Finite Group Databasebeta

← #34070194

Subgroups — #34070194

Order 19328.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#14558993C211yesmaximal, characteristic
2C22×#14558991C211yesmaximal, characteristic
3C2×#18012737C211yesmaximal, characteristic, complemented
4C2×#18012662C211yesmaximal, characteristic, complemented
5#23752113C211yesmaximal, characteristic
6#23751966C211yesmaximal, characteristic, complemented
7C2×#103×C151C211yesmaximal, characteristic, complemented
8C22×Dic302C2211yescharacteristic
9C22×D604C2211yescharacteristic
10C2×#14558993—22no—
11C2×#14558993—22no—
12C2×#14558993—22no—
13C2×#14558991—22no—
14C2×#14558991—22no—
15C2×#14558991—22no—
16C22×C151⋊C8C2211yescharacteristic
17#18012737—22no—
18#18012737—22no—
19C2×Dic151⋊C4—22no—
20C2×(C2×D151)⋊C4—22no—
21C2×C4×Dic151C2211yescharacteristic
22#18012662—22no—
23C22×Q8×C151C2211yescharacteristic
24C22×C8×C151C2211yescharacteristic
25C2×C4⋊C4×C151C2211yescharacteristic
26#103×C151—22no—
27C23×D151—21no—
28C2×Dic302—21no—
29C2×Dic302—21no—
30C2×Dic302—21no—
31C2×Dic302—21no—
32C2×Dic302—21no—
33C2×Dic302D412yes—
34C2×D604—21no—
35C2×D604—21no—
36C2×D604—21no—
37C2×D604—21no—
38C2×D604—21no—
39C2×D604D412yes—
40C22×Dic151—21no—
41C22×Dic151D412yes—
42#14558993—28no—
43#14558991—28no—
44C2×C151⋊C8—21no—
45C2×C151⋊C8—21no—
46C2×C151⋊C8D412yes—
47Dic151⋊C4—28no—
48(C2×D151)⋊C4—44no—
49C4×Dic151—21no—
50C4×Dic151—21no—
51C2×Q8×C151—21no—
52C2×Q8×C151—21no—
53C2×Q8×C151—21no—
54C2×Q8×C151—21no—
55C2×Q8×C151—21no—
56C2×Q8×C151D412yes—
57C22×C4×C151—21no—
58C22×C4×C151—21no—
59C22×C4×C151C2311yescharacteristic
60C2×C8×C151—21no—
61C2×C8×C151—21no—
62C2×C8×C151D412yes—
63C4⋊C4×C151—21no—
64C4⋊C4×C151—21no—
65C22×D151—22no—
66C22×D151—41no—
67C22×D151—41no—
68C22×D151—42no—
69C22×D151—42no—
70Dic302—22no—
71Dic302—22no—
72Dic302—41no—
73Dic302—41no—
74D604—22no—
75D604—22no—
76D604—41no—
77D604—41no—
78C2×Dic151—22no—
79C2×Dic151—22no—
80C2×Dic151—22no—
81C2×Dic151—41no—
82C2×Dic151—41no—
83C2×Dic151SD1614yescomplemented
84C151⋊C8—22no—
85C23×C151C2×D411yescharacteristic
86Q8×C151—22no—
87Q8×C151—22no—
88Q8×C151—41no—
89Q8×C151—41no—
90C2×C4×C151—22no—
91C2×C4×C151—41no—
92C2×C4×C151—41no—
93C2×C4×C151—41no—
94C2×C4×C151—42no—
95C2×C4×C151C2×D411yescharacteristic
96C2×C4×C151C2×D411yescharacteristic
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151C2×D411yescharacteristic
100C2×C4×C151#4111yescharacteristic
101C8×C151—22no—
102C22×C151#12011yescharacteristic
103C22×C151#12111yescharacteristic
104C22×C151#12711yescharacteristic
105C22×C151C2×SD1612yes—
106C22×C151#13712yes—
107C2×D151—42no—
108C2×D151—44no—
109C2×D151—82no—
110C2×D151—81no—
111C2×D151—81no—
112C4×C151—42no—
113C4×C151—81no—
114C4×C151#12011yescharacteristic
115C4×C151#12011yescharacteristic
116C4×C151#12111yescharacteristic
117C4×C151#12111yescharacteristic
118Dic151—24no—
119Dic151—42no—
120C2×C151#39211yescharacteristic
121C2×C151#44812yes—
122C2×C151#46112yes—
123C2×C151#49211yescharacteristic
124C2×C151#49711yescharacteristic
125D151—82no—
