Finite Group Databasebeta

← #34045815

Subgroups — #34045815

Order 19072.

638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 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×#18011879C212yesmaximal, complemented
2C2×#18011826C212yesmaximal, complemented
3#23749480C211yesmaximal, characteristic, complemented
4#23749392C211yesmaximal, characteristic, complemented
5#534×C149C211yesmaximal, characteristic, complemented
6C24×D149C2211yescharacteristic
7C22×C22⋊D149—22no—
8#18011879—24no—
9#18011879—24no—
10C2×C22⋊Dic149C2211yescharacteristic
11C2×C22⋊Dic149C2212yes—
12C2×#14558713—22no—
13C2×#14558713—22no—
14#18011826—24no—
15C22×D4×C149C2212yes—
16#123×C149—22no—
17#121×C149—22no—
18#120×C149—22no—
19C2×C22⋊C4×C149C2211yescharacteristic
20C23×D149—22no—
21C23×D149—21no—
22C23×D149—22no—
23C23×D149—21no—
24C23×D149—44no—
25C23×D149D412yescomplemented
26C2×C22⋊D149—28no—
27C2×C22⋊D149—48no—
28C22×Dic149—22no—
29C22×Dic149—21no—
30C22⋊Dic149—22no—
31C22⋊Dic149—22no—
32C22⋊Dic149D414yescomplemented
33#14558713—28no—
34#14558713—44no—
35C24×C149D412yescomplemented
36C24×C149C2311yescharacteristic
37C2×D4×C149—22no—
38C2×D4×C149—22no—
39C2×D4×C149—22no—
40C2×D4×C149—22no—
41C2×D4×C149—22no—
42C2×D4×C149—22no—
43C2×D4×C149—22no—
44C22×C4×C149D412yescomplemented
45C22×C4×C149D412yescomplemented
46C4⋊C4×C149—22no—
47C22⋊C4×C149—24no—
48C22⋊C4×C149—22no—
49C22×D149—28no—
50C22×D149—24no—
51C22×D149—24no—
52C22×D149—22no—
53C22×D149—44no—
54C22×D149—48no—
55C22×D149—44no—
56C22×D149—42no—
57C22×D149—44no—
58C22×D149—41no—
59C22×D149—42no—
60C22×D149—41no—
61C22⋊D149—416no—
62C2×Dic149—24no—
63C2×Dic149—44no—
64C2×Dic149—42no—
65C2×Dic149—41no—
66C23×C149—22no—
67C23×C149—22no—
68C23×C149—22no—
69C23×C149—42no—
70C23×C149—44no—
71C23×C149C2×D411yescharacteristic
72C23×C149C2×D412yes—
73C23×C149C2×D412yes—
74C23×C149C2×D411yescharacteristic
75C23×C149#4111yescharacteristic
76D4×C149—42no—
77D4×C149—42no—
78D4×C149—42no—
79D4×C149—42no—
80D4×C149—82no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149—42no—
86C22×C149—22no—
87C22×C149—24no—
88C22×C149—41no—
89C22×C149—42no—
90C22×C149—41no—
91C22×C149—44no—
92C22×C149—42no—
93C22×C149—44no—
94C22×C149—82no—
95C22×C149#12012yes—
96C22×C149#12011yescharacteristic
97C22×C149#12111yescharacteristic
98C22×C149#12112yes—
99C22×C149#12711yescharacteristic
100C2×D149—28no—
101C2×D149—24no—
102C2×D149—44no—
103C2×D149—44no—
104C2×D149—42no—
105C2×D149—48no—
106C2×D149—42no—
107C2×D149—44no—
108C4×C149—42no—
109C4×C149—42no—
110Dic149—44no—
111Dic149—81no—
112C2×C149—22no—
113C2×C149—21no—
114C2×C149—21no—
115C2×C149—22no—
116C2×C149—82no—
117C2×C149#39211yescharacteristic
118C2×C149B(4,𝔽2)12yes—
119D149—44no—
120C149#202111yescharacteristic, complemented, Sylow
