Finite Group Databasebeta

← #49121792

Subgroups — #49121792

Order 36224.

362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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#31827034C211yesmaximal, characteristic
2#31826939C211yesmaximal, characteristic, complemented
3#31826483C211yesmaximal, characteristic, complemented
4#31826481C211yesmaximal, characteristic, complemented
5C2×#22583526C211yesmaximal, characteristic, complemented
6#31826221C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C22×D1132C2211yescharacteristic
10C2×#17985376C2211yescharacteristic
11#22583607C412yescomplemented
12#22583598C412yescomplemented
13#22583585—22no—
14#22583580—22no—
15C4×D1132—22no—
16#22583572—22no—
17#22583569C2211yescharacteristic
18C22⋊C4×D283—22no—
19#22583538—22no—
20#22583536—22no—
21#22583526—22no—
22C2×M16×C283C2211yescharacteristic
23#117×C283C2211yescharacteristic
24#117×C283C2211yescharacteristic
25C23×D283D412yes—
26#17985392—21no—
27#17985392—21no—
28#17985392—21no—
29#17985392—21no—
30C2×Dic566C2×C411yescharacteristic, complemented
31C2×D1132—24no—
32C2×D1132—21no—
33C2×D1132—21no—
34C2×D1132—21no—
35C2×D1132—21no—
36C2×D1132C2×C412yes—
37C2×D1132C2×C411yescharacteristic, complemented
38C2×D1132D412yes—
39C2×C22⋊D283—21no—
40C2×C4×D283—24no—
41C2×C4×D283—21no—
42#17985376—21no—
43#17985376—21no—
44C2×C283⋊C8—21no—
45C4⋊Dic283—21no—
46C22⋊Dic283—21no—
47(C2×D283)⋊C4—24no—
48(C2×D283)⋊C4—24no—
49C4×Dic283D412yescomplemented
50C22×C4×C283C2311yescharacteristic
51M16×C283—21no—
52M16×C283—21no—
53C2×C8×C283—21no—
54C4⋊C4×C283—21no—
55C4⋊C4×C283—21no—
56C22⋊C4×C283—21no—
57C22⋊C4×C283—21no—
58C42×C283C2×C412yescomplemented
59C42×C283D412yescomplemented
60C22×D283—22no—
61C22×D283—22no—
62C22×D283—21no—
63C22×D283—82no—
64C22×D283C22⋊C414yes—
65Dic566—21no—
66Dic566—21no—
67D1132—22no—
68D1132—22no—
69D1132—21no—
70D1132—21no—
71D1132—22no—
72D1132—22no—
73D1132—84no—
74C22⋊D283—41no—
75C22⋊D283—41no—
76C2×Dic283—21no—
77C2×Dic283—22no—
78C4×D283—41no—
79C4×D283—41no—
80C4×D283—84no—
81C283⋊C8—41no—
82C23×C283C2×D411yescharacteristic
83C2×C4×C283—22no—
84C2×C4×C283—22no—
85C2×C4×C283C22×C411yescharacteristic
86C2×C4×C283C2×D411yescharacteristic
87C2×C4×C283C2×D411yescharacteristic
88C2×C4×C283C2×D411yescharacteristic
89C2×C4×C283#4111yescharacteristic
90C2×C4×C283#4111yescharacteristic
91C8×C283—41no—
92C22×C283—41no—
93C22×C283C2×C22⋊C411yescharacteristic
94C22×C283#12011yescharacteristic
95C22×C283#12311yescharacteristic
96C2×D283—24no—
97C2×D283—44no—
98C2×D283—44no—
99C2×D283—42no—
100C2×D283—41no—
101C2×D283—82no—
102C4×C283—42no—
103C4×C283—42no—
104C4×C283C4×D411yescharacteristic
105C4×C283C4×D411yescharacteristic
106C4×C283#12111yescharacteristic
107C4×C283#12111yescharacteristic
108Dic283—42no—
109Dic283—41no—
110C2×C283—21no—
111C2×C283—21no—
112C2×C283—21no—
113C2×C283#38611yescharacteristic
114D283—44no—
115D283—81no—
116C283#191111yescharacteristic, complemented, Sylow
117#1911—2831nomaximal, Sylow
118#535—2831no—
119#518—2831no—
120#421—2831no—
121#421—2831no—
122C2×#100—2831no—
