Finite Group Databasebeta

← #49121363

Subgroups — #49121363

Order 36224.

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

normal subgroups only

This group has 262 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#31826933C211yesmaximal, characteristic
2#31826447C211yesmaximal, characteristic
3#31826438C211yesmaximal, characteristic
4#31826226C211yesmaximal, characteristic, complemented
5#31826224C211yesmaximal, characteristic, complemented
6#31826221C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C2×#17985376C2211yescharacteristic
10#22583575—21no—
11#22583572—21no—
12(C22⋊D283)⋊C4—22no—
13#22583569C2211yescharacteristic
14#22583567C412yescomplemented
15C2×C4×Dic283C2211yescharacteristic
16C42×D283C412yescomplemented
17#22583528—21no—
18#22583526—21no—
19#22583524—22no—
20C2×M16×C283C2211yescharacteristic
21#117×C283C2211yescharacteristic
22#117×C283C2211yescharacteristic
23#17985392—21no—
24#17985392—21no—
25#17985392—21no—
26#17985392—21no—
27C2×Dic566D411yescharacteristic
28C2×D1132D411yescharacteristic
29C2×C22⋊D283D412yes—
30C22×Dic283—21no—
31C2×C4×D283—22no—
32C2×C4×D283C2×C412yes—
33#17985376—21no—
34#17985376—21no—
35C2×C283⋊C8—21no—
36C4⋊Dic283—21no—
37Dic283⋊C4—22no—
38C22⋊Dic283—21no—
39(C2×D283)⋊C4—22no—
40C4×Dic283—22no—
41C4×Dic283—21no—
42C4×Dic283—21no—
43C4×Dic283C2×C411yescharacteristic
44C4×Dic283C2×C411yescharacteristic
45C22×C4×C283C2311yescharacteristic
46M16×C283—21no—
47M16×C283—21no—
48C2×C8×C283—21no—
49C4⋊C4×C283—21no—
50C4⋊C4×C283—21no—
51C22⋊C4×C283—21no—
52C22⋊C4×C283—21no—
53C42×C283—21no—
54C42×C283C2×C412yes—
55C22×D283C22⋊C412yes—
56Dic566—21no—
57Dic566—21no—
58D1132—21no—
59D1132—21no—
60C22⋊D283—22no—
61C22⋊D283—22no—
62C2×Dic283—21no—
63C2×Dic283—21no—
64C2×Dic283—42no—
65C2×Dic283—41no—
66C2×Dic283C22⋊C412yes—
67C4×D283—22no—
68C4×D283—22no—
69C4×D283—44no—
70C283⋊C8—41no—
71C23×C283C2×D411yescharacteristic
72C2×C4×C283—22no—
73C2×C4×C283—41no—
74C2×C4×C283C22×C411yescharacteristic
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283#4111yescharacteristic
77C2×C4×C283#4111yescharacteristic
78C2×C4×C283#4111yescharacteristic
79C2×C4×C283#4111yescharacteristic
80C8×C283—41no—
81C22×C283—41no—
82C22×C283C2×C22⋊C411yescharacteristic
83C22×C283#12311yescharacteristic
84C22×C283#12311yescharacteristic
85C2×D283—22no—
86C2×D283—42no—
87C4×C283—42no—
88C4×C283—81no—
89C4×C283#11711yescharacteristic
90C4×C283#11711yescharacteristic
91C4×C283#12311yescharacteristic
92C4×C283#12311yescharacteristic
93Dic283—22no—
94Dic283—22no—
95Dic283—41no—
96Dic283—81no—
97C2×C283—21no—
98C2×C283—21no—
99C2×C283—21no—
100C2×C283#38111yescharacteristic
101D283—42no—
102C283#182711yescharacteristic, complemented, Sylow
103#1827—2831nomaximal, Sylow
104C4×#41—2831no—
105#413—2831no—
106#410—2831no—
107#339—2831no—
108#339—2831no—
109H(3,ℤ/4)—2831no—
110H(3,ℤ/4)D28311yescharacteristic, complemented
111C2×#41—2831no—
112C2×M16—2831no—
113C2×M16C2×D28311yescharacteristic
114C4×Q8—5661no—
115C4×D4—5662no—
116C4×D4—5661no—
117#117—2832no—
118#117—2831no—
119#117C2×D28311yescharacteristic
120#117C2×D28311yescharacteristic
121C2×C42—2831no—
122C2×C42—2832no—
123#101—5661no—
124#100—5661no—
125#99—5662no—
126#41—5661no—
127#41—5661no—
128#41—5661no—
129#41—5661no—
130C2×Q8—2831no—
131C2×D4—2832no—
132C2×D4—2831no—
133C22×C4—2832no—
134C22×C4—5662no—
135C22×C4—5661no—
136C22×C4C22×D28311yescharacteristic
137M16—21no—
138M16—21no—
139M16—5661no—
140M16—5661no—
141C2×C8—21no—
142C2×C8—5661no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—5662no—
146C4⋊C4—5661no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—5662no—
150C22⋊C4—5661no—
151C42—21no—
152C42—2831no—
153C42—2831no—
154C42—5662no—
155C42—5661no—
156C42—5661no—
157C42C4×D28312yes—
158C23—2832no—
159C23D4×D28311yescharacteristic
160Q8—5661no—
161Q8—5661no—
162D4—5662no—
163D4—5662no—
164D4—5661no—
165D4—5661no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—2832no—
169C2×C4—5661no—
170C2×C4—5662no—
171C2×C4—5662no—
172C2×C4—5661no—
173C2×C4—11324no—
174C2×C4—11322no—
175C2×C4—11321no—
176C2×C4C2×C4×D28311yescharacteristic
177C2×C4D4×D28311yescharacteristic
178C2×C4#1798539111yescharacteristic
179C2×C4#1798539211yescharacteristic
180C2×C4#1798539211yescharacteristic
181C2×C4#1798539311yescharacteristic
182C8—41no—
183C8—11321no—
184C22—41no—
185C22—5662no—
186C22—11322no—
187C22C22⋊C4×D28311yescharacteristic
188C22#2258359211yescharacteristic
189C22#2258359511yescharacteristic
190C4—42no—
191C4—81no—
192C4—5662no—
193C4—5662no—
194C4—11321no—
195C4—22641no—
196C4#2258356711yescharacteristic
197C4#2258356811yescharacteristic
198C4#2258359211yescharacteristic
199C4#2258359511yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—11322no—
204C2#3182632711yescharacteristic
subgroupG/H
centerC4#22583567
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingH(3,ℤ/4)×C283C2
socleC2×C283#381
prime radicalC2×#17985392C22
cosocleC22×C4×C283C23
hypercenterH(3,ℤ/4)D283
hypocenterC283#1827
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #31826226C2semidirect
5. #31826224C2semidirect
6. #31826221C2semidirect
7. H(3,ℤ/4)×C283C2semidirect
14. #22583567C4semidirect
16. C42×D283C4semidirect
102. C283#1827semidirect
110. H(3,ℤ/4)D283semidirect

Maximal subgroups

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

subgroupindex
#318269332
#318264472
#318264382
#318262262
#318262242
#318262212
H(3,ℤ/4)×C2832
#1827283