Finite Group Databasebeta

← #34060006

Subgroups — #34060006

Order 19072.

234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 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×C4⋊#11924753C211yesmaximal, characteristic, complemented
2C4×#14558745C211yesmaximal, characteristic, complemented
3#23750475C212yesmaximal, complemented
4D4⋊#11924753C212yesmaximal, complemented
5#23750156C211yesmaximal, characteristic
6C2×#14558745—21no—
7C22×#11924753—21no—
8C4⋊#11924753—21no—
9C4⋊#11924753C2212yes—
10#18011966—21no—
11C4×#11924753C2212yes—
12#18011904—21no—
13#18011902C411yescharacteristic
14#18011898C411yescharacteristic
15#18011892—21no—
16#18011890C411yescharacteristic
17#18011876C2211yescharacteristic
18D4×Dic149—21no—
19D4×Dic149C2211yescharacteristic
20#18011867—21no—
21C2×C4×Dic149C2211yescharacteristic
22#121×C149C411yescharacteristic
23#14558745—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×#11924753—42no—
27C2×Dic298C2×C411yescharacteristic
28C22×Dic149—21no—
29C22×Dic149D411yescharacteristic
30C22×Dic149D411yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149C2×C411yescharacteristic
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36C22⋊Dic149—21no—
37C22⋊Dic149—21no—
38C22⋊Dic149—21no—
39C22⋊Dic149—21no—
40C4×Dic149—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45C2×D4×C149—21no—
46C2×D4×C149C2×C411yescharacteristic
47C22×C4×C149C2×C411yescharacteristic
48C4⋊C4×C149C2×C411yescharacteristic
49C22⋊C4×C149—21no—
50#11924753—24no—
51#11924753—42no—
52Dic298—22no—
53C2×Dic149—22no—
54C2×Dic149—21no—
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C2×Dic149—41no—
59C2×Dic149—41no—
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C22⋊C411yescharacteristic
62C2×Dic149C2×D411yescharacteristic
63C2×Dic149C2×D411yescharacteristic
64C23×C149—21no—
65C23×C149C22⋊C411yescharacteristic
66D4×C149—22no—
67D4×C149—42no—
68C2×C4×C149—22no—
69C2×C4×C149—21no—
70C2×C4×C149C22⋊C411yescharacteristic
71C2×C4×C149C22×C411yescharacteristic
72C22×C149—21no—
73C22×C149—21no—
74C22×C149—41no—
75C22×C149—41no—
76C22×C149—41no—
77C22×C149#10412yes—
78C22×C149C2×C22⋊C411yescharacteristic
79C4×C149—21no—
80C4×C149—41no—
81C4×C149#13112yes—
82Dic149—21no—
83Dic149—21no—
84Dic149—21no—
85Dic149—41no—
86Dic149—41no—
87Dic149AGL(1,ℤ/8)11yescharacteristic
88Dic149#13711yescharacteristic
89C2×C149—22no—
90C2×C149—81no—
91C2×C149#40811yescharacteristic
92C2×C149#41711yescharacteristic
93C2×C149C2×#10411yescharacteristic
94C149#148311yescharacteristic, complemented, Sylow
95#1483—1491nomaximal, Sylow
96#529—1491no—
97C2×C4⋊C8—1491no—
98C4×M16—1491no—
99Q8⋊C8—1492no—
100D4⋊C8—1492no—
101C2×M16—2981no—
102C22×C8—2981no—
103#126—2981no—
104#125—1491no—
105#124—1491no—
106#123—2981no—
107C22⋊Q8—1491no—
108#121#1059701011yescharacteristic
109C4×Q8—1491no—
110C4×D4—2981no—
111C4×D4—1491no—
112#117—2981no—
113C2×C42—1491no—
114C4⋊C8—2981no—
115C4⋊C8—1492no—
116#97—2981no—
117C4×C8—1492no—
118C2×Q8—1491no—
119C2×D4—21no—
120C2×D4C2×#1059701011yescharacteristic
121C22×C4—2981no—
122C22×C4—1491no—
123C22×C4—1491no—
124C22×C4C2×#1059701011yescharacteristic
125M16—2984no—
126C2×C8—2982no—
127C2×C8—2982no—
128C2×C8—5962no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—2981no—
132C4⋊C4—2981no—
133C4⋊C4—1491no—
134C4⋊C4C2×#1059701011yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—2981no—
137C22⋊C4—2981no—
138C22⋊C4—2981no—
139C22⋊C4—2981no—
140C42—2981no—
141C42—1491no—
142C42—1491no—
143C42—1491no—
144C42—1491no—
145C23—21no—
146C23C22⋊#1059701011yescharacteristic
147Q8—2982no—
148D4—22no—
149D4—42no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—2982no—
153C2×C4—2981no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—2981no—
157C2×C4—5961no—
158C2×C4—5961no—
159C2×C4—1491no—
160C2×C4—1491no—
161C2×C4—1491no—
162C2×C4—1491no—
163C2×C4C22⋊#1059701011yescharacteristic
164C2×C4C22×#1059701011yescharacteristic
165C8—2984no—
166C8—5962no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1801197512yes—
173C22C2×C22⋊#1059701011yescharacteristic
174C4—21no—
175C4—41no—
176C4—2981no—
177C4—2981no—
178C4—2981no—
179C4—5961no—
180C4—5961no—
181C4—1491no—
182C4—1491no—
183C4#1801199812yes—
184C2—22no—
185C2—81no—
186C2#2375059811yescharacteristic
187C2#2375061611yescharacteristic
188C2C2×#1801197511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting, prime radical#121×C149C4
socleC22×C149C2×C22⋊C4
cosocleC4×Dic149C23
hypercenter#121#10597010
hypocenterC149#1483
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#11924753C2semidirect
2. C4×#14558745C2semidirect
3. #23750475C2semidirect
4. D4⋊#11924753C2semidirect
94. C149#1483semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#119247532
C4×#145587452
#237504752
D4⋊#119247532
#237501562
#1483149