Finite Group Databasebeta

← #34069306

Subgroups — #34069306

Order 19328.

316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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×#18012697C211yesmaximal, characteristic
2C2×#18012670C211yesmaximal, characteristic, complemented
3C2×(C2×D151)⋊C8C211yesmaximal, characteristic
4#23752069C211yesmaximal, characteristic
5#23751975C211yesmaximal, characteristic, complemented
6#23751974C211yesmaximal, characteristic, complemented
7C2×#107×C151C211yesmaximal, characteristic, complemented
8C22×C4×D151C2211yescharacteristic
9C22×C151⋊C8C2211yescharacteristic
10#18012697—22no—
11#18012697—22no—
12C2×C4⋊Dic151C2211yescharacteristic
13C2×C4⋊Dic151C2211yescharacteristic
14C2×(C2×D151)⋊C4—21no—
15C2×(C2×D151)⋊C4—21no—
16C2×C4×Dic151—21no—
17#18012670—22no—
18(C2×D151)⋊C8C414yescomplemented
19C151⋊#95—21no—
20C22×C8×C151C2211yescharacteristic
21C2×C4⋊C4×C151C2211yescharacteristic
22C2×C4⋊C4×C151C2211yescharacteristic
23#107×C151—22no—
24C23×D151D411yescharacteristic
25C22×Dic151—21no—
26C22×Dic151—21no—
27C22×Dic151D411yescharacteristic
28C2×C4×D151—21no—
29C2×C4×D151—21no—
30C2×C4×D151—21no—
31C2×C4×D151—21no—
32C2×C4×D151C2×C412yes—
33C2×C4×D151Q812yes—
34C2×C151⋊C8—21no—
35C2×C151⋊C8—21no—
36C2×C151⋊C8C2×C412yes—
37C4⋊Dic151—21no—
38C4⋊Dic151—21no—
39C4⋊Dic151—21no—
40C4⋊Dic151D412yes—
41(C2×D151)⋊C4—24no—
42(C2×D151)⋊C4—42no—
43C4×Dic151—24no—
44C22×C4×C151—21no—
45C22×C4×C151—21no—
46C22×C4×C151C2311yescharacteristic
47C2×C8×C151—21no—
48C2×C8×C151—21no—
49C2×C8×C151C2×C412yes—
50C4⋊C4×C151—21no—
51C4⋊C4×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151D412yes—
54C22×D151—21no—
55C22×D151—21no—
56C22×D151—21no—
57C22×D151—21no—
58C22×D151—21no—
59C22×D151—21no—
60C22×D151C4⋊C412yes—
61C2×Dic151—21no—
62C2×Dic151—21no—
63C2×Dic151—22no—
64C2×Dic151—41no—
65C2×Dic151—41no—
66C2×Dic151—41no—
67C2×Dic151—41no—
68C2×Dic151—41no—
69C2×Dic151C4⋊C412yes—
70C4×D151—22no—
71C4×D151—22no—
72C4×D151—22no—
73C4×D151—22no—
74C151⋊C8—22no—
75C23×C151C2×D411yescharacteristic
76C2×C4×C151—22no—
77C2×C4×C151—41no—
78C2×C4×C151—41no—
79C2×C4×C151—41no—
80C2×C4×C151—41no—
81C2×C4×C151—41no—
82C2×C4×C151C22×C411yescharacteristic
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2×Q811yescharacteristic
86C2×C4×C151#4111yescharacteristic
87C2×C4×C151#4111yescharacteristic
88C8×C151—22no—
89C22×C151C2×C4⋊C411yescharacteristic
90C22×C151#12011yescharacteristic
91C22×C151#12311yescharacteristic
92C22×C151#13511yescharacteristic
93C22×C151#13511yescharacteristic
94C22×C151AGL(1,ℤ/8)11yescharacteristic
95C22×C151#13711yescharacteristic
96C2×D151—22no—
97C2×D151—22no—
98C2×D151—22no—
99C2×D151—41no—
100C2×D151—41no—
101C2×D151—41no—
102C2×D151—41no—
103C4×C151—42no—
104C4×C151—81no—
105C4×C151C4×D411yescharacteristic
106C4×C151C4×D411yescharacteristic
107C4×C151C22⋊Q811yescharacteristic
108C4×C151C22⋊Q811yescharacteristic
109Dic151—22no—
110Dic151—42no—
111Dic151—81no—
112C2×C151#38511yescharacteristic
113C2×C151#42711yescharacteristic
114C2×C151#42811yescharacteristic
115C2×C151#44911yescharacteristic
116C2×C151#45211yescharacteristic
117C2×C151#48211yescharacteristic
118C2×C151#48511yescharacteristic
