Finite Group Databasebeta

← #49123205

Subgroups — #49123205

Order 36224.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#31827262C211yesmaximal, characteristic, complemented
2#31826901C211yesmaximal, characteristic, complemented
3#31826715C211yesmaximal, characteristic, complemented
4#31826276C211yesmaximal, characteristic, complemented
5#31826275C211yesmaximal, characteristic, complemented
6#31826246C211yesmaximal, characteristic, complemented
7#509×C283C211yesmaximal, characteristic, complemented
8#41×D283—21no—
9#22583642—21no—
10#22583639—21no—
11#22583637—21no—
12#22583634—21no—
13#22583632C2211yescharacteristic
14#22583630—21no—
15C2×#17985375C2211yescharacteristic
16#22583581—21no—
17#22583554—21no—
18#22583551—21no—
19#22583550C2211yescharacteristic, complemented
20#22583542C2211yescharacteristic, complemented
21#22583531—21no—
22#135×C283C2211yescharacteristic
23C2×D8×C283C2211yescharacteristic, complemented
24SD32×C283—21no—
25D16×C283—21no—
26M32×C283C2211yescharacteristic, complemented
27#17985393—21no—
28#17985392—21no—
29#17985392—41no—
30#17985391—21no—
31#17985391—41no—
32Q8×D283—21no—
33C2×C22⋊D283—41no—
34D4×D283—21no—
35D4×D283—41no—
36C2×C4×D283—41no—
37C2×C4×D283D411yescharacteristic
38Dic1132D411yescharacteristic, complemented
39#17985382—21no—
40#17985381—21no—
41#17985380—21no—
42#17985379—21no—
43D2264D411yescharacteristic, complemented
44#17985377—21no—
45#17985375—21no—
46#17985375—21no—
47C2×C283⋊C8D411yescharacteristic
48C4⋊Dic283—21no—
49C22⋊Dic283—41no—
50C283⋊C16—21no—
51#41×C283—21no—
52C2×D4×C283—21no—
53Q16×C283D411yescharacteristic, complemented
54SD16×C283—21no—
55D8×C283—21no—
56D8×C283—21no—
57D8×C283D411yescharacteristic, complemented
58C2×C8×C283C2311yescharacteristic
59C16×C283—21no—
60C22×D283—41no—
61C22×D283D811yescharacteristic
62Dic566—21no—
63Dic566—41no—
64D1132—21no—
65D1132—41no—
66C22⋊D283—41no—
67C22⋊D283—41no—
68C22⋊D283—41no—
69C22⋊D283—82no—
70C2×Dic283—41no—
71C2×Dic283—41no—
72C2×Dic283D811yescharacteristic
73C4×D283—21no—
74C4×D283—21no—
75C4×D283—41no—
76C4×D283—41no—
77C4×D283—41no—
78C283⋊C8—21no—
79C23×C283—41no—
80Q8×C283—21no—
81D4×C283—21no—
82D4×C283—41no—
83D4×C283—41no—
84D4×C283—41no—
85C2×C4×C283—41no—
86C2×C4×C283C2×D411yescharacteristic
87C8×C283C2×D411yescharacteristic
88C8×C283C2×D411yescharacteristic
89C22×C283—41no—
90C22×C283—81no—
91C22×C283—81no—
92C22×C283—81no—
93C22×C283C2×D811yescharacteristic
94C2×D283—21no—
95C2×D283—41no—
96C2×D283—41no—
97C2×D283—82no—
98C4×C283—41no—
99C4×C283#12011yescharacteristic
100C4×C283AGL(1,ℤ/8)11yescharacteristic
101Dic283—21no—
102Dic283—41no—
103Dic283—81no—
104C2×C283—21no—
105C2×C283—81no—
106C2×C283—161no—
107C2×C283#44711yescharacteristic
108D283—41no—
109D283—81no—
110C283#219011yescharacteristic, complemented, Sylow
111#2190—2831nomaximal, Sylow
112#575—2831no—
