Finite Group Databasebeta

← #34045122

Subgroups — #34045122

Order 19072.

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

normal subgroups only

This group has 360 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
2C2×#18011890C211yesmaximal, characteristic
3C2×#18011834C212yesmaximal, complemented
4#23749387C212yesmaximal, complemented
5#380×C149C211yesmaximal, characteristic
6C22×Dic298C2211yescharacteristic
7C2×#14558720—24no—
8C2×#14558720—22no—
9C22×#11924746C2212yes—
10#18011890—22no—
11#18011890C414yescomplemented
12C2×C4⋊Dic149C2211yescharacteristic
13C2×#14558715—21no—
14C2×C22⋊Dic149—21no—
15#18011834—24no—
16C23×C4×C149C2211yescharacteristic
17C2×C4⋊C4×C149C2212yes—
18C2×C22⋊C4×C149—21no—
19#95×C149—21no—
20C2×Dic298—21no—
21C2×Dic298—22no—
22C2×Dic298—22no—
23C2×Dic298C2×C412yes—
24C22×Dic149—21no—
25C22×Dic149—21no—
26#14558720—28no—
27C2×#11924746—22no—
28C2×#11924746—22no—
29C2×#11924746D414yes—
30C4⋊Dic149—21no—
31C4⋊Dic149C2×C412yes—
32#14558715—24no—
33C22⋊Dic149—24no—
34C24×C149D411yescharacteristic
35C22×C4×C149—22no—
36C22×C4×C149—22no—
37C22×C4×C149—22no—
38C22×C4×C149C2×C412yes—
39C22×C4×C149D411yescharacteristic
40C22×C4×C149D412yes—
41C22×C4×C149C2311yescharacteristic
42C4⋊C4×C149—22no—
43C4⋊C4×C149—22no—
44C22⋊C4×C149—42no—
45Dic298—24no—
46Dic298—41no—
47Dic298—41no—
48C2×Dic149—22no—
49C2×Dic149—22no—
50C2×Dic149—42no—
51C2×Dic149—41no—
52C2×Dic149—41no—
53#11924746—24no—
54C23×C149—22no—
55C23×C149—21no—
56C23×C149—22no—
57C23×C149—21no—
58C23×C149C22⋊C412yes—
59C23×C149C2×D411yescharacteristic
60C2×C4×C149—22no—
61C2×C4×C149—24no—
62C2×C4×C149—22no—
63C2×C4×C149—22no—
64C2×C4×C149—42no—
65C2×C4×C149—42no—
66C2×C4×C149—42no—
67C2×C4×C149C22⋊C412yes—
68C2×C4×C149C22×C411yescharacteristic
69C2×C4×C149C2×D412yes—
70C2×C4×C149C2×D411yescharacteristic
71C2×C4×C149#4112yes—
72C22×C149—22no—
73C22×C149—22no—
74C22×C149—22no—
75C22×C149—42no—
76C22×C149—42no—
77C22×C149C2×C22⋊C411yescharacteristic
78C22×C149#12112yes—
79C22×C149AGL(1,ℤ/8)11yescharacteristic
80C22×C149#13712yes—
81C22×C149#13711yescharacteristic
82C4×C149—22no—
83C4×C149—82no—
84C4×C149C4×D412yes—
85C4×C149#12011yescharacteristic
86C4×C149#12311yescharacteristic
87Dic149—42no—
88Dic149—42no—
89C2×C149—42no—
90C2×C149#38611yescharacteristic
91C2×C149#41711yescharacteristic
92C2×C149#41911yescharacteristic
93C2×C149#46812yes—
94C2×C149#47012yes—
95C149#189411yescharacteristic, complemented, Sylow
96#1894—1491nomaximal, Sylow
97C22×M16—1491no—
98C2×C22⋊Q8—1491no—
99C2×#103—1492no—
100#380D14911yescharacteristic
101#340—1492no—
102C22×Q8—1491no—
103C23×C4C2×D14911yescharacteristic
104C2×M16—2982no—
105C2×M16—2984no—
106C22×C8—1492no—
107C22⋊Q8—2982no—
108C22⋊Q8—1494no—
109C2×C4⋊C4—2981no—
110C2×C4⋊C4—1491no—
111C2×C4⋊C4C2×D14912yes—
112C2×C22⋊C4—21no—
113C2×C22⋊C4—2981no—
114#103—2984no—
115#95—21no—
116C24C22⋊D14911yescharacteristic
117C2×Q8—2981no—
118C2×Q8—2982no—
119C2×Q8—2982no—
120C2×Q8—1492no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—22no—
124C22×C4—2981no—
125C22×C4—2981no—
126C22×C4C4×D14912yes—
127C22×C4C22⋊D14911yescharacteristic
128C22×C4D59612yes—
129C22×C4C22×D14911yescharacteristic
130M16—2988no—
131C2×C8—2982no—
132C2×C8—2982no—
133C2×C8—1494no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—2981no—
137C4⋊C4—2984no—
138C4⋊C4—1492no—
139C22⋊C4—42no—
140C22⋊C4—2984no—
141C23—21no—
142C23—22no—
143C23—21no—
144C23—22no—
145C23#1455871312yes—
146C23C2×C22⋊D14911yescharacteristic
147Q8—2984no—
148Q8—5961no—
149Q8—5961no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—2982no—
158C2×C4—2982no—
159C2×C4—5961no—
160C2×C4—5961no—
161C2×C4—5962no—
162C2×C4#1455871312yes—
163C2×C4C2×C4×D14911yescharacteristic
164C2×C4D4×D14912yes—
165C2×C4C2×D59611yescharacteristic
166C2×C4#1455873512yes—
167C8—2984no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22C2×#1455871311yescharacteristic
174C22#1801188312yes—
175C22#1801193711yescharacteristic
176C22#1801194112yes—
177C22#1801194211yescharacteristic
178C4—22no—
179C4—82no—
180C4—5962no—
181C4—5962no—
182C4#1801187112yes—
183C4#1801188111yescharacteristic
184C4#1801189511yescharacteristic
185C2—42no—
186C2#2374950211yescharacteristic
187C2#2374962411yescharacteristic
188C2#2374963311yescharacteristic
189C2#2374986912yes—
190C2#2374988112yes—
subgroupG/H
centerC23C2×C22⋊D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#380×C149C2
socleC23×C149C2×D4
prime radicalC24×C149D4
cosocleC22×C4×C149C23
hypercenter#380D149
hypocenterC149#1894
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
3. C2×#18011834C2semidirect
4. #23749387C2semidirect
11. #18011890C4semidirect
95. C149#1894semidirect

Maximal subgroups

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

subgroupindex
C22×#145587202
C2×#180118902
C2×#180118342
#237493872
#380×C1492
#1894149