Finite Group Databasebeta

← #49134342

Subgroups — #49134342

Order 36224.

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

normal subgroups only

This group has 356 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#31827188C212yesmaximal, complemented
2#31826859C212yesmaximal, complemented
3#31826849C211yesmaximal, characteristic
4#31826688C212yesmaximal, complemented
5#31826681C212yesmaximal
6#31826676C212yesmaximal, complemented
7#31826567C212yesmaximal, complemented
8C4×Dic1132C211yesmaximal, characteristic, complemented
9#446×C283C211yesmaximal, characteristic, complemented
10C2×Dic1132C2211yescharacteristic
11C2×Dic1132C2212yes—
12C2×Dic1132C2211yescharacteristic
13C2×#17985381C2212yes—
14C2×#17985381C2212yes—
15C2×D2264C2211yescharacteristic
16#22583610C2212yes—
17#22583605—22no—
18#22583605—22no—
19#22583598C2212yes—
20#22583598C2212yes—
21#22583586—22no—
22C4×Dic566C2212yes—
23C4×Dic566C2212yes—
24C4×D1132C2212yes—
25#22583568—22no—
26#22583544C2211yescharacteristic
27#22583535C2212yes—
28#22583535C2212yes—
29#22583532C2212yes—
30C4×Q8×C283C2211yescharacteristic
31C4⋊C8×C283C2211yescharacteristic
32C4⋊C8×C283C2212yes—
33#97×C283C2212yes—
34C4×C8×C283C2211yescharacteristic
35C2×Dic566C2312yes—
36C2×Dic566C2312yes—
37C2×D1132C2312yes—
38C2×C4×D283—22no—
39Dic1132—22no—
40Dic1132—41no—
41Dic1132—42no—
42#17985381—24no—
43#17985381—42no—
44D2264—41no—
45C4⋊Dic283—22no—
46C4⋊Dic283—22no—
47C4⋊Dic283C2312yes—
48Dic283⋊C4—22no—
49Dic283⋊C4—22no—
50(C2×D283)⋊C4—22no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53(C2×D283)⋊C4—22no—
54(C2×D283)⋊C4—22no—
55C4×Dic283—22no—
56C4×Dic283—22no—
57C2×Q8×C283D411yescharacteristic
58C2×C8×C283C2311yescharacteristic
59C2×C8×C283C2312yes—
60C2×C8×C283C2311yescharacteristic
61C4⋊C4×C283D412yes—
62C4⋊C4×C283D411yescharacteristic
63C42×C283C2312yes—
64C42×C283C2311yescharacteristic
65C22×D283—22no—
66Dic566—22no—
67Dic566—22no—
68Dic566—22no—
69Dic566—22no—
70D1132—22no—
71D1132—22no—
72C2×Dic283—22no—
73C2×Dic283—22no—
74C2×Dic283—22no—
75C4×D283—44no—
76Q8×C283—41no—
77C2×C4×C283C2×D411yescharacteristic
78C2×C4×C283C2×D412yes—
79C2×C4×C283C2×D411yescharacteristic
80C2×C4×C283C2×D412yes—
81C2×C4×C283C2411yescharacteristic
82C8×C283—21no—
83C8×C283—22no—
84C8×C283#4112yes—
85C22×C283C22×D411yescharacteristic
86C2×D283—42no—
87C2×D283—42no—
88C2×D283—42no—
89C4×C283—21no—
90C4×C283—22no—
91C4×C283—21no—
92C4×C283—22no—
93C4×C283C2×#4111yescharacteristic
94C4×C283H(5,𝔽2)11yescharacteristic
95Dic283—42no—
96Dic283—42no—
97Dic283—42no—
98C2×C283#55011yescharacteristic
99C2×C283#57511yescharacteristic
100C2×C283#57811yescharacteristic
101D283—82no—
102C283#340211yescharacteristic, complemented, Sylow
103#3402—2831nomaximal, Sylow
104#556—2832no—
105#497—2832no—
106#495—2831no—
107#464—2832no—
108#463—2832no—
109#462—2832no—
110#446D28311yescharacteristic, complemented
111#440—2832no—
112C4×Q16—2831no—
113C2×Q16—2831no—
114C2×Q16—2831no—
115C2×Q16—2832no—
116C2×SD16—2832no—
117C2×SD16—2832no—
118C2×D8—2831no—
119C4⋊Q8—2832no—
120#126—5662no—
121#126—5662no—
122#124—2832no—
123#124—2832no—
124C22⋊Q8—5662no—
125C4×Q8—2832no—
126C4×Q8—2832no—
127C4×Q8C2×D28311yescharacteristic
128C4×D4—2832no—
129#117—5662no—
130#107—2831no—
131C4⋊C8C2×D28312yes—
132C4⋊C8C2×D28311yescharacteristic
133#103—2832no—
134#103—2832no—
135#102—2832no—
136#97C2×D28312yes—
137C4×C8C2×D28311yescharacteristic
138C2×Q8—2832no—
139C2×Q8—2832no—
140C2×Q8D113211yescharacteristic
141C2×D4—2832no—
142C22×C4—5662no—
143Q16—5662no—
144Q16—11321no—
145Q16—11322no—
146SD16—5664no—
147SD16—11322no—
148D8—11321no—
149C2×C8C22×D28311yescharacteristic
150C2×C8C22×D28312yes—
151C2×C8C22×D28311yescharacteristic
152C4⋊C4—2832no—
153C4⋊C4—5662no—
154C4⋊C4—5662no—
155C4⋊C4—5662no—
156C4⋊C4—5662no—
157C4⋊C4D113212yes—
158C4⋊C4D113211yescharacteristic
159C22⋊C4—5662no—
160C22⋊C4—5662no—
161C22⋊C4—5662no—
162C22⋊C4—5662no—
163C22⋊C4—5662no—
164C42—5662no—
165C42—5662no—
166C42C22×D28311yescharacteristic
167C42C22×D28312yes—
168C23—5662no—
169Q8—41no—
170Q8—5662no—
171Q8—5662no—
172Q8—5662no—
173Q8—5662no—
174D4—5662no—
175D4—5662no—
176C2×C4—5662no—
177C2×C4—5662no—
178C2×C4—5662no—
179C2×C4—11324no—
180C2×C4C2×D113211yescharacteristic
181C2×C4C2×D113212yes—
182C2×C4C2×D113211yescharacteristic
183C2×C4C2×D113212yes—
184C2×C4C23×D28311yescharacteristic
185C8—21no—
186C8—22no—
187C8#1798539312yes—
188C22—11322no—
189C22—11322no—
190C22—11322no—
191C22C22×D113211yescharacteristic
192C4—22no—
193C4—21no—
194C4—21no—
195C4—22no—
196C4—11322no—
197C4—11322no—
198C4—11322no—
199C4C2×#1798539311yescharacteristic
200C4#2258365611yescharacteristic
201C2—22642no—
202C2#3182713711yescharacteristic
203C2#3182726511yescharacteristic
204C2#3182728211yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#446×C283C2
socleC22×C283C22×D4
prime radicalC2×D2264C22
hypercenter#446D283
hypocenterC283#3402
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #31827188C2semidirect
2. #31826859C2semidirect
4. #31826688C2semidirect
6. #31826676C2semidirect
7. #31826567C2semidirect
8. C4×Dic1132C2semidirect
9. #446×C283C2semidirect
102. C283#3402semidirect
110. #446D283semidirect

Maximal subgroups

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

subgroupindex
#318271882
#318268592
#318268492
#318266882
#318266812
#318266762
#318265672
C4×Dic11322
#446×C2832
#3402283