Finite Group Databasebeta

← #49131429

Subgroups — #49131429

Order 36224.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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#31826996C211yesmaximal, characteristic
2C2×#22583575C211yesmaximal, characteristic, complemented
3#31826800C211yesmaximal, characteristic, complemented
4#31826775C212yesmaximal, complemented
5#31826686C212yesmaximal, complemented
6#31826623C211yesmaximal, characteristic, complemented
7#31826603C211yesmaximal, characteristic
8#31826571C212yesmaximal, complemented
9#31826562C212yesmaximal, complemented
10#31826519C211yesmaximal, characteristic, complemented
11#481×C283C211yesmaximal, characteristic
12C22×Dic566C2211yescharacteristic
13C2×Dic1132C2212yes—
14C2×#17985380C2212yes—
15#22583603—21no—
16#22583601C2211yescharacteristic
17#22583597C2211yescharacteristic
18#22583591—21no—
19#22583589C2211yescharacteristic
20#22583575—21no—
21#22583575—21no—
22#22583575C2211yescharacteristic
23#22583575C2212yes—
24#22583575C2212yes—
25D4×Dic283—21no—
26D4×Dic283C2211yescharacteristic
27#22583566—21no—
28C2×Dic283⋊C4—21no—
29C2×C4×Dic283—21no—
30C2×C4×Dic283C2211yescharacteristic
31#22583543C2212yes—
32Dic283⋊C8C2212yes—
33#22583535C2212yes—
34#22583533C2212yes—
35#22583533C2212yes—
36C22⋊(C283⋊C8)C2211yescharacteristic
37#22583520C2212yes—
38#121×C283C2211yescharacteristic
39C2×C4⋊C4×C283C2211yescharacteristic
40#106×C283C2212yes—
41#102×C283C2212yes—
42C22⋊C8×C283C2211yescharacteristic
43C2×Dic566—24no—
44C2×Dic566—21no—
45C2×Dic566C2311yescharacteristic
46C2×Dic566C2312yes—
47C22×Dic283—21no—
48C22×Dic283—21no—
49C22×Dic283D411yescharacteristic
50C22×Dic283D411yescharacteristic
51Dic1132—24no—
52#17985380—24no—
53C2×C283⋊C8C2312yes—
54C4⋊Dic283—21no—
55C4⋊Dic283C2311yescharacteristic
56Dic283⋊C4—22no—
57Dic283⋊C4—22no—
58Dic283⋊C4—21no—
59Dic283⋊C4—21no—
60Dic283⋊C4—21no—
61C22⋊Dic283—21no—
62C22⋊Dic283—21no—
63C22⋊Dic283—21no—
64C22⋊Dic283—21no—
65C4×Dic283—22no—
66C4×Dic283—22no—
67C4×Dic283—21no—
68C4×Dic283D411yescharacteristic
69C4×Dic283D411yescharacteristic
70C4×Dic283C2311yescharacteristic
71C4×Dic283C2311yescharacteristic
72C2×D4×C283—21no—
73C2×D4×C283C2311yescharacteristic
74C22×C4×C283—21no—
75C22×C4×C283C2311yescharacteristic
76C2×C8×C283C2312yes—
77C4⋊C4×C283—21no—
78C4⋊C4×C283C2312yes—
79C4⋊C4×C283C2311yescharacteristic
80C22⋊C4×C283—21no—
81Dic566—24no—
82Dic566—22no—
83Dic566—22no—
84Dic566#4114yes—
85C2×Dic283—24no—
86C2×Dic283—22no—
87C2×Dic283—22no—
88C2×Dic283—21no—
89C2×Dic283—21no—
90C2×Dic283—41no—
91C2×Dic283—42no—
92C2×Dic283C2×D411yescharacteristic
93C2×Dic283C2×D411yescharacteristic
94C2×Dic283C2×D411yescharacteristic
95C2×Dic283C2×D411yescharacteristic
96C283⋊C8—22no—
97C23×C283—21no—
98C23×C283C2×D411yescharacteristic
99D4×C283—22no—
100D4×C283—42no—
101C2×C4×C283—22no—
102C2×C4×C283—21no—
103C2×C4×C283—22no—
104C2×C4×C283—42no—
105C2×C4×C283C2×D411yescharacteristic
106C2×C4×C283C2411yescharacteristic
107C8×C283—22no—
108C22×C283—21no—
109C22×C283—21no—
110C22×C283—41no—
111C22×C283—41no—
112C22×C283—41no—
113C22×C283#13712yes—
114C22×C283C22×D411yescharacteristic
115C4×C283—21no—
116C4×C283—41no—
117C4×C283—42no—
118C4×C283C2×#4112yes—
119Dic283—24no—
120Dic283—21no—
121Dic283—21no—
122Dic283—21no—
