Finite Group Databasebeta

← #49132702

Subgroups — #49132702

Order 36224.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#31827070C211yesmaximal, characteristic
2#31826772C212yesmaximal, complemented
3#31826762C212yesmaximal, complemented
4#31826713C212yesmaximal, complemented
5#31826696C212yesmaximal, complemented
6#31826667C212yesmaximal, complemented
7#31826665C212yesmaximal, complemented
8#31826492C211yesmaximal, characteristic, complemented
9#541×C283C211yesmaximal, characteristic, complemented
10C2×#17985379C2212yes—
11C2×#17985379C2212yes—
12C2×#17985376C2211yescharacteristic
13C22×C283⋊C8C2211yescharacteristic
14#22583607C2211yescharacteristic
15#22583602C2211yescharacteristic
16#22583595—22no—
17#22583584C2212yes—
18#22583583—22no—
19C4×D1132C2212yes—
20#22583543C2212yes—
21#22583541C2212yes—
22C4⋊(C283⋊C8)C2212yes—
23C4⋊(C283⋊C8)C2212yes—
24#22583534C2212yes—
25#22583534C2212yes—
26#22583530C2212yes—
27#22583530C2212yes—
28C4⋊Q8×C283C2211yescharacteristic
29#126×C283—22no—
30#125×C283—22no—
31#125×C283C2211yescharacteristic
32C22⋊Q8×C283C2212yes—
33C4×Q8×C283C2212yes—
34#117×C283C2211yescharacteristic
35C2×D1132—22no—
36C2×D1132C2312yes—
37C2×C22⋊D283—22no—
38C2×C4×D283—22no—
39#17985379—42no—
40#17985379—42no—
41#17985376—41no—
42C2×C283⋊C8—41no—
43C2×C283⋊C8C2312yes—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283C2312yes—
46Dic283⋊C4—22no—
47(C2×D283)⋊C4—22no—
48(C2×D283)⋊C4—22no—
49C2×Q8×C283C2312yes—
50C22×C4×C283C2311yescharacteristic
51C4⋊C4×C283—22no—
52C4⋊C4×C283—22no—
53C4⋊C4×C283—22no—
54C4⋊C4×C283—22no—
55C4⋊C4×C283D412yes—
56C4⋊C4×C283C2312yes—
57C22⋊C4×C283—22no—
58C22⋊C4×C283D412yes—
59C42×C283—22no—
60C42×C283C2311yescharacteristic
61C42×C283C2311yescharacteristic
62C22×D283—22no—
63D1132—22no—
64D1132—22no—
65D1132—82no—
66C22⋊D283—82no—
67C2×Dic283—22no—
68C4×D283—82no—
69C283⋊C8—22no—
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×D412yes—
79C2×C4×C283C2×D412yes—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2411yescharacteristic
82C22×C283—21no—
83C22×C283—22no—
84C22×C283C22×D411yescharacteristic
85C2×D283—42no—
86C2×D283—42no—
87C2×D283—42no—
88C4×C283—21no—
89C4×C283—22no—
90C4×C283—22no—
91C4×C283—42no—
92C4×C283—42no—
93C4×C283H(5,𝔽2)11yescharacteristic
94C4×C2832−1+411yescharacteristic
95Dic283—42no—
96C2×C283—41no—
97C2×C283#53711yescharacteristic
98C2×C283#57712yes—
99D283—82no—
100C283#326011yescharacteristic, complemented, Sylow
101#3260—2831nomaximal, Sylow
102#541D28311yescharacteristic, complemented
103#540—2831no—
104#479—2832no—
105#478—2832no—
106#468—2832no—
107#465—2832no—
108#461—2832no—
109#460—2832no—
110#424—2831no—
111C2×SD16—2832no—
112C2×SD16—2832no—
113C2×M16—2831no—
114C22×C8—2831no—
115C4⋊Q8C2×D28311yescharacteristic
116#127—2831no—
117#126—22no—
118#125—22no—
119#125—2831no—
120#125C2×D28311yescharacteristic
121#123—5662no—
122C22⋊Q8C2×D28312yes—
123#121—2832no—
124#121—5662no—
125C4×Q8C2×D28312yes—
126C4×D4—2832no—
127#117C2×D28311yescharacteristic
128#107—2832no—
129#106—2832no—
130C4⋊C8—2832no—
131C4⋊C8—2832no—
132#103—2832no—
133#103—2832no—
134#102—2832no—
135#102—2832no—
136C2×Q8C22×D28312yes—
137C2×D4—2832no—
138C2×D4—5662no—
139C2×D4—5662no—
140C22×C4—5662no—
141C22×C4C22×D28311yescharacteristic
142SD16—11322no—
143SD16—11322no—
144M16—11321no—
145C2×C8—2832no—
146C2×C8—2832no—
147C2×C8—11321no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—2832no—
153C4⋊C4—5662no—
154C4⋊C4C22⋊D28312yes—
155C4⋊C4C22×D28312yes—
156C22⋊C4—22no—
157C22⋊C4—5662no—
158C22⋊C4—5662no—
159C22⋊C4C22⋊D28312yes—
160C42—22no—
161C42C22×D28311yescharacteristic
162C42C22×D28311yescharacteristic
163C23—5662no—
164C23C2×C22⋊D28311yescharacteristic
165Q8—22no—
166Q8—22no—
167D4—5662no—
168D4—5662no—
169D4—22642no—
170D4—22642no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—5662no—
176C2×C4—22642no—
177C2×C4C2×C22⋊D28312yes—
178C2×C4C2×C22⋊D28312yes—
179C2×C4C2×C22⋊D28311yescharacteristic
180C2×C4C23×D28311yescharacteristic
181C8—5662no—
182C8—5662no—
183C22—22no—
184C22—21no—
185C22—11322no—
186C22—11322no—
187C22—11322no—
188C22C22×C22⋊D28311yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—42no—
193C4—42no—
194C4—11322no—
195C4#2258365611yescharacteristic
196C4#2258365711yescharacteristic
197C2—41no—
198C2—22642no—
199C2#3182704311yescharacteristic
200C2#3182727312yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#541×C283C2
socleC22×C283C22×D4
prime radical#31827070C2
hypercenter#541D283
hypocenterC283#3260
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #31826772C2semidirect
3. #31826762C2semidirect
4. #31826713C2semidirect
5. #31826696C2semidirect
6. #31826667C2semidirect
7. #31826665C2semidirect
8. #31826492C2semidirect
9. #541×C283C2semidirect
100. C283#3260semidirect
102. #541D283semidirect

Maximal subgroups

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

subgroupindex
#318270702
#318267722
#318267622
#318267132
#318266962
#318266672
#318266652
#318264922
#541×C2832
#3260283