Finite Group Databasebeta

← #27173076

Subgroups — #27173076

Order 12928.

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#20265974C211yesmaximal, characteristic, complemented
2#20265613C211yesmaximal, characteristic, complemented
3#20265427C211yesmaximal, characteristic, complemented
4#20264988C211yesmaximal, characteristic, complemented
5#20264987C211yesmaximal, characteristic, complemented
6#20264958C211yesmaximal, characteristic, complemented
7#509×C101C211yesmaximal, characteristic, complemented
8#41×D101—21no—
9#15692287—21no—
10#15692284—21no—
11#15692282—21no—
12#15692279—21no—
13#15692277C2211yescharacteristic
14#15692275—21no—
15C2×#13108057C2211yescharacteristic
16#15692226—21no—
17#15692199—21no—
18#15692196—21no—
19#15692195C2211yescharacteristic, complemented
20#15692187C2211yescharacteristic, complemented
21#15692176—21no—
22#135×C101C2211yescharacteristic
23C2×D8×C101C2211yescharacteristic, complemented
24SD32×C101—21no—
25D16×C101—21no—
26M32×C101C2211yescharacteristic, complemented
27#13108075—21no—
28#13108074—21no—
29#13108074—41no—
30#13108073—21no—
31#13108073—41no—
32Q8×D101—21no—
33C2×C22⋊D101—41no—
34D4×D101—21no—
35D4×D101—41no—
36C2×C4×D101—41no—
37C2×C4×D101D411yescharacteristic
38Dic404D411yescharacteristic, complemented
39#13108064—21no—
40#13108063—21no—
41#13108062—21no—
42#13108061—21no—
43D808D411yescharacteristic, complemented
44#13108059—21no—
45#13108057—21no—
46#13108057—21no—
47C2×#11717579D411yescharacteristic
48C4⋊Dic101—21no—
49C22⋊Dic101—41no—
50#13108049—21no—
51#41×C101—21no—
52C2×D4×C101—21no—
53Q16×C101D411yescharacteristic, complemented
54SD16×C101—21no—
55D8×C101—21no—
56D8×C101—21no—
57D8×C101D411yescharacteristic, complemented
58C2×C8×C101C2311yescharacteristic
59C16×C101—21no—
60C23×C101—41no—
61C22×D101—41no—
62C22×D101D811yescharacteristic
63Q8×C101—21no—
64D4×C101—21no—
65D4×C101—41no—
66D4×C101—41no—
67D4×C101—41no—
68C2×C4×C101—41no—
69C2×C4×C101C2×D411yescharacteristic
70C22⋊D101—41no—
71C22⋊D101—41no—
72C22⋊D101—41no—
73C22⋊D101—82no—
74C2×Dic101—41no—
75C2×Dic101—41no—
76C2×Dic101D811yescharacteristic
77D404—21no—
78D404—41no—
79C4×D101—21no—
80C4×D101—21no—
81C4×D101—41no—
82C4×D101—41no—
83C4×D101—41no—
84Dic202—21no—
85Dic202—41no—
86C8×C101C2×D411yescharacteristic
87C8×C101C2×D411yescharacteristic
88#11717579—21no—
89C22×C101—41no—
90C22×C101—81no—
91C22×C101—81no—
92C22×C101—81no—
93C22×C101C2×D811yescharacteristic
94C2×D101—21no—
95C2×D101—41no—
96C2×D101—41no—
97C2×D101—82no—
98C4×C101—41no—
99C4×C101#12011yescharacteristic
100C4×C101AGL(1,ℤ/8)11yescharacteristic
101Dic101—21no—
102Dic101—41no—
103Dic101—81no—
104C2×C101—21no—
105C2×C101—81no—
106C2×C101—161no—
107C2×C101#44711yescharacteristic
108D101—41no—
109D101—81no—
110#2190—1011nomaximal, Sylow
111C101#219011yescharacteristic, complemented, Sylow
112#575—1011no—