123Dic283—21no—
124Dic283—41no—
125Dic283—41no—
126C2×C283—22no—
127C2×C283—81no—
128C2×C283#52511yescharacteristic
129C2×C283C2×#13711yescharacteristic
130C2×C283#57511yescharacteristic
131C283#311711yescharacteristic, complemented, Sylow
132#3117—2831nomaximal, Sylow
133#529—2831no—
134C2×C4×Q8—2831no—
135#484—2831no—
136#481D28311yescharacteristic
137#479—2832no—
138#464—2832no—
139#451—2831no—
140#448—2831no—
141#441—2832no—
142#440—2832no—
143#432—2831no—
144C22×Q8—2831no—
145C2×Q16—2832no—
146C2×SD16—2832no—
147#126—5661no—
148#125—2831no—
149#124—2831no—
150#123—5661no—
151C22⋊Q8—2831no—
152#121C2×D28311yescharacteristic
153C4×Q8—2832no—
154C4×Q8—2832no—
155C4×Q8—2831no—
156C4×Q8—5661no—
157C4×Q8—5661no—
158C4×D4—2831no—
159C4×D4—5661no—
160#117—5661no—
161C2×C4⋊C4—5661no—
162C2×C4⋊C4C2×D28311yescharacteristic
163C2×C42—2831no—
164C2×C42—5661no—
165#107—2832no—
166#106C2×D28312yes—
167C4⋊C8—2832no—
168#103—2832no—
169#103—2832no—
170#103—2832no—
171#102C2×D28312yes—
172C22⋊C8—2831no—
173C22⋊C8C2×D28311yescharacteristic
174#97—2832no—
175C2×Q8—2832no—
176C2×Q8—2831no—
177C2×Q8—5664no—
178C2×Q8—5661no—
179C2×D4—21no—
180C2×D4C22×D28311yescharacteristic
181C22×C4—21no—
182C22×C4—2831no—
183C22×C4—2831no—
184C22×C4—5661no—
185C22×C4—5661no—
186C22×C4C22×D28311yescharacteristic
187Q16—5664no—
188SD16—5664no—
189C2×C8—2832no—
190C2×C8C22×D28312yes—
191C4⋊C4—21no—
192C4⋊C4—2831no—
193C4⋊C4—5662no—
194C4⋊C4—5662no—
195C4⋊C4—5661no—
196C4⋊C4—5661no—
197C4⋊C4—5661no—
198C4⋊C4—5661no—
199C4⋊C4C22×D28312yes—
200C4⋊C4C22×D28311yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—5661no—
203C22⋊C4—5661no—
204C22⋊C4—5661no—
205C22⋊C4—5661no—
206C42—2831no—
207C42—2831no—
208C42—2831no—
209C42—2831no—
210C42—5662no—
211C42—5662no—
212C42—5661no—
213C23—21no—
214C23D4×D28311yescharacteristic
215Q8—2834no—
216Q8—5664no—
217Q8—5662no—
218Q8—5662no—
219D4—22no—
220D4—42no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—2831no—
226C2×C4—2831no—
227C2×C4—2831no—
228C2×C4—2831no—
229C2×C4—5664no—
230C2×C4—5662no—
231C2×C4—5662no—
232C2×C4—5661no—
233C2×C4—5661no—
234C2×C4—11321no—
235C2×C4—11322no—
236C2×C4D4×D28311yescharacteristic
237C2×C4C23×D28311yescharacteristic
238C8—22no—
239C8—5662no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#2258363912yes—
246C22C2×D4×D28311yescharacteristic
247C4—21no—
248C4—41no—
249C4—42no—
250C4—5664no—
251C4—5661no—
252C4—5661no—
253C4—5661no—
254C4—5661no—
255C4—11321no—
256C4—11321no—
257C4#41×D28312yes—
258C2—22no—
259C2—81no—
260C2#3182697311yescharacteristic
261C2C2×#2258363911yescharacteristic
262C2#3182726111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#481×C283C2
socleC22×C283C22×D4
prime radical#121×C283C22
hypercenter#481D283
hypocenterC283#3117
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#22583575C2semidirect
3. #31826800C2semidirect
4. #31826775C2semidirect
5. #31826686C2semidirect
6. #31826623C2semidirect
8. #31826571C2semidirect
9. #31826562C2semidirect
10. #31826519C2semidirect
131. C283#3117semidirect

Maximal subgroups

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

subgroupindex
#318269962
C2×#225835752
#318268002
#318267752
#318266862
#318266232
#318266032
#318265712
#318265622
#318265192
#481×C2832
#3117283