Finite Group Databasebeta

← #34068172

Subgroups — #34068172

Order 19328.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752882C211yesmaximal, characteristic, complemented
2#23752409C211yesmaximal, characteristic, complemented
3#23752404C211yesmaximal, characteristic, complemented
4#23751956C211yesmaximal, characteristic, complemented
5#23751944C211yesmaximal, characteristic, complemented
6#23751941C211yesmaximal, characteristic, complemented
7#493×C151C211yesmaximal, characteristic, complemented
8C2×#14559003—21no—
9C2×#14558992—21no—
10C2×#14558989—21no—
11#18012735—21no—
12#18012711—22no—
13#18012710—21no—
14C4×Dic302C2211yescharacteristic
15C4×D604C2211yescharacteristic
16D4×Dic151—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18C4⋊(C151⋊C8)C2211yescharacteristic
19#18012660—21no—
20#18012660—21no—
21C2×D8×C151—22no—
22#127×C151C2211yescharacteristic
23#127×C151C2211yescharacteristic
24C4×C8×C151C2211yescharacteristic
25#14559003—42no—
26#14559003—42no—
27C2×Dic302D411yescharacteristic
28C2×D604D411yescharacteristic
29C2×C22⋊D151—22no—
30C2×C22⋊D151—22no—
31C22×Dic151—22no—
32C2×C4×D151—21no—
33#14558992—42no—
34#14558989—42no—
35C2×C151⋊C8—21no—
36C2×C151⋊C8—21no—
37C4⋊Dic151D411yescharacteristic
38C4⋊Dic151D411yescharacteristic
39Dic151⋊C4—21no—
40C22⋊Dic151—22no—
41(C2×D151)⋊C4—21no—
42C4×Dic151—21no—
43C2×D4×C151—21no—
44C2×D4×C151—21no—
45C2×D4×C151—21no—
46C2×D4×C151—21no—
47C2×D4×C151—21no—
48C2×D4×C151D412yes—
49D8×C151—44no—
50C2×C8×C151—21no—
51C42×C151C2311yescharacteristic
52C22×D151—21no—
53Dic302—21no—
54Dic302D812yescomplemented
55D604—21no—
56D604—21no—
57C22⋊D151—44no—
58C22⋊D151—82no—
59C2×Dic151—21no—
60C2×Dic151—21no—
61C2×Dic151—21no—
62C2×Dic151—44no—
63C4×D151—41no—
64C4×D151—41no—
65C151⋊C8—41no—
66C151⋊C8—41no—
67C23×C151—22no—
68C23×C151—41no—
69D4×C151—42no—
70D4×C151—42no—
71D4×C151—41no—
72D4×C151—41no—
73D4×C151—41no—
74D4×C151—41no—
75D4×C151—41no—
76D4×C151—41no—
77D4×C151—41no—
78D4×C151—41no—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C8×C151—22no—
83C22×C151—42no—
84C22×C151—42no—
85C22×C151—42no—
86C22×C151—81no—
87C22×C151—81no—
88C22×C151—81no—
89C22×C151#12011yescharacteristic
90C2×D151—41no—
91C2×D151—41no—
92C2×D151—41no—
93C4×C151—21no—
94C4×C151C2×D811yescharacteristic
95C4×C151#13511yescharacteristic
96C4×C151AGL(1,ℤ/8)11yescharacteristic
97C4×C151AGL(1,ℤ/8)11yescharacteristic
98Dic151—22no—
99Dic151—41no—
100Dic151—41no—
101C2×C151—82no—
102C2×C151—161no—
103C2×C151#44711yescharacteristic
104C2×C151#44911yescharacteristic
105C2×C151#45311yescharacteristic
106D151—81no—
107C151#162111yescharacteristic, complemented, Sylow
108#1621—1511nomaximal, Sylow
109#550—1511no—
110#493D15111yescharacteristic, complemented
111#460—1511no—
112#459—1511no—
113#331—1511no—
114Q8⋊C8—1511no—
115D4⋊C8—1511no—
116C2×#41—3021no—
117C2×SD16—3021no—
118C2×D8—22no—
119C2×D8—3021no—
120#127—3021no—
121#127C2×D15111yescharacteristic
122#127C2×D15111yescharacteristic
123#121—3022no—
124#121—3021no—
125C4×Q8—1511no—
126C4×D4—3021no—
127C4×D4—1511no—
128C4⋊C8—1511no—
129C4⋊C8—1511no—
130#102—3021no—
131#102—3021no—
132C4×C8C2×D15111yescharacteristic
133#41—6042no—
134#41—6042no—
135C2×Q8—1511no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—3022no—
142C2×D4—3022no—
143C2×D4—1511no—
144C2×D4C22⋊D15112yes—
145C22×C4—3022no—
146C22×C4—3021no—
147SD16—6042no—
148D8—44no—
149D8—6042no—
150C2×C8—21no—
151C2×C8—3021no—
152C2×C8—3021no—
153C4⋊C4—3021no—
154C4⋊C4—1511no—
155C4⋊C4—1511no—
156C22⋊C4—3022no—
157C22⋊C4—3021no—
158C42—3021no—
159C42C22×D15111yescharacteristic
160C23—22no—
161C23—41no—
162C23—3021no—
163Q8—3021no—
164Q8—1512no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—3021no—
176D4—3021no—
177D4—6044no—
178D4—12082no—
179C2×C4—3021no—
180C2×C4—3021no—
181C2×C4—3021no—
182C2×C4—6044no—
183C2×C4—6041no—
184C2×C4—6041no—
185C2×C4D4×D15111yescharacteristic
186C2×C4D4×D15111yescharacteristic
187C2×C4C2×C22⋊D15111yescharacteristic
188C8—22no—
189C8—6041no—
190C8—6041no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—6041no—
198C22—6041no—
199C22—6041no—
200C22#1801270711yescharacteristic
201C4—21no—
202C4—3022no—
203C4—6041no—
204C4—6041no—
205C4D8×D15111yescharacteristic
206C4#1801275811yescharacteristic
207C4#1801276311yescharacteristic
208C4#1801276311yescharacteristic
209C2—82no—
210C2—161no—
211C2—12081no—
212C2#2375234411yescharacteristic
213C2#2375235411yescharacteristic
214C2#2375237911yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#493×C151C2
socleC22×C151#120
hypercenter#493D151
hypocenterC151#1621
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #23752882C2semidirect
2. #23752409C2semidirect
3. #23752404C2semidirect
4. #23751956C2semidirect
5. #23751944C2semidirect
6. #23751941C2semidirect
7. #493×C151C2semidirect
54. Dic302D8semidirect
107. C151#1621semidirect
110. #493D151semidirect

Maximal subgroups

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

subgroupindex
#237528822
#237524092
#237524042
#237519562
#237519442
#237519412
#493×C1512
#1621151