Finite Group Databasebeta

← #27181744

Subgroups — #27181744

Order 12928.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#20265794C212yesmaximal, complemented
2#20265574C211yesmaximal, characteristic, complemented
3#20265560C211yesmaximal, characteristic, complemented
4#20265535C212yesmaximal, complemented
5#20265435C211yesmaximal, characteristic, complemented
6#20265404C212yesmaximal, complemented
7#20265289C211yesmaximal, characteristic, complemented
8#20265283C211yesmaximal, characteristic, complemented
9#20265268C212yesmaximal, complemented
10#20265135C211yesmaximal, characteristic, complemented
11#469×C101C211yesmaximal, characteristic
12C2×Dic404C2211yescharacteristic
13C2×#13108062C2212yes—
14C22×#11717579C2211yescharacteristic
15#15692254C2212yes—
16#15692248—22no—
17#15692242—22no—
18#15692242C2212yes—
19#15692236—22no—
20#15692234C2212yes—
21#15692232—22no—
22#15692220C2212yes—
23D4×Dic101C2212yes—
24#15692214C2211yescharacteristic
25#15692187C2211yescharacteristic
26#15692186C2212yes—
27#15692180C2212yes—
28#15692178C2212yes—
29#15692176C2212yes—
30#15692165C2211yescharacteristic
31#15692165C2211yescharacteristic
32C8×Dic101C2211yescharacteristic
33C8×Dic101C2211yescharacteristic
34C2×D8×C101C2211yescharacteristic
35C2×M16×C101C2211yescharacteristic
36#121×C101C2212yes—
37#106×C101C2211yescharacteristic
38#102×C101C2212yes—
39C2×Dic202—22no—
40C2×Dic202C2312yes—
41C22×Dic101—22no—
42Dic404—22no—
43#13108062—24no—
44C2×#11717579—22no—
45C2×#11717579C2311yescharacteristic
46C2×#11717579C2311yescharacteristic
47C4⋊Dic101D412yes—
48C4⋊Dic101C2312yes—
49#13108053—22no—
50#13108053—22no—
51#13108053—22no—
52C22⋊Dic101—22no—
53C22⋊Dic101—22no—
54C22⋊Dic101—22no—
55C22⋊Dic101—22no—
56C22⋊Dic101D412yes—
57C4×Dic101—22no—
58C4×Dic101C2311yescharacteristic
59C4×Dic101C2311yescharacteristic
60C2×D4×C101—22no—
61C2×D4×C101C2312yes—
62C22×C4×C101C2311yescharacteristic
63D8×C101—22no—
64M16×C101—22no—
65C2×C8×C101C2311yescharacteristic
66C2×C8×C101C2311yescharacteristic
67C4⋊C4×C101C2312yes—
68C22⋊C4×C101—22no—
69C23×C101—22no—
70C23×C101C2×D411yescharacteristic
71D4×C101—22no—
72D4×C101—22no—
73D4×C101—82no—
74C2×C4×C101—21no—
75C2×C4×C101—21no—
76C2×C4×C101—22no—
77C2×C4×C101C2×D411yescharacteristic
78C2×C4×C101C2411yescharacteristic
79C2×Dic101—22no—
80C2×Dic101—22no—
81C2×Dic101—82no—
82C2×Dic101C2×D412yes—
83C2×Dic101C2×D412yes—
84Dic202—22no—
85Dic202—22no—
86Dic202—82no—
87C8×C101—21no—
88C8×C101#4112yes—
89#11717579—21no—
90#11717579#4112yes—
91C22×C101—21no—
92C22×C101—22no—
93C22×C101—42no—
94C22×C101—42no—
95C22×C101—42no—
96C22×C101C22×D411yescharacteristic
97C4×C101—21no—
98C4×C101—42no—
99C4×C101C2×#4111yescharacteristic
100C4×C101C2×#4111yescharacteristic
101Dic101—22no—
102Dic101—22no—
103Dic101—42no—
104Dic101—42no—
105C2×C101—41no—
106C2×C101—82no—
