Finite Group Databasebeta

← #34071120

Subgroups — #34071120

Order 19328.

260 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 41 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#23752949C211yesmaximal, characteristic, complemented
2#23752403C211yesmaximal, characteristic, complemented
3#23752400C211yesmaximal, characteristic, complemented
4#23752379C211yesmaximal, characteristic, complemented
5#23752001C211yesmaximal, characteristic, complemented
6#23751998C211yesmaximal, characteristic, complemented
7#353×C151C211yesmaximal, characteristic, complemented
8#18012784C2211yescharacteristic
9#18012765—21no—
10#18012733—21no—
11#18012723—21no—
12#18012720—21no—
13#18012720C2211yescharacteristic
14#18012711—21no—
15#18012711—21no—
16#18012711—21no—
17#18012709—21no—
18#18012707—21no—
19#18012707C2211yescharacteristic
20#18012667—21no—
21#18012656C2211yescharacteristic
22#18012653—21no—
23#18012653—21no—
24#127×C151C2211yescharacteristic
25#99×C151C2211yescharacteristic
26#99×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28#14559004—21no—
29#14559003—41no—
30C2×D604—41no—
31C2×C22⋊D151—21no—
32C2×C22⋊D151—21no—
33C2×C22⋊D151—21no—
34C2×C22⋊D151—21no—
35C2×C22⋊D151—21no—
36D4×D151—41no—
37C22×Dic151—21no—
38C22×Dic151D411yescharacteristic, complemented
39#14558992—41no—
40#14558989—41no—
41#14558988—21no—
42C4⋊Dic151—41no—
43Dic151⋊C4—21no—
44Dic151⋊C4—21no—
45Dic151⋊C4—21no—
46C22⋊Dic151—21no—
47C22⋊Dic151—21no—
48C22⋊Dic151D411yescharacteristic
49C22⋊Dic151D411yescharacteristic, complemented
50(C2×D151)⋊C4—21no—
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—21no—
53(C2×D151)⋊C4—41no—
54(C2×D151)⋊C4—41no—
55C2×D4×C151—21no—
56C2×D4×C151—21no—
57C2×D4×C151D411yescharacteristic, complemented
58C2×D4×C151C2311yescharacteristic
59C22⋊C4×C151—21no—
60C22⋊C4×C151—21no—
61C42×C151D411yescharacteristic, complemented
62C22×D151—21no—
63C22×D151—21no—
64C22×D151—21no—
65C22×D151—41no—
66C22×D151—81no—
67Dic302—21no—
68D604—21no—
69D604—82no—
70C22⋊D151—41no—
71C22⋊D151—41no—
72C22⋊D151—41no—
73C22⋊D151—81no—
74C22⋊D151—81no—
75C22⋊D151—81no—
76C2×Dic151—21no—
77C2×Dic151—21no—
78C2×Dic151—21no—
79C2×Dic151—21no—
80C2×Dic151—21no—
81C2×Dic151—41no—
82C2×Dic151—81no—
83C4×D151—41no—
84C151⋊C8—41no—
85C23×C151—21no—
86C23×C151C2×D411yescharacteristic
87C23×C151C2×D411yescharacteristic
88D4×C151—41no—
89D4×C151—41no—
90D4×C151—81no—
91D4×C151—81no—
92C2×C4×C151—21no—
93C2×C4×C151—41no—
94C2×C4×C151—41no—
95C2×C4×C151C2×D411yescharacteristic
96C22×C151—21no—
97C22×C151—21no—
98C22×C151—41no—
99C22×C151—41no—
100C22×C151—41no—
101C22×C151—41no—
102C22×C151—41no—
103C22×C151#12011yescharacteristic
104C2×D151—41no—
105C2×D151—41no—
106C2×D151—42no—
107C2×D151—41no—
108C2×D151—41no—
109C2×D151—81no—
110C2×D151—81no—
111C2×D151—81no—
112C4×C151—21no—
113C4×C151—41no—
114C4×C151—81no—
115C4×C151—81no—
116Dic151—41no—
117Dic151—41no—
118Dic151—41no—
119Dic151—41no—
120C2×C151—21no—
121C2×C151—41no—
122C2×C151—41no—
123C2×C151—81no—
124C2×C151B(4,𝔽2)11yescharacteristic
