Finite Group Databasebeta

← #49130787

Subgroups — #49130787

Order 36224.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#22583640C211yesmaximal, characteristic
2C22×#17985382C211yesmaximal, characteristic, complemented
3#31826942C211yesmaximal, characteristic, complemented
4#31826684C214yesmaximal, complemented
5#31826672C214yesmaximal, complemented
6#31826492C211yesmaximal, characteristic, complemented
7#31826474C211yesmaximal, characteristic, complemented
8#31826461C211yesmaximal, characteristic
9#536×C283C211yesmaximal, characteristic
10C22×Dic566C2211yescharacteristic
11#22583640—24no—
12C2×#17985382—24no—
13C2×#17985382C2214yes—
14C2×#17985382C2212yes—
15C2×#17985380C2212yes—
16C2×#17985376C2211yescharacteristic
17C22×C283⋊C8C2211yescharacteristic
18C4×Dic566C2214yes—
19#22583575—22no—
20#22583569C2211yescharacteristic
21#22583566—22no—
22C4⋊(C283⋊C8)C2214yes—
23#22583534C2212yes—
24#22583534C2214yes—
25#22583531C2212yes—
26C2×#41×C283C2211yescharacteristic
27C22×Q8×C283C2211yescharacteristic
28C4⋊Q8×C283C2212yes—
29#124×C283C2212yes—
30#123×C283—22no—
31C22⋊Q8×C283—22no—
32#117×C283C2211yescharacteristic
33C2×Dic566—21no—
34C2×Dic566—22no—
35C2×Dic566D414yes—
36C2×Dic566C2312yes—
37C22×Dic283—21no—
38#17985382—28no—
39#17985382—24no—
40#17985380—24no—
41#17985376—22no—
42C2×C283⋊C8—22no—
43C2×C283⋊C8C2312yes—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283C2312yes—
46Dic283⋊C4—24no—
47C22⋊Dic283—21no—
48C4×Dic283—24no—
49C4×Dic283—21no—
50#41×C283—22no—
51#41×C283—22no—
52C2×Q8×C283—21no—
53C2×Q8×C283—22no—
54C2×Q8×C283—22no—
55C2×Q8×C283C2312yes—
56C2×Q8×C283C2311yescharacteristic
57C2×D4×C283—21no—
58C2×D4×C283C2311yescharacteristic
59C22×C4×C283—21no—
60C22×C4×C283—21no—
61C22×C4×C283C2311yescharacteristic
62C4⋊C4×C283—24no—
63C4⋊C4×C283D412yes—
64C22⋊C4×C283—24no—
65C22⋊C4×C283D412yes—
66C42×C283C2312yes—
67Dic566—24no—
68Dic566—22no—
69Dic566C2×D414yes—
70C2×Dic283—24no—
71C2×Dic283—22no—
72C2×Dic283—22no—
73C283⋊C8—22no—
74C283⋊C8—22no—
75C23×C283—21no—
76C23×C283C2×D411yescharacteristic
77Q8×C283—22no—
78Q8×C283—21no—
79Q8×C283—22no—
80Q8×C283—21no—
81Q8×C283—42no—
82D4×C283—21no—
83D4×C283—21no—
84D4×C283—42no—
85C2×C4×C283—22no—
86C2×C4×C283—21no—
87C2×C4×C283—42no—
88C2×C4×C283—42no—
89C2×C4×C283C2×D412yes—
90C2×C4×C283C2×D414yes—
91C2×C4×C283C2×D411yescharacteristic
92C2×C4×C283#4112yes—
93C2×C4×C283C2411yescharacteristic
94C22×C283—22no—
95C22×C283—41no—
96C22×C283—42no—
97C22×C283#12112yes—
98C22×C283C22×D411yescharacteristic
99C4×C283—24no—
100C4×C283—41no—
101C4×C283—42no—
102C4×C283#12112yes—
103C4×C283C22×D411yescharacteristic
104C4×C283C2×#4111yescharacteristic
105Dic283—24no—
106Dic283—42no—
107C2×C283—22no—
108C2×C283—81no—
109C2×C283C2×#12111yescharacteristic
110C2×C283#57812yes—
111C283#304411yescharacteristic, complemented, Sylow
112#3044—2831nomaximal, Sylow
113C2×#137—2831no—
114C22×Q16—2831no—
115#536D28311yescharacteristic
116#519—2831no—
117#464—2834no—
118#462—2834no—
119#424—2831no—
120#419—2831no—
121#416—2831no—
122C2×#41C2×D28311yescharacteristic
123C22×Q8—2831no—
124C22×Q8C2×D28311yescharacteristic
125#137—5664no—
126C2×Q16—2834no—
127C2×Q16—2832no—
128C2×Q16—5664no—
129C2×SD16—2832no—
130C2×M16—2831no—
131C22×C8—2831no—
132C4⋊Q8C2×D28312yes—
133#124C2×D28312yes—
134#123—22no—
135C22⋊Q8—22no—
136C4×Q8—2834no—
137C4×Q8—5662no—
138#117—2831no—
139#117—5662no—
140#117C2×D28311yescharacteristic
141C4⋊C8—2834no—
142#103—2832no—
143#103—2834no—
144#102—2832no—
145#41—22no—
146#41—22no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—2834no—
151C2×Q8—2832no—
152C2×Q8—5661no—
153C2×Q8—5662no—
154C2×Q8C22×D28312yes—
155C2×Q8C22×D28311yescharacteristic
156C2×D4—21no—
157C2×D4C22×D28311yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—5661no—
161C22×C4C22×D28311yescharacteristic
162Q16—5668no—
163Q16—5664no—
164SD16—5664no—
165M16—5662no—
166C2×C8—2832no—
167C2×C8—2832no—
168C2×C8—5662no—
169C4⋊C4—24no—
170C4⋊C4—2832no—
171C4⋊C4—5664no—
172C4⋊C4C22⋊D28312yes—
173C22⋊C4—24no—
174C22⋊C4—5661no—
175C22⋊C4C22⋊D28312yes—
176C42—5661no—
177C42—5664no—
178C42C22×D28312yes—
179C23—21no—
180C23C2×C22⋊D28311yescharacteristic
181Q8—22no—
182Q8—21no—
183Q8—22no—
184Q8—21no—
185Q8—42no—
186Q8—2834no—
187Q8—5664no—
188Q8—5662no—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—5664no—
197C2×C4—5662no—
198C2×C4—5662no—
199C2×C4D4×D28312yes—
200C2×C4C2×C22⋊D28314yes—
201C2×C4C2×C22⋊D28311yescharacteristic
202C2×C4#1798539112yes—
203C2×C4C23×D28311yescharacteristic
204C8—5662no—
205C8—5662no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22#2258358112yes—
210C22C22×C22⋊D28311yescharacteristic
211C4—24no—
212C4—41no—
213C4—42no—
214C4—5664no—
215C4—11322no—
216C4#2258358112yes—
217C4C2×D4×D28311yescharacteristic
218C4C2×#1798539111yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#2258358111yescharacteristic
222C2#3182728012yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#536×C283C2
socleC22×C283C22×D4
prime radicalC2×#41×C283C22
hypercenter#536D283
hypocenterC283#3044
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C22×#17985382C2semidirect
3. #31826942C2semidirect
4. #31826684C2semidirect
5. #31826672C2semidirect
6. #31826492C2semidirect
7. #31826474C2semidirect
111. C283#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#225836402
C22×#179853822
#318269422
#318266842
#318266722
#318264922
#318264742
#318264612
#536×C2832
#3044283