Finite Group Databasebeta

← #34052791

Subgroups — #34052791

Order 19072.

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

normal subgroups only

This group has 464 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#23749564C212yesmaximal, complemented
2#23749554C212yesmaximal, complemented
3#23749547C212yesmaximal, complemented
4#23749542C212yesmaximal, complemented
5#23749541C212yesmaximal, complemented
6#23749534C211yesmaximal, characteristic
7#23749502C212yesmaximal, complemented
8#23749497C211yesmaximal, characteristic, complemented
9#399×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic
11C22×C22⋊D149C2212yes—
12C23×Dic149C2211yescharacteristic
13C2×C4⋊Dic149C2212yes—
14C2×#14558715C2212yes—
15C2×C22⋊Dic149C2211yescharacteristic
16C2×#14558713C2212yes—
17C2×#14558713C2212yes—
18C2×#14558713C2212yes—
19C2×#14558713C2212yes—
20C2×#14558713C2212yes—
21#18011818C2212yes—
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2211yescharacteristic
25#18011818C2212yes—
26C2×C4⋊C4×C149C2212yes—
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C22⋊C4×C149C2211yescharacteristic
29C2×C22⋊C4×C149C2212yes—
30#95×C149C2211yescharacteristic
31C23×D149C2312yes—
32C2×D596—41no—
33C2×D596—42no—
34C2×C22⋊D149—24no—
35C2×C22⋊D149—42no—
36C2×C22⋊D149—42no—
37C22×Dic149—42no—
38C22×Dic149—41no—
39C22×Dic149C2312yes—
40C22×Dic149C2312yes—
41C22×Dic149C2312yes—
42C4⋊Dic149—42no—
43#14558715—42no—
44C22⋊Dic149—22no—
45#14558713—42no—
46#14558713—42no—
47#14558713—42no—
48#14558713—42no—
49#14558713—42no—
50C24×C149C2311yescharacteristic
51C22×C4×C149C2311yescharacteristic
52C22×C4×C149C2312yes—
53C22×C4×C149C2311yescharacteristic
54C22×C4×C149C2312yes—
55C4⋊C4×C149—42no—
56C4⋊C4×C149—41no—
57C22⋊C4×C149—41no—
58C22⋊C4×C149—42no—
59C22×D149—22no—
60C22×D149—22no—
61C22×D149—22no—
62C22×D149—22no—
63C22×D149—22no—
64C22×D149—22no—
65C22×D149—22no—
66D596—44no—
67C22⋊D149—48no—
68C2×Dic149—22no—
69C2×Dic149—22no—
70C2×Dic149—22no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149—22no—
75C2×Dic149—22no—
76C2×Dic149—22no—
77C2×Dic149—44no—
78C23×C149—22no—
79C23×C149—21no—
80C23×C149—22no—
81C23×C149—21no—
82C23×C149#4112yes—
83C23×C149C2411yescharacteristic
84C2×C4×C149—21no—
85C2×C4×C149—22no—
86C2×C4×C149—21no—
87C2×C4×C149—22no—
88C2×C4×C149—22no—
89C2×C4×C149—22no—
90C2×C4×C149—22no—
91C2×C4×C149—22no—
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C22×C149—24no—
95C22×C149—22no—
96C22×C149—41no—
97C22×C149—41no—
98C22×C149—42no—
99C22×C149C2×#4111yescharacteristic
100C22×C149H(5,𝔽2)12yes—
101C22×C149H(5,𝔽2)11yescharacteristic
102C22×C149H(5,𝔽2)12yes—
103C22×C1492−1+411yescharacteristic
104C2×D149—42no—
105C2×D149—42no—
106C2×D149—42no—
107C2×D149—42no—
108C2×D149—42no—
109C2×D149—42no—
110C2×D149—42no—
111C4×C149—42no—
112C4×C149—41no—
113C4×C149—41no—
114C4×C149—42no—
115Dic149—42no—
116Dic149—42no—
117Dic149—42no—
118C2×C149—42no—
119C2×C149#53812yes—
120C2×C149#53911yescharacteristic
121C2×C149#56011yescharacteristic
