Finite Group Databasebeta

← #34060463

Subgroups — #34060463

Order 19072.

324 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 100 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×#18011974C212yesmaximal
2#23750584C211yesmaximal, characteristic
3C4×C4⋊#10597010C211yesmaximal, characteristic
4#23750498C212yesmaximal
5C4×Q8×D149C211yesmaximal, characteristic
6C2×D149⋊C8C2212yes—
7C2×C4⋊#10597010C2212yes—
8C2×C4×#10597010—21no—
9#18011974C418yescomplemented
10#18011966—21no—
11#18011966—21no—
12(C2×#10597010)⋊C4—21no—
13C2×Q8×D149C2211yescharacteristic
14Q8×Dic149C411yescharacteristic, complemented
15C4×Dic298—21no—
16C4×Dic298C411yescharacteristic, complemented
17#18011876—21no—
18#18011876C411yescharacteristic, complemented
19C4⋊C4×D149—21no—
20C4⋊C4×D149C2211yescharacteristic
21C42×D149—21no—
22C42×D149C2211yescharacteristic
23C4×Q8×C149C411yescharacteristic, complemented
24C22×#10597010—22no—
25D149⋊C8—22no—
26D149⋊C8C2×C414yes—
27C2×#11924753—22no—
28C4⋊#10597010—22no—
29C4⋊#10597010C2×C414yes—
30C4×#10597010—42no—
31C2×Dic298—21no—
32C2×Dic298C2×C411yescharacteristic
33Q8×D149—22no—
34Q8×D149C2×C414yes—
35C2×C4×D149—21no—
36C2×C4×D149—21no—
37C2×C4×D149D411yescharacteristic
38C2×C4×D149D411yescharacteristic
39C2×C4×D149C2311yescharacteristic
40C4⋊Dic149—21no—
41C4⋊Dic149C2×C411yescharacteristic
42#14558715—21no—
43#14558715—21no—
44#14558715—21no—
45C4×Dic149—21no—
46C4×Dic149—21no—
47C4×Dic149—21no—
48C4×Dic149C2×C411yescharacteristic
49C4×Dic149D411yescharacteristic
50C4×Dic149D411yescharacteristic
51C2×Q8×C149C2×C411yescharacteristic
52C4⋊C4×C149—21no—
53C4⋊C4×C149C2×C411yescharacteristic
54C42×C149—21no—
55C42×C149C2×C411yescharacteristic
56C2×#10597010—24no—
57C2×#10597010—42no—
58C2×#10597010—42no—
59#11924753—24no—
60C22×D149C2×D411yescharacteristic
61Dic298—21no—
62Dic298—24no—
63Dic298C4212yescomplemented
64C2×Dic149—21no—
65C2×Dic149—21no—
66C2×Dic149C22⋊C411yescharacteristic
67C2×Dic149C22⋊C411yescharacteristic
68C2×Dic149C2×D411yescharacteristic
69C4×D149—24no—
70C4×D149—21no—
71C4×D149—21no—
72C4×D149—22no—
73C4×D149—41no—
74C4×D149—41no—
75C4×D149C22×C412yes—
76C4×D149#4112yes—
77Q8×C149—21no—
78Q8×C149C4212yescomplemented
79C2×C4×C149—21no—
80C2×C4×C149—21no—
81C2×C4×C149C22⋊C411yescharacteristic
82C2×C4×C149C22⋊C411yescharacteristic
83C2×C4×C149C22×C411yescharacteristic
84C22×C149C2×C22⋊C411yescharacteristic
85C2×D149C4×D412yes—
86C2×D149AGL(1,ℤ/8)11yescharacteristic
87C2×D149#13712yes—
88C2×D149#13711yescharacteristic
89#10597010—44no—
90C4×C149—22no—
91C4×C149—21no—
92C4×C149—21no—
93C4×C149—41no—
94C4×C149C2×C4211yescharacteristic
95C4×C149#11711yescharacteristic
96Dic149—22no—
97Dic149—21no—
98Dic149—21no—
99Dic149—41no—
100Dic149C4×D412yes—
101C2×C149C4×C22⋊C411yescharacteristic
