Finite Group Databasebeta

← C101×#9022 #38791173

Subgroups — C101×#9022 #38791173

Order 25856.

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

normal subgroups only

This group has 572 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×#400×C101C211yesmaximal, characteristic
2C101×#2313C211yesmaximal, characteristic
3C101×#1824C212yesmaximal
4C2×#324×C101C211yesmaximal, characteristic
5C101×#1294C212yesmaximal
6C22×C4⋊C4×C101C2211yescharacteristic
7C22×C4⋊C4×C101C2211yescharacteristic
8C2×C22⋊C8×C101C2212yes—
9#400×C101—22no—
10#400×C101C414yescomplemented
11#387×C101—24no—
12#381×C101—21no—
13#380×C101C2212yes—
14C4×C22⋊C4×C101—21no—
15C2×#95×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—21no—
31C2×C4⋊C4×C101C2×C412yes—
32C2×C4⋊C4×C101C2×C412yes—
33C2×C4⋊C4×C101D412yes—
34C2×C4⋊C4×C101D414yes—
35C2×C22⋊C4×C101—22no—
36C2×C42×C101—22no—
37C22⋊C8×C101—22no—
38C22⋊C8×C101—22no—
39#95×C101—22no—
40#95×C101—24no—
41#95×C101—24no—
42#95×C101—24no—
43#95×C101—21no—
44#95×C101—22no—
45#95×C101C2×C412yes—
46C24×C101C2×D411yescharacteristic
47C22×C4×C101—21no—
48C22×C4×C101—21no—
49C22×C4×C101—21no—
50C22×C4×C101—22no—
51C22×C4×C101—22no—
52C22×C4×C101—21no—
53C22×C4×C101—22no—
54C22×C4×C101—22no—
55C22×C4×C101—24no—
56C22×C4×C101—42no—
57C22×C4×C101—42no—
58C22×C4×C101—42no—
59C22×C4×C101—42no—
60C22×C4×C101—44no—
61C22×C4×C101—41no—
62C22×C4×C101—41no—
63C22×C4×C101—42no—
64C22×C4×C101C22⋊C412yes—
65C22×C4×C101C22⋊C412yes—
66C22×C4×C101C22×C411yescharacteristic
67C22×C4×C101C2×D412yes—
68C22×C4×C101C2×D411yescharacteristic
69C22×C4×C101#4112yes—
70C2×C8×C101—44no—
71C2×C8×C101—42no—
72C4⋊C4×C101—24no—
73C4⋊C4×C101—24no—
74C4⋊C4×C101—24no—
75C4⋊C4×C101—44no—
76C4⋊C4×C101—42no—
77C22⋊C4×C101—42no—
78C22⋊C4×C101—42no—
79C42×C101—82no—
80C23×C101—22no—
81C23×C101—22no—
82C23×C101C2×C22⋊C411yescharacteristic
83C23×C101#12011yescharacteristic
84C23×C101#12311yescharacteristic
85C23×C101#13512yes—
86C23×C101#13712yes—
87C2×C4×C101—24no—
88C2×C4×C101—22no—
89C2×C4×C101—22no—
90C2×C4×C101—22no—
91C2×C4×C101—22no—
92C2×C4×C101—41no—
93C2×C4×C101—41no—
94C2×C4×C101—42no—
95C2×C4×C101—42no—
96C2×C4×C101—42no—
97C2×C4×C101—42no—
98C2×C4×C101—42no—
99C2×C4×C101—42no—
100C2×C4×C101—42no—
101C2×C4×C101—44no—
102C2×C4×C101—42no—
103C2×C4×C101—42no—
104C2×C4×C101—44no—
105C2×C4×C101—44no—
106C2×C4×C101—44no—
107C2×C4×C101—81no—
108C2×C4×C101—84no—
109C2×C4×C101—82no—
110C2×C4×C101—82no—
111C2×C4×C101C4×D412yes—
112C2×C4×C101#12112yes—
113C8×C101—82no—
114C22×C101—24no—
115C22×C101—24no—
116C22×C101—21no—
117C22×C101—21no—
118C22×C101—21no—
119C22×C101—21no—
120C22×C101#38611yescharacteristic
121C22×C101#41611yescharacteristic
122C22×C101#41911yescharacteristic
123C22×C101#45212yes—
124C22×C101#45412yes—
125C22×C101#45812yes—
126C22×C101#48512yes—
127C4×C101—22no—
128C4×C101—22no—
129C4×C101—42no—
130C4×C101—42no—
131C4×C101—82no—
132C4×C101—84no—
133C4×C101—82no—
