Finite Group Databasebeta

← #49131435

Subgroups — #49131435

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#31827001C211yesmaximal, characteristic
2C2×#22583575C211yesmaximal, characteristic, complemented
3#31826783C211yesmaximal, characteristic
4#31826771C212yesmaximal, complemented
5#31826690C212yesmaximal, complemented
6#31826620C211yesmaximal, characteristic, complemented
7#31826606C211yesmaximal, characteristic
8#31826569C212yesmaximal, complemented
9#31826564C212yesmaximal, complemented
10#31826519C211yesmaximal, characteristic, complemented
11#484×C283C211yesmaximal, characteristic, complemented
12C22×Dic566C2211yescharacteristic
13C2×#17985382C2212yes—
14C2×#17985381C2212yes—
15#22583605—21no—
16#22583601C2211yescharacteristic
17#22583599C2211yescharacteristic
18#22583594—21no—
19#22583584C2211yescharacteristic
20Q8×Dic283C2211yescharacteristic
21#22583575—21no—
22#22583575—21no—
23#22583575C2212yes—
24#22583575C2212yes—
25#22583572C2211yescharacteristic
26(C22⋊D283)⋊C4—21no—
27#22583568—21no—
28C2×Dic283⋊C4—21no—
29C2×C4×Dic283—21no—
30C2×C4×Dic283C2211yescharacteristic
31#22583541C2212yes—
32Dic283⋊C8C2212yes—
33#22583535C2212yes—
34#22583533C2212yes—
35#22583530C2212yes—
36C22⋊(C283⋊C8)C2211yescharacteristic
37#22583520C2212yes—
38C22⋊Q8×C283C2211yescharacteristic
39C2×C4⋊C4×C283C2211yescharacteristic
40#107×C283C2212yes—
41#103×C283C2212yes—
42C22⋊C8×C283C2211yescharacteristic
43C2×Dic566—24no—
44C2×Dic566—21no—
45C2×Dic566C2312yes—
46C2×D1132C2311yescharacteristic
47C2×C22⋊D283—21no—
48C22×Dic283—21no—
49C22×Dic283D411yescharacteristic
50C22×Dic283D411yescharacteristic
51C2×C4×D283—21no—
52#17985382—24no—
53#17985381—24no—
54C2×C283⋊C8C2312yes—
55C4⋊Dic283—21no—
56C4⋊Dic283—21no—
57C4⋊Dic283C2311yescharacteristic
58Dic283⋊C4—22no—
59Dic283⋊C4—22no—
60Dic283⋊C4—21no—
61(C2×D283)⋊C4—21no—
62(C2×D283)⋊C4—21no—
63(C2×D283)⋊C4—21no—
64(C2×D283)⋊C4—21no—
65C4×Dic283—22no—
66C4×Dic283—22no—
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×C283C2311yescharacteristic
79C4⋊C4×C283C2312yes—
80C22⋊C4×C283—21no—
81C22×D283—21no—
82Dic566—24no—
83Dic566—22no—
84Dic566#4114yes—
85D1132—22no—
86C22⋊D283—42no—
87C2×Dic283—24no—
88C2×Dic283—22no—
89C2×Dic283—22no—
90C2×Dic283—21no—
91C2×Dic283—41no—
92C2×Dic283C2×D411yescharacteristic
93C2×Dic283C2×D411yescharacteristic
94C2×Dic283C2×D411yescharacteristic
95C2×Dic283C2×D411yescharacteristic
96C4×D283—42no—
97C283⋊C8—22no—
98C23×C283C2×D411yescharacteristic
99Q8×C283—22no—
100C2×C4×C283—22no—
101C2×C4×C283—21no—
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#13712yes—
111C22×C283C22×D411yescharacteristic
112C2×D283—41no—
113C2×D283—41no—
114C2×D283—41no—
115C4×C283—21no—
116C4×C283—41no—
117C4×C283—42no—
118C4×C283—41no—
119C4×C283C2×#4112yes—
120Dic283—24no—
121Dic283—21no—
122Dic283—21no—
123Dic283—21no—
124Dic283—21no—
125Dic283—41no—
126C2×C283—22no—
127C2×C283#52511yescharacteristic
128C2×C283C2×#13711yescharacteristic
129C2×C283#57511yescharacteristic
130D283—81no—
131C283#311711yescharacteristic, complemented, Sylow
132#3117—2831nomaximal, Sylow
133#529—2831no—
134C2×C4×Q8—2831no—
135#484D28311yescharacteristic, complemented
136#481—2831no—
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⋊Q8C2×D28311yescharacteristic
152#121—2831no—
153C4×Q8—2831no—
154C4×Q8—2832no—
155C4×Q8—2832no—
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#107C2×D28312yes—
166#106—2832no—
167C4⋊C8—2832no—
168#103—2832no—
169#103—2832no—
170#103C2×D28312yes—
171#102—2832no—
172C22⋊C8—2831no—
173C22⋊C8C2×D28311yescharacteristic
174#97—2832no—
175C2×Q8—2832no—
176C2×Q8—5664no—
177C2×Q8—5661no—
178C2×Q8C22×D28311yescharacteristic
179C2×D4—2831no—
180C2×D4—5661no—
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—21no—
193C4⋊C4—2831no—
194C4⋊C4—5662no—
195C4⋊C4—5662no—
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—5661no—
214C23D4×D28311yescharacteristic
215Q8—22no—
216Q8—2834no—
217Q8—5664no—
218Q8—5662no—
219D4—5662no—
220D4—11322no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—2831no—
227C2×C4—2831no—
228C2×C4—2831no—
229C2×C4—2831no—
230C2×C4—5664no—
231C2×C4—5662no—
232C2×C4—5662no—
233C2×C4—5661no—
234C2×C4—11322no—
235C2×C4—11321no—
236C2×C4D4×D28311yescharacteristic
237C2×C4C23×D28311yescharacteristic
238C8—22no—
239C8—5662no—
240C22—21no—
241C22—21no—
242C22—11321no—
243C22—11321no—
244C22—11321no—
245C22#2258364212yes—
246C22C2×D4×D28311yescharacteristic
247C4—21no—
248C4—41no—
249C4—42no—
250C4—41no—
251C4—5664no—
252C4—5661no—
253C4—5661no—
254C4—5661no—
255C4—5661no—
256C4—11321no—
257C4#41×D28312yes—
258C2—22no—
259C2—22641no—
260C2#3182697311yescharacteristic
261C2C2×#2258364211yescharacteristic
262C2#3182726111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#484×C283C2
socleC22×C283C22×D4
prime radical#22583584C22
hypercenter#484D283
hypocenterC283#3117
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#22583575C2semidirect
4. #31826771C2semidirect
5. #31826690C2semidirect
6. #31826620C2semidirect
8. #31826569C2semidirect
9. #31826564C2semidirect
10. #31826519C2semidirect
11. #484×C283C2semidirect
131. C283#3117semidirect
135. #484D283semidirect

Maximal subgroups

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

subgroupindex
#318270012
C2×#225835752
#318267832
#318267712
#318266902
#318266202
#318266062
#318265692
#318265642
#318265192
#484×C2832
#3117283