Finite Group Databasebeta

← #34060596

Subgroups — #34060596

Order 19072.

300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D149⋊(C22⋊C8)C211yesmaximal, characteristic
2#23750567C211yesmaximal, characteristic
3#23750498C212yesmaximal, complemented
4#23750498C212yesmaximal, complemented
5#117×D149C211yesmaximal, characteristic
6C2×D149⋊C8C2212yes—
7C2×C4⋊#10597010C2212yes—
8C2×C22⋊#10597010—21no—
9#18011968—21no—
10C22⋊#11924753—21no—
11(C2×#10597010)⋊C4—21no—
12C22×C4×D149C2211yescharacteristic
13#18011870C411yescharacteristic, complemented
14#18011869C411yescharacteristic, complemented
15#18011869C411yescharacteristic, complemented
16#18011868—21no—
17#18011867—21no—
18C4⋊C4×D149C2211yescharacteristic
19C4⋊C4×D149C2211yescharacteristic
20C22⋊C4×D149—21no—
21C42×D149—21no—
22#117×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24D149⋊C8—24no—
25C2×#11924753—22no—
26C4⋊#10597010—24no—
27C22⋊#10597010—42no—
28C23×D149D411yescharacteristic
29C22×Dic149D411yescharacteristic
30C2×C4×D149—24no—
31C2×C4×D149—21no—
32C2×C4×D149—21no—
33C2×C4×D149C2×C411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149C2311yescharacteristic
37C4⋊Dic149C2×C411yescharacteristic
38C4⋊Dic149C2×C411yescharacteristic
39#14558715—21no—
40#14558715—21no—
41C22⋊Dic149—21no—
42#14558713—21no—
43#14558713—21no—
44C4×Dic149—21no—
45C4×Dic149—21no—
46C4×Dic149—21no—
47C22×C4×C149C2×C411yescharacteristic
48C4⋊C4×C149C2×C411yescharacteristic
49C4⋊C4×C149C2×C411yescharacteristic
50C22⋊C4×C149—21no—
51C42×C149—21no—
52C2×#10597010—42no—
53C2×#10597010—42no—
54C2×#10597010—42no—
55#11924753—42no—
56C22×D149—22no—
57C22×D149—22no—
58C22×D149—21no—
59C22×D149—21no—
60C22×D149C22⋊C411yescharacteristic
61C22×D149C2×D411yescharacteristic
62C2×Dic149—22no—
63C2×Dic149—21no—
64C2×Dic149—21no—
65C2×Dic149C22⋊C411yescharacteristic
66C2×Dic149C2×D411yescharacteristic
67C4×D149—22no—
68C4×D149—22no—
69C4×D149—22no—
70C4×D149—42no—
71C4×D149—41no—
72C4×D149—41no—
73C4×D149#4114yes—
74C23×C149C22⋊C411yescharacteristic
75C2×C4×C149—22no—
76C2×C4×C149—21no—
77C2×C4×C149—21no—
78C2×C4×C149C22⋊C411yescharacteristic
79C2×C4×C149C22×C411yescharacteristic
80C22×C149—21no—
81C22×C149—21no—
82C22×C149—21no—
83C22×C149C2×C22⋊C411yescharacteristic
84C2×D149—21no—
85C2×D149—21no—
86C2×D149—21no—
87C2×D149—42no—
88C2×D149—42no—
89C2×D149#12312yes—
90C2×D149#13512yes—
91C2×D149AGL(1,ℤ/8)11yescharacteristic
92C2×D149#13711yescharacteristic
93#10597010—82no—
94C4×C149—21no—
95C4×C149—41no—
96C4×C149—41no—
97C4×C149#11712yes—
98Dic149—21no—
99Dic149—41no—
100Dic149—41no—
101Dic149#12312yes—
102C2×C149—41no—
103C2×C149#38111yescharacteristic
104C2×C149#41611yescharacteristic
105C2×C149#41711yescharacteristic
106D149—41no—
107D149#48212yes—
108D149#48512yes—
109C149#182511yescharacteristic, complemented, Sylow
110#1825—1491nomaximal, Sylow
111C2×#117—1491no—
112C2×C22⋊C8—1491no—
113#380—1491no—
114#340—1492no—
115#340—1492no—
116C23×C4—1491no—
117C22×C8—1492no—
118#117—2981no—
119#117—2981no—
120#117—1491no—
121#117—1491no—
122#117—1491no—
123#117#1059701011yescharacteristic, complemented
124C2×C4⋊C4—1492no—
125C2×C4⋊C4—1491no—
126C2×C4⋊C4—1491no—
127C2×C22⋊C4—2981no—
128C2×C22⋊C4—2981no—
129C2×C42—2981no—
130C22⋊C8—2981no—
131C22⋊C8—2981no—
132#95—2981no—
133C24—1491no—
134C22×C4—2984no—
135C22×C4—2981no—
136C22×C4—2981no—
137C22×C4—2982no—
138C22×C4—1491no—
139C22×C4—1491no—
140C22×C4—1491no—
141C22×C4—1491no—
142C22×C4—1491no—
143C22×C4C2×#1059701011yescharacteristic
144C2×C8—2982no—
145C2×C8—2984no—
146C4⋊C4—2981no—
147C4⋊C4—2981no—
148C4⋊C4—2984no—
149C4⋊C4—1491no—
150C4⋊C4—1491no—
151C4⋊C4C2×#1059701011yescharacteristic
152C4⋊C4C2×#1059701011yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2981no—
155C22⋊C4—2981no—
156C22⋊C4—2981no—
157C22⋊C4—5962no—
158C42—21no—
159C42—2981no—
160C42—2981no—
161C42—2981no—
162C23—2981no—
163C23—2982no—
164C23—2982no—
165C23—2981no—
166C23—1491no—
167C23—1491no—
168C23C22⋊#1059701011yescharacteristic
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—2982no—
173C2×C4—2982no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—2981no—
177C2×C4—2981no—
178C2×C4—5962no—
179C2×C4—5961no—
180C2×C4—5961no—
181C2×C4—5962no—
182C2×C4—5962no—
183C2×C4—5962no—
184C2×C4—1491no—
185C2×C4—1491no—
186C2×C4—1494no—
187C2×C4C22⋊#1059701011yescharacteristic
188C2×C4C22×#1059701011yescharacteristic
189C8—5962no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—2981no—
194C22—2981no—
195C22—2981no—
196C22—5962no—
197C22—5962no—
198C22—1492no—
199C22—1492no—
200C22—1491no—
201C22—1491no—
202C22C2×C22⋊#1059701011yescharacteristic
203C4—21no—
204C4—41no—
205C4—41no—
206C4—2981no—
207C4—5961no—
208C4—5961no—
209C4—1492no—
210C4—11922no—
211C4#1801199012yes—
212C2—41no—
213C2—5961no—
214C2—1492no—
215C2—1492no—
216C2#2375056811yescharacteristic
217C2#2375061511yescharacteristic
218C2#2375061611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#117×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149D4
cosocleC2×C4×D149C23
hypercenter#117#10597010
hypocenterC149#1825
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #23750498C2semidirect
4. #23750498C2semidirect
13. #18011870C4semidirect
14. #18011869C4semidirect
15. #18011869C4semidirect
22. #117×C149C4semidirect
109. C149#1825semidirect
123. #117#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊(C22⋊C8)2
#237505672
#237504982
#117×D1492
#1825149