Finite Group Databasebeta

← #34080463

Subgroups — #34080463

Order 19328.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#23752748C212yesmaximal, complemented
2#23752521C212yesmaximal, complemented
3#23752515C212yesmaximal, complemented
4#23752448C211yesmaximal, characteristic
5#23752443C212yesmaximal, complemented
6#23752436C212yesmaximal, complemented
7#23752430C212yesmaximal, complemented
8C2×Dic151⋊C8C211yesmaximal, characteristic, complemented
9#467×C151C211yesmaximal, characteristic, complemented
10C2×#14558991C2212yes—
11C2×D1208C2211yescharacteristic
12C22×C151⋊C8C2211yescharacteristic
13#18012734—22no—
14#18012730C2212yes—
15#18012728C2212yes—
16#18012723—22no—
17#18012713C2212yes—
18Q8×Dic151C2212yes—
19#18012701C2212yes—
20(C22⋊D151)⋊C4—22no—
21#18012697—22no—
22C2×C4×Dic151C2211yescharacteristic
23#18012673C2211yescharacteristic
24#18012670C2212yes—
25Dic151⋊C8C2212yes—
26Dic151⋊C8C2212yes—
27#18012663C2212yes—
28#18012661C2212yes—
29#18012659C2212yes—
30C2×Q16×C151C2211yescharacteristic
31C22×C8×C151C2211yescharacteristic
32C22⋊Q8×C151C2212yes—
33#107×C151C2211yescharacteristic
34#103×C151C2212yes—
35C2×D604C2312yes—
36C2×C22⋊D151—22no—
37C22×Dic151D411yescharacteristic
38C22×Dic151D411yescharacteristic
39C2×C4×D151—22no—
40#14558991—42no—
41D1208—41no—
42C2×C151⋊C8—41no—
43C2×C151⋊C8C2312yes—
44C4⋊Dic151—22no—
45C4⋊Dic151—22no—
46C4⋊Dic151C2312yes—
47Dic151⋊C4—22no—
48(C2×D151)⋊C4—22no—
49(C2×D151)⋊C4—22no—
50(C2×D151)⋊C4—22no—
51(C2×D151)⋊C4—22no—
52C4×Dic151—22no—
53C4×Dic151D412yes—
54C4×Dic151C2312yes—
55C2×Q8×C151C2312yes—
56C22×C4×C151C2311yescharacteristic
57Q16×C151—41no—
58C2×C8×C151—41no—
59C2×C8×C151C2311yescharacteristic
60C2×C8×C151C2311yescharacteristic
61C4⋊C4×C151—22no—
62C4⋊C4×C151C2312yes—
63C22⋊C4×C151—22no—
64C22×D151—22no—
65D604—22no—
66D604—22no—
67C22⋊D151—44no—
68C2×Dic151—22no—
69C2×Dic151—22no—
70C2×Dic151—41no—
71C2×Dic151C2×D412yes—
72C2×Dic151C2×D412yes—
73C4×D151—44no—
74C151⋊C8—22no—
75C23×C151C2×D411yescharacteristic
76Q8×C151—22no—
77Q8×C151—22no—
78C2×C4×C151—21no—
79C2×C4×C151—21no—
80C2×C4×C151—22no—
81C2×C4×C151—22no—
82C2×C4×C151C2×D411yescharacteristic
83C2×C4×C151C2411yescharacteristic
84C8×C151—21no—
85C8×C151—21no—
86C22×C151—21no—
87C22×C151—21no—
88C22×C151#13512yes—
89C22×C151C22×D411yescharacteristic
90C2×D151—42no—
91C2×D151—42no—
92C2×D151—42no—
93C4×C151—21no—
94C4×C151—42no—
95C4×C151—42no—
96C4×C151H(5,𝔽2)11yescharacteristic
97C4×C1512−1+411yescharacteristic
98Dic151—22no—
99Dic151—22no—
100Dic151—42no—
101C2×C151—22no—
102C2×C151#53711yescharacteristic
103C2×C151C2×#13511yescharacteristic
104C2×C151#57511yescharacteristic
105D151—82no—
