Finite Group Databasebeta

← #49131861

Subgroups — #49131861

Order 36224.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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#31826999C211yesmaximal, characteristic
2#31826871C211yesmaximal, characteristic, complemented
3#31826857C211yesmaximal, characteristic, complemented
4#31826833C211yesmaximal, characteristic, complemented
5#31826827C211yesmaximal, characteristic, complemented
6#31826721C212yesmaximal, complemented
7#31826713C212yesmaximal
8C4×#17985382C212yesmaximal, complemented
9C4×#17985379C212yesmaximal, complemented
10C4×#17985376C211yesmaximal, characteristic, complemented
11#533×C283C211yesmaximal, characteristic, complemented
12C2×#17985382C2212yes—
13C2×#17985379C2212yes—
14C2×#17985376C2212yes—
15#22583604—21no—
16#22583602C2211yescharacteristic
17#22583598C2211yescharacteristic
18#22583593—21no—
19#22583589C2211yescharacteristic
20#22583584C2211yescharacteristic
21C4×Dic566C2211yescharacteristic
22C4×D1132C2211yescharacteristic
23C4×C22⋊D283—21no—
24#22583567—21no—
25#22583543C2212yes—
26#22583541C2212yes—
27#22583534C2212yes—
28#22583534C2212yes—
29#22583533C2212yes—
30#22583530C2212yes—
31#22583521C2211yescharacteristic
32#22583521C2211yescharacteristic
33C4×C283⋊C8C2212yes—
34C4⋊Q8×C283C2211yescharacteristic
35C4⋊Q8×C283C2211yescharacteristic
36#125×C283—21no—
37C22⋊Q8×C283—21no—
38C22⋊Q8×C283C2212yes—
39C4×Q8×C283—21no—
40C4×Q8×C283C2212yes—
41#117×C283—21no—
42C2×C42×C283C2211yescharacteristic
43C2×Dic566C2311yescharacteristic
44C2×D1132C2311yescharacteristic
45C2×C22⋊D283—21no—
46C2×C4×D283—21no—
47#17985382—24no—
48#17985379—24no—
49#17985376—24no—
50C2×C283⋊C8C2312yes—
51C2×C283⋊C8C2312yes—
52C4⋊Dic283C2311yescharacteristic
53C4⋊Dic283C2311yescharacteristic
54Dic283⋊C4—21no—
55Dic283⋊C4—21no—
56Dic283⋊C4—21no—
57Dic283⋊C4—21no—
58C22⋊Dic283—21no—
59(C2×D283)⋊C4—21no—
60(C2×D283)⋊C4—21no—
61(C2×D283)⋊C4—21no—
62(C2×D283)⋊C4—21no—
63C4×Dic283—21no—
64C2×Q8×C283—21no—
65C2×Q8×C283C2312yes—
66C22×C4×C283D411yescharacteristic
67C22×C4×C283D411yescharacteristic
68C22×C4×C283C2311yescharacteristic
69C4⋊C4×C283—21no—
70C4⋊C4×C283—21no—
71C4⋊C4×C283—21no—
72C4⋊C4×C283—22no—
73C4⋊C4×C283—22no—
74C4⋊C4×C283C2312yes—
75C22⋊C4×C283—22no—
76C42×C283—22no—
77C42×C283D411yescharacteristic
78C42×C283D411yescharacteristic
79C42×C283C2311yescharacteristic
80C42×C283C2311yescharacteristic
81C22×D283—21no—
82Dic566—22no—
83D1132—22no—
84C22⋊D283—42no—
85C2×Dic283—21no—
86C2×Dic283—21no—
87C2×Dic283—21no—
88C4×D283—42no—
89C283⋊C8—22no—
90C283⋊C8#4114yes—
91C23×C283C2×D411yescharacteristic
92Q8×C283—22no—
93Q8×C283—22no—
94Q8×C283—42no—
95C2×C4×C283—22no—
96C2×C4×C283—22no—
97C2×C4×C283—22no—
98C2×C4×C283—22no—
99C2×C4×C283—41no—
100C2×C4×C283C2×D411yescharacteristic
101C2×C4×C283C2×D411yescharacteristic
102C2×C4×C283C2×D411yescharacteristic
103C2×C4×C283C2×D411yescharacteristic
104C2×C4×C283C2×D411yescharacteristic
105C2×C4×C283C2411yescharacteristic
106C22×C283—21no—
107C22×C283—21no—
108C22×C283—21no—
109C22×C283C22×D411yescharacteristic
110C2×D283—41no—
111C2×D283—41no—
112C2×D283—41no—
113C4×C283—21no—
114C4×C283—21no—
115C4×C283—21no—
116C4×C283—21no—
117C4×C283—42no—
118C4×C283—42no—
119C4×C283#13712yes—
120C4×C283C2×#4112yes—
121Dic283—41no—
122Dic283—41no—
123Dic283—41no—
