Finite Group Databasebeta

← #49130776

Subgroups — #49130776

Order 36224.

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

normal subgroups only

This group has 494 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×#22583635C211yesmaximal, characteristic
2C22×#17985381C211yesmaximal, characteristic, complemented
3#31827036C211yesmaximal, characteristic, complemented
4#31826939C211yesmaximal, characteristic, complemented
5#31826679C214yesmaximal, complemented
6#31826669C214yesmaximal, complemented
7#31826491C211yesmaximal, characteristic, complemented
8#31826473C211yesmaximal, characteristic, complemented
9#416×C283C211yesmaximal, characteristic, complemented
10C22×Dic566C2211yescharacteristic
11C22×D1132C2211yescharacteristic
12#22583635—24no—
13C2×#17985381—24no—
14C2×#17985381C2214yes—
15C2×#17985379C2212yes—
16C2×#17985377C2212yes—
17C2×#17985376C2211yescharacteristic
18#22583608C2212yescomplemented
19#22583597C2212yescomplemented
20#22583591—22no—
21#22583589—22no—
22C4×D1132—22no—
23#22583572C2214yes—
24#22583569C2211yescharacteristic
25C22⋊C4×D283—22no—
26Dic283⋊C8C2214yescomplemented
27#22583533C2214yescomplemented
28C2×#41×C283C2211yescharacteristic
29C22×C8×C283C2211yescharacteristic
30#117×C283C2211yescharacteristic
31#103×C283C2212yescomplemented
32#102×C283C2212yescomplemented
33C23×D283—21no—
34C2×Dic566—21no—
35C2×Dic566—22no—
36C2×Dic566—22no—
37C2×Dic566C2312yes—
38C2×D1132—21no—
39C2×D1132—22no—
40C2×D1132D414yes—
41C2×D1132C2312yes—
42C22×Dic283—21no—
43C2×C4×D283—24no—
44#17985381—28no—
45#17985379—24no—
46#17985377—24no—
47#17985376—22no—
48C2×C283⋊C8C2312yes—
49C4⋊Dic283D412yes—
50Dic283⋊C4—24no—
51C22⋊Dic283—24no—
52C22⋊Dic283D412yes—
53(C2×D283)⋊C4—24no—
54C4×Dic283C2312yes—
55#41×C283—22no—
56#41×C283—22no—
57C2×Q8×C283C2311yescharacteristic
58C2×D4×C283—21no—
59C2×D4×C283C2311yescharacteristic
60C22×C4×C283—21no—
61C22×C4×C283C2311yescharacteristic
62C2×C8×C283—22no—
63C2×C8×C283C2312yes—
64C4⋊C4×C283C2312yes—
65C22⋊C4×C283—21no—
66C42×C283—21no—
67C22×D283—22no—
68C22×D283—24no—
69C22×D283—82no—
70Dic566—22no—
71Dic566—22no—
72Dic566—42no—
73D1132—24no—
74D1132—22no—
75D1132C2×D414yes—
76C2×Dic283—22no—
77C2×Dic283—42no—
78C2×Dic283C2×D414yes—
79C4×D283—84no—
80C283⋊C8—22no—
81C23×C283—21no—
82C23×C283C2×D411yescharacteristic
83Q8×C283—21no—
84Q8×C283—21no—
85D4×C283—21no—
86D4×C283—21no—
87D4×C283—42no—
88C2×C4×C283—22no—
89C2×C4×C283—21no—
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—41no—
98C22×C283—42no—
99C22×C283#12112yes—
100C22×C283C22×D411yescharacteristic
101C2×D283—24no—
102C2×D283—44no—
103C2×D283—84no—
104C4×C283—41no—
105C4×C283—42no—
106C4×C283#12112yes—
107C4×C283C22×D411yescharacteristic
108C4×C283C2×#4111yescharacteristic
109Dic283—24no—
110Dic283—42no—
111C2×C283—22no—
112C2×C283—81no—
113C2×C283C2×#12111yescharacteristic
114C2×C283#57712yes—
115D283—44no—
116C283#304211yescharacteristic, complemented, Sylow
