Finite Group Databasebeta

← #34055145

Subgroups — #34055145

Order 19072.

552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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×#18011940C214yesmaximal, complemented
2#23750173C211yesmaximal, characteristic
3C4⋊Q8×D149C211yesmaximal, characteristic, complemented
4#23750016C214yesmaximal, complemented
5#23750005C211yesmaximal, characteristic, complemented
6#23750004C211yesmaximal, characteristic, complemented
7#23749997C211yesmaximal, characteristic, complemented
8C4×#14558719C211yesmaximal, characteristic, complemented
9#492×C149C211yesmaximal, characteristic, complemented
10C2×#14558735C2212yes—
11C2×Q8×D149C2212yes—
12#18011940—216no—
13C2×Dic596C2214yes—
14C2×#14558726C2214yes—
15C2×#14558724C2214yes—
16C2×#14558719C2212yes—
17#18011911C2211yescharacteristic
18#18011911C2211yescharacteristic
19#18011910—22no—
20#18011909C2212yes—
21#18011898C2212yes—
22#18011882—22no—
23D4×Dic149—22no—
24C4⋊C4×D149—22no—
25C42×D149C2211yescharacteristic
26#18011821C2212yes—
27C4×#11924746C2211yescharacteristic
28C2×SD16×C149C2214yes—
29C4⋊Q8×C149C2211yescharacteristic
30#127×C149C2211yescharacteristic
31C4×C8×C149C2211yescharacteristic
32#14558735—28no—
33C2×Dic298—22no—
34C2×Dic298C2312yes—
35C2×Dic298C2312yes—
36Q8×D149—28no—
37C2×C22⋊D149—22no—
38C22×Dic149—22no—
39C2×C4×D149—22no—
40C2×C4×D149D412yes—
41C2×C4×D149C2311yescharacteristic
42Dic596—28no—
43#14558726—28no—
44#14558724—28no—
45#14558719D418yescomplemented
46C2×#11924746C2312yes—
47C4⋊Dic149—22no—
48C4⋊Dic149—22no—
49#14558715—24no—
50C22⋊Dic149—24no—
51C4×Dic149D412yes—
52C4×Dic149C2311yescharacteristic
53C2×Q8×C149C2312yes—
54C2×D4×C149—22no—
55C2×D4×C149C2312yes—
56SD16×C149—28no—
57C2×C8×C149C2312yes—
58C4⋊C4×C149—22no—
59C42×C149C2311yescharacteristic
60C22×D149C2×D411yescharacteristic
61Dic298—24no—
62Dic298—24no—
63Dic298—44no—
64C22⋊D149—44no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149—44no—
68C2×Dic149C2×D412yes—
69C2×Dic149C2×D411yescharacteristic
70C4×D149—24no—
71C4×D149—44no—
72C4×D149C2×D414yes—
73#11924746C2×D414yes—
74C23×C149—22no—
75Q8×C149—24no—
76D4×C149—24no—
77D4×C149—44no—
78C2×C4×C149—22no—
79C2×C4×C149C2×D412yes—
80C2×C4×C149C2411yescharacteristic
81C8×C149C2×D414yes—
82C22×C149—42no—
83C22×C149—44no—
84C22×C149C22×D411yescharacteristic
85C2×D149—22no—
86C2×D149#12712yes—
87C4×C149—42no—
88C4×C149#13714yescomplemented
89C4×C149C22×D412yes—
90Dic149—22no—
91Dic149—42no—
92Dic149—42no—
93Dic149#12712yes—
94C2×C149—82no—
95C2×C149C2×#12711yescharacteristic
96C2×C149C2×#13712yes—
97D149—22no—
98C149#315211yescharacteristic, complemented, Sylow
99#3152—1491nomaximal, Sylow
100C2×#137—1494no—
101#532—1491no—
102C2×C4⋊Q8—1491no—
103#497—1494no—
104#494—1491no—
105#494—1491no—
106#492—1491no—
107#492D14911yescharacteristic, complemented
108C4×M16—1491no—
109C2×#41—1492no—
110C22×Q8—1492no—
111#137—29816no—
112C2×Q16—1494no—
113C2×Q16—1494no—
114C2×SD16—1494no—
115C2×SD16C2×D14914yes—
116C2×M16—1492no—
117C4⋊Q8—2982no—
118C4⋊Q8—1492no—
119C4⋊Q8—1491no—
120C4⋊Q8—1491no—
121C4⋊Q8C2×D14911yescharacteristic
122#127C2×D14911yescharacteristic
123#124—1492no—
124#121—2982no—
125C4×D4—2982no—
126C2×C4⋊C4—2982no—
127C2×C42—1491no—
128#97—1492no—
129C4×C8—1491no—
130C4×C8C2×D14911yescharacteristic
131#41—2988no—
132C2×Q8—2982no—
133C2×Q8—2988no—
134C2×Q8—1492no—
135C2×Q8—1492no—
136C2×Q8C22×D14912yes—
137C2×D4—22no—
138C2×D4—2982no—
139C2×D4C22×D14912yes—
140C22×C4—2982no—
141C22×C4—2982no—
142C22×C4—1492no—
143C22×C4—1491no—
144Q16—2988no—
145Q16—2988no—
146SD16—28no—
147SD16—2988no—
148M16—1498no—
149C2×C8—1492no—
150C2×C8C22×D14912yes—
151C4⋊C4—22no—
152C4⋊C4—2984no—
153C4⋊C4—2982no—
154C4⋊C4—2982no—
155C22⋊C4—2984no—
156C42—1492no—
157C42—1491no—
158C42C22×D14911yescharacteristic
159C23—22no—
160C23—1491no—
161Q8—24no—
162Q8—2984no—
163Q8—2984no—
164Q8—5964no—
165D4—24no—
166D4—44no—
167D4—5964no—
168C2×C4—22no—
169C2×C4—2984no—
170C2×C4—2982no—
171C2×C4—2982no—
172C2×C4—5964no—
173C2×C4—5964no—
174C2×C4—1492no—
175C2×C4—1491no—
176C2×C4—1494no—
177C2×C4D4×D14912yes—
178C2×C4C23×D14911yescharacteristic
179C8—1494no—
180C8D4×D14914yes—
181C22—44no—
182C22—42no—
183C22—2982no—
184C22—1492no—
185C22C2×D4×D14911yescharacteristic
186C4—42no—
187C4—2982no—
188C4—5962no—
189C4—5962no—
190C4—1492no—
191C4#1801194014yescomplemented
192C4C2×D4×D14912yes—
193C2—82no—
194C2—2982no—
195C2#127×D14911yescharacteristic
196C2C2×#1801194012yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#492×C149C2
socleC22×C149C22×D4
prime radical#23750173C2
hypercenter#492D149
hypocenterC149#3152
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#18011940C2semidirect
3. C4⋊Q8×D149C2semidirect
4. #23750016C2semidirect
5. #23750005C2semidirect
6. #23750004C2semidirect
7. #23749997C2semidirect
8. C4×#14558719C2semidirect
9. #492×C149C2semidirect
45. #14558719D4semidirect
88. C4×C149#137semidirect
98. C149#3152semidirect
107. #492D149semidirect
191. C4#18011940semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
#237501732
C4⋊Q8×D1492
#237500162
#237500052
#237500042
#237499972
C4×#145587192
#492×C1492
#3152149