124C2×C283—41no—
125C2×C283#53211yescharacteristic
126C2×C283C2×#13711yescharacteristic
127C2×C283#57511yescharacteristic
128D283—81no—
129C283#317211yescharacteristic, complemented, Sylow
130#3172—2831nomaximal, Sylow
131#533D28311yescharacteristic, complemented
132#529—2831no—
133#501—2831no—
134#497—2831no—
135#491—2831no—
136#489—2831no—
137#470—2832no—
138#468—2832no—
139C4×Q16—2832no—
140C4×SD16—2832no—
141C4×M16—2831no—
142C2×Q16—2832no—
143C2×SD16—2832no—
144C2×M16—2832no—
145C4⋊Q8C2×D28311yescharacteristic
146C4⋊Q8C2×D28311yescharacteristic
147#126—5661no—
148#125—21no—
149#125—2831no—
150#124—2831no—
151#123—5661no—
152C22⋊Q8—21no—
153C22⋊Q8—2831no—
154C22⋊Q8C2×D28312yes—
155#121—2831no—
156C4×Q8—21no—
157C4×Q8—2831no—
158C4×Q8C2×D28312yes—
159C4×D4—2831no—
160C4×D4—5661no—
161#117—21no—
162#117—5661no—
163C2×C42C2×D28311yescharacteristic
164#107—2832no—
165#106—2832no—
166#103—2832no—
167#103—2832no—
168#103—2832no—
169#102—2832no—
170#97—2831no—
171#97—2831no—
172C4×C8—2832no—
173C2×Q8—21no—
174C2×Q8—2831no—
175C2×Q8C22×D28312yes—
176C2×D4—2831no—
177C2×D4—5661no—
178C22×C4—5661no—
179C22×C4C22⋊D28311yescharacteristic
180C22×C4C22⋊D28311yescharacteristic
181C22×C4C22×D28311yescharacteristic
182Q16—5664no—
183SD16—5664no—
184M16—5664no—
185C2×C8—2832no—
186C2×C8—2832no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—2831no—
193C4⋊C4—2831no—
194C4⋊C4—5661no—
195C4⋊C4—5661no—
196C4⋊C4—5661no—
197C4⋊C4—5661no—
198C4⋊C4C22×D28312yes—
199C22⋊C4—22no—
200C22⋊C4—5661no—
201C22⋊C4—5661no—
202C22⋊C4—5661no—
203C22⋊C4—5661no—
204C22⋊C4—5661no—
205C42—22no—
206C42—5661no—
207C42C22⋊D28311yescharacteristic
208C42C22⋊D28311yescharacteristic
209C42C22×D28311yescharacteristic
210C42C22×D28311yescharacteristic
211C23—5661no—
212C23C2×C22⋊D28311yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—5662no—
217D4—5662no—
218D4—11322no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—5661no—
225C2×C4—5661no—
226C2×C4—5661no—
227C2×C4—11322no—
228C2×C4C2×C22⋊D28311yescharacteristic
229C2×C4C2×C22⋊D28311yescharacteristic
230C2×C4C2×C22⋊D28311yescharacteristic
231C2×C4C2×C22⋊D28311yescharacteristic
232C2×C4C2×C22⋊D28311yescharacteristic
233C2×C4C23×D28311yescharacteristic
234C8—2834no—
235C8—5662no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—11321no—
240C22—11321no—
241C22—11321no—
242C22C22×C22⋊D28311yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—11321no—
250C4—11321no—
251C4—11321no—
252C4#2258364112yes—
253C4#41×D28312yes—
254C2—41no—
255C2—22641no—
256C2#3182701111yescharacteristic
257C2C2×#2258364111yescharacteristic
258C2#3182726311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#533×C283C2
socleC22×C283C22×D4
prime radical#22583584C22
hypercenter#533D283
hypocenterC283#3172
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #31826871C2semidirect
3. #31826857C2semidirect
4. #31826833C2semidirect
5. #31826827C2semidirect
6. #31826721C2semidirect
8. C4×#17985382C2semidirect
9. C4×#17985379C2semidirect
10. C4×#17985376C2semidirect
11. #533×C283C2semidirect
129. C283#3172semidirect
131. #533D283semidirect

Maximal subgroups

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

subgroupindex
#318269992
#318268712
#318268572
#318268332
#318268272
#318267212
#318267132
C4×#179853822
C4×#179853792
C4×#179853762
#533×C2832
#3172283