Finite Group Databasebeta

← #27171234

Subgroups — #27171234

Order 12928.

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

normal subgroups only

This group has 262 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
1#20265645C211yesmaximal, characteristic
2#20265159C211yesmaximal, characteristic
3#20265150C211yesmaximal, characteristic
4#20264938C211yesmaximal, characteristic, complemented
5#20264936C211yesmaximal, characteristic, complemented
6#20264933C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C101C211yesmaximal, characteristic, complemented
8C2×#13108074C2211yescharacteristic
9C2×#13108058C2211yescharacteristic
10#15692220—21no—
11#15692217—21no—
12#15692215—22no—
13#15692214C2211yescharacteristic
14#15692212C412yescomplemented
15C2×C4×Dic101C2211yescharacteristic
16C42×D101C412yescomplemented
17#15692173—21no—
18#15692171—21no—
19#15692169—22no—
20C2×M16×C101C2211yescharacteristic
21#117×C101C2211yescharacteristic
22#117×C101C2211yescharacteristic
23#13108074—21no—
24#13108074—21no—
25#13108074—21no—
26#13108074—21no—
27C2×Dic202D411yescharacteristic
28C2×D404D411yescharacteristic
29C2×C22⋊D101D412yes—
30C22×Dic101—21no—
31C2×C4×D101—22no—
32C2×C4×D101C2×C412yes—
33#13108058—21no—
34#13108058—21no—
35C2×#11717579—21no—
36C4⋊Dic101—21no—
37#13108053—22no—
38C22⋊Dic101—21no—
39#13108051—22no—
40C4×Dic101—21no—
41C4×Dic101—22no—
42C4×Dic101—21no—
43C4×Dic101C2×C411yescharacteristic
44C4×Dic101C2×C411yescharacteristic
45C22×C4×C101C2311yescharacteristic
46M16×C101—21no—
47M16×C101—21no—
48C2×C8×C101—21no—
49C4⋊C4×C101—21no—
50C4⋊C4×C101—21no—
51C22⋊C4×C101—21no—
52C22⋊C4×C101—21no—
53C42×C101—21no—
54C42×C101C2×C412yes—
55C23×C101C2×D411yescharacteristic
56C22×D101C22⋊C412yes—
57C2×C4×C101—22no—
58C2×C4×C101—41no—
59C2×C4×C101C22×C411yescharacteristic
60C2×C4×C101C2×D411yescharacteristic
61C2×C4×C101#4111yescharacteristic
62C2×C4×C101#4111yescharacteristic
63C2×C4×C101#4111yescharacteristic
64C2×C4×C101#4111yescharacteristic
65C22⋊D101—22no—
66C22⋊D101—22no—
67C2×Dic101—21no—
68C2×Dic101—21no—
69C2×Dic101—42no—
70C2×Dic101—41no—
71C2×Dic101C22⋊C412yes—
72D404—21no—
73D404—21no—
74C4×D101—22no—
75C4×D101—22no—
76C4×D101—44no—
77Dic202—21no—
78Dic202—21no—
79C8×C101—41no—
80#11717579—41no—
81C22×C101—41no—
82C22×C101C2×C22⋊C411yescharacteristic
83C22×C101#12311yescharacteristic
84C22×C101#12311yescharacteristic
85C2×D101—22no—
86C2×D101—42no—
87C4×C101—42no—
88C4×C101—81no—
89C4×C101#11711yescharacteristic
90C4×C101#11711yescharacteristic
91C4×C101#12311yescharacteristic
92C4×C101#12311yescharacteristic
93Dic101—22no—
94Dic101—22no—
95Dic101—41no—
96Dic101—81no—
97C2×C101—21no—
98C2×C101—21no—
99C2×C101—21no—
100C2×C101#38111yescharacteristic
101D101—42no—
102#1827—1011nomaximal, Sylow
103C101#182711yescharacteristic, complemented, Sylow
104C4×#41—1011no—
105#413—1011no—
106#410—1011no—
107#339—1011no—
108#339—1011no—
109H(3,ℤ/4)—1011no—
110H(3,ℤ/4)D10111yescharacteristic, complemented
111C2×#41—1011no—
112C2×M16—1011no—
113C2×M16C2×D10111yescharacteristic
114C4×Q8—2021no—
115C4×D4—2022no—
116C4×D4—2021no—
117#117—1012no—
118#117—1011no—
119#117C2×D10111yescharacteristic
120#117C2×D10111yescharacteristic
121C2×C42—1011no—
122C2×C42—1012no—
123#101—2021no—
124#100—2021no—
125#99—2022no—
126#41—2021no—
127#41—2021no—
128#41—2021no—
129#41—2021no—
130C2×Q8—1011no—
131C2×D4—1012no—
132C2×D4—1011no—
133C22×C4—1012no—
134C22×C4—2022no—
135C22×C4—2021no—
136C22×C4C22×D10111yescharacteristic
137M16—21no—
138M16—21no—
139M16—2021no—
140M16—2021no—
141C2×C8—21no—
142C2×C8—2021no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2022no—
146C4⋊C4—2021no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—2022no—
150C22⋊C4—2021no—
151C42—21no—
152C42—1011no—
153C42—1011no—
154C42—2022no—
155C42—2021no—
156C42—2021no—
157C42C4×D10112yes—
158C23—1012no—
159C23D4×D10111yescharacteristic
160Q8—2021no—
161Q8—2021no—
162D4—2022no—
163D4—2022no—
164D4—2021no—
165D4—2021no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—1012no—
169C2×C4—4044no—
170C2×C4—4041no—
171C2×C4—4042no—
172C2×C4—2021no—
173C2×C4—2021no—
174C2×C4—2022no—
175C2×C4—2022no—
176C2×C4C2×C4×D10111yescharacteristic
177C2×C4D4×D10111yescharacteristic
178C2×C4#1310807311yescharacteristic
179C2×C4#1310807411yescharacteristic
180C2×C4#1310807411yescharacteristic
181C2×C4#1310807511yescharacteristic
182C8—41no—
183C8—4041no—
184C22—41no—
185C22—4042no—
186C22—2022no—
187C22C22⋊C4×D10111yescharacteristic
188C22#1569223711yescharacteristic
189C22#1569224011yescharacteristic
190C4—42no—
191C4—81no—
192C4—8081no—
193C4—4041no—
194C4—2022no—
195C4—2022no—
196C4#1569221211yescharacteristic
197C4#1569221311yescharacteristic
198C4#1569223711yescharacteristic
199C4#1569224011yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—4042no—
204C2#2026503911yescharacteristic
subgroupG/H
centerC4#15692212
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
FittingH(3,ℤ/4)×C101C2
socleC2×C101#381
prime radicalC2×#13108074C22
cosocleC22×C4×C101C23
hypercenterH(3,ℤ/4)D101
hypocenterC101#1827
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #20264938C2semidirect
5. #20264936C2semidirect
6. #20264933C2semidirect
7. H(3,ℤ/4)×C101C2semidirect
14. #15692212C4semidirect
16. C42×D101C4semidirect
103. C101#1827semidirect
110. H(3,ℤ/4)D101semidirect

Maximal subgroups

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

subgroupindex
#202656452
#202651592
#202651502
#202649382
#202649362
#202649332
H(3,ℤ/4)×C1012
#1827101