Finite Group Databasebeta

← #49119893

Subgroups — #49119893

Order 36224.

200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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#31826999C211yesmaximal, characteristic
2#31826522C211yesmaximal, characteristic, complemented
3#31826206C212yesmaximal, complemented
4#31826204C212yesmaximal, complemented
5#432×C283C211yesmaximal, characteristic, complemented
6#22583604—21no—
7#22583602C2211yescharacteristic
8#22583598C2211yescharacteristic
9#22583593—21no—
10#22583589C411yescharacteristic
11#22583584C411yescharacteristic
12C4×Dic566C411yescharacteristic
13C4×D1132C411yescharacteristic
14C4×C22⋊D283—21no—
15#22583567—21no—
16C4⋊(C283⋊C8)—21no—
17C22⋊(C283⋊C8)—21no—
18#22583521C2212yes—
19C2×C42×C283C2211yescharacteristic
20C4⋊C8×C283—21no—
21C22⋊C8×C283—21no—
22#97×C283C2212yes—
23C2×Dic566C2×C411yescharacteristic
24C2×D1132C2×C411yescharacteristic
25C2×C22⋊D283—21no—
26C2×C4×D283—21no—
27C2×C283⋊C8—22no—
28C4⋊Dic283C2×C411yescharacteristic
29C4⋊Dic283C2×C411yescharacteristic
30Dic283⋊C4—21no—
31Dic283⋊C4—21no—
32Dic283⋊C4—21no—
33Dic283⋊C4—21no—
34C22⋊Dic283—21no—
35(C2×D283)⋊C4—21no—
36(C2×D283)⋊C4—21no—
37(C2×D283)⋊C4—21no—
38(C2×D283)⋊C4—21no—
39C4×Dic283—21no—
40C22×C4×C283C2×C411yescharacteristic
41C22×C4×C283D411yescharacteristic
42C22×C4×C283D411yescharacteristic
43C2×C8×C283—22no—
44C42×C283C2×C411yescharacteristic
45C42×C283D411yescharacteristic
46C42×C283D411yescharacteristic
47C42×C283C2311yescharacteristic
48C22×D283—21no—
49Dic566—41no—
50D1132—41no—
51C22⋊D283—42no—
52C2×Dic283—21no—
53C2×Dic283—21no—
54C2×Dic283—21no—
55C4×D283—42no—
56C283⋊C8—42no—
57C23×C283C22⋊C411yescharacteristic
58C2×C4×C283—41no—
59C2×C4×C283—41no—
60C2×C4×C283—41no—
61C2×C4×C283C22⋊C411yescharacteristic
62C2×C4×C283C22⋊C411yescharacteristic
63C2×C4×C283C22⋊C411yescharacteristic
64C2×C4×C283C22×C411yescharacteristic
65C2×C4×C283C2×D411yescharacteristic
66C2×C4×C283C2×D411yescharacteristic
67C8×C283—42no—
68C22×C283—21no—
69C22×C283—21no—
70C22×C283—21no—
71C22×C283C2×C22⋊C411yescharacteristic
72C2×D283—41no—
73C2×D283—41no—
74C2×D283—41no—
75C4×C283—21no—
76C4×C283—21no—
77C4×C283—21no—
78C4×C283—21no—
79C4×C283—21no—
80C4×C283—21no—
81Dic283—41no—
82Dic283—41no—
83Dic283—41no—
84C2×C283—41no—
85C2×C283#41311yescharacteristic
86C2×C283#42111yescharacteristic
87C2×C283#42111yescharacteristic
88D283—81no—
89C283#153511yescharacteristic, complemented, Sylow
90#1535—2831nomaximal, Sylow
91#529—2831no—
92#432—2831no—
93#432D28311yescharacteristic, complemented
94#330—2832no—
95#329—2832no—
96#126—5661no—
97#125—2831no—
98#124—2831no—
99#123—5661no—
100C22⋊Q8—2831no—
101#121—2831no—
102C4×Q8—2831no—
103C4×D4—2831no—
104C4×D4—5661no—
105#117—5661no—
106C2×C42C2×D28311yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—5661no—
109C22⋊C8—21no—
110C22⋊C8—5661no—
111#97—2832no—
112#97C2×D28312yes—
113C2×Q8—2831no—
114C2×D4—2831no—
115C2×D4—5661no—
116C22×C4—5661no—
117C22×C4C4×D28311yescharacteristic
118C22×C4C22⋊D28311yescharacteristic
119C22×C4D113211yescharacteristic
120C2×C8—22no—
121C2×C8—5662no—
122C4⋊C4—2831no—
123C4⋊C4—2831no—
124C4⋊C4—5661no—
125C4⋊C4—5661no—
126C4⋊C4—5661no—
127C4⋊C4—5661no—
128C22⋊C4—5661no—
129C22⋊C4—5661no—
130C22⋊C4—5661no—
131C22⋊C4—5661no—
132C22⋊C4—5661no—
133C42—5661no—
134C42C4×D28311yescharacteristic
135C42C22⋊D28311yescharacteristic
136C42D113211yescharacteristic
137C42C22×D28311yescharacteristic
138C23—5661no—
139C23(C2×D283)⋊C411yescharacteristic
140Q8—11321no—
141D4—11321no—
142D4—11322no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—5661no—
147C2×C4—5661no—
148C2×C4—5661no—
149C2×C4—11322no—
150C2×C4(C2×D283)⋊C411yescharacteristic
151C2×C4(C2×D283)⋊C411yescharacteristic
152C2×C4(C2×D283)⋊C411yescharacteristic
153C2×C4C2×C4×D28311yescharacteristic
154C2×C4C2×C22⋊D28311yescharacteristic
155C2×C4C2×D113211yescharacteristic
156C8—42no—
157C8—11322no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—11321no—
162C22—11321no—
163C22—11321no—
164C22C2×(C2×D283)⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—11321no—
172C4—11321no—
173C4—11321no—
174C2—41no—
175C2—22641no—
176C2#3182644711yescharacteristic
177C2#3182648111yescharacteristic
178C2#3182648311yescharacteristic
subgroupG/H
centerC22C2×(C2×D283)⋊C4
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#432×C283C2
socleC22×C283C2×C22⋊C4
prime radical#22583584C4
cosocleC42×C283C23
hypercenter#432D283
hypocenterC283#1535
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #31826522C2semidirect
3. #31826206C2semidirect
4. #31826204C2semidirect
5. #432×C283C2semidirect
89. C283#1535semidirect
93. #432D283semidirect

Maximal subgroups

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

subgroupindex
#318269992
#318265222
#318262062
#318262042
#432×C2832
#1535283