Finite Group Databasebeta

← C101×#7326 #38789477

Subgroups — C101×#7326 #38789477

Order 25856.

374 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 78 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×#1463C212yesmaximal
2C101×#1445C211yesmaximal, characteristic
3C22×C4⋊C4×C101C2211yescharacteristic
4#407×C101—22no—
5C2×#95×C101—22no—
6C2×#95×C101C411yescharacteristic
7C2×#95×C101C411yescharacteristic
8#324×C101—22no—
9#324×C101C414yescomplemented
10C23×C4×C101—21no—
11C23×C4×C101—21no—
12C23×C4×C101C2×C411yescharacteristic
13C23×C4×C101D412yes—
14C2×M16×C101—42no—
15C2×C4⋊C4×C101—41no—
16C2×C4⋊C4×C101—41no—
17C2×C4⋊C4×C101C2×C412yes—
18C2×C4⋊C4×C101D411yescharacteristic
19C2×C4⋊C4×C101Q811yescharacteristic
20C22⋊C8×C101—24no—
21C22⋊C8×C101—42no—
22#95×C101—44no—
23#95×C101—41no—
24#95×C101—41no—
25C24×C101C22⋊C411yescharacteristic
26C22×C4×C101—21no—
27C22×C4×C101—21no—
28C22×C4×C101—22no—
29C22×C4×C101—22no—
30C22×C4×C101—22no—
31C22×C4×C101—22no—
32C22×C4×C101—42no—
33C22×C4×C101—42no—
34C22×C4×C101—42no—
35C22×C4×C101—42no—
36C22×C4×C101—42no—
37C22×C4×C101—42no—
38C22×C4×C101—41no—
39C22×C4×C101—41no—
40C22×C4×C101—42no—
41C22×C4×C101—41no—
42C22×C4×C101—41no—
43C22×C4×C101C4211yescharacteristic
44C22×C4×C101C22⋊C412yes—
45C22×C4×C101C4⋊C411yescharacteristic
46C22×C4×C101C4⋊C412yes—
47M16×C101—82no—
48M16×C101—82no—
49C2×C8×C101—44no—
50C4⋊C4×C101—42no—
51C4⋊C4×C101—41no—
52C4⋊C4×C101—41no—
53C23×C101—22no—
54C23×C101—21no—
55C23×C101—21no—
56C23×C101—21no—
57C23×C101—21no—
58C23×C101#9511yescharacteristic
59C23×C101#9911yescharacteristic
60C23×C101#9911yescharacteristic
61C2×C4×C101—22no—
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101—22no—
65C2×C4×C101—22no—
66C2×C4×C101—22no—
67C2×C4×C101—42no—
68C2×C4×C101—42no—
69C2×C4×C101—42no—
70C2×C4×C101—42no—
71C2×C4×C101—42no—
72C2×C4×C101—42no—
73C2×C4×C101—44no—
74C2×C4×C101—44no—
75C2×C4×C101—42no—
76C2×C4×C101—42no—
77C2×C4×C101—82no—
78C2×C4×C101—82no—
79C2×C4×C101—82no—
80C2×C4×C101—81no—
81C2×C4×C101—81no—
82C2×C4×C101—81no—
83C2×C4×C101—81no—
84C8×C101—84no—
85C22×C101—22no—
86C22×C101—22no—
87C22×C101—22no—
88C22×C101—22no—
89C22×C101—21no—
90C22×C101—21no—
91C22×C101—21no—
92C22×C101—21no—
93C22×C101—21no—
94C22×C101—21no—
95C22×C101#34211yescharacteristic
96C22×C101#34412yes—
97C22×C101#35311yescharacteristic
98C22×C101#35411yescharacteristic
99C22×C101#35511yescharacteristic
100C22×C101#35611yescharacteristic
101C4×C101—41no—
102C4×C101—41no—
103C4×C101—42no—
104C4×C101—42no—
105C4×C101—82no—
106C4×C101—82no—
107#7326C10111yesmaximal, characteristic, direct product factor, Sylow
108C2×C101—21no—
109C2×C101—21no—
110C2×C101—22no—
111C2×C101—21no—
112C2×C101—21no—
113C2×C101#130611yescharacteristic
114C2×C101#139311yescharacteristic
115C2×C101#139411yescharacteristic
116#1463C2×C10112yes—
117#1445C2×C10111yescharacteristic
118C101#732611yescharacteristic, direct product factor, Sylow
119C22×C4⋊C4C22×C10111yescharacteristic
120#407—22no—
121C2×#95—22no—
122C2×#95C4×C10111yescharacteristic
123C2×#95C4×C10111yescharacteristic
124#324—22no—
125#324C4×C10114yescomplemented
126C23×C4—21no—
127C23×C4—21no—
128C23×C4C2×C4×C10111yescharacteristic
129C23×C4D4×C10112yes—
130C2×M16—42no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4C2×C4×C10112yes—
134C2×C4⋊C4D4×C10111yescharacteristic
135C2×C4⋊C4Q8×C10111yescharacteristic
136C22⋊C8—24no—
137C22⋊C8—42no—
138#95—41no—
139#95—41no—
140#95—44no—
141C24C22⋊C4×C10111yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—42no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4C42×C10111yescharacteristic
160C22×C4C22⋊C4×C10112yes—
161C22×C4C4⋊C4×C10111yescharacteristic
162C22×C4C4⋊C4×C10112yes—
163M16—82no—
164M16—82no—
165C2×C8—44no—
166C4⋊C4—42no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C23—22no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23#95×C10111yescharacteristic
175C23#99×C10111yescharacteristic
176C23#99×C10111yescharacteristic
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—44no—
190C2×C4—44no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C8—84no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#342×C10111yescharacteristic
212C22#344×C10112yes—
213C22#353×C10111yescharacteristic
214C22#354×C10111yescharacteristic
215C22#355×C10111yescharacteristic
216C22#356×C10111yescharacteristic
217C4—42no—
218C4—42no—
219C4—41no—
220C4—41no—
221C4—82no—
222C4—82no—
223C2—21no—
224C2—21no—
225C2—22no—
226C2—21no—
227C2—21no—
228C2C101×#130611yescharacteristic
229C2C101×#139311yescharacteristic
230C2C101×#139411yescharacteristic
subgroupG/H
center, socleC22×C101#342
commutatorC22×C4C42×C101
Frattini, cosocleC22×C4⋊C4C22×C101
prime radicalC24×C101C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C24×C101 ◁ C22×C4⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
9. #324×C101C4semidirect
107. #7326C101direct (N × H)
118. C101#7326direct (N × H)
125. #324C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#14632
C101×#14452
#7326101