Finite Group Databasebeta

← #49130770

Subgroups — #49130770

Order 36224.

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

normal subgroups only

This group has 494 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×#22583636C211yesmaximal, characteristic
2#31827039C211yesmaximal, characteristic, complemented
3#31826940C211yesmaximal, characteristic, complemented
4#31826682C214yesmaximal, complemented
5#31826668C214yesmaximal, complemented
6#31826491C211yesmaximal, characteristic, complemented
7#31826474C211yesmaximal, characteristic, complemented
8#31826462C211yesmaximal, characteristic, complemented
9C22×SD16×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11#22583636—24no—
12C2×#17985380C2212yes—
13C2×#17985377C2212yes—
14C2×#17985376C2211yescharacteristic
15#22583608C2212yescomplemented
16#22583599C2212yescomplemented
17#22583593—22no—
18#22583586—22no—
19D4×Dic283—22no—
20D4×Dic283C2214yes—
21#22583569C2211yescharacteristic
22#22583569C2211yescharacteristic
23C2×C22⋊Dic283—22no—
24Dic283⋊C8C2214yescomplemented
25#22583535C2212yescomplemented
26#22583534C2214yescomplemented
27#22583532C2212yescomplemented
28C22×Q8×C283C2211yescharacteristic
29C22×D4×C283C2211yescharacteristic
30C2×SD16×C283—24no—
31C2×SD16×C283C2214yes—
32C22×C8×C283C2211yescharacteristic
33#17985392—22no—
34#17985392—22no—
35C2×Dic566C2311yescharacteristic
36C2×D1132C2311yescharacteristic
37C2×C22⋊D283—21no—
38C22×Dic283—24no—
39C2×C4×D283—21no—
40#17985380—24no—
41#17985377—24no—
42#17985376—22no—
43C2×C283⋊C8C2312yes—
44C4⋊Dic283D412yes—
45C4⋊Dic283C2312yes—
46Dic283⋊C4—24no—
47C22⋊Dic283—24no—
48C22⋊Dic283—21no—
49C22⋊Dic283D412yes—
50(C2×D283)⋊C4—24no—
51C4×Dic283—21no—
52C4×Dic283C2312yes—
53C24×C283—21no—
54C2×Q8×C283—21no—
55C2×Q8×C283—22no—
56C2×Q8×C283—22no—
57C2×Q8×C283C2312yes—
58C2×D4×C283—21no—
59C2×D4×C283—22no—
60C2×D4×C283D414yes—
61C2×D4×C283C2312yes—
62C22×C4×C283—21no—
63C22×C4×C283C2311yescharacteristic
64SD16×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×Dic283—84no—
76C2×Dic283C2×D414yes—
77C4×D283—42no—
78C283⋊C8—22no—
79C23×C283—22no—
80C23×C283—24no—
81C23×C283—82no—
82C23×C283C2×D411yescharacteristic
83Q8×C283—22no—
84Q8×C283—22no—
85Q8×C283—42no—
86D4×C283—24no—
87D4×C283—22no—
88D4×C283C2×D414yes—
89C2×C4×C283—22no—
90C2×C4×C283—42no—
91C2×C4×C283C2×D411yescharacteristic
92C2×C4×C283C2×D412yes—
93C2×C4×C283#4112yes—
94C2×C4×C283C2411yescharacteristic
95C8×C283—22no—
96C22×C283—22no—
97C22×C283—24no—
98C22×C283—44no—
99C22×C283—84no—
100C22×C283#12112yes—
101C22×C283C22×D411yescharacteristic
102C2×D283—41no—
103C2×D283—42no—
104C4×C283—42no—
105C4×C283#12112yes—
106C4×C283C22×D411yescharacteristic
107C4×C283C2×#4111yescharacteristic
108Dic283—24no—
109Dic283—41no—
110Dic283—42no—
111C2×C283—22no—
112C2×C283—44no—
113C2×C283C2×#12111yescharacteristic
114C2×C283#57712yes—
115D283—81no—
116C283#304211yescharacteristic, complemented, Sylow
117#3042—2831nomaximal, Sylow
