Finite Group Databasebeta

← C101×#12164 #38794315

Subgroups — C101×#12164 #38794315

Order 25856.

374 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3259C211yesmaximal, characteristic, complemented
2C101×#2184C212yesmaximal, complemented
3C101×#2045C211yesmaximal, characteristic, complemented
4C101×#1349C212yesmaximal, complemented
5C101×#1323C211yesmaximal, characteristic, complemented
6C22×D8×C101C2211yescharacteristic
7#540×C101—21no—
8C2×D16×C101—22no—
9#478×C101—22no—
10#469×C101—21no—
11#466×C101C2212yes—
12#459×C101—22no—
13#424×C101C2211yescharacteristic
14#418×C101—21no—
15C2×#100×C101—21no—
16#357×C101—22no—
17C22⋊C16×C101C2212yes—
18#341×C101C2211yescharacteristic
19C22×D4×C101—21no—
20C2×D8×C101—21no—
21C2×D8×C101—22no—
22C2×D8×C101—42no—
23C2×D8×C101D412yes—
24C2×M16×C101—21no—
25C2×M16×C101D411yescharacteristic
26C22×C8×C101C2311yescharacteristic
27#127×C101—21no—
28#125×C101—21no—
29#123×C101—42no—
30#121×C101—22no—
31#121×C101—42no—
32C4×D4×C101—22no—
33#117×C101D411yescharacteristic
34D16×C101—44no—
35C2×C16×C101—22no—
36#107×C101D412yes—
37#106×C101—21no—
38C4⋊C8×C101—22no—
39#102×C101—22no—
40#102×C101—22no—
41#102×C101—42no—
42#100×C101—42no—
43C24×C101—41no—
44C2×D4×C101—22no—
45C2×D4×C101—22no—
46C2×D4×C101—41no—
47C2×D4×C101—41no—
48C2×D4×C101—41no—
49C2×D4×C101—42no—
50C2×D4×C101—42no—
51C2×D4×C101—41no—
52C2×D4×C101—41no—
53C22×C4×C101—42no—
54C22×C4×C101C2×D411yescharacteristic
55D8×C101—24no—
56D8×C101—42no—
57D8×C101—42no—
58D8×C101—81no—
59M16×C101—41no—
60M16×C101—41no—
61M16×C101—41no—
62C2×C8×C101—21no—
63C2×C8×C101—41no—
64C2×C8×C101—41no—
65C2×C8×C101C2×D412yes—
66C4⋊C4×C101—22no—
67C4⋊C4×C101—42no—
68C4⋊C4×C101D812yes—
69C22⋊C4×C101—21no—
70C22⋊C4×C101—42no—
71C22⋊C4×C101—42no—
72C42×C101—21no—
73C16×C101—42no—
74C23×C101—42no—
75C23×C101—42no—
76C23×C101—81no—
77C23×C101—81no—
78C23×C101—162no—
79C23×C101AGL(1,ℤ/8)11yescharacteristic
80D4×C101—42no—
81D4×C101—42no—
82D4×C101—42no—
83D4×C101—42no—
84D4×C101—81no—
85D4×C101—81no—
86D4×C101—162no—
87D4×C101—162no—
88C2×C4×C101—21no—
89C2×C4×C101—21no—
90C2×C4×C101—22no—
91C2×C4×C101—42no—
92C2×C4×C101—162no—
93C2×C4×C101#12011yescharacteristic
94C2×C4×C101C2×D811yescharacteristic
95C8×C101—22no—
96C8×C101—41no—
97C8×C101—81no—
98C22×C101—21no—
99C22×C101—22no—
100C22×C101—82no—
101C22×C101—82no—
102C22×C101—82no—
103C22×C101—82no—
104C22×C101—162no—
105C22×C101—162no—
106C22×C101—162no—
107C22×C101#44711yescharacteristic
108C4×C101—21no—
109C4×C101—42no—
110C4×C101—82no—
111C4×C101#45411yescharacteristic
112C4×C101B(4,𝔽2)11yescharacteristic
113#12164C10111yesmaximal, characteristic, direct product factor, Sylow
114C2×C101—41no—
115C2×C101—162no—
116C2×C101—162no—
117C2×C101#159811yescharacteristic
118C2×C101#219212yes—
119#3259C2×C10111yescharacteristic, complemented
