Finite Group Databasebeta

← #34080551

Subgroups — #34080551

Order 19328.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752817C211yesmaximal, characteristic
2#23752519C212yesmaximal, complemented
3#23752509C212yesmaximal, complemented
4#23752460C212yesmaximal, complemented
5#23752443C212yesmaximal, complemented
6#23752414C212yesmaximal, complemented
7#23752412C212yesmaximal, complemented
8#23752239C211yesmaximal, characteristic, complemented
9#541×C151C211yesmaximal, characteristic, complemented
10C2×#14558991C2212yes—
11C2×#14558991C2212yes—
12C2×#14558988C2211yescharacteristic
13C22×C151⋊C8C2211yescharacteristic
14#18012736C2211yescharacteristic
15#18012731C2211yescharacteristic
16#18012724—22no—
17#18012713C2212yes—
18#18012712—22no—
19C4×D604C2212yes—
20#18012672C2212yes—
21#18012670C2212yes—
22C4⋊(C151⋊C8)C2212yes—
23C4⋊(C151⋊C8)C2212yes—
24#18012663C2212yes—
25#18012663C2212yes—
26#18012659C2212yes—
27#18012659C2212yes—
28C4⋊Q8×C151C2211yescharacteristic
29#126×C151—22no—
30#125×C151—22no—
31#125×C151C2211yescharacteristic
32C22⋊Q8×C151C2212yes—
33C4×Q8×C151C2212yes—
34#117×C151C2211yescharacteristic
35C2×D604—22no—
36C2×D604C2312yes—
37C2×C22⋊D151—22no—
38C2×C4×D151—22no—
39#14558991—42no—
40#14558991—42no—
41#14558988—41no—
42C2×C151⋊C8—41no—
43C2×C151⋊C8C2312yes—
44C2×C151⋊C8C2312yes—
45C4⋊Dic151C2312yes—
46Dic151⋊C4—22no—
47(C2×D151)⋊C4—22no—
48(C2×D151)⋊C4—22no—
49C2×Q8×C151C2312yes—
50C22×C4×C151C2311yescharacteristic
51C4⋊C4×C151—22no—
52C4⋊C4×C151—22no—
53C4⋊C4×C151—22no—
54C4⋊C4×C151—22no—
55C4⋊C4×C151D412yes—
56C4⋊C4×C151C2312yes—
57C22⋊C4×C151—22no—
58C22⋊C4×C151D412yes—
59C42×C151—22no—
60C42×C151C2311yescharacteristic
61C42×C151C2311yescharacteristic
62C22×D151—22no—
63D604—22no—
64D604—22no—
65D604—82no—
66C22⋊D151—82no—
67C2×Dic151—22no—
68C4×D151—82no—
69C151⋊C8—22no—
70C151⋊C8—22no—
71C23×C151C2×D411yescharacteristic
72Q8×C151—22no—
73Q8×C151—22no—
74C2×C4×C151—21no—
75C2×C4×C151—21no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151C2×D411yescharacteristic
79C2×C4×C151C2×D412yes—
80C2×C4×C151C2×D412yes—
81C2×C4×C151C2411yescharacteristic
82C22×C151—21no—
83C22×C151—22no—
84C22×C151C22×D411yescharacteristic
85C2×D151—42no—
86C2×D151—42no—
87C2×D151—42no—
88C4×C151—21no—
89C4×C151—22no—
90C4×C151—22no—
91C4×C151—42no—
92C4×C151—42no—
93C4×C151H(5,𝔽2)11yescharacteristic
94C4×C1512−1+411yescharacteristic
95Dic151—42no—
96C2×C151—41no—
97C2×C151#53711yescharacteristic
98C2×C151#57712yes—
99D151—82no—
100C151#326011yescharacteristic, complemented, Sylow
101#3260—1511nomaximal, Sylow
102#541D15111yescharacteristic, complemented
103#540—1511no—
104#479—1512no—
105#478—1512no—
106#468—1512no—
107#465—1512no—
108#461—1512no—
109#460—1512no—
110#424—1511no—
111C2×SD16—1512no—
112C2×SD16—1512no—
113C2×M16—1511no—
114C22×C8—1511no—
115C4⋊Q8C2×D15111yescharacteristic
116#127—1511no—
117#126—22no—
118#125—22no—
119#125—1511no—
120#125C2×D15111yescharacteristic
121#123—3022no—
122C22⋊Q8C2×D15112yes—
123#121—3022no—
124#121—1512no—
125C4×Q8C2×D15112yes—
126C4×D4—1512no—
127#117C2×D15111yescharacteristic
128#107—1512no—
129#106—1512no—
130C4⋊C8—1512no—
131C4⋊C8—1512no—
132#103—1512no—
133#103—1512no—
134#102—1512no—
135#102—1512no—
136C2×Q8C22×D15112yes—
137C2×D4—3022no—
138C2×D4—3022no—
139C2×D4—1512no—
140C22×C4—3022no—
141C22×C4C22×D15111yescharacteristic
142SD16—6042no—
143SD16—6042no—
144M16—6041no—
145C2×C8—6041no—
146C2×C8—1512no—
147C2×C8—1512no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—3022no—
153C4⋊C4—1512no—
154C4⋊C4C22⋊D15112yes—
155C4⋊C4C22×D15112yes—
156C22⋊C4—22no—
157C22⋊C4—3022no—
158C22⋊C4—3022no—
159C22⋊C4C22⋊D15112yes—
160C42—22no—
161C42C22×D15111yescharacteristic
162C42C22×D15111yescharacteristic
163C23—3022no—
164C23C2×C22⋊D15111yescharacteristic
165Q8—22no—
166Q8—22no—
167D4—3022no—
168D4—3022no—
169D4—12082no—
170D4—12082no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—3022no—
176C2×C4—12082no—
177C2×C4C2×C22⋊D15112yes—
178C2×C4C2×C22⋊D15112yes—
179C2×C4C2×C22⋊D15111yescharacteristic
180C2×C4C23×D15111yescharacteristic
181C8—3022no—
182C8—3022no—
183C22—22no—
184C22—21no—
185C22—6042no—
186C22—6042no—
187C22—6042no—
188C22C22×C22⋊D15111yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—42no—
193C4—42no—
194C4—6042no—
195C4#1801278511yescharacteristic
196C4#1801278611yescharacteristic
197C2—41no—
198C2—12082no—
199C2#2375279011yescharacteristic
200C2#2375302012yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#541×C151C2
socleC22×C151C22×D4
prime radical#23752817C2
hypercenter#541D151
hypocenterC151#3260
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #23752519C2semidirect
3. #23752509C2semidirect
4. #23752460C2semidirect
5. #23752443C2semidirect
6. #23752414C2semidirect
7. #23752412C2semidirect
8. #23752239C2semidirect
9. #541×C151C2semidirect
100. C151#3260semidirect
102. #541D151semidirect

Maximal subgroups

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

subgroupindex
#237528172
#237525192
#237525092
#237524602
#237524432
#237524142
#237524122
#237522392
#541×C1512
#3260151