106C151#325011yescharacteristic, complemented, Sylow
107#3250—1511nomaximal, Sylow
108#529—1512no—
109#479—1512no—
110#478—1512no—
111#467D15111yescharacteristic, complemented
112#466—1511no—
113#465—1512no—
114#464—1512no—
115#463—1512no—
116C2×C4⋊C8—1511no—
117C2×Q16C2×D15111yescharacteristic
118C2×SD16—1512no—
119C2×D8—1511no—
120C22×C8—1511no—
121C22×C8C2×D15111yescharacteristic
122#126—3022no—
123#125—1512no—
124#124—1512no—
125#123—3022no—
126C22⋊Q8C2×D15112yes—
127#121—1512no—
128C4×Q8—1512no—
129C4×D4—3022no—
130C4×D4—1512no—
131#117—3022no—
132C2×C42—1511no—
133#107—1511no—
134#107C2×D15111yescharacteristic
135#106—1512no—
136C4⋊C8—1512no—
137C4⋊C8—1512no—
138#103—1512no—
139#103C2×D15112yes—
140#102—1512no—
141#102—1512no—
142C2×Q8C22×D15112yes—
143C2×D4—3022no—
144C2×D4—1512no—
145C22×C4—3022no—
146C22×C4—1511no—
147C22×C4—1511no—
148C22×C4C22×D15111yescharacteristic
149Q16—41no—
150SD16—6042no—
151D8—6041no—
152C2×C8—41no—
153C2×C8—6041no—
154C2×C8—1512no—
155C2×C8C22×D15111yescharacteristic
156C2×C8C22×D15111yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—3022no—
159C4⋊C4—3022no—
160C4⋊C4—3022no—
161C4⋊C4—1512no—
162C4⋊C4C22×D15112yes—
163C22⋊C4—22no—
164C22⋊C4—3022no—
165C22⋊C4—3022no—
166C22⋊C4—3022no—
167C22⋊C4—3022no—
168C42—3022no—
169C42—1512no—
170C42—1512no—
171C23—3022no—
172C23D4×D15111yescharacteristic
173Q8—22no—
174Q8—22no—
175D4—3022no—
176D4—3022no—
177D4—6044no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—3022no—
183C2×C4—3022no—
184C2×C4—6044no—
185C2×C4—6041no—
186C2×C4—1512no—
187C2×C4—1512no—
188C2×C4D4×D15111yescharacteristic
189C2×C4C23×D15111yescharacteristic
190C8—21no—
191C8—21no—
192C8—3022no—
193C22—21no—
194C22—21no—
195C22—6042no—
196C22—6042no—
197C22—6042no—
198C22#1801276212yes—
199C22C2×D4×D15111yescharacteristic
200C4—21no—
201C4—42no—
202C4—42no—
203C4—3022no—
204C4—3022no—
205C4—6042no—
206C4#1801278411yescharacteristic
207C4#1801278611yescharacteristic
208C2—22no—
209C2—12082no—
210C2#2375278911yescharacteristic
211C2C2×#1801276211yescharacteristic
212C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#467×C151C2
socleC22×C151C22×D4
prime radical#23752448C2
hypercenter#467D151
hypocenterC151#3250
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #23752748C2semidirect
2. #23752521C2semidirect
3. #23752515C2semidirect
5. #23752443C2semidirect
6. #23752436C2semidirect
7. #23752430C2semidirect
8. C2×Dic151⋊C8C2semidirect
9. #467×C151C2semidirect
106. C151#3250semidirect
111. #467D151semidirect

Maximal subgroups

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

subgroupindex
#237527482
#237525212
#237525152
#237524482
#237524432
#237524362
#237524302
C2×Dic151⋊C82
#467×C1512
#3250151