Finite Group Databasebeta

← #49122173

Subgroups — #49122173

Order 36224.

276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×#17985382C211yesmaximal, characteristic
2C2×#22583545C211yesmaximal, characteristic
3#31826475C211yesmaximal, characteristic
4#31826474C211yesmaximal, characteristic
5C2×#22583528C211yesmaximal, characteristic
6#31826423C211yesmaximal, characteristic
7C2×#101×C283C211yesmaximal, characteristic
8C22×Dic566C2211yescharacteristic
9C2×#17985382—21no—
10C2×#17985382—21no—
11C2×#17985382—22no—
12C2×#17985382C414yescomplemented
13C2×#17985376C2211yescharacteristic
14C22×C283⋊C8C2211yescharacteristic
15#22583569C2211yescharacteristic
16#22583545—22no—
17#22583535—22no—
18#22583534—22no—
19#22583528—22no—
20#22583520—21no—
21C8×Dic283—21no—
22C22×Q8×C283C2211yescharacteristic
23C2×M16×C283C2211yescharacteristic
24C2×M16×C283C2211yescharacteristic
25#101×C283—22no—
26C2×Dic566—21no—
27C2×Dic566—21no—
28C2×Dic566—21no—
29C2×Dic566—21no—
30C2×Dic566—21no—
31C2×Dic566C2×C412yes—
32C22×Dic283—21no—
33#17985382—24no—
34#17985382—24no—
35#17985376—21no—
36#17985376—21no—
37C2×C283⋊C8—21no—
38C2×C283⋊C8C2×C412yes—
39C2×C283⋊C8D411yescharacteristic
40C2×C283⋊C8D411yescharacteristic
41C2×C283⋊C8D412yes—
42C4⋊Dic283D412yes—
43C22⋊Dic283—21no—
44C4×Dic283—21no—
45C2×Q8×C283—21no—
46C2×Q8×C283—21no—
47C2×Q8×C283—21no—
48C2×Q8×C283—21no—
49C2×Q8×C283—21no—
50C2×Q8×C283C2×C412yes—
51C22×C4×C283—21no—
52C22×C4×C283C2311yescharacteristic
53M16×C283—21no—
54M16×C283—21no—
55M16×C283—21no—
56M16×C283D412yes—
57C2×C8×C283—21no—
58C2×C8×C283—21no—
59Dic566—22no—
60Dic566—22no—
61Dic566—41no—
62Dic566—41no—
63C2×Dic283—22no—
64C2×Dic283—22no—
65C2×Dic283—41no—
66C2×Dic283—41no—
67C283⋊C8—41no—
68C283⋊C8C22⋊C412yes—
69C283⋊C8C22⋊C412yes—
70C23×C283#4111yescharacteristic
71Q8×C283—22no—
72Q8×C283—22no—
73Q8×C283—41no—
74Q8×C283—41no—
75C2×C4×C283—22no—
76C2×C4×C283—41no—
77C2×C4×C283—41no—
78C2×C4×C283C22×C411yescharacteristic
79C2×C4×C283C2×D411yescharacteristic
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283#4111yescharacteristic
84C8×C283—22no—
85C8×C283—41no—
86C22×C283—22no—
87C22×C283C4×D411yescharacteristic
88C22×C283#12111yescharacteristic
89C22×C283#12411yescharacteristic
90C4×C283—42no—
91C4×C283C2×C22⋊C411yescharacteristic
92C4×C283C4×D411yescharacteristic
93C4×C283#12111yescharacteristic
94C4×C283#12711yescharacteristic
95Dic283—42no—
96Dic283—42no—
97C2×C283—21no—
98C2×C283—21no—
99C2×C283#39011yescharacteristic
100C2×C283#47312yes—
101C283#197911yescharacteristic, complemented, Sylow
102#1979—2831nomaximal, Sylow
103C22×Q16—2831no—
104C2×#108—2831no—
105#419—2831no—
106#419—2831no—
107C2×#101—2831no—
108C2×#101D28311yescharacteristic
109#405—2831no—
110C22×Q8—2831no—
111C22×Q8C2×D28311yescharacteristic
112C2×Q16—2834no—
113C2×Q16—5661no—
114C2×Q16—5661no—
115C2×Q16—5662no—
116C2×M16—2831no—
117C2×M16C2×D28311yescharacteristic
118C2×M16C2×D28311yescharacteristic
119C22×C8—2831no—
120#117—2831no—
121#108—5662no—
122#103—5662no—
123#103—5662no—
124#101—22no—
125#101—5662no—
126#97—5661no—
127C4×C8—5661no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—2832no—
134C2×Q8—5661no—
135C2×Q8—5661no—
136C2×Q8—5661no—
137C2×Q8—5661no—
138C2×Q8—5661no—
139C2×Q8C4×D28312yes—
140C22×C4—21no—
141C22×C4—5661no—
142C22×C4C22×D28311yescharacteristic
143Q16—5664no—
144Q16—5664no—
145M16—21no—
146M16—21no—
147M16—21no—
148M16—5661no—
149M16—5661no—
150M16C22⋊D28312yes—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—2832no—
154C2×C8—2831no—
155C2×C8—2831no—
156C2×C8—2832no—
157C2×C8—5661no—
158C4⋊C4—2832no—
159C22⋊C4—5661no—
160C42—5661no—
161C23#1798539211yescharacteristic
162Q8—22no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—5662no—
167Q8—5662no—
168Q8—11321no—
169Q8—11321no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—5662no—
174C2×C4—5662no—
175C2×C4—11321no—
176C2×C4—11321no—
177C2×C4C2×C4×D28311yescharacteristic
178C2×C4D4×D28311yescharacteristic
179C2×C4D4×D28311yescharacteristic
180C2×C4D4×D28311yescharacteristic
181C2×C4C2×C22⋊D28311yescharacteristic
182C2×C4#1798539111yescharacteristic
183C8—22no—
184C8—41no—
185C8—2832no—
186C8—2832no—
187C8—11321no—
188C22—22no—
189C22C4×C22⋊D28311yescharacteristic
190C22#2258358311yescharacteristic
191C22#2258359611yescharacteristic
192C4—42no—
193C4—11322no—
194C4—11322no—
195C4C22⋊C4×D28311yescharacteristic
196C4(C22⋊D283)⋊C411yescharacteristic
197C4#2258358211yescharacteristic
198C4#2258360611yescharacteristic
199C2—21no—
200C2—21no—
201C2#3182636511yescharacteristic
202C2#3182673912yes—
subgroupG/H
centerC22#22583583
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#101×C283C2
socleC22×C283#121
prime radicalC23×C283#41
cosocleC22×C4×C283C23
hypercenterC2×#101D283
hypocenterC283#1979
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
12. C2×#17985382C4semidirect
101. C283#1979semidirect

Maximal subgroups

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

subgroupindex
C22×#179853822
C2×#225835452
#318264752
#318264742
C2×#225835282
#318264232
C2×#101×C2832
#1979283