Finite Group Databasebeta

← #34070454

Subgroups — #34070454

Order 19328.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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#23752840C211yesmaximal, characteristic
2#23752255C211yesmaximal, characteristic
3#23752254C211yesmaximal, characteristic
4#23752082C211yesmaximal, characteristic
5#23751980C211yesmaximal, characteristic
6#23751972C211yesmaximal, characteristic
7#339×C151C211yesmaximal, characteristic
8C2×#14558988C2211yescharacteristic
9#18012739—21no—
10#18012738—21no—
11#18012731—21no—
12#18012730—21no—
13#18012716—22no—
14#18012698C2211yescharacteristic
15C2×C4⋊Dic151—22no—
16C2×C4⋊Dic151C2211yescharacteristic
17C2×C4⋊Dic151C2211yescharacteristic
18#18012673—21no—
19#18012672—21no—
20#18012671—21no—
21#18012670—21no—
22C2×M16×C151C2211yescharacteristic
23#117×C151C2211yescharacteristic
24C2×C42×C151C2211yescharacteristic
25C2×Dic302—22no—
26C22×Dic151—21no—
27C22×Dic151D412yes—
28#14558988—21no—
29#14558988Q812yescomplemented
30C2×C151⋊C8—21no—
31C4⋊Dic151—22no—
32C4⋊Dic151—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151—44no—
37C4⋊Dic151D411yescharacteristic
38C4⋊Dic151D411yescharacteristic
39Dic151⋊C4—22no—
40Dic151⋊C4—22no—
41C22⋊Dic151—21no—
42C4×Dic151—21no—
43C22×C4×C151—21no—
44C22×C4×C151C2311yescharacteristic
45M16×C151—21no—
46M16×C151Q812yescomplemented
47C2×C8×C151—21no—
48C4⋊C4×C151D411yescharacteristic
49C4⋊C4×C151D411yescharacteristic
50C22⋊C4×C151—21no—
51C42×C151—21no—
52C42×C151—21no—
53C42×C151Q812yescomplemented
54Dic302—82no—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C2×Dic151—22no—
58C2×Dic151—42no—
59C2×Dic151—42no—
60C2×Dic151—41no—
61C151⋊C8—22no—
62C23×C151C2×D411yescharacteristic
63C2×C4×C151—22no—
64C2×C4×C151—22no—
65C2×C4×C151—22no—
66C2×C4×C151—21no—
67C2×C4×C151—21no—
68C2×C4×C151C2×D411yescharacteristic
69C2×C4×C151C2×D411yescharacteristic
70C2×C4×C151C2×Q811yescharacteristic
71C2×C4×C151C2×Q811yescharacteristic
72C2×C4×C151C2×Q811yescharacteristic
73C2×C4×C151#4111yescharacteristic
74C8×C151—22no—
75C22×C151—21no—
76C22×C151—21no—
77C22×C151#12011yescharacteristic
78C22×C151C22⋊Q811yescharacteristic
79C22×C151C4⋊Q811yescharacteristic
80C4×C151—24no—
81C4×C151—41no—
82C4×C151—41no—
83C4×C151C22⋊Q811yescharacteristic
84C4×C151C22⋊Q811yescharacteristic
85C4×C151C4⋊Q811yescharacteristic
86C4×C151C4⋊Q811yescharacteristic
87Dic151—42no—
88Dic151—41no—
89Dic151—41no—
90Dic151—81no—
91C2×C151—21no—
92C2×C151—21no—
93C2×C151#39511yescharacteristic
94C2×C151#45311yescharacteristic
95C2×C151#45611yescharacteristic
96C151#206011yescharacteristic, complemented, Sylow
97#2060—1511nomaximal, Sylow
98#544—1511no—
99#428—1511no—
100#428—1511no—
101#384—1511no—
102#343—1511no—
103#339—1511no—
104#339D15111yescharacteristic
105C2×M16—1511no—
106C2×M16C2×D15111yescharacteristic
107C4⋊Q8—3021no—
108C4⋊Q8—3021no—
109#125—3021no—
110#125—3021no—
111C22⋊Q8—3022no—
112#117—1511no—
113#117C2×D15111yescharacteristic
114C2×C4⋊C4—3022no—
115C2×C4⋊C4—1511no—
116C2×C4⋊C4—1511no—
117C2×C42C2×D15111yescharacteristic
118#107—3021no—
119#107—3021no—
120#106—3021no—
121#106—3021no—
122C2×Q8—3022no—
123C22×C4—21no—
124C22×C4—3021no—
125C22×C4—1512no—
126C22×C4C22×D15111yescharacteristic
127M16—21no—
128M16—3021no—
129M16—1512no—
130M16Dic30212yescomplemented
131C2×C8—21no—
132C2×C8—3021no—
133C4⋊C4—3022no—
134C4⋊C4—3022no—
135C4⋊C4—3022no—
136C4⋊C4—3021no—
137C4⋊C4—3021no—
138C4⋊C4—3021no—
139C4⋊C4—3021no—
140C4⋊C4—6044no—
141C4⋊C4—1511no—
142C4⋊C4—1511no—
143C4⋊C4D60411yescharacteristic
144C4⋊C4D60411yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—3021no—
147C42—21no—
148C42—21no—
149C42—3021no—
150C42Dic30212yescomplemented
151C23D4×D15111yescharacteristic
152Q8—12082no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—3021no—
159C2×C4—3021no—
160C2×C4—3022no—
161C2×C4—6042no—
162C2×C4—6042no—
163C2×C4—6041no—
164C2×C4D4×D15111yescharacteristic
165C2×C4C2×D60411yescharacteristic
166C2×C4Q8×D15111yescharacteristic
167C2×C4C2×Dic30211yescharacteristic
168C2×C4C2×Dic30211yescharacteristic
169C2×C4#1455900311yescharacteristic
170C8—22no—
171C8—3022no—
172C22—21no—
173C22—21no—
174C22#1801270911yescharacteristic
175C22#1801271611yescharacteristic
176C22#1801273811yescharacteristic
177C4—24no—
178C4—41no—
179C4—41no—
180C4—6042no—
181C4—6041no—
182C4—6041no—
183C4—12081no—
184C4#1801271611yescharacteristic
185C4#1801271911yescharacteristic
186C4#1801273811yescharacteristic
187C4#1801273911yescharacteristic
188C2—21no—
189C2—21no—
190C2#2375213311yescharacteristic
191C2#2375238111yescharacteristic
192C2#2375239611yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#339×C151C2
socleC22×C151#120
prime radicalC23×C151C2×D4
hypercenter#339D151
hypocenterC151#2060
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
29. #14558988Q8semidirect
46. M16×C151Q8semidirect
53. C42×C151Q8semidirect
96. C151#2060semidirect
130. M16Dic302semidirect
150. C42Dic302semidirect

Maximal subgroups

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

subgroupindex
#237528402
#237522552
#237522542
#237520822
#237519802
#237519722
#339×C1512
#2060151