Finite Group Databasebeta

← C2×D97⋊#101 #27158342

Subgroups — C2×D97⋊#101 #27158342

Order 12416.

736 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 210 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×D97⋊M16C212yesmaximal
2D97⋊#101C218yesmaximal, direct product factor
3C2×#15690871C214yesmaximal, complemented
4C22×Q8×D97C211yesmaximal, characteristic
5C2×#13095521—22no—
6D97⋊M16—24no—
7D97⋊M16C2218yes—
8C2×#13095520C2214yes—
9C2×#13095519—22no—
10#15690871C22116yescomplemented
11C22×Dic194C411yescharacteristic
12C22×Dic194C2212yes—
13C2×Q8×D97—22no—
14C2×Q8×D97—24no—
15C2×Q8×D97—22no—
16C2×Q8×D97C414yes—
17C2×Q8×D97C2214yes—
18C22×C4×D97C412yes—
19C22×C4×D97C2211yescharacteristic
20C22×Q8×C97C411yescharacteristic
21#13095521—28no—
22#13095520—24no—
23#13095520C2318yes—
24#13095519—28no—
25C2×#11715897—24no—
26C23×D97C2×C411yescharacteristic
27C2×Dic194—22no—
28C2×Dic194—22no—
29C2×Dic194—24no—
30C2×Dic194—24no—
31C2×Dic194C2×C414yes—
32C2×Dic194C2×C414yes—
33C2×Dic194C2314yes—
34Q8×D97—28no—
35Q8×D97—28no—
36Q8×D97—28no—
37Q8×D97—28no—
38C22×Dic97C2×C412yes—
39C22×Dic97C2311yescharacteristic
40C2×C4×D97—24no—
41C2×C4×D97—22no—
42C2×C4×D97—22no—
43C2×C4×D97C2×C418yes—
44C2×C4×D97C2×C412yes—
45C2×C4×D97D412yes—
46C2×C4×D97D414yes—
47C2×C4×D97D412yes—
48C2×C4×D97C2312yes—
49C2×Q8×C97—22no—
50C2×Q8×C97—22no—
51C2×Q8×C97C2×C414yes—
52C22×C4×C97C2×C412yes—
53C22×C4×C97C2×C411yescharacteristic
54C23×C97C22×C411yescharacteristic
55C22×D97—24no—
56C22×D97C22⋊C412yes—
57C22×D97C22⋊C411yescharacteristic
58C22×D97C22⋊C411yescharacteristic
59C22×D97C22×C412yes—
60Q8×C97—28no—
61C2×C4×C97—22no—
62C2×C4×C97—22no—
63C2×C4×C97C22⋊C412yes—
64C2×C4×C97C22⋊C412yes—
65C2×C4×C97C22×C414yes—
66C2×C4×C97C22×C412yes—
67C2×Dic97—22no—
68C2×Dic97—22no—
69C2×Dic97C22×C414yes—
70C2×Dic97C22×C411yescharacteristic
71C2×Dic97C2×D412yes—
72C2×Dic97C2×D412yes—
73C2×Dic97C2411yescharacteristic
74C4×D97—28no—
75C4×D97—28no—
76C4×D97C22⋊C414yes—
77C4×D97C22⋊C414yes—
78C4×D97C2×D414yes—
79C4×D97C2×D414yes—
80Dic194—28no—
81Dic194—28no—
82Dic194—28no—
83#11715897—28no—
84C22×C97—22no—
85C22×C97C2×C22⋊C411yescharacteristic
86C22×C97C2×C22⋊C411yescharacteristic
87C22×C97C23×C411yescharacteristic
88C2×D97—22no—
89C2×D97—24no—
90C2×D97—24no—
91C2×D97#10114yescomplemented
92C2×D97C2×C22⋊C412yes—
93C2×D97C2×C22⋊C412yes—
94C4×C97—24no—
95C4×C97C2×C22⋊C414yes—
96Dic97—24no—
97Dic97C2×C22⋊C412yes—
98Dic97C22×D412yes—
99C2×C97—21no—
100C2×C97—21no—
101C2×C97C2×#10112yescomplemented
102C2×C97C22×C22⋊C411yescharacteristic
103D97—22no—
104D97C2×#10114yescomplemented
