Finite Group Databasebeta

← #34045127

Subgroups — #34045127

Order 19072.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×#14558720C211yesmaximal, characteristic, complemented
2C2×#18011885C211yesmaximal, characteristic
3C2×#18011831C212yesmaximal, complemented
4#23749387C212yesmaximal, complemented
5#380×C149C211yesmaximal, characteristic, complemented
6C22×D596C2211yescharacteristic
7C22×C22⋊D149—21no—
8C2×#14558720—24no—
9C2×#14558720—22no—
10C22×#11924746C2212yes—
11#18011885—22no—
12#18011885C414yescomplemented
13C2×C4⋊Dic149C2211yescharacteristic
14C2×#14558713—21no—
15#18011831—24no—
16C23×C4×C149C2211yescharacteristic
17C2×C4⋊C4×C149C2212yes—
18C2×C22⋊C4×C149—21no—
19#95×C149—21no—
20C23×D149—21no—
21C2×D596—22no—
22C2×D596—21no—
23C2×D596—22no—
24C2×D596C2×C412yes—
25C2×C22⋊D149—24no—
26C2×C22⋊D149—44no—
27C22×Dic149—21no—
28#14558720—28no—
29C2×#11924746—22no—
30C2×#11924746—22no—
31C2×#11924746D414yescomplemented
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C412yes—
34#14558713—24no—
35C24×C149D411yescharacteristic
36C22×C4×C149—22no—
37C22×C4×C149—22no—
38C22×C4×C149—22no—
39C22×C4×C149C2×C412yes—
40C22×C4×C149D411yescharacteristic
41C22×C4×C149D412yes—
42C22×C4×C149C2311yescharacteristic
43C4⋊C4×C149—22no—
44C4⋊C4×C149—22no—
45C22⋊C4×C149—42no—
46C22×D149—22no—
47C22×D149—42no—
48C22×D149—42no—
49C22×D149—41no—
50C22×D149—41no—
51D596—24no—
52D596—41no—
53D596—41no—
54C22⋊D149—48no—
55C2×Dic149—22no—
56C2×Dic149—42no—
57#11924746—24no—
58C23×C149—22no—
59C23×C149—22no—
60C23×C149—21no—
61C23×C149—21no—
62C23×C149C22⋊C412yes—
63C23×C149C2×D411yescharacteristic
64C2×C4×C149—22no—
65C2×C4×C149—24no—
66C2×C4×C149—22no—
67C2×C4×C149—22no—
68C2×C4×C149—42no—
69C2×C4×C149—42no—
70C2×C4×C149—42no—
71C2×C4×C149C22⋊C412yes—
72C2×C4×C149C22×C411yescharacteristic
73C2×C4×C149C2×D412yes—
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149#4112yes—
76C22×C149—22no—
77C22×C149—22no—
78C22×C149—22no—
79C22×C149—42no—
80C22×C149—42no—
81C22×C149C2×C22⋊C411yescharacteristic
82C22×C149#12112yes—
83C22×C149AGL(1,ℤ/8)12yes—
84C22×C149AGL(1,ℤ/8)11yescharacteristic
85C22×C149#13711yescharacteristic
86C2×D149—42no—
87C2×D149—42no—
88C2×D149—42no—
89C2×D149—82no—
90C2×D149—82no—
91C4×C149—22no—
92C4×C149—82no—
93C4×C149C4×D412yes—
94C4×C149#12011yescharacteristic
95C4×C149#12311yescharacteristic
96Dic149—42no—
97C2×C149—42no—
98C2×C149#38611yescharacteristic
99C2×C149#41711yescharacteristic
100C2×C149#41811yescharacteristic
101C2×C149#46812yes—
102C2×C149#46912yes—
103D149—82no—
104C149#189511yescharacteristic, complemented, Sylow
105#1895—1491nomaximal, Sylow
106C22×M16—1491no—
107C2×#121—1491no—
108C2×#102—1492no—
109#380D14911yescharacteristic, complemented
110#340—1492no—
111C22×D4—2981no—
112C22×D4—1491no—
113C23×C4C2×D14911yescharacteristic
114C2×M16—2982no—
115C2×M16—2984no—
116C22×C8—1492no—
117#121—2982no—
118#121—1494no—
119C2×C4⋊C4—1491no—
120C2×C4⋊C4C2×D14912yes—
121C2×C22⋊C4—21no—
122C2×C22⋊C4—2981no—
123#102—2984no—
124#95—21no—
125C24—2981no—
126C24C22⋊D14911yescharacteristic
127C2×D4—2984no—
128C2×D4—2982no—
129C2×D4—2981no—
130C2×D4—2982no—
131C2×D4—5964no—
132C2×D4—1492no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—2981no—
137C22×C4C4×D14912yes—
138C22×C4C22⋊D14911yescharacteristic
139C22×C4D59612yes—
140C22×C4C22×D14911yescharacteristic
141M16—2988no—
142C2×C8—2982no—
143C2×C8—2982no—
144C2×C8—1494no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C4⋊C4—2981no—
148C4⋊C4—1492no—
149C22⋊C4—42no—
150C22⋊C4—2984no—
151C23—22no—
152C23—21no—
153C23—21no—
154C23—22no—
155C23—2982no—
156C23—5962no—
157C23—5961no—
158C23—5961no—
159C23—5962no—
160C23#1455871312yes—
161C23C2×C22⋊D14911yescharacteristic
162D4—2984no—
163D4—5968no—
164D4—5961no—
165D4—5961no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—2982no—
174C2×C4—5962no—
175C2×C4#1455871312yes—
176C2×C4C2×C4×D14911yescharacteristic
177C2×C4D4×D14912yes—
178C2×C4C2×D59611yescharacteristic
179C2×C4#1455873512yes—
180C8—2984no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—5962no—
187C22—5962no—
188C22—5962no—
189C22—11922no—
190C22—11922no—
191C22C2×#1455871311yescharacteristic
192C22#1801188312yes—
193C22#1801193612yes—
194C22#1801193711yescharacteristic
195C22#1801194211yescharacteristic
196C4—22no—
197C4—82no—
198C4—5962no—
199C4#1801187112yes—
200C4#1801188111yescharacteristic
201C4#1801189511yescharacteristic
202C2—42no—
203C2—11922no—
204C2#2374950211yescharacteristic
205C2#2374962411yescharacteristic
206C2#2374962911yescharacteristic
207C2#2374987312yes—
208C2#2374987612yes—
subgroupG/H
centerC23C2×C22⋊D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#380×C149C2
socleC23×C149C2×D4
prime radicalC2×#18011885C2
cosocleC22×C4×C149C23
hypercenter#380D149
hypocenterC149#1895
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C22×#14558720C2semidirect
3. C2×#18011831C2semidirect
4. #23749387C2semidirect
5. #380×C149C2semidirect
12. #18011885C4semidirect
31. C2×#11924746D4semidirect
104. C149#1895semidirect
109. #380D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587202
C2×#180118852
C2×#180118312
#237493872
#380×C1492
#1895149