Finite Group Databasebeta

← #49121703

Subgroups — #49121703

Order 36224.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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#31826977C211yesmaximal, characteristic
2C2×C42×D283C211yesmaximal, characteristic, complemented
3C2×#22583538C211yesmaximal, characteristic, complemented
4C2×#22583536C211yesmaximal, characteristic, complemented
5#31826428C211yesmaximal, characteristic, complemented
6#31826224C211yesmaximal, characteristic, complemented
7#339×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C22×C4×D283—21no—
10C22×C4×D283C2211yescharacteristic
11C2×#17985376C2211yescharacteristic
12#22583594—21no—
13#22583590C412yescomplemented
14#22583585C412yescomplemented
15#22583580—21no—
16C4×D1132—22no—
17C2×C4×Dic283—21no—
18C2×C4×Dic283C2211yescharacteristic
19C42×D283—22no—
20C42×D283—22no—
21#22583538—22no—
22#22583536—22no—
23(C2×D283)⋊C8—22no—
24C2×M16×C283C2211yescharacteristic
25#117×C283C2211yescharacteristic
26C2×C42×C283C2211yescharacteristic
27C23×D283D411yescharacteristic
28#17985392—21no—
29#17985392—21no—
30#17985392—21no—
31#17985392—21no—
32C2×Dic566C2×C411yescharacteristic, complemented
33C2×D1132—22no—
34C2×D1132C2×C411yescharacteristic, complemented
35C2×C22⋊D283—21no—
36C22×Dic283—21no—
37C22×Dic283D411yescharacteristic
38C2×C4×D283—24no—
39C2×C4×D283—28no—
40C2×C4×D283—21no—
41C2×C4×D283—21no—
42C2×C4×D283—21no—
43C2×C4×D283—21no—
44C2×C4×D283—21no—
45C2×C4×D283C2×C412yes—
46C2×C4×D283D412yes—
47#17985376—21no—
48#17985376—21no—
49C2×C283⋊C8—21no—
50C4⋊Dic283—22no—
51(C2×D283)⋊C4—22no—
52(C2×D283)⋊C4—22no—
53C4×Dic283—24no—
54C4×Dic283—21no—
55C4×Dic283D412yescomplemented
56C22×C4×C283—21no—
57C22×C4×C283C2311yescharacteristic
58M16×C283—21no—
59M16×C283—21no—
60C2×C8×C283—21no—
61C4⋊C4×C283C2×C412yescomplemented
62C22⋊C4×C283—21no—
63C42×C283—21no—
64C42×C283—21no—
65C42×C283D412yescomplemented
66C22×D283—21no—
67C22×D283—21no—
68C22×D283—24no—
69C22×D283—21no—
70C22×D283C22⋊C412yes—
71Dic566—21no—
72Dic566—21no—
73D1132—21no—
74D1132—21no—
75D1132—44no—
76C22⋊D283—41no—
77C22⋊D283—41no—
78C2×Dic283—24no—
79C2×Dic283—21no—
80C2×Dic283—22no—
81C2×Dic283—21no—
82C2×Dic283—21no—
83C2×Dic283C22⋊C412yes—
84C4×D283—216no—
85C4×D283—22no—
86C4×D283—22no—
87C4×D283—22no—
88C4×D283—22no—
89C4×D283—41no—
90C4×D283—41no—
91C283⋊C8—41no—
92C23×C283C2×D411yescharacteristic
93C2×C4×C283—24no—
94C2×C4×C283—22no—
95C2×C4×C283—22no—
96C2×C4×C283C22×C411yescharacteristic
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283#4111yescharacteristic
101C2×C4×C283#4111yescharacteristic
102C8×C283—41no—
103C22×C283—22no—
104C22×C283C2×C22⋊C411yescharacteristic
105C22×C283#12011yescharacteristic
106C22×C283#12311yescharacteristic
107C2×D283—24no—
108C2×D283—24no—
109C2×D283—22no—
110C2×D283—22no—
111C2×D283—41no—
112C2×D283—42no—
113C2×D283#10414yescomplemented
114C4×C283—24no—
115C4×C283—42no—
116C4×C283C4×D411yescharacteristic
117C4×C283C4×D411yescharacteristic
118C4×C283#12111yescharacteristic
119C4×C283#12111yescharacteristic
120Dic283—24no—
121Dic283—22no—
122Dic283—41no—
123C2×C283—21no—
124C2×C283—21no—
125C2×C283#38611yescharacteristic
126C2×C283C2×#10412yes—
127D283—24no—
128D283—81no—
129C283#189611yescharacteristic, complemented, Sylow
130#1896—2831nomaximal, Sylow
131#525—2831no—
132C22×C42—2831no—
133C2×#104—2831no—
