Finite Group Databasebeta

← #49132663

Subgroups — #49132663

Order 36224.

354 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 109 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#31827001C212yesmaximal, complemented
2#31826770C212yesmaximal, complemented
3#31826764C212yesmaximal, complemented
4#31826718C211yesmaximal, characteristic
5#31826713C212yesmaximal, complemented
6#31826689C212yesmaximal, complemented
7#31826683C212yesmaximal, complemented
8#31826488C211yesmaximal, characteristic, complemented
9#470×C283C211yesmaximal, characteristic, complemented
10C2×#17985379C2212yes—
11C2×D2264C2211yescharacteristic
12C2×#17985376C2211yescharacteristic
13#22583605—22no—
14#22583601C2212yes—
15#22583599C2212yes—
16#22583594—22no—
17#22583584C2212yes—
18Q8×Dic283C2212yes—
19#22583572C2212yes—
20(C22⋊D283)⋊C4—22no—
21#22583568—22no—
22C2×C4×Dic283C2211yescharacteristic
23#22583543C2212yes—
24#22583542C2211yescharacteristic
25Dic283⋊C8C2212yes—
26Dic283⋊C8C2212yes—
27#22583534C2212yes—
28#22583532C2212yes—
29#22583530C2212yes—
30C2×Q16×C283C2211yescharacteristic
31C2×M16×C283C2211yescharacteristic
32C22⋊Q8×C283C2212yes—
33#106×C283C2211yescharacteristic
34#103×C283C2212yes—
35C2×D1132C2312yes—
36C2×C22⋊D283—22no—
37C22×Dic283D412yes—
38C2×C4×D283—22no—
39#17985379—42no—
40D2264—41no—
41#17985376—41no—
42C2×C283⋊C8C2312yes—
43C4⋊Dic283—22no—
44C4⋊Dic283—22no—
45C4⋊Dic283C2312yes—
46Dic283⋊C4—22no—
47(C2×D283)⋊C4—22no—
48(C2×D283)⋊C4—22no—
49(C2×D283)⋊C4—22no—
50(C2×D283)⋊C4—22no—
51C4×Dic283—22no—
52C4×Dic283D411yescharacteristic
53C4×Dic283D411yescharacteristic
54C4×Dic283C2312yes—
55C2×Q8×C283C2312yes—
56C22×C4×C283C2311yescharacteristic
57Q16×C283—41no—
58M16×C283—41no—
59C2×C8×C283C2311yescharacteristic
60C2×C8×C283C2311yescharacteristic
61C4⋊C4×C283—22no—
62C4⋊C4×C283C2312yes—
63C22⋊C4×C283—22no—
64C22×D283—22no—
65D1132—22no—
66D1132—22no—
67C22⋊D283—44no—
68C2×Dic283—22no—
69C2×Dic283—42no—
70C2×Dic283C2×D412yes—
71C2×Dic283C2×D412yes—
72C4×D283—44no—
73C283⋊C8—22no—
74C23×C283C2×D411yescharacteristic
75Q8×C283—22no—
76Q8×C283—22no—
77C2×C4×C283—21no—
78C2×C4×C283—21no—
79C2×C4×C283—22no—
80C2×C4×C283—22no—
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2411yescharacteristic
83C8×C283—21no—
84C8×C283—21no—
85C22×C283—21no—
86C22×C283—22no—
87C22×C283C22×D411yescharacteristic
88C2×D283—42no—
89C2×D283—42no—
90C2×D283—42no—
91C4×C283—21no—
92C4×C283—42no—
93C4×C283—42no—
94C4×C283H(5,𝔽2)11yescharacteristic
95C4×C2832−1+411yescharacteristic
96Dic283—22no—
97Dic283—22no—
98Dic283—42no—
99C2×C283—41no—
100C2×C283#53711yescharacteristic
101C2×C283#57512yes—
102D283—82no—
103C283#325611yescharacteristic, complemented, Sylow
104#3256—2831nomaximal, Sylow
105#529—2832no—
106#479—2832no—
107#478—2832no—
108#470D28311yescharacteristic, complemented
109#469—2831no—
110#468—2832no—
111#464—2832no—
112#463—2832no—
113#423—2831no—
114C2×Q16C2×D28311yescharacteristic
115C2×SD16—2832no—
116C2×D8—2831no—
117C2×M16—2831no—
118C2×M16C2×D28311yescharacteristic
119#126—5662no—
120#125—2832no—
121#124—2832no—
122#123—5662no—
123C22⋊Q8C2×D28312yes—
124#121—2832no—
125C4×Q8—2832no—
126C4×D4—2832no—
127C4×D4—5662no—
128#117—5662no—
129C2×C42—2831no—
130#107—2832no—
131#106—2831no—
132#106C2×D28311yescharacteristic
133C4⋊C8—2832no—
134C4⋊C8—2832no—
135#103—2832no—
136#103C2×D28312yes—
137#102—2832no—
138#102—2832no—
139C2×Q8C22×D28312yes—
140C2×D4—2832no—
141C2×D4—5662no—
142C22×C4—2832no—
143C22×C4—5662no—
144C22×C4C22×D28311yescharacteristic
145Q16—41no—
146SD16—11322no—
147D8—11321no—
148M16—41no—
149M16—11321no—
150C2×C8—2832no—
151C2×C8C22×D28311yescharacteristic
152C2×C8C22×D28311yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—2832no—
155C4⋊C4—5662no—
156C4⋊C4—5662no—
157C4⋊C4—5662no—
158C4⋊C4C22×D28312yes—
159C22⋊C4—22no—
160C22⋊C4—5662no—
161C22⋊C4—5662no—
162C22⋊C4—5662no—
163C22⋊C4—5662no—
164C42—2831no—
165C42—2831no—
166C42—2832no—
167C42—5662no—
168C23—5662no—
169C23D4×D28311yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—5662no—
173D4—5662no—
174D4—11324no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—2832no—
180C2×C4—2832no—
181C2×C4—5662no—
182C2×C4—11324no—
183C2×C4—11322no—
184C2×C4D4×D28311yescharacteristic
185C2×C4C23×D28311yescharacteristic
186C8—21no—
187C8—21no—
188C8—5662no—
189C22—22no—
190C22—21no—
191C22—11322no—
192C22—11322no—
193C22—11322no—
194C22C2×D4×D28311yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—5662no—
199C4—5662no—
200C4—11322no—
201C4#2258365511yescharacteristic
202C4#2258365711yescharacteristic
203C2—41no—
204C2—22642no—
205C2#3182704211yescharacteristic
206C2#3182726412yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#470×C283C2
socleC22×C283C22×D4
prime radical#31826718C2
hypercenter#470D283
hypocenterC283#3256
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #31827001C2semidirect
2. #31826770C2semidirect
3. #31826764C2semidirect
5. #31826713C2semidirect
6. #31826689C2semidirect
7. #31826683C2semidirect
8. #31826488C2semidirect
9. #470×C283C2semidirect
103. C283#3256semidirect
108. #470D283semidirect

Maximal subgroups

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

subgroupindex
#318270012
#318267702
#318267642
#318267182
#318267132
#318266892
#318266832
#318264882
#470×C2832
#3256283