Finite Group Databasebeta

← #34078642

Subgroups — #34078642

Order 19328.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14558994C211yesmaximal, characteristic, complemented
2#23752783C211yesmaximal, characteristic
3#23752690C211yesmaximal, characteristic, complemented
4#23752432C214yesmaximal, complemented
5#23752420C214yesmaximal, complemented
6#23752240C211yesmaximal, characteristic, complemented
7#23752222C211yesmaximal, characteristic, complemented
8#23752208C211yesmaximal, characteristic
9C2×#137×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11C2×#14558994—24no—
12C2×#14558994C2214yes—
13C22×C151⋊C8C2211yescharacteristic
14#18012737C2212yes—
15#18012726C2212yes—
16#18012720—22no—
17#18012718—22no—
18Q8×Dic151—22no—
19Q8×Dic151C2214yes—
20#18012698—22no—
21#18012698C2211yescharacteristic
22#18012698C2211yescharacteristic
23Dic151⋊C8C2214yes—
24#18012664C2214yes—
25#18012663C2212yes—
26#18012660C2212yes—
27C2×#41×C151C2211yescharacteristic
28C22×Q8×C151C2211yescharacteristic
29#137×C151—24no—
30C2×Q16×C151C2212yes—
31C2×SD16×C151C2212yes—
32C2×M16×C151C2211yescharacteristic
33C2×Dic302—21no—
34C2×Dic302—22no—
35C2×Dic302—22no—
36C2×Dic302C2312yes—
37C22×Dic151—21no—
38#14558994—28no—
39C2×C151⋊C8—22no—
40C2×C151⋊C8C2312yes—
41C4⋊Dic151—24no—
42C4⋊Dic151D412yes—
43C4⋊Dic151C2312yes—
44Dic151⋊C4—24no—
45C22⋊Dic151—24no—
46C22⋊Dic151—21no—
47C22⋊Dic151D412yes—
48C4×Dic151—24no—
49C4×Dic151—21no—
50C4×Dic151C2312yes—
51#41×C151—22no—
52#41×C151—22no—
53C2×Q8×C151—21no—
54C2×Q8×C151—22no—
55C2×Q8×C151D414yes—
56C2×Q8×C151C2311yescharacteristic
57C2×Q8×C151C2312yes—
58C2×D4×C151—21no—
59C2×D4×C151C2311yescharacteristic
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151C2311yescharacteristic
63Q16×C151—24no—
64SD16×C151—24no—
65M16×C151—22no—
66C2×C8×C151C2312yes—
67Dic302—22no—
68Dic302—22no—
69Dic302—42no—
70C2×Dic151—22no—
71C2×Dic151—22no—
72C2×Dic151—42no—
73C2×Dic151C2×D414yes—
74C151⋊C8—22no—
75C23×C151—21no—
76C23×C151C2×D411yescharacteristic
77Q8×C151—24no—
78Q8×C151—22no—
79Q8×C151—21no—
80Q8×C151—21no—
81Q8×C151C2×D414yes—
82D4×C151—21no—
83D4×C151—21no—
84D4×C151—42no—
85C2×C4×C151—24no—
86C2×C4×C151—22no—
87C2×C4×C151—21no—
88C2×C4×C151—42no—
89C2×C4×C151C2×D411yescharacteristic
90C2×C4×C151C2×D412yes—
91C2×C4×C151#4112yes—
92C2×C4×C151C2411yescharacteristic
93C8×C151—22no—
94C22×C151—22no—
95C22×C151—41no—
96C22×C151—42no—
97C22×C151#12112yes—
98C22×C151C22×D411yescharacteristic
99C4×C151—24no—
100C4×C151—41no—
101C4×C151#12112yes—
102C4×C151C22×D411yescharacteristic
103C4×C151C2×#4111yescharacteristic
104Dic151—24no—
105Dic151—42no—
106Dic151—42no—
107C2×C151—22no—
108C2×C151—81no—
109C2×C151C2×#12111yescharacteristic
110C2×C151#57812yes—
111C151#304411yescharacteristic, complemented, Sylow
112#3044—1511nomaximal, Sylow
113C2×#137D15111yescharacteristic
114C22×Q16—1511no—
115#536—1511no—
116#519—1511no—
117#464—1514no—
118#462—1514no—
119#424—1511no—
120#419—1511no—
121#416—1511no—
122C2×#41C2×D15111yescharacteristic
123C22×Q8—1511no—
124C22×Q8C2×D15111yescharacteristic
125#137—24no—
126C2×Q16—3024no—
127C2×Q16—1514no—
128C2×Q16C2×D15112yes—
129C2×SD16C2×D15112yes—
130C2×M16C2×D15111yescharacteristic
131C22×C8—1511no—
132C4⋊Q8—1512no—
133#124—1512no—
134#123—3022no—
135C22⋊Q8—3022no—
136C4×Q8—3022no—
137C4×Q8—1514no—
138#117—3022no—
139#117—1511no—
140#117—1511no—
141C4⋊C8—1514no—
142#103—1512no—
143#103—1514no—
144#102—1512no—
145#41—22no—
146#41—22no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—3021no—
150C2×Q8—3022no—
151C2×Q8—3022no—
152C2×Q8—1512no—
153C2×Q8C22⋊D15114yes—
154C2×Q8C22×D15111yescharacteristic
155C2×Q8C22×D15112yes—
156C2×D4—21no—
157C2×D4C22×D15111yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—3021no—
161C22×C4C22×D15111yescharacteristic
162Q16—24no—
163Q16—3028no—
164SD16—24no—
165M16—22no—
166C2×C8—3022no—
167C2×C8—1512no—
168C2×C8C22×D15112yes—
169C4⋊C4—3024no—
170C4⋊C4—3024no—
171C4⋊C4—1512no—
172C4⋊C4—1512no—
173C22⋊C4—3021no—
174C22⋊C4—3024no—
175C22⋊C4—1512no—
176C42—3024no—
177C42—3021no—
178C42—1512no—
179C23—21no—
180C23D4×D15111yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—21no—
184Q8—21no—
185Q8—3022no—
186Q8—3022no—
187Q8—6042no—
188Q8C2×C22⋊D15114yes—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—42no—
196C2×C4—3022no—
197C2×C4—3022no—
198C2×C4—6042no—
199C2×C4—1514no—
200C2×C4D4×D15111yescharacteristic
201C2×C4C2×C22⋊D15112yes—
202C2×C4#1455900312yes—
203C2×C4C23×D15111yescharacteristic
204C8—22no—
205C8—3022no—
206C22—22no—
207C22—42no—
208C22—41no—
209C22#1801271112yes—
210C22C2×D4×D15111yescharacteristic
211C4—24no—
212C4—41no—
213C4—3024no—
214C4—6042no—
215C4—6042no—
216C4#1801271112yes—
217C4C22×C22⋊D15111yescharacteristic
218C4C2×#1455900311yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#1801271111yescharacteristic
222C2#2375302812yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#137×C151C2
socleC22×C151C22×D4
prime radicalC2×#41×C151C22
hypercenterC2×#137D151
hypocenterC151#3044
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#14558994C2semidirect
3. #23752690C2semidirect
4. #23752432C2semidirect
5. #23752420C2semidirect
6. #23752240C2semidirect
7. #23752222C2semidirect
111. C151#3044semidirect

Maximal subgroups

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

subgroupindex
C22×#145589942
#237527832
#237526902
#237524322
#237524202
#237522402
#237522222
#237522082
C2×#137×C1512
#3044151