Finite Group Databasebeta

← #49131388

Subgroups — #49131388

Order 36224.

380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#31827017C211yesmaximal, characteristic
2C2×#22583575C211yesmaximal, characteristic
3#31826795C211yesmaximal, characteristic
4#31826749C212yesmaximal, complemented
5#31826674C212yesmaximal, complemented
6#31826623C211yesmaximal, characteristic
7#31826620C211yesmaximal, characteristic
8#31826571C212yesmaximal, complemented
9#31826569C212yesmaximal, complemented
10#31826519C211yesmaximal, characteristic
11#483×C283C211yesmaximal, characteristic
12C22×Dic566C2211yescharacteristic
13C2×Dic1132C2212yes—
14C2×#17985382C2212yes—
15#22583609C2211yescharacteristic
16#22583608C2211yescharacteristic
17#22583600—21no—
18#22583589C2211yescharacteristic
19#22583587—21no—
20Q8×Dic283C2211yescharacteristic
21#22583575—21no—
22#22583575—21no—
23#22583575—21no—
24#22583575C2212yes—
25#22583575C2211yescharacteristic
26#22583575C2212yes—
27#22583566—21no—
28C2×Dic283⋊C4—21no—
29C2×C4×Dic283—21no—
30C2×C4×Dic283C2211yescharacteristic
31#22583541C2212yes—
32Dic283⋊C8C2212yes—
33#22583535C2212yes—
34#22583533C2212yes—
35#22583533C2212yes—
36C22⋊(C283⋊C8)C2211yescharacteristic
37#22583520C2212yes—
38C22⋊Q8×C283C2211yescharacteristic
39C2×C4⋊C4×C283C2211yescharacteristic
40#106×C283C2212yes—
41#103×C283C2212yes—
42C22⋊C8×C283C2211yescharacteristic
43C2×Dic566—24no—
44C2×Dic566—21no—
45C2×Dic566—21no—
46C2×Dic566C2311yescharacteristic
47C2×Dic566C2312yes—
48C22×Dic283—21no—
49C22×Dic283D411yescharacteristic
50C22×Dic283D411yescharacteristic
51Dic1132—24no—
52#17985382—24no—
53C2×C283⋊C8C2312yes—
54C4⋊Dic283—21no—
55C4⋊Dic283C2311yescharacteristic
56Dic283⋊C4—22no—
57Dic283⋊C4—22no—
58Dic283⋊C4—21no—
59Dic283⋊C4—21no—
60Dic283⋊C4—21no—
61Dic283⋊C4—21no—
62Dic283⋊C4—21no—
63C22⋊Dic283—21no—
64C4×Dic283—22no—
65C4×Dic283—22no—
66C4×Dic283—21no—
67C4×Dic283—21no—
68C4×Dic283D411yescharacteristic
69C4×Dic283D411yescharacteristic
70C4×Dic283C2311yescharacteristic
71C4×Dic283C2311yescharacteristic
72C2×Q8×C283C2311yescharacteristic
73C22×C4×C283—21no—
74C22×C4×C283C2311yescharacteristic
75C2×C8×C283C2312yes—
76C4⋊C4×C283—21no—
77C4⋊C4×C283—21no—
78C4⋊C4×C283C2312yes—
79C4⋊C4×C283C2311yescharacteristic
80C22⋊C4×C283—21no—
81Dic566—24no—
82Dic566—22no—
83Dic566—22no—
84Dic566—42no—
85Dic566#4114yes—
86C2×Dic283—24no—
87C2×Dic283—22no—
88C2×Dic283—22no—
89C2×Dic283—22no—
90C2×Dic283—21no—
91C2×Dic283—21no—
92C2×Dic283C2×D411yescharacteristic
93C2×Dic283C2×D411yescharacteristic
94C2×Dic283C2×D411yescharacteristic
95C2×Dic283C2×D411yescharacteristic
96C283⋊C8—22no—
97C23×C283C2×D411yescharacteristic
98Q8×C283—22no—
99C2×C4×C283—22no—
100C2×C4×C283—21no—
101C2×C4×C283—21no—
102C2×C4×C283—22no—
103C2×C4×C283—42no—
104C2×C4×C283C2×D411yescharacteristic
105C2×C4×C283C2411yescharacteristic
106C8×C283—22no—
107C22×C283—21no—
108C22×C283—21no—
109C22×C283#13712yes—
110C22×C283C22×D411yescharacteristic
111C4×C283—21no—
112C4×C283—41no—
113C4×C283—42no—
114C4×C283—41no—
115C4×C283C2×#4112yes—
116Dic283—24no—
117Dic283—21no—
118Dic283—21no—
119Dic283—21no—
