Finite Group Databasebeta

← #49121790

Subgroups — #49121790

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#31827029C211yesmaximal, characteristic
2#31826939C211yesmaximal, characteristic, complemented
3#31826482C211yesmaximal, characteristic, complemented
4C2×#22583526C211yesmaximal, characteristic, complemented
5#31826222C211yesmaximal, characteristic, complemented
6#31826221C211yesmaximal, characteristic, complemented
7#421×C283C211yesmaximal, characteristic, complemented
8C22×D1132C2211yescharacteristic
9C2×#17985376C2211yescharacteristic
10#22583606C412yescomplemented
11#22583599C412yescomplemented
12#22583584—22no—
13#22583578—22no—
14C4×D1132—22no—
15#22583572—22no—
16#22583569C2211yescharacteristic
17#22583569C2211yescharacteristic
18C22⋊C4×D283—22no—
19#22583537—22no—
20#22583526—22no—
21C2×#41×C283C2211yescharacteristic
22C2×M16×C283C2211yescharacteristic
23#117×C283C2211yescharacteristic
24#104×C283—22no—
25C23×D283D412yes—
26C2×D1132—21no—
27C2×D1132—21no—
28C2×D1132—21no—
29C2×D1132—21no—
30C2×D1132C2×C412yes—
31C2×D1132D412yes—
32C2×C22⋊D283—24no—
33C2×C4×D283—24no—
34#17985376—21no—
35#17985376—21no—
36C2×C283⋊C8—21no—
37C4⋊Dic283—21no—
38C4⋊Dic283—21no—
39C22⋊Dic283—21no—
40C22⋊Dic283—21no—
41(C2×D283)⋊C4—24no—
42(C2×D283)⋊C4—24no—
43C4×Dic283C2×C412yescomplemented
44C4×Dic283D412yescomplemented
45#41×C283—21no—
46#41×C283—21no—
47#41×C283—21no—
48#41×C283—21no—
49C2×Q8×C283C2×C411yescharacteristic, complemented
50C2×D4×C283—21no—
51C2×D4×C283C2×C411yescharacteristic, complemented
52C22×C4×C283—21no—
53C22×C4×C283C2311yescharacteristic
54M16×C283—21no—
55M16×C283—21no—
56C2×C8×C283—21no—
57C4⋊C4×C283—21no—
58C22⋊C4×C283—21no—
59C42×C283D412yescomplemented
60C22×D283—22no—
61C22×D283—22no—
62C22×D283—82no—
63C22×D283C22⋊C414yes—
64D1132—22no—
65D1132—22no—
66D1132—22no—
67D1132—22no—
68C22⋊D283—84no—
69C2×Dic283—22no—
70C2×Dic283—22no—
71C4×D283—84no—
72C283⋊C8—41no—
73C23×C283—21no—
74C23×C283C2×D411yescharacteristic
75Q8×C283—21no—
76Q8×C283—21no—
77D4×C283—21no—
78D4×C283—21no—
79D4×C283—41no—
80D4×C283—41no—
81C2×C4×C283—21no—
82C2×C4×C283—22no—
83C2×C4×C283—41no—
84C2×C4×C283—41no—
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×C283—42no—
94C22×C283—41no—
95C22×C283C2×C22⋊C411yescharacteristic
96C22×C283#12011yescharacteristic
97C22×C283#12311yescharacteristic
98C2×D283—24no—
99C2×D283—44no—
100C2×D283—44no—
101C2×D283—82no—
102C4×C283—42no—
103C4×C283—41no—
104C4×C283C4×D411yescharacteristic
105C4×C283C4×D411yescharacteristic
106C4×C283#12111yescharacteristic
107C4×C283#12111yescharacteristic
108Dic283—42no—
109Dic283—42no—
110C2×C283—21no—
111C2×C283—21no—
112C2×C283—21no—
113C2×C283—81no—
114C2×C283#38611yescharacteristic
115D283—44no—
116C283#191111yescharacteristic, complemented, Sylow
117#1911—2831nomaximal, Sylow
118#535—2831no—
119#518—2831no—
120#421—2831no—
121#421D28311yescharacteristic, complemented
