Finite Group Databasebeta

← #34052961

Subgroups — #34052961

Order 19072.

348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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#23749566C212yesmaximal
2#23749559C212yesmaximal
3#23749557C212yesmaximal
4#23749555C212yesmaximal
5#23749546C212yesmaximal
6#23749545C211yesmaximal, characteristic
7#23749494C211yesmaximal, characteristic
8#23749492C212yesmaximal
9#400×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11C2×C4⋊Dic149C2211yescharacteristic
12C2×C4⋊Dic149C2212yes—
13C2×C4⋊Dic149C2212yes—
14C2×#14558715C2212yes—
15C2×#14558715C2212yes—
16C2×#14558715C2212yes—
17C2×#14558715C2212yes—
18C2×C4×Dic149C2211yescharacteristic
19#18011818C2212yes—
20#18011818C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2211yescharacteristic
25#18011818C2212yes—
26C2×C4⋊C4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28#95×C149C2212yes—
29#95×C149C2212yes—
30#95×C149C2211yescharacteristic
31C2×Dic298—41no—
32C2×Dic298—42no—
33C22×Dic149C2312yes—
34C22×Dic149C2312yes—
35C22×Dic149C2312yes—
36C22×Dic149C2312yes—
37C4⋊Dic149—41no—
38C4⋊Dic149—42no—
39C4⋊Dic149—42no—
40#14558715—42no—
41#14558715—42no—
42#14558715—42no—
43#14558715—42no—
44C4×Dic149Q814yescomplemented
45C22×C4×C149C2311yescharacteristic
46C22×C4×C149C2312yes—
47C22×C4×C149C2312yes—
48C22×C4×C149C2311yescharacteristic
49C22×C4×C149C2311yescharacteristic
50C4⋊C4×C149—41no—
51C4⋊C4×C149—41no—
52Dic298—44no—
53C2×Dic149—22no—
54C2×Dic149—22no—
55C2×Dic149—22no—
56C2×Dic149—22no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149C2×Q814yes—
65C23×C149C2411yescharacteristic
66C2×C4×C149—21no—
67C2×C4×C149—21no—
68C2×C4×C149—21no—
69C2×C4×C149—22no—
70C2×C4×C149—21no—
71C2×C4×C149—22no—
72C2×C4×C149—22no—
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—24no—
77C2×C4×C149C2×Q812yes—
78C22×C149C22×Q811yescharacteristic
79C22×C149H(5,𝔽2)11yescharacteristic
80C22×C149H(5,𝔽2)12yes—
81C22×C1492−1+411yescharacteristic
82C22×C1492−1+412yes—
83C4×C149—22no—
84C4×C149—41no—
85C4×C149—41no—
86C4×C149—42no—
87C4×C149—42no—
88Dic149—24no—
89Dic149—42no—
90Dic149—42no—
91Dic149—42no—
92C2×C149#54411yescharacteristic
93C2×C149#54412yes—
94C2×C149#56011yescharacteristic
95C2×C149#56311yescharacteristic
96C2×C149#56312yes—
97C149#284311yescharacteristic, complemented, Sylow
98#2843—1491nomaximal, Sylow
99#400—1492no—
100#400D14911yescharacteristic
101#398—1492no—
102#398—1492no—
103#398—1492no—
104#395—1491no—
105#395—1492no—
106#384—1491no—
107#383—1492no—
108C22×Q8—1491no—
109C2×C4⋊C4—1492no—
110C2×C4⋊C4—1492no—
111C2×C4⋊C4—1491no—
112C2×C4⋊C4—1492no—
113C2×C4⋊C4—1492no—
114C2×C4⋊C4—1492no—
115C2×C4⋊C4—1492no—
116C2×C4⋊C4C2×D14911yescharacteristic
117C2×C4⋊C4C2×D14911yescharacteristic
118C2×C42—1491no—
119#95—1492no—
120#95—1492no—
121#95—1492no—
122#95—1492no—
123#95—1492no—
124#95—1491no—
125#95—1492no—
126#95C2×D14912yes—
127#95C2×D14912yes—
128#95C2×D14911yescharacteristic
129C2×Q8—5961no—
130C2×Q8—5962no—
131C22×C4—1492no—
132C22×C4—1492no—
133C22×C4—1492no—
134C22×C4—1492no—
135C22×C4C22×D14912yes—
136C22×C4C22×D14912yes—
137C22×C4C22×D14911yescharacteristic
138C22×C4C22×D14911yescharacteristic
139C22×C4C22×D14911yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—5962no—
143C4⋊C4—5962no—
144C4⋊C4—5962no—
145C4⋊C4—5962no—
146C4⋊C4—5961no—
147C4⋊C4—5962no—
148C4⋊C4—5962no—
149C42—1494no—
150C23C23×D14911yescharacteristic
151Q8—5964no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—2982no—
164C2×C4—2982no—
165C2×C4—2982no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—2982no—
169C2×C4—2982no—
170C2×C4—2982no—
171C2×C4—2982no—
172C2×C4—2982no—
173C2×C4—2982no—
174C2×C4—1494no—
175C2×C4Q8×D14912yes—
176C22C2×Q8×D14911yescharacteristic
177C22#1801195611yescharacteristic
178C22#1801195712yes—
179C22#1801195811yescharacteristic
180C22#1801195812yes—
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—2984no—
187C4—5962no—
188C4—5962no—
189C4—5962no—
190C2#2375025411yescharacteristic
191C2#2375025512yes—
192C2#2375036511yescharacteristic
193C2#2375037511yescharacteristic
194C2#2375037712yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, prime radical, cosocleC23×C149C24
Fitting#400×C149C2
hypercenter#400D149
hypocenterC149#2843
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic149Q8semidirect
97. C149#2843semidirect

Maximal subgroups

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

subgroupindex
#237495662
#237495592
#237495572
#237495552
#237495462
#237495452
#237494942
#237494922
#400×C1492
#2843149