Finite Group Databasebeta

← C101×#7402 #38789553

Subgroups — C101×#7402 #38789553

Order 25856.

334 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C101×#2011C211yesmaximal, characteristic
2C101×#1393C211yesmaximal, characteristic, complemented
3C101×#1318C211yesmaximal, characteristic, complemented
4C22×D8×C101—21no—
5C2×#127×C101C411yescharacteristic, complemented
6C2×#102×C101—21no—
7C2×#99×C101—21no—
8#390×C101C2211yescharacteristic
9#336×C101C411yescharacteristic, complemented
10#324×C101—21no—
11C22×D4×C101—21no—
12C22×D4×C101—41no—
13C22×D4×C101D411yescharacteristic
14C2×D8×C101—42no—
15C2×D8×C101—42no—
16C2×D8×C101—41no—
17C2×D8×C101—41no—
18C22×C8×C101—21no—
19#127×C101—42no—
20C2×C4⋊C4×C101D411yescharacteristic
21C2×C22⋊C4×C101—41no—
22C2×C22⋊C4×C101—41no—
23C2×C42×C101C2×C411yescharacteristic
24#102×C101—42no—
25#99×C101—22no—
26#99×C101—41no—
27C22⋊C8×C101—41no—
28C24×C101—21no—
29C24×C101—41no—
30C2×D4×C101—22no—
31C2×D4×C101—21no—
32C2×D4×C101—41no—
33C2×D4×C101—41no—
34C2×D4×C101—41no—
35C2×D4×C101—41no—
36C2×D4×C101—41no—
37C2×D4×C101—42no—
38C2×D4×C101—42no—
39C2×D4×C101—41no—
40C2×D4×C101—41no—
41C2×D4×C101—82no—
42C2×D4×C101—82no—
43C2×D4×C101D811yescharacteristic
44C2×D4×C101SD1611yescharacteristic
45C22×C4×C101—21no—
46C22×C4×C101—21no—
47C22×C4×C101—81no—
48C22×C4×C101C22⋊C411yescharacteristic
49D8×C101—44no—
50D8×C101—44no—
51C2×C8×C101—22no—
52C2×C8×C101—41no—
53C2×C8×C101—41no—
54C2×C8×C101—81no—
55C4⋊C4×C101—41no—
56C22⋊C4×C101—42no—
57C22⋊C4×C101—82no—
58C22⋊C4×C101—81no—
59C42×C101—41no—
60C23×C101—21no—
61C23×C101—21no—
62C23×C101—41no—
63C23×C101—41no—
64C23×C101—42no—
65C23×C101—81no—
66C23×C101—81no—
67C23×C101—82no—
68C23×C101—82no—
69C23×C101—81no—
70C23×C101—81no—
71C23×C101#9911yescharacteristic
72D4×C101—41no—
73D4×C101—41no—
74D4×C101—42no—
75D4×C101—42no—
76D4×C101—81no—
77D4×C101—81no—
78D4×C101—81no—
79D4×C101—84no—
80D4×C101—84no—
81C2×C4×C101—21no—
82C2×C4×C101—21no—
83C2×C4×C101—22no—
84C2×C4×C101—41no—
85C2×C4×C101—41no—
86C2×C4×C101—41no—
87C2×C4×C101—81no—
88C2×C4×C101—82no—
89C2×C4×C101—161no—
90C2×C4×C101—161no—
91C2×C4×C101#10211yescharacteristic
92C2×C4×C101#10411yescharacteristic
93C8×C101—42no—
94C8×C101—161no—
95C22×C101—21no—
96C22×C101—21no—
97C22×C101—41no—
98C22×C101—41no—
99C22×C101—81no—
100C22×C101—81no—
101C22×C101—84no—
102C22×C101—81no—
103C22×C101—81no—
104C22×C101—82no—
105C22×C101—161no—
106C22×C101—162no—
107C22×C101—161no—
108C22×C101—161no—
109C22×C101#32711yescharacteristic
110C22×C101AΣL(1,𝔽16)11yescharacteristic
111C22×C101#35311yescharacteristic
112C4×C101—21no—
113C4×C101—21no—
114C4×C101—42no—
115C4×C101—81no—
116C4×C101—162no—
117#7402C10111yesmaximal, characteristic, direct product factor, Sylow
118C2×C101—21no—
119C2×C101—21no—
120C2×C101—81no—
121C2×C101—81no—
122C2×C101—162no—
123C2×C101#134311yescharacteristic
124C2×C101#140611yescharacteristic
