Finite Group Databasebeta

← #34054817

Subgroups — #34054817

Order 19072.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×Dic298C211yesmaximal, characteristic
2#23749953C212yesmaximal
3#23749907C212yesmaximal, complemented
4#23749832C212yesmaximal, complemented
5#23749780C212yesmaximal
6#23749730C214yesmaximal, complemented
7#23749682C211yesmaximal, characteristic
8#533×C149C211yesmaximal, characteristic
9C22×Dic298C2211yescharacteristic
10C2×#14558726C2214yes—
11C4×Dic298—21no—
12C4×Dic298—21no—
13C4×Dic298C2212yes—
14C4×Dic298C2212yes—
15C2×C4⋊Dic149C2211yescharacteristic
16C2×#14558715—21no—
17C2×C4×Dic149—21no—
18#18011842C2214yes—
19C4⋊#11924746C2212yes—
20#18011835C2214yes—
21#18011834C2214yes—
22C22⋊#11924746C2212yes—
23#18011822C2212yes—
24C4⋊Q8×C149C2211yescharacteristic
25C4⋊Q8×C149C2211yescharacteristic
26#125×C149—21no—
27C22⋊Q8×C149—21no—
28C22⋊Q8×C149C2212yes—
29C4×Q8×C149—21no—
30C4×Q8×C149C2212yes—
31#117×C149—21no—
32C2×C42×C149C2211yescharacteristic
33C2×Dic298—24no—
34C2×Dic298—21no—
35C2×Dic298C2312yes—
36C22×Dic149—21no—
37C22×Dic149—21no—
38#14558726—28no—
39C2×#11924746C2314yes—
40C4⋊Dic149—21no—
41C4⋊Dic149C2312yes—
42#14558715—22no—
43#14558715—22no—
44C4×Dic149—22no—
45C4×Dic149—22no—
46C2×Q8×C149—21no—
47C2×Q8×C149C2312yes—
48C22×C4×C149D411yescharacteristic
49C22×C4×C149D411yescharacteristic
50C22×C4×C149C2311yescharacteristic
51C4⋊C4×C149—21no—
52C4⋊C4×C149—21no—
53C4⋊C4×C149—21no—
54C4⋊C4×C149—22no—
55C4⋊C4×C149—22no—
56C4⋊C4×C149C2312yes—
57C22⋊C4×C149—22no—
58C42×C149—22no—
59C42×C149D411yescharacteristic
60C42×C149D411yescharacteristic
61C42×C149C2311yescharacteristic
62C42×C149C2311yescharacteristic
63Dic298—24no—
64Dic298—22no—
65Dic298#4114yes—
66C2×Dic149—24no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69C2×Dic149—42no—
70#11924746—24no—
71C23×C149C2×D411yescharacteristic
72Q8×C149—24no—
73Q8×C149—42no—
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149—22no—
78C2×C4×C149—22no—
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2411yescharacteristic
85C22×C149—21no—
86C22×C149—21no—
87C22×C149#13712yes—
88C22×C149C22×D411yescharacteristic
89C4×C149—21no—
90C4×C149—21no—
91C4×C149—21no—
92C4×C149—21no—
93C4×C149—42no—
94C4×C149—42no—
95C4×C149#13712yes—
96C4×C149C2×#4112yes—
97Dic149—24no—
98Dic149—42no—
99C2×C149—22no—
100C2×C149#52511yescharacteristic
101C2×C149C2×#13711yescharacteristic
102C2×C149C2×#13711yescharacteristic
103C149#311311yescharacteristic, complemented, Sylow
104#3113—1491nomaximal, Sylow
105#533D14911yescharacteristic
106C2×C4×Q8—1491no—
107#483—1492no—
108#475—1492no—
109#462—1492no—
110#451—1492no—
111#441—1494no—
112#432—1491no—
113C22×Q8—1491no—
114C2×Q16—1494no—
115C4⋊Q8C2×D14911yescharacteristic
116C4⋊Q8C2×D14911yescharacteristic
117#125—21no—
118C22⋊Q8—21no—
119C22⋊Q8C2×D14912yes—
120C4×Q8—21no—
121C4×Q8—2981no—
122C4×Q8—2981no—
123C4×Q8—1492no—
124C4×Q8—1492no—
125C4×Q8C2×D14912yes—
126#117—21no—
127C2×C4⋊C4—2981no—
128C2×C4⋊C4—1491no—
129C2×C42—2981no—
130C2×C42C2×D14911yescharacteristic
131#106—1494no—
132C4⋊C8—1492no—
133#103—1494no—
134#103—1494no—
135C22⋊C8—1492no—
136#97—1492no—
137C2×Q8—21no—
138C2×Q8—2984no—
139C2×Q8—2981no—
140C2×Q8—1492no—
141C2×Q8C22×D14912yes—
142C22×C4—2981no—
143C22×C4—2981no—
144C22×C4C22⋊D14911yescharacteristic
145C22×C4C22⋊D14911yescharacteristic
146C22×C4C22×D14911yescharacteristic
147Q16—2988no—
148C2×C8—1494no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—2982no—
155C4⋊C4—2982no—
156C4⋊C4—2981no—
157C4⋊C4—1492no—
158C4⋊C4C22×D14912yes—
159C22⋊C4—22no—
160C42—22no—
161C42—2982no—
162C42—2982no—
163C42C22⋊D14911yescharacteristic
164C42C22⋊D14911yescharacteristic
165C42C22×D14911yescharacteristic
166C42C22×D14911yescharacteristic
167C23C2×C22⋊D14911yescharacteristic
168Q8—24no—
169Q8—42no—
170Q8—2984no—
171Q8—2982no—
172Q8—1494no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2984no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—5962no—
182C2×C4C2×C22⋊D14911yescharacteristic
183C2×C4C2×C22⋊D14911yescharacteristic
184C2×C4C2×C22⋊D14911yescharacteristic
185C2×C4C2×C22⋊D14911yescharacteristic
186C2×C4C2×C22⋊D14911yescharacteristic
187C2×C4C23×D14911yescharacteristic
188C8—2984no—
189C22—21no—
190C22—21no—
191C22#1801194212yes—
192C22C22×C22⋊D14911yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—2984no—
200C4—5962no—
201C4#1801194112yes—
202C4#41×D14912yes—
203C2—22no—
204C2#2375013211yescharacteristic
205C2C2×#1801194111yescharacteristic
206C2C2×#1801194211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#533×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenter#533D149
hypocenterC149#3113
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #23749907C2semidirect
4. #23749832C2semidirect
6. #23749730C2semidirect
103. C149#3113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic2982
#237499532
#237499072
#237498322
#237497802
#237497302
#237496822
#533×C1492
#3113149