Finite Group Databasebeta

← #34068176

Subgroups — #34068176

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#23752588C211yesmaximal, characteristic, complemented
3#23752413C211yesmaximal, characteristic, complemented
4#23752408C211yesmaximal, characteristic, complemented
5#23751942C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic, complemented
7#331×C151C211yesmaximal, characteristic, complemented
8C2×#14559003—21no—
9C2×#14558993—21no—
10C2×D1208—21no—
11C2×#14558989—22no—
12#18012736C2211yescharacteristic
13#18012735—21no—
14#18012711—22no—
15#18012710—21no—
16C4×Dic302C2211yescharacteristic
17C4×D604C2211yescharacteristic
18D4×Dic151—21no—
19#18012661—21no—
20#18012661—21no—
21C4×C151⋊C8C2211yescharacteristic
22#127×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4⋊C8×C151C2211yescharacteristic
25#14559003—42no—
26#14559003—42no—
27C2×Dic302D411yescharacteristic
28C2×D604—21no—
29C2×D604—21no—
30C2×D604—21no—
31C2×D604D411yescharacteristic
32C2×C22⋊D151—22no—
33C2×C22⋊D151—22no—
34C22×Dic151—22no—
35C2×C4×D151—21no—
36#14558993—42no—
37D1208—42no—
38#14558989—44no—
39C2×C151⋊C8—21no—
40C4⋊Dic151D411yescharacteristic
41C4⋊Dic151D411yescharacteristic
42Dic151⋊C4—21no—
43C22⋊Dic151—22no—
44(C2×D151)⋊C4—21no—
45C4×Dic151—21no—
46C2×D4×C151—21no—
47C2×D4×C151—21no—
48C2×D4×C151D412yes—
49C2×C8×C151—21no—
50C2×C8×C151—21no—
51C42×C151C2311yescharacteristic
52C22×D151—21no—
53C22×D151—41no—
54Dic302—21no—
55Dic302D812yescomplemented
56D604—21no—
57D604—21no—
58D604—42no—
59D604—41no—
60D604—41no—
61D604—41no—
62D604—41no—
63C22⋊D151—44no—
64C22⋊D151—82no—
65C2×Dic151—21no—
66C2×Dic151—21no—
67C2×Dic151—21no—
68C2×Dic151—44no—
69C4×D151—41no—
70C4×D151—41no—
71C151⋊C8—22no—
72C23×C151—22no—
73D4×C151—42no—
74D4×C151—41no—
75D4×C151—41no—
76D4×C151—41no—
77D4×C151—41no—
78C2×C4×C151C2×D411yescharacteristic
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C8×C151—41no—
82C8×C151—41no—
83C22×C151—42no—
84C22×C151—42no—
85C22×C151—42no—
86C22×C151#12011yescharacteristic
87C2×D151—41no—
88C2×D151—41no—
89C2×D151—41no—
90C2×D151—81no—
91C2×D151—81no—
92C2×D151—81no—
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#44711yescharacteristic
103C2×C151#44911yescharacteristic
104C2×C151#45311yescharacteristic
105D151—81no—
106D151—161no—
107C151#162111yescharacteristic, complemented, Sylow
108#1621—1511nomaximal, Sylow
109#550—1511no—
110#493—1511no—
111#460—1511no—
112#459—1511no—
113#331D15111yescharacteristic, complemented
114Q8⋊C8—1511no—
115D4⋊C8—1511no—
116C2×#41—3021no—
117C2×SD16—3021no—
118C2×D8—3021no—
119C2×D8—3022no—
120#127—3021no—
121#127—1511no—
122#127C2×D15111yescharacteristic
123#121—3022no—
124#121—3021no—
125C4×Q8—1511no—
126C4×D4—3021no—
127C4×D4—1511no—
128C4⋊C8C2×D15111yescharacteristic
129C4⋊C8C2×D15111yescharacteristic
130#102—3021no—
131#102—3021no—
132C4×C8—1511no—
133#41—6042no—
134#41—6042no—
135C2×Q8—1511no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—3022no—
139C2×D4—3022no—
140C2×D4—3021no—
141C2×D4—3021no—
142C2×D4—3021no—
143C2×D4—1511no—
144C2×D4D60412yes—
145C22×C4—3022no—
146C22×C4—3021no—
147SD16—6042no—
148D8—6042no—
149D8—6044no—
150C2×C8—21no—
151C2×C8—21no—
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—3021no—
162C23—6041no—
163Q8—3021no—
164Q8—1512no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—3021no—
171D4—3021no—
172D4—6042no—
173D4—6044no—
174D4—6041no—
175D4—6041no—
176D4—6041no—
177D4—6041no—
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×D60411yescharacteristic
188C8—41no—
189C8—41no—
190C8—3022no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—6041no—
195C22—6041no—
196C22—6041no—
197C22—12081no—
198C22—12081no—
199C22—12081no—
200C22#1801270911yescharacteristic
201C4—21no—
202C4—3022no—
203C4—6041no—
204C4—6041no—
205C4D8×D15111yescharacteristic
206C4#1801276011yescharacteristic
207C4#1801276311yescharacteristic
208C4#1801276611yescharacteristic
209C2—82no—
210C2—24161no—
211C2—12081no—
212C2#2375234711yescharacteristic
213C2#2375235811yescharacteristic
214C2#2375238211yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#331×C151C2
socleC22×C151#120
hypercenter#331D151
hypocenterC151#1621
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #23752882C2semidirect
2. #23752588C2semidirect
3. #23752413C2semidirect
4. #23752408C2semidirect
5. #23751942C2semidirect
6. #23751939C2semidirect
7. #331×C151C2semidirect
55. Dic302D8semidirect
107. C151#1621semidirect
113. #331D151semidirect

Maximal subgroups

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

subgroupindex
#237528822
#237525882
#237524132
#237524082
#237519422
#237519392
#331×C1512
#1621151