Finite Group Databasebeta

← #34078619

Subgroups — #34078619

Order 19328.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#18012765C211yesmaximal, characteristic
2#23752786C211yesmaximal, characteristic, complemented
3#23752687C211yesmaximal, characteristic, complemented
4#23752429C214yesmaximal, complemented
5#23752415C214yesmaximal, complemented
6#23752238C211yesmaximal, characteristic, complemented
7#23752221C211yesmaximal, characteristic, complemented
8#23752209C211yesmaximal, characteristic, complemented
9C22×SD16×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic
11#18012765—24no—
12C2×#14558992C2212yes—
13C2×#14558989C2212yes—
14C2×#14558988C2211yescharacteristic
15#18012737C2212yescomplemented
16#18012728C2212yescomplemented
17#18012722—22no—
18#18012715—22no—
19D4×Dic151—22no—
20D4×Dic151C2214yes—
21#18012698C2211yescharacteristic
22#18012698C2211yescharacteristic
23C2×C22⋊Dic151—22no—
24Dic151⋊C8C2214yescomplemented
25#18012664C2212yescomplemented
26#18012663C2214yescomplemented
27#18012661C2212yescomplemented
28C22×Q8×C151C2211yescharacteristic
29C22×D4×C151C2211yescharacteristic
30C2×SD16×C151—24no—
31C2×SD16×C151C2214yes—
32C22×C8×C151C2211yescharacteristic
33#14559004—22no—
34#14559004—22no—
35C2×Dic302C2311yescharacteristic
36C2×D604C2311yescharacteristic
37C2×C22⋊D151—21no—
38C22×Dic151—24no—
39C2×C4×D151—21no—
40#14558992—24no—
41#14558989—24no—
42#14558988—22no—
43C2×C151⋊C8C2312yes—
44C4⋊Dic151D412yes—
45C4⋊Dic151C2312yes—
46Dic151⋊C4—24no—
47C22⋊Dic151—24no—
48C22⋊Dic151—21no—
49C22⋊Dic151D412yes—
50(C2×D151)⋊C4—24no—
51C4×Dic151—21no—
52C4×Dic151C2312yes—
53C24×C151—21no—
54C2×Q8×C151—21no—
55C2×Q8×C151—22no—
56C2×Q8×C151—22no—
57C2×Q8×C151C2312yes—
58C2×D4×C151—21no—
59C2×D4×C151—22no—
60C2×D4×C151D414yes—
61C2×D4×C151C2312yes—
62C22×C4×C151—21no—
63C22×C4×C151C2311yescharacteristic
64SD16×C151—28no—
65C2×C8×C151—22no—
66C2×C8×C151C2312yes—
67C22×D151—21no—
68Dic302—21no—
69Dic302—21no—
70D604—21no—
71D604—21no—
72C22⋊D151—42no—
73C2×Dic151—22no—
74C2×Dic151—21no—
75C2×Dic151—84no—
76C2×Dic151C2×D414yes—
77C4×D151—42no—
78C151⋊C8—22no—
79C23×C151—22no—
80C23×C151—24no—
81C23×C151—82no—
82C23×C151C2×D411yescharacteristic
83Q8×C151—22no—
84Q8×C151—22no—
85Q8×C151—42no—
86D4×C151—24no—
87D4×C151—22no—
88D4×C151C2×D414yes—
89C2×C4×C151—22no—
90C2×C4×C151—42no—
91C2×C4×C151C2×D411yescharacteristic
92C2×C4×C151C2×D412yes—
93C2×C4×C151#4112yes—
94C2×C4×C151C2411yescharacteristic
95C8×C151—22no—
96C22×C151—22no—
97C22×C151—24no—
98C22×C151—44no—
99C22×C151—84no—
100C22×C151#12112yes—
101C22×C151C22×D411yescharacteristic
102C2×D151—41no—
103C2×D151—42no—
104C4×C151—42no—
105C4×C151#12112yes—
106C4×C151C22×D411yescharacteristic
107C4×C151C2×#4111yescharacteristic
108Dic151—24no—
109Dic151—41no—
110Dic151—42no—
111C2×C151—22no—
112C2×C151—44no—
113C2×C151C2×#12111yescharacteristic
114C2×C151#57712yes—
115D151—81no—
116C151#304211yescharacteristic, complemented, Sylow
