Finite Group Databasebeta

← #27184218

Subgroups — #27184218

Order 12928.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#20265910C212yesmaximal, complemented
2#20265565C212yesmaximal, complemented
3#20265561C211yesmaximal, characteristic, complemented
4#20265398C212yesmaximal, complemented
5#20265392C212yesmaximal, complemented
6#20265371C212yesmaximal, complemented
7#20265307C211yesmaximal, characteristic, complemented
8#20265276C212yesmaximal, complemented
9C4×D8×C101C211yesmaximal, characteristic, complemented
10C2×Dic404C2211yescharacteristic
11C2×#13108063C2212yes—
12C2×#13108062C2212yes—
13C2×D808C2211yescharacteristic
14C2×#13108059C2212yes—
15#15692251C2212yes—
16#15692243C2212yes—
17#15692242C2212yes—
18#15692241—22no—
19#15692238—22no—
20#15692237—22no—
21C4×Dic202C2211yescharacteristic
22#15692220C2212yes—
23#15692217C2212yes—
24C4×C22⋊D101—22no—
25C4⋊#11717579C2211yescharacteristic
26#15692184C2212yes—
27#15692178C2212yes—
28#15692175C2212yes—
29#15692165C2212yes—
30C2×D8×C101C2211yescharacteristic
31C4×D4×C101C2212yes—
32#107×C101C2211yescharacteristic
33#102×C101C2212yes—
34C4×C8×C101C2211yescharacteristic
35C2×Dic202D411yescharacteristic
36C2×Dic202C2312yes—
37C2×D404C2312yes—
38C2×C22⋊D101—22no—
39C2×C22⋊D101—22no—
40C2×C4×D101—22no—
41Dic404—41no—
42#13108063—24no—
43#13108062—42no—
44D808—41no—
45#13108059—42no—
46C2×#11717579C2312yes—
47C4⋊Dic101D411yescharacteristic
48#13108053—22no—
49#13108053D412yes—
50C22⋊Dic101—22no—
51C22⋊Dic101—22no—
52#13108051—22no—
53#13108051—22no—
54#13108051—22no—
55C4×Dic101—22no—
56C4×Dic101C2312yes—
57C2×D4×C101C2312yes—
58C22×C4×C101—22no—
59D8×C101—22no—
60C2×C8×C101C2311yescharacteristic
61C2×C8×C101C2311yescharacteristic
62C4⋊C4×C101C2312yes—
63C22⋊C4×C101—22no—
64C42×C101C2311yescharacteristic
65C23×C101—22no—
66C22×D101—22no—
67D4×C101—22no—
68D4×C101—22no—
69C2×C4×C101—22no—
70C2×C4×C101—82no—
71C2×C4×C101C2×D411yescharacteristic
72C2×C4×C101C2×D411yescharacteristic
73C2×C4×C101C2411yescharacteristic
74C22⋊D101—44no—
75C22⋊D101—82no—
76C2×Dic101—22no—
77C2×Dic101C2×D412yes—
78C2×Dic101C2×D412yes—
79D404—22no—
80D404—22no—
81C4×D101—82no—
82Dic202—22no—
83Dic202—22no—
84Dic202—41no—
85C8×C101—21no—
86C8×C101#4112yes—
87#11717579—22no—
88C22×C101—42no—
89C22×C101—42no—
90C22×C101—42no—
91C22×C101C22×D411yescharacteristic
92C2×D101—42no—
93C2×D101—42no—
94C2×D101—42no—
95C4×C101—21no—
96C4×C101—21no—
97C4×C101—42no—
98C4×C101C2×#4111yescharacteristic
99C4×C101H(5,𝔽2)11yescharacteristic
100Dic101—22no—
101Dic101—22no—
102Dic101—42no—
103C2×C101—82no—
104C2×C101#55011yescharacteristic
105C2×C101#57511yescharacteristic
106C2×C101#57611yescharacteristic
107D101—82no—
108#3403—1011nomaximal, Sylow
109C101#340311yescharacteristic, complemented, Sylow
110#559—1012no—
111#496—1012no—
112#495—1011no—
113#464—1012no—
114#463—1012no—
115#459—1012no—
116#446—1011no—
117#440—1012no—
118C4×D8D10111yescharacteristic, complemented
119C2×Q16—1011no—
120C2×SD16—1012no—
121C2×SD16—1012no—
122C2×D8—1012no—
123C2×D8—1011no—
124C2×D8C2×D10111yescharacteristic
125#127—1012no—
126#124—1012no—
127#124—1012no—
128#124—2022no—
129#123—2022no—
130#123—2022no—
131C4×Q8—1011no—
132C4×Q8—1012no—
133C4×D4—1012no—
134C4×D4—2022no—
135C4×D4C2×D10112yes—
136#107C2×D10111yescharacteristic
137C4⋊C8—1012no—
138C4⋊C8—1011no—
139#103—1012no—
140#102—1012no—
141#102C2×D10112yes—
142#97—1012no—
143C4×C8C2×D10111yescharacteristic
144C2×Q8—1011no—
145C2×Q8—1012no—
146C2×D4—1012no—
147C2×D4—2022no—
148C2×D4—2022no—
149C2×D4C22×D10112yes—
150C22×C4—22no—
151C22×C4—2022no—
152Q16—4041no—
153SD16—4042no—
154SD16—2024no—
155D8—22no—
156D8—4041no—
157D8—4042no—
158C2×C8—1012no—
159C2×C8C22×D10111yescharacteristic
160C2×C8C22×D10111yescharacteristic
161C4⋊C4—1012no—
162C4⋊C4—1011no—
163C4⋊C4—2022no—
164C4⋊C4C22×D10112yes—
165C22⋊C4—22no—
166C22⋊C4—2022no—
167C22⋊C4—2022no—
168C22⋊C4—2022no—
169C22⋊C4—2022no—
170C22⋊C4—2022no—
171C42—1012no—
172C42—2022no—
173C42C22×D10111yescharacteristic
174C23—22no—
175C23—2022no—
176Q8—4041no—
177Q8—2022no—
178Q8—2022no—
179D4—22no—
180D4—22no—
181D4—8082no—
182D4—4044no—
183D4—2022no—
184D4—2022no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—8082no—
188C2×C4—1012no—
189C2×C4—1012no—
190C2×C4—2022no—
191C2×C4D4×D10111yescharacteristic
192C2×C4D4×D10111yescharacteristic
193C2×C4C23×D10111yescharacteristic
194C8—21no—
195C8—2022no—
196C8#1310807412yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—4042no—
201C22—4042no—
202C22—4042no—
203C22C2×D4×D10111yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—4042no—
208C4—2022no—
209C4—2022no—
210C4C2×#1310807411yescharacteristic
211C4#1569230111yescharacteristic
212C2—82no—
213C2—8082no—
214C2#2026584811yescharacteristic
215C2#2026597411yescharacteristic
216C2#2026597811yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
FittingC4×D8×C101C2
socleC22×C101C22×D4
hypercenterC4×D8D101
hypocenterC101#3403
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20265910C2semidirect
2. #20265565C2semidirect
3. #20265561C2semidirect
4. #20265398C2semidirect
5. #20265392C2semidirect
6. #20265371C2semidirect
7. #20265307C2semidirect
8. #20265276C2semidirect
9. C4×D8×C101C2semidirect
109. C101#3403semidirect
118. C4×D8D101semidirect

Maximal subgroups

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

subgroupindex
#202659102
#202655652
#202655612
#202653982
#202653922
#202653712
#202653072
#202652762
C4×D8×C1012
#3403101