119D151—42no—
120C151#185411yescharacteristic, complemented, Sylow
121#1854—1511nomaximal, Sylow
122C2×#117—1511no—
123C2×#107D15111yescharacteristic, complemented
124C2×#106—1511no—
125C2×C22⋊C8—1511no—
126#380—1511no—
127#340—1511no—
128#340—1511no—
129C23×C4—1511no—
130C22×C8—1511no—
131C22×C8C2×D15111yescharacteristic
132#117—3022no—
133#117—3022no—
134C2×C4⋊C4—1511no—
135C2×C4⋊C4—1511no—
136C2×C4⋊C4C2×D15111yescharacteristic
137C2×C4⋊C4C2×D15111yescharacteristic
138C2×C22⋊C4—3021no—
139C2×C22⋊C4—3021no—
140C2×C42—3021no—
141#107—22no—
142#106—3022no—
143C22⋊C8—1514no—
144#95—3021no—
145C24—1511no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—3021no—
149C22×C4—3021no—
150C22×C4—3021no—
151C22×C4—3021no—
152C22×C4—3021no—
153C22×C4—3021no—
154C22×C4—1511no—
155C22×C4—1512no—
156C22×C4—1512no—
157C22×C4C22×D15111yescharacteristic
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—3021no—
161C2×C8—3021no—
162C2×C8—1512no—
163C2×C8C4×D15112yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—3021no—
168C4⋊C4—3021no—
169C4⋊C4—3021no—
170C4⋊C4—1512no—
171C4⋊C4C22⋊D15112yes—
172C22⋊C4—3024no—
173C22⋊C4—6042no—
174C42—3024no—
175C23—3021no—
176C23—3021no—
177C23—3021no—
178C23—3021no—
179C23—3021no—
180C23—3021no—
181C23—1512no—
182C23D4×D15111yescharacteristic
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—3021no—
190C2×C4—3021no—
191C2×C4—3022no—
192C2×C4—3022no—
193C2×C4—3022no—
194C2×C4—3022no—
195C2×C4—3022no—
196C2×C4—6041no—
197C2×C4—6041no—
198C2×C4—6041no—
199C2×C4—6041no—
200C2×C4—6041no—
201C2×C4—1512no—
202C2×C4C2×C4×D15111yescharacteristic
203C2×C4D4×D15111yescharacteristic
204C2×C4C2×C22⋊D15111yescharacteristic
205C2×C4Q8×D15111yescharacteristic
206C2×C4#1455900411yescharacteristic
207C2×C4#1455900511yescharacteristic
208C8—22no—
209C8—3022no—
210C22—3022no—
211C22—3022no—
212C22—3022no—
213C22—6041no—
214C22—6041no—
215C22—6041no—
216C22—6041no—
217C22C4⋊C4×D15111yescharacteristic
218C22#1801270711yescharacteristic
219C22#1801272411yescharacteristic
220C22#1801275811yescharacteristic
221C22#1801276211yescharacteristic
222C22#1801276311yescharacteristic
223C22#1801277111yescharacteristic
224C4—42no—
225C4—81no—
226C4—3022no—
227C4—6042no—
228C4—12081no—
229C4C4×C22⋊D15111yescharacteristic
230C4#1801270111yescharacteristic
231C4#1801271511yescharacteristic
232C4#1801271711yescharacteristic
233C2—6042no—
234C2#2375208311yescharacteristic
235C2#2375224911yescharacteristic
236C2#2375225311yescharacteristic
237C2#2375235411yescharacteristic
238C2#2375237311yescharacteristic
239C2#2375253911yescharacteristic
240C2#2375255511yescharacteristic
subgroupG/H
centerC23D4×D151
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
FittingC2×#107×C151C2
socleC23×C151C2×D4
prime radicalC23×D151D4
cosocleC22×C4×C151C23
hypercenterC2×#107D151
hypocenterC151#1854
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#18012670C2semidirect
5. #23751975C2semidirect
6. #23751974C2semidirect
7. C2×#107×C151C2semidirect
18. (C2×D151)⋊C8C4semidirect
120. C151#1854semidirect
123. C2×#107D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180126972
C2×#180126702
C2×(C2×D151)⋊C82
#237520692
#237519752
#237519742
C2×#107×C1512
#1854151