Finite Group Databasebeta

← #34070306

Subgroups — #34070306

Order 19328.

316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#18012718C211yesmaximal, characteristic
2C2×#18012670C211yesmaximal, characteristic, complemented
3C2×#18012662C211yesmaximal, characteristic, complemented
4C2×#18012662C211yesmaximal, characteristic, complemented
5C2×C22⋊(C151⋊C8)C211yesmaximal, characteristic
6#23751974C211yesmaximal, characteristic, complemented
7#380×C151C211yesmaximal, characteristic
8C22×Dic302C2211yescharacteristic
9C22×C151⋊C8C2211yescharacteristic
10C22×C151⋊C8C2211yescharacteristic
11#18012718—22no—
12#18012718—22no—
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4—21no—
15C2×C22⋊Dic151—21no—
16#18012670—22no—
17#18012662—22no—
18#18012662—22no—
19C22⋊(C151⋊C8)—22no—
20C23×C4×C151C2211yescharacteristic
21C2×C4⋊C4×C151C2211yescharacteristic
22C2×C4⋊C4×C151C2211yescharacteristic
23C2×C22⋊C4×C151—21no—
24#95×C151—21no—
25C2×Dic302—21no—
26C2×Dic302—21no—
27C2×Dic302—21no—
28C2×Dic302—21no—
29C2×Dic302—21no—
30C2×Dic302D412yes—
31C22×Dic151—21no—
32C22×Dic151—21no—
33C2×C151⋊C8—21no—
34C2×C151⋊C8—21no—
35C2×C151⋊C8—21no—
36C2×C151⋊C8—21no—
37C2×C151⋊C8—21no—
38C2×C151⋊C8D412yes—
39C4⋊Dic151—21no—
40C4⋊Dic151D412yes—
41Dic151⋊C4—24no—
42C22⋊Dic151—24no—
43C24×C151D411yescharacteristic
44C22×C4×C151—21no—
45C22×C4×C151—21no—
46C22×C4×C151—21no—
47C22×C4×C151—21no—
48C22×C4×C151—21no—
49C22×C4×C151—21no—
50C22×C4×C151—21no—
51C22×C4×C151—21no—
52C22×C4×C151D411yescharacteristic
53C22×C4×C151C2311yescharacteristic
54C4⋊C4×C151—21no—
55C4⋊C4×C151—21no—
56C4⋊C4×C151—21no—
57C4⋊C4×C151—21no—
58C22⋊C4×C151—42no—
59Dic302—22no—
60Dic302—22no—
61Dic302—41no—
62Dic302—41no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—41no—
66C2×Dic151—41no—
67C2×Dic151—41no—
68C2×Dic151—41no—
69C151⋊C8—22no—
70C151⋊C8—41no—
71C23×C151—21no—
72C23×C151—21no—
73C23×C151—21no—
74C23×C151—21no—
75C23×C151—21no—
76C23×C151—21no—
77C23×C151SD1612yes—
78C23×C151C2×D411yescharacteristic
79C2×C4×C151—21no—
80C2×C4×C151—21no—
81C2×C4×C151—21no—
82C2×C4×C151—41no—
83C2×C4×C151—41no—
84C2×C4×C151—41no—
85C2×C4×C151—41no—
86C2×C4×C151—41no—
87C2×C4×C151—41no—
88C2×C4×C151—41no—
89C2×C4×C151—41no—
90C2×C4×C151—41no—
91C2×C4×C151—41no—
92C2×C4×C151C2×D411yescharacteristic
93C2×C4×C151C2×D411yescharacteristic
94C2×C4×C151C2×D411yescharacteristic
95C2×C4×C151#4111yescharacteristic
96C2×C4×C151#4111yescharacteristic
97C2×C4×C151#4111yescharacteristic
98C22×C151—22no—
99C22×C151—22no—
100C22×C151—22no—
101C22×C151—41no—
102C22×C151—41no—
103C22×C151—41no—
104C22×C151—41no—
105C22×C151#12011yescharacteristic
106C22×C151#12111yescharacteristic
107C22×C151#12311yescharacteristic
108C22×C151C2×SD1611yescharacteristic
109C22×C151#13511yescharacteristic
110C22×C151#13711yescharacteristic
111C22×C151#13711yescharacteristic
112C4×C151—41no—
113C4×C151—81no—
114C4×C151—81no—
115C4×C151#12111yescharacteristic
116C4×C151#12111yescharacteristic
117C4×C151#12311yescharacteristic
118C4×C151#12411yescharacteristic
119Dic151—42no—
120Dic151—42no—
121C2×C151—42no—
122C2×C151#39411yescharacteristic
123C2×C151#44811yescharacteristic
