Finite Group Databasebeta

← #49119672

Subgroups — #49119672

Order 36224.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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#31826195C212yesmaximal, complemented
4#31826192C212yesmaximal, complemented
5C2×C4⋊C8×C283C211yesmaximal, characteristic, complemented
6C2×#17985376—21no—
7#22583604—21no—
8#22583602C411yescharacteristic
9#22583598C411yescharacteristic
10#22583593—21no—
11#22583589C411yescharacteristic
12#22583584C411yescharacteristic
13C4×Dic566C2211yescharacteristic
14C4×D1132C2211yescharacteristic
15C4×C22⋊D283—21no—
16#22583567—21no—
17#22583521—21no—
18C4×C283⋊C8C2212yes—
19C22×C8×C283—21no—
20C2×C42×C283C2211yescharacteristic
21C4⋊C8×C283—21no—
22C4⋊C8×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—22no—
45C2×C8×C283—42no—
46C42×C283C2×C411yescharacteristic
47C42×C283D411yescharacteristic
48C42×C283D411yescharacteristic
49C42×C283C2311yescharacteristic
50C22×D283—21no—
51Dic566—22no—
52D1132—22no—
53C22⋊D283—42no—
54C2×Dic283—21no—
55C2×Dic283—21no—
56C2×Dic283—21no—
57C4×D283—41no—
58C4×D283—41no—
59C283⋊C8—24no—
60C23×C283C22⋊C411yescharacteristic
61C2×C4×C283—22no—
62C2×C4×C283—22no—
63C2×C4×C283—21no—
64C2×C4×C283—21no—
65C2×C4×C283C22⋊C411yescharacteristic
66C2×C4×C283C22⋊C411yescharacteristic
67C2×C4×C283C22⋊C411yescharacteristic
68C2×C4×C283C22×C411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283C2×D411yescharacteristic
71C8×C283—42no—
72C22×C283—21no—
73C22×C283—21no—
74C22×C283#10412yes—
75C22×C283C2×C22⋊C411yescharacteristic
76C2×D283—41no—
77C2×D283—41no—
78C2×D283—41no—
79C4×C283—21no—
80C4×C283—21no—
81C4×C283—21no—
82C4×C283—21no—
83C4×C283#13112yes—
84C4×C283AGL(1,ℤ/8)11yescharacteristic
85C4×C283#13711yescharacteristic
86Dic283—41no—
87Dic283—41no—
88Dic283—41no—
89C2×C283—22no—
90C2×C283#40811yescharacteristic
91C2×C283#41711yescharacteristic
92C2×C283C2×#10411yescharacteristic
93D283—81no—
94C283#148311yescharacteristic, complemented, Sylow
95#1483—2831nomaximal, Sylow
96#529—2831no—
97C2×C4⋊C8D28311yescharacteristic, complemented
98C4×M16—2831no—
99Q8⋊C8—2832no—
100D4⋊C8—2832no—
101C2×M16—5661no—
102C22×C8—21no—
103#126—5661no—
104#125—2831no—
105#124—2831no—
106#123—5661no—
107C22⋊Q8—2831no—
108#121—2831no—
109C4×Q8—2831no—
110C4×D4—2831no—
111C4×D4—5661no—
112#117—5661no—
113C2×C42C2×D28311yescharacteristic
114C4⋊C8—21no—
115C4⋊C8C2×D28312yes—
116#97—5661no—
117C4×C8—2832no—
118C2×Q8—2831no—
119C2×D4—2831no—
120C2×D4—5661no—
121C22×C4—5661no—
122C22×C4C4×D28311yescharacteristic
123C22×C4C22⋊D28311yescharacteristic
124C22×C4D113211yescharacteristic
125M16—5664no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—5662no—
129C4⋊C4—2831no—
130C4⋊C4—2831no—
131C4⋊C4—5661no—
132C4⋊C4—5661no—
133C4⋊C4—5661no—
134C4⋊C4—5661no—
135C22⋊C4—5661no—
136C22⋊C4—5661no—
137C22⋊C4—5661no—
138C22⋊C4—5661no—
139C22⋊C4—5661no—
140C42—5661no—
141C42C4×D28311yescharacteristic
142C42C22⋊D28311yescharacteristic
143C42D113211yescharacteristic
144C42C22×D28311yescharacteristic
145C23—5661no—
146C23(C2×D283)⋊C411yescharacteristic
147Q8—5662no—
148D4—5662no—
149D4—11322no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—5661no—
155C2×C4—5661no—
156C2×C4—5661no—
157C2×C4—11321no—
158C2×C4—11321no—
159C2×C4(C2×D283)⋊C411yescharacteristic
160C2×C4(C2×D283)⋊C411yescharacteristic
161C2×C4(C2×D283)⋊C411yescharacteristic
162C2×C4C2×C4×D28311yescharacteristic
163C2×C4C2×C22⋊D28311yescharacteristic
164C2×C4C2×D113211yescharacteristic
165C8—42no—
166C8—5664no—
167C22—21no—
168C22—21no—
169C22—11321no—
170C22—11321no—
171C22—11321no—
172C22#2258353612yes—
173C22C2×(C2×D283)⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—11321no—
179C4—11321no—
180C4—11321no—
181C4#2258361612yes—
182C4#2258363611yescharacteristic
183C4#2258364111yescharacteristic
184C2—22no—
185C2—22641no—
186C2#3182643111yescharacteristic
187C2#3182646411yescharacteristic
188C2C2×#2258353611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
FittingC2×C4⋊C8×C283C2
socleC22×C283C2×C22⋊C4
prime radical#22583584C4
cosocleC42×C283C23
hypercenterC2×C4⋊C8D283
hypocenterC283#1483
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#17985376C2semidirect
3. #31826195C2semidirect
4. #31826192C2semidirect
5. C2×C4⋊C8×C283C2semidirect
94. C283#1483semidirect
97. C2×C4⋊C8D283semidirect

Maximal subgroups

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

subgroupindex
#318269992
C4×#179853762
#318261952
#318261922
C2×C4⋊C8×C2832
#1483283