Finite Group Databasebeta

← #34055899

Subgroups — #34055899

Order 19072.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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
2C2×#18011903C211yesmaximal, characteristic
3#23750034C212yesmaximal, complemented
4#23749994C212yesmaximal, complemented
5#23749961C212yesmaximal
6#23749956C212yesmaximal
7#23749933C214yesmaximal, complemented
8#432×C149C211yesmaximal, characteristic
9#18011911C2211yescharacteristic
10#18011911C2211yescharacteristic
11#18011903—21no—
12#18011903—21no—
13#18011903—21no—
14#18011903C2212yes—
15#18011903C2212yes—
16#18011890—21no—
17#18011890C2212yes—
18C4×Dic298—21no—
19C4×Dic298C2212yes—
20#18011870—21no—
21C2×C4⋊Dic149C2211yescharacteristic
22C2×C4⋊Dic149C2211yescharacteristic
23C2×#14558715—21no—
24C2×#14558715—21no—
25#18011845C2214yes—
26#18011843C2214yes—
27#18011836C2214yes—
28#18011836C2214yes—
29C2×C42×C149C2211yescharacteristic
30C4⋊C8×C149C2212yes—
31C22⋊C8×C149C2212yes—
32#97×C149C2212yes—
33C2×Dic298—21no—
34C2×Dic298C2312yes—
35C22×Dic149—21no—
36C22×Dic149—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39C4⋊Dic149—21no—
40C4⋊Dic149—21no—
41C4⋊Dic149—21no—
42C4⋊Dic149C2312yes—
43C4⋊Dic149C2312yes—
44C4⋊Dic149C2312yes—
45#14558715—22no—
46#14558715—22no—
47#14558715—22no—
48#14558715—22no—
49#14558715—22no—
50#14558715—22no—
51C22⋊Dic149—22no—
52C4×Dic149—22no—
53C22×C4×C149D411yescharacteristic
54C22×C4×C149D411yescharacteristic
55C22×C4×C149C2311yescharacteristic
56C2×C8×C149C2314yes—
57C42×C149D411yescharacteristic
58C42×C149D411yescharacteristic
59C42×C149C2311yescharacteristic
60C42×C149C2311yescharacteristic
61Dic298—24no—
62Dic298—42no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149—42no—
68C2×Dic149—42no—
69C23×C149C2×D411yescharacteristic
70C2×C4×C149—22no—
71C2×C4×C149—22no—
72C2×C4×C149—41no—
73C2×C4×C149C2×D411yescharacteristic
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149C2×D411yescharacteristic
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2411yescharacteristic
79C8×C149—24no—
80C22×C149—21no—
81C22×C149—21no—
82C22×C149#13712yes—
83C22×C149C22×D411yescharacteristic
84C4×C149—21no—
85C4×C149—21no—
86C4×C149—21no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C1492−1+412yes—
90Dic149—42no—
91Dic149—42no—
92Dic149—42no—
93Dic149—42no—
94C2×C149—22no—
95C2×C149#53611yescharacteristic
96C2×C149C2×#13711yescharacteristic
97C2×C149#57511yescharacteristic
98C149#323611yescharacteristic, complemented, Sylow
99#3236—1491nomaximal, Sylow
100#533—1491no—
101C2×#125—1491no—
102#501—1492no—
103#491—1492no—
104#484—1492no—
105#483—1492no—
106#479—1494no—
107#432D14911yescharacteristic
108C4⋊Q8—1491no—
109C4⋊Q8—1491no—
110#125—2981no—
111#125—2981no—
112#125—2981no—
113#125—1492no—
114#125—1492no—
115C22⋊Q8—2981no—
116C22⋊Q8—1492no—
117C4×Q8—2981no—
118C4×Q8—1492no—
119#117—2981no—
120C2×C4⋊C4—2981no—
121C2×C4⋊C4—2981no—
122C2×C4⋊C4—1491no—
123C2×C4⋊C4—1491no—
124C2×C42C2×D14911yescharacteristic
125#107—1494no—
126#106—1494no—
127C4⋊C8C2×D14912yes—
128#103—1494no—
129#103—1494no—
130C22⋊C8C2×D14912yes—
131#97C2×D14912yes—
132C2×Q8—2981no—
133C2×Q8—1492no—
134C22×C4—2981no—
135C22×C4—2981no—
136C22×C4D59611yescharacteristic
137C22×C4D59611yescharacteristic
138C22×C4C22×D14911yescharacteristic
139C2×C8C22×D14914yes—
140C4⋊C4—2982no—
141C4⋊C4—2982no—
142C4⋊C4—2982no—
143C4⋊C4—2982no—
144C4⋊C4—2981no—
145C4⋊C4—2981no—
146C4⋊C4—2981no—
147C4⋊C4—2981no—
148C4⋊C4—2981no—
149C4⋊C4—2982no—
150C4⋊C4—2982no—
151C4⋊C4—1492no—
152C4⋊C4—1492no—
153C4⋊C4—1492no—
154C22⋊C4—2982no—
155C42—2982no—
156C42D59611yescharacteristic
157C42D59611yescharacteristic
158C42C22×D14911yescharacteristic
159C42C22×D14911yescharacteristic
160C23C2×D59611yescharacteristic
161Q8—2984no—
162Q8—5962no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—2982no—
169C2×C4—2982no—
170C2×C4—5962no—
171C2×C4—5962no—
172C2×C4C2×D59611yescharacteristic
173C2×C4C2×D59611yescharacteristic
174C2×C4C2×D59611yescharacteristic
175C2×C4C2×D59611yescharacteristic
176C2×C4C2×D59611yescharacteristic
177C2×C4C23×D14911yescharacteristic
178C8—24no—
179C22—21no—
180C22—21no—
181C22#1801194412yes—
182C22C22×D59611yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—5962no—
189C4—5962no—
190C4—5962no—
191C4—5962no—
192C4#1801195812yes—
193C2—22no—
194C2#2375020111yescharacteristic
195C2C2×#1801194411yescharacteristic
196C2#2375042511yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#432×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenter#432D149
hypocenterC149#3236
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
3. #23750034C2semidirect
4. #23749994C2semidirect
7. #23749933C2semidirect
98. C149#3236semidirect

Maximal subgroups

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

subgroupindex
#237501822
C2×#180119032
#237500342
#237499942
#237499612
#237499562
#237499332
#432×C1492
#3236149