Finite Group Databasebeta

← #49130788

Subgroups — #49130788

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×#22583641C211yesmaximal, characteristic
2#31827039C211yesmaximal, characteristic
3#31826943C211yesmaximal, characteristic, complemented
4#31826689C214yesmaximal, complemented
5#31826673C214yesmaximal, complemented
6#31826491C211yesmaximal, characteristic, complemented
7#31826474C211yesmaximal, characteristic, complemented
8#31826462C211yesmaximal, characteristic
9C22×Q16×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11#22583641—24no—
12C2×#17985382C2212yes—
13C2×#17985379C2212yes—
14C2×#17985376C2211yescharacteristic
15#22583608C2212yes—
16#22583599C2212yes—
17#22583593—22no—
18#22583586—22no—
19Q8×Dic283—22no—
20Q8×Dic283C2214yes—
21#22583569—22no—
22#22583569C2211yescharacteristic
23#22583569C2211yescharacteristic
24Dic283⋊C8C2214yes—
25#22583535C2212yes—
26#22583534C2214yes—
27#22583532C2212yes—
28C22×Q8×C283C2211yescharacteristic
29C22×Q8×C283C2211yescharacteristic
30C2×Q16×C283—24no—
31C2×Q16×C283C2214yes—
32C22×C8×C283C2211yescharacteristic
33#17985392—22no—
34#17985392—22no—
35C2×Dic566C2311yescharacteristic
36C2×D1132C2311yescharacteristic
37C2×C22⋊D283—21no—
38C2×C4×D283—21no—
39#17985382—24no—
40#17985379—24no—
41#17985376—22no—
42C2×C283⋊C8C2312yes—
43C4⋊Dic283—24no—
44C4⋊Dic283D412yes—
45C4⋊Dic283C2312yes—
46Dic283⋊C4—24no—
47C22⋊Dic283—21no—
48C22⋊Dic283D412yes—
49(C2×D283)⋊C4—24no—
50C4×Dic283—24no—
51C4×Dic283—21no—
52C4×Dic283C2312yes—
53C2×Q8×C283—21no—
54C2×Q8×C283—21no—
55C2×Q8×C283—22no—
56C2×Q8×C283—22no—
57C2×Q8×C283—22no—
58C2×Q8×C283D414yes—
59C2×Q8×C283C2312yes—
60C2×Q8×C283C2312yes—
61C22×C4×C283—21no—
62C22×C4×C283—21no—
63C22×C4×C283C2311yescharacteristic
64Q16×C283—28no—
65C2×C8×C283—22no—
66C2×C8×C283C2312yes—
67C22×D283—21no—
68Dic566—21no—
69Dic566—21no—
70D1132—21no—
71D1132—21no—
72C22⋊D283—42no—
73C2×Dic283—22no—
74C2×Dic283—21no—
75C2×Dic283C2×D414yes—
76C4×D283—42no—
77C283⋊C8—22no—
78C23×C283C2×D411yescharacteristic
79Q8×C283—24no—
80Q8×C283—22no—
81Q8×C283—22no—
82Q8×C283—22no—
83Q8×C283—42no—
84Q8×C283C2×D414yes—
85C2×C4×C283—24no—
86C2×C4×C283—22no—
87C2×C4×C283—22no—
88C2×C4×C283—42no—
89C2×C4×C283C2×D411yescharacteristic
90C2×C4×C283C2×D412yes—
91C2×C4×C283#4112yes—
92C2×C4×C283C2411yescharacteristic
93C8×C283—22no—
94C22×C283—22no—
95C22×C283#12112yes—
96C22×C283C22×D411yescharacteristic
97C2×D283—41no—
98C2×D283—42no—
99C4×C283—24no—
100C4×C283—42no—
101C4×C283#12112yes—
102C4×C283C22×D411yescharacteristic
103C4×C283C2×#4111yescharacteristic
104Dic283—24no—
105Dic283—41no—
106Dic283—42no—
107C2×C283—22no—
108C2×C283C2×#12111yescharacteristic
109C2×C283#57812yes—
110D283—81no—
111C283#304411yescharacteristic, complemented, Sylow
112#3044—2831nomaximal, Sylow
113C2×#137—2831no—
114C22×Q16D28311yescharacteristic, complemented
115#536—2831no—
116#519—2831no—
117#464—2834no—
118#462—2834no—
119#424—2831no—
120#419—2831no—
121#416—2831no—
122C2×#41—2831no—
123C22×Q8C2×D28311yescharacteristic
124C22×Q8C2×D28311yescharacteristic
125#137—5664no—
126C2×Q16—24no—
127C2×Q16—2832no—
128C2×Q16C2×D28314yes—
129C2×SD16—2832no—
130C2×M16—2831no—
131C22×C8C2×D28311yescharacteristic
132C4⋊Q8—2832no—
133#124—2832no—
134#123—5662no—
135C22⋊Q8—5662no—
136C4×Q8—2834no—
137C4×Q8—5662no—
138#117—2831no—
139#117—2831no—
140#117—5662no—
141C4⋊C8—2834no—
142#103—2834no—
143#103—2832no—
144#102—2832no—
145#41—5662no—
146#41—5662no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—2831no—
153C2×Q8C22⋊D28314yes—
154C2×Q8C22×D28312yes—
155C2×Q8C22×D28312yes—
156C2×D4—2831no—
157C2×D4—5661no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—5661no—
161C22×C4C22×D28311yescharacteristic
162Q16—28no—
163Q16—5664no—
164SD16—5664no—
165M16—5662no—
166C2×C8—22no—
167C2×C8—2832no—
168C2×C8C22×D28312yes—
169C4⋊C4—2832no—
170C4⋊C4—2832no—
171C4⋊C4—5664no—
172C4⋊C4—5664no—
173C22⋊C4—2832no—
174C22⋊C4—5664no—
175C22⋊C4—5661no—
176C42—2832no—
177C42—5664no—
178C42—5661no—
179C23—5661no—
180C23D4×D28311yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—22no—
184Q8—22no—
185Q8—42no—
186Q8—5661no—
187Q8—5661no—
188Q8C2×C22⋊D28314yes—
189D4—5661no—
190D4—5661no—
191D4—11322no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—2834no—
197C2×C4—5662no—
198C2×C4—5661no—
199C2×C4—11322no—
200C2×C4D4×D28311yescharacteristic
201C2×C4C2×C22⋊D28312yes—
202C2×C4#1798539112yes—
203C2×C4C23×D28311yescharacteristic
204C8—22no—
205C8—5662no—
206C22—22no—
207C22—11321no—
208C22—11322no—
209C22#2258358212yes—
210C22C2×D4×D28311yescharacteristic
211C4—24no—
212C4—42no—
213C4—5664no—
214C4—11321no—
215C4—11322no—
216C4#2258358212yes—
217C4C22×C22⋊D28311yescharacteristic
218C4C2×#1798539111yescharacteristic
219C2—22no—
220C2—22641no—
221C2C2×#2258358211yescharacteristic
222C2#3182727812yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×Q16×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985392C22
hypercenterC22×Q16D283
hypocenterC283#3044
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
3. #31826943C2semidirect
4. #31826689C2semidirect
5. #31826673C2semidirect
6. #31826491C2semidirect
7. #31826474C2semidirect
9. C22×Q16×C283C2semidirect
111. C283#3044semidirect
114. C22×Q16D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836412
#318270392
#318269432
#318266892
#318266732
#318264912
#318264742
#318264622
C22×Q16×C2832
#3044283