Finite Group Databasebeta

← #34053167

Subgroups — #34053167

Order 19072.

756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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×#18011956C211yesmaximal, characteristic
2#23750391C212yesmaximal, complemented
3#23749607C212yesmaximal, complemented
4#23749606C214yesmaximal, complemented
5C2×#18011828C211yesmaximal, characteristic, complemented
6#100×D149C214yesmaximal, complemented
7C2×#100×C149C211yesmaximal, characteristic, complemented
8#18011956—24no—
9#18011956—24no—
10C2×#14558736C2211yescharacteristic
11C2×#14558736C2211yescharacteristic
12C2×#14558735C412yes—
13C2×#14558735C2212yes—
14C22×C22⋊D149C414yes—
15C2×D4×D149C412yes—
16C2×D4×D149C2212yes—
17#18011919—24no—
18#18011917—24no—
19C2×#14558720C2212yescomplemented
20M16×D149C2218yescomplemented
21#18011829C2214yescomplemented
22#18011828C2214yescomplemented
23#18011827C2214yescomplemented
24C22×D4×C149C2211yescharacteristic
25C2×M16×C149C2212yescomplemented
26#100×C149C2214yescomplemented
27C23×D149C2×C414yes—
28#14558736—22no—
29#14558736—22no—
30#14558736D414yes—
31#14558736D414yes—
32#14558735—28no—
33#14558735—28no—
34C2×Dic298C2×C411yescharacteristic
35C2×Dic298C2311yescharacteristic
36C2×D596C2×C411yescharacteristic
37C2×D596C2311yescharacteristic
38C2×C22⋊D149—28no—
39C2×C22⋊D149—28no—
40C2×C22⋊D149C2×C414yes—
41C2×C22⋊D149C2×C414yes—
42C2×C22⋊D149C2×C412yes—
43C2×C22⋊D149C2×C412yes—
44D4×D149—28no—
45D4×D149—28no—
46C22×Dic149C2×C414yes—
47C2×C4×D149C2×C412yes—
48C2×C4×D149C2312yes—
49#14558720—22no—
50#14558720C2314yes—
51#14558719—28no—
52C2×#11924746—22no—
53C8×D149—28no—
54C24×C149C2×C412yes—
55C2×D4×C149—22no—
56C2×D4×C149—22no—
57C2×D4×C149C2×C412yes—
58C2×D4×C149C2312yes—
59C22×C4×C149C2311yescharacteristic
60M16×C149—22no—
61M16×C149C2314yes—
62C2×C8×C149—22no—
63C22×D149—28no—
64C22×D149—84no—
65C22×D149C22×C412yes—
66C22×D149C22×C412yes—
67Dic298—22no—
68Dic298C22⋊C414yes—
69D596—22no—
70D596C22⋊C414yes—
71C22⋊D149—22no—
72C22⋊D149—22no—
73C22⋊D149—28no—
74C22⋊D149—28no—
75C22⋊D149C22⋊C414yes—
76C22⋊D149C22⋊C414yes—
77C2×Dic149—28no—
78C2×Dic149C22×C412yes—
79C2×Dic149C22×C412yes—
80C4×D149—24no—
81C4×D149C2×D418yes—
82#11924746—24no—
83C23×C149—22no—
84C23×C149—22no—
85C23×C149—82no—
86C23×C149C22×C414yes—
87C23×C149C22×C411yescharacteristic
88D4×C149—24no—
89D4×C149—24no—
90C2×C4×C149C22×C411yescharacteristic
91C2×C4×C149C2×D412yes—
92C2×C4×C149C2×D412yes—
93C2×C4×C149C2411yescharacteristic
94C8×C149—24no—
95C22×C149—24no—
96C22×C149—41no—
97C22×C149—44no—
98C22×C149—82no—
99C22×C149—82no—
100C22×C149C2×C22⋊C411yescharacteristic
101C22×C149C2×C22⋊C411yescharacteristic
102C22×C149C23×C411yescharacteristic
103C2×D149—22no—
104C2×D149—42no—
105C2×D149—42no—
106C2×D149—88no—
107C2×D149C2×C22⋊C414yes—
108C4×C149C2×C22⋊C412yes—
109C4×C149C22×D412yes—
110Dic149—22no—
111Dic149C2×C22⋊C414yes—
112C2×C149—21no—
113C2×C149—21no—
114C2×C149—21no—
115C2×C149—44no—
116C2×C149C22×C22⋊C411yescharacteristic
117D149—24no—
118D149—42no—
119C149#288811yescharacteristic, complemented, Sylow
