Finite Group Databasebeta

← #34060599

Subgroups — #34060599

Order 19072.

306 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 68 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#23750596C211yesmaximal, characteristic
2C4×C22⋊#10597010C211yesmaximal, characteristic
3#23750495C212yesmaximal, complemented
4#23750495C212yesmaximal, complemented
5#117×D149C211yesmaximal, characteristic
6C2×#14558746C2212yes—
7C2×C22⋊#10597010—21no—
8C2×C4×#10597010C2212yes—
9#18011968—21no—
10C22⋊#11924753—21no—
11(C2×#10597010)⋊C4—21no—
12C22×C4×D149C2211yescharacteristic
13#18011870C411yescharacteristic, complemented
14#18011869C2211yescharacteristic
15#18011869C2211yescharacteristic
16#18011868—21no—
17#18011867—21no—
18C4⋊C4×D149C411yescharacteristic, complemented
19C4⋊C4×D149C411yescharacteristic, complemented
20C22⋊C4×D149—21no—
21C42×D149—21no—
22#117×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24#14558746—24no—
25C2×#11924753—22no—
26C22⋊#10597010—24no—
27C4×#10597010—24no—
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—24no—
53C2×#10597010—42no—
54C2×#10597010—42no—
55#11924753—42no—
56C22×D149—22no—
57C22×D149—22no—
58C22×D149—41no—
59C22×D149C22⋊C411yescharacteristic
60C22×D149C2×D411yescharacteristic
61C2×Dic149—22no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C2×D411yescharacteristic
66C4×D149—22no—
67C4×D149—22no—
68C4×D149—22no—
69C4×D149—42no—
70C4×D149—42no—
71C4×D149#4114yes—
72C23×C149C22⋊C411yescharacteristic
73C2×C4×C149—22no—
74C2×C4×C149—21no—
75C2×C4×C149—21no—
76C2×C4×C149C22⋊C411yescharacteristic
77C2×C4×C149C22×C411yescharacteristic
78C22×C149—21no—
79C22×C149—21no—
80C22×C149—21no—
81C22×C149C2×C22⋊C411yescharacteristic
82C2×D149—21no—
83C2×D149—21no—
84C2×D149—21no—
85C2×D149—21no—
86C2×D149—44no—
87C2×D149#10412yes—
88C2×D149#12312yes—
89#10597010—44no—
90C4×C149—21no—
91C4×C149—41no—
92C4×C149—41no—
93C4×C149#11712yes—
94Dic149—21no—
95Dic149—41no—
96Dic149—41no—
97Dic149#12312yes—
98C2×C149—41no—
99C2×C149#38111yescharacteristic
100C2×C149C2×#10411yescharacteristic
101C2×C149#42111yescharacteristic
102D149—22no—
103D149—22no—
104C149#182611yescharacteristic, complemented, Sylow
105#1826—1491nomaximal, Sylow
106C2×#117—1491no—
107#407—1491no—
108C4×C22⋊C4—1491no—
109#339—1492no—
110#339—1492no—
111C23×C4—1491no—
112C2×M16—1492no—
113#117—2981no—
114#117—2981no—
115#117—1491no—
116#117—1491no—
117#117—1491no—
118#117#1059701011yescharacteristic, complemented
119C2×C4⋊C4—1491no—
120C2×C4⋊C4—1491no—
121C2×C22⋊C4—2981no—
122C2×C22⋊C4—2981no—
123C2×C42—2981no—
124C2×C42—1492no—
125C22⋊C8—2981no—
126C22⋊C8—2981no—
127#95—2981no—
128C24—1491no—
129C22×C4—2984no—
130C22×C4—2981no—
131C22×C4—2981no—
132C22×C4—2982no—
133C22×C4—1491no—
134C22×C4—1491no—
135C22×C4—1491no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4C2×#1059701011yescharacteristic
139M16—2984no—
140C2×C8—2982no—
141C4⋊C4—2981no—
142C4⋊C4—2981no—
143C4⋊C4—1491no—
144C4⋊C4—1491no—
145C4⋊C4C2×#1059701011yescharacteristic
146C4⋊C4C2×#1059701011yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—2981no—
149C22⋊C4—2981no—
150C22⋊C4—2984no—
151C22⋊C4—2981no—
152C42—21no—
153C42—2981no—
154C42—2981no—
155C42—2981no—
156C42—2984no—
157C23—2982no—
158C23—2982no—
159C23—5961no—
160C23—1491no—
161C23—1491no—
162C23C22⋊#1059701011yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—2982no—
169C2×C4—2982no—
170C2×C4—2984no—
171C2×C4—2981no—
172C2×C4—2981no—
173C2×C4—5962no—
174C2×C4—5962no—
175C2×C4—5962no—
176C2×C4—5962no—
177C2×C4—1491no—
178C2×C4—1491no—
179C2×C4—1494no—
180C2×C4C22⋊#1059701011yescharacteristic
181C2×C4C22×#1059701011yescharacteristic
182C8—5962no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—2981no—
187C22—2981no—
188C22—2981no—
189C22—2981no—
190C22—5964no—
191C22—1492no—
192C22—1492no—
193C22C2×C22⋊#1059701011yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—2981no—
198C4—5964no—
199C4—5961no—
200C4—5961no—
201C4—1492no—
202C4#1801199012yes—
203C2—41no—
204C2—2982no—
205C2—2982no—
206C2#2375056811yescharacteristic
207C2D149⋊#10411yescharacteristic
208C2#2375062211yescharacteristic
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#1826
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. #23750495C2semidirect
4. #23750495C2semidirect
13. #18011870C4semidirect
18. C4⋊C4×D149C4semidirect
19. C4⋊C4×D149C4semidirect
22. #117×C149C4semidirect
104. C149#1826semidirect
118. #117#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505962
C4×C22⋊#105970102
#237504952
#117×D1492
#1826149