Finite Group Databasebeta

← #34077481

Subgroups — #34077481

Order 19328.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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×#18012730C211yesmaximal, characteristic, complemented
2C2×#18012726C211yesmaximal, characteristic
3#23752118C211yesmaximal, characteristic, complemented
4#23752117C211yesmaximal, characteristic, complemented
5#23752115C211yesmaximal, characteristic
6#23752105C214yesmaximal, complemented
7#23752100C214yesmaximal, complemented
8C42×Dic151C211yesmaximal, characteristic, complemented
9#390×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11#18012730—24no—
12#18012726—24no—
13C2×C4⋊Dic151C2212yes—
14C2×C4⋊Dic151C2211yescharacteristic
15C2×Dic151⋊C4C2212yes—
16C2×C22⋊Dic151C2212yes—
17C2×C22⋊Dic151C2212yes—
18C2×C22⋊Dic151C2214yes—
19C2×C4×Dic151C2212yes—
20C2×C4×Dic151C2212yes—
21C2×C4×Dic151C2211yescharacteristic
22C2×C4×Dic151C2211yescharacteristic
23C151⋊#95C2214yes—
24C151⋊#95C2214yes—
25C22×D4×C151C2211yescharacteristic
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C22⋊C4×C151C2214yes—
28C2×C42×C151C2211yescharacteristic
29C2×Dic302—22no—
30C2×Dic302—22no—
31C2×Dic302—22no—
32C22×Dic151C2312yes—
33C22×Dic151C2312yes—
34C22×Dic151C2311yescharacteristic
35C22×Dic151C2311yescharacteristic
36C22×Dic151C2312yes—
37C4⋊Dic151—24no—
38C4⋊Dic151—22no—
39Dic151⋊C4—24no—
40C22⋊Dic151—24no—
41C22⋊Dic151—24no—
42C22⋊Dic151—28no—
43C4×Dic151—24no—
44C4×Dic151—24no—
45C4×Dic151—22no—
46C4×Dic151D414yes—
47C24×C151C2312yes—
48C2×D4×C151—22no—
49C2×D4×C151—22no—
50C2×D4×C151—22no—
51C22×C4×C151C2312yes—
52C22×C4×C151C2312yes—
53C22×C4×C151C2311yescharacteristic
54C4⋊C4×C151—22no—
55C22⋊C4×C151—28no—
56C42×C151—22no—
57Dic302—44no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—24no—
65C2×Dic151—22no—
66C2×Dic151—22no—
67C2×Dic151C2×D412yes—
68C2×Dic151C2×D412yes—
69C2×Dic151#4114yes—
70C23×C151—22no—
71C23×C151—24no—
72C23×C151—24no—
73C23×C151—22no—
74C23×C151—22no—
75C23×C151C2411yescharacteristic
76D4×C151—44no—
77C2×C4×C151—22no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151—24no—
81C2×C4×C151C2×D412yes—
82C2×C4×C151#4114yes—
83C2×C4×C151#4112yes—
84C2×C4×C151#4112yes—
85C22×C151—42no—
86C22×C151—44no—
87C22×C151—44no—
88C22×C151—42no—
89C22×C151—42no—
90C22×C151C22×D411yescharacteristic
91C22×C151C2×#4112yes—
92C22×C151C2×#4111yescharacteristic
93C22×C151C2×#4112yes—
94C22×C151C2×#4111yescharacteristic
95C4×C151—24no—
96C4×C151—42no—
97C4×C151#12414yes—
98Dic151—24no—
99Dic151—22no—
100Dic151—22no—
101Dic151—42no—
102Dic151—42no—
103C2×C151—82no—
104C2×C151C2×#12411yescharacteristic
105C2×C151#52912yes—
106C2×C151#52912yes—
107C2×C151#53211yescharacteristic
108C2×C151#53211yescharacteristic
109C151#286111yescharacteristic, complemented, Sylow
110#2861—1511nomaximal, Sylow
111C2×#125—1511no—
112C2×#124—1511no—
113#391—1511no—
114#391—1511no—
115#390—1511no—
116#390D15111yescharacteristic
117#388—1514no—
118#388—1514no—
119C43—1511no—
120C22×Q8—1511no—
121C22×D4C2×D15111yescharacteristic
122#125—3024no—
123#124—3024no—
124C2×C4⋊C4—1512no—
125C2×C4⋊C4—1512no—
126C2×C4⋊C4—1511no—
127C2×C4⋊C4C2×D15111yescharacteristic
128C2×C22⋊C4—1512no—
129C2×C22⋊C4—1512no—
130C2×C22⋊C4—1514no—
131C2×C22⋊C4C2×D15114yes—
132C2×C42—1512no—
133C2×C42—1512no—
134C2×C42—1511no—
135C2×C42—1511no—
136C2×C42C2×D15111yescharacteristic
137#95—1514no—
138#95—1514no—
139C24C22×D15112yes—
140C2×Q8—3022no—
141C2×Q8—3022no—
142C2×Q8—3022no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4—22no—
146C22×C4—1512no—
147C22×C4—1512no—
148C22×C4—1512no—
149C22×C4—1511no—
150C22×C4—1511no—
151C22×C4C22×D15112yes—
152C22×C4C22×D15112yes—
153C22×C4C22×D15111yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—3024no—
156C4⋊C4—3024no—
157C4⋊C4—3022no—
158C22⋊C4—28no—
159C22⋊C4—3028no—
160C22⋊C4—3024no—
161C22⋊C4—3024no—
162C42—22no—
163C42—3024no—
164C42—3024no—
165C42—3022no—
166C42—1514no—
167C23—22no—
168C23—24no—
169C23—24no—
170C23—22no—
171C23—22no—
172C23C23×D15111yescharacteristic
173Q8—6044no—
174D4—44no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4—3022no—
184C2×C4—3022no—
185C2×C4—3024no—
186C2×C4—3022no—
187C2×C4—3022no—
188C2×C4—1512no—
189C2×C4—1512no—
190C2×C4—1514no—
191C2×C4D4×D15112yes—
192C2×C4#1455900314yes—
193C2×C4#1455900312yes—
194C2×C4#1455900412yes—
195C22—42no—
196C22—44no—
197C22—44no—
198C22—42no—
199C22—42no—
200C22C2×D4×D15111yescharacteristic
201C22#41×D15112yes—
202C22C2×#1455900311yescharacteristic
203C22C2×#1455900312yes—
204C22C2×#1455900411yescharacteristic
205C4—24no—
206C4—42no—
207C4—3024no—
208C4—3022no—
209C4—3022no—
210C4—6042no—
211C4—6042no—
212C4#1801272514yes—
213C2—82no—
214C2C2×#1801272511yescharacteristic
215C2#2375274312yes—
216C2#2375274412yes—
217C2#2375276011yescharacteristic
218C2#2375276111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#390×C151C2
prime radicalC22×D4×C151C22
hypercenter#390D151
hypocenterC151#2861
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#18012730C2semidirect
3. #23752118C2semidirect
4. #23752117C2semidirect
6. #23752105C2semidirect
7. #23752100C2semidirect
8. C42×Dic151C2semidirect
109. C151#2861semidirect

Maximal subgroups

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

subgroupindex
C2×#180127302
C2×#180127262
#237521182
#237521172
#237521152
#237521052
#237521002
C42×Dic1512
#390×C1512
#2861151