Finite Group Databasebeta

← #34068401

Subgroups — #34068401

Order 19328.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#23752956C211yesmaximal, characteristic, complemented
2#23752599C211yesmaximal, characteristic, complemented
3#23752576C211yesmaximal, characteristic, complemented
4#23751953C211yesmaximal, characteristic, complemented
5#23751952C211yesmaximal, characteristic, complemented
6#23751951C211yesmaximal, characteristic, complemented
7#496×C151C211yesmaximal, characteristic, complemented
8C2×#14558992—21no—
9C2×#14558989—21no—
10#18012731C2211yescharacteristic
11#18012727C2211yescharacteristic
12#18012723—21no—
13#18012721—21no—
14#18012716—21no—
15#18012715—21no—
16#18012712—21no—
17#18012711—21no—
18#18012660—21no—
19#18012660—21no—
20#18012650C2211yescharacteristic
21#18012650C2211yescharacteristic
22C2×SD16×C151—21no—
23C2×D8×C151—21no—
24#127×C151C2211yescharacteristic
25#124×C151C2211yescharacteristic
26#97×C151C2211yescharacteristic
27C2×Dic302D411yescharacteristic
28C2×D604D411yescharacteristic
29C2×C22⋊D151—21no—
30C2×C22⋊D151—21no—
31C22×Dic151—21no—
32C2×C4×D151—21no—
33#14558992—42no—
34#14558989—42no—
35C2×C151⋊C8—21no—
36C2×C151⋊C8—21no—
37C4⋊Dic151—21no—
38C4⋊Dic151D411yescharacteristic
39C4⋊Dic151D411yescharacteristic
40Dic151⋊C4—21no—
41Dic151⋊C4—21no—
42Dic151⋊C4—21no—
43C22⋊Dic151—21no—
44(C2×D151)⋊C4—21no—
45(C2×D151)⋊C4—21no—
46(C2×D151)⋊C4—21no—
47C2×Q8×C151D411yescharacteristic
48C2×D4×C151—21no—
49C2×D4×C151—21no—
50C2×D4×C151—21no—
51C2×D4×C151D411yescharacteristic
52SD16×C151—42no—
53D8×C151—42no—
54C2×C8×C151—21no—
55C22⋊C4×C151—21no—
56C22⋊C4×C151—21no—
57C42×C151C2311yescharacteristic
58C22×D151—21no—
59Dic302—41no—
60D604—41no—
61C22⋊D151—81no—
62C22⋊D151—81no—
63C2×Dic151—21no—
64C2×Dic151—21no—
65C2×Dic151—21no—
66C2×Dic151—81no—
67C4×D151—81no—
68C151⋊C8—22no—
69C151⋊C8—41no—
70C23×C151—21no—
71C23×C151—41no—
72Q8×C151—41no—
73D4×C151—41no—
74D4×C151—41no—
75D4×C151—41no—
76D4×C151—41no—
77D4×C151—41no—
78D4×C151—42no—
79C2×C4×C151—21no—
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C8×C151—22no—
84C22×C151—41no—
85C22×C151—41no—
86C22×C151—41no—
87C22×C151—81no—
88C22×C151—81no—
89C22×C151—81no—
90C22×C151#12011yescharacteristic
91C2×D151—41no—
92C2×D151—41no—
93C2×D151—41no—
94C4×C151—21no—
95C4×C151—21no—
96C4×C151—21no—
97C4×C151—41no—
98Dic151—41no—
99Dic151—41no—
100Dic151—41no—
101C2×C151—81no—
102C2×C151—161no—
103C2×C151#45311yescharacteristic
104C2×C151#45311yescharacteristic
105C2×C151#45411yescharacteristic
106D151—81no—
107C151#165611yescharacteristic, complemented, Sylow
108#1656—1511nomaximal, Sylow
109#562—1511no—
110#496—1511no—
111#496D15111yescharacteristic, complemented
112#490—1511no—
113#330—1511no—
114#329—1511no—
115#329—1511no—
116C2×SD16—21no—
117C2×SD16—3021no—
118C2×D8—21no—
119C2×D8—3021no—
120#127C2×D15111yescharacteristic
121#125—1511no—
122#124—1511no—
123#124C2×D15111yescharacteristic
124#123—3021no—
125#123—3021no—
126C22⋊Q8—3021no—
127C22⋊Q8—3021no—
128#121—3021no—
129#121—3021no—
130#102—3021no—
131#102—3021no—
132#97—1511no—
133#97—1511no—
134#97C2×D15111yescharacteristic
135C2×Q8—1511no—
136C2×Q8C22⋊D15111yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—3021no—
141C2×D4—3021no—
142C2×D4—1511no—
143C2×D4C22⋊D15111yescharacteristic
144C22×C4—3021no—
145C22×C4—3021no—
146SD16—42no—
147SD16—6042no—
148D8—42no—
149D8—6042no—
150C2×C8—21no—
151C2×C8—3021no—
152C2×C8—3021no—
153C4⋊C4—3021no—
154C4⋊C4—3021no—
155C4⋊C4—3021no—
156C4⋊C4—3021no—
157C4⋊C4—1511no—
158C4⋊C4—1511no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—3021no—
162C22⋊C4—3021no—
163C22⋊C4—3021no—
164C22⋊C4—3021no—
165C42C22×D15111yescharacteristic
166C23—21no—
167C23—41no—
168C23—3021no—
169Q8—41no—
170Q8—6041no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—41no—
176D4—42no—
177D4—6041no—
178D4—12081no—
179D4—12081no—
180C2×C4—21no—
181C2×C4—3021no—
182C2×C4—3021no—
183C2×C4—3021no—
184C2×C4—12081no—
185C2×C4—12081no—
186C2×C4D4×D15111yescharacteristic
187C2×C4D4×D15111yescharacteristic
188C2×C4C2×C22⋊D15111yescharacteristic
189C8—22no—
190C8—3022no—
191C8—6041no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22—81no—
197C22—81no—
198C22—6041no—
199C22—6041no—
200C22—6041no—
201C22#1801270711yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—6041no—
207C4—6041no—
208C4—6041no—
209C2—81no—
210C2—161no—
211C2—12081no—
212C2#2375237811yescharacteristic
213C2#2375237911yescharacteristic
214C2#2375238311yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#496×C151C2
socleC22×C151#120
hypercenter#496D151
hypocenterC151#1656
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #23752956C2semidirect
2. #23752599C2semidirect
3. #23752576C2semidirect
4. #23751953C2semidirect
5. #23751952C2semidirect
6. #23751951C2semidirect
7. #496×C151C2semidirect
107. C151#1656semidirect
111. #496D151semidirect

Maximal subgroups

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

subgroupindex
#237529562
#237525992
#237525762
#237519532
#237519522
#237519512
#496×C1512
#1656151