124C2×C151#45211yescharacteristic
125C2×C151#46511yescharacteristic
126C2×C151#47011yescharacteristic
127C2×C151#48311yescharacteristic
128C2×C151#48511yescharacteristic
129C151#203511yescharacteristic, complemented, Sylow
130#2035—1511nomaximal, Sylow
131C2×C22⋊Q8—1511no—
132C2×#106—1511no—
133C2×#103—1511no—
134C2×#103—1511no—
135C2×C22⋊C8—1511no—
136#380D15111yescharacteristic
137#340—1511no—
138C22×Q8—1511no—
139C23×C4C2×D15111yescharacteristic
140C22×C8—1511no—
141C22×C8—1511no—
142C22⋊Q8—3022no—
143C22⋊Q8—3022no—
144C2×C4⋊C4—3021no—
145C2×C4⋊C4—1511no—
146C2×C4⋊C4C2×D15111yescharacteristic
147C2×C4⋊C4C2×D15111yescharacteristic
148C2×C22⋊C4—21no—
149C2×C22⋊C4—3021no—
150#106—3022no—
151#103—3022no—
152#103—3022no—
153C22⋊C8—3022no—
154#95—21no—
155C24C22⋊D15111yescharacteristic
156C2×Q8—3021no—
157C2×Q8—3021no—
158C2×Q8—3021no—
159C2×Q8—3021no—
160C2×Q8—3021no—
161C2×Q8—1512no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—3021no—
171C22×C4—3021no—
172C22×C4C22⋊D15111yescharacteristic
173C22×C4C22×D15111yescharacteristic
174C2×C8—3021no—
175C2×C8—3021no—
176C2×C8—3021no—
177C2×C8—3021no—
178C2×C8—3021no—
179C2×C8—1512no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—3024no—
185C4⋊C4—3021no—
186C4⋊C4—1512no—
187C22⋊C4—42no—
188C22⋊C4—3024no—
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23#1455899212yes—
196C23C2×C22⋊D15111yescharacteristic
197Q8—3022no—
198Q8—3022no—
199Q8—6041no—
200Q8—6041no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—3022no—
215C2×C4—3022no—
216C2×C4—6041no—
217C2×C4—6041no—
218C2×C4—6041no—
219C2×C4—6041no—
220C2×C4D4×D15111yescharacteristic
221C2×C4D4×D15111yescharacteristic
222C2×C4D4×D15111yescharacteristic
223C2×C4#1455900311yescharacteristic
224C2×C4#1455900411yescharacteristic
225C2×C4#1455900411yescharacteristic
226C8—3022no—
227C8—6041no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22#1801270711yescharacteristic
236C22#1801271111yescharacteristic
237C22#1801272211yescharacteristic
238C22C2×#1455899211yescharacteristic
239C22#1801275911yescharacteristic
240C22#1801276911yescharacteristic
241C22#1801277011yescharacteristic
242C4—41no—
243C4—81no—
244C4—81no—
245C4—6042no—
246C4—6042no—
247C4#1801271211yescharacteristic
248C4#1801271211yescharacteristic
249C4#1801272111yescharacteristic
250C4#1801272511yescharacteristic
251C2—42no—
252C2#2375212711yescharacteristic
253C2#2375235011yescharacteristic
254C2#2375237211yescharacteristic
255C2#2375243911yescharacteristic
256C2#2375246811yescharacteristic
257C2#2375254211yescharacteristic
258C2#2375255311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D151
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#380×C151C2
socleC23×C151C2×D4
prime radicalC24×C151D4
hypercenter#380D151
hypocenterC151#2035
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#18012670C2semidirect
3. C2×#18012662C2semidirect
4. C2×#18012662C2semidirect
6. #23751974C2semidirect
129. C151#2035semidirect

Maximal subgroups

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

subgroupindex
C2×#180127182
C2×#180126702
C2×#180126622
C2×C22⋊(C151⋊C8)2
#237519742
#380×C1512
#2035151