121#2021—1491nomaximal, Sylow
122#534D14911yescharacteristic, complemented
123C2×#120—1492no—
124C2×#99—1492no—
125#379—1491no—
126#342—1491no—
127C25—1491no—
128C22×D4—2982no—
129C22×D4C2×D14912yes—
130#123—22no—
131#121—22no—
132#120—22no—
133#120—2984no—
134#120—2984no—
135C2×C22⋊C4—2982no—
136C2×C22⋊C4—2982no—
137C2×C22⋊C4—1491no—
138C2×C22⋊C4—1492no—
139C2×C22⋊C4C2×D14911yescharacteristic
140#99—2984no—
141C24—2981no—
142C24—2982no—
143C24—2982no—
144C24—2981no—
145C24—5964no—
146C24—1492no—
147C24C22⋊D14912yescomplemented
148C24C22×D14911yescharacteristic
149C2×D4—22no—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—2988no—
157C2×D4—5968no—
158C22×C4—2982no—
159C22×C4—2981no—
160C22×C4C22⋊D14912yescomplemented
161C22×C4C22⋊D14912yescomplemented
162C4⋊C4—22no—
163C22⋊C4—24no—
164C22⋊C4—22no—
165C22⋊C4—2988no—
166C22⋊C4—2982no—
167C22⋊C4—2982no—
168C22⋊C4—5964no—
169C22⋊C4—1494no—
170C23—22no—
171C23—22no—
172C23—22no—
173C23—42no—
174C23—44no—
175C23—2984no—
176C23—2988no—
177C23—2984no—
178C23—2982no—
179C23—5962no—
180C23—5964no—
181C23—5964no—
182C23—5968no—
183C23—5964no—
184C23—5961no—
185C23—5961no—
186C23—5962no—
187C23D4×D14912yes—
188C23D4×D14911yescharacteristic
189C23C2×C22⋊D14911yescharacteristic
190C23C2×C22⋊D14912yes—
191C23#1455873511yescharacteristic
192D4—42no—
193D4—42no—
194D4—42no—
195D4—42no—
196D4—82no—
197D4—59616no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—2984no—
204C2×C4—5964no—
205C2×C4—5962no—
206C2×C4—5961no—
207C22—22no—
208C22—24no—
209C22—41no—
210C22—42no—
211C22—41no—
212C22—44no—
213C22—42no—
214C22—44no—
215C22—82no—
216C22—2988no—
217C22—2984no—
218C22—5964no—
219C22—5964no—
220C22—5968no—
221C22—5962no—
222C22—5962no—
223C22—5964no—
224C22#1801187912yes—
225C22#1801188011yescharacteristic
226C22#1801188211yescharacteristic
227C22#1801188312yes—
228C22#1801190711yescharacteristic
229C4—42no—
230C4—42no—
231C4—5964no—
232C4—11921no—
233C2—22no—
234C2—21no—
235C2—22no—
236C2—21no—
237C2—82no—
238C2—5964no—
239C2#2374953311yescharacteristic
240C2#2374981212yes—
subgroupG/H
centerC22#18011880
commutator, cosocleC24×C149C23
FrattiniC24C22×D149
Fitting#534×C149C2
socleC22×C149#120
hypercenter#534D149
hypocenterC149#2021
LCSG ▷ C24×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#18011879C2semidirect
2. C2×#18011826C2semidirect
3. #23749480C2semidirect
4. #23749392C2semidirect
5. #534×C149C2semidirect
25. C23×D149D4semidirect
32. C22⋊Dic149D4semidirect
35. C24×C149D4semidirect
44. C22×C4×C149D4semidirect
45. C22×C4×C149D4semidirect
120. C149#2021semidirect
122. #534D149semidirect
147. C24C22⋊D149semidirect
160. C22×C4C22⋊D149semidirect
161. C22×C4C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118792
C2×#180118262
#237494802
#237493922
#534×C1492
#2021149