Finite Group Databasebeta

← #49134338

Subgroups — #49134338

Order 36224.

356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 356 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#31827187C212yesmaximal, complemented
2#31826858C212yesmaximal, complemented
3#31826849C211yesmaximal, characteristic
4#31826687C212yesmaximal, complemented
5#31826683C212yesmaximal
6#31826674C212yesmaximal, complemented
7#31826595C211yesmaximal, characteristic, complemented
8#31826564C212yesmaximal, complemented
9C4×Q16×C283C211yesmaximal, characteristic, complemented
10C2×Dic1132C2211yescharacteristic
11C2×#17985382C2212yes—
12C2×#17985381C2212yes—
13C2×#17985379C2212yes—
14C2×D2264C2211yescharacteristic
15#22583608C2212yes—
16#22583605—22no—
17#22583604—22no—
18#22583599C2212yes—
19#22583598C2212yes—
20#22583588—22no—
21C4×Dic566C2211yescharacteristic
22#22583575C2212yes—
23#22583572C2212yes—
24#22583567—22no—
25C4⋊(C283⋊C8)C2211yescharacteristic
26Dic283⋊C8C2212yes—
27#22583533C2212yes—
28#22583530C2212yes—
29#22583520C2212yes—
30C2×Q16×C283C2211yescharacteristic
31C4×Q8×C283C2212yes—
32#107×C283C2211yescharacteristic
33#103×C283C2212yes—
34C4×C8×C283C2211yescharacteristic
35C2×Dic566D411yescharacteristic
36C2×Dic566C2312yes—
37C2×D1132C2312yes—
38C2×C4×D283—22no—
39Dic1132—41no—
40#17985382—42no—
41#17985381—24no—
42#17985379—42no—
43D2264—41no—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283D411yescharacteristic
46Dic283⋊C4—22no—
47Dic283⋊C4—22no—
48Dic283⋊C4—22no—
49Dic283⋊C4D412yes—
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×Dic283C2312yes—
57C2×Q8×C283C2312yes—
58Q16×C283—22no—
59C2×C8×C283C2311yescharacteristic
60C2×C8×C283C2311yescharacteristic
61C4⋊C4×C283—22no—
62C4⋊C4×C283C2312yes—
63C42×C283—22no—
64C42×C283C2311yescharacteristic
65C22×D283—22no—
66Dic566—22no—
67Dic566—22no—
68Dic566—41no—
69D1132—22no—
70D1132—22no—
71C2×Dic283—22no—
72C2×Dic283C2×D412yes—
73C2×Dic283C2×D412yes—
74C4×D283—44no—
75C283⋊C8—22no—
76Q8×C283—22no—
77Q8×C283—22no—
78C2×C4×C283—22no—
79C2×C4×C283—22no—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2411yescharacteristic
83C8×C283—21no—
84C8×C283#4112yes—
85C22×C283C22×D411yescharacteristic
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×C283H(5,𝔽2)11yescharacteristic
95Dic283—22no—
96Dic283—22no—
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#446—2831no—
111#440—2832no—
112C4×Q16D28311yescharacteristic, complemented
113C2×Q16—2832no—
114C2×Q16—2831no—
115C2×Q16C2×D28311yescharacteristic
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—2831no—
126C4×Q8—2832no—
127C4×Q8C2×D28312yes—
128C4×D4—2832no—
129#117—5662no—
130#107C2×D28311yescharacteristic
131C4⋊C8—2832no—
132C4⋊C8—2831no—
133#103—2832no—
134#103C2×D28312yes—
135#102—2832no—
136#97—2832no—
137C4×C8C2×D28311yescharacteristic
138C2×Q8—2831no—
139C2×Q8—2832no—
140C2×Q8C22×D28312yes—
141C2×D4—2832no—
142C22×C4—5662no—
143Q16—22no—
144Q16—11321no—
145Q16—11322no—
146SD16—5664no—
147SD16—11322no—
148D8—11321no—
149C2×C8—2832no—
150C2×C8C22×D28311yescharacteristic
151C2×C8C22×D28311yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—2832no—
154C4⋊C4—2831no—
155C4⋊C4—5662no—
156C4⋊C4—5662no—
157C4⋊C4—5662no—
158C4⋊C4C22×D28312yes—
159C22⋊C4—5662no—
160C22⋊C4—5662no—
161C22⋊C4—5662no—
162C22⋊C4—5662no—
163C22⋊C4—5662no—
164C42—22no—
165C42—2832no—
166C42—5662no—
167C42C22×D28311yescharacteristic
168C23—5662no—
169Q8—22no—
170Q8—22no—
171Q8—5662no—
172Q8—5662no—
173Q8—11321no—
174D4—5662no—
175D4—5662no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2832no—
179C2×C4—2832no—
180C2×C4—5662no—
181C2×C4—11324no—
182C2×C4D4×D28311yescharacteristic
183C2×C4D4×D28311yescharacteristic
184C2×C4C23×D28311yescharacteristic
185C8—21no—
186C8—5662no—
187C8#1798539212yes—
188C22—11322no—
189C22—11322no—
190C22—11322no—
191C22C2×D4×D28311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—5662no—
197C4—5662no—
198C4—11322no—
199C4C2×#1798539211yescharacteristic
200C4#2258365611yescharacteristic
201C2—22642no—
202C2#3182713611yescharacteristic
203C2#3182726211yescharacteristic
204C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×Q16×C283C2
socleC22×C283C22×D4
prime radicalC2×D2264C22
hypercenterC4×Q16D283
hypocenterC283#3402
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #31827187C2semidirect
2. #31826858C2semidirect
4. #31826687C2semidirect
6. #31826674C2semidirect
7. #31826595C2semidirect
8. #31826564C2semidirect
9. C4×Q16×C283C2semidirect
102. C283#3402semidirect
112. C4×Q16D283semidirect

Maximal subgroups

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

subgroupindex
#318271872
#318268582
#318268492
#318266872
#318266832
#318266742
#318265952
#318265642
C4×Q16×C2832
#3402283