Finite Group Databasebeta

← #34070458

Subgroups — #34070458

Order 19328.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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#23752252C211yesmaximal, characteristic
3#23752077C211yesmaximal, characteristic
4#23751980C211yesmaximal, characteristic
5#23751973C211yesmaximal, characteristic
6#23751971C211yesmaximal, characteristic
7#428×C151C211yesmaximal, characteristic
8C2×#14558988C2211yescharacteristic
9#18012739—21no—
10#18012738—21no—
11#18012731—21no—
12#18012730—21no—
13#18012716—22no—
14#18012698C2211yescharacteristic
15C2×C4⋊Dic151C2211yescharacteristic
16C2×C4×Dic151C2211yescharacteristic
17#18012672—21no—
18#18012670—21no—
19C151⋊#95—22no—
20C2×M16×C151C2211yescharacteristic
21#117×C151C2211yescharacteristic
22C2×C4⋊C4×C151C2211yescharacteristic
23#107×C151—21no—
24#106×C151—21no—
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⋊Dic151D411yescharacteristic
35C4⋊Dic151D411yescharacteristic
36Dic151⋊C4—22no—
37Dic151⋊C4—22no—
38C22⋊Dic151—21no—
39C4×Dic151—21no—
40C4×Dic151—21no—
41C4×Dic151Q812yescomplemented
42C22×C4×C151—21no—
43C22×C4×C151C2311yescharacteristic
44M16×C151—21no—
45M16×C151Q812yescomplemented
46C2×C8×C151—21no—
47C4⋊C4×C151—21no—
48C4⋊C4×C151—21no—
49C4⋊C4×C151D411yescharacteristic
50C4⋊C4×C151D411yescharacteristic
51C22⋊C4×C151—21no—
52C42×C151—21no—
53Dic302—82no—
54C2×Dic151—21no—
55C2×Dic151—21no—
56C2×Dic151—22no—
57C2×Dic151—22no—
58C2×Dic151—41no—
59C2×Dic151—41no—
60C2×Dic151—42no—
61C151⋊C8—22no—
62C23×C151C2×D411yescharacteristic
63C2×C4×C151—21no—
64C2×C4×C151—21no—
65C2×C4×C151—42no—
66C2×C4×C151—41no—
67C2×C4×C151C2×D411yescharacteristic
68C2×C4×C151C2×D411yescharacteristic
69C2×C4×C151C2×Q811yescharacteristic
70C2×C4×C151C2×Q811yescharacteristic
71C2×C4×C151C2×Q811yescharacteristic
72C2×C4×C151#4111yescharacteristic
73C8×C151—22no—
74C22×C151—21no—
75C22×C151—21no—
76C22×C151#12011yescharacteristic
77C22×C151C22⋊Q811yescharacteristic
78C22×C151C4⋊Q811yescharacteristic
79C4×C151—41no—
80C4×C151—41no—
81C4×C151—81no—
82C4×C151C22⋊Q811yescharacteristic
83C4×C151C22⋊Q811yescharacteristic
84C4×C151C4⋊Q811yescharacteristic
85C4×C151C4⋊Q811yescharacteristic
86Dic151—42no—
87Dic151—41no—
88Dic151—42no—
89Dic151—41no—
90C2×C151—21no—
91C2×C151—21no—
92C2×C151#39511yescharacteristic
93C2×C151#45411yescharacteristic
94C2×C151#45511yescharacteristic
95C151#206111yescharacteristic, complemented, Sylow
96#2061—1511nomaximal, Sylow
97#544—1511no—
98#428—1511no—
99#428D15111yescharacteristic
100#382—1511no—
101#343—1511no—
102#339—1511no—
103#339—1511no—
104C2×M16—1511no—
105C2×M16C2×D15111yescharacteristic
106C4⋊Q8—3021no—
107C4⋊Q8—3021no—
108#125—3021no—
109#125—3021no—
110C22⋊Q8—3022no—
111#117—1511no—
112#117C2×D15111yescharacteristic
113C2×C4⋊C4—1511no—
114C2×C4⋊C4C2×D15111yescharacteristic
115C2×C42—1511no—
116#107—21no—
117#107—3021no—
118#106—21no—
119#106—3021no—
120#95—3022no—
121C2×Q8—3022no—
122C22×C4—21no—
123C22×C4—3021no—
124C22×C4—1512no—
125C22×C4C22×D15111yescharacteristic
126M16—21no—
127M16—3021no—
128M16—1512no—
129M16Dic30212yescomplemented
130C2×C8—21no—
131C2×C8—3021no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—3022no—
135C4⋊C4—3022no—
136C4⋊C4—3022no—
137C4⋊C4—3021no—
138C4⋊C4—3021no—
139C4⋊C4—1511no—
140C4⋊C4—1511no—
141C4⋊C4C22⋊D15111yescharacteristic
142C4⋊C4C22⋊D15111yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—3021no—
145C42—21no—
146C42—3021no—
147C42—3021no—
148C42—1512no—
149C23D4×D15111yescharacteristic
150Q8—12082no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—3021no—
156C2×C4—3021no—
157C2×C4—3022no—
158C2×C4—3022no—
159C2×C4—6041no—
160C2×C4—6041no—
161C2×C4—6042no—
162C2×C4D4×D15111yescharacteristic
163C2×C4C2×C22⋊D15111yescharacteristic
164C2×C4Q8×D15111yescharacteristic
165C2×C4Q8×D15111yescharacteristic
166C2×C4C2×Dic30211yescharacteristic
167C2×C4#1455900411yescharacteristic
168C8—22no—
169C8—3022no—
170C22—21no—
171C22—21no—
172C22#1801270711yescharacteristic
173C22#1801271711yescharacteristic
174C22#1801273811yescharacteristic
175C4—41no—
176C4—41no—
177C4—81no—
178C4—6042no—
179C4—6041no—
180C4—6042no—
181C4—6041no—
182C4#1801271711yescharacteristic
183C4#1801271811yescharacteristic
184C4#1801273711yescharacteristic
185C4#1801273811yescharacteristic
186C2—21no—
187C2—21no—
188C2#2375213211yescharacteristic
189C2#2375238311yescharacteristic
190C2#2375238811yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#428×C151C2
socleC22×C151#120
prime radicalC23×C151C2×D4
hypercenter#428D151
hypocenterC151#2061
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
29. #14558988Q8semidirect
41. C4×Dic151Q8semidirect
45. M16×C151Q8semidirect
95. C151#2061semidirect
129. M16Dic302semidirect

Maximal subgroups

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

subgroupindex
#237528402
#237522522
#237520772
#237519802
#237519732
#237519712
#428×C1512
#2061151