126C151#201311yescharacteristic, complemented, Sylow
127#2013—1511nomaximal, Sylow
128C22×SD16—1511no—
129C22×SD16—1511no—
130C2×C4⋊Q8—1511no—
131C2×#103—1511no—
132C2×#103D15111yescharacteristic, complemented
133#390—1511no—
134#336—1511no—
135C22×Q8—1511no—
136C22×Q8C2×D15111yescharacteristic
137C22×D4—1511no—
138C2×SD16—3022no—
139C2×SD16—3022no—
140C2×SD16—3022no—
141C2×SD16—3022no—
142C2×SD16—3022no—
143C2×SD16—3022no—
144C22×C8—1511no—
145C22×C8C2×D15111yescharacteristic
146C4⋊Q8—3022no—
147C4⋊Q8—3022no—
148C2×C4⋊C4—3022no—
149C2×C4⋊C4C2×D15111yescharacteristic
150C2×C22⋊C4—3022no—
151C2×C42—1511no—
152#103—22no—
153#103—3022no—
154C24—3021no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—3021no—
161C2×Q8—3021no—
162C2×Q8—3021no—
163C2×Q8—3021no—
164C2×Q8—3021no—
165C2×Q8—1512no—
166C2×Q8D60412yes—
167C2×D4—3021no—
168C2×D4—3021no—
169C2×D4—3021no—
170C2×D4—3021no—
171C2×D4—3021no—
172C2×D4—1512no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—3021no—
176C22×C4—1512no—
177C22×C4C22×D15111yescharacteristic
178SD16—3028no—
179SD16—3028no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—3021no—
183C2×C8—3021no—
184C2×C8—1512no—
185C2×C8C22⋊D15112yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—3028no—
189C22⋊C4—6044no—
190C42—3021no—
191C42—3021no—
192C23—3022no—
193C23—6041no—
194C23—6041no—
195C23—6042no—
196C23—6042no—
197C23D4×D15111yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—3022no—
203Q8—3022no—
204Q8—6041no—
205Q8—6041no—
206D4—3022no—
207D4—3022no—
208D4—6041no—
209D4—6041no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—3022no—
216C2×C4—3022no—
217C2×C4—3022no—
218C2×C4—6041no—
219C2×C4—6041no—
220C2×C4—1514no—
221C2×C4D4×D15111yescharacteristic
222C2×C4D4×D15111yescharacteristic
223C2×C4D4×D15111yescharacteristic
224C2×C4C2×C22⋊D15111yescharacteristic
225C2×C4C2×D60411yescharacteristic
226C2×C4#1455900411yescharacteristic
227C8—22no—
228C8—3022no—
229C22—6042no—
230C22—6044no—
231C22—12081no—
232C22—12081no—
233C22—12082no—
234C22#1801270911yescharacteristic
235C22#1801271211yescharacteristic
236C22#1801273511yescharacteristic
237C22SD16×D15112yes—
238C22#1801277112yes—
239C4—42no—
240C4—81no—
241C4—3024no—
242C4—6042no—
243C4#1801270711yescharacteristic
244C4#1801270911yescharacteristic
245C4#1801271211yescharacteristic
246C4#1801271311yescharacteristic
247C2—12082no—
248C2#2375212111yescharacteristic
249C2#2375235212yes—
250C2#2375241612yes—
251C2#2375258311yescharacteristic
252C2#2375260511yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
FittingC2×#103×C151C2
socleC23×C151C2×D4
prime radicalC22×D604C22
hypercenterC2×#103D151
hypocenterC151#2013
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#18012737C2semidirect
4. C2×#18012662C2semidirect
6. #23751966C2semidirect
7. C2×#103×C151C2semidirect
83. C2×Dic151SD16semidirect
126. C151#2013semidirect
132. C2×#103D151semidirect

Maximal subgroups

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

subgroupindex
C22×#145589932
C22×#145589912
C2×#180127372
C2×#180126622
#237521132
#237519662
C2×#103×C1512
#2013151