Finite Group Databasebeta

← #34059982

Subgroups — #34059982

Order 19072.

276 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 94 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#23750641C211yesmaximal, characteristic, complemented
2C2×C4×#11924753C211yesmaximal, characteristic, complemented
3Q8⋊#11924753C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5#41×Dic149C211yesmaximal, characteristic
6C22×#11924753—21no—
7C4⋊#11924753C2212yes—
8C22⋊#11924753—21no—
9C4×#11924753—21no—
10C4×#11924753—21no—
11C4×#11924753C2212yes—
12Q8×Dic149C411yescharacteristic
13Q8×Dic149C2211yescharacteristic
14D4×Dic149—21no—
15D4×Dic149—21no—
16D4×Dic149C411yescharacteristic
17D4×Dic149C2211yescharacteristic
18#18011870—21no—
19#18011870C411yescharacteristic
20C2×C4×Dic149—21no—
21C2×C4×Dic149C2211yescharacteristic
22C2×#41×C149C411yescharacteristic
23C2×#11924753—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C22×Dic149—21no—
27C22×Dic149—21no—
28C22×Dic149D411yescharacteristic
29C22×Dic149D411yescharacteristic
30C4⋊Dic149—21no—
31C4⋊Dic149—21no—
32C4⋊Dic149C2×C411yescharacteristic
33C4⋊Dic149C2×C411yescharacteristic
34C22⋊Dic149—21no—
35C22⋊Dic149—21no—
36C22⋊Dic149—21no—
37C4×Dic149—21no—
38C4×Dic149—21no—
39C4×Dic149—21no—
40C4×Dic149C2×C411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149C2311yescharacteristic
44#41×C149—22no—
45#41×C149C814yescomplemented
46C2×Q8×C149C2×C411yescharacteristic
47C2×D4×C149—21no—
48C2×D4×C149C2×C411yescharacteristic
49C22×C4×C149—21no—
50C22×C4×C149C2×C411yescharacteristic
51#11924753—24no—
52#11924753—42no—
53C2×Dic149—22no—
54C2×Dic149—22no—
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149—42no—
58C2×Dic149—42no—
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C2×Dic149C2×D411yescharacteristic
63C23×C149—21no—
64C23×C149C22⋊C411yescharacteristic
65Q8×C149—21no—
66Q8×C149C2×C812yescomplemented
67D4×C149—24no—
68D4×C149—21no—
69D4×C149C2×C812yescomplemented
70C2×C4×C149—21no—
71C2×C4×C149—24no—
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C2×C812yes—
74C2×C4×C149M1612yes—
75C2×C4×C149C22×C411yescharacteristic
76C22×C149—21no—
77C22×C149—21no—
78C22×C149—22no—
79C22×C149—41no—
80C22×C149—41no—
81C22×C149C22⋊C812yes—
82C22×C149C2×C22⋊C411yescharacteristic
83C4×C149—22no—
84C4×C149C22⋊C812yes—
85C4×C149C22×C811yescharacteristic
86C4×C149C2×M1611yescharacteristic
87Dic149—21no—
88Dic149—21no—
89Dic149—41no—
90Dic149—41no—
91Dic149#10412yes—
92Dic149#13512yes—
93C2×C149—22no—
94C2×C149—42no—
95C2×C149C2×C22⋊C811yescharacteristic
96C2×C149#41611yescharacteristic
97C2×C149C2×#10411yescharacteristic
98C149#147611yescharacteristic, complemented, Sylow
99#1476—1491nomaximal, Sylow
100C4×#41—1491no—
101#431—1491no—
102C2×C4×C8—1491no—
103Q8⋊C8—1492no—
104D4⋊C8—1492no—
105C2×#41#1059701011yescharacteristic
106C22×C8—2981no—
107C4×Q8—1491no—
108C4×Q8—1491no—
109C4×D4—2981no—
110C4×D4—2981no—
111C4×D4—1491no—
112C4×D4—1491no—
113#117—2981no—
114#117—1491no—
115C2×C42—2981no—
116C2×C42—1491no—
117C4⋊C8—1492no—
118C22⋊C8—2981no—
119C4×C8—2981no—
120C4×C8—2981no—
121C4×C8—1492no—
122#41—22no—
123#41#1192475314yescomplemented
124C2×Q8C2×#1059701011yescharacteristic
125C2×D4—21no—
126C2×D4C2×#1059701011yescharacteristic
127C22×C4—21no—
128C22×C4—2981no—
129C22×C4—2981no—
130C22×C4—1491no—
131C22×C4—1491no—
132C22×C4C2×#1059701011yescharacteristic
133C2×C8—2984no—
134C2×C8—2982no—
135C2×C8—2982no—
136C4⋊C4—2981no—
137C4⋊C4—2981no—
138C4⋊C4—1491no—
139C4⋊C4—1491no—
140C22⋊C4—2981no—
141C22⋊C4—2981no—
142C22⋊C4—2981no—
143C42—2981no—
144C42—2981no—
145C42—2981no—
146C42—1491no—
147C42—1491no—
148C42—1491no—
149C42—1491no—
150C23—21no—
151C23C22⋊#1059701011yescharacteristic
152Q8—21no—
153Q8C2×#1192475312yescomplemented
154D4—24no—
155D4—21no—
156D4C2×#1192475312yescomplemented
157C2×C4—21no—
158C2×C4—24no—
159C2×C4—2982no—
160C2×C4—2982no—
161C2×C4—2981no—
162C2×C4—2981no—
163C2×C4—5962no—
164C2×C4—5962no—
165C2×C4—1491no—
166C2×C4—1491no—
167C2×C4—1491no—
168C2×C4—1491no—
169C2×C4C22⋊#1059701011yescharacteristic
170C2×C4C2×#1192475312yes—
171C2×C4#1455874512yes—
172C2×C4C22×#1059701011yescharacteristic
173C8—2984no—
174C8—5962no—
175C22—21no—
176C22—21no—
177C22—22no—
178C22—41no—
179C22—41no—
180C22C22⋊#1192475312yes—
181C22C2×C22⋊#1059701011yescharacteristic
182C4—22no—
183C4—2981no—
184C4—2981no—
185C4—5961no—
186C4—5961no—
187C4—1492no—
188C4—1492no—
189C4C22⋊#1192475312yes—
190C4C22×#1192475311yescharacteristic
191C4C2×#1455874511yescharacteristic
192C2—22no—
193C2—42no—
194C2C2×C22⋊#1192475311yescharacteristic
195C2#2375061511yescharacteristic
196C2D149⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597010
commutatorC4×C149C22×C8
FrattiniC2×C4C22×#10597010
Fitting, prime radicalC2×#41×C149C4
socleC22×C149C2×C22⋊C4
cosocleC4×Dic149C23
hypercenterC2×#41#10597010
hypocenterC149#1476
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23750641C2semidirect
2. C2×C4×#11924753C2semidirect
3. Q8⋊#11924753C2semidirect
4. D4⋊#11924753C2semidirect
45. #41×C149C8semidirect
66. Q8×C149C2×C8semidirect
69. D4×C149C2×C8semidirect
98. C149#1476semidirect
123. #41#11924753semidirect
153. Q8C2×#11924753semidirect
156. D4C2×#11924753semidirect

Maximal subgroups

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

subgroupindex
#237506412
C2×C4×#119247532
Q8⋊#119247532
D4⋊#119247532
#41×Dic1492
#1476149