Finite Group Databasebeta

← #34068065

Subgroups — #34068065

Order 19328.

256 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 51 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#23752837C211yesmaximal, characteristic
2#23752368C211yesmaximal, characteristic, complemented
3#23752123C211yesmaximal, characteristic
4#23751950C211yesmaximal, characteristic, complemented
5#23751949C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic
7#451×C151C211yesmaximal, characteristic, complemented
8C2×#14558994—21no—
9#18012719—21no—
10#18012718C2211yescharacteristic
11#18012717—21no—
12#18012717—21no—
13#18012716—21no—
14#18012715—21no—
15C2×(C2×D151)⋊C4—21no—
16C2×(C2×D151)⋊C4C2211yescharacteristic
17C22⋊C4×D151—21no—
18#18012663—21no—
19C22⋊(C151⋊C8)C2211yescharacteristic
20C151⋊#95—21no—
21C151⋊#95C2211yescharacteristic
22C22×Q8×C151C2211yescharacteristic
23C2×Q16×C151—21no—
24C22⋊Q8×C151C2211yescharacteristic
25#103×C151—21no—
26C22⋊C8×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28C2×Dic302—21no—
29C2×Dic302D411yescharacteristic
30C22×Dic151—21no—
31C22×Dic151D411yescharacteristic
32C2×C4×D151—21no—
33C2×C4×D151—21no—
34#14558994—42no—
35C2×C151⋊C8—21no—
36C4⋊Dic151—21no—
37C4⋊Dic151D411yescharacteristic
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40Dic151⋊C4—21no—
41C22⋊Dic151—21no—
42(C2×D151)⋊C4—21no—
43(C2×D151)⋊C4—21no—
44(C2×D151)⋊C4—21no—
45(C2×D151)⋊C4—21no—
46(C2×D151)⋊C4—42no—
47C2×Q8×C151—21no—
48C2×Q8×C151—21no—
49C2×Q8×C151—42no—
50C2×Q8×C151D411yescharacteristic
51C22×C4×C151—21no—
52C22×C4×C151C2311yescharacteristic
53Q16×C151—42no—
54C2×C8×C151—21no—
55C4⋊C4×C151—21no—
56C4⋊C4×C151D411yescharacteristic
57C22⋊C4×C151—21no—
58C22×D151—21no—
59C22×D151—21no—
60C22×D151—41no—
61C22×D151—41no—
62C22×D151Q1612yescomplemented
63Dic302—41no—
64Dic302—81no—
65C2×Dic151—21no—
66C2×Dic151—21no—
67C2×Dic151—21no—
68C2×Dic151—41no—
69C2×Dic151—41no—
70C2×Dic151—41no—
71C2×Dic151—41no—
72C4×D151—81no—
73C4×D151—81no—
74C151⋊C8—41no—
75C23×C151C2×D411yescharacteristic
76Q8×C151—22no—
77Q8×C151—22no—
78Q8×C151—41no—
79Q8×C151—41no—
80Q8×C151—41no—
81C2×C4×C151—22no—
82C2×C4×C151—21no—
83C2×C4×C151—21no—
84C2×C4×C151—41no—
85C2×C4×C151—41no—
86C2×C4×C151—41no—
87C2×C4×C151C2×D411yescharacteristic
88C2×C4×C151C2×D411yescharacteristic
89C8×C151—41no—
90C22×C151—21no—
91C22×C151—21no—
92C22×C151#12011yescharacteristic
93C22×C151C2×Q1611yescharacteristic
94C22×C151#13711yescharacteristic
95C2×D151—22no—
96C2×D151—41no—
97C2×D151—41no—
98C2×D151—42no—
99C2×D151—81no—
100C4×C151—21no—
101C4×C151—21no—
102C4×C151—41no—
103C4×C151—42no—
104C4×C151—41no—
105Dic151—41no—
106Dic151—41no—
107Dic151—41no—
108Dic151—81no—
109C2×C151—21no—
110C2×C151—21no—
111C2×C151#45111yescharacteristic
