Finite Group Databasebeta

← #49133866

Subgroups — #49133866

Order 36224.

360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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#31827161C212yesmaximal, complemented
2#31826867C211yesmaximal, characteristic, complemented
3#31826790C212yesmaximal, complemented
4#31826779C212yesmaximal, complemented
5#31826766C212yesmaximal, complemented
6#31826718C212yesmaximal, complemented
7C4×D2264C211yesmaximal, characteristic, complemented
8#31826507C212yesmaximal, complemented
9#436×C283C211yesmaximal, characteristic, complemented
10C2×D2264C2211yescharacteristic
11#22583605—22no—
12#22583602C2212yes—
13#22583592—22no—
14#22583584C2212yes—
15#22583584C2212yes—
16#22583582—22no—
17C4×D1132C2212yes—
18(C22⋊D283)⋊C4—22no—
19#22583569C2212yes—
20C2×C4⋊Dic283C2212yes—
21#22583544C2211yescharacteristic
22#22583544C2212yes—
23#22583544C2211yescharacteristic
24#22583544C2211yescharacteristic
25#22583542C2212yes—
26#22583542C2212yes—
27#22583532C2212yes—
28#22583532C2212yes—
29#22583532C2212yes—
30C2×M16×C283C2212yes—
31C4×D4×C283C2211yescharacteristic
32C4⋊C8×C283C2211yescharacteristic
33C22⋊C8×C283C2212yes—
34C4×C8×C283C2211yescharacteristic
35C2×D1132C2312yes—
36C2×C22⋊D283—22no—
37C2×C22⋊D283—22no—
38C22×Dic283—22no—
39C2×C4×D283—22no—
40D2264—22no—
41C4⋊Dic283—22no—
42C4⋊Dic283C2312yes—
43C4⋊Dic283C2312yes—
44C4⋊Dic283C2312yes—
45Dic283⋊C4—22no—
46Dic283⋊C4—22no—
47C22⋊Dic283—22no—
48(C2×D283)⋊C4—22no—
49(C2×D283)⋊C4—22no—
50(C2×D283)⋊C4—22no—
51C4×Dic283—22no—
52C2×D4×C283D411yescharacteristic
53C22×C4×C283C2312yes—
54M16×C283—24no—
55C2×C8×C283C2311yescharacteristic
56C2×C8×C283C2312yes—
57C2×C8×C283C2311yescharacteristic
58C4⋊C4×C283D411yescharacteristic
59C22⋊C4×C283D412yes—
60C42×C283C2311yescharacteristic
61C22×D283—22no—
62D1132—22no—
63D1132—22no—
64C22⋊D283—44no—
65C22⋊D283—82no—
66C2×Dic283—22no—
67C2×Dic283—22no—
68C2×Dic283—22no—
69C2×Dic283—82no—
70C4×D283—82no—
71C23×C283C2×D412yes—
72D4×C283—41no—
73C2×C4×C283—22no—
74C2×C4×C283—22no—
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283C2×D411yescharacteristic
77C2×C4×C283C2×D412yes—
78C2×C4×C283C2411yescharacteristic
79C8×C283—22no—
80C8×C283—21no—
81C8×C283#4112yes—
82C22×C283—22no—
83C22×C283—22no—
84C22×C283—22no—
85C22×C283C22×D411yescharacteristic
86C2×D283—42no—
87C2×D283—42no—
88C2×D283—42no—
89C4×C283—22no—
90C4×C283—21no—
91C4×C283—21no—
92C4×C283C2×#4111yescharacteristic
93C4×C2832−1+411yescharacteristic
94Dic283—42no—
95Dic283—42no—
96Dic283—42no—
97C2×C283—42no—
98C2×C283#54711yescharacteristic
99C2×C283#57511yescharacteristic
100C2×C283#57611yescharacteristic
101D283—82no—
102C283#335511yescharacteristic, complemented, Sylow
103#3355—2831nomaximal, Sylow
104#553—2832no—
105#499—2831no—
106#482—2832no—
107#480—2832no—
108#478—2832no—
109#469—2832no—
110C4×D8—2831no—
111#436D28311yescharacteristic, complemented
112#428—2832no—
113C2×D8—2831no—
114C2×M16C2×D28312yes—
115#126—5662no—
116#125—2832no—
117#123—5662no—
118#121—2832no—
119#121—2832no—
120#121—5662no—
121C4×D4—2832no—
122C4×D4—5662no—
123C4×D4C2×D28311yescharacteristic
124#117—2832no—
125C2×C4⋊C4—2832no—
126#107—2831no—
127#107—2832no—
128#107—2831no—
129#107—2831no—
130#106—2832no—
131#106—2832no—
132C4⋊C8C2×D28311yescharacteristic
133#102—2832no—
134#102—2832no—
135#102—2832no—
136C22⋊C8C2×D28312yes—
137C4×C8C2×D28311yescharacteristic
138C2×D4—2832no—
139C2×D4—5662no—
140C2×D4—5662no—
141C2×D4D113211yescharacteristic
142C22×C4—5662no—
143C22×C4—5662no—
144C22×C4C22×D28312yes—
145D8—5662no—
146M16—24no—
147C2×C8C22×D28311yescharacteristic
148C2×C8C22×D28312yes—
149C2×C8C22×D28311yescharacteristic
150C4⋊C4—2832no—
151C4⋊C4—2832no—
152C4⋊C4—2832no—
153C4⋊C4—5662no—
154C4⋊C4—5662no—
155C4⋊C4—5662no—
156C4⋊C4D113211yescharacteristic
157C22⋊C4—5662no—
158C22⋊C4—5662no—
159C22⋊C4—5662no—
160C22⋊C4—5662no—
161C22⋊C4D113212yes—
162C42—5662no—
163C42C22×D28311yescharacteristic
164C23—5662no—
165C23C2×D113212yes—
166D4—41no—
167D4—5662no—
168D4—5662no—
169D4—11324no—
170D4—22642no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—5662no—
174C2×C4—5662no—
175C2×C4—5662no—
176C2×C4—22642no—
177C2×C4—22642no—
178C2×C4C2×D113212yes—
179C2×C4C2×D113211yescharacteristic
180C2×C4C2×D113211yescharacteristic
181C2×C4C23×D28311yescharacteristic
182C8—22no—
183C8—21no—
184C8#1798539112yes—
185C22—22no—
186C22—22no—
187C22—22no—
188C22—11322no—
189C22—11322no—
190C22—11322no—
191C22C22×D113211yescharacteristic
192C4—21no—
193C4—21no—
194C4—22no—
195C4—11322no—
196C4—11322no—
197C4—11322no—
198C4C2×#1798539111yescharacteristic
199C4#2258365711yescharacteristic
200C2—42no—
201C2—22642no—
202C2#3182711911yescharacteristic
203C2#3182726511yescharacteristic
204C2#3182727011yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#436×C283C2
socleC22×C283C22×D4
hypercenter#436D283
hypocenterC283#3355
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #31827161C2semidirect
2. #31826867C2semidirect
3. #31826790C2semidirect
4. #31826779C2semidirect
5. #31826766C2semidirect
6. #31826718C2semidirect
7. C4×D2264C2semidirect
8. #31826507C2semidirect
9. #436×C283C2semidirect
102. C283#3355semidirect
111. #436D283semidirect

Maximal subgroups

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

subgroupindex
#318271612
#318268672
#318267902
#318267792
#318267662
#318267182
C4×D22642
#318265072
#436×C2832
#3355283