134#9022C10111yesmaximal, characteristic, direct product factor, Sylow
135C2×C101—21no—
136C2×C101—21no—
137C2×C101—22no—
138C2×C101#161514yes—
139C2×C101#187311yescharacteristic
140C2×C101#188811yescharacteristic
141C2×C101#189011yescharacteristic
142C2×#400C2×C10111yescharacteristic
143#2313C2×C10111yescharacteristic
144#1824C2×C10112yes—
145C2×#324C2×C10111yescharacteristic
146#1294C2×C10112yes—
147C101#902211yescharacteristic, direct product factor, Sylow
148C22×C4⋊C4C22×C10111yescharacteristic
149C22×C4⋊C4C22×C10111yescharacteristic
150C2×C22⋊C8C22×C10112yes—
151#400—22no—
152#400C4×C10114yescomplemented
153#387—24no—
154#381—21no—
155#380C22×C10112yes—
156C4×C22⋊C4—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95C22×C10111yescharacteristic
160#340—24no—
161#324—22no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4D4×C10111yescharacteristic
165C23×C4D4×C10111yescharacteristic
166C23×C4C23×C10111yescharacteristic
167C22×C8—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C2×C4×C10112yes—
174C2×C4⋊C4C2×C4×C10112yes—
175C2×C4⋊C4D4×C10112yes—
176C2×C4⋊C4D4×C10114yes—
177C2×C22⋊C4—22no—
178C2×C42—22no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181#95—22no—
182#95—24no—
183#95—24no—
184#95—24no—
185#95—21no—
186#95—22no—
187#95C2×C4×C10112yes—
188C24C2×D4×C10111yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—24no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—44no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—42no—
206C22×C4C22⋊C4×C10112yes—
207C22×C4C22⋊C4×C10112yes—
208C22×C4C22×C4×C10111yescharacteristic
209C22×C4C2×D4×C10112yes—
210C22×C4C2×D4×C10111yescharacteristic
211C22×C4#41×C10112yes—
212C2×C8—44no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—44no—
218C4⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C42—82no—
222C23—22no—
223C23—22no—
224C23C2×C22⋊C4×C10111yescharacteristic
225C23#120×C10111yescharacteristic
226C23#123×C10111yescharacteristic
227C23#135×C10112yes—
228C23#137×C10112yes—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—44no—
247C2×C4—44no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—84no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4C4×D4×C10112yes—
254C2×C4#121×C10112yes—
255C8—82no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—24no—
261C22—24no—
262C22#386×C10111yescharacteristic
263C22#416×C10111yescharacteristic
264C22#419×C10111yescharacteristic
265C22#452×C10112yes—
266C22#454×C10112yes—
267C22#458×C10112yes—
268C22#485×C10112yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—82no—
274C4—82no—
275C4—84no—
276C2—21no—
277C2—21no—
278C2—22no—
279C2C101×#161514yes—
280C2C101×#187311yescharacteristic
281C2C101×#188811yescharacteristic
282C2C101×#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
10. #400×C101C4semidirect
134. #9022C101direct (N × H)
147. C101#9022direct (N × H)
152. #400C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#400×C1012
C101×#23132
C101×#18242
C2×#324×C1012
C101×#12942
#9022101