Finite Group Databasebeta

← #34052834

Subgroups — #34052834

Order 19072.

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

normal subgroups only

This group has 408 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
1#23749555C211yesmaximal, characteristic, complemented
2#23749553C212yesmaximal, complemented
3#23749553C212yesmaximal, complemented
4#23749548C212yesmaximal, complemented
5#23749545C211yesmaximal, characteristic, complemented
6#23749539C212yesmaximal
7#23749537C212yesmaximal, complemented
8#23749509C212yesmaximal, complemented
9#390×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11C2×C4⋊Dic149C2211yescharacteristic
12C2×#14558715C2212yes—
13C2×#14558715C2212yes—
14C2×#14558715C2212yes—
15C2×C22⋊Dic149C2212yes—
16C2×C22⋊Dic149C2212yes—
17C2×C22⋊Dic149C2212yes—
18C2×C22⋊Dic149C2212yes—
19#18011818C2212yes—
20#18011818C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2211yescharacteristic
25#18011818C2211yescharacteristic
26C22×D4×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C22⋊C4×C149C2212yes—
29C2×C22⋊C4×C149C2212yes—
30C2×C42×C149C2211yescharacteristic
31C2×Dic298—42no—
32C2×Dic298—41no—
33C22×Dic149C2312yes—
34C22×Dic149C2312yes—
35C22×Dic149C2312yes—
36C22×Dic149C2312yes—
37C4⋊Dic149—41no—
38#14558715—24no—
39#14558715—42no—
40#14558715—42no—
41C22⋊Dic149—42no—
42C22⋊Dic149—42no—
43C22⋊Dic149—42no—
44C22⋊Dic149—42no—
45C24×C149C2312yes—
46C2×D4×C149—22no—
47C2×D4×C149—41no—
48C2×D4×C149—41no—
49C22×C4×C149C2311yescharacteristic
50C22×C4×C149C2312yes—
51C22×C4×C149C2311yescharacteristic
52C22×C4×C149C2311yescharacteristic
53C4⋊C4×C149—41no—
54C22⋊C4×C149—42no—
55C22⋊C4×C149—42no—
56C42×C149—41no—
57Dic298—44no—
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×Dic149—22no—
68C2×Dic149—22no—
69C2×Dic149—22no—
70C23×C149—22no—
71C23×C149—22no—
72C23×C149—22no—
73C23×C149—22no—
74C23×C149—22no—
75C23×C149—22no—
76C23×C149—22no—
77C23×C149C2411yescharacteristic
78D4×C149—44no—
79C2×C4×C149—21no—
80C2×C4×C149—21no—
81C2×C4×C149—22no—
82C2×C4×C149—21no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—21no—
87C2×C4×C149—22no—
88C2×C4×C149#4112yes—
89C22×C149—42no—
90C22×C149—42no—
91C22×C149—42no—
92C22×C149—42no—
93C22×C149—42no—
94C22×C149—42no—
95C22×C149—42no—
96C22×C149C2×#4111yescharacteristic
97C22×C149H(5,𝔽2)11yescharacteristic
98C22×C149H(5,𝔽2)11yescharacteristic
99C22×C149H(5,𝔽2)12yes—
100C22×C1492−1+412yes—
101C4×C149—22no—
102C4×C149—41no—
103C4×C149—41no—
104C4×C149—42no—
105Dic149—42no—
106Dic149—42no—
107Dic149—42no—
108Dic149—42no—
109C2×C149—82no—
110C2×C149#53811yescharacteristic
111C2×C149#54212yes—
112C2×C149#56011yescharacteristic
113C2×C149#56212yes—
114C2×C149#56311yescharacteristic
115C149#283011yescharacteristic, complemented, Sylow
116#2830—1491nomaximal, Sylow
117#398—1491no—
118#397—1492no—
119#397—1492no—
120#396—1492no—
121#395—1491no—
122#394—1492no—
123#393—1492no—
124#390D14911yescharacteristic
125#387—1492no—
126C22×Q8—1491no—
127C22×D4C2×D14911yescharacteristic
128C2×C4⋊C4—1492no—
129C2×C4⋊C4—1492no—
130C2×C4⋊C4—1492no—
131C2×C4⋊C4—1491no—
132C2×C4⋊C4C2×D14911yescharacteristic
133C2×C22⋊C4—1492no—
134C2×C22⋊C4—1492no—
135C2×C22⋊C4—1492no—
136C2×C22⋊C4—1492no—
137C2×C22⋊C4C2×D14912yes—
138C2×C22⋊C4C2×D14912yes—
139C2×C42C2×D14911yescharacteristic
140#95—1492no—
141#95—1492no—
142#95—1492no—
143#95—1492no—
144#95—1492no—
145#95—1491no—
146#95—1491no—
147C24C22×D14912yes—
148C2×Q8—5962no—
149C2×Q8—5961no—
150C2×D4—22no—
151C2×D4—41no—
152C2×D4—41no—
153C22×C4—1492no—
154C22×C4—1492no—
155C22×C4—1492no—
156C22×C4—1492no—
157C22×C4C22×D14912yes—
158C22×C4C22×D14911yescharacteristic
159C22×C4C22×D14911yescharacteristic
160C22×C4C22×D14911yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—2984no—
163C4⋊C4—5962no—
164C4⋊C4—5962no—
165C4⋊C4—5961no—
166C22⋊C4—42no—
167C22⋊C4—42no—
168C22⋊C4—5962no—
169C22⋊C4—5962no—
170C22⋊C4—5962no—
171C22⋊C4—5962no—
172C42—41no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23C23×D14911yescharacteristic
181Q8—5964no—
182D4—44no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—2982no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—2982no—
198C2×C4—2982no—
199C2×C4—2982no—
200C2×C4—2982no—
201C2×C4—2982no—
202C2×C4—2982no—
203C2×C4—2982no—
204C2×C4#1455873612yes—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22C2×#1455873611yescharacteristic
213C22#1801195611yescharacteristic
214C22#1801195611yescharacteristic
215C22#1801195612yes—
216C22#1801195812yes—
217C4—22no—
218C4—41no—
219C4—41no—
220C4—42no—
221C4—5962no—
222C4—5962no—
223C4—5962no—
224C4—5962no—
225C2—82no—
226C2#2375021311yescharacteristic
227C2#2375024012yes—
228C2#2375036211yescharacteristic
229C2#2375037012yes—
230C2#2375037511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#390×C149C2
prime radicalC22×D4×C149C22
hypercenter#390D149
hypocenterC149#2830
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #23749555C2semidirect
2. #23749553C2semidirect
3. #23749553C2semidirect
4. #23749548C2semidirect
5. #23749545C2semidirect
7. #23749537C2semidirect
8. #23749509C2semidirect
115. C149#2830semidirect

Maximal subgroups

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

subgroupindex
#237495552
#237495532
#237495482
#237495452
#237495392
#237495372
#237495092
#390×C1492
#2830149