Finite Group Databasebeta

← #34043731

Subgroups — #34043731

Order 19072.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#23750254C211yesmaximal, characteristic
2#23749960C211yesmaximal, characteristic
3#23749563C211yesmaximal, characteristic
4#23749363C211yesmaximal, characteristic
5#23749362C211yesmaximal, characteristic
6#23749350C211yesmaximal, characteristic
7#484×C149C211yesmaximal, characteristic
8#18011910—21no—
9#18011909—21no—
10#18011901—21no—
11#18011901—21no—
12#18011890C2211yescharacteristic
13#18011888—21no—
14#18011867—21no—
15C2×#14558715C2211yescharacteristic
16#18011844—21no—
17#18011834—21no—
18C22⋊#11924746C2211yescharacteristic
19#18011818—21no—
20#18011818—21no—
21#18011818C2211yescharacteristic
22C22⋊Q8×C149C2211yescharacteristic
23C2×C4⋊C4×C149C2211yescharacteristic
24#107×C149—21no—
25#103×C149—21no—
26C22⋊C8×C149C2211yescharacteristic
27C2×Dic298—21no—
28C2×Dic298D411yescharacteristic
29C22×Dic149—21no—
30C22×Dic149D411yescharacteristic
31C22×Dic149D411yescharacteristic
32C2×#11924746—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149D411yescharacteristic
35#14558715—21no—
36#14558715—21no—
37#14558715—21no—
38#14558715—21no—
39#14558715—21no—
40#14558715—21no—
41#14558715—21no—
42C22⋊Dic149—21no—
43C4×Dic149—21no—
44C4×Dic149—21no—
45C2×Q8×C149D411yescharacteristic
46C22×C4×C149—21no—
47C22×C4×C149C2311yescharacteristic
48C2×C8×C149—21no—
49C4⋊C4×C149—21no—
50C4⋊C4×C149—21no—
51C4⋊C4×C149—21no—
52C4⋊C4×C149D411yescharacteristic
53C22⋊C4×C149—21no—
54Dic298—41no—
55Dic298—81no—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C2×Dic149—41no—
62C2×Dic149—41no—
63C2×Dic149—41no—
64C2×Dic149—41no—
65C2×Dic149Q1612yes—
66#11924746—41no—
67C23×C149C2×D411yescharacteristic
68Q8×C149—41no—
69C2×C4×C149—21no—
70C2×C4×C149—21no—
71C2×C4×C149—41no—
72C2×C4×C149—42no—
73C2×C4×C149—41no—
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C8×C149—41no—
77C22×C149—21no—
78C22×C149—21no—
79C22×C149#12011yescharacteristic
80C22×C149C2×Q1611yescharacteristic
81C22×C149#13711yescharacteristic
82C4×C149—21no—
83C4×C149—21no—
84C4×C149—41no—
85C4×C149—41no—
86C4×C149—81no—
87Dic149—22no—
88Dic149—41no—
89Dic149—41no—
90Dic149—41no—
91Dic149—81no—
92C2×C149—21no—
93C2×C149—21no—
94C2×C149#45111yescharacteristic
95C2×C149#45411yescharacteristic
96C2×C149#45811yescharacteristic
97C149#161711yescharacteristic, complemented, Sylow
98#1617—1491nomaximal, Sylow
99#544—1491no—
100#484—1491no—
101#484D14911yescharacteristic
102#400—1491no—
103#328—1491no—
104#328—1491no—
105#324—1491no—
106C4⋊Q8—2981no—
107C4⋊Q8—2981no—
108#125—2981no—
109#125—2981no—
110C22⋊Q8—2981no—
111C22⋊Q8—1491no—
112C22⋊Q8C2×D14911yescharacteristic
113#117—2981no—
114C2×C4⋊C4—1491no—
115C2×C4⋊C4C2×D14911yescharacteristic
116#107—21no—
117#107—2981no—
118#103—21no—
119#103—2981no—
120C22⋊C8—1491no—
121C22⋊C8C2×D14911yescharacteristic
122#95—2981no—
123#95—2981no—
124#95—1491no—
125C2×Q8—2981no—
126C2×Q8—1491no—
127C2×Q8C22⋊D14911yescharacteristic
128C22×C4—21no—
129C22×C4—2981no—
130C22×C4—1491no—
131C22×C4—1491no—
132C22×C4C22×D14911yescharacteristic
133C2×C8—21no—
134C2×C8—2981no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2981no—
139C4⋊C4—2981no—
140C4⋊C4—2981no—
141C4⋊C4—2981no—
142C4⋊C4—2981no—
143C4⋊C4—2981no—
144C4⋊C4—2981no—
145C4⋊C4—2981no—
146C4⋊C4—1491no—
147C4⋊C4C22⋊D14911yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—2981no—
150C42—2981no—
151C42—2981no—
152C23D4×D14911yescharacteristic
153Q8—41no—
154Q8—5961no—
155Q8—11921no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—2981no—
162C2×C4—2981no—
163C2×C4—2981no—
164C2×C4—2981no—
165C2×C4—2981no—
166C2×C4—5961no—
167C2×C4—5961no—
168C2×C4—5961no—
169C2×C4—5961no—
170C2×C4—1492no—
171C2×C4D4×D14911yescharacteristic
172C2×C4C2×C22⋊D14911yescharacteristic
173C8—41no—
174C8—5961no—
175C22—21no—
176C22—21no—
177C22#1801187911yescharacteristic
178C22Q16×D14911yescharacteristic
179C22#1801194311yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—2982no—
186C4—5961no—
187C4—5961no—
188C4—5961no—
189C4—11921no—
190C2—21no—
191C2—21no—
192C2#2374977911yescharacteristic
193C2#2374979611yescharacteristic
194C2#2374981411yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#484×C149C2
socleC22×C149#120
prime radicalC23×C149C2×D4
hypercenter#484D149
hypocenterC149#1617
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
97. C149#1617semidirect

Maximal subgroups

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

subgroupindex
#237502542
#237499602
#237495632
#237493632
#237493622
#237493502
#484×C1492
#1617149