Finite Group Databasebeta

← #34068136

Subgroups — #34068136

Order 19328.

236 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 51 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#23752837C211yesmaximal, characteristic
2#23752548C211yesmaximal, characteristic, complemented
3#23752545C211yesmaximal, characteristic, complemented
4#23752149C211yesmaximal, characteristic
5#23751948C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic
7#328×C151C211yesmaximal, characteristic, complemented
8#18012719—21no—
9#18012718C2211yescharacteristic
10#18012717—21no—
11#18012717—21no—
12#18012716—21no—
13#18012715—21no—
14C2×C4⋊Dic151—21no—
15C2×C4⋊Dic151C2211yescharacteristic
16C2×(C2×D151)⋊C4—21no—
17C2×(C2×D151)⋊C4C2211yescharacteristic
18C22⋊C4×D151—21no—
19#18012673—21no—
20#18012672—21no—
21#18012664—21no—
22#18012663—21no—
23C22⋊(C151⋊C8)C2211yescharacteristic
24C22⋊Q8×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28C2×Dic302—21no—
29C2×Dic302D411yescharacteristic
30C22×Dic151—21no—
31C22×Dic151D411yescharacteristic
32C2×C4×D151—21no—
33C2×C4×D151—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151—21no—
37C4⋊Dic151—21no—
38C4⋊Dic151—42no—
39C4⋊Dic151D411yescharacteristic
40Dic151⋊C4—21no—
41Dic151⋊C4—21no—
42Dic151⋊C4—21no—
43C22⋊Dic151—21no—
44(C2×D151)⋊C4—21no—
45(C2×D151)⋊C4—21no—
46(C2×D151)⋊C4—21no—
47(C2×D151)⋊C4—21no—
48(C2×D151)⋊C4—42no—
49C2×Q8×C151D411yescharacteristic
50C22×C4×C151—21no—
51C22×C4×C151C2311yescharacteristic
52C2×C8×C151—21no—
53C4⋊C4×C151—21no—
54C4⋊C4×C151D411yescharacteristic
55C22⋊C4×C151—21no—
56C22×D151—21no—
57C22×D151—21no—
58C22×D151—41no—
59C22×D151—41no—
60C22×D151Q1612yes—
61Dic302—41no—
62Dic302—81no—
63C2×Dic151—21no—
64C2×Dic151—21no—
65C2×Dic151—21no—
66C2×Dic151—41no—
67C2×Dic151—41no—
68C2×Dic151—41no—
69C2×Dic151—41no—
70C4×D151—81no—
71C4×D151—81no—
72C151⋊C8—41no—
73C23×C151C2×D411yescharacteristic
74Q8×C151—41no—
75C2×C4×C151—22no—
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151—41no—
79C2×C4×C151—41no—
80C2×C4×C151—41no—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C8×C151—41no—
84C22×C151—21no—
85C22×C151—21no—
86C22×C151#12011yescharacteristic
87C22×C151C2×Q1611yescharacteristic
88C22×C151#13711yescharacteristic
89C2×D151—22no—
90C2×D151—41no—
91C2×D151—41no—
92C2×D151—42no—
93C2×D151—81no—
94C4×C151—21no—
95C4×C151—21no—
96C4×C151—42no—
97C4×C151—41no—
98C4×C151—41no—
99Dic151—41no—
100Dic151—41no—
101Dic151—41no—
102Dic151—81no—
103C2×C151—21no—
104C2×C151—21no—
105C2×C151#45111yescharacteristic
106C2×C151#45311yescharacteristic
107C2×C151#45811yescharacteristic
108D151—42no—
109C151#161411yescharacteristic, complemented, Sylow
110#1614—1511nomaximal, Sylow
111#543—1511no—
112#484—1511no—
113#484—1511no—
114#399—1511no—
115#328—1511no—
116#328D15111yescharacteristic, complemented
117#323—1511no—
118C22⋊Q8—3021no—
119C22⋊Q8—3021no—
120C22⋊Q8—3021no—
121C22⋊Q8—3021no—
122C22⋊Q8—3021no—
123C22⋊Q8—1511no—
124C22⋊Q8C2×D15111yescharacteristic
125C2×C4⋊C4—3021no—
126C2×C4⋊C4—1511no—
127C2×C22⋊C4—3021no—
128C2×C22⋊C4—3021no—
129C2×C22⋊C4—1511no—
130#107—3021no—
131#107—3021no—
132#103—3021no—
133#103—3021no—
134C22⋊C8—1511no—
135C22⋊C8C2×D15111yescharacteristic
136#95C2×D15111yescharacteristic
137C24—1511no—
138C2×Q8—3021no—
139C2×Q8—1511no—
140C2×Q8D60411yescharacteristic
141C22×C4—21no—
142C22×C4—3021no—
143C22×C4—3021no—
144C22×C4—3021no—
145C22×C4—1511no—
146C22×C4C22×D15111yescharacteristic
147C2×C8—21no—
148C2×C8—3021no—
149C4⋊C4—21no—
150C4⋊C4—3021no—
151C4⋊C4—3021no—
152C4⋊C4—3021no—
153C4⋊C4—3021no—
154C4⋊C4—3021no—
155C4⋊C4—3021no—
156C4⋊C4—6042no—
157C4⋊C4—1511no—
158C4⋊C4D60411yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—3021no—
161C22⋊C4—3021no—
162C22⋊C4—3021no—
163C22⋊C4—3021no—
164C22⋊C4—3021no—
165C22⋊C4—6042no—
166C23—3021no—
167C23—3021no—
168C23—6041no—
169C23—6041no—
170C23—1512no—
171C23D4×D15111yescharacteristic
172Q8—41no—
173Q8—6041no—
174Q8—12081no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—3021no—
182C2×C4—3021no—
183C2×C4—3021no—
184C2×C4—6041no—
185C2×C4—6041no—
186C2×C4—6041no—
187C2×C4—6041no—
188C2×C4—12081no—
189C2×C4—12081no—
190C2×C4D4×D15111yescharacteristic
191C2×C4C2×D60411yescharacteristic
192C8—41no—
193C8—6041no—
194C22—21no—
195C22—21no—
196C22—3022no—
197C22—6042no—
198C22—6041no—
199C22—6041no—
200C22—12081no—
201C22#1801270911yescharacteristic
202C22Q16×D15111yescharacteristic
203C22#1801276811yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—6041no—
210C4—6041no—
211C4—6041no—
212C4—12081no—
213C2—21no—
214C2—21no—
215C2—6042no—
216C2#2375236911yescharacteristic
217C2#2375238111yescharacteristic
218C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#328×C151C2
socleC22×C151#120
prime radicalC23×D151D4
hypercenter#328D151
hypocenterC151#1614
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. #23752548C2semidirect
3. #23752545C2semidirect
5. #23751948C2semidirect
7. #328×C151C2semidirect
109. C151#1614semidirect
116. #328D151semidirect

Maximal subgroups

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

subgroupindex
#237528372
#237525482
#237525452
#237521492
#237519482
#237519352
#328×C1512
#1614151