125D151—81no—
126D151—81no—
127C151#220011yescharacteristic, complemented, Sylow
128#2200—1511nomaximal, Sylow
129#560—1511no—
130#458—1511no—
131B(4,𝔽2)—1511no—
132#453—1511no—
133#353D15111yescharacteristic, complemented
134#352—1511no—
135AΣL(1,𝔽16)—1511no—
136H(5,𝔽2)—1511no—
137AGL(1,ℤ/8)—3021no—
138#127C2×D15111yescharacteristic
139#126—3021no—
140#123—3021no—
141#123—3021no—
142#123—1511no—
143#121—3021no—
144#121—3021no—
145#121—3021no—
146#120—3021no—
147#120—3021no—
148#120—1511no—
149#104—3021no—
150#100—1511no—
151#99—3021no—
152#99—3021no—
153#99C2×D15111yescharacteristic
154#99C2×D15111yescharacteristic
155C24—1511no—
156#41—3021no—
157#41—6041no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—3021no—
161C2×D4—3021no—
162C2×D4—3021no—
163C2×D4—3021no—
164C2×D4—3021no—
165C2×D4—6041no—
166C2×D4—6041no—
167C2×D4D60411yescharacteristic, complemented
168C2×D4C22×D15111yescharacteristic
169C22×C4—3021no—
170C22×C4—1511no—
171SD16—6041no—
172D8—6041no—
173M16—3021no—
174C4⋊C4—3021no—
175C4⋊C4—3021no—
176C4⋊C4—3021no—
177C4⋊C4—6041no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—3021no—
181C22⋊C4—3021no—
182C22⋊C4—3021no—
183C22⋊C4—3021no—
184C22⋊C4—3021no—
185C22⋊C4—6041no—
186C22⋊C4—6041no—
187C22⋊C4—1511no—
188C22⋊C4—1511no—
189C42D60411yescharacteristic, complemented
190C23—21no—
191C23—3021no—
192C23—3021no—
193C23—3021no—
194C23—6041no—
195C23—12081no—
196C23D4×D15111yescharacteristic
197C23D4×D15111yescharacteristic
198Q8—3021no—
199D4—41no—
200D4—41no—
201D4—81no—
202D4—81no—
203D4—3021no—
204D4—6041no—
205D4—6041no—
206D4—6041no—
207D4—12082no—
208D4—12081no—
209D4—12081no—
210D4—12081no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—3021no—
215C2×C4—3021no—
216C2×C4—3021no—
217C2×C4—3021no—
218C2×C4—3021no—
219C2×C4—6041no—
220C2×C4—6041no—
221C2×C4—12081no—
222C2×C4C2×D60411yescharacteristic
223C8—6041no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—6041no—
232C22—6041no—
233C22—6042no—
234C22—6041no—
235C22—6041no—
236C22—12081no—
237C22—12081no—
238C22—12081no—
239C22#1801270911yescharacteristic
240C4—21no—
241C4—41no—
242C4—81no—
243C4—81no—
244C4—6041no—
245C4—6041no—
246C4—6041no—
247C4—6041no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—12081no—
253C2—12081no—
254C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
Fitting#353×C151C2
socleC2×C151B(4,𝔽2)
hypercenter#353D151
hypocenterC151#2200
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
1. #23752949C2semidirect
2. #23752403C2semidirect
3. #23752400C2semidirect
4. #23752379C2semidirect
5. #23752001C2semidirect
6. #23751998C2semidirect
7. #353×C151C2semidirect
38. C22×Dic151D4semidirect
49. C22⋊Dic151D4semidirect
57. C2×D4×C151D4semidirect
61. C42×C151D4semidirect
127. C151#2200semidirect
133. #353D151semidirect
167. C2×D4D604semidirect
189. C42D604semidirect

Maximal subgroups

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

subgroupindex
#237529492
#237524032
#237524002
#237523792
#237520012
#237519982
#353×C1512
#2200151