Finite Group Databasebeta

← #34079834

Subgroups — #34079834

Order 19328.

370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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#23752743C212yesmaximal, complemented
2#23752612C211yesmaximal, characteristic, complemented
3#23752595C211yesmaximal, characteristic, complemented
4#23752565C212yesmaximal, complemented
5#23752470C211yesmaximal, characteristic, complemented
6#23752456C212yesmaximal, complemented
7#23752324C211yesmaximal, characteristic, complemented
8#23752318C211yesmaximal, characteristic, complemented
9#23752309C212yesmaximal, complemented
10M16×Dic151C211yesmaximal, characteristic, complemented
11#469×C151C211yesmaximal, characteristic
12C2×Dic604C2211yescharacteristic
13C2×#14558992C2212yes—
14C2×#14558988C2211yescharacteristic
15#18012732—22no—
16#18012730C2212yes—
17#18012726C2212yes—
18#18012720—22no—
19#18012718C2212yes—
20#18012704C2212yes—
21D4×Dic151—22no—
22D4×Dic151C2212yes—
23#18012695—22no—
24C2×C4×Dic151C2211yescharacteristic
25#18012672C2212yes—
26#18012671C2211yescharacteristic
27#18012664C2212yes—
28#18012662C2212yes—
29#18012660C2212yes—
30#18012649C2211yescharacteristic
31#18012649C2211yescharacteristic
32C8×Dic151C2211yescharacteristic
33C8×Dic151C2211yescharacteristic
34C2×D8×C151C2211yescharacteristic
35C2×M16×C151C2211yescharacteristic
36#121×C151C2212yes—
37#106×C151C2211yescharacteristic
38#102×C151C2212yes—
39C2×Dic302C2312yes—
40C22×Dic151—22no—
41C22×Dic151D412yes—
42Dic604—22no—
43#14558992—24no—
44#14558988—22no—
45C2×C151⋊C8C2311yescharacteristic
46C2×C151⋊C8C2311yescharacteristic
47C4⋊Dic151—22no—
48C4⋊Dic151C2312yes—
49Dic151⋊C4—22no—
50Dic151⋊C4—22no—
51Dic151⋊C4—22no—
52C22⋊Dic151—22no—
53C22⋊Dic151—22no—
54C22⋊Dic151—22no—
55C22⋊Dic151—22no—
56C4×Dic151—22no—
57C4×Dic151D412yes—
58C4×Dic151C2311yescharacteristic
59C4×Dic151C2311yescharacteristic
60C2×D4×C151—22no—
61C2×D4×C151C2312yes—
62C22×C4×C151C2311yescharacteristic
63D8×C151—22no—
64M16×C151—22no—
65C2×C8×C151C2311yescharacteristic
66C2×C8×C151C2311yescharacteristic
67C4⋊C4×C151C2312yes—
68C22⋊C4×C151—22no—
69Dic302—22no—
70Dic302—22no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—42no—
74C2×Dic151—44no—
75C2×Dic151C2×D412yes—
76C2×Dic151C2×D412yes—
77C151⋊C8—21no—
78C151⋊C8#4112yes—
79C23×C151—22no—
80C23×C151C2×D411yescharacteristic
81D4×C151—22no—
82D4×C151—22no—
83D4×C151—44no—
84C2×C4×C151—21no—
85C2×C4×C151—21no—
86C2×C4×C151—22no—
87C2×C4×C151C2×D411yescharacteristic
88C2×C4×C151C2411yescharacteristic
89C8×C151—21no—
90C8×C151#4112yes—
91C22×C151—21no—
92C22×C151—22no—
93C22×C151—42no—
94C22×C151—42no—
95C22×C151—42no—
96C22×C151C22×D411yescharacteristic
97C4×C151—21no—
98C4×C151—42no—
99C4×C151C2×#4111yescharacteristic
100C4×C151C2×#4111yescharacteristic
101Dic151—22no—
102Dic151—22no—
103Dic151—42no—
104Dic151—42no—