120#2888—1491nomaximal, Sylow
121C2×H(5,𝔽2)—1491no—
122#568—1492no—
123#413—1492no—
124#413—1494no—
125C2×#100—1491no—
126C2×#100—1494no—
127C2×#100D14911yescharacteristic, complemented
128H(5,𝔽2)—2984no—
129H(5,𝔽2)—2984no—
130C2×#41—1492no—
131C2×#41—1492no—
132C2×#41—1491no—
133C2×#41—1491no—
134C22×D4—1494no—
135C22×D4—1492no—
136C22×D4—1492no—
137C22×D4C2×D14911yescharacteristic
138#131—2984no—
139#131—2984no—
140C2×M16—1492no—
141C2×M16—1498no—
142C2×M16C2×D14912yescomplemented
143#101—1494no—
144#100—1494no—
145#100—1494no—
146#100C2×D14914yescomplemented
147C24—1494no—
148C24C4×D14912yes—
149#41—2988no—
150#41—2988no—
151#41—2982no—
152#41—2982no—
153#41—1494no—
154#41—1494no—
155C2×Q8—1491no—
156C2×Q8—1491no—
157C2×D4—22no—
158C2×D4—22no—
159C2×D4—2988no—
160C2×D4—2988no—
161C2×D4—2988no—
162C2×D4—2988no—
163C2×D4—1494no—
164C2×D4—1492no—
165C2×D4—1494no—
166C2×D4—1492no—
167C2×D4—1491no—
168C2×D4—1491no—
169C2×D4C4×D14912yes—
170C2×D4C22×D14912yes—
171C22×C4—1494no—
172C22×C4—1492no—
173C22×C4—1492no—
174C22×C4C22×D14911yescharacteristic
175M16—22no—
176M16—2988no—
177M16—2982no—
178M16—1494no—
179M16C22×D14914yes—
180C2×C8—22no—
181C2×C8—2988no—
182C2×C8—2982no—
183C23—22no—
184C23—22no—
185C23—82no—
186C23—2988no—
187C23—1492no—
188C23—1492no—
189C23—11924no—
190C23C2×C4×D14914yes—
191C23C2×C4×D14911yescharacteristic
192Q8—2982no—
193Q8—1494no—
194D4—24no—
195D4—24no—
196D4—2988no—
197D4—2982no—
198D4—2982no—
199D4—2988no—
200D4—2982no—
201D4—1494no—
202D4—1494no—
203D4—1494no—
204C2×C4—2988no—
205C2×C4—2984no—
206C2×C4—1492no—
207C2×C4—1492no—
208C2×C4—1498no—
209C2×C4C2×C4×D14911yescharacteristic
210C2×C4D4×D14912yes—
211C2×C4D4×D14912yes—
212C2×C4C23×D14911yescharacteristic
213C8—24no—
214C8—2984no—
215C22—24no—
216C22—41no—
217C22—44no—
218C22—82no—
219C22—82no—
220C22—2982no—
221C22—5962no—
222C22—5962no—
223C22—1494no—
224C22—11928no—
225C22C22⋊C4×D14911yescharacteristic
226C22C22⋊C4×D14911yescharacteristic
227C22C22×C4×D14911yescharacteristic
228C4—2982no—
229C4—1494no—
230C4C22⋊C4×D14912yes—
231C4C2×D4×D14912yes—
232C2—21no—
233C2—21no—
234C2—21no—
235C2—44no—
236C2—2984no—
237C2—5962no—
238C2C2×C22⋊C4×D14911yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D149
commutatorC22×C149C23×C4
FrattiniC2×C4C23×D149
FittingC2×#100×C149C2
socleC2×C149C22×C22⋊C4
prime radicalC2×#18011956C2
cosocleC2×C4×C149C24
hypercenterC2×#100D149
hypocenterC149#2888
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #23750391C2semidirect
3. #23749607C2semidirect
4. #23749606C2semidirect
5. C2×#18011828C2semidirect
6. #100×D149C2semidirect
7. C2×#100×C149C2semidirect
19. C2×#14558720C22semidirect
20. M16×D149C22semidirect
21. #18011829C22semidirect
22. #18011828C22semidirect
23. #18011827C22semidirect
25. C2×M16×C149C22semidirect
26. #100×C149C22semidirect
119. C149#2888semidirect
127. C2×#100D149semidirect
142. C2×M16C2×D149semidirect
146. #100C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119562
#237503912
#237496072
#237496062
C2×#180118282
#100×D1492
C2×#100×C1492
#2888149