Finite Group Databasebeta

← #34060854

Subgroups — #34060854

Order 19072.

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

normal subgroups only

This group has 336 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
1C2×#18011976C214yesmaximal, complemented
2C4×#14558746C211yesmaximal, characteristic, complemented
3C4×C4⋊#10597010C211yesmaximal, characteristic, complemented
4#23750176C211yesmaximal, characteristic
5C2×#14558746C2212yes—
6C2×C4⋊#10597010—21no—
7C2×C4×#10597010C2212yes—
8#18011976—28no—
9#18011966—21no—
10C4×#11924753—21no—
11(C2×#10597010)⋊C4—21no—
12C2×#14558737C2212yes—
13#18011908C411yescharacteristic, complemented
14#18011900C412yescomplemented
15#18011886—21no—
16#18011886—21no—
17#18011873—21no—
18#18011873—21no—
19C42×D149C2211yescharacteristic
20C4⋊Q8×C149C411yescharacteristic, complemented
21C22×#10597010—22no—
22#14558746—22no—
23#14558746D414yescomplemented
24C2×#11924753—22no—
25C4⋊#10597010—24no—
26C4×#10597010—24no—
27#14558737—24no—
28#14558737—24no—
29C2×D596—22no—
30C2×D596—21no—
31C2×D596—21no—
32C2×D596C2×C412yes—
33C2×C4×D149—22no—
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149C2311yescharacteristic
37#14558713—22no—
38#14558713—22no—
39C4×Dic149C2×C411yescharacteristic
40C4×Dic149D411yescharacteristic
41C4×Dic149D411yescharacteristic
42C2×Q8×C149C2×C412yes—
43C4⋊C4×C149—21no—
44C4⋊C4×C149—21no—
45C42×C149C2×C411yescharacteristic
46C2×#10597010—24no—
47C2×#10597010—42no—
48C2×#10597010—42no—
49#11924753—24no—
50C22×D149—22no—
51C22×D149C2×D411yescharacteristic
52D596—24no—
53D596—42no—
54D596—42no—
55D596—42no—
56D596—42no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C4×D149—22no—
61C4×D149—41no—
62C4×D149—44no—
63C4×D149C2×D412yes—
64C4×D149#4112yes—
65Q8×C149—24no—
66C2×C4×C149—22no—
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22×C411yescharacteristic
70C22×C149C2×C22⋊C411yescharacteristic
71C2×D149—21no—
72C2×D149—21no—
73C2×D149—42no—
74C2×D149—42no—
75C2×D149—42no—
76C2×D149#12411yescharacteristic
77C2×D149#12711yescharacteristic
78#10597010—44no—
79C4×C149—21no—
80C4×C149—42no—
81C4×C149#10412yescomplemented
82C4×C149C4×D412yes—
83Dic149—21no—
84Dic149—21no—
85Dic149#12112yes—
86C2×C149#39011yescharacteristic
87C2×C149C2×#10411yescharacteristic
88C2×C149#42111yescharacteristic
89D149—21no—
90D149—21no—
91D149—82no—
92C149#198011yescharacteristic, complemented, Sylow
93#1980—1491nomaximal, Sylow
94#532—1491no—
95C2×#104—1494no—
96C4×M16—1491no—
97C4×C4⋊C4—1491no—
98C2×#41—1492no—
99C2×M16—1492no—
100C4⋊Q8#1059701011yescharacteristic, complemented
101#127—1491no—
102#124—1492no—
103#121—2981no—
104#121—2981no—
105C4×D4—2981no—
106C4×D4—2981no—
107C2×C4⋊C4—2981no—
108C2×C42—1492no—
109C2×C42—1491no—
110#104—2988no—
111#97—2981no—
112C4×C8—2981no—
113#95—2981no—
114#41—2984no—
115#41—2984no—
116C2×Q8C2×#1059701012yes—
117C2×D4—2982no—
118C2×D4—2981no—
119C2×D4—2981no—
120C2×D4—1492no—
121C22×C4—2982no—
122C22×C4—2982no—
123C22×C4—1491no—
124C22×C4—1491no—
125C22×C4—1491no—
126M16—2982no—
127M16—1494no—
128C2×C8—2982no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2984no—
132C22⋊C4—2982no—
133C22⋊C4—2982no—
134C42—2984no—
135C42—1491no—
136C42—1491no—
137C42—1491no—
138C42C2×#1059701011yescharacteristic
139C23—2982no—
140C23—1491no—
141Q8—24no—
142D4—2984no—
143D4—5962no—
144D4—5962no—
145D4—5962no—
146D4—5962no—
147C2×C4—22no—
148C2×C4—2982no—
149C2×C4—2984no—
150C2×C4—5961no—
151C2×C4—5964no—
152C2×C4—5962no—
153C2×C4—5962no—
154C2×C4—1491no—
155C2×C4—1491no—
156C2×C4—1491no—
157C2×C4—1492no—
158C2×C4—1492no—
159C2×C4C22⋊#1059701011yescharacteristic
160C2×C4C22⋊#1059701011yescharacteristic
161C2×C4C22×#1059701011yescharacteristic
162C8—2984no—
163C22—2981no—
164C22—2981no—
165C22—5962no—
166C22—5962no—
167C22—5962no—
168C22—1491no—
169C22—1491no—
170C22C2×C22⋊#1059701011yescharacteristic
171C4—21no—
172C4—42no—
173C4—2981no—
174C4—2981no—
175C4—5964no—
176C4—1492no—
177C4#1801197612yescomplemented
178C4D4×#1059701012yes—
179C2—2981no—
180C2—2981no—
181C2—11922no—
182C2#2375057711yescharacteristic
183C2C2×#1801197611yescharacteristic
184C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750176C2
cosocleC2×C4×D149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1980
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#18011976C2semidirect
2. C4×#14558746C2semidirect
3. C4×C4⋊#10597010C2semidirect
13. #18011908C4semidirect
14. #18011900C4semidirect
20. C4⋊Q8×C149C4semidirect
23. #14558746D4semidirect
81. C4×C149#104semidirect
92. C149#1980semidirect
100. C4⋊Q8#10597010semidirect
177. C4#18011976semidirect

Maximal subgroups

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

subgroupindex
C2×#180119762
C4×#145587462
C4×C4⋊#105970102
#237501762
#1980149