125C2×C101#140811yescharacteristic
126#2011C2×C10111yescharacteristic
127#1393C2×C10111yescharacteristic, complemented
128#1318C2×C10111yescharacteristic, complemented
129C101#740211yescharacteristic, direct product factor, Sylow
130C22×D8—21no—
131C2×#127C4×C10111yescharacteristic, complemented
132C2×#102—21no—
133C2×#99—21no—
134#390C22×C10111yescharacteristic
135#336C4×C10111yescharacteristic, complemented
136#324—21no—
137C22×D4—21no—
138C22×D4—41no—
139C22×D4D4×C10111yescharacteristic
140C2×D8—42no—
141C2×D8—42no—
142C2×D8—41no—
143C2×D8—41no—
144C22×C8—21no—
145#127—42no—
146C2×C4⋊C4D4×C10111yescharacteristic
147C2×C22⋊C4—41no—
148C2×C22⋊C4—41no—
149C2×C42C2×C4×C10111yescharacteristic
150#102—42no—
151#99—22no—
152#99—41no—
153C22⋊C8—41no—
154C24—21no—
155C24—41no—
156C2×D4—22no—
157C2×D4—21no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—42no—
164C2×D4—42no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—82no—
168C2×D4—82no—
169C2×D4D8×C10111yescharacteristic
170C2×D4SD16×C10111yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—81no—
174C22×C4C22⋊C4×C10111yescharacteristic
175D8—44no—
176D8—44no—
177C2×C8—22no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—81no—
181C4⋊C4—41no—
182C22⋊C4—42no—
183C22⋊C4—82no—
184C22⋊C4—81no—
185C42—41no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—41no—
190C23—42no—
191C23—81no—
192C23—81no—
193C23—82no—
194C23—82no—
195C23—81no—
196C23—81no—
197C23#99×C10111yescharacteristic
198D4—41no—
199D4—41no—
200D4—42no—
201D4—42no—
202D4—81no—
203D4—81no—
204D4—81no—
205D4—84no—
206D4—84no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—81no—
214C2×C4—82no—
215C2×C4—161no—
216C2×C4—161no—
217C2×C4#102×C10111yescharacteristic
218C2×C4#104×C10111yescharacteristic
219C8—42no—
220C8—161no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22—84no—
228C22—81no—
229C22—81no—
230C22—82no—
231C22—161no—
232C22—162no—
233C22—161no—
234C22—161no—
235C22#327×C10111yescharacteristic
236C22AΣL(1,𝔽16)×C10111yescharacteristic
237C22#353×C10111yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—81no—
242C4—162no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—81no—
247C2—162no—
248C2C101×#134311yescharacteristic
249C2C101×#140611yescharacteristic
250C2C101×#140811yescharacteristic
subgroupG/H
center, socleC22×C101#353
commutatorC2×C42C2×C4×C101
Frattini, cosocle#390C22×C101
prime radicalC101×#2011C2
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C101 ◁ C22×C4×C101 ◁ #390×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#1393C2semidirect
3. C101×#1318C2semidirect
5. C2×#127×C101C4semidirect
9. #336×C101C4semidirect
117. #7402C101direct (N × H)
127. #1393C2×C101semidirect
128. #1318C2×C101semidirect
129. C101#7402direct (N × H)
131. C2×#127C4×C101semidirect
135. #336C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#20112
C101×#13932
C101×#13182
#7402101