113#509—2831no—
114#509D28311yescharacteristic, complemented
115#469—2831no—
116#360—2831no—
117#360—2831no—
118#349—2831no—
119C2×#41—5661no—
120#137—5661no—
121#137—5661no—
122AGL(1,ℤ/8)—5661no—
123AGL(1,ℤ/8)—5661no—
124#135—2831no—
125#135—5661no—
126#135C2×D28311yescharacteristic
127C2×D8C2×D28311yescharacteristic, complemented
128C2×M16—2831no—
129#121—5661no—
130SD32—21no—
131SD32—5661no—
132D16—21no—
133D16—5661no—
134M32—2831no—
135M32C2×D28311yescharacteristic, complemented
136#106—2831no—
137#102—5661no—
138#41—21no—
139#41—5661no—
140#41—5661no—
141#41—5661no—
142#41—11321no—
143#41—11321no—
144C2×Q8—5661no—
145C2×D4—21no—
146C2×D4—5661no—
147C2×D4—11321no—
148C2×D4—11321no—
149C22×C4—2831no—
150C22×C4—11321no—
151Q16—2831no—
152Q16—5661no—
153Q16C22⋊D28311yescharacteristic, complemented
154SD16—21no—
155SD16—5661no—
156SD16—5661no—
157SD16—5661no—
158D8—21no—
159D8—21no—
160D8—2831no—
161D8—5661no—
162D8C22⋊D28311yescharacteristic, complemented
163M16—5661no—
164M16—5661no—
165C2×C8—2831no—
166C2×C8C22×D28311yescharacteristic
167C4⋊C4—5661no—
168C22⋊C4—11321no—
169C16—21no—
170C16—5661no—
171C23—41no—
172C23—2831no—
173C23—11321no—
174Q8—21no—
175Q8—5661no—
176Q8—11321no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—5661no—
182D4—11321no—
183D4—11321no—
184D4—11321no—
185D4—11321no—
186D4—22642no—
187C2×C4—41no—
188C2×C4—2831no—
189C2×C4—5661no—
190C2×C4—5661no—
191C2×C4—11321no—
192C2×C4—11321no—
193C2×C4—11321no—
194C2×C4—11321no—
195C2×C4—11321no—
196C2×C4D4×D28311yescharacteristic
197C8—5661no—
198C8D4×D28311yescharacteristic
199C8C2×C22⋊D28311yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—5661no—
205C22—11321no—
206C22—11321no—
207C22—22642no—
208C22D8×D28311yescharacteristic
209C4—41no—
210C4—5661no—
211C4—11321no—
212C4—22641no—
213C4#2258357811yescharacteristic
214C4#2258363411yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—11321no—
219C2—22641no—
220C2#3182659711yescharacteristic
subgroupG/H
centerC2#31826597
commutator, cosocleC2×C8×C283C23
FrattiniC2×C8C22×D283
Fitting#509×C283C2
socleC2×C283#447
hypercenter#509D283
hypocenterC283#2190
LCSG ▷ C2×C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #31827262C2semidirect
2. #31826901C2semidirect
3. #31826715C2semidirect
4. #31826276C2semidirect
5. #31826275C2semidirect
6. #31826246C2semidirect
7. #509×C283C2semidirect
19. #22583550C22semidirect
20. #22583542C22semidirect
23. C2×D8×C283C22semidirect
26. M32×C283C22semidirect
38. Dic1132D4semidirect
43. D2264D4semidirect
53. Q16×C283D4semidirect
57. D8×C283D4semidirect
110. C283#2190semidirect
114. #509D283semidirect
127. C2×D8C2×D283semidirect
135. M32C2×D283semidirect
153. Q16C22⋊D283semidirect
162. D8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318272622
#318269012
#318267152
#318262762
#318262752
#318262462
#509×C2832
#2190283