105C22×#101—971nomaximal, Sylow
106C97C22×#10111yescharacteristic, complemented, Sylow
107C23×Q8—971no—
108C22×M16—972no—
109C2×#101—974no—
110C2×#101—978no—
111C22×Q8—974no—
112C22×Q8—974no—
113C22×Q8—972no—
114C22×Q8—971no—
115C22×Q8—1942no—
116C22×Q8—1944no—
117C22×Q8—1942no—
118C22×Q8#8760411yescharacteristic
119C23×C4—971no—
120C23×C4—972no—
121C2×M16—974no—
122C2×M16—978no—
123C2×M16—1944no—
124C2×M16—1942no—
125C22×C8—1942no—
126#101—9716no—
127C24—971no—
128C2×Q8—22no—
129C2×Q8—22no—
130C2×Q8—974no—
131C2×Q8—974no—
132C2×Q8—974no—
133C2×Q8—1944no—
134C2×Q8—1944no—
135C2×Q8—1948no—
136C2×Q8—1948no—
137C2×Q8—1948no—
138C2×Q8—1948no—
139C2×Q8—1942no—
140C2×Q8—1942no—
141C2×Q8C2×#8760414yes—
142C22×C4—971no—
143C22×C4—972no—
144C22×C4—974no—
145C22×C4—972no—
146C22×C4—972no—
147C22×C4—972no—
148C22×C4—972no—
149C22×C4—978no—
150C22×C4—1944no—
151C22×C4—1942no—
152C22×C4—1942no—
153C22×C4C2×#8760412yes—
154C22×C4C2×#8760411yescharacteristic
155M16—978no—
156M16—1944no—
157M16—1948no—
158C2×C8—1944no—
159C2×C8—1948no—
160C23—971no—
161C23—972no—
162C23—971no—
163C23—972no—
164C23—1944no—
165C23C22×#8760411yescharacteristic
166Q8—28no—
167Q8—1948no—
168Q8—1948no—
169Q8—1948no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—972no—
173C2×C4—972no—
174C2×C4—971no—
175C2×C4—971no—
176C2×C4—974no—
177C2×C4—974no—
178C2×C4—974no—
179C2×C4—974no—
180C2×C4—974no—
181C2×C4—1948no—
182C2×C4—1948no—
183C2×C4—1942no—
184C2×C4—1942no—
185C2×C4C22⋊#8760412yes—
186C2×C4C22⋊#8760412yes—
187C2×C4C22×#8760414yes—
188C2×C4C22×#8760412yes—
189C8—1948no—
190C22—22no—
191C22—974no—
192C22—972no—
193C22—972no—
194C22—1944no—
195C22—1944no—
196C22—1942no—
197C22C2×C22⋊#8760411yescharacteristic
198C22C2×C22⋊#8760411yescharacteristic
199C22C23×#8760411yescharacteristic
200C4—24no—
201C4—972no—
202C4—972no—
203C4—1944no—
204C4C2×C22⋊#8760414yes—
205C2—21no—
206C2—21no—
207C2—974no—
208C2—1942no—
209C2D97⋊#10112yesdirect product factor
210C2C22×C22⋊#8760411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87604
commutatorC22×C97C23×C4
FrattiniC22C23×#87604
FittingC22×Q8×C97C4
socleC22×C97C2×C22⋊C4
prime radicalC23×D97C2×C4
cosocleC2×Dic97C24
hypercenterC22×Q8#87604
hypocenterC97C22×#101
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. D97⋊#101C2direct (N × H)
3. C2×#15690871C2semidirect
10. #15690871C22semidirect
91. C2×D97#101semidirect
101. C2×C97C2×#101semidirect
104. D97C2×#101semidirect
106. C97C22×#101semidirect
209. C2D97⋊#101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D97⋊M162
D97⋊#1012
C2×#156908712
C22×Q8×D972
C22×#10197