Finite Group Databasebeta

← #34060953

Subgroups — #34060953

Order 19072.

234 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 54 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#23750611C211yesmaximal, characteristic
2#23750604C211yesmaximal, characteristic
3#23750527C214yesmaximal, complemented
4#23750199C211yesmaximal, characteristic
5D149⋊M16—21no—
6#18011990—21no—
7#18011972—21no—
8#18011971C2212yes—
9#18011970—21no—
10#18011969C2212yes—
11C2×#14558736C2211yescharacteristic
12#18011909—21no—
13#18011900—21no—
14#18011894C412yescomplemented
15#18011894C2212yes—
16#18011887—21no—
17#18011887—21no—
18#18011870C411yescharacteristic, complemented
19C22×Q8×C149C411yescharacteristic, complemented
20#14558746—41no—
21#14558745—22no—
22D149⋊C8—41no—
23C4⋊#10597010—41no—
24C22⋊#10597010—22no—
25C4×#10597010—41no—
26#14558736—41no—
27#14558736—41no—
28C2×Dic298D411yescharacteristic
29C2×D596D411yescharacteristic
30C2×C22⋊D149C2×C411yescharacteristic
31C2×C22⋊D149C2311yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149D411yescharacteristic
34C4⋊Dic149—21no—
35#14558715—22no—
36#14558715—22no—
37C22⋊Dic149C2×C412yes—
38#14558713—22no—
39#14558713—22no—
40C4×Dic149—21no—
41C2×Q8×C149—21no—
42C2×Q8×C149—21no—
43C2×Q8×C149—41no—
44C2×Q8×C149—41no—
45C22×C4×C149C2×C411yescharacteristic
46C22×C4×C149C2×C412yes—
47C2×#10597010—42no—
48#11924753—42no—
49C22×D149C22⋊C411yescharacteristic
50C22×D149C2×D411yescharacteristic
51Dic298—41no—
52D596—41no—
53C22⋊D149—41no—
54C22⋊D149—41no—
55C2×Dic149—22no—
56C2×Dic149C22⋊C411yescharacteristic
57C2×Dic149C2×D411yescharacteristic
58C4×D149—21no—
59C4×D149—21no—
60C4×D149—21no—
61C4×D149—21no—
62C23×C149C22×C411yescharacteristic
63Q8×C149—42no—
64Q8×C149—41no—
65Q8×C149—41no—
66C2×C4×C149—21no—
67C2×C4×C149—21no—
68C2×C4×C149—22no—
69C2×C4×C149—42no—
70C2×C4×C149C22⋊C411yescharacteristic
71C2×C4×C149C22⋊C411yescharacteristic
72C22×C149—21no—
73C22×C149—41no—
74C22×C149C2×C22⋊C411yescharacteristic
75C2×D149—21no—
76C2×D149—21no—
77C2×D149—41no—
78C2×D149—41no—
79#10597010—82no—
80C4×C149—21no—
81C4×C149—42no—
82C4×C149#9911yescharacteristic
83C4×C149#9911yescharacteristic
84Dic149—21no—
85Dic149—21no—
86Dic149—42no—
87C2×C149—21no—
88C2×C149—41no—
89C2×C149C2×#9911yescharacteristic
90D149—41no—
91D149—41no—
92C149#212311yescharacteristic, complemented, Sylow
93#2123—1491nomaximal, Sylow
94#536—1491no—
95#413—1491no—
96#410—1491no—
97#352—1494no—
98C2×#41—1491no—
99C22×Q8#1059701011yescharacteristic, complemented
100C2×M16—2981no—
101C4⋊Q8—2981no—
102#124—2981no—
103#123—1492no—
104#123—1492no—
105C22⋊Q8—2981no—
106C22⋊Q8—2981no—
107#117—2981no—
108#117—1491no—
109#101—2981no—
110#100—1492no—
111#99—2981no—
112#99—1492no—
113#41—5961no—
114#41—5961no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8—1491no—
120C2×D4—1491no—
121C2×D4—1491no—
122C2×D4—1491no—
123C22×C4—1491no—
124C22×C4—1491no—
125C22×C4C2×#1059701012yes—
126C22×C4C2×#1059701011yescharacteristic
127M16—2982no—
128M16—5961no—
129C2×C8—5961no—
130C4⋊C4—2982no—
131C4⋊C4—2982no—
132C4⋊C4—2981no—
133C4⋊C4—5961no—
134C22⋊C4—2982no—
135C22⋊C4—2982no—
136C22⋊C4—2982no—
137C22⋊C4—1492no—
138C42—2981no—
139C42—5961no—
140C23—1491no—
141C23—1491no—
142C23C22×#1059701011yescharacteristic
143Q8—42no—
144Q8—41no—
145Q8—41no—
146Q8—5961no—
147D4—5961no—
148D4—5961no—
149D4—5961no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—2981no—
157C2×C4—2981no—
158C2×C4—2982no—
159C2×C4—5962no—
160C2×C4—1491no—
161C2×C4—1491no—
162C2×C4C22⋊#1059701011yescharacteristic
163C2×C4C22⋊#1059701011yescharacteristic
164C8—5962no—
165C22—21no—
166C22—41no—
167C22—2981no—
168C22—2981no—
169C22—5961no—
170C22—5961no—
171C22C2×C22⋊#1059701011yescharacteristic
172C4—21no—
173C4—42no—
174C4—2981no—
175C4—2981no—
176C4—5962no—
177C4—11922no—
178C4#1801196911yescharacteristic
179C4#1801196911yescharacteristic
180C2—21no—
181C2—41no—
182C2—5961no—
183C2—5961no—
184C2C2×#1801196911yescharacteristic
subgroupG/H
centerC2C2×#18011969
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC22×Q8×C149C4
socleC2×C149C2×#99
prime radicalC2×#14558736C22
cosocleC2×C22⋊D149C23
hypercenterC22×Q8#10597010
hypocenterC149#2123
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #23750527C2semidirect
14. #18011894C4semidirect
18. #18011870C4semidirect
19. C22×Q8×C149C4semidirect
92. C149#2123semidirect
99. C22×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506112
#237506042
#237505272
#237501992
#2123149