24C23×C4×C101C2311yescharacteristic
25C22×C8×C101—22no—
26C2×C4⋊C4×C101—22no—
27C2×C4⋊C4×C101—22no—
28C2×C4⋊C4×C101—22no—
29C2×C4⋊C4×C101—22no—
30C2×C4⋊C4×C101—24no—
31C2×C4⋊C4×C101—21no—
32C2×C4⋊C4×C101—44no—
33C2×C4⋊C4×C101C2×C412yes—
34C2×C4⋊C4×C101C2×C412yes—
35C2×C4⋊C4×C101D412yes—
36C2×C4⋊C4×C101D414yes—
37C2×C22⋊C4×C101—22no—
38C2×C42×C101—22no—
39C22⋊C8×C101—22no—
40C22⋊C8×C101—22no—
41#95×C101—22no—
42#95×C101—24no—
43#95×C101—24no—
44#95×C101—21no—
45#95×C101—22no—
46#95×C101C2×C412yes—
47C24×C101C2×D411yescharacteristic
48C22×C4×C101—24no—
49C22×C4×C101—22no—
50C22×C4×C101—21no—
51C22×C4×C101—21no—
52C22×C4×C101—21no—
53C22×C4×C101—22no—
54C22×C4×C101—22no—
55C22×C4×C101—21no—
56C22×C4×C101—22no—
57C22×C4×C101—24no—
58C22×C4×C101—42no—
59C22×C4×C101—42no—
60C22×C4×C101—42no—
61C22×C4×C101—42no—
62C22×C4×C101—41no—
63C22×C4×C101—41no—
64C22×C4×C101—42no—
65C22×C4×C101—42no—
66C22×C4×C101C22⋊C412yes—
67C22×C4×C101C22⋊C412yes—
68C22×C4×C101C22×C411yescharacteristic
69C22×C4×C101C2×D412yes—
70C22×C4×C101C2×D411yescharacteristic
71C22×C4×C101#4112yes—
72C2×C8×C101—44no—
73C2×C8×C101—42no—
74C4⋊C4×C101—24no—
75C4⋊C4×C101—24no—
76C4⋊C4×C101—24no—
77C4⋊C4×C101—44no—
78C4⋊C4×C101—48no—
79C4⋊C4×C101—42no—
80C22⋊C4×C101—42no—
81C22⋊C4×C101—42no—
82C42×C101—82no—
83C23×C101—22no—
84C23×C101—22no—
85C23×C101C2×C22⋊C411yescharacteristic
86C23×C101#12011yescharacteristic
87C23×C101#12311yescharacteristic
88C23×C101#13512yes—
89C23×C101AGL(1,ℤ/8)12yes—
90C2×C4×C101—24no—
91C2×C4×C101—24no—
92C2×C4×C101—22no—
93C2×C4×C101—22no—
94C2×C4×C101—22no—
95C2×C4×C101—22no—
96C2×C4×C101—41no—
97C2×C4×C101—41no—
98C2×C4×C101—42no—
99C2×C4×C101—48no—
100C2×C4×C101—42no—
101C2×C4×C101—42no—
102C2×C4×C101—42no—
103C2×C4×C101—42no—
104C2×C4×C101—42no—
105C2×C4×C101—42no—
106C2×C4×C101—42no—
107C2×C4×C101—42no—
108C2×C4×C101—42no—
109C2×C4×C101—44no—
110C2×C4×C101—44no—
111C2×C4×C101—44no—
112C2×C4×C101—81no—
113C2×C4×C101—82no—
114C2×C4×C101—82no—
115C2×C4×C101C4×D412yes—
116C2×C4×C101#12112yes—
117C8×C101—82no—
118C22×C101—24no—
119C22×C101—24no—
120C22×C101—21no—
121C22×C101—21no—
122C22×C101—21no—
123C22×C101—21no—
124C22×C101#38611yescharacteristic
125C22×C101#41611yescharacteristic
126C22×C101#41811yescharacteristic
127C22×C101#44912yes—
128C22×C101#45612yes—
129C22×C101#45812yes—
130C22×C101#48212yes—
131C4×C101—22no—
132C4×C101—22no—
133C4×C101—44no—
134C4×C101—42no—
135C4×C101—42no—
136C4×C101—84no—
137C4×C101—82no—
138#9026C10111yesmaximal, characteristic, direct product factor, Sylow
139C2×C101—21no—
140C2×C101—21no—
141C2×C101—22no—
142C2×C101#160914yes—
143C2×C101#187511yescharacteristic
144C2×C101#188611yescharacteristic
145C2×C101#189011yescharacteristic
146C2×#398C2×C10111yescharacteristic
147#2313C2×C10111yescharacteristic
