Finite Group Databasebeta

← #34068063

Subgroups — #34068063

Order 19328.

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

normal subgroups only

This group has 308 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#23752770C211yesmaximal, characteristic
2#23752353C211yesmaximal, characteristic, complemented
3#23752350C211yesmaximal, characteristic, complemented
4#23752125C211yesmaximal, characteristic, complemented
5#23751945C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic, complemented
7#327×C151C211yesmaximal, characteristic, complemented
8C22×Dic302C2211yescharacteristic, complemented
9C2×D4×D151—21no—
10C2×#14558993—21no—
11C2×#14558992—21no—
12#18012724—21no—
13#18012721—21no—
14#18012713C2211yescharacteristic
15#18012711—21no—
16#18012709—21no—
17#18012707—21no—
18C2×(C2×D151)⋊C4—21no—
19C2×(C2×D151)⋊C4C2211yescharacteristic
20#18012664—21no—
21#18012662—21no—
22C22⋊(C151⋊C8)C2211yescharacteristic, complemented
23C151⋊#95—21no—
24#121×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic, complemented
26#95×C151C2211yescharacteristic, complemented
27C23×D151—21no—
28C23×D151D411yescharacteristic
29C2×Dic302—21no—
30C2×Dic302—21no—
31C2×Dic302—42no—
32C2×D604—21no—
33C2×D604D411yescharacteristic
34C2×C22⋊D151—21no—
35C2×C22⋊D151—21no—
36C2×C22⋊D151—21no—
37D4×D151—42no—
38D4×D151—42no—
39C22×Dic151—21no—
40C22×Dic151D411yescharacteristic
41C2×C4×D151—21no—
42#14558993—42no—
43#14558992—42no—
44C2×C151⋊C8—21no—
45C4⋊Dic151D411yescharacteristic
46Dic151⋊C4—21no—
47C22⋊Dic151—21no—
48(C2×D151)⋊C4—21no—
49(C2×D151)⋊C4—21no—
50(C2×D151)⋊C4—21no—
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—42no—
53C2×D4×C151—21no—
54C2×D4×C151D411yescharacteristic
55C22×C4×C151—21no—
56C22×C4×C151C2311yescharacteristic
57C2×C8×C151—21no—
58C4⋊C4×C151D411yescharacteristic
59C22⋊C4×C151—21no—
60C22×D151—21no—
61C22×D151—21no—
62C22×D151—21no—
63C22×D151—42no—
64C22×D151—41no—
65C22×D151—41no—
66C22×D151—81no—
67C22×D151—81no—
68C22×D151SD1612yescomplemented
69Dic302—22no—
70Dic302—22no—
71Dic302—41no—
72Dic302—41no—
73D604—41no—
74D604—42no—
75C22⋊D151—42no—
76C22⋊D151—41no—
77C22⋊D151—41no—
78C22⋊D151—81no—
79C2×Dic151—22no—
80C2×Dic151—21no—
81C2×Dic151—21no—
82C2×Dic151—41no—
83C2×Dic151—41no—
84C2×Dic151—41no—
85C4×D151—42no—
86C151⋊C8—41no—
87C23×C151—21no—
88C23×C151C2×D411yescharacteristic
89D4×C151—41no—
90D4×C151—41no—
91D4×C151—41no—
92C2×C4×C151—21no—
93C2×C4×C151—41no—
94C2×C4×C151—41no—
95C2×C4×C151—41no—
96C2×C4×C151—41no—
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2×D411yescharacteristic
99C8×C151—41no—
100C22×C151—21no—
101C22×C151—21no—
102C22×C151—41no—
103C22×C151—41no—
104C22×C151—41no—
105C22×C151#12011yescharacteristic
106C22×C151C2×SD1611yescharacteristic
107C22×C151AGL(1,ℤ/8)11yescharacteristic
108C2×D151—22no—
109C2×D151—41no—
110C2×D151—41no—
111C2×D151—42no—
112C2×D151—41no—
113C2×D151—41no—
114C2×D151—41no—
115C2×D151—81no—
116C2×D151—84no—
117C4×C151—21no—
118C4×C151—21no—
119C4×C151—41no—
120C4×C151—81no—
121Dic151—41no—
122Dic151—41no—
123Dic151—42no—
124C2×C151—21no—
125C2×C151—21no—
126C2×C151—81no—
127C2×C151#45011yescharacteristic
128C2×C151#45511yescharacteristic
