Finite Group Databasebeta

← #27187042

Subgroups — #27187042

Order 12928.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#20266163C211yesmaximal, characteristic
2#20266156C211yesmaximal, characteristic
3#20266048C212yesmaximal, complemented
4#20266044C212yesmaximal, complemented
5#20265645C211yesmaximal, characteristic
6D101⋊M16C2212yes—
7#15692334C2212yes—
8#15692316—21no—
9#15692315—21no—
10#15692314—21no—
11#15692313—21no—
12C2×#13108074C2211yescharacteristic
13#15692220—21no—
14#15692217—21no—
15#15692215—21no—
16#15692215—21no—
17#15692212C411yescharacteristic, complemented
18#15692212C2211yescharacteristic
19C2×C4×Dic101C411yescharacteristic, complemented
20C42×D101C411yescharacteristic, complemented
21C42×D101C2211yescharacteristic
22#117×C101C411yescharacteristic, complemented
23#13108084—22no—
24#13108083—22no—
25D101⋊C8—22no—
26C4⋊#87938—22no—
27C22⋊#87938—22no—
28C4×#87938—22no—
29#13108074—22no—
30#13108074—22no—
31C2×Dic202D411yescharacteristic
32C2×D404D411yescharacteristic
33C2×C22⋊D101D411yescharacteristic
34C2×C22⋊D101D411yescharacteristic
35C22×Dic101—21no—
36C2×C4×D101—21no—
37C2×C4×D101—21no—
38C2×C4×D101C2×C411yescharacteristic
39C2×C4×D101C2311yescharacteristic
40#13108053—21no—
41#13108053—21no—
42#13108051—21no—
43#13108051—21no—
44C4×Dic101—21no—
45C4×Dic101—21no—
46C4×Dic101—21no—
47C4×Dic101C2×C411yescharacteristic
48C4×Dic101C2×C411yescharacteristic
49C22×C4×C101C2×C411yescharacteristic
50C4⋊C4×C101—21no—
51C22⋊C4×C101—21no—
52C42×C101C2×C411yescharacteristic
53C42×C101C2×C411yescharacteristic
54C23×C101C22⋊C411yescharacteristic
55C22×D101C22⋊C411yescharacteristic
56C22×D101C2×D411yescharacteristic
57C2×#87938—42no—
58C2×C4×C101—21no—
59C2×C4×C101—21no—
60C2×C4×C101—21no—
61C2×C4×C101—21no—
62C2×C4×C101C22⋊C411yescharacteristic
63C2×C4×C101C22×C411yescharacteristic
64C22⋊D101—22no—
65C22⋊D101—22no—
66C2×Dic101—21no—
67C2×Dic101—21no—
68C2×Dic101—42no—
69C2×Dic101C22⋊C411yescharacteristic
70C2×Dic101C2×D411yescharacteristic
71D404—22no—
72C4×D101—21no—
73C4×D101—21no—
74C4×D101—42no—
75C4×D101—42no—
76C4×D101#4112yes—
77C4×D101#4112yes—
78Dic202—22no—
79#11717581—42no—
80C22×C101—21no—
81C22×C101—41no—
82C22×C101C2×C22⋊C411yescharacteristic
83C2×D101—21no—
84C2×D101—41no—
85C2×D101—41no—
86C2×D101#12312yes—
87#87938—82no—
88C4×C101—21no—
89C4×C101—41no—
90C4×C101—41no—
91C4×C101#11711yescharacteristic
92C4×C101#11711yescharacteristic
93Dic101—22no—
94Dic101—21no—
95Dic101—41no—
96Dic101#12312yes—
97C2×C101—21no—
98C2×C101—41no—
99C2×C101#38111yescharacteristic
100D101—22no—
101D101—41no—
102#1827—1011nomaximal, Sylow
103C101#182711yescharacteristic, complemented, Sylow
104C4×#41—1011no—
105#413—1011no—
106#410—1011no—
107#339—1012no—
108H(3,ℤ/4)—1012no—
109C2×#41—1011no—
110C2×M16—1012no—
111C4×Q8—2021no—
112C4×D4—2021no—
113C4×D4—2021no—
114C4×D4—2021no—
115#117—1011no—
116#117—1011no—
117#117—1012no—
118#117#8793811yescharacteristic, complemented
119C2×C42—1011no—
120C2×C42—1011no—
121C2×C42—1011no—
122#101—2021no—
123#100—2021no—
124#99—2021no—
125#99—2021no—
126#41—2022no—
127#41—2022no—
128C2×Q8—1011no—
129C2×D4—1011no—
130C2×D4—1011no—
131C2×D4—1011no—
132C22×C4—1011no—
133C22×C4—1011no—
134C22×C4—2021no—
135C22×C4—2021no—
136C22×C4—2021no—
137C22×C4C2×#8793811yescharacteristic
138M16—2022no—
139M16—2022no—
140C2×C8—2022no—
141C4⋊C4—21no—
142C4⋊C4—2021no—
143C4⋊C4—2021no—
144C4⋊C4—2022no—
145C22⋊C4—21no—
146C22⋊C4—2021no—
147C22⋊C4—2021no—
148C22⋊C4—2022no—
149C42—1011no—
150C42—1011no—
151C42—2021no—
152C42—2021no—
153C42—2022no—
154C42—2021no—
155C42C2×#8793811yescharacteristic
156C42C2×#8793811yescharacteristic
157C23—1011no—
158C23—1011no—
159C23C22⋊#8793811yescharacteristic
160Q8—2022no—
161D4—2022no—
162D4—2022no—
163D4—2022no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—1011no—
169C2×C4—1012no—
170C2×C4—1012no—
171C2×C4—1011no—
172C2×C4—4042no—
173C2×C4—4042no—
174C2×C4—4042no—
175C2×C4—4042no—
176C2×C4—2021no—
177C2×C4—2021no—
178C2×C4—2021no—
179C2×C4—2021no—
180C2×C4C22⋊#8793811yescharacteristic
181C2×C4C22×#8793811yescharacteristic
182C8—4042no—
183C22—21no—
184C22—41no—
185C22—1012no—
186C22—4041no—
187C22—4041no—
188C22—2021no—
189C22C2×C22⋊#8793811yescharacteristic
190C4—21no—
191C4—41no—
192C4—41no—
193C4—8082no—
194C4—1012no—
195C4—4041no—
196C4—2022no—
197C4—2021no—
198C4#1569233411yescharacteristic
199C4#1569233411yescharacteristic
200C2—21no—
201C2—41no—
202C2—4041no—
203C2—2022no—
204C2#2026612011yescharacteristic
subgroupG/H
centerC4#15692334
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#117×C101C4
socleC2×C101#381
prime radicalC2×#13108074C22
cosocleC2×C4×D101C23
hypercenter#117#87938
hypocenterC101#1827
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C42 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #20266048C2semidirect
4. #20266044C2semidirect
17. #15692212C4semidirect
19. C2×C4×Dic101C4semidirect
20. C42×D101C4semidirect
22. #117×C101C4semidirect
103. C101#1827semidirect
118. #117#87938semidirect

Maximal subgroups

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

subgroupindex
#202661632
#202661562
#202660482
#202660442
#202656452
#1827101