Finite Group Databasebeta

← #49133868

Subgroups — #49133868

Order 36224.

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

normal subgroups only

This group has 360 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#31827165C212yesmaximal, complemented
2#31826867C211yesmaximal, characteristic, complemented
3#31826787C212yesmaximal, complemented
4#31826777C212yesmaximal, complemented
5#31826765C212yesmaximal, complemented
6#31826715C212yesmaximal, complemented
7#31826544C211yesmaximal, characteristic, complemented
8#31826506C212yesmaximal, complemented
9C4×D8×C283C211yesmaximal, characteristic, complemented
10C2×#17985375C2212yes—
11#22583603—22no—
12#22583602C2212yes—
13#22583593—22no—
14#22583583—22no—
15#22583581C2212yes—
16#22583581C2212yes—
17C4×D1132C2211yescharacteristic
18C4×C22⋊D283—22no—
19#22583568C2212yes—
20C4⋊C4×D283C2212yes—
21#22583544C2211yescharacteristic
22#22583544C2211yescharacteristic
23#22583543C2212yes—
24#22583542C2212yes—
25#22583541C2212yes—
26C4⋊(C283⋊C8)C2211yescharacteristic
27#22583531C2212yes—
28#22583531C2212yes—
29(C2×D283)⋊C8C2212yes—
30C2×D8×C283C2211yescharacteristic
31C4×D4×C283C2212yes—
32#107×C283C2211yescharacteristic
33#102×C283C2212yes—
34C4×C8×C283C2211yescharacteristic
35C2×D1132D411yescharacteristic
36C2×C22⋊D283—22no—
37C2×C22⋊D283—22no—
38C2×C4×D283—22no—
39C2×C4×D283C2312yes—
40#17985375—24no—
41C2×C283⋊C8C2312yes—
42C4⋊Dic283D411yescharacteristic
43C4⋊Dic283C2312yes—
44C4⋊Dic283C2312yes—
45Dic283⋊C4—22no—
46Dic283⋊C4—22no—
47Dic283⋊C4—22no—
48C22⋊Dic283—22no—
49C22⋊Dic283—22no—
50(C2×D283)⋊C4—22no—
51(C2×D283)⋊C4D412yes—
52C4×Dic283—22no—
53C2×D4×C283C2312yes—
54C22×C4×C283—22no—
55D8×C283—22no—
56C2×C8×C283C2311yescharacteristic
57C2×C8×C283C2311yescharacteristic
58C4⋊C4×C283C2312yes—
59C22⋊C4×C283—22no—
60C42×C283C2311yescharacteristic
61C22×D283C2×D412yes—
62D1132—41no—
63C22⋊D283—44no—
64C22⋊D283—82no—
65C2×Dic283—22no—
66C2×Dic283—22no—
67C2×Dic283C2×D412yes—
68C4×D283—22no—
69C4×D283—22no—
70C4×D283—82no—
71C283⋊C8—22no—
72C23×C283—22no—
73D4×C283—22no—
74D4×C283—22no—
75C2×C4×C283—22no—
76C2×C4×C283—82no—
77C2×C4×C283C2×D411yescharacteristic
78C2×C4×C283C2×D411yescharacteristic
79C2×C4×C283C2411yescharacteristic
80C8×C283—21no—
81C8×C283#4112yes—
82C22×C283—42no—
83C22×C283—42no—
84C22×C283—42no—
85C22×C283C22×D411yescharacteristic
86C2×D283—22no—
87C2×D283—22no—
88C2×D283—22no—
89C4×C283—21no—
90C4×C283—21no—
91C4×C283—42no—
92C4×C283C2×#4111yescharacteristic
93C4×C2832−1+411yescharacteristic
94Dic283—22no—
95Dic283—42no—
96Dic283—42no—
97C2×C283—82no—
98C2×C283#54711yescharacteristic
99C2×C283#57511yescharacteristic
100C2×C283#57611yescharacteristic
101D283—42no—
102C283#335511yescharacteristic, complemented, Sylow
103#3355—2831nomaximal, Sylow
104#553—2832no—
105#499—2831no—
106#482—2832no—
107#480—2832no—
108#478—2832no—
109#469—2832no—
110C4×D8D28311yescharacteristic, complemented
111#436—2831no—
112#428—2832no—
113C2×D8C2×D28311yescharacteristic
114C2×M16—2832no—
115#126—5662no—
116#125—2832no—
117#123—5662no—
118#121—2832no—
119#121—2832no—
120#121—5662no—
121C4×D4—2831no—
122C4×D4—5662no—
123C4×D4C2×D28312yes—
124#117—2832no—
125C2×C4⋊C4—2832no—
126#107—2831no—
127#107—2831no—
128#107—2832no—
129#107C2×D28311yescharacteristic
130#106—2832no—
131#106—2832no—
132C4⋊C8—2831no—
133#102—2832no—
134#102—2832no—
135#102C2×D28312yes—
136C22⋊C8—2832no—
137C4×C8C2×D28311yescharacteristic
138C2×D4—2831no—
139C2×D4—5662no—
140C2×D4—5662no—
141C2×D4C22×D28312yes—
142C22×C4—22no—
143C22×C4—2832no—
144C22×C4—5662no—
145D8—22no—
146M16—5664no—
147C2×C8—2832no—
148C2×C8C22×D28311yescharacteristic
149C2×C8C22×D28311yescharacteristic
150C4⋊C4—2831no—
151C4⋊C4—2832no—
152C4⋊C4—2832no—
153C4⋊C4—5662no—
154C4⋊C4—5662no—
155C4⋊C4—5662no—
156C4⋊C4C22×D28312yes—
157C22⋊C4—22no—
158C22⋊C4—2832no—
159C22⋊C4—5662no—
160C22⋊C4—5662no—
161C22⋊C4—5662no—
162C42—5662no—
163C42C22×D28311yescharacteristic
164C23—22no—
165C23—2832no—
166D4—22no—
167D4—22no—
168D4—11321no—
169D4—11324no—
170D4—22642no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—2832no—
174C2×C4—5662no—
175C2×C4—5662no—
176C2×C4—5662no—
177C2×C4—5662no—
178C2×C4—22642no—
179C2×C4D4×D28311yescharacteristic
180C2×C4D4×D28311yescharacteristic
181C2×C4C23×D28311yescharacteristic
182C8—21no—
183C8—5662no—
184C8#1798539212yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—5662no—
189C22—5662no—
190C22—5662no—
191C22C2×D4×D28311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—5662no—
196C4—11322no—
197C4—11322no—
198C4C2×#1798539211yescharacteristic
199C4#2258365711yescharacteristic
200C2—82no—
201C2—11322no—
202C2#3182712011yescharacteristic
203C2#3182726211yescharacteristic
204C2#3182726611yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×D8×C283C2
socleC22×C283C22×D4
hypercenterC4×D8D283
hypocenterC283#3355
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31827165C2semidirect
2. #31826867C2semidirect
3. #31826787C2semidirect
4. #31826777C2semidirect
5. #31826765C2semidirect
6. #31826715C2semidirect
7. #31826544C2semidirect
8. #31826506C2semidirect
9. C4×D8×C283C2semidirect
102. C283#3355semidirect
110. C4×D8D283semidirect

Maximal subgroups

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

subgroupindex
#318271652
#318268672
#318267872
#318267772
#318267652
#318267152
#318265442
#318265062
C4×D8×C2832
#3355283