Finite Group Databasebeta

← #34052874

Subgroups — #34052874

Order 19072.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C149⋊#401C212yesmaximal, complemented
2#23749561C211yesmaximal, characteristic
3#23749559C212yesmaximal, complemented
4#23749558C212yesmaximal, complemented
5#23749556C212yesmaximal, complemented
6#23749553C212yesmaximal
7#23749550C211yesmaximal, characteristic
8#23749498C212yesmaximal
9#385×C149C211yesmaximal, characteristic
10C2×C4⋊Dic149C2211yescharacteristic
11C2×C4⋊Dic149C2211yescharacteristic
12C2×#14558715C2212yes—
13C2×#14558715C2212yes—
14C2×#14558715C2212yes—
15C2×#14558715C2212yes—
16C2×C22⋊Dic149C2212yes—
17C2×C22⋊Dic149C2212yes—
18#18011818C2212yes—
19#18011818C2212yes—
20#18011818C2211yescharacteristic
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2212yes—
25#18011818C2211yescharacteristic
26C23×C4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2212yes—
28C2×C22⋊C4×C149C2211yescharacteristic
29C2×C22⋊C4×C149C2211yescharacteristic
30#95×C149C2212yes—
31C22×Dic149C2312yes—
32C22×Dic149C2312yes—
33C22×Dic149C2312yes—
34C22×Dic149C2312yes—
35C4⋊Dic149—41no—
36C4⋊Dic149—41no—
37#14558715—42no—
38#14558715—42no—
39#14558715—42no—
40#14558715—42no—
41C22⋊Dic149—24no—
42C22⋊Dic149—42no—
43C24×C149C2311yescharacteristic
44C22×C4×C149—42no—
45C22×C4×C149—41no—
46C22×C4×C149C2311yescharacteristic
47C22×C4×C149C2312yes—
48C22×C4×C149C2312yes—
49C22×C4×C149C2311yescharacteristic
50C4⋊C4×C149—42no—
51C22⋊C4×C149—22no—
52C22⋊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—22no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C23×C149—21no—
66C23×C149—22no—
67C23×C149—22no—
68C23×C149—21no—
69C23×C149#4112yes—
70C23×C149C2411yescharacteristic
71C2×C4×C149—22no—
72C2×C4×C149—21no—
73C2×C4×C149—21no—
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149—22no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—44no—
82C22×C149—24no—
83C22×C149—22no—
84C22×C149—41no—
85C22×C149—42no—
86C22×C149—41no—
87C22×C149C2×#4111yescharacteristic
88C22×C149H(5,𝔽2)12yes—
89C22×C149H(5,𝔽2)11yescharacteristic
90C22×C1492−1+412yes—
91C22×C1492−1+411yescharacteristic
92C4×C149—42no—
93C4×C149—41no—
94C4×C149—42no—
95C4×C149—41no—
96Dic149—42no—
97Dic149—42no—
98Dic149—42no—
99Dic149—42no—
100C2×C149—42no—
101C2×C149#53912yes—
102C2×C149#53911yescharacteristic
103C2×C149#56011yescharacteristic
104C2×C149#56312yes—
105C2×C149#56311yescharacteristic
106C149#283411yescharacteristic, complemented, Sylow
107#2834—1491nomaximal, Sylow
108#401—1492no—
109#399—1491no—
110#398—1492no—
111#398—1492no—
112#398—1492no—
113#397—1491no—
114#397—1492no—
115#385—1492no—
116#385D14911yescharacteristic
117C23×C4C2×D14911yescharacteristic
118C2×C4⋊C4—1492no—
119C2×C4⋊C4—1492no—
120C2×C4⋊C4—1492no—
121C2×C4⋊C4—1491no—
122C2×C4⋊C4—1492no—
123C2×C4⋊C4—1491no—
124C2×C4⋊C4C2×D14912yes—
125C2×C22⋊C4—1492no—
126C2×C22⋊C4—1492no—
127C2×C22⋊C4C2×D14911yescharacteristic
128C2×C22⋊C4C2×D14911yescharacteristic
129#95—1492no—
130#95—1492no—
131#95—1491no—
132#95—1492no—
133#95—1492no—
134#95—1492no—
135#95—1492no—
136#95—1491no—
137#95C2×D14912yes—
138C24C22×D14911yescharacteristic
139C22×C4—42no—
140C22×C4—41no—
141C22×C4—1492no—
142C22×C4—1492no—
143C22×C4—1492no—
144C22×C4—1492no—
145C22×C4C22×D14911yescharacteristic
146C22×C4C22×D14912yes—
147C22×C4C22×D14912yes—
148C22×C4C22×D14911yescharacteristic
149C4⋊C4—42no—
150C4⋊C4—5962no—
151C4⋊C4—5962no—
152C4⋊C4—5962no—
153C4⋊C4—5962no—
154C4⋊C4—5961no—
155C4⋊C4—5961no—
156C22⋊C4—22no—
157C22⋊C4—41no—
158C22⋊C4—2984no—
159C22⋊C4—5962no—
160C23—21no—
161C23—22no—
162C23—22no—
163C23—21no—
164C23#1455873612yes—
165C23C23×D14911yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—2982no—
178C2×C4—2982no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—2982no—
184C2×C4—2982no—
185C2×C4—2982no—
186C2×C4—2982no—
187C2×C4—2982no—
188C2×C4—2982no—
189C22—24no—
190C22—22no—
191C22—41no—
192C22—42no—
193C22—41no—
194C22C2×#1455873611yescharacteristic
195C22#1801195612yes—
196C22#1801195611yescharacteristic
197C22#1801195812yes—
198C22#1801195911yescharacteristic
199C4—42no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—5962no—
204C4—5962no—
205C4—5962no—
206C4—5962no—
207C2—42no—
208C2#2375021712yes—
209C2#2375022211yescharacteristic
210C2#2375036411yescharacteristic
211C2#2375037612yes—
212C2#2375037811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#385×C149C2
prime radicalC24×C149C23
hypercenter#385D149
hypocenterC149#2834
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C149⋊#401C2semidirect
3. #23749559C2semidirect
4. #23749558C2semidirect
5. #23749556C2semidirect
106. C149#2834semidirect

Maximal subgroups

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

subgroupindex
C149⋊#4012
#237495612
#237495592
#237495582
#237495562
#237495532
#237495502
#237494982
#385×C1492
#2834149