Finite Group Databasebeta

← #34060663

Subgroups — #34060663

Order 19072.

260 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750703C211yesmaximal, characteristic
2#23750631C212yesmaximal, complemented
3#23750598C211yesmaximal, characteristic
4#23750506C212yesmaximal, complemented
5#23749597C211yesmaximal, characteristic
6#18011998—22no—
7#18011998—22no—
8D149⋊M16—21no—
9C2×#14558745—21no—
10C2×#14558745C2211yescharacteristic
11C2×#14558745C2212yes—
12C22×#11924753C2211yescharacteristic
13#18011978—22no—
14C4⋊#11924753—22no—
15#18011968—21no—
16C22⋊#11924753—21no—
17C2×#14558735C2211yescharacteristic
18#18011867C2212yes—
19#18011826C411yescharacteristic
20#18011825C412yes—
21#99×C149C411yescharacteristic
22#14558746—21no—
23#14558746—21no—
24#14558745—22no—
25#14558745—22no—
26#14558745—22no—
27#14558745—22no—
28D149⋊C8—22no—
29C2×#11924753—21no—
30C2×#11924753—21no—
31C2×#11924753—21no—
32C2×#11924753—21no—
33C2×#11924753—22no—
34C2×#11924753D412yes—
35C2×#11924753D412yes—
36#14558735—22no—
37#14558735—22no—
38C2×Dic298Q811yescharacteristic
39C2×C22⋊D149C2×C411yescharacteristic
40C2×C22⋊D149Q811yescharacteristic
41C22×Dic149D411yescharacteristic
42C22×Dic149C2311yescharacteristic
43C2×C4×D149D411yescharacteristic
44#14558715—22no—
45C22⋊Dic149C2×C412yes—
46C4×Dic149—22no—
47C2×D4×C149C2×C411yescharacteristic
48C22⋊C4×C149C2×C412yes—
49#11924753—22no—
50#11924753—22no—
51#11924753—41no—
52#11924753—41no—
53C22×D149C4⋊C411yescharacteristic
54Dic298—22no—
55C22⋊D149—22no—
56C22⋊D149—22no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149—22no—
60C2×Dic149C4⋊C411yescharacteristic
61C2×Dic149C2×D412yes—
62C2×Dic149C2×D411yescharacteristic
63C2×Dic149C2×Q811yescharacteristic
64C2×Dic149#4112yes—
65C4×D149—21no—
66C4×D149—21no—
67C23×C149C4⋊C411yescharacteristic
68C23×C149C22×C411yescharacteristic
69D4×C149—22no—
70C2×C4×C149—22no—
71C2×C4×C149C4⋊C411yescharacteristic
72C22×C149—21no—
73C22×C149—41no—
74C22×C149—41no—
75C22×C149C2×C4⋊C411yescharacteristic
76C22×C149C4×D412yes—
77C2×D149—21no—
78C2×D149—41no—
79C4×C149—21no—
80C4×C149—42no—
81Dic149—21no—
82Dic149—42no—
83Dic149#12011yescharacteristic
84Dic149C22⋊Q812yes—
85Dic149#12311yescharacteristic
86C2×C149—22no—
87C2×C149—21no—
88C2×C149—41no—
89C2×C149#38511yescharacteristic
90D149—41no—
91C149#186811yescharacteristic, complemented, Sylow
92#1868—1491nomaximal, Sylow
93#568—1491no—
94#424—1492no—
95#410—1491no—
96#408—1491no—
97#344—1492no—
98C2×#41—1491no—
99#131—2982no—
100#131—2982no—
101C2×M16—2981no—
102C2×M16—2981no—
103C2×M16—1491no—
104C2×M16—1492no—
105C22×C8—1491no—
106#117—1492no—
107C4⋊C8—2982no—
108C4⋊C8—2982no—
109#99—1491no—
110#99—1492no—
111#99#1059701011yescharacteristic
112C22⋊C8—2981no—
113C22⋊C8—2981no—
114#41—2982no—
115#41—2982no—
116C2×Q8—1491no—
117C2×D4—1491no—
118C2×D4—1491no—
119C2×D4C2×#1059701011yescharacteristic
120C22×C4—1491no—
121C22×C4—1491no—
122C22×C4—1491no—
123M16—2982no—
124M16—2981no—
125M16—2981no—
126M16—2982no—
127M16—2982no—
128M16—2982no—
129C2×C8—2981no—
130C2×C8—2981no—
131C2×C8—2982no—
132C2×C8—2981no—
133C2×C8—2981no—
134C2×C8—2982no—
135C2×C8—1492no—
136C2×C8—1492no—
137C4⋊C4—2982no—
138C22⋊C4—1492no—
139C22⋊C4C2×#1059701012yes—
140C42—2982no—
141C23—1491no—
142C23C4⋊#1059701011yescharacteristic
143C23C22×#1059701011yescharacteristic
144Q8—2982no—
145D4—22no—
146D4—2982no—
147D4—2982no—
148C2×C4—22no—
149C2×C4—2981no—
150C2×C4—2981no—
151C2×C4—2981no—
152C2×C4—2981no—
153C2×C4—2982no—
154C2×C4—1491no—
155C2×C4—1491no—
156C2×C4—1491no—
157C2×C4—1492no—
158C2×C4—1492no—
159C2×C4C4⋊#1059701011yescharacteristic
160C8—2982no—
161C8—2982no—
162C8—5961no—
163C8—5961no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—2981no—
168C22—5961no—
169C22C2×C4⋊#1059701011yescharacteristic
170C22D4×#1059701012yes—
171C4—21no—
172C4—42no—
173C4—2981no—
174C4—5962no—
175C4—1491no—
176C4—1491no—
177C4—1492no—
178C2—22no—
179C2—21no—
180C2—41no—
181C2—5961no—
182C2#2375057211yescharacteristic
subgroupG/H
centerC2#23750572
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting#99×C149C4
socleC2×C149#385
prime radicalC2×#14558735C22
cosocleC22×Dic149C23
hypercenter#99#10597010
hypocenterC149#1868
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #23750631C2semidirect
4. #23750506C2semidirect
91. C149#1868semidirect

Maximal subgroups

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

subgroupindex
#237507032
#237506312
#237505982
#237505062
#237495972
#1868149