112C2×C151#45511yescharacteristic
113C2×C151B(4,𝔽2)11yescharacteristic
114D151—42no—
115C151#160211yescharacteristic, complemented, Sylow
116#1602—1511nomaximal, Sylow
117#543—1511no—
118#451—1511no—
119#451D15111yescharacteristic, complemented
120#393—1511no—
121#328—1511no—
122#328—1511no—
123#323—1511no—
124C22×Q8C2×D15111yescharacteristic
125C2×Q16—21no—
126C2×Q16—3021no—
127C22⋊Q8—3021no—
128C22⋊Q8—3021no—
129C22⋊Q8—3021no—
130C22⋊Q8—3021no—
131C22⋊Q8—3021no—
132C22⋊Q8—1511no—
133C22⋊Q8C2×D15111yescharacteristic
134C2×C22⋊C4—3021no—
135C2×C22⋊C4—3021no—
136C2×C22⋊C4—1511no—
137#103—21no—
138#103—3021no—
139C22⋊C8—1511no—
140C22⋊C8C2×D15111yescharacteristic
141#95—3021no—
142#95—1511no—
143C24—1511no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—42no—
147C2×Q8—3021no—
148C2×Q8—1511no—
149C2×Q8C22⋊D15111yescharacteristic
150C22×C4—21no—
151C22×C4—3021no—
152C22×C4—3021no—
153C22×C4—3021no—
154C22×C4—1511no—
155C22×C4C22×D15111yescharacteristic
156Q16—42no—
157Q16—6042no—
158C2×C8—21no—
159C2×C8—3021no—
160C4⋊C4—21no—
161C4⋊C4—3021no—
162C4⋊C4—3021no—
163C4⋊C4—3021no—
164C4⋊C4—3021no—
165C4⋊C4—1511no—
166C4⋊C4C22⋊D15111yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—3021no—
169C22⋊C4—3021no—
170C22⋊C4—3021no—
171C22⋊C4—3021no—
172C22⋊C4—3021no—
173C22⋊C4—6042no—
174C23—3021no—
175C23—3021no—
176C23—6041no—
177C23—6041no—
178C23—1512no—
179C23D4×D15111yescharacteristic
180Q8—22no—
181Q8—22no—
182Q8—41no—
183Q8—41no—
184Q8—41no—
185Q8—6041no—
186Q8—12081no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—3021no—
194C2×C4—3021no—
195C2×C4—3021no—
196C2×C4—6041no—
197C2×C4—6041no—
198C2×C4—6041no—
199C2×C4—6041no—
200C2×C4—12081no—
201C2×C4—12081no—
202C2×C4D4×D15111yescharacteristic
203C2×C4C2×C22⋊D15111yescharacteristic
204C8—41no—
205C8—6041no—
206C22—21no—
207C22—21no—
208C22—3022no—
209C22—6042no—
210C22—6041no—
211C22—6041no—
212C22—12081no—
213C22#1801270711yescharacteristic
214C22Q16×D15111yescharacteristic
215C22#1801277111yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—42no—
220C4—41no—
221C4—6041no—
222C4—6041no—
223C4—6041no—
224C4—12081no—
225C2—21no—
226C2—21no—
227C2—6042no—
228C2#2375236611yescharacteristic
229C2#2375238811yescharacteristic
230C2#2375239811yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#451×C151C2
socleC22×C151#120
prime radicalC23×D151D4
hypercenter#451D151
hypocenterC151#1602
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #23752368C2semidirect
4. #23751950C2semidirect
5. #23751949C2semidirect
7. #451×C151C2semidirect
62. C22×D151Q16semidirect
115. C151#1602semidirect
119. #451D151semidirect

Maximal subgroups

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

subgroupindex
#237528372
#237523682
#237521232
#237519502
#237519492
#237519352
#451×C1512
#1602151