120#2184C2×C10112yescomplemented
121#2045C2×C10111yescharacteristic, complemented
122#1349C2×C10112yescomplemented
123#1323C2×C10111yescharacteristic, complemented
124C101#1216411yescharacteristic, direct product factor, Sylow
125C22×D8C22×C10111yescharacteristic
126#540—21no—
127C2×D16—22no—
128#478—22no—
129#469—21no—
130#466C22×C10112yes—
131#459—22no—
132#424C22×C10111yescharacteristic
133#418—21no—
134C2×#100—21no—
135#357—22no—
136C22⋊C16C22×C10112yes—
137#341C22×C10111yescharacteristic
138C22×D4—21no—
139C2×D8—21no—
140C2×D8—22no—
141C2×D8—42no—
142C2×D8D4×C10112yes—
143C2×M16—21no—
144C2×M16D4×C10111yescharacteristic
145C22×C8C23×C10111yescharacteristic
146#127—21no—
147#125—21no—
148#123—42no—
149#121—22no—
150#121—42no—
151C4×D4—22no—
152#117D4×C10111yescharacteristic
153D16—44no—
154C2×C16—22no—
155#107D4×C10112yes—
156#106—21no—
157C4⋊C8—22no—
158#102—22no—
159#102—22no—
160#102—42no—
161#100—42no—
162C24—41no—
163C2×D4—22no—
164C2×D4—22no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4—41no—
168C2×D4—42no—
169C2×D4—42no—
170C2×D4—41no—
171C2×D4—41no—
172C22×C4—42no—
173C22×C4C2×D4×C10111yescharacteristic
174D8—24no—
175D8—42no—
176D8—42no—
177D8—81no—
178M16—41no—
179M16—41no—
180M16—41no—
181C2×C8—21no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8C2×D4×C10112yes—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4D8×C10112yes—
188C22⋊C4—21no—
189C22⋊C4—42no—
190C22⋊C4—42no—
191C42—21no—
192C16—42no—
193C23—42no—
194C23—42no—
195C23—81no—
196C23—81no—
197C23—162no—
198C23AGL(1,ℤ/8)×C10111yescharacteristic
199D4—42no—
200D4—42no—
201D4—42no—
202D4—42no—
203D4—81no—
204D4—81no—
205D4—162no—
206D4—162no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—162no—
212C2×C4#120×C10111yescharacteristic
213C2×C4C2×D8×C10111yescharacteristic
214C8—22no—
215C8—41no—
216C8—81no—
217C22—22no—
218C22—21no—
219C22—82no—
220C22—82no—
221C22—82no—
222C22—82no—
223C22—162no—
224C22—162no—
225C22—162no—
226C22#447×C10111yescharacteristic
227C4—21no—
228C4—42no—
229C4—82no—
230C4#454×C10111yescharacteristic
231C4B(4,𝔽2)×C10111yescharacteristic
232C2—41no—
233C2—162no—
234C2—162no—
235C2C101×#159811yescharacteristic
236C2C101×#219212yes—
subgroupG/H
center, socleC22×C101#447
commutator, Frattini, cosocleC22×C8C23×C101
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ #424×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3259C2semidirect
2. C101×#2184C2semidirect
3. C101×#2045C2semidirect
4. C101×#1349C2semidirect
5. C101×#1323C2semidirect
113. #12164C101direct (N × H)
119. #3259C2×C101semidirect
120. #2184C2×C101semidirect
121. #2045C2×C101semidirect
122. #1349C2×C101semidirect
123. #1323C2×C101semidirect
124. C101#12164direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32592
C101×#21842
C101×#20452
C101×#13492
C101×#13232
#12164101