Finite Group Databasebeta

← #49119847

Subgroups — #49119847

Order 36224.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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
2C4×#17985376C211yesmaximal, characteristic, complemented
3#31826206C212yesmaximal, complemented
4#31826204C212yesmaximal, complemented
5C2×#97×C283C211yesmaximal, characteristic, complemented
6C2×#17985376—21no—
7#22583604—21no—
8#22583602C2211yescharacteristic
9#22583598C2211yescharacteristic
10#22583593—21no—
11#22583589C411yescharacteristic
12#22583584C411yescharacteristic
13C4×Dic566C411yescharacteristic
14C4×D1132C411yescharacteristic
15C4×C22⋊D283—21no—
16#22583567—21no—
17#22583521C2212yes—
18C4×C283⋊C8—21no—
19C22×C8×C283—21no—
20C2×C42×C283C2211yescharacteristic
21#97×C283—21no—
22#97×C283C2212yes—
23C2×Dic566C2×C411yescharacteristic
24C2×D1132C2×C411yescharacteristic
25C2×C22⋊D283—21no—
26C2×C4×D283—21no—
27#17985376—24no—
28C2×C283⋊C8—22no—
29C4⋊Dic283C2×C411yescharacteristic
30C4⋊Dic283C2×C411yescharacteristic
31Dic283⋊C4—21no—
32Dic283⋊C4—21no—
33Dic283⋊C4—21no—
34Dic283⋊C4—21no—
35C22⋊Dic283—21no—
36(C2×D283)⋊C4—21no—
37(C2×D283)⋊C4—21no—
38(C2×D283)⋊C4—21no—
39(C2×D283)⋊C4—21no—
40C4×Dic283—21no—
41C22×C4×C283C2×C411yescharacteristic
42C22×C4×C283D411yescharacteristic
43C22×C4×C283D411yescharacteristic
44C2×C8×C283—24no—
45C2×C8×C283—22no—
46C42×C283C2×C411yescharacteristic
47C42×C283D411yescharacteristic
48C42×C283D411yescharacteristic
49C42×C283C2311yescharacteristic
50C22×D283—21no—
51Dic566—41no—
52D1132—41no—
53C22⋊D283—42no—
54C2×Dic283—21no—
55C2×Dic283—21no—
56C2×Dic283—21no—
57C4×D283—42no—
58C283⋊C8—24no—
59C23×C283C22⋊C411yescharacteristic
60C2×C4×C283—22no—
61C2×C4×C283—22no—
62C2×C4×C283—41no—
63C2×C4×C283C22⋊C411yescharacteristic
64C2×C4×C283C22⋊C411yescharacteristic
65C2×C4×C283C22⋊C411yescharacteristic
66C2×C4×C283C22×C411yescharacteristic
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C8×C283—24no—
70C22×C283—21no—
71C22×C283—21no—
72C22×C283#10412yes—
73C22×C283C2×C22⋊C411yescharacteristic
74C2×D283—41no—
75C2×D283—41no—
76C2×D283—41no—
77C4×C283—21no—
78C4×C283—21no—
79C4×C283—21no—
80C4×C283—21no—
81C4×C283—21no—
82C4×C283#10412yes—
83Dic283—41no—
84Dic283—41no—
85Dic283—41no—
86C2×C283—22no—
87C2×C283#41311yescharacteristic
88C2×C283C2×#10411yescharacteristic
89C2×C283C2×#10411yescharacteristic
90D283—81no—
91C283#152411yescharacteristic, complemented, Sylow
92#1524—2831nomaximal, Sylow
93#529—2831no—
94C4×M16—2831no—
95C2×#97D28311yescharacteristic, complemented
96#330—2832no—
97#329—2832no—
98C2×M16—5661no—
99C22×C8—21no—
100#126—5661no—
101#125—2831no—
102#124—2831no—
103#123—5661no—
104C22⋊Q8—2831no—
105#121—2831no—
106C4×Q8—2831no—
107C4×D4—2831no—
108C4×D4—5661no—
109#117—5661no—
110C2×C42C2×D28311yescharacteristic
111#97—21no—
112#97—2832no—
113#97C2×D28312yes—
114C4×C8—5661no—
115C2×Q8—2831no—
116C2×D4—2831no—
117C2×D4—5661no—
118C22×C4—5661no—
119C22×C4C4×D28311yescharacteristic
120C22×C4C22⋊D28311yescharacteristic
121C22×C4D113211yescharacteristic
122M16—5664no—
123C2×C8—24no—
124C2×C8—22no—
125C2×C8—5662no—
126C4⋊C4—2831no—
127C4⋊C4—2831no—
128C4⋊C4—5661no—
129C4⋊C4—5661no—
130C4⋊C4—5661no—
131C4⋊C4—5661no—
132C22⋊C4—5661no—
133C22⋊C4—5661no—
134C22⋊C4—5661no—
135C22⋊C4—5661no—
136C22⋊C4—5661no—
137C42—5661no—
138C42C4×D28311yescharacteristic
139C42C22⋊D28311yescharacteristic
140C42D113211yescharacteristic
141C42C22×D28311yescharacteristic
142C23—5661no—
143C23(C2×D283)⋊C411yescharacteristic
144Q8—11321no—
145D4—11321no—
146D4—11322no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—5661no—
151C2×C4—5661no—
152C2×C4—5661no—
153C2×C4—11322no—
154C2×C4(C2×D283)⋊C411yescharacteristic
155C2×C4(C2×D283)⋊C411yescharacteristic
156C2×C4(C2×D283)⋊C411yescharacteristic
157C2×C4C2×C4×D28311yescharacteristic
158C2×C4C2×C22⋊D28311yescharacteristic
159C2×C4C2×D113211yescharacteristic
160C8—24no—
161C8—5664no—
162C22—21no—
163C22—21no—
164C22—11321no—
165C22—11321no—
166C22—11321no—
167C22#2258353612yes—
168C22C2×(C2×D283)⋊C411yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—11321no—
175C4—11321no—
176C4—11321no—
177C4#2258353812yes—
178C2—22no—
179C2—22641no—
180C2#3182644711yescharacteristic
181C2C2×#2258353611yescharacteristic
182C2C2×#2258353811yescharacteristic
subgroupG/H
centerC2×C4(C2×D283)⋊C4
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
FittingC2×#97×C283C2
socleC22×C283C2×C22⋊C4
prime radical#22583584C4
cosocleC42×C283C23
hypercenterC2×#97D283
hypocenterC283#1524
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C4×#17985376C2semidirect
3. #31826206C2semidirect
4. #31826204C2semidirect
5. C2×#97×C283C2semidirect
91. C283#1524semidirect
95. C2×#97D283semidirect

Maximal subgroups

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

subgroupindex
#318269992
C4×#179853762
#318262062
#318262042
C2×#97×C2832
#1524283