102C2×C149#41711yescharacteristic
103C2×C149#41911yescharacteristic
104D149#44012yes—
105D149#44112yes—
106C149#176311yescharacteristic, complemented, Sylow
107#1763—1491nomaximal, Sylow
108C2×C4×Q8—1491no—
109C2×#103—1492no—
110C2×#97—1491no—
111C4×C4⋊C4—1491no—
112#340—1492no—
113C22×Q8—1491no—
114C22×C8—1492no—
115C4×Q8—2981no—
116C4×Q8—2981no—
117C4×Q8—1491no—
118C4×Q8—1491no—
119C4×Q8—1491no—
120C4×Q8#1059701011yescharacteristic, complemented
121C2×C4⋊C4—2981no—
122C2×C4⋊C4—1492no—
123C2×C4⋊C4—1491no—
124C2×C42—2981no—
125C2×C42—2981no—
126C2×C42—1491no—
127#103—1498no—
128#97—2981no—
129#97—2981no—
130#95—2981no—
131C2×Q8—2981no—
132C2×Q8—2982no—
133C2×Q8—1494no—
134C2×Q8—1491no—
135C2×Q8C2×#1059701011yescharacteristic
136C22×C4—2981no—
137C22×C4—2981no—
138C22×C4—2982no—
139C22×C4—1491no—
140C22×C4—1491no—
141C22×C4—1491no—
142C2×C8—2982no—
143C2×C8—2982no—
144C2×C8—1494no—
145C4⋊C4—21no—
146C4⋊C4—2981no—
147C4⋊C4—2981no—
148C4⋊C4—2981no—
149C4⋊C4—2982no—
150C4⋊C4—2981no—
151C4⋊C4—1494no—
152C4⋊C4—1491no—
153C4⋊C4C2×#1059701011yescharacteristic
154C42—21no—
155C42—2981no—
156C42—2981no—
157C42—2981no—
158C42—5962no—
159C42—1491no—
160C42—1491no—
161C42—1491no—
162C42C2×#1059701011yescharacteristic
163C23—1491no—
164Q8—21no—
165Q8—2984no—
166Q8—2981no—
167Q8—1492no—
168Q8C4×#1059701012yescomplemented
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—2981no—
172C2×C4—2984no—
173C2×C4—2981no—
174C2×C4—2982no—
175C2×C4—2981no—
176C2×C4—2984no—
177C2×C4—2981no—
178C2×C4—5961no—
179C2×C4—5961no—
180C2×C4—5962no—
181C2×C4—5962no—
182C2×C4—1491no—
183C2×C4—1491no—
184C2×C4—1491no—
185C2×C4—1492no—
186C2×C4—1492no—
187C2×C4C22⋊#1059701011yescharacteristic
188C2×C4C22⋊#1059701011yescharacteristic
189C2×C4C22×#1059701011yescharacteristic
190C8—2984no—
191C22—1492no—
192C22—1491no—
193C22—1491no—
194C22—1492no—
195C22C2×C22⋊#1059701011yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—2982no—
201C4—2981no—
202C4—2981no—
203C4—5964no—
204C4—5961no—
205C4—1492no—
206C4C2×C4×#1059701011yescharacteristic
207C4#1801199011yescharacteristic
208C2—1492no—
209C2—1492no—
210C2C4×C22⋊#1059701011yescharacteristic
211C2#2375061611yescharacteristic
212C2#2375061811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC4×C149C2×C42
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenterC4×Q8#10597010
hypocenterC149#1763
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
9. #18011974C4semidirect
14. Q8×Dic149C4semidirect
16. C4×Dic298C4semidirect
18. #18011876C4semidirect
23. C4×Q8×C149C4semidirect
63. Dic298C42semidirect
78. Q8×C149C42semidirect
106. C149#1763semidirect
120. C4×Q8#10597010semidirect
168. Q8C4×#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119742
#237505842
C4×C4⋊#105970102
#237504982
C4×Q8×D1492
#1763149