Finite Group Databasebeta

← #34080002

Subgroups — #34080002

Order 19328.

378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752785C212yesmaximal
2#23752556C212yesmaximal, complemented
3#23752551C212yesmaximal, complemented
4#23752470C211yesmaximal, characteristic, complemented
5#23752451C212yesmaximal, complemented
6#23752369C212yesmaximal, complemented
7#23752366C212yesmaximal, complemented
8#23752180C211yesmaximal, characteristic
9#470×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic
11C2×Q8×D151C2212yes—
12C2×Dic604C2211yescharacteristic
13C2×#14558994C2212yes—
14C22×C151⋊C8C2211yescharacteristic
15#18012738—22no—
16#18012725—22no—
17#18012724—22no—
18#18012721—22no—
19#18012719C2212yes—
20#18012718C2212yes—
21#18012715C2212yes—
22#18012697C2212yes—
23#18012672C2212yes—
24#18012671C2211yescharacteristic
25#18012664C2212yes—
26#18012663C2212yes—
27#18012662C2212yes—
28(C2×D151)⋊C8C2212yes—
29(C2×D151)⋊C8C2212yes—
30C2×Q16×C151C2211yescharacteristic
31C2×M16×C151C2211yescharacteristic
32C22⋊Q8×C151C2212yes—
33#106×C151C2211yescharacteristic
34#103×C151C2212yes—
35#14559004—41no—
36#14559004—41no—
37C2×Dic302—22no—
38C2×Dic302D411yescharacteristic
39C2×Dic302C2312yes—
40Q8×D151—42no—
41Q8×D151—42no—
42C2×D604D411yescharacteristic
43C2×C22⋊D151D412yes—
44C2×C4×D151—22no—
45C2×C4×D151C2312yes—
46Dic604—41no—
47#14558994—42no—
48C2×C151⋊C8—41no—
49C2×C151⋊C8C2312yes—
50C4⋊Dic151—22no—
51C4⋊Dic151C2312yes—
52Dic151⋊C4—22no—
53Dic151⋊C4—22no—
54C22⋊Dic151—22no—
55(C2×D151)⋊C4—22no—
56(C2×D151)⋊C4—22no—
57(C2×D151)⋊C4—22no—
58C4×Dic151—22no—
59C2×Q8×C151C2312yes—
60C22×C4×C151C2311yescharacteristic
61Q16×C151—41no—
62M16×C151—41no—
63C2×C8×C151C2311yescharacteristic
64C2×C8×C151C2311yescharacteristic
65C4⋊C4×C151—22no—
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22×D151C2×D412yes—
69Dic302—22no—
70Dic302—22no—
71Dic302—41no—
72Dic302—44no—
73D604—41no—
74C22⋊D151—42no—
75C2×Dic151—22no—
76C2×Dic151—22no—
77C2×Dic151C2×D412yes—
78C4×D151—22no—
79C4×D151—22no—
80C4×D151—44no—
81C151⋊C8—22no—
82C23×C151C2×D411yescharacteristic
83Q8×C151—22no—
84Q8×C151—22no—
85C2×C4×C151—21no—
86C2×C4×C151—21no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151C2×D411yescharacteristic
90C2×C4×C151C2411yescharacteristic
91C8×C151—21no—
92C8×C151—21no—
93C22×C151—21no—
94C22×C151—22no—
95C22×C151C22×D411yescharacteristic
96C2×D151—22no—
97C2×D151—24no—
98C4×C151—21no—
99C4×C151—42no—
100C4×C151—42no—
101C4×C151H(5,𝔽2)11yescharacteristic
102C4×C151H(5,𝔽2)11yescharacteristic
103Dic151—22no—
104Dic151—42no—
105Dic151—42no—
106C2×C151—41no—
107C2×C151#53411yescharacteristic
108C2×C151#57812yes—
109D151—42no—
110C151#320211yescharacteristic, complemented, Sylow
111#3202—1511nomaximal, Sylow
112#536—1512no—
113#485—1512no—
114#485—1512no—
115#470—1511no—
116#470D15111yescharacteristic, complemented
117#467—1512no—
118#451—1512no—
119#451—1512no—
120#408—1511no—
121C2×#41—1511no—
122C22×Q8—1512no—
123C2×Q16—1512no—
124C2×Q16—1511no—
125C2×Q16C2×D15111yescharacteristic
126C2×M16C2×D15111yescharacteristic
127C22×C8—1511no—
128C4⋊Q8—3022no—
129#124—3022no—
130#123—3022no—
131#123—3022no—
132C22⋊Q8—1512no—
133C22⋊Q8—1512no—
134C22⋊Q8—1512no—
135C22⋊Q8C2×D15112yes—
136#117—1512no—
137#107—1512no—
138#106—1511no—
139#106C2×D15111yescharacteristic
140#103—1512no—
141#103—1512no—
142#103—1512no—
143#103C2×D15112yes—
144C22⋊C8—1512no—
145C22⋊C8—1512no—
146#41—6041no—
147#41—6041no—
148C2×Q8—3022no—
149C2×Q8—6042no—
150C2×Q8—6042no—
151C2×Q8—1512no—
152C2×Q8—1511no—
153C2×Q8C22×D15112yes—
154C2×D4—1512no—
155C2×D4—1511no—
156C22×C4—3022no—
157C22×C4—1512no—
158C22×C4C22×D15111yescharacteristic
159Q16—41no—
160Q16—6041no—
161Q16—6042no—
162M16—41no—
163C2×C8—6041no—
164C2×C8—1512no—
165C2×C8C22×D15111yescharacteristic
166C2×C8C22×D15111yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—3022no—
169C4⋊C4—3022no—
170C4⋊C4—3022no—
171C4⋊C4—1512no—
172C4⋊C4C22×D15112yes—
173C22⋊C4—22no—
174C22⋊C4—3022no—
175C22⋊C4—3022no—
176C22⋊C4—3022no—
177C22⋊C4—3022no—
178C42—3022no—
179C23—1512no—
180C23D4×D15111yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—3022no—
184Q8—3022no—
185Q8—6041no—
186Q8—6044no—
187D4—6041no—
188D4—6042no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—3022no—
194C2×C4—3022no—
195C2×C4—3022no—
196C2×C4—3022no—
197C2×C4—6044no—
198C2×C4—1512no—
199C2×C4D4×D15111yescharacteristic
200C2×C4C23×D15111yescharacteristic
201C8—21no—
202C8—21no—
203C8—3022no—
204C22—21no—
205C22—22no—
206C22—3022no—
207C22—3024no—
208C22C2×D4×D15111yescharacteristic
209C4—21no—
210C4—42no—
211C4—42no—
212C4—3022no—
213C4—6042no—
214C4—6042no—
215C4#1801278411yescharacteristic
216C4#1801278511yescharacteristic
217C2—41no—
218C2—6042no—
219C2#2375277011yescharacteristic
220C2#2375302812yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#470×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559004C22
hypercenter#470D151
hypocenterC151#3202
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #23752556C2semidirect
3. #23752551C2semidirect
4. #23752470C2semidirect
5. #23752451C2semidirect
6. #23752369C2semidirect
7. #23752366C2semidirect
9. #470×C151C2semidirect
110. C151#3202semidirect
116. #470D151semidirect

Maximal subgroups

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

subgroupindex
#237527852
#237525562
#237525512
#237524702
#237524512
#237523692
#237523662
#237521802
#470×C1512
#3202151