120Dic283—41no—
121Dic283—41no—
122Dic283#13712yes—
123C2×C283—22no—
124C2×C283#52511yescharacteristic
125C2×C283C2×#13711yescharacteristic
126C2×C283C2×#13711yescharacteristic
127C283#311311yescharacteristic, complemented, Sylow
128#3113—2831nomaximal, Sylow
129#533—2831no—
130C2×C4×Q8—2831no—
131#483—2831no—
132#483D28311yescharacteristic
133#475—2832no—
134#462—2832no—
135#451—2831no—
136#451—2831no—
137#441—2832no—
138#441—2832no—
139#432—2831no—
140C22×Q8—2831no—
141C2×Q16—2832no—
142C2×Q16—2832no—
143C4⋊Q8—2831no—
144C4⋊Q8—2831no—
145#125—5661no—
146C22⋊Q8—2831no—
147C22⋊Q8—5661no—
148C22⋊Q8C2×D28311yescharacteristic
149C4×Q8—2831no—
150C4×Q8—2832no—
151C4×Q8—2832no—
152C4×Q8—2831no—
153C4×Q8—5661no—
154C4×Q8—5661no—
155C4×Q8—5661no—
156#117—5661no—
157C2×C4⋊C4—5661no—
158C2×C4⋊C4C2×D28311yescharacteristic
159C2×C42—2831no—
160C2×C42—5661no—
161#106—2832no—
162#106C2×D28312yes—
163C4⋊C8—2832no—
164#103—2832no—
165#103—2832no—
166#103—2832no—
167#103C2×D28312yes—
168C22⋊C8—2831no—
169C22⋊C8C2×D28311yescharacteristic
170#97—2832no—
171C2×Q8—2832no—
172C2×Q8—2831no—
173C2×Q8—5661no—
174C2×Q8—5664no—
175C2×Q8—5661no—
176C2×Q8C22×D28311yescharacteristic
177C22×C4—21no—
178C22×C4—2831no—
179C22×C4—2831no—
180C22×C4—5661no—
181C22×C4C22×D28311yescharacteristic
182Q16—5664no—
183Q16—5664no—
184C2×C8—2832no—
185C2×C8C22×D28312yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—2831no—
189C4⋊C4—5662no—
190C4⋊C4—5662no—
191C4⋊C4—5661no—
192C4⋊C4—5661no—
193C4⋊C4—5661no—
194C4⋊C4—5661no—
195C4⋊C4—5661no—
196C4⋊C4—5661no—
197C4⋊C4C22×D28311yescharacteristic
198C4⋊C4C22×D28312yes—
199C22⋊C4—21no—
200C22⋊C4—5661no—
201C42—2831no—
202C42—2831no—
203C42—2831no—
204C42—2831no—
205C42—5662no—
206C42—5662no—
207C42—5661no—
208C42—5661no—
209C23D4×D28311yescharacteristic
210Q8—22no—
211Q8—2834no—
212Q8—5664no—
213Q8—5662no—
214Q8—5662no—
215Q8—11322no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—2831no—
222C2×C4—2831no—
223C2×C4—2831no—
224C2×C4—2831no—
225C2×C4—5662no—
226C2×C4—5664no—
227C2×C4—5662no—
228C2×C4—5662no—
229C2×C4—5661no—
230C2×C4—5661no—
231C2×C4D4×D28311yescharacteristic
232C2×C4C23×D28311yescharacteristic
233C8—22no—
234C8—5662no—
235C22—21no—
236C22—21no—
237C22#2258363912yes—
238C22C2×D4×D28311yescharacteristic
239C4—21no—
240C4—41no—
241C4—41no—
242C4—42no—
243C4—2832no—
244C4—5664no—
245C4—5661no—
246C4—5661no—
247C4—5661no—
248C4—11321no—
249C4—11321no—
250C4#41×D28312yes—
251C2—22no—
252C2#3182697311yescharacteristic
253C2#137×D28311yescharacteristic
254C2C2×#2258363911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#483×C283C2
socleC22×C283C22×D4
prime radicalC23×C283C2×D4
hypercenter#483D283
hypocenterC283#3113
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
4. #31826749C2semidirect
5. #31826674C2semidirect
8. #31826571C2semidirect
9. #31826569C2semidirect
127. C283#3113semidirect

Maximal subgroups

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

subgroupindex
#318270172
C2×#225835752
#318267952
#318267492
#318266742
#318266232
#318266202
#318265712
#318265692
#318265192
#483×C2832
#3113283