Finite Group Databasebeta

← #49122292

Subgroups — #49122292

Order 36224.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#22583643C211yesmaximal, characteristic, complemented
2#31827032C211yesmaximal, characteristic
3C2×#22583597C211yesmaximal, characteristic, complemented
4C2×#22583536C211yesmaximal, characteristic, complemented
5#31826475C211yesmaximal, characteristic, complemented
6#31826226C211yesmaximal, characteristic, complemented
7C2×#100×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C22×Dic566C2211yescharacteristic
10#22583643—22no—
11#22583643—22no—
12C2×Dic1132—21no—
13C2×#17985381—21no—
14#22583606—21no—
15#22583597—21no—
16#22583597—22no—
17#22583597—22no—
18#22583581—22no—
19#22583579—22no—
20#22583569C2211yescharacteristic
21C2×C22⋊Dic283—22no—
22C2×C4×Dic283C2211yescharacteristic
23#22583536—22no—
24#22583535—22no—
25C22×D4×C283C2211yescharacteristic
26C2×M16×C283C2211yescharacteristic
27C2×M16×C283C2211yescharacteristic
28#100×C283—22no—
29#17985392—21no—
30#17985392—21no—
31#17985392—21no—
32#17985392—21no—
33C2×Dic566—21no—
34C2×Dic566—21no—
35C2×Dic566—21no—
36C2×Dic566—21no—
37C2×Dic566—21no—
38C2×Dic566D411yescharacteristic
39C2×Dic566D412yescomplemented
40C2×D1132D411yescharacteristic
41C2×C22⋊D283—24no—
42C2×C22⋊D283—21no—
43C22×Dic283—21no—
44C22×Dic283—21no—
45C2×C4×D283—21no—
46Dic1132—24no—
47#17985381—24no—
48C4⋊Dic283D412yes—
49C22⋊Dic283—28no—
50C22⋊Dic283—24no—
51C22⋊Dic283—21no—
52C4×Dic283—21no—
53C4×Dic283—21no—
54C4×Dic283D412yescomplemented
55C24×C283D412yes—
56C2×D4×C283—21no—
57C2×D4×C283—21no—
58C2×D4×C283—21no—
59C2×D4×C283—21no—
60C2×D4×C283—21no—
61C2×D4×C283—21no—
62C22×C4×C283C2311yescharacteristic
63M16×C283—21no—
64M16×C283—21no—
65M16×C283—21no—
66M16×C283D412yescomplemented
67C2×C8×C283—21no—
68C2×C8×C283—21no—
69C22×D283—21no—
70Dic566—22no—
71Dic566—21no—
72Dic566—22no—
73Dic566—21no—
74Dic566—41no—
75Dic566—41no—
76D1132—21no—
77D1132—21no—
78C22⋊D283—41no—
79C22⋊D283—41no—
80C22⋊D283—84no—
81C2×Dic283—22no—
82C2×Dic283—22no—
83C2×Dic283—21no—
84C2×Dic283—22no—
85C2×Dic283—42no—
86C2×Dic283—41no—
87C2×Dic283—41no—
88C4×D283—41no—
89C4×D283—41no—
90C23×C283—22no—
91C23×C283—22no—
92C23×C283—22no—
93C23×C283—44no—
94C23×C283C2×D411yescharacteristic
95D4×C283—41no—
96D4×C283—41no—
97D4×C283—41no—
98D4×C283—41no—
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2×D411yescharacteristic
101C2×C4×C283C2×D411yescharacteristic
102C2×C4×C283C2×D411yescharacteristic
103C2×C4×C283C2×D411yescharacteristic
104C2×C4×C283#4111yescharacteristic
105C8×C283—22no—
106C8×C283—41no—
107C22×C283—22no—
108C22×C283—44no—
109C22×C283—42no—
110C22×C283—44no—
111C22×C283—82no—
112C22×C283#12011yescharacteristic
113C22×C283#12011yescharacteristic
114C22×C283#12111yescharacteristic
115C2×D283—41no—
116C2×D283—42no—
117C4×C283#12011yescharacteristic
118C4×C283#12111yescharacteristic
119C4×C283#12111yescharacteristic
120C4×C283#12711yescharacteristic
121Dic283—42no—
122Dic283—41no—
123Dic283—42no—
124Dic283—42no—
125C2×C283—21no—
126C2×C283—21no—
127C2×C283—82no—
128C2×C283#39211yescharacteristic
129C2×C283#45512yes—