134C2×#104—2831no—
135#407—2831no—
136#339—2831no—
137#339D28311yescharacteristic, complemented
138C2×#41—2831no—
139C23×C4—2831no—
140C23×C4—5661no—
141C2×M16—2831no—
142C2×M16C2×D28311yescharacteristic
143#123—5661no—
144C22⋊Q8—2832no—
145#121—2832no—
146#120—5661no—
147C4×D4—5662no—
148#117C2×D28311yescharacteristic
149C2×C42—2831no—
150C2×C42—5662no—
151C2×C42—5661no—
152C2×C42—5662no—
153C2×C42C2×D28311yescharacteristic
154#104—5662no—
155#104—5662no—
156C22⋊C8—5662no—
157C24—2831no—
158#41—5661no—
159#41—5661no—
160#41—5661no—
161#41—5661no—
162C2×Q8—2831no—
163C2×D4—2831no—
164C2×D4—5662no—
165C2×D4—5661no—
166C22×C4—21no—
167C22×C4—2831no—
168C22×C4—2832no—
169C22×C4—2832no—
170C22×C4—5664no—
171C22×C4—5668no—
172C22×C4—5661no—
173C22×C4—5661no—
174C22×C4—5661no—
175C22×C4—5661no—
176C22×C4—5661no—
177C22×C4—5661no—
178C22×C4C22×D28311yescharacteristic
179M16—21no—
180M16—21no—
181M16—5661no—
182M16—5661no—
183C2×C8—21no—
184C2×C8—5661no—
185C4⋊C4—5662no—
186C4⋊C4C4×D28312yescomplemented
187C22⋊C4—21no—
188C22⋊C4—5662no—
189C22⋊C4—5662no—
190C42—21no—
191C42—21no—
192C42—2832no—
193C42—5664no—
194C42—5661no—
195C42D113212yescomplemented
196C23—2832no—
197C23—5664no—
198C23—5661no—
199C23—5661no—
200C23—5661no—
201C23D4×D28311yescharacteristic
202Q8—5661no—
203Q8—5661no—
204D4—5661no—
205D4—5661no—
206D4—11324no—
207D4—11321no—
208D4—11321no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—2832no—
213C2×C4—56616no—
214C2×C4—5664no—
215C2×C4—5662no—
216C2×C4—5661no—
217C2×C4—5661no—
218C2×C4—5662no—
219C2×C4—5662no—
220C2×C4—5662no—
221C2×C4—5662no—
222C2×C4—5661no—
223C2×C4—11321no—
224C2×C4—11321no—
225C2×C4C2×C4×D28311yescharacteristic
226C2×C4D4×D28311yescharacteristic
227C2×C4D4×D28311yescharacteristic
228C2×C4C2×D113211yescharacteristic
229C2×C4#1798539211yescharacteristic
230C2×C4#1798539311yescharacteristic
231C8—41no—
232C8—11321no—
233C22—22no—
234C22—2834no—
235C22—5664no—
236C22—5664no—
237C22—5662no—
238C22—5662no—
239C22—11322no—
240C22—11321no—
241C22C22⋊C4×D28311yescharacteristic
242C22#2258358011yescharacteristic
243C22#2258359511yescharacteristic
244C4—24no—
245C4—42no—
246C4—5664no—
247C4—5662no—
248C4—11321no—
249C4#2258357211yescharacteristic
250C4C4×D113211yescharacteristic
251C4#2258358311yescharacteristic
252C4#2258358511yescharacteristic
253C2—21no—
254C2—21no—
255C2—5664no—
256C2—22641no—
257C2#3182634311yescharacteristic
258C2#104×D28312yes—
subgroupG/H
centerC2×C4D4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#339×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31826977C2
cosocleC22×C4×C283C23
hypercenter#339D283
hypocenterC283#1896
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×C42×D283C2semidirect
3. C2×#22583538C2semidirect
4. C2×#22583536C2semidirect
5. #31826428C2semidirect
6. #31826224C2semidirect
7. #339×C283C2semidirect
13. #22583590C4semidirect
14. #22583585C4semidirect
32. C2×Dic566C2×C4semidirect
34. C2×D1132C2×C4semidirect
55. C4×Dic283D4semidirect
61. C4⋊C4×C283C2×C4semidirect
65. C42×C283D4semidirect
113. C2×D283#104semidirect
129. C283#1896semidirect
137. #339D283semidirect
186. C4⋊C4C4×D283semidirect
195. C42D1132semidirect

Maximal subgroups

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

subgroupindex
#318269772
C2×C42×D2832
C2×#225835382
C2×#225835362
#318264282
#318262242
#339×C2832
#1896283