Finite Group Databasebeta

← #34080565

Subgroups — #34080565

Order 19328.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752829C212yesmaximal, complemented
2#23752506C212yesmaximal, complemented
3#23752490C212yesmaximal, complemented
4#23752456C212yesmaximal, complemented
5#23752453C211yesmaximal, characteristic, complemented
6#23752433C212yesmaximal, complemented
7#23752425C212yesmaximal, complemented
8#23752238C211yesmaximal, characteristic, complemented
9#466×C151C211yesmaximal, characteristic
10C2×Dic604C2211yescharacteristic
11C2×#14558992C2212yes—
12C2×#14558988C2211yescharacteristic
13#18012738C2212yes—
14#18012732—22no—
15#18012726—22no—
16#18012726C2212yes—
17#18012720—22no—
18#18012718C2212yes—
19#18012716—22no—
20#18012704C2212yes—
21D4×Dic151C2212yes—
22#18012698C2211yescharacteristic
23#18012673C2211yescharacteristic
24#18012672C2212yes—
25Dic151⋊C8C2212yes—
26Dic151⋊C8C2212yes—
27#18012664C2212yes—
28#18012662C2212yes—
29#18012660C2212yes—
30C2×D8×C151C2211yescharacteristic
31C22×C8×C151C2211yescharacteristic
32#121×C151C2212yes—
33#107×C151C2211yescharacteristic
34#102×C151C2212yes—
35C2×Dic302—22no—
36C2×Dic302C2312yes—
37C22×Dic151—22no—
38Dic604—41no—
39#14558992—42no—
40#14558988—41no—
41C2×C151⋊C8C2312yes—
42C4⋊Dic151D411yescharacteristic
43C4⋊Dic151D411yescharacteristic
44C4⋊Dic151C2312yes—
45Dic151⋊C4—22no—
46Dic151⋊C4—22no—
47Dic151⋊C4—22no—
48C22⋊Dic151—22no—
49C22⋊Dic151—22no—
50C22⋊Dic151—22no—
51C22⋊Dic151—22no—
52C22⋊Dic151D412yes—
53C4×Dic151—22no—
54C4×Dic151C2312yes—
55C2×D4×C151—22no—
56C2×D4×C151C2312yes—
57C22×C4×C151C2311yescharacteristic
58D8×C151—41no—
59C2×C8×C151—41no—
60C2×C8×C151C2311yescharacteristic
61C2×C8×C151C2311yescharacteristic
62C4⋊C4×C151C2312yes—
63C22⋊C4×C151—22no—
64Dic302—22no—
65Dic302—22no—
66Dic302—82no—
67C2×Dic151—22no—
68C2×Dic151—22no—
69C2×Dic151—82no—
70C2×Dic151C2×D412yes—
71C2×Dic151C2×D412yes—
72C151⋊C8—22no—
73C23×C151—22no—
74C23×C151C2×D411yescharacteristic
75D4×C151—22no—
76D4×C151—22no—
77D4×C151—82no—
78C2×C4×C151—21no—
79C2×C4×C151—21no—
80C2×C4×C151—22no—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2411yescharacteristic
83C8×C151—21no—
84C8×C151—21no—
85C22×C151—21no—
86C22×C151—21no—
87C22×C151—21no—
88C22×C151—42no—
89C22×C151—42no—
90C22×C151—42no—
91C22×C151C22×D411yescharacteristic
92C4×C151—21no—
93C4×C151—42no—
94C4×C151H(5,𝔽2)11yescharacteristic
95C4×C1512−1+411yescharacteristic
96Dic151—22no—
97Dic151—22no—
98Dic151—42no—
99Dic151—42no—
100C2×C151—41no—
101C2×C151—82no—
102C2×C151#53711yescharacteristic
103C2×C151#57611yescharacteristic
104C2×C151#57811yescharacteristic
105C151#326211yescharacteristic, complemented, Sylow
106#3262—1511nomaximal, Sylow
107#542—1512no—
108#477—1512no—
109#474—1512no—
110#468—1512no—
111#467—1511no—
112#466D15111yescharacteristic
113#464—1512no—
114#463—1512no—
115#424—1511no—
116C2×Q16—1511no—
117C2×SD16—1512no—
118C2×D8C2×D15111yescharacteristic
119C2×M16—1511no—
120C22×C8C2×D15111yescharacteristic
121C4⋊Q8—1512no—
122#126—3022no—
123#124—3022no—
124#124—1512no—
125#123—3022no—
126C22⋊Q8—3022no—
127C22⋊Q8—1512no—
128#121C2×D15112yes—
129C4×Q8—1512no—
130C4×D4—1512no—
131#117—1511no—
132#107—1511no—
133#107—1512no—
134#107C2×D15111yescharacteristic
135C4⋊C8—1512no—
136C4⋊C8—1512no—
137#103—1512no—
138#103—1512no—
139#102—1512no—
140#102C2×D15112yes—
141C2×Q8—3022no—
142C2×Q8—1512no—
143C2×D4—22no—
144C2×D4C22×D15112yes—
145C22×C4—3022no—
146C22×C4C22×D15111yescharacteristic
147Q16—6041no—
148SD16—6042no—
149D8—41no—
150M16—6041no—
151C2×C8—41no—
152C2×C8—1512no—
153C2×C8C22×D15111yescharacteristic
154C2×C8C22×D15111yescharacteristic
155C4⋊C4—3022no—
156C4⋊C4—3022no—
157C4⋊C4—3022no—
158C4⋊C4—1512no—
159C4⋊C4—1511no—
160C4⋊C4—1511no—
161C4⋊C4C22×D15112yes—
162C22⋊C4—22no—
163C22⋊C4—3022no—
164C22⋊C4—3022no—
165C22⋊C4—3022no—
166C22⋊C4—3022no—
167C22⋊C4—1512no—
168C42—3022no—
169C42—1512no—
170C23—22no—
171C23D4×D15111yescharacteristic
172Q8—3022no—
173Q8—3022no—
174Q8—12082no—
175D4—22no—
176D4—22no—
177D4—82no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4—1512no—
184C2×C4—1512no—
185C2×C4—12082no—
186C2×C4D4×D15111yescharacteristic
187C2×C4C23×D15111yescharacteristic
188C8—21no—
189C8—21no—
190C8—3022no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C2×D4×D15111yescharacteristic
198C4—21no—
199C4—42no—
200C4—3022no—
201C4—3022no—
202C4—6042no—
203C4—6042no—
204C4#1801278411yescharacteristic
205C4#1801278611yescharacteristic
206C2—41no—
207C2—82no—
208C2#2375278911yescharacteristic
209C2#2375301311yescharacteristic
210C2#2375302611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting, prime radical#466×C151C2
socleC22×C151C22×D4
hypercenter#466D151
hypocenterC151#3262
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #23752829C2semidirect
2. #23752506C2semidirect
3. #23752490C2semidirect
4. #23752456C2semidirect
5. #23752453C2semidirect
6. #23752433C2semidirect
7. #23752425C2semidirect
8. #23752238C2semidirect
105. C151#3262semidirect

Maximal subgroups

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

subgroupindex
#237528292
#237525062
#237524902
#237524562
#237524532
#237524332
#237524252
#237522382
#466×C1512
#3262151