130D283—81no—
131C283#200411yescharacteristic, complemented, Sylow
132#2004—2831nomaximal, Sylow
133C2×#137—2831no—
134#535—2831no—
135C2×#124—2831no—
136C2×#104—2831no—
137#419—2831no—
138C2×#100D28311yescharacteristic, complemented
139#339—2831no—
140C2×#41—2831no—
141C22×Q8—2831no—
142C22×D4C2×D28311yescharacteristic
143#137—5662no—
144#137—5662no—
145C2×Q16—5661no—
146C2×SD16—5661no—
147C2×M16C2×D28311yescharacteristic
148C2×M16C2×D28311yescharacteristic
149#127—5661no—
150#124—5662no—
151#124—5662no—
152#124—5661no—
153#121—5662no—
154#120—5662no—
155#117—2831no—
156C2×C22⋊C4—5662no—
157C2×C42—2831no—
158#104—5662no—
159#103—5662no—
160#100—22no—
161C24D113212yes—
162#41—5661no—
163#41—5661no—
164#41—5661no—
165#41—5661no—
166C2×Q8—2831no—
167C2×Q8—2832no—
168C2×Q8—5661no—
169C2×Q8—5661no—
170C2×Q8—5661no—
171C2×Q8—5661no—
172C2×Q8—5661no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—2831no—
180C2×D4—5661no—
181C2×D4—5664no—
182C22×C4—5661no—
183C22×C4—5661no—
184C22×C4—5661no—
185C22×C4C22×D28311yescharacteristic
186Q16—5664no—
187SD16—5664no—
188M16—21no—
189M16—21no—
190M16—21no—
191M16C22⋊D28312yescomplemented
192C2×C8—21no—
193C2×C8—21no—
194C4⋊C4—2832no—
195C22⋊C4—5668no—
196C22⋊C4—5664no—
197C22⋊C4—5661no—
198C42—2832no—
199C42—5661no—
200C42—5661no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—5661no—
206C23C2×D113211yescharacteristic
207Q8—5662no—
208Q8—5661no—
209Q8—5662no—
210Q8—5661no—
211Q8—11321no—
212Q8—11321no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—5661no—
218D4—5661no—
219D4—11321no—
220D4—11321no—
221D4—22644no—
222C2×C4—5662no—
223C2×C4—5662no—
224C2×C4—5662no—
225C2×C4—5661no—
226C2×C4—11322no—
227C2×C4—11321no—
228C2×C4—11321no—
229C2×C4—11321no—
230C2×C4—11321no—
231C2×C4D4×D28311yescharacteristic
232C2×C4D4×D28311yescharacteristic
233C2×C4D4×D28311yescharacteristic
234C2×C4D4×D28311yescharacteristic
235C2×C4C2×C22⋊D28311yescharacteristic
236C2×C4#1798539211yescharacteristic
237C8—22no—
238C8—41no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—11321no—
245C22—11322no—
246C22#2258358011yescharacteristic
247C22#2258358011yescharacteristic
248C22#2258358411yescharacteristic
249C4—11322no—
250C4—11321no—
251C4—11322no—
252C4—11322no—
253C4#2258357811yescharacteristic
254C4#2258358311yescharacteristic
255C4#2258358311yescharacteristic
256C4#2258360611yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—22641no—
261C2#3182637411yescharacteristic
262C2#3182664512yes—
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingC2×#100×C283C2
socleC22×C283#120
prime radical#31827032C2
hypercenterC2×#100D283
hypocenterC283#2004
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#22583643C2semidirect
3. C2×#22583597C2semidirect
4. C2×#22583536C2semidirect
5. #31826475C2semidirect
6. #31826226C2semidirect
7. C2×#100×C283C2semidirect
39. C2×Dic566D4semidirect
54. C4×Dic283D4semidirect
66. M16×C283D4semidirect
131. C283#2004semidirect
138. C2×#100D283semidirect
191. M16C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
#318270322
C2×#225835972
C2×#225835362
#318264752
#318262262
C2×#100×C2832
#2004283