148#1823C2×C10112yes—
149C2×#324C2×C10111yescharacteristic
150#1294C2×C10112yes—
151C101#902611yescharacteristic, direct product factor, Sylow
152C22×C4⋊C4—21no—
153C22×C4⋊C4C22×C10111yescharacteristic
154C22×C4⋊C4C22×C10111yescharacteristic
155C2×C22⋊C8C22×C10112yes—
156#398—22no—
157#398C4×C10114yescomplemented
158#387—24no—
159#381—21no—
160#380C22×C10112yes—
161C4×C22⋊C4—21no—
162C2×#95—21no—
163C2×#95C22×C10111yescharacteristic
164#340—24no—
165#324—22no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4D4×C10111yescharacteristic
169C23×C4D4×C10111yescharacteristic
170C23×C4C23×C10111yescharacteristic
171C22×C8—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—44no—
179C2×C4⋊C4C2×C4×C10112yes—
180C2×C4⋊C4C2×C4×C10112yes—
181C2×C4⋊C4D4×C10112yes—
182C2×C4⋊C4D4×C10114yes—
183C2×C22⋊C4—22no—
184C2×C42—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187#95—22no—
188#95—24no—
189#95—24no—
190#95—21no—
191#95—22no—
192#95C2×C4×C10112yes—
193C24C2×D4×C10111yescharacteristic
194C22×C4—24no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—24no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4C22⋊C4×C10112yes—
213C22×C4C22⋊C4×C10112yes—
214C22×C4C22×C4×C10111yescharacteristic
215C22×C4C2×D4×C10112yes—
216C22×C4C2×D4×C10111yescharacteristic
217C22×C4#41×C10112yes—
218C2×C8—44no—
219C2×C8—42no—
220C4⋊C4—24no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—44no—
224C4⋊C4—48no—
225C4⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C42—82no—
229C23—22no—
230C23—22no—
231C23C2×C22⋊C4×C10111yescharacteristic
232C23#120×C10111yescharacteristic
233C23#123×C10111yescharacteristic
234C23#135×C10112yes—
235C23AGL(1,ℤ/8)×C10112yes—
236C2×C4—24no—
237C2×C4—24no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—48no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4C4×D4×C10112yes—
262C2×C4#121×C10112yes—
263C8—82no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—24no—
269C22—24no—
270C22#386×C10111yescharacteristic
271C22#416×C10111yescharacteristic
272C22#418×C10111yescharacteristic
273C22#449×C10112yes—
274C22#456×C10112yes—
275C22#458×C10112yes—
276C22#482×C10112yes—
277C4—22no—
278C4—22no—
279C4—44no—
280C4—42no—
281C4—42no—
282C4—84no—
283C4—82no—
284C2—21no—
285C2—21no—
286C2—22no—
287C2C101×#160914yes—
288C2C101×#187511yescharacteristic
289C2C101×#188611yescharacteristic
290C2C101×#189011yescharacteristic
subgroupG/H
center, socleC23×C101#120
commutatorC22×C4C22×C4×C101
Frattini, cosocleC23×C4C23×C101
prime radicalC24×C101C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
11. #398×C101C4semidirect
138. #9026C101direct (N × H)
151. C101#9026direct (N × H)
157. #398C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1012
C101×#23132
C101×#18232
C2×#324×C1012
C101×#12942
#9026101