Finite Group Databasebeta

← #49122175

Subgroups — #49122175

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#31826473C211yesmaximal, characteristic
4C2×#22583529C211yesmaximal, characteristic
5C2×#22583528C211yesmaximal, characteristic
6#31826421C211yesmaximal, characteristic
7#419×C283C211yesmaximal, characteristic
8C22×Dic566C2211yescharacteristic
9C2×#17985382—21no—
10C2×#17985382—21no—
11C2×#17985382—22no—
12C2×#17985382C414yescomplemented
13C2×#17985376C2211yescharacteristic
14C2×#17985376C2211yescharacteristic
15C22×C283⋊C8C2211yescharacteristic
16#22583545—22no—
17#22583533—22no—
18#22583529—22no—
19#22583528—22no—
20#22583521—21no—
21C4×C283⋊C8—21no—
22C22×Q8×C283C2211yescharacteristic
23C2×M16×C283C2211yescharacteristic
24#117×C283C2211yescharacteristic
25#103×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—
37#17985376—21no—
38#17985376D412yes—
39C2×C283⋊C8—21no—
40C2×C283⋊C8—21no—
41C2×C283⋊C8C2×C412yes—
42C2×C283⋊C8D411yescharacteristic
43C2×C283⋊C8D411yescharacteristic
44C2×C283⋊C8D412yes—
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—
55C2×C8×C283—21no—
56C4⋊C4×C283D412yes—
57C22⋊C4×C283—21no—
58C42×C283—21no—
59Dic566—22no—
60Dic566—22no—
61Dic566—41no—
62Dic566—41no—
63C2×Dic283—22no—
64C2×Dic283—41no—
65C2×Dic283—41no—
66C283⋊C8—22no—
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—22no—
77C2×C4×C283—41no—
78C2×C4×C283—41no—
79C2×C4×C283C22×C411yescharacteristic
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283#4111yescharacteristic
85C8×C283—41no—
86C22×C283—22no—
87C22×C283C4×D411yescharacteristic
88C22×C283#12111yescharacteristic
89C22×C283#12411yescharacteristic
90C4×C283—42no—
91C4×C283—42no—
92C4×C283C2×C22⋊C411yescharacteristic
93C4×C283C4×D411yescharacteristic
94C4×C283#12111yescharacteristic
95C4×C283#12711yescharacteristic
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#419D28311yescharacteristic
107C2×#101—2831no—
108C2×#101—2831no—
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×M16—2831no—
118C2×M16C2×D28311yescharacteristic
119C22×C8—2831no—
120#117C2×D28311yescharacteristic
121#108—5662no—
122#103—22no—
123#103—5662no—
124#101—5662no—
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—2832no—
148M16—5661no—
149M16—5661no—
150M16—5661no—
151C2×C8—21no—
152C2×C8—2832no—
153C2×C8—2831no—
154C2×C8—2831no—
155C2×C8—2832no—
156C2×C8—5661no—
157C2×C8—5661no—
158C4⋊C4C22⋊D28312yes—
159C22⋊C4—21no—
160C42—21no—
161C23#1798539111yescharacteristic
162Q8—22no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—5662no—
167Q8—5662no—
168Q8—11321no—
169Q8—11321no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
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#1798539211yescharacteristic
183C8—41no—
184C8—2832no—
185C8—2832no—
186C8—5662no—
187C8—11321no—
188C22—22no—
189C22(C22⋊D283)⋊C411yescharacteristic
190C22#2258358211yescharacteristic
191C22#2258359611yescharacteristic
192C4—42no—
193C4—42no—
194C4—11322no—
195C4C22⋊C4×D28311yescharacteristic
196C4C4×C22⋊D28311yescharacteristic
197C4#2258358311yescharacteristic
198C4#2258360611yescharacteristic
199C2—21no—
200C2—21no—
201C2#3182636511yescharacteristic
202C2#3182673812yes—
subgroupG/H
centerC22#22583582
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#419×C283C2
socleC22×C283#121
prime radicalC23×C283#41
cosocleC22×C4×C283C23
hypercenter#419D283
hypocenterC283#1979
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

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
#318264732
C2×#225835292
C2×#225835282
#318264212
#419×C2832
#1979283