Finite Group Databasebeta

← #49130790

Subgroups — #49130790

Order 36224.

458 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22583643C211yesmaximal, characteristic
2C22×#17985382C211yesmaximal, characteristic, complemented
3#31827039C211yesmaximal, characteristic
4#31826942C211yesmaximal, characteristic, complemented
5#31826690C214yesmaximal, complemented
6#31826674C214yesmaximal, complemented
7#31826493C211yesmaximal, characteristic, complemented
8#31826459C211yesmaximal, characteristic
9#419×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×Dic566C2211yescharacteristic
12#22583643—24no—
13C2×Dic1132C2212yes—
14C2×#17985382—24no—
15C2×#17985382C2214yes—
16C2×#17985381C2212yes—
17C22×C283⋊C8C2211yescharacteristic
18#22583608C2212yes—
19#22583599C2212yes—
20#22583593—22no—
21#22583586—22no—
22C4×Dic566—22no—
23#22583575C2214yes—
24#22583569C2211yescharacteristic
25#22583566—22no—
26Dic283⋊C8C2214yes—
27#22583533C2212yes—
28#22583530C2212yes—
29C22×Q8×C283C2211yescharacteristic
30C2×M16×C283C2211yescharacteristic
31#117×C283C2211yescharacteristic
32#103×C283C2214yes—
33#17985392—22no—
34#17985392—22no—
35C2×Dic566—21no—
36C2×Dic566—22no—
37C2×Dic566D414yes—
38C2×Dic566C2311yescharacteristic
39C2×Dic566C2312yes—
40C2×D1132C2311yescharacteristic
41C2×C22⋊D283—21no—
42C22×Dic283—21no—
43C2×C4×D283—21no—
44Dic1132—24no—
45#17985382—28no—
46#17985381—24no—
47C2×C283⋊C8—22no—
48C2×C283⋊C8C2312yes—
49C4⋊Dic283D412yes—
50Dic283⋊C4—24no—
51Dic283⋊C4—24no—
52C22⋊Dic283D412yes—
53(C2×D283)⋊C4—24no—
54C4×Dic283—24no—
55C4×Dic283C2312yes—
56C2×Q8×C283—21no—
57C2×Q8×C283—22no—
58C2×Q8×C283—22no—
59C2×Q8×C283C2312yes—
60C22×C4×C283—21no—
61C22×C4×C283C2311yescharacteristic
62M16×C283—22no—
63C2×C8×C283C2312yes—
64C4⋊C4×C283C2312yes—
65C22⋊C4×C283—21no—
66C42×C283—21no—
67C22×D283—21no—
68Dic566—24no—
69Dic566—22no—
70Dic566—21no—
71Dic566—21no—
72Dic566C2×D414yes—
73D1132—21no—
74D1132—21no—
75C22⋊D283—42no—
76C2×Dic283—24no—
77C2×Dic283—22no—
78C2×Dic283—21no—
79C2×Dic283C2×D414yes—
80C4×D283—42no—
81C283⋊C8—22no—
82C23×C283C2×D411yescharacteristic
83Q8×C283—22no—
84Q8×C283—22no—
85Q8×C283—42no—
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—42no—
100C4×C283—42no—
101C4×C283#12112yes—
102C4×C283C22×D411yescharacteristic
103C4×C283C2×#4111yescharacteristic
104Dic283—24no—
105Dic283—24no—
106Dic283—41no—
107C2×C283—22no—
108C2×C283C2×#12111yescharacteristic
109C2×C283#57812yes—
110D283—81no—
111C283#304411yescharacteristic, complemented, Sylow
112#3044—2831nomaximal, Sylow
113C2×#137—2831no—
114C22×Q16—2831no—
115#536—2831no—
116#519—2831no—
117#464—2834no—
118#462—2834no—
119#424—2831no—
120#419D28311yescharacteristic, complemented
121#416—2831no—
122C2×#41—2831no—
123C22×Q8—2831no—
124C22×Q8C2×D28311yescharacteristic
125#137—5664no—
126C2×Q16—2834no—
127C2×Q16—2832no—
128C2×Q16—5664no—
129C2×SD16—2832no—
130C2×M16C2×D28311yescharacteristic
131C22×C8—2831no—
132C4⋊Q8—2832no—
133#124—2832no—
134#123—5662no—
135C22⋊Q8—5662no—
136C4×Q8—2834no—
137C4×Q8—5662no—
138#117—2831no—
139#117—5662no—
140#117C2×D28311yescharacteristic
141C4⋊C8—2834no—
142#103—2832no—
143#103C2×D28314yes—
144#102—2832no—
145#41—5662no—
146#41—5662no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—2834no—
151C2×Q8—2832no—
152C2×Q8—2831no—
153C2×Q8—5661no—
154C2×Q8—5662no—
155C2×Q8C22×D28312yes—
156C2×D4—2831no—
157C2×D4—5661no—
158C22×C4—21no—
159C22×C4—5661no—
160C22×C4—5661no—
161C22×C4C22×D28311yescharacteristic
162Q16—5664no—
163Q16—5668no—
164SD16—5664no—
165M16—22no—
166C2×C8—2832no—
167C2×C8—5662no—
168C2×C8C22×D28312yes—
169C4⋊C4—2832no—
170C4⋊C4—5664no—
171C4⋊C4—5664no—
172C4⋊C4C22×D28312yes—
173C22⋊C4—21no—
174C22⋊C4—2832no—
175C22⋊C4—5664no—
176C42—21no—
177C42—2832no—
178C42—5664no—
179C23—5661no—
180C23D4×D28311yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—42no—
184Q8—2834no—
185Q8—5664no—
186Q8—5662no—
187Q8—5661no—
188Q8—5661no—
189D4—5661no—
190D4—5661no—
191D4—11322no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—2834no—
196C2×C4—5664no—
197C2×C4—5662no—
198C2×C4—5661no—
199C2×C4—11322no—
200C2×C4D4×D28311yescharacteristic
201C2×C4D4×D28312yes—
202C2×C4#1798539212yes—
203C2×C4C23×D28311yescharacteristic
204C8—22no—
205C8—5662no—
206C22—22no—
207C22—11321no—
208C22—11322no—
209C22#2258358312yes—
210C22C2×D4×D28311yescharacteristic
211C4—42no—
212C4—42no—
213C4—5664no—
214C4—5664no—
215C4—11321no—
216C4#2258358312yes—
217C4C2×D4×D28311yescharacteristic
218C4C2×#1798539211yescharacteristic
219C2—22no—
220C2—22641no—
221C2C2×#2258358311yescharacteristic
222C2#3182728112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#419×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985392C22
hypercenter#419D283
hypocenterC283#3044
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
2. C22×#17985382C2semidirect
4. #31826942C2semidirect
5. #31826690C2semidirect
6. #31826674C2semidirect
7. #31826493C2semidirect
9. #419×C283C2semidirect
111. C283#3044semidirect
120. #419D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
C22×#179853822
#318270392
#318269422
#318266902
#318266742
#318264932
#318264592
#419×C2832
#3044283