Finite Group Databasebeta

← #34068057

Subgroups — #34068057

Order 19328.

320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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#23752799C211yesmaximal, characteristic, complemented
2#23752365C211yesmaximal, characteristic, complemented
3#23752345C211yesmaximal, characteristic, complemented
4#23752122C211yesmaximal, characteristic, complemented
5#23751948C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic, complemented
7#327×C151C211yesmaximal, characteristic, complemented
8C22×D604—21no—
9C22×D604C2211yescharacteristic
10C2×#14558993—21no—
11C2×#14558989—21no—
12#18012734—21no—
13#18012725—21no—
14#18012723—21no—
15#18012718C2211yescharacteristic
16#18012711—21no—
17#18012707—21no—
18D4×Dic151—21no—
19C2×(C2×D151)⋊C4—21no—
20C2×(C2×D151)⋊C4C2211yescharacteristic
21#18012661—21no—
22#18012659—21no—
23C22⋊(C151⋊C8)C2211yescharacteristic
24#121×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C23×D151—21no—
28C23×D151D411yescharacteristic
29C2×Dic302D411yescharacteristic, complemented
30C2×D604—21no—
31C2×D604—21no—
32C2×D604—42no—
33C2×D604—42no—
34C2×D604—42no—
35C2×D604—42no—
36C2×C22⋊D151—21no—
37C2×C22⋊D151—21no—
38C22×Dic151—21no—
39C22×Dic151D411yescharacteristic
40#14558993—42no—
41#14558989—42no—
42C2×C151⋊C8—21no—
43C4⋊Dic151—21no—
44C4⋊Dic151D411yescharacteristic, complemented
45Dic151⋊C4—21no—
46C22⋊Dic151—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—
53C4×Dic151—21no—
54C2×D4×C151—21no—
55C2×D4×C151D411yescharacteristic, complemented
56C22×C4×C151—21no—
57C22×C4×C151C2311yescharacteristic
58C2×C8×C151—21no—
59C4⋊C4×C151D411yescharacteristic, complemented
60C22⋊C4×C151—21no—
61C22×D151—22no—
62C22×D151—21no—
63C22×D151—21no—
64C22×D151—21no—
65C22×D151—41no—
66C22×D151—41no—
67C22×D151—41no—
68C22×D151—41no—
69C22×D151—41no—
70C22×D151—41no—
71C22×D151—41no—
72C22×D151—41no—
73Dic302—41no—
74D604—22no—
75D604—22no—
76D604—41no—
77D604—41no—
78D604—48no—
79C22⋊D151—81no—
80C22⋊D151—81no—
81C2×Dic151—21no—
82C2×Dic151—21no—
83C2×Dic151—21no—
84C2×Dic151—41no—
85C2×Dic151—81no—
86C151⋊C8—41no—
87C23×C151—21no—
88C23×C151C2×D411yescharacteristic
89D4×C151—41no—
90D4×C151—41no—
91D4×C151—41no—
92C2×C4×C151—22no—
93C2×C4×C151—21no—
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×C151#13511yescharacteristic
107C22×C151AGL(1,ℤ/8)11yescharacteristic
108C2×D151—42no—
109C2×D151—42no—
110C2×D151—42no—
111C2×D151—41no—
112C2×D151—41no—
113C2×D151—41no—
114C2×D151—42no—
115C2×D151—81no—
116C2×D151—81no—
117C2×D151—81no—
118C2×D151—81no—
119C2×D151—81no—
120C4×C151—21no—
121C4×C151—21no—
122C4×C151—42no—
123C4×C151—41no—
124Dic151—41no—
125Dic151—41no—
126Dic151—41no—
127C2×C151—21no—
128C2×C151—21no—
129C2×C151—81no—
130C2×C151#44911yescharacteristic
131C2×C151#45311yescharacteristic
132C2×C151B(4,𝔽2)11yescharacteristic
133D151—81no—
134D151—82no—
135C151#160011yescharacteristic, complemented, Sylow
136#1600—1511nomaximal, Sylow
137#538—1511no—
138#450—1511no—
139#447—1511no—
140#392—1511no—