129C2×C151B(4,𝔽2)11yescharacteristic
130D151—42no—
131D151—81no—
132C151#160111yescharacteristic, complemented, Sylow
133#1601—1511nomaximal, Sylow
134#534—1511no—
135#448—1511no—
136#448—1511no—
137#393—1511no—
138#327—1511no—
139#327D15111yescharacteristic, complemented
140#323—1511no—
141C22×Q8—1511no—
142C22×D4—3021no—
143C2×SD16—3021no—
144C2×SD16—3021no—
145#123—3021no—
146#123—3021no—
147#121—3021no—
148#121—1511no—
149#121C2×D15111yescharacteristic
150#120—3021no—
151#120—3021no—
152C2×C22⋊C4—3021no—
153C2×C22⋊C4—1511no—
154#103—3021no—
155#103—3021no—
156C22⋊C8—1511no—
157C22⋊C8C2×D15111yescharacteristic, complemented
158#95—3021no—
159#95C2×D15111yescharacteristic, complemented
160C24—3021no—
161C24—1511no—
162C2×Q8—3021no—
163C2×Q8—3021no—
164C2×Q8—6042no—
165C2×D4—21no—
166C2×D4—3021no—
167C2×D4—3021no—
168C2×D4—3021no—
169C2×D4—3021no—
170C2×D4—6042no—
171C2×D4—6042no—
172C2×D4—1511no—
173C2×D4D60411yescharacteristic
174C22×C4—21no—
175C22×C4—3021no—
176C22×C4—3021no—
177C22×C4—1511no—
178C22×C4C22×D15111yescharacteristic
179SD16—6042no—
180SD16—6042no—
181C2×C8—21no—
182C2×C8—3021no—
183C4⋊C4—3021no—
184C4⋊C4—1511no—
185C4⋊C4D60411yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—3021no—
188C22⋊C4—3021no—
189C22⋊C4—3021no—
190C22⋊C4—3021no—
191C22⋊C4—3021no—
192C22⋊C4—6042no—
193C23—21no—
194C23—3021no—
195C23—3021no—
196C23—3021no—
197C23—6041no—
198C23—6041no—
199C23—6042no—
200C23—1512no—
201C23—12081no—
202C23—12081no—
203C23D4×D15111yescharacteristic
204Q8—3022no—
205Q8—3022no—
206Q8—6041no—
207Q8—6041no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—6041no—
212D4—6042no—
213D4—6042no—
214D4—6041no—
215D4—6041no—
216D4—12081no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—3022no—
223C2×C4—3021no—
224C2×C4—3021no—
225C2×C4—6042no—
226C2×C4—6041no—
227C2×C4—6041no—
228C2×C4—6041no—
229C2×C4D4×D15111yescharacteristic
230C2×C4C2×D60411yescharacteristic
231C8—41no—
232C8—6041no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—3022no—
239C22—6042no—
240C22—6041no—
241C22—6041no—
242C22—6041no—
243C22—6041no—
244C22—6041no—
245C22—12081no—
246C22—12084no—
247C22#1801270911yescharacteristic
248C22SD16×D15111yescharacteristic
249C22#1801276311yescharacteristic
250C4—21no—
251C4—21no—
252C4—41no—
253C4—81no—
254C4—6041no—
255C4—6041no—
256C4—6042no—
257C2—21no—
258C2—21no—
259C2—81no—
260C2—6042no—
261C2—12081no—
262C2#2375236411yescharacteristic
263C2#2375239111yescharacteristic
264C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#327×C151C2
socleC22×C151#120
prime radical#23752770C2
hypercenter#327D151
hypocenterC151#1601
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #23752353C2semidirect
3. #23752350C2semidirect
4. #23752125C2semidirect
5. #23751945C2semidirect
6. #23751935C2semidirect
7. #327×C151C2semidirect
8. C22×Dic302C22semidirect
22. C22⋊(C151⋊C8)C22semidirect
25. C22⋊C8×C151C22semidirect
26. #95×C151C22semidirect
68. C22×D151SD16semidirect
132. C151#1601semidirect
139. #327D151semidirect
157. C22⋊C8C2×D151semidirect
159. #95C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527702
#237523532
#237523502
#237521252
#237519452
#237519352
#327×C1512
#1601151