Finite Group Databasebeta

← #49132712

Subgroups — #49132712

Order 36224.

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

normal subgroups only

This group has 322 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#31827075C212yesmaximal
2#31826775C212yesmaximal, complemented
3#31826770C212yesmaximal, complemented
4#31826723C211yesmaximal, characteristic
5#31826704C212yesmaximal
6#31826674C212yesmaximal, complemented
7#31826673C212yesmaximal, complemented
8#31826493C211yesmaximal, characteristic
9#470×C283C211yesmaximal, characteristic
10C2×Dic1132C2211yescharacteristic
11C2×#17985382C2212yes—
12C22×C283⋊C8C2211yescharacteristic
13#22583608C2212yes—
14#22583603—22no—
15#22583603—22no—
16#22583601—22no—
17#22583601C2212yes—
18#22583600—22no—
19#22583589C2212yes—
20Q8×Dic283C2212yes—
21#22583575C2212yes—
22#22583569C2211yescharacteristic
23#22583543C2212yes—
24#22583542C2211yescharacteristic
25Dic283⋊C8C2212yes—
26Dic283⋊C8C2212yes—
27#22583535C2212yes—
28#22583534C2212yes—
29#22583533C2212yes—
30C2×Q16×C283C2211yescharacteristic
31C2×M16×C283C2211yescharacteristic
32C22⋊Q8×C283C2212yes—
33#106×C283C2211yescharacteristic
34#103×C283C2212yes—
35C2×Dic566C2312yes—
36Dic1132—41no—
37#17985382—42no—
38C2×C283⋊C8—41no—
39C2×C283⋊C8C2312yes—
40C4⋊Dic283—22no—
41C4⋊Dic283—22no—
42C4⋊Dic283D412yes—
43C4⋊Dic283C2312yes—
44Dic283⋊C4—22no—
45Dic283⋊C4—22no—
46Dic283⋊C4—22no—
47Dic283⋊C4—22no—
48Dic283⋊C4—22no—
49C22⋊Dic283—22no—
50C22⋊Dic283D411yescharacteristic
51C22⋊Dic283D411yescharacteristic
52C4×Dic283—22no—
53C4×Dic283—22no—
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—
64Dic566—22no—
65Dic566—22no—
66C2×Dic283—22no—
67C2×Dic283—22no—
68C2×Dic283C2×D412yes—
69C2×Dic283C2×D412yes—
70C283⋊C8—22no—
71C23×C283C2×D411yescharacteristic
72Q8×C283—22no—
73Q8×C283—22no—
74C2×C4×C283—21no—
75C2×C4×C283—21no—
76C2×C4×C283—22no—
77C2×C4×C283—22no—
78C2×C4×C283C2×D411yescharacteristic
79C2×C4×C283C2411yescharacteristic
80C8×C283—21no—
81C8×C283—21no—
82C22×C283—21no—
83C22×C283—22no—
84C22×C283C22×D411yescharacteristic
85C4×C283—21no—
86C4×C283—42no—
87C4×C283—42no—
88C4×C283H(5,𝔽2)11yescharacteristic
89C4×C2832−1+411yescharacteristic
90Dic283—22no—
91Dic283—22no—
92Dic283—42no—
93Dic283—42no—
94C2×C283—41no—
95C2×C283#53711yescharacteristic
96C2×C283#57812yes—
97C283#326111yescharacteristic, complemented, Sylow
98#3261—2831nomaximal, Sylow
99#541—2832no—
100#479—2832no—
101#479—2832no—
102#470—2831no—
103#470D28311yescharacteristic
104#467—2832no—
105#462—2832no—
106#462—2832no—
107#424—2831no—
108C2×Q16—2832no—
109C2×Q16—2831no—
110C2×Q16C2×D28311yescharacteristic
111C2×M16C2×D28311yescharacteristic
112C22×C8—2831no—
113C4⋊Q8—2832no—
114#126—5662no—
115#126—5662no—
116#125—2832no—
117#125—5662no—
118#125—5662no—
119C22⋊Q8—2832no—
120C22⋊Q8C2×D28312yes—
121C4×Q8—2832no—
122C4×Q8—2832no—
123#117—2831no—
124#107—2832no—
125#106—2831no—
126#106C2×D28311yescharacteristic
127C4⋊C8—2832no—
128C4⋊C8—2832no—
129#103—2832no—
130#103—2832no—
131#103—2832no—
132#103C2×D28312yes—
133C2×Q8—2832no—
134C2×Q8C22×D28312yes—
135C22×C4C22×D28311yescharacteristic
136Q16—41no—
137Q16—11321no—
138Q16—11322no—
139M16—41no—
140C2×C8—2832no—
141C2×C8—11321no—
142C2×C8C22×D28311yescharacteristic
143C2×C8C22×D28311yescharacteristic
144C4⋊C4—22no—
145C4⋊C4—2832no—
146C4⋊C4—2832no—
147C4⋊C4—5662no—
148C4⋊C4—5662no—
149C4⋊C4—5662no—
150C4⋊C4—5662no—
151C4⋊C4—5662no—
152C4⋊C4—5662no—
153C4⋊C4—5662no—
154C4⋊C4C22×D28312yes—
155C22⋊C4—22no—
156C22⋊C4—2831no—
157C22⋊C4—2831no—
158C22⋊C4—5662no—
159C42—2832no—
160C42—5662no—
161C42—5662no—
162C23D4×D28311yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—5662no—
166Q8—5662no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—2832no—
172C2×C4—2832no—
173C2×C4—5662no—
174C2×C4—5662no—
175C2×C4D4×D28311yescharacteristic
176C2×C4C23×D28311yescharacteristic
177C8—21no—
178C8—21no—
179C8—5662no—
180C22—22no—
181C22—21no—
182C22C2×D4×D28311yescharacteristic
183C4—21no—
184C4—42no—
185C4—42no—
186C4—5662no—
187C4—5662no—
188C4—11322no—
189C4—11322no—
190C4#2258365511yescharacteristic
191C4#2258365711yescharacteristic
192C2—41no—
193C2#3182704211yescharacteristic
194C2#3182728112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#470×C283C2
socleC22×C283C22×D4
prime radicalC23×C283C2×D4
hypercenter#470D283
hypocenterC283#3261
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
2. #31826775C2semidirect
3. #31826770C2semidirect
6. #31826674C2semidirect
7. #31826673C2semidirect
97. C283#3261semidirect

Maximal subgroups

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

subgroupindex
#318270752
#318267752
#318267702
#318267232
#318267042
#318266742
#318266732
#318264932
#470×C2832
#3261283