113#509—1011no—
114#509D10111yescharacteristic, complemented
115#469—1011no—
116#360—1011no—
117#360—1011no—
118#349—1011no—
119C2×#41—2021no—
120#137—2021no—
121#137—2021no—
122AGL(1,ℤ/8)—2021no—
123AGL(1,ℤ/8)—2021no—
124#135—1011no—
125#135—2021no—
126#135C2×D10111yescharacteristic
127C2×D8C2×D10111yescharacteristic, complemented
128C2×M16—1011no—
129#121—2021no—
130SD32—21no—
131SD32—2021no—
132D16—21no—
133D16—2021no—
134M32—1011no—
135M32C2×D10111yescharacteristic, complemented
136#106—1011no—
137#102—2021no—
138#41—21no—
139#41—4041no—
140#41—4041no—
141#41—2021no—
142#41—2021no—
143#41—2021no—
144C2×Q8—2021no—
145C2×D4—21no—
146C2×D4—4041no—
147C2×D4—4041no—
148C2×D4—2021no—
149C22×C4—1011no—
150C22×C4—4041no—
151Q16—1011no—
152Q16—2021no—
153Q16C22⋊D10111yescharacteristic, complemented
154SD16—21no—
155SD16—2021no—
156SD16—2021no—
157SD16—2021no—
158D8—21no—
159D8—21no—
160D8—1011no—
161D8—2021no—
162D8C22⋊D10111yescharacteristic, complemented
163M16—2021no—
164M16—2021no—
165C2×C8—1011no—
166C2×C8C22×D10111yescharacteristic
167C4⋊C4—2021no—
168C22⋊C4—4041no—
169C16—21no—
170C16—2021no—
171C23—41no—
172C23—1011no—
173C23—4041no—
174Q8—21no—
175Q8—4041no—
176Q8—2021no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—8082no—
182D4—4041no—
183D4—4041no—
184D4—4041no—
185D4—4041no—
186D4—2021no—
187C2×C4—41no—
188C2×C4—1011no—
189C2×C4—4041no—
190C2×C4—4041no—
191C2×C4—4041no—
192C2×C4—4041no—
193C2×C4—4041no—
194C2×C4—2021no—
195C2×C4—2021no—
196C2×C4D4×D10111yescharacteristic
197C8—2021no—
198C8D4×D10111yescharacteristic
199C8C2×C22⋊D10111yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—8082no—
205C22—4041no—
206C22—4041no—
207C22—2021no—
208C22D8×D10111yescharacteristic
209C4—41no—
210C4—8081no—
211C4—4041no—
212C4—2021no—
213C4#1569222311yescharacteristic
214C4#1569227911yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—8081no—
219C2—4041no—
220C2#2026530911yescharacteristic
subgroupG/H
centerC2#20265309
commutator, cosocleC2×C8×C101C23
FrattiniC2×C8C22×D101
Fitting#509×C101C2
socleC2×C101#447
hypercenter#509D101
hypocenterC101#2190
LCSG ▷ C2×C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #20265974C2semidirect
2. #20265613C2semidirect
3. #20265427C2semidirect
4. #20264988C2semidirect
5. #20264987C2semidirect
6. #20264958C2semidirect
7. #509×C101C2semidirect
19. #15692195C22semidirect
20. #15692187C22semidirect
23. C2×D8×C101C22semidirect
26. M32×C101C22semidirect
38. Dic404D4semidirect
43. D808D4semidirect
53. Q16×C101D4semidirect
57. D8×C101D4semidirect
111. C101#2190semidirect
114. #509D101semidirect
127. C2×D8C2×D101semidirect
135. M32C2×D101semidirect
153. Q16C22⋊D101semidirect
162. D8C22⋊D101semidirect

Maximal subgroups

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

subgroupindex
#202659742
#202656132
#202654272
#202649882
#202649872
#202649582
#509×C1012
#2190101