Finite Group Databasebeta

← #34047854

Subgroups — #34047854

Order 19072.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#18011890C211yesmaximal, characteristic
2#23749529C212yesmaximal, complemented
3#23749520C212yesmaximal, complemented
4#23749519C212yesmaximal
5#23749513C212yesmaximal
6#23749508C212yesmaximal, complemented
7#23749506C212yesmaximal, complemented
8#23749488C211yesmaximal, characteristic
9#380×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11#18011890C418yescomplemented
12C2×C4⋊Dic149C2211yescharacteristic
13C2×#14558715C2212yes—
14C2×#14558715C2212yes—
15C2×#14558715C2212yes—
16C2×C22⋊Dic149C2212yes—
17C2×C22⋊Dic149C2212yes—
18C2×C4×Dic149C2212yes—
19C2×C4×Dic149C2212yes—
20#18011818C2211yescharacteristic
21#18011818C2212yes—
22#18011818C2211yescharacteristic
23#18011818C2212yes—
24#18011818C2212yes—
25#18011818C2212yes—
26#18011818C2212yes—
27C23×C4×C149C2211yescharacteristic
28C2×C4⋊C4×C149C2212yes—
29C2×C22⋊C4×C149C2211yescharacteristic
30C2×C22⋊C4×C149C2211yescharacteristic
31#95×C149C2212yes—
32C2×Dic298—42no—
33C2×Dic298C2×C414yes—
34C22×Dic149C2312yes—
35C22×Dic149C2312yes—
36C22×Dic149C2312yes—
37C22×Dic149C2312yes—
38C4⋊Dic149C2×C414yes—
39#14558715—42no—
40#14558715—42no—
41#14558715C2×C418yes—
42C22⋊Dic149—42no—
43C22⋊Dic149C2×C418yes—
44C4×Dic149—42no—
45C4×Dic149—42no—
46C24×C149C2311yescharacteristic
47C22×C4×C149—42no—
48C22×C4×C149C2×C414yes—
49C22×C4×C149C2312yes—
50C22×C4×C149C2312yes—
51C22×C4×C149C2311yescharacteristic
52C22×C4×C149C2311yescharacteristic
53C4⋊C4×C149—42no—
54C22⋊C4×C149—41no—
55C22⋊C4×C149—41no—
56Dic298—44no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149C22×C414yes—
68C2×Dic149C22×C414yes—
69C23×C149—21no—
70C23×C149—22no—
71C23×C149—22no—
72C23×C149—21no—
73C23×C149C22×C412yes—
74C23×C149C2411yescharacteristic
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—22no—
82C2×C4×C149—22no—
83C2×C4×C149—44no—
84C2×C4×C149C22×C412yes—
85C2×C4×C149C22×C412yes—
86C22×C149—22no—
87C22×C149—22no—
88C22×C149—22no—
89C22×C149—42no—
90C22×C149—42no—
91C22×C149C23×C411yescharacteristic
92C22×C149H(5,𝔽2)12yes—
93C22×C149H(5,𝔽2)11yescharacteristic
94C22×C1492−1+412yes—
95C22×C1492−1+411yescharacteristic
96C4×C149—22no—
97C4×C149—22no—
98C4×C149—42no—
99C4×C149—42no—
100Dic149—24no—
101Dic149—24no—
102Dic149—42no—
103Dic149—42no—
104C2×C149—42no—
105C2×C149#51811yescharacteristic
106C2×C149#51911yescharacteristic
107C2×C149#52011yescharacteristic
108C2×C149#56212yes—
109C2×C149#56312yes—
110C149#237811yescharacteristic, complemented, Sylow
111#2378—1491nomaximal, Sylow
112C2×C22⋊Q8—1491no—
113#391—1492no—
114#389—1492no—
115#388—1492no—
116#388—1492no—
117#387—1492no—
118#387—1492no—
119#381—1491no—
120#380D14911yescharacteristic
121C22×Q8—1491no—
122C23×C4C2×D14911yescharacteristic
123C22⋊Q8—1498no—
124C2×C4⋊C4—1492no—
125C2×C4⋊C4—1492no—
126C2×C4⋊C4—1491no—
127C2×C4⋊C4—1492no—
128C2×C4⋊C4C2×D14912yes—
129C2×C22⋊C4—1492no—
130C2×C22⋊C4—1492no—
131C2×C22⋊C4C2×D14911yescharacteristic
132C2×C22⋊C4C2×D14911yescharacteristic
133C2×C42—1492no—
134C2×C42—1492no—
135#95—1491no—
136#95—1492no—
137#95—1491no—
138#95—1492no—
139#95—1492no—
140#95—1492no—
141#95—1492no—
142#95C2×D14912yes—
143C24C22×D14911yescharacteristic
144C2×Q8—5962no—
145C2×Q8—1494no—
146C22×C4—42no—
147C22×C4—1492no—
148C22×C4—1492no—
149C22×C4—1492no—
150C22×C4—1492no—
151C22×C4C4×D14914yes—
152C22×C4C22×D14912yes—
153C22×C4C22×D14912yes—
154C22×C4C22×D14911yescharacteristic
155C22×C4C22×D14911yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—5962no—
158C4⋊C4—5962no—
159C4⋊C4—1498no—
160C4⋊C4—1494no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C22⋊C4—5962no—
164C22⋊C4—1498no—
165C42—5962no—
166C42—5962no—
167C23—21no—
168C23—22no—
169C23—22no—
170C23—21no—
171C23C2×C4×D14912yes—
172C23C23×D14911yescharacteristic
173Q8—5964no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—2982no—
184C2×C4—2982no—
185C2×C4—2982no—
186C2×C4—2982no—
187C2×C4—2982no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—2982no—
191C2×C4—2982no—
192C2×C4—2982no—
193C2×C4—1494no—
194C2×C4—1494no—
195C2×C4C2×C4×D14912yes—
196C2×C4C2×C4×D14912yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D14911yescharacteristic
203C22#1801195612yes—
204C22#1801195611yescharacteristic
205C22#1801195812yes—
206C22#1801195911yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—2984no—
212C4—2984no—
213C4—5962no—
214C4—5962no—
215C2—42no—
216C2#2375009811yescharacteristic
217C2#2375010211yescharacteristic
218C2#2375010611yescharacteristic
219C2#2375037012yes—
220C2#2375037612yes—
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#380×C149C2
socle, cosocleC23×C149C24
prime radicalC24×C149C23
hypercenter#380D149
hypocenterC149#2378
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #23749529C2semidirect
3. #23749520C2semidirect
6. #23749508C2semidirect
7. #23749506C2semidirect
11. #18011890C4semidirect
110. C149#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#180118902
#237495292
#237495202
#237495192
#237495132
#237495082
#237495062
#237494882
#380×C1492
#2378149