141#328—1511no—
142#327D15111yescharacteristic, complemented
143#323—1511no—
144C22×D4—3021no—
145C22×D4—1511no—
146C2×SD16—3021no—
147C2×D8—3021no—
148#126—3021no—
149#124—3021no—
150#123—3021no—
151C22⋊Q8—1511no—
152#121—3021no—
153#121C2×D15111yescharacteristic
154#120—3021no—
155C4×D4—3021no—
156C2×C22⋊C4—3021no—
157C2×C22⋊C4—1511no—
158#102—3021no—
159#102—3021no—
160C22⋊C8—1511no—
161C22⋊C8C2×D15111yescharacteristic
162#95C2×D15111yescharacteristic
163C24—3021no—
164C24—1511no—
165C2×Q8—1511no—
166C2×D4—21no—
167C2×D4—3021no—
168C2×D4—3021no—
169C2×D4—3021no—
170C2×D4—3021no—
171C2×D4—6042no—
172C2×D4—6042no—
173C2×D4—6042no—
174C2×D4—6042no—
175C2×D4D60411yescharacteristic, complemented
176C22×C4—21no—
177C22×C4—3021no—
178C22×C4—1511no—
179C22×C4C22×D15111yescharacteristic
180SD16—6042no—
181D8—6042no—
182C2×C8—21no—
183C2×C8—3021no—
184C4⋊C4—3021no—
185C4⋊C4—3021no—
186C4⋊C4—1511no—
187C4⋊C4D60411yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—3021no—
190C22⋊C4—3021no—
191C22⋊C4—3021no—
192C22⋊C4—3021no—
193C22⋊C4—3021no—
194C22⋊C4—3021no—
195C22⋊C4—6042no—
196C42—3021no—
197C23—21no—
198C23—3022no—
199C23—3021no—
200C23—3021no—
201C23—3021no—
202C23—6041no—
203C23—6041no—
204C23—6041no—
205C23—6041no—
206C23—6041no—
207C23—6041no—
208C23—6041no—
209C23—6041no—
210C23D4×D15111yescharacteristic
211Q8—6041no—
212D4—41no—
213D4—41no—
214D4—41no—
215D4—3022no—
216D4—3022no—
217D4—6041no—
218D4—6041no—
219D4—6048no—
220D4—12081no—
221D4—12081no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—3021no—
228C2×C4—3021no—
229C2×C4—3021no—
230C2×C4—6041no—
231C2×C4—12081no—
232C2×C4D4×D15111yescharacteristic
233C2×C4C2×D60411yescharacteristic
234C8—41no—
235C8—6041no—
236C22—21no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—6042no—
242C22—6042no—
243C22—6042no—
244C22—6041no—
245C22—6041no—
246C22—6042no—
247C22—6041no—
248C22—12081no—
249C22—12081no—
250C22—12081no—
251C22—12081no—
252C22—12081no—
253C22#1801270911yescharacteristic
254C22#1801276011yescharacteristic
255C22#1801276311yescharacteristic
256C4—21no—
257C4—21no—
258C4—42no—
259C4—41no—
260C4—6041no—
261C4—6041no—
262C4—6041no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2—12081no—
267C2—12082no—
268C2#2375235811yescharacteristic
269C2#2375238111yescharacteristic
270C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#327×C151C2
socleC22×C151#120
hypercenter#327D151
hypocenterC151#1600
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
1. #23752799C2semidirect
2. #23752365C2semidirect
3. #23752345C2semidirect
4. #23752122C2semidirect
5. #23751948C2semidirect
6. #23751935C2semidirect
7. #327×C151C2semidirect
29. C2×Dic302D4semidirect
44. C4⋊Dic151D4semidirect
55. C2×D4×C151D4semidirect
59. C4⋊C4×C151D4semidirect
135. C151#1600semidirect
142. #327D151semidirect
175. C2×D4D604semidirect
187. C4⋊C4D604semidirect

Maximal subgroups

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

subgroupindex
#237527992
#237523652
#237523452
#237521222
#237519482
#237519352
#327×C1512
#1600151