107C2×C101#53211yescharacteristic
108C2×C101#57712yes—
109#3173—1011nomaximal, Sylow
110C101#317311yescharacteristic, complemented, Sylow
111#542—1012no—
112#498—1011no—
113#495—1011no—
114#489—1012no—
115#470—1011no—
116#469D10111yescharacteristic
117#465—1012no—
118#442—1011no—
119#441—1011no—
120C4×SD16—1012no—
121#405—1011no—
122C2×Q16—1011no—
123C2×SD16—1012no—
124C2×D8C2×D10111yescharacteristic
125C2×M16C2×D10111yescharacteristic
126C22×C8—1011no—
127C4⋊Q8—1012no—
128#126—2022no—
129#124—1012no—
130#124—2022no—
131#123—2022no—
132C22⋊Q8—1012no—
133C22⋊Q8—2022no—
134#121C2×D10112yes—
135C4×Q8—1012no—
136C4×D4—1012no—
137#117—1011no—
138#106—1011no—
139#106—1012no—
140#106C2×D10111yescharacteristic
141#103—1012no—
142#103—1012no—
143#102—1012no—
144#102C2×D10112yes—
145#97—1011no—
146#97—1011no—
147C4×C8—1011no—
148C4×C8—1011no—
149C2×Q8—1012no—
150C2×Q8—2022no—
151C2×D4—22no—
152C2×D4C22×D10112yes—
153C22×C4—2022no—
154C22×C4C22×D10111yescharacteristic
155Q16—2022no—
156SD16—2024no—
157D8—22no—
158M16—22no—
159C2×C8—1011no—
160C2×C8—1011no—
161C2×C8—2022no—
162C2×C8C22×D10111yescharacteristic
163C2×C8C22×D10111yescharacteristic
164C4⋊C4—1012no—
165C4⋊C4—1012no—
166C4⋊C4—2022no—
167C4⋊C4—2022no—
168C4⋊C4—2022no—
169C4⋊C4C22×D10112yes—
170C22⋊C4—22no—
171C22⋊C4—1012no—
172C22⋊C4—2022no—
173C22⋊C4—2022no—
174C22⋊C4—2022no—
175C22⋊C4—2022no—
176C42—1011no—
177C42—1011no—
178C42—2022no—
179C23—22no—
180C23D4×D10111yescharacteristic
181Q8—8082no—
182Q8—2022no—
183Q8—2022no—
184D4—22no—
185D4—22no—
186D4—82no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—8082no—
191C2×C4—1012no—
192C2×C4—1012no—
193C2×C4—2022no—
194C2×C4—2022no—
195C2×C4D4×D10111yescharacteristic
196C2×C4C23×D10111yescharacteristic
197C8—21no—
198C8—1012no—
199C8—2021no—
200C8#1310807312yes—
201C22—22no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22C2×D4×D10111yescharacteristic
207C4—21no—
208C4—42no—
209C4—4042no—
210C4—4042no—
211C4—2022no—
212C4—2022no—
213C4#41×D10111yescharacteristic
214C4C2×#1310807311yescharacteristic
215C2—41no—
216C2—82no—
217C2#2026572211yescharacteristic
218C2#2026598712yes—
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting, prime radical#469×C101C2
socleC22×C101C22×D4
hypercenter#469D101
hypocenterC101#3173
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20265794C2semidirect
2. #20265574C2semidirect
3. #20265560C2semidirect
4. #20265535C2semidirect
5. #20265435C2semidirect
6. #20265404C2semidirect
7. #20265289C2semidirect
8. #20265283C2semidirect
9. #20265268C2semidirect
10. #20265135C2semidirect
110. C101#3173semidirect

Maximal subgroups

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

subgroupindex
#202657942
#202655742
#202655602
#202655352
#202654352
#202654042
#202652892
#202652832
#202652682
#202651352
#469×C1012
#3173101