Finite Group Databasebeta

← #34052757

Subgroups — #34052757

Order 19072.

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

normal subgroups only

This group has 380 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
1C2×#18011901C212yesmaximal
2#23749567C212yesmaximal
3#23749566C212yesmaximal
4#23749559C212yesmaximal
5#23749558C212yesmaximal
6#23749558C212yesmaximal
7#23749555C211yesmaximal, characteristic
8#23749490C211yesmaximal, characteristic
9#398×C149C211yesmaximal, characteristic
10#18011901—28no—
11C2×C4⋊Dic149C2212yes—
12C2×C4⋊Dic149C2211yescharacteristic
13C2×C4⋊Dic149C2211yescharacteristic
14C2×#14558715C2212yes—
15C2×#14558715C2212yes—
16C2×#14558715C2212yes—
17C2×#14558715C2212yes—
18C2×#14558715C2212yes—
19C2×C4×Dic149C2211yescharacteristic
20#18011818C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2211yescharacteristic
24#18011818C2212yes—
25#18011818C2212yes—
26#18011818C2212yes—
27C2×C4⋊C4×C149C2212yes—
28C2×C4⋊C4×C149C2211yescharacteristic
29C2×C4⋊C4×C149C2211yescharacteristic
30#95×C149C2212yes—
31#95×C149C2211yescharacteristic
32C22×Dic149C2312yes—
33C22×Dic149C2312yes—
34C22×Dic149C2312yes—
35C22×Dic149C2312yes—
36C4⋊Dic149—24no—
37C4⋊Dic149—41no—
38C4⋊Dic149—41no—
39#14558715—24no—
40#14558715—24no—
41#14558715—24no—
42#14558715—24no—
43#14558715—42no—
44C4×Dic149D414yes—
45C22×C4×C149C2311yescharacteristic
46C22×C4×C149C2312yes—
47C22×C4×C149C2311yescharacteristic
48C22×C4×C149C2312yes—
49C22×C4×C149C2311yescharacteristic
50C4⋊C4×C149—24no—
51C4⋊C4×C149—41no—
52C4⋊C4×C149—41no—
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—24no—
63C2×Dic149C2×D414yes—
64C23×C149C2411yescharacteristic
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149—22no—
68C2×C4×C149—22no—
69C2×C4×C149—21no—
70C2×C4×C149—22no—
71C2×C4×C149—21no—
72C2×C4×C149—22no—
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149C2×D412yes—
78C22×C149C22×D411yescharacteristic
79C22×C149H(5,𝔽2)11yescharacteristic
80C22×C1492−1+412yes—
81C22×C1492−1+411yescharacteristic
82C22×C1492−1+412yes—
83C4×C149—22no—
84C4×C149—42no—
85C4×C149—42no—
86C4×C149—41no—
87C4×C149—41no—
88Dic149—24no—
89Dic149—42no—
90Dic149—42no—
91Dic149—42no—
92C2×C149#53612yes—
93C2×C149#53711yescharacteristic
94C2×C149#56311yescharacteristic
95C2×C149#56311yescharacteristic
96C2×C149#56412yes—
97C149#282211yescharacteristic, complemented, Sylow
98#2822—1491nomaximal, Sylow
99C2×#125—1492no—
100#400—1492no—
101#400—1492no—
102#398—1491no—
103#398—1492no—
104#398—1492no—
105#398—1492no—
106#398D14911yescharacteristic
107#382—1491no—
108#125—2988no—
109C2×C4⋊C4—1492no—
110C2×C4⋊C4—1492no—
111C2×C4⋊C4—1492no—
112C2×C4⋊C4—1492no—
113C2×C4⋊C4—1492no—
114C2×C4⋊C4—1491no—
115C2×C4⋊C4—1492no—
116C2×C4⋊C4—1491no—
117C2×C4⋊C4C2×D14912yes—
118C2×C4⋊C4C2×D14911yescharacteristic
119C2×C4⋊C4C2×D14911yescharacteristic
120C2×C42—1491no—
121#95—1492no—
122#95—1492no—
123#95—1492no—
124#95—1492no—
125#95—1492no—
126#95—1492no—
127#95—1491no—
128#95C2×D14912yes—
129#95C2×D14911yescharacteristic
130C22×C4—1492no—
131C22×C4—1492no—
132C22×C4—1492no—
133C22×C4—1492no—
134C22×C4C22×D14911yescharacteristic
135C22×C4C22×D14911yescharacteristic
136C22×C4C22×D14912yes—
137C22×C4C22×D14912yes—
138C22×C4C22×D14911yescharacteristic
139C4⋊C4—24no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—2984no—
143C4⋊C4—2984no—
144C4⋊C4—2984no—
145C4⋊C4—2984no—
146C4⋊C4—2984no—
147C4⋊C4—5962no—
148C4⋊C4—5961no—
149C4⋊C4—5961no—
150C42—1494no—
151C23C23×D14911yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
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—2984no—
174C2×C4—1494no—
175C2×C4D4×D14912yes—
176C22C2×D4×D14911yescharacteristic
177C22#1801195611yescharacteristic
178C22#1801195812yes—
179C22#1801195811yescharacteristic
180C22#1801195912yes—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—2984no—
187C4—5962no—
188C4—5962no—
189C4—5962no—
190C2#2375019812yes—
191C2#2375020211yescharacteristic
192C2#2375037411yescharacteristic
193C2#2375037811yescharacteristic
194C2C149⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, prime radical, cosocleC23×C149C24
Fitting#398×C149C2
hypercenter#398D149
hypocenterC149#2822
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
97. C149#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#180119012
#237495672
#237495662
#237495592
#237495582
#237495552
#237494902
#398×C1492
#2822149