118C2×AGL(1,ℤ/8)—2831no—
119C22×SD16D28311yescharacteristic, complemented
120#536—2831no—
121#518—2831no—
122#463—2834no—
123#461—2834no—
124#424—2831no—
125#419—2831no—
126#416—2831no—
127C2×#41—2831no—
128C22×Q8C2×D28311yescharacteristic
129C22×D4C2×D28311yescharacteristic
130AGL(1,ℤ/8)—5664no—
131C2×SD16—24no—
132C2×SD16—2832no—
133C2×SD16C2×D28314yes—
134C2×D8—2832no—
135C2×M16—2831no—
136C22×C8C2×D28311yescharacteristic
137C4⋊Q8—2832no—
138#124—2832no—
139#123—5662no—
140C22⋊Q8—5662no—
141C4×D4—2834no—
142C4×D4—5662no—
143#117—2831no—
144#117—2831no—
145C2×C22⋊C4—5662no—
146C4⋊C8—2834no—
147#103—2834no—
148#103—2832no—
149#102—2832no—
150C24—21no—
151#41—5662no—
152#41—5662no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—2831no—
157C2×Q8C22×D28312yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—2831no—
161C2×D4—5661no—
162C2×D4C22⋊D28314yes—
163C2×D4C22×D28312yes—
164C22×C4—21no—
165C22×C4—5664no—
166C22×C4—5661no—
167C22×C4C22×D28311yescharacteristic
168SD16—28no—
169SD16—5664no—
170D8—5664no—
171M16—5662no—
172C2×C8—22no—
173C2×C8—2832no—
174C2×C8C22×D28312yes—
175C4⋊C4—2832no—
176C4⋊C4—2832no—
177C4⋊C4—5664no—
178C22⋊C4—2832no—
179C22⋊C4—5664no—
180C22⋊C4—5664no—
181C22⋊C4—5661no—
182C42—2832no—
183C42—5661no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—5661no—
188C23D4×D28311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—5661no—
193Q8—5661no—
194D4—24no—
195D4—22no—
196D4—5661no—
197D4—5661no—
198D4—11322no—
199D4C2×C22⋊D28314yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—2834no—
203C2×C4—5662no—
204C2×C4—5661no—
205C2×C4—11322no—
206C2×C4—22644no—
207C2×C4D4×D28311yescharacteristic
208C2×C4C2×C22⋊D28312yes—
209C2×C4#1798539112yes—
210C2×C4C23×D28311yescharacteristic
211C8—22no—
212C8—5662no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—11321no—
218C22—11322no—
219C22#2258358212yes—
220C22C2×D4×D28311yescharacteristic
221C4—42no—
222C4—5664no—
223C4—11321no—
224C4—11322no—
225C4#2258358212yes—
226C4C22×C22⋊D28311yescharacteristic
227C4C2×#1798539111yescharacteristic
228C2—22no—
229C2—44no—
230C2—22641no—
231C2C2×#2258358211yescharacteristic
232C2#3182727112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×SD16×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583636C2
hypercenterC22×SD16D283
hypocenterC283#3042
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #31827039C2semidirect
3. #31826940C2semidirect
4. #31826682C2semidirect
5. #31826668C2semidirect
6. #31826491C2semidirect
7. #31826474C2semidirect
8. #31826462C2semidirect
9. C22×SD16×C283C2semidirect
15. #22583608C22semidirect
16. #22583599C22semidirect
24. Dic283⋊C8C22semidirect
25. #22583535C22semidirect
26. #22583534C22semidirect
27. #22583532C22semidirect
116. C283#3042semidirect
119. C22×SD16D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836362
#318270392
#318269402
#318266822
#318266682
#318264912
#318264742
#318264622
C22×SD16×C2832
#3042283