105C2×C151—41no—
106C2×C151—82no—
107C2×C151#53211yescharacteristic
108C2×C151#57512yes—
109C151#318311yescharacteristic, complemented, Sylow
110#3183—1511nomaximal, Sylow
111#529—1512no—
112#499—1511no—
113#495—1511no—
114#488—1512no—
115#470—1511no—
116#469D15111yescharacteristic
117#468—1512no—
118#442—1511no—
119#441—1511no—
120#440—1512no—
121C4×M16—1511no—
122C2×Q16—1511no—
123C2×SD16—1512no—
124C2×D8C2×D15111yescharacteristic
125C2×M16—1511no—
126C2×M16C2×D15111yescharacteristic
127#126—3022no—
128#125—1512no—
129#124—1512no—
130#123—3022no—
131C22⋊Q8—1512no—
132#121C2×D15112yes—
133C4×Q8—1512no—
134C4×D4—3022no—
135C4×D4—1512no—
136#117—3022no—
137C2×C42—1511no—
138#107—1512no—
139#106—1511no—
140#106C2×D15111yescharacteristic
141#103—1512no—
142#103—1512no—
143#102—1512no—
144#102C2×D15112yes—
145#97—1511no—
146#97—1511no—
147C4×C8—1511no—
148C4×C8—1511no—
149C2×Q8—1512no—
150C2×D4—22no—
151C2×D4C22×D15112yes—
152C22×C4—3022no—
153C22×C4—1512no—
154C22×C4C22×D15111yescharacteristic
155Q16—3022no—
156SD16—3024no—
157D8—22no—
158M16—22no—
159M16—3022no—
160C2×C8—1511no—
161C2×C8—1511no—
162C2×C8C22×D15111yescharacteristic
163C2×C8C22×D15111yescharacteristic
164C4⋊C4—3022no—
165C4⋊C4—3022no—
166C4⋊C4—3022no—
167C4⋊C4—3022no—
168C4⋊C4—1512no—
169C4⋊C4C22×D15112yes—
170C22⋊C4—22no—
171C22⋊C4—3022no—
172C22⋊C4—3022no—
173C22⋊C4—3022no—
174C22⋊C4—3022no—
175C42—3022no—
176C42—1512no—
177C42—1511no—
178C42—1511no—
179C23—22no—
180C23D4×D15111yescharacteristic
181Q8—3022no—
182Q8—3022no—
183D4—22no—
184D4—22no—
185D4—44no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—3022no—
190C2×C4—3022no—
191C2×C4—6042no—
192C2×C4—6044no—
193C2×C4—1512no—
194C2×C4—1512no—
195C2×C4D4×D15111yescharacteristic
196C2×C4C23×D15111yescharacteristic
197C8—21no—
198C8—3021no—
199C8—1512no—
200C8#1455900312yes—
201C22—22no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22C2×D4×D15111yescharacteristic
207C4—21no—
208C4—42no—
209C4—3022no—
210C4—3022no—
211C4—6042no—
212C4—6042no—
213C4#41×D15111yescharacteristic
214C4C2×#1455900311yescharacteristic
215C2—41no—
216C2—82no—
217C2#2375275711yescharacteristic
218C2#2375300812yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting, prime radical#469×C151C2
socleC22×C151C22×D4
hypercenter#469D151
hypocenterC151#3183
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23752743C2semidirect
2. #23752612C2semidirect
3. #23752595C2semidirect
4. #23752565C2semidirect
5. #23752470C2semidirect
6. #23752456C2semidirect
7. #23752324C2semidirect
8. #23752318C2semidirect
9. #23752309C2semidirect
10. M16×Dic151C2semidirect
109. C151#3183semidirect

Maximal subgroups

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

subgroupindex
#237527432
#237526122
#237525952
#237525652
#237524702
#237524562
#237523242
#237523182
#237523092
M16×Dic1512
#469×C1512
#3183151