Finite Group Databasebeta

← #34068076

Subgroups — #34068076

Order 19328.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#23752811C211yesmaximal, characteristic
2#23752367C211yesmaximal, characteristic, complemented
3#23752353C211yesmaximal, characteristic
4#23752133C211yesmaximal, characteristic, complemented
5#23751945C211yesmaximal, characteristic
6#23751937C211yesmaximal, characteristic, complemented
7#328×C151C211yesmaximal, characteristic, complemented
8C22×Dic302C2211yescharacteristic
9C2×#14558994—21no—
10C2×#14558993—21no—
11#18012734—21no—
12#18012730—21no—
13#18012724—21no—
14#18012723—21no—
15#18012715—21no—
16#18012713C2211yescharacteristic
17(C22⋊D151)⋊C4—21no—
18C2×C4⋊Dic151—21no—
19C2×Dic151⋊C4C2211yescharacteristic
20#18012664—21no—
21#18012662—21no—
22C22⋊(C151⋊C8)C2211yescharacteristic
23C151⋊#95—21no—
24C22⋊Q8×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C2×Dic302—21no—
28C2×Dic302—21no—
29C2×Dic302—42no—
30C2×D604D411yescharacteristic
31C2×C22⋊D151—21no—
32C22×Dic151—21no—
33C22×Dic151D411yescharacteristic
34C22×Dic151D411yescharacteristic
35C2×C4×D151—21no—
36#14558994—42no—
37#14558993—42no—
38C2×C151⋊C8—21no—
39C4⋊Dic151—21no—
40C4⋊Dic151—21no—
41C4⋊Dic151—42no—
42C4⋊Dic151D411yescharacteristic
43Dic151⋊C4—21no—
44Dic151⋊C4—21no—
45Dic151⋊C4—21no—
46(C2×D151)⋊C4—21no—
47(C2×D151)⋊C4—21no—
48(C2×D151)⋊C4—21no—
49(C2×D151)⋊C4—21no—
50C4×Dic151—21no—
51C2×Q8×C151D411yescharacteristic
52C22×C4×C151—21no—
53C22×C4×C151C2311yescharacteristic
54C2×C8×C151—21no—
55C4⋊C4×C151—21no—
56C4⋊C4×C151D411yescharacteristic
57C22⋊C4×C151—21no—
58C22×D151—21no—
59Dic302—22no—
60Dic302—22no—
61Dic302—41no—
62Dic302—41no—
63D604—41no—
64C22⋊D151—41no—
65C22⋊D151—41no—
66C2×Dic151—22no—
67C2×Dic151—21no—
68C2×Dic151—21no—
69C2×Dic151—21no—
70C2×Dic151—21no—
71C2×Dic151—21no—
72C2×Dic151—41no—
73C2×Dic151—41no—
74C2×Dic151—41no—
75C4×D151—81no—
76C151⋊C8—41no—
77C23×C151C2×D411yescharacteristic
78Q8×C151—41no—
79C2×C4×C151—22no—
80C2×C4×C151—21no—
81C2×C4×C151—21no—
82C2×C4×C151—41no—
83C2×C4×C151—41no—
84C2×C4×C151—41no—
85C2×C4×C151C2×D411yescharacteristic
86C2×C4×C151C2×D411yescharacteristic
87C8×C151—41no—
88C22×C151—21no—
89C22×C151—21no—
90C22×C151#12011yescharacteristic
91C22×C151#13511yescharacteristic
92C22×C151#13711yescharacteristic
93C2×D151—41no—
94C2×D151—41no—
95C2×D151—41no—
96C4×C151—21no—
97C4×C151—21no—
98C4×C151—42no—
99C4×C151—41no—
100C4×C151—41no—
101Dic151—41no—
102Dic151—41no—
103Dic151—41no—
104Dic151—42no—
105C2×C151—21no—
106C2×C151—21no—
107C2×C151#45211yescharacteristic
108C2×C151#45611yescharacteristic
109C2×C151B(4,𝔽2)11yescharacteristic
110D151—81no—
111C151#160311yescharacteristic, complemented, Sylow
112#1603—1511nomaximal, Sylow
113#539—1511no—
114#451—1511no—
115#448—1511no—
116#395—1511no—
117#328D15111yescharacteristic, complemented
118#327—1511no—
119#324—1511no—
120C22×Q8—1511no—
121C2×Q16—3021no—
122C2×SD16—3021no—
123#126—3021no—
124#125—3021no—
125#123—3021no—
126#123—3021no—
127C22⋊Q8—3021no—
128C22⋊Q8C2×D15111yescharacteristic
129#121—1511no—
130C4×D4—3021no—
131C2×C4⋊C4—3021no—
132C2×C4⋊C4—1511no—
133#103—3021no—
134#103—3021no—
135C22⋊C8—1511no—
136C22⋊C8C2×D15111yescharacteristic
137#95—3021no—
138#95C2×D15111yescharacteristic
139C2×Q8—3021no—
140C2×Q8—3021no—
141C2×Q8—6042no—
142C2×Q8D60411yescharacteristic
143C2×D4—3021no—
144C2×D4—1511no—
145C22×C4—21no—
146C22×C4—3021no—
147C22×C4—3021no—
148C22×C4—1511no—
149C22×C4—1511no—
150C22×C4C22×D15111yescharacteristic
151Q16—6042no—
152SD16—6042no—
153C2×C8—21no—
154C2×C8—3021no—
155C4⋊C4—21no—
156C4⋊C4—3021no—
157C4⋊C4—3021no—
158C4⋊C4—3021no—
159C4⋊C4—3021no—
160C4⋊C4—3021no—
161C4⋊C4—6042no—
162C4⋊C4—1511no—
163C4⋊C4D60411yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—3021no—
166C22⋊C4—3021no—
167C22⋊C4—3021no—
168C22⋊C4—3021no—
169C42—3021no—
170C23—3021no—
171C23D4×D15111yescharacteristic
172Q8—41no—
173Q8—3022no—
174Q8—3022no—
175Q8—6041no—
176Q8—6041no—
177D4—6041no—
178D4—6041no—
179D4—6041no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—3022no—
187C2×C4—3021no—
188C2×C4—3021no—
189C2×C4—3021no—
190C2×C4—3021no—
191C2×C4—3021no—
192C2×C4—6041no—
193C2×C4—6041no—
194C2×C4—6041no—
195C2×C4—12081no—
196C2×C4D4×D15111yescharacteristic
197C2×C4C2×D60411yescharacteristic
198C8—41no—
199C8—6041no—
200C22—21no—
201C22—21no—
202C22—6041no—
203C22—6041no—
204C22—6041no—
205C22#1801270911yescharacteristic
206C22#1801276011yescharacteristic
207C22#1801277111yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—6041no—
214C4—6041no—
215C4—6042no—
216C4—6041no—
217C2—21no—
218C2—21no—
219C2—12081no—
220C2#2375237711yescharacteristic
221C2#2375239611yescharacteristic
222C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#328×C151C2
socleC22×C151#120
prime radical#18012713C22
hypercenter#328D151
hypocenterC151#1603
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #23752367C2semidirect
4. #23752133C2semidirect
6. #23751937C2semidirect
7. #328×C151C2semidirect
111. C151#1603semidirect
117. #328D151semidirect

Maximal subgroups

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

subgroupindex
#237528112
#237523672
#237523532
#237521332
#237519452
#237519372
#328×C1512
#1603151