117#3042—1511nomaximal, Sylow
118C2×AGL(1,ℤ/8)—1511no—
119C22×SD16D15111yescharacteristic, complemented
120#536—1511no—
121#518—1511no—
122#463—1514no—
123#461—1514no—
124#424—1511no—
125#419—1511no—
126#416—1511no—
127C2×#41—1511no—
128C22×Q8C2×D15111yescharacteristic
129C22×D4C2×D15111yescharacteristic
130AGL(1,ℤ/8)—3024no—
131C2×SD16—24no—
132C2×SD16—1512no—
133C2×SD16C2×D15114yes—
134C2×D8—1512no—
135C2×M16—1511no—
136C22×C8C2×D15111yescharacteristic
137C4⋊Q8—1512no—
138#124—1512no—
139#123—3022no—
140C22⋊Q8—3022no—
141C4×D4—3022no—
142C4×D4—1514no—
143#117—1511no—
144#117—1511no—
145C2×C22⋊C4—3022no—
146C4⋊C8—1514no—
147#103—1514no—
148#103—1512no—
149#102—1512no—
150C24—21no—
151#41—3022no—
152#41—3022no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—1511no—
157C2×Q8C22×D15112yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—3021no—
161C2×D4—1511no—
162C2×D4C22⋊D15114yes—
163C2×D4C22×D15112yes—
164C22×C4—21no—
165C22×C4—3021no—
166C22×C4—3024no—
167C22×C4C22×D15111yescharacteristic
168SD16—28no—
169SD16—3024no—
170D8—3024no—
171M16—3022no—
172C2×C8—22no—
173C2×C8—1512no—
174C2×C8C22×D15112yes—
175C4⋊C4—3024no—
176C4⋊C4—1512no—
177C4⋊C4—1512no—
178C22⋊C4—3024no—
179C22⋊C4—3021no—
180C22⋊C4—3024no—
181C22⋊C4—1512no—
182C42—3021no—
183C42—1512no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—3021no—
188C23D4×D15111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—3021no—
193Q8—3021no—
194D4—24no—
195D4—22no—
196D4—3021no—
197D4—3021no—
198D4—6042no—
199D4C2×C22⋊D15114yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—3022no—
203C2×C4—3021no—
204C2×C4—6042no—
205C2×C4—1514no—
206C2×C4—12084no—
207C2×C4D4×D15111yescharacteristic
208C2×C4C2×C22⋊D15112yes—
209C2×C4#1455900312yes—
210C2×C4C23×D15111yescharacteristic
211C8—22no—
212C8—3022no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—6042no—
218C22—6041no—
219C22#1801271112yes—
220C22C2×D4×D15111yescharacteristic
221C4—42no—
222C4—3024no—
223C4—6042no—
224C4—6041no—
225C4#1801271112yes—
226C4C22×C22⋊D15111yescharacteristic
227C4C2×#1455900311yescharacteristic
228C2—22no—
229C2—44no—
230C2—12081no—
231C2C2×#1801271111yescharacteristic
232C2#2375301812yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×SD16×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012765C2
hypercenterC22×SD16D151
hypocenterC151#3042
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #23752786C2semidirect
3. #23752687C2semidirect
4. #23752429C2semidirect
5. #23752415C2semidirect
6. #23752238C2semidirect
7. #23752221C2semidirect
8. #23752209C2semidirect
9. C22×SD16×C151C2semidirect
15. #18012737C22semidirect
16. #18012728C22semidirect
24. Dic151⋊C8C22semidirect
25. #18012664C22semidirect
26. #18012663C22semidirect
27. #18012661C22semidirect
116. C151#3042semidirect
119. C22×SD16D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127652
#237527862
#237526872
#237524292
#237524152
#237522382
#237522212
#237522092
C22×SD16×C1512
#3042151