Finite Group Databasebeta

← #49120396

Subgroups — #49120396

Order 36224.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#31827176C211yesmaximal, characteristic
2#31826844C211yesmaximal, characteristic, complemented
3#31826761C211yesmaximal, characteristic, complemented
4#31826756C211yesmaximal, characteristic
5#31826195C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic
7#333×C283C211yesmaximal, characteristic, complemented
8C2×#17985382—22no—
9#22583610C2211yescharacteristic
10#22583601—21no—
11#22583590—21no—
12#22583586—22no—
13C4×Dic566C2211yescharacteristic
14C4×D1132C2211yescharacteristic
15#22583572—21no—
16C4⋊C4×D283—21no—
17#22583544—21no—
18#22583542—21no—
19#22583535—21no—
20#22583532—21no—
21C4×C283⋊C8C2211yescharacteristic
22C4⋊Q8×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25C2×Dic566—21no—
26C2×Dic566D411yescharacteristic
27C2×D1132D411yescharacteristic
28C2×C4×D283—22no—
29C2×C4×D283—21no—
30#17985382—44no—
31C2×C283⋊C8—21no—
32C4⋊Dic283—22no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283D411yescharacteristic
36C4⋊Dic283D411yescharacteristic
37Dic283⋊C4—22no—
38Dic283⋊C4—21no—
39(C2×D283)⋊C4—22no—
40(C2×D283)⋊C4—21no—
41C4×Dic283—21no—
42C2×Q8×C283D412yes—
43C2×C8×C283—21no—
44C2×C8×C283—21no—
45C4⋊C4×C283—21no—
46C4⋊C4×C283—21no—
47C42×C283C2311yescharacteristic
48C22×D283—21no—
49Dic566—21no—
50Dic566—21no—
51Dic566—42no—
52D1132—21no—
53D1132Q1612yescomplemented
54C2×Dic283—21no—
55C2×Dic283—21no—
56C2×Dic283—21no—
57C2×Dic283—41no—
58C4×D283—41no—
59C4×D283—41no—
60C4×D283—82no—
61C283⋊C8—22no—
62Q8×C283—42no—
63C2×C4×C283—22no—
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283C2×D411yescharacteristic
66C2×C4×C283C2×D411yescharacteristic
67C8×C283—41no—
68C8×C283—41no—
69C22×C283#12011yescharacteristic
70C2×D283—22no—
71C2×D283—41no—
72C2×D283—41no—
73C4×C283—21no—
74C4×C283—42no—
75C4×C283C2×Q1611yescharacteristic
76C4×C283#13511yescharacteristic
77C4×C283#13711yescharacteristic
78C4×C283#13711yescharacteristic
79Dic283—41no—
80Dic283—41no—
81Dic283—41no—
82Dic283—81no—
83C2×C283#45111yescharacteristic
84C2×C283#45211yescharacteristic
85C2×C283#45311yescharacteristic
86D283—42no—
87C283#163211yescharacteristic, complemented, Sylow
88#1632—2831nomaximal, Sylow
89#554—2831no—
90#494—2831no—
91#477—2831no—
92#476—2831no—
93#333D28311yescharacteristic, complemented
94Q8⋊C8—2831no—
95D4⋊C8—2831no—
96C2×Q16—5662no—
97C4⋊Q8—2831no—
98C4⋊Q8C2×D28311yescharacteristic
99#125—5661no—
100C22⋊Q8—5661no—
101C22⋊Q8—5662no—
102C4×Q8—2831no—
103C4×D4—2831no—
104C4×D4—5661no—
105C2×C4⋊C4—5661no—
106#107—5661no—
107#106—5661no—
108C4⋊C8C2×D28311yescharacteristic
109C4⋊C8C2×D28311yescharacteristic
110#103—5661no—
111#102—5661no—
112C4×C8—2831no—
113C2×Q8—2831no—
114C2×Q8—5661no—
115C2×Q8D113212yes—
116C2×D4—2831no—
117C22×C4—5662no—
118C22×C4—5661no—
119Q16—11324no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5661no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—2831no—
126C4⋊C4—2831no—
127C4⋊C4—5662no—
128C4⋊C4—5662no—
129C4⋊C4—5661no—
130C4⋊C4—5661no—
131C4⋊C4—5661no—
132C22⋊C4—5662no—
133C22⋊C4—5661no—
134C42—5661no—
135C42C22×D28311yescharacteristic
136C23—5661no—
137Q8—42no—
138Q8—5661no—
139Q8—5661no—
140Q8—11322no—
141D4—2832no—
142D4—5661no—
143C2×C4—22no—
144C2×C4—5661no—
145C2×C4—5661no—
146C2×C4—5661no—
147C2×C4—11321no—
148C2×C4—11321no—
149C2×C4—11321no—
150C2×C4—22642no—
151C2×C4D4×D28311yescharacteristic
152C2×C4D4×D28311yescharacteristic
153C2×C4C2×D113211yescharacteristic
154C8—41no—
155C8—41no—
156C8—5662no—
157C22—5662no—
158C22—11321no—
159C22—11321no—
160C22#2258358011yescharacteristic
161C4—21no—
162C4—42no—
163C4—11321no—
164C4—11321no—
165C4—11321no—
166C4—22641no—
167C4Q16×D28311yescharacteristic
168C4#2258363111yescharacteristic
169C4#2258363911yescharacteristic
170C4#2258364211yescharacteristic
171C2—11322no—
172C2#3182662211yescharacteristic
173C2#3182663011yescharacteristic
174C2#3182663511yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#333×C283C2
socleC22×C283#120
prime radicalC2×D1132D4
hypercenter#333D283
hypocenterC283#1632
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #31826844C2semidirect
3. #31826761C2semidirect
5. #31826195C2semidirect
7. #333×C283C2semidirect
53. D1132Q16semidirect
87. C283#1632semidirect
93. #333D283semidirect

Maximal subgroups

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

subgroupindex
#318271762
#318268442
#318267612
#318267562
#318261952
#318261922
#333×C2832
#1632283