122C2×#100—2831no—
123H(3,ℤ/4)—2831no—
124H(3,ℤ/4)—2831no—
125C2×#41C2×D28311yescharacteristic
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#117—2831no—
137#117C2×D28311yescharacteristic
138C2×C22⋊C4—5662no—
139#104—22no—
140#104—5662no—
141#100—5662no—
142C24—2832no—
143#41—21no—
144#41—21no—
145#41—21no—
146#41—21no—
147C2×Q8C4×D28311yescharacteristic, complemented
148C2×D4—21no—
149C2×D4—2832no—
150C2×D4—2832no—
151C2×D4—5664no—
152C2×D4—5661no—
153C2×D4—5661no—
154C2×D4—5661no—
155C2×D4—5661no—
156C2×D4C4×D28311yescharacteristic, complemented
157C22×C4—21no—
158C22×C4—5664no—
159C22×C4C22×D28311yescharacteristic
160M16—21no—
161M16—21no—
162M16—5661no—
163M16—5661no—
164C2×C8—21no—
165C2×C8—5661no—
166C4⋊C4—21no—
167C4⋊C4—5661no—
168C4⋊C4—5661no—
169C22⋊C4—21no—
170C22⋊C4—5664no—
171C22⋊C4—5664no—
172C22⋊C4—5661no—
173C22⋊C4—5661no—
174C42—2832no—
175C42—2832no—
176C42C22⋊D28312yescomplemented
177C23—21no—
178C23—2834no—
179C23—5662no—
180C23—5662no—
181C23—22642no—
182C23D4×D28311yescharacteristic
183Q8—21no—
184Q8—21no—
185D4—21no—
186D4—21no—
187D4—41no—
188D4—41no—
189D4—5662no—
190D4—5662no—
191D4—5662no—
192D4—5662no—
193D4—22644no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—5662no—
199C2×C4—5662no—
200C2×C4—22644no—
201C2×C4C2×C4×D28311yescharacteristic
202C2×C4D4×D28311yescharacteristic
203C2×C4D4×D28311yescharacteristic
204C2×C4C2×C22⋊D28311yescharacteristic
205C2×C4#1798539111yescharacteristic
206C2×C4#1798539211yescharacteristic
207C8—41no—
208C8—11321no—
209C22—41no—
210C22—42no—
211C22—41no—
212C22—5664no—
213C22—11324no—
214C22—11324no—
215C22—22642no—
216C22C22⋊C4×D28311yescharacteristic
217C22#2258357811yescharacteristic
218C22#2258359211yescharacteristic
219C4—42no—
220C4—41no—
221C4—11322no—
222C4—11322no—
223C4(C22⋊D283)⋊C411yescharacteristic
224C4C4×C22⋊D28311yescharacteristic
225C4#2258358111yescharacteristic
226C4#2258358311yescharacteristic
227C2—21no—
228C2—21no—
229C2—21no—
230C2—81no—
231C2—11324no—
232C2#3182634111yescharacteristic
subgroupG/H
centerC2#31826341
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#421×C283C2
socleC2×C283#386
prime radical#31827029C2
cosocleC22×C4×C283C23
hypercenter#421D283
hypocenterC283#1911
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #31826939C2semidirect
3. #31826482C2semidirect
4. C2×#22583526C2semidirect
5. #31826222C2semidirect
6. #31826221C2semidirect
7. #421×C283C2semidirect
10. #22583606C4semidirect
11. #22583599C4semidirect
43. C4×Dic283C2×C4semidirect
44. C4×Dic283D4semidirect
49. C2×Q8×C283C2×C4semidirect
51. C2×D4×C283C2×C4semidirect
59. C42×C283D4semidirect
116. C283#1911semidirect
121. #421D283semidirect
147. C2×Q8C4×D283semidirect
156. C2×D4C4×D283semidirect
176. C42C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318270292
#318269392
#318264822
C2×#225835262
#318262222
#318262212
#421×C2832
#1911283