117#3042—2831nomaximal, Sylow
118C2×AGL(1,ℤ/8)—2831no—
119C22×SD16—2831no—
120#536—2831no—
121#518—2831no—
122#463—2834no—
123#461—2834no—
124#424—2831no—
125#419—2831no—
126#416D28311yescharacteristic, complemented
127C2×#41C2×D28311yescharacteristic
128C22×Q8—2831no—
129C22×D4—2831no—
130AGL(1,ℤ/8)—5664no—
131C2×SD16—2832no—
132C2×SD16—2834no—
133C2×SD16—5664no—
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#117C2×D28311yescharacteristic
145C2×C22⋊C4—5662no—
146C4⋊C8—2834no—
147#103—2834no—
148#103C2×D28312yescomplemented
149#102C2×D28312yescomplemented
150C24—5661no—
151#41—22no—
152#41—22no—
153C2×Q8—2832no—
154C2×Q8—5661no—
155C2×Q8—5662no—
156C2×Q8—5662no—
157C2×Q8C22×D28311yescharacteristic
158C2×D4—21no—
159C2×D4—2834no—
160C2×D4—2832no—
161C2×D4—5661no—
162C2×D4—5662no—
163C2×D4C22×D28311yescharacteristic
164C22×C4—21no—
165C22×C4—5664no—
166C22×C4—5661no—
167C22×C4C22×D28311yescharacteristic
168SD16—5668no—
169SD16—5664no—
170D8—5664no—
171M16—5662no—
172C2×C8—22no—
173C2×C8—2832no—
174C2×C8C22×D28312yes—
175C4⋊C4—2832no—
176C4⋊C4—5664no—
177C4⋊C4C22×D28312yes—
178C22⋊C4—21no—
179C22⋊C4—2832no—
180C22⋊C4—5664no—
181C22⋊C4—5664no—
182C42—21no—
183C42—2832no—
184C23—21no—
185C23—5662no—
186C23—5664no—
187C23—22642no—
188C23D4×D28311yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—5662no—
192Q8—5662no—
193Q8—11322no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—2834no—
198D4—5664no—
199D4—5662no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—2834no—
204C2×C4—5662no—
205C2×C4—11322no—
206C2×C4—22644no—
207C2×C4D4×D28311yescharacteristic
208C2×C4D4×D28312yes—
209C2×C4#1798539212yes—
210C2×C4C23×D28311yescharacteristic
211C8—22no—
212C8—5662no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—5664no—
217C22—11324no—
218C22—22644no—
219C22#2258358312yes—
220C22C2×D4×D28311yescharacteristic
221C4—41no—
222C4—42no—
223C4—5664no—
224C4—11322no—
225C4#2258358312yes—
226C4C2×D4×D28311yescharacteristic
227C4C2×#1798539211yescharacteristic
228C2—22no—
229C2—81no—
230C2—11324no—
231C2C2×#2258358311yescharacteristic
232C2#3182727212yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#416×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583635C2
hypercenter#416D283
hypocenterC283#3042
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C22×#17985381C2semidirect
3. #31827036C2semidirect
4. #31826939C2semidirect
5. #31826679C2semidirect
6. #31826669C2semidirect
7. #31826491C2semidirect
8. #31826473C2semidirect
9. #416×C283C2semidirect
18. #22583608C22semidirect
19. #22583597C22semidirect
26. Dic283⋊C8C22semidirect
27. #22583533C22semidirect
31. #103×C283C22semidirect
32. #102×C283C22semidirect
116. C283#3042semidirect
126. #416D283semidirect
148. #103C2×D283semidirect
149. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836352
C22×#179853812
#318270362
#318269392
#318266792
#318266692
#318264912
#318264732
#416×C2832
#3042283