Finite Group Databasebeta

← #355×D283 #49122937

Subgroups — #355×D283 #49122937

Order 36224.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D283C211yesmaximal, characteristic
2#101×D283C212yesmaximal, complemented
3#31826262C211yesmaximal, characteristic, complemented
4#31826261C212yesmaximal, complemented
5#355×C283C211yesmaximal, characteristic, complemented
6C2×Q8×D283C2211yescharacteristic
7C2×D4×D283C411yescharacteristic
8M16×D283—22no—
9#22583599C2211yescharacteristic
10#22583598C411yescharacteristic
11#22583597C411yescharacteristic
12#22583596—22no—
13C22⋊C4×D283—22no—
14C42×D283C411yescharacteristic
15#22583529C2212yescomplemented
16#22583528—22no—
17#124×C283C2211yescharacteristic
18#101×C283C2212yescomplemented
19C23×D283—21no—
20C2×Dic566C2×C411yescharacteristic
21C2×Dic566D412yes—
22Q8×D283—41no—
23Q8×D283—41no—
24C2×D1132C2×C411yescharacteristic
25C2×C22⋊D283—21no—
26D4×D283—41no—
27D4×D283—41no—
28C2×C4×D283—21no—
29C2×C4×D283C2×C411yescharacteristic
30C2×C4×D283D412yes—
31#17985376—22no—
32#17985375—42no—
33C8×D283—42no—
34C22⋊Dic283—22no—
35(C2×D283)⋊C4—22no—
36(C2×D283)⋊C4—22no—
37C4×Dic283—21no—
38C4×Dic283C2×C411yescharacteristic
39C2×Q8×C283C2311yescharacteristic
40C2×D4×C283C2×C411yescharacteristic
41M16×C283—22no—
42C22⋊C4×C283—22no—
43C42×C283C2×C411yescharacteristic
44C22×D283—21no—
45C22×D283—44no—
46C22×D283—41no—
47C22×D283—41no—
48C22×D283C22⋊C411yescharacteristic
49Dic566—41no—
50Dic566—42no—
51D1132—41no—
52C22⋊D283—42no—
53C2×Dic283—21no—
54C2×Dic283C22⋊C411yescharacteristic
55C2×Dic283C22⋊C412yes—
56C4×D283—22no—
57C4×D283—22no—
58C4×D283—21no—
59C4×D283—21no—
60C4×D283—42no—
61C283⋊C8—42no—
62C23×C283—21no—
63Q8×C283—41no—
64D4×C283—41no—
65C2×C4×C283—21no—
66C2×C4×C283C22×C411yescharacteristic
67C2×C4×C283C2×D412yes—
68C8×C283—42no—
69C22×C283—42no—
70C22×C283—41no—
71C22×C283C2×C22⋊C411yescharacteristic
72C2×D283—22no—
73C2×D283—42no—
74C2×D283—41no—
75C2×D283—82no—
76C2×D283—82no—
77C2×D283#9911yescharacteristic
78C2×D283#9911yescharacteristic
79C4×C283—22no—
80C4×C283—21no—
81C4×C283—41no—
82Dic283—21no—
83Dic283—22no—
84Dic283—41no—
85C2×C283—21no—
86C2×C283—81no—
87C2×C283C2×#9911yescharacteristic
88D283—21no—
89D283—81no—
90D283#35512yesdirect product factor
91C283C2×#35511yescharacteristic, complemented, Sylow
92C2×#355—2831nomaximal, Sylow
93C2×#124—2831no—
94C2×#101—2832no—
95#355—2831no—
96#355—2832no—
97#355D28311yescharacteristic, direct product factor
98C22×Q8—2831no—
99C22×D4—2831no—
100C2×M16—5662no—
101#124—2831no—
102#124—2831no—
103#124—2831no—
104#124—5662no—
105#124C2×D28311yescharacteristic
106C2×C22⋊C4—5662no—
107C2×C42—2831no—
108#101—2832no—
109#101—5662no—
110#101C2×D28312yescomplemented
111C24—5661no—
112C2×Q8—2831no—
113C2×Q8—2832no—
114C2×Q8—11321no—
115C2×Q8—11321no—
116C2×Q8C22×D28311yescharacteristic
117C2×D4—2831no—
118C2×D4—5661no—
119C2×D4—11321no—
120C2×D4—11321no—
121C2×D4C4×D28311yescharacteristic
122C22×C4—2831no—
123C22×C4—2832no—
124C22×C4—5661no—
125M16—22no—
126M16—5662no—
127M16—11322no—
128C2×C8—11322no—
129C22⋊C4—22no—
130C22⋊C4—5662no—
131C22⋊C4—5662no—
132C22⋊C4—5662no—
133C42—2831no—
134C42—5661no—
135C42C4×D28311yescharacteristic
136C23—21no—
137C23—2831no—
138C23—5661no—
139C23—11321no—
140C23—11321no—
141C23—11324no—
142Q8—41no—
143Q8—11322no—
144Q8—11321no—
145D4—41no—
146D4—11321no—
147D4—11322no—
148C2×C4—21no—
149C2×C4—2831no—
150C2×C4—2832no—
151C2×C4—5662no—
152C2×C4—5662no—
153C2×C4—5661no—
154C2×C4—5661no—
155C2×C4—5661no—
156C2×C4—11322no—
157C2×C4C2×C4×D28311yescharacteristic
158C2×C4D4×D28312yes—
159C8—42no—
160C8—11322no—
161C22—42no—
162C22—41no—
163C22—2831no—
164C22—2831no—
165C22—5662no—
166C22—11322no—
167C22—11321no—
168C22—22642no—
169C22—22642no—
170C22C22⋊C4×D28311yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—5661no—
175C4—5662no—
176C4—11321no—
177C2—21no—
178C2—81no—
179C2—2832no—
180C2—5661no—
181C2—22641no—
182C2#99×D28311yescharacteristic
subgroupG/H
centerC2#99×D283
commutatorC2×C4×C283C22×C4
FrattiniC2×Q8C22×D283
Fitting#355×C283C2
socleC2×C283C2×#99
prime radicalC2×D4×D283C4
cosocleC2×Q8×C283C23
hypercenter#355D283
hypocenterC283C2×#355
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D283C2semidirect
3. #31826262C2semidirect
4. #31826261C2semidirect
5. #355×C283C2semidirect
15. #22583529C22semidirect
18. #101×C283C22semidirect
90. D283#355direct (N × H)
91. C283C2×#355semidirect
97. #355D283direct (N × H)
110. #101C2×D283semidirect

Maximal subgroups

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

subgroupindex
#124×D2832
#101×D2832
#318262622
#318262612
#355×C2832
C2×#355283