Finite Group Databasebeta

← #34055835

Subgroups — #34055835

Order 19072.

360 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 141 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
1#23750182C211yesmaximal, characteristic
2#23750021C212yesmaximal, complemented
3#23749977C212yesmaximal, complemented
4#23749955C214yesmaximal
5#23749907C214yesmaximal, complemented
6#23749678C211yesmaximal, characteristic
7C2×C4⋊Q8×C149C211yesmaximal, characteristic
8#18011911C2211yescharacteristic
9#18011911C2211yescharacteristic
10#18011903—21no—
11#18011890—21no—
12#18011890C2212yes—
13C4×Dic298—21no—
14C4×Dic298C2212yes—
15#18011870—21no—
16#18011842C2218yes—
17C4⋊#11924746C2212yes—
18#18011834C2218yes—
19C22⋊#11924746C2212yes—
20C4×#11924746C2212yes—
21C22×Q8×C149—21no—
22C4⋊Q8×C149—21no—
23C4⋊Q8×C149—21no—
24C4⋊Q8×C149C2212yes—
25C4⋊Q8×C149C2212yes—
26C2×C4⋊C4×C149—21no—
27C2×C4⋊C4×C149C2212yes—
28C2×C42×C149C2211yescharacteristic
29C2×Dic298—21no—
30C2×Dic298C2312yes—
31C2×#11924746C2314yes—
32C4⋊Dic149—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35C4⋊Dic149C2312yes—
36#14558715—22no—
37#14558715—22no—
38C22⋊Dic149—22no—
39C4×Dic149—22no—
40C2×Q8×C149—22no—
41C2×Q8×C149—22no—
42C2×Q8×C149—44no—
43C22×C4×C149—22no—
44C22×C4×C149D411yescharacteristic
45C22×C4×C149D411yescharacteristic
46C22×C4×C149C2311yescharacteristic
47C4⋊C4×C149—22no—
48C4⋊C4×C149—22no—
49C4⋊C4×C149—22no—
50C4⋊C4×C149C2314yes—
51C42×C149D411yescharacteristic
52C42×C149D411yescharacteristic
53C42×C149C2311yescharacteristic
54C42×C149C2311yescharacteristic
55Dic298—24no—
56Dic298—42no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59#11924746—24no—
60C23×C149C2×D411yescharacteristic
61Q8×C149—44no—
62Q8×C149—44no—
63C2×C4×C149—22no—
64C2×C4×C149—22no—
65C2×C4×C149—24no—
66C2×C4×C149—44no—
67C2×C4×C149SD1614yes—
68C2×C4×C149C2×D411yescharacteristic
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2×D411yescharacteristic
71C2×C4×C149C2×D411yescharacteristic
72C2×C4×C149C2×D411yescharacteristic
73C2×C4×C149C2411yescharacteristic
74C22×C149—21no—
75C22×C149—21no—
76C22×C149C2×SD1612yes—
77C22×C149C22×D411yescharacteristic
78C4×C149—21no—
79C4×C149—21no—
80C4×C149—44no—
81C4×C149C2×SD1612yes—
82C4×C149C2×SD1612yes—
83C4×C149#13712yes—
84C4×C1492−1+412yes—
85Dic149—42no—
86Dic149—42no—
87C2×C149—22no—
88C2×C149#53611yescharacteristic
89C2×C149C22×SD1611yescharacteristic
90C2×C149C2×#13711yescharacteristic
91C149#322911yescharacteristic, complemented, Sylow
92#3229—1491nomaximal, Sylow
93#533—1491no—
94C2×C4⋊Q8D14911yescharacteristic
95#498—1492no—
96#487—1492no—
97#483—1494no—
98#475—1494no—
99#431—1491no—
100C22×Q8—21no—
101C4⋊Q8—21no—
102C4⋊Q8—21no—
103C4⋊Q8—1491no—
104C4⋊Q8—1491no—
105C4⋊Q8C2×D14912yes—
106C4⋊Q8C2×D14912yes—
107#125—2981no—
108C22⋊Q8—2981no—
109C22⋊Q8—1492no—
110C4×Q8—2981no—
111C4×Q8—1492no—
112#117—2981no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4C2×D14912yes—
115C2×C42C2×D14911yescharacteristic
116#106—1498no—
117C4⋊C8—1492no—
118#103—1498no—
119C22⋊C8—1492no—
120C4×C8—1492no—
121C2×Q8—22no—
122C2×Q8—22no—
123C2×Q8—44no—
124C2×Q8—2981no—
125C2×Q8—1492no—
126C22×C4—22no—
127C22×C4C22⋊D14911yescharacteristic
128C22×C4C22⋊D14911yescharacteristic
129C22×C4C22×D14911yescharacteristic
130C2×C8—1494no—
131C4⋊C4—22no—
132C4⋊C4—22no—
133C4⋊C4—22no—
134C4⋊C4—2981no—
135C4⋊C4—2981no—
136C4⋊C4—2981no—
137C4⋊C4—2982no—
138C4⋊C4—2982no—
139C4⋊C4—1492no—
140C4⋊C4C22×D14914yes—
141C22⋊C4—2982no—
142C42—2982no—
143C42C22⋊D14911yescharacteristic
144C42C22⋊D14911yescharacteristic
145C42C22×D14911yescharacteristic
146C42C22×D14911yescharacteristic
147C23C2×C22⋊D14911yescharacteristic
148Q8—44no—
149Q8—44no—
150Q8—2984no—
151Q8—5962no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—44no—
156C2×C4—2982no—
157C2×C4—2982no—
158C2×C4#1455872414yes—
159C2×C4C2×C22⋊D14911yescharacteristic
160C2×C4C2×C22⋊D14911yescharacteristic
161C2×C4C2×C22⋊D14911yescharacteristic
162C2×C4C2×C22⋊D14911yescharacteristic
163C2×C4C2×C22⋊D14911yescharacteristic
164C2×C4C23×D14911yescharacteristic
165C8—2984no—
166C22—21no—
167C22—21no—
168C22C2×#1455872412yes—
169C22C22×C22⋊D14911yescharacteristic
170C4—21no—
171C4—21no—
172C4—44no—
173C4—5962no—
174C4—5962no—
175C4C2×#1455872412yes—
176C4C2×#1455872412yes—
177C4#1801194212yes—
178C4#1801195912yes—
179C2—22no—
180C2#2375019911yescharacteristic
181C2C22×#1455872411yescharacteristic
182C2C2×#1801194211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×C4⋊Q8×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenterC2×C4⋊Q8D149
hypocenterC149#3229
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #23750021C2semidirect
3. #23749977C2semidirect
5. #23749907C2semidirect
91. C149#3229semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237500212
#237499772
#237499552
#237499072
#237496782
C2×C4⋊Q8×C1492
#3229149