Finite Group Databasebeta

← #49133865

Subgroups — #49133865

Order 36224.

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#31827168C212yesmaximal, complemented
2#31826792C212yesmaximal, complemented
3#31826780C212yesmaximal, complemented
4#31826762C212yesmaximal, complemented
5#31826719C212yesmaximal, complemented
6C4×D2264C211yesmaximal, characteristic, complemented
7#31826544C211yesmaximal, characteristic, complemented
8#31826504C212yesmaximal, complemented
9#499×C283C211yesmaximal, characteristic, complemented
10C2×D2264C2211yescharacteristic
11C2×#17985375C2212yes—
12#22583605—22no—
13#22583595—22no—
14#22583585—22no—
15#22583585C2212yes—
16#22583585C2212yes—
17C4×D1132C2212yes—
18C4×D1132C2211yescharacteristic
19#22583572—22no—
20#22583568C2212yes—
21C4⋊C4×D283C2212yes—
22#22583544C2211yescharacteristic
23#22583543C2212yes—
24#22583541C2212yes—
25C4⋊(C283⋊C8)C2211yescharacteristic
26#22583532C2212yes—
27#22583530C2212yes—
28#22583530C2212yes—
29(C2×D283)⋊C8C2212yes—
30#125×C283C2212yes—
31#107×C283C2211yescharacteristic
32#107×C283C2211yescharacteristic
33#106×C283C2212yes—
34C4×C8×C283C2211yescharacteristic
35C2×D1132—22no—
36C2×D1132—22no—
37C2×D1132D411yescharacteristic
38C2×D1132C2312yes—
39C2×C4×D283—22no—
40C2×C4×D283—22no—
41C2×C4×D283C2312yes—
42D2264—22no—
43#17985375—24no—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283D411yescharacteristic
46C4⋊Dic283C2312yes—
47Dic283⋊C4—22no—
48(C2×D283)⋊C4—22no—
49(C2×D283)⋊C4—22no—
50(C2×D283)⋊C4—22no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4D412yes—
53C4×Dic283—22no—
54C2×C8×C283C2311yescharacteristic
55C2×C8×C283C2311yescharacteristic
56C4⋊C4×C283—22no—
57C4⋊C4×C283—22no—
58C4⋊C4×C283C2312yes—
59C4⋊C4×C283C2312yes—
60C42×C283C2311yescharacteristic
61C22×D283—22no—
62C22×D283C2×D412yes—
63D1132—22no—
64D1132—22no—
65D1132—41no—
66D1132—44no—
67D1132—82no—
68C2×Dic283—22no—
69C2×Dic283C2×D412yes—
70C4×D283—22no—
71C4×D283—22no—
72C4×D283—82no—
73C4×D283—82no—
74C283⋊C8—22no—
75C2×C4×C283—22no—
76C2×C4×C283—22no—
77C2×C4×C283C2×D411yescharacteristic
78C2×C4×C283C2×D411yescharacteristic
79C2×C4×C283C2411yescharacteristic
80C8×C283—21no—
81C8×C283#4112yes—
82C22×C283C22×D411yescharacteristic
83C2×D283—22no—
84C2×D283—22no—
85C2×D283—22no—
86C2×D283—42no—
87C2×D283—42no—
88C2×D283—42no—
89C4×C283—21no—
90C4×C283—21no—
91C4×C283—42no—
92C4×C283—42no—
93C4×C283C2×#4111yescharacteristic
94C4×C2832−1+411yescharacteristic
95Dic283—22no—
96Dic283—42no—
97C2×C283#54711yescharacteristic
98C2×C283#57511yescharacteristic
99C2×C283#57611yescharacteristic
100D283—42no—
101D283—82no—
102C283#335511yescharacteristic, complemented, Sylow
103#3355—2831nomaximal, Sylow
104#553—2832no—
105#499D28311yescharacteristic, complemented
106#482—2832no—
107#480—2832no—
108#478—2832no—
109#469—2832no—
110C4×D8—2831no—
111#436—2831no—
112#428—2832no—
113C2×D8—2831no—
114C2×M16—2832no—
115#126—5662no—
116#125C2×D28312yes—
117#123—5662no—
118#121—2832no—
119#121—2832no—
120#121—5662no—
121C4×D4—2831no—
122C4×D4—2832no—
123C4×D4—5662no—
124#117—2832no—
125C2×C4⋊C4—2832no—
126#107—2831no—
127#107—2832no—
128#107C2×D28311yescharacteristic
129#107C2×D28311yescharacteristic
130#106—2832no—
131#106C2×D28312yes—
132C4⋊C8—2831no—
133#102—2832no—
134#102—2832no—
135#102—2832no—
136C22⋊C8—2832no—
137C4×C8C2×D28311yescharacteristic
138C2×D4—2831no—
139C2×D4—2832no—
140C2×D4—5662no—
141C2×D4—5662no—
142C22×C4—2832no—
143C22×C4—5662no—
144C22×C4—5662no—
145D8—5662no—
146M16—5664no—
147C2×C8—2832no—
148C2×C8C22×D28311yescharacteristic
149C2×C8C22×D28311yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—2831no—
153C4⋊C4—2832no—
154C4⋊C4—5662no—
155C4⋊C4C22×D28312yes—
156C4⋊C4C22×D28312yes—
157C22⋊C4—2832no—
158C22⋊C4—5662no—
159C22⋊C4—5662no—
160C22⋊C4—5662no—
161C22⋊C4—5662no—
162C42—5662no—
163C42C22×D28311yescharacteristic
164C23—2832no—
165C23—5662no—
166D4—5662no—
167D4—5662no—
168D4—11321no—
169D4—11324no—
170D4—22642no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—2832no—
174C2×C4—5662no—
175C2×C4—5662no—
176C2×C4—5662no—
177C2×C4—22642no—
178C2×C4—22642no—
179C2×C4D4×D28311yescharacteristic
180C2×C4D4×D28311yescharacteristic
181C2×C4C23×D28311yescharacteristic
182C8—21no—
183C8—5662no—
184C8#1798539312yes—
185C22—5662no—
186C22—5662no—
187C22—5662no—
188C22—11322no—
189C22—11322no—
190C22—11322no—
191C22C2×D4×D28311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—5662no—
197C4—11322no—
198C4C2×#1798539311yescharacteristic
199C4#2258365811yescharacteristic
200C2—11322no—
201C2—22642no—
202C2#3182711811yescharacteristic
203C2#3182726211yescharacteristic
204C2#3182726711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#499×C283C2
socleC22×C283C22×D4
hypercenter#499D283
hypocenterC283#3355
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #31827168C2semidirect
2. #31826792C2semidirect
3. #31826780C2semidirect
4. #31826762C2semidirect
5. #31826719C2semidirect
6. C4×D2264C2semidirect
7. #31826544C2semidirect
8. #31826504C2semidirect
9. #499×C283C2semidirect
102. C283#3355semidirect
105. #499D283semidirect

Maximal subgroups

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

subgroupindex
#318271682
#318267922
#318267802
#318267622
#318267192
C4×D22642
#318265442
#318265042
#499×C2832
#3355283