Finite Group Databasebeta

← #34080572

Subgroups — #34080572

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#23752835C212yesmaximal, complemented
2#23752505C212yesmaximal, complemented
3#23752491C212yesmaximal, complemented
4#23752460C212yesmaximal, complemented
5#23752448C211yesmaximal, characteristic
6#23752436C212yesmaximal, complemented
7#23752430C212yesmaximal, complemented
8#23752238C211yesmaximal, characteristic, complemented
9#467×C151C211yesmaximal, characteristic, complemented
10C2×#14558991C2212yes—
11C2×D1208C2211yescharacteristic
12C2×#14558988C2211yescharacteristic
13#18012738C2212yes—
14#18012734—22no—
15#18012728C2212yes—
16#18012725—22no—
17#18012721—22no—
18#18012719—22no—
19#18012713C2212yes—
20Q8×Dic151C2212yes—
21#18012701C2212yes—
22#18012698C2211yescharacteristic
23#18012673C2211yescharacteristic
24#18012672C2212yes—
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×Dic302—22no—
36C2×D604C2312yes—
37C2×C22⋊D151—22no—
38C2×C4×D151—22no—
39#14558991—42no—
40D1208—41no—
41#14558988—41no—
42C2×C151⋊C8C2312yes—
43C4⋊Dic151—22no—
44C4⋊Dic151D411yescharacteristic
45C4⋊Dic151D411yescharacteristic
46C4⋊Dic151C2312yes—
47Dic151⋊C4—22no—
48C22⋊Dic151D412yes—
49(C2×D151)⋊C4—22no—
50(C2×D151)⋊C4—22no—
51(C2×D151)⋊C4—22no—
52(C2×D151)⋊C4—22no—
53C4×Dic151—22no—
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—
65Dic302—82no—
66D604—22no—
67D604—22no—
68C22⋊D151—82no—
69C2×Dic151—22no—
70C2×Dic151C2×D412yes—
71C2×Dic151C2×D412yes—
72C4×D151—82no—
73C151⋊C8—22no—
74C23×C151C2×D411yescharacteristic
75Q8×C151—22no—
76Q8×C151—22no—
77C2×C4×C151—21no—
78C2×C4×C151—21no—
79C2×C4×C151—22no—
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×C151C22×D411yescharacteristic
89C2×D151—42no—
90C2×D151—42no—
91C2×D151—42no—
92C4×C151—21no—
93C4×C151—42no—
94C4×C151—42no—
95C4×C151H(5,𝔽2)11yescharacteristic
96C4×C1512−1+411yescharacteristic
97Dic151—22no—
98Dic151—22no—
99Dic151—42no—
100C2×C151—41no—
101C2×C151#53711yescharacteristic
102C2×C151#57611yescharacteristic
103C2×C151#57811yescharacteristic
104D151—82no—
105C151#326211yescharacteristic, complemented, Sylow
106#3262—1511nomaximal, Sylow
107#542—1512no—
108#477—1512no—
109#474—1512no—
110#468—1512no—
111#467D15111yescharacteristic, complemented
112#466—1511no—
113#464—1512no—
114#463—1512no—
115#424—1511no—
116C2×Q16C2×D15111yescharacteristic
117C2×SD16—1512no—
118C2×D8—1511no—
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⋊Q8C2×D15112yes—
128#121—1512no—
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#103C2×D15112yes—
139#102—1512no—
140#102—1512no—
141C2×Q8—3022no—
142C2×Q8C22×D15112yes—
143C2×D4—3022no—
144C2×D4—1512no—
145C22×C4—3022no—
146C22×C4C22×D15111yescharacteristic
147Q16—41no—
148SD16—6042no—
149D8—6041no—
150M16—6041no—
151C2×C8—41no—
152C2×C8—1512no—
153C2×C8C22×D15111yescharacteristic
154C2×C8C22×D15111yescharacteristic
155C4⋊C4—22no—
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—3022no—
171C23D4×D15111yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—12082no—
175D4—3022no—
176D4—3022no—
177D4—12082no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
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—6042no—
195C22—6042no—
196C22—6042no—
197C22C2×D4×D15111yescharacteristic
198C4—21no—
199C4—42no—
200C4—42no—
201C4—3022no—
202C4—3022no—
203C4—6042no—
204C4#1801278411yescharacteristic
205C4#1801278611yescharacteristic
206C2—41no—
207C2—12082no—
208C2#2375278911yescharacteristic
209C2#2375301411yescharacteristic
210C2#2375302511yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#467×C151C2
socleC22×C151C22×D4
prime radical#23752448C2
hypercenter#467D151
hypocenterC151#3262
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. #23752835C2semidirect
2. #23752505C2semidirect
3. #23752491C2semidirect
4. #23752460C2semidirect
6. #23752436C2semidirect
7. #23752430C2semidirect
8. #23752238C2semidirect
9. #467×C151C2semidirect
105. C151#3262semidirect
111. #467D151semidirect

Maximal subgroups

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

subgroupindex
#237528352
#237525052
#237524912
#237524602
#237524482
#237524362
#237524302
#237522382
#467×C1512
#3262151