123H(3,ℤ/4)—2831no—
124H(3,ℤ/4)D28311yescharacteristic, complemented
125C2×#41—2831no—
126C22×D4—2831no—
127C2×M16—2831no—
128C2×M16C2×D28311yescharacteristic
129#127—2832no—
130#124—2832no—
131#121—5662no—
132#120—5662no—
133C4×D4—5662no—
134C4×D4—5662no—
135#117—2831no—
136#117C2×D28311yescharacteristic
137#117C2×D28311yescharacteristic
138C2×C22⋊C4—5662no—
139#104—5662no—
140#104—5662no—
141#100—5662no—
142C24—2832no—
143#41—5661no—
144#41—5661no—
145#41—5661no—
146#41—5661no—
147C2×Q8—2831no—
148C2×D4—2832no—
149C2×D4—2831no—
150C2×D4—2832no—
151C2×D4—5664no—
152C2×D4—5661no—
153C2×D4—5661no—
154C2×D4—5661no—
155C2×D4—5661no—
156C2×D4—5661no—
157C22×C4—5664no—
158C22×C4—5661no—
159C22×C4C22×D28311yescharacteristic
160M16—21no—
161M16—21no—
162M16—5661no—
163M16—5661no—
164C2×C8—21no—
165C2×C8—5661no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—5661no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—5664no—
172C22⋊C4—5664no—
173C22⋊C4—5661no—
174C42—2832no—
175C42C4×D28312yescomplemented
176C42D113212yescomplemented
177C23—2834no—
178C23—5662no—
179C23—5662no—
180C23—5661no—
181C23—22642no—
182C23D4×D28311yescharacteristic
183Q8—5661no—
184Q8—5661no—
185D4—5662no—
186D4—5661no—
187D4—5662no—
188D4—5661no—
189D4—5662no—
190D4—5662no—
191D4—11321no—
192D4—11321no—
193D4—22644no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—5661no—
197C2×C4—5662no—
198C2×C4—11321no—
199C2×C4—11321no—
200C2×C4—22644no—
201C2×C4C2×C4×D28311yescharacteristic
202C2×C4D4×D28311yescharacteristic
203C2×C4D4×D28311yescharacteristic
204C2×C4C2×D113211yescharacteristic
205C2×C4#1798539211yescharacteristic
206C2×C4#1798539311yescharacteristic
207C8—41no—
208C8—11321no—
209C22—41no—
210C22—5664no—
211C22—11324no—
212C22—11324no—
213C22—11322no—
214C22—11321no—
215C22—22642no—
216C22C22⋊C4×D28311yescharacteristic
217C22#2258358011yescharacteristic
218C22#2258359511yescharacteristic
219C4—42no—
220C4—42no—
221C4—11322no—
222C4—11321no—
223C4#2258357211yescharacteristic
224C4C4×D113211yescharacteristic
225C4#2258358311yescharacteristic
226C4#2258358511yescharacteristic
227C2—21no—
228C2—21no—
229C2—21no—
230C2—11324no—
231C2—22641no—
232C2#3182634311yescharacteristic
subgroupG/H
centerC2#31826343
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingH(3,ℤ/4)×C283C2
socleC2×C283#386
prime radical#31827034C2
cosocleC22×C4×C283C23
hypercenterH(3,ℤ/4)D283
hypocenterC283#1911
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #31826939C2semidirect
3. #31826483C2semidirect
4. #31826481C2semidirect
5. C2×#22583526C2semidirect
6. #31826221C2semidirect
7. H(3,ℤ/4)×C283C2semidirect
11. #22583607C4semidirect
12. #22583598C4semidirect
30. C2×Dic566C2×C4semidirect
37. C2×D1132C2×C4semidirect
49. C4×Dic283D4semidirect
58. C42×C283C2×C4semidirect
59. C42×C283D4semidirect
116. C283#1911semidirect
124. H(3,ℤ/4)D283semidirect
175. C42C4×D283semidirect
176. C42D1132semidirect

Maximal subgroups

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

subgroupindex
#318270342
#318269392
#318264832
#318264812
C2×#225835262
#318262212
H(3,ℤ/4)×C2832
#1911283