Finite Group Databasebeta

← #27172291

Subgroups — #27172291

Order 12928.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#20265805C211yesmaximal, characteristic
2#20265186C211yesmaximal, characteristic
3#20265084C211yesmaximal, characteristic
4#20264945C211yesmaximal, characteristic
5#20264938C211yesmaximal, characteristic
6#20264936C211yesmaximal, characteristic
7#419×C101C211yesmaximal, characteristic
8C2×#13108058C2211yescharacteristic
9#15692255—21no—
10#15692254—21no—
11#15692247—21no—
12#15692246—21no—
13#15692232—22no—
14#15692214C2211yescharacteristic
15C2×C4⋊Dic101C2211yescharacteristic
16C2×C4×Dic101C2211yescharacteristic
17#15692179—21no—
18#15692179—21no—
19#15692162—22no—
20C22×Q8×C101C2211yescharacteristic
21C2×M16×C101C2211yescharacteristic
22#117×C101C2211yescharacteristic
23#103×C101—21no—
24#103×C101—21no—
25C2×Dic202—22no—
26C22×Dic101—21no—
27C22×Dic101D412yes—
28#13108058—21no—
29#13108058—21no—
30C2×#11717579—21no—
31C4⋊Dic101—22no—
32C4⋊Dic101—21no—
33C4⋊Dic101—21no—
34C4⋊Dic101D411yescharacteristic
35C4⋊Dic101D411yescharacteristic
36#13108053—22no—
37#13108053—22no—
38C22⋊Dic101—21no—
39C4×Dic101—21no—
40C4×Dic101—21no—
41C4×Dic101—21no—
42C2×Q8×C101—21no—
43C2×Q8×C101—21no—
44C2×Q8×C101—21no—
45C2×Q8×C101—21no—
46C2×Q8×C101—21no—
47C2×Q8×C101Q812yescomplemented
48C22×C4×C101—21no—
49C22×C4×C101C2311yescharacteristic
50M16×C101—21no—
51M16×C101—21no—
52C2×C8×C101—21no—
53C4⋊C4×C101D411yescharacteristic
54C4⋊C4×C101D411yescharacteristic
55C22⋊C4×C101—21no—
56C42×C101—21no—
57C23×C101C2×D411yescharacteristic
58Q8×C101—22no—
59Q8×C101—22no—
60Q8×C101—41no—
61Q8×C101—41no—
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101—22no—
65C2×C4×C101—41no—
66C2×C4×C101—41no—
67C2×C4×C101C2×D411yescharacteristic
68C2×C4×C101C2×D411yescharacteristic
69C2×C4×C101C2×Q811yescharacteristic
70C2×C4×C101#4111yescharacteristic
71C2×C4×C101#4111yescharacteristic
72C2×C4×C101#4111yescharacteristic
73C2×Dic101—22no—
74C2×Dic101—21no—
75C2×Dic101—21no—
76C2×Dic101—22no—
77C2×Dic101—41no—
78C2×Dic101—41no—
79C2×Dic101—42no—
80Dic202—82no—
81C8×C101—41no—
82#11717579—41no—
83C22×C101—21no—
84C22×C101—21no—
85C22×C101#12011yescharacteristic
86C22×C101C22⋊Q811yescharacteristic
87C22×C101#12411yescharacteristic
88C4×C101—42no—
89C4×C101—41no—
90C4×C101—41no—
91C4×C101C22⋊Q811yescharacteristic
92C4×C101C22⋊Q811yescharacteristic
93C4×C101#12411yescharacteristic
94C4×C101#12411yescharacteristic
95Dic101—42no—
96Dic101—41no—
97Dic101—42no—
98Dic101—41no—
99C2×C101—21no—
100C2×C101—21no—
101C2×C101#39311yescharacteristic
102C2×C101#45511yescharacteristic
103C2×C101#45611yescharacteristic
104#2028—1011nomaximal, Sylow
105C101#202811yescharacteristic, complemented, Sylow
106#544—1011no—
107#419—1011no—
108#419D10111yescharacteristic
109#391—1011no—
110#343—1011no—
111#339—1011no—
112#339—1011no—
113C22×Q8C2×D10111yescharacteristic
114C2×M16—1011no—
115C2×M16C2×D10111yescharacteristic
116C4⋊Q8—2021no—
117C4⋊Q8—2021no—
118#125—2021no—
119#125—2021no—
120C22⋊Q8—2022no—
121#117—1011no—
122#117C2×D10111yescharacteristic
123C2×C4⋊C4—1011no—
124C2×C42—1011no—
125#103—21no—
126#103—21no—
127#103—2021no—
128#103—2021no—
129#95—2022no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—2022no—
136C2×Q8Dic20212yescomplemented
137C22×C4—21no—
138C22×C4—1012no—
139C22×C4—2021no—
140C22×C4C22×D10111yescharacteristic
141M16—21no—
142M16—21no—
143M16—2021no—
144M16—2021no—
145C2×C8—21no—
146C2×C8—2021no—
147C4⋊C4—1011no—
148C4⋊C4—1011no—
149C4⋊C4—2022no—
150C4⋊C4—2022no—
151C4⋊C4—2022no—
152C4⋊C4—2021no—
153C4⋊C4—2021no—
154C4⋊C4C22⋊D10111yescharacteristic
155C4⋊C4C22⋊D10111yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—2021no—
158C42—21no—
159C42—2021no—
160C42—2021no—
161C42—2021no—
162C23D4×D10111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—8082no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—4041no—
174C2×C4—4041no—
175C2×C4—4042no—
176C2×C4—2022no—
177C2×C4—2021no—
178C2×C4—2021no—
179C2×C4—2022no—
180C2×C4D4×D10111yescharacteristic
181C2×C4C2×C22⋊D10111yescharacteristic
182C2×C4C2×Dic20211yescharacteristic
183C2×C4#1310807311yescharacteristic
184C2×C4#1310807311yescharacteristic
185C2×C4#1310807411yescharacteristic
186C8—41no—
187C8—4041no—
188C22—21no—
189C22—21no—
190C22#1569222311yescharacteristic
191C22#1569223211yescharacteristic
192C22#1569224111yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—4042no—
197C4—4042no—
198C4—4041no—
199C4—4041no—
200C4#1569223211yescharacteristic
201C4#1569223411yescharacteristic
202C4#1569224111yescharacteristic
203C4#1569224211yescharacteristic
204C2—21no—
205C2—21no—
206C2#2026508911yescharacteristic
207C2#2026535311yescharacteristic
208C2#2026535811yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#419×C101C2
socleC22×C101#120
prime radicalC23×C101C2×D4
hypercenter#419D101
hypocenterC101#2028
LCSG ▷ C22×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C101Q8semidirect
105. C101#2028semidirect
136. C2×Q8Dic202semidirect

Maximal subgroups

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

subgroupindex
#202658052
#202651862
#202650842
#202649452
#202649382
#202649362
#419×C1012
#2028101