Finite Group Databasebeta

← C101×#10429 #38792580

Subgroups — C101×#10429 #38792580

Order 25856.

402 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2822C211yesmaximal, characteristic
2C101×#1992C212yesmaximal
3C101×#1847C211yesmaximal, characteristic
4C2×#330×C101C212yesmaximal
5C101×#1295C211yesmaximal, characteristic
6C2×#125×C101C2212yes—
7C2×#107×C101—21no—
8C2×#106×C101—21no—
9C2×#97×C101C2212yes—
10C2×#97×C101C2211yescharacteristic
11#400×C101—22no—
12#398×C101—21no—
13#398×C101—21no—
14#398×C101—22no—
15#384×C101C2211yescharacteristic
16#382×C101C2211yescharacteristic
17#340×C101—22no—
18#340×C101—22no—
19#330×C101—24no—
20C22×C8×C101—21no—
21C22×C8×C101—22no—
22#125×C101—22no—
23#125×C101—22no—
24#125×C101—22no—
25#125×C101—22no—
26C2×C4⋊C4×C101—22no—
27C2×C4⋊C4×C101—22no—
28C2×C4⋊C4×C101—21no—
29C2×C4⋊C4×C101—22no—
30C2×C4⋊C4×C101—21no—
31C2×C4⋊C4×C101—21no—
32C2×C4⋊C4×C101D412yes—
33C2×C4⋊C4×C101D412yes—
34C2×C4⋊C4×C101D411yescharacteristic
35C2×C4⋊C4×C101D411yescharacteristic
36C2×C42×C101C2311yescharacteristic
37#107×C101—42no—
38#106×C101—42no—
39#97×C101—22no—
40#97×C101—21no—
41#97×C101—22no—
42#97×C101D412yes—
43#95×C101—22no—
44#95×C101—22no—
45#95×C101—21no—
46#95×C101—21no—
47#95×C101—22no—
48C22×C4×C101—21no—
49C22×C4×C101—21no—
50C22×C4×C101—22no—
51C22×C4×C101—22no—
52C22×C4×C101—41no—
53C22×C4×C101C2×D412yes—
54C22×C4×C101C2×D411yescharacteristic
55C2×C8×C101—22no—
56C2×C8×C101—22no—
57C2×C8×C101—22no—
58C2×C8×C101—24no—
59C2×C8×C101—42no—
60C2×C8×C101—42no—
61C4⋊C4×C101—22no—
62C4⋊C4×C101—22no—
63C4⋊C4×C101—22no—
64C4⋊C4×C101—22no—
65C4⋊C4×C101—41no—
66C4⋊C4×C101—41no—
67C4⋊C4×C101—41no—
68C4⋊C4×C101—41no—
69C4⋊C4×C101—44no—
70C4⋊C4×C101—42no—
71C4⋊C4×C101—42no—
72C4⋊C4×C101—42no—
73C4⋊C4×C101—42no—
74C4⋊C4×C101—81no—
75C4⋊C4×C101—81no—
76C42×C101C2×D411yescharacteristic
77C42×C101#4111yescharacteristic
78C42×C101#4112yes—
79C23×C101#12011yescharacteristic
80C2×C4×C101—21no—
81C2×C4×C101—22no—
82C2×C4×C101—22no—
83C2×C4×C101—21no—
84C2×C4×C101—42no—
85C2×C4×C101—42no—
86C2×C4×C101—41no—
87C2×C4×C101—41no—
88C2×C4×C101—42no—
89C2×C4×C101—42no—
90C2×C4×C101—42no—
91C2×C4×C101—42no—
92C2×C4×C101—42no—
93C2×C4×C101—42no—
94C2×C4×C101—81no—
95C2×C4×C101—82no—
96C2×C4×C101#12112yes—
97C2×C4×C101#12111yescharacteristic
98C2×C4×C101#12312yes—
99C2×C4×C101#12411yescharacteristic
100C8×C101—24no—
101C8×C101—44no—
102C22×C101#39411yescharacteristic
103C22×C101#45311yescharacteristic
104C22×C101#45412yes—
105C22×C101#45612yes—
106C22×C101#45611yescharacteristic
107C4×C101—22no—
108C4×C101—22no—
109C4×C101—21no—
110C4×C101—21no—
111C4×C101—81no—
112C4×C101—81no—
113C4×C101—82no—
114C4×C101—82no—
115C4×C101—161no—
116#10429C10111yesmaximal, characteristic, direct product factor, Sylow
117C2×C101#165711yescharacteristic
118C2×C101#166011yescharacteristic
119C2×C101#166312yes—
120C2×C101#203812yes—
121C2×C101#203911yescharacteristic
122#2822C2×C10111yescharacteristic
123#1992C2×C10112yes—
124#1847C2×C10111yescharacteristic
125C2×#330C2×C10112yes—
126#1295C2×C10111yescharacteristic
127C101#1042911yescharacteristic, direct product factor, Sylow
128C2×#125C22×C10112yes—
129C2×#107—21no—
130C2×#106—21no—
131C2×#97C22×C10112yes—
132C2×#97C22×C10111yescharacteristic
133#400—22no—
134#398—21no—
135#398—21no—
136#398—22no—
137#384C22×C10111yescharacteristic
138#382C22×C10111yescharacteristic
139#340—22no—
140#340—22no—
141#330—24no—
142C22×C8—21no—
143C22×C8—22no—
144#125—22no—
145#125—22no—
146#125—22no—
147#125—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4D4×C10112yes—
155C2×C4⋊C4D4×C10112yes—
156C2×C4⋊C4D4×C10111yescharacteristic
157C2×C4⋊C4D4×C10111yescharacteristic
158C2×C42C23×C10111yescharacteristic
159#107—42no—
160#106—42no—
161#97—22no—
162#97—21no—
163#97—22no—
164#97D4×C10112yes—
165#95—22no—
166#95—22no—
167#95—21no—
168#95—21no—
169#95—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4C2×D4×C10112yes—
176C22×C4C2×D4×C10111yescharacteristic
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—24no—
181C2×C8—42no—
182C2×C8—42no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—44no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C42C2×D4×C10111yescharacteristic
199C42#41×C10111yescharacteristic
200C42#41×C10112yes—
201C23#120×C10111yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—81no—
217C2×C4—82no—
218C2×C4#121×C10112yes—
219C2×C4#121×C10111yescharacteristic
220C2×C4#123×C10112yes—
221C2×C4#124×C10111yescharacteristic
222C8—24no—
223C8—44no—
224C22#394×C10111yescharacteristic
225C22#453×C10111yescharacteristic
226C22#454×C10112yes—
227C22#456×C10112yes—
228C22#456×C10111yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—82no—
236C4—82no—
237C4—161no—
238C2C101×#165711yescharacteristic
239C2C101×#166011yescharacteristic
240C2C101×#166312yes—
241C2C101×#203812yes—
242C2C101×#203911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C101#120
commutator, Frattini, cosocleC2×C42C23×C101
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
116. #10429C101direct (N × H)
127. C101#10429direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#28222
C101×#19922
C101×#18472
C2×#330×C1012
C101×#12952
#10429101