122C2×C149#56011yescharacteristic
123C2×C149#56212yes—
124D149—82no—
125C149#282611yescharacteristic, complemented, Sylow
126#2826—1491nomaximal, Sylow
127#400—1492no—
128#399D14911yescharacteristic, complemented
129#397—1492no—
130#396—1492no—
131#394—1492no—
132#394—1492no—
133#392—1491no—
134#386—1492no—
135#385—1491no—
136C22×D4—1492no—
137C22×D4—1491no—
138C23×C4—1491no—
139C2×C4⋊C4—1492no—
140C2×C4⋊C4—1492no—
141C2×C4⋊C4C2×D14912yes—
142C2×C4⋊C4C2×D14911yescharacteristic
143C2×C22⋊C4—1491no—
144C2×C22⋊C4—1492no—
145C2×C22⋊C4—1492no—
146C2×C22⋊C4—1492no—
147C2×C22⋊C4—1492no—
148C2×C22⋊C4—1492no—
149C2×C22⋊C4C2×D14911yescharacteristic
150C2×C22⋊C4C2×D14912yes—
151#95—1492no—
152#95—1492no—
153#95—1492no—
154#95—1491no—
155#95—1492no—
156#95C2×D14911yescharacteristic
157C24—1492no—
158C24C22×D14911yescharacteristic
159C2×D4—2984no—
160C2×D4—5961no—
161C2×D4—5962no—
162C2×D4—5962no—
163C2×D4—5962no—
164C22×C4—5961no—
165C22×C4—5962no—
166C22×C4—1492no—
167C22×C4—1492no—
168C22×C4—1492no—
169C22×C4C22×D14911yescharacteristic
170C22×C4C22×D14912yes—
171C22×C4C22×D14912yes—
172C22×C4C22×D14911yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—5962no—
176C4⋊C4—5962no—
177C22⋊C4—42no—
178C22⋊C4—41no—
179C22⋊C4—2982no—
180C22⋊C4—5962no—
181C22⋊C4—5962no—
182C22⋊C4—5962no—
183C22⋊C4—5962no—
184C22⋊C4—5962no—
185C23—21no—
186C23—22no—
187C23—22no—
188C23—21no—
189C23—2982no—
190C23—2982no—
191C23—2982no—
192C23—2982no—
193C23—2982no—
194C23—2982no—
195C23—2982no—
196C23#1455873712yes—
197C23C23×D14911yescharacteristic
198D4—5964no—
199D4—5968no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—2982no—
211C2×C4—2982no—
212C2×C4—2982no—
213C2×C4—2982no—
214C2×C4—2982no—
215C2×C4—2982no—
216C2×C4—2982no—
217C2×C4—2982no—
218C2×C4—2982no—
219C2×C4—5964no—
220C22—24no—
221C22—22no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—5962no—
226C22—5962no—
227C22—5962no—
228C22—5962no—
229C22—5962no—
230C22—5962no—
231C22—5962no—
232C22C2×#1455873711yescharacteristic
233C22#1801195612yes—
234C22#1801195611yescharacteristic
235C22#1801195712yes—
236C22#1801195811yescharacteristic
237C4—41no—
238C4—42no—
239C4—41no—
240C4—42no—
241C4—5962no—
242C4—5962no—
243C4—5962no—
244C2—42no—
245C2—11922no—
246C2#2375021512yes—
247C2#2375022411yescharacteristic
248C2#2375036211yescharacteristic
249C2#2375036511yescharacteristic
250C2#2375037212yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#399×C149C2
prime radical#23749534C2
hypercenter#399D149
hypocenterC149#2826
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #23749564C2semidirect
2. #23749554C2semidirect
3. #23749547C2semidirect
4. #23749542C2semidirect
5. #23749541C2semidirect
7. #23749502C2semidirect
8. #23749497C2semidirect
9. #399×C149C2semidirect
125. C149#2826semidirect
128. #399D149semidirect

Maximal subgroups

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

subgroupindex
#237495642
#237495542
#237495472
#237495422
#237495412
#237495342
#237495022
#237494972
#399×C1492
#2826149