Finite Group Databasebeta

← #28362016

Subgroups — #28362016

Order 13952.

280 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 51 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#20295584C211yesmaximal, characteristic
2#20295339C211yesmaximal, characteristic, complemented
3#20294952C211yesmaximal, characteristic, complemented
4#20294761C211yesmaximal, characteristic, complemented
5#20294760C211yesmaximal, characteristic, complemented
6#20294749C211yesmaximal, characteristic, complemented
7#480×C109C211yesmaximal, characteristic, complemented
8C2×D4×D109—21no—
9#16812684—21no—
10#16812681—21no—
11#16812673C2211yescharacteristic
12#16812671—21no—
13#16812669—21no—
14#16812667—21no—
15C2×#13182006—21no—
16C2×#13182006C2211yescharacteristic
17#16812632—21no—
18#16812619—21no—
19C22⋊#11724784C2211yescharacteristic, complemented
20#16812606—21no—
21#16812606C2211yescharacteristic, complemented
22#121×C109C2211yescharacteristic
23C2×C4⋊C4×C109C2211yescharacteristic, complemented
24#107×C109—21no—
25#102×C109—21no—
26C22⋊C8×C109C2211yescharacteristic, complemented
27C23×D109—21no—
28C23×D109D411yescharacteristic
29C2×D436—21no—
30C2×D436D411yescharacteristic
31C2×C22⋊D109—21no—
32C2×C22⋊D109—21no—
33C2×C22⋊D109—21no—
34D4×D109—42no—
35D4×D109—42no—
36C22×Dic109—21no—
37C22×Dic109D411yescharacteristic
38C2×C4×D109—21no—
39C2×#11724784—21no—
40C4⋊Dic109D411yescharacteristic
41#13182008—21no—
42C22⋊Dic109—21no—
43#13182006—21no—
44#13182006—21no—
45#13182006—21no—
46#13182006—21no—
47#13182006—42no—
48C2×D4×C109—21no—
49C2×D4×C109D411yescharacteristic
50C22×C4×C109—21no—
51C22×C4×C109C2311yescharacteristic
52C2×C8×C109—21no—
53C4⋊C4×C109—21no—
54C4⋊C4×C109—21no—
55C4⋊C4×C109D411yescharacteristic
56C22⋊C4×C109—21no—
57C23×C109—21no—
58C23×C109C2×D411yescharacteristic
59C22×D109—21no—
60C22×D109—21no—
61C22×D109—21no—
62C22×D109—42no—
63C22×D109—41no—
64C22×D109—41no—
65C22×D109—81no—
66C22×D109—81no—
67C22×D109D812yes—
68D4×C109—41no—
69D4×C109—41no—
70D4×C109—41no—
71C2×C4×C109—21no—
72C2×C4×C109—41no—
73C2×C4×C109—41no—
74C2×C4×C109—41no—
75C2×C4×C109—41no—
76C2×C4×C109C2×D411yescharacteristic
77C2×C4×C109C2×D411yescharacteristic
78C22⋊D109—42no—
79C22⋊D109—41no—
80C22⋊D109—41no—
81C22⋊D109—81no—
82C2×Dic109—21no—
83C2×Dic109—21no—
84C2×Dic109—41no—
85C2×Dic109—41no—
86C2×Dic109—41no—
87C2×Dic109—41no—
88D436—41no—
89D436—42no—
90C4×D109—42no—
91C8×C109—41no—
92#11724784—41no—
93C22×C109—21no—
94C22×C109—21no—
95C22×C109—41no—
96C22×C109—41no—
97C22×C109—41no—
98C22×C109#12011yescharacteristic
99C22×C109C2×D811yescharacteristic
100C22×C109AGL(1,ℤ/8)11yescharacteristic
101C2×D109—22no—
102C2×D109—41no—
103C2×D109—41no—
104C2×D109—42no—
105C2×D109—41no—
106C2×D109—41no—
107C2×D109—41no—
108C2×D109—81no—
109C2×D109—84no—
110C4×C109—21no—
111C4×C109—21no—
112C4×C109—41no—
113C4×C109—81no—
114Dic109—41no—
115Dic109—41no—
116Dic109—81no—
117C2×C109—21no—
118C2×C109—21no—
119C2×C109—81no—
120C2×C109#44711yescharacteristic
121C2×C109#45511yescharacteristic
122C2×C109#45811yescharacteristic
123D109—42no—
124D109—81no—
125#1607—1091nomaximal, Sylow
126C109#160711yescharacteristic, complemented, Sylow
127#534—1091no—
128#480—1091no—
129#480D10911yescharacteristic, complemented
130#397—1091no—
131#327—1091no—
132#327—1091no—
133#323—1091no—
134C22×D4—2181no—
135#123—2181no—
136#123—2181no—
137#121—1091no—
138#121—2181no—
139#121C2×D10911yescharacteristic
140#120—2181no—
141#120—2181no—
142C2×C4⋊C4C2×D10911yescharacteristic, complemented
143C2×C22⋊C4—1091no—
144C2×C22⋊C4—2181no—
145#107—21no—
146#107—2181no—
147#102—21no—
148#102—2181no—
149C22⋊C8—1091no—
150C22⋊C8C2×D10911yescharacteristic, complemented
151#95—1091no—
152#95—2181no—
153C24—1091no—
154C24—2181no—
155C2×D4—21no—
156C2×D4—1091no—
157C2×D4—4362no—
158C2×D4—4362no—
159C2×D4—2181no—
160C2×D4—2181no—
161C2×D4—2181no—
162C2×D4—2181no—
163C2×D4C22⋊D10911yescharacteristic
164C22×C4—21no—
165C22×C4—1091no—
166C22×C4—2181no—
167C22×C4—2181no—
168C22×C4C22×D10911yescharacteristic
169C2×C8—21no—
170C2×C8—2181no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—1091no—
174C4⋊C4—2181no—
175C4⋊C4C22⋊D10911yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—4362no—
178C22⋊C4—2181no—
179C22⋊C4—2181no—
180C22⋊C4—2181no—
181C22⋊C4—2181no—
182C22⋊C4—2181no—
183C23—21no—
184C23—8721no—
185C23—8721no—
186C23—1092no—
187C23—4361no—
188C23—4361no—
189C23—4362no—
190C23—2181no—
191C23—2181no—
192C23—2181no—
193C23D4×D10911yescharacteristic
194D4—41no—
195D4—41no—
196D4—41no—
197D4—8721no—
198D4—4361no—
199D4—4362no—
200D4—4362no—
201D4—4361no—
202D4—4361no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—4362no—
209C2×C4—4361no—
210C2×C4—4361no—
211C2×C4—4361no—
212C2×C4—4361no—
213C2×C4—2181no—
214C2×C4—2181no—
215C2×C4D4×D10911yescharacteristic
216C2×C4C2×C22⋊D10911yescharacteristic
217C8—41no—
218C8—4361no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—8721no—
225C22—8724no—
226C22—4362no—
227C22—4361no—
228C22—4361no—
229C22—4361no—
230C22—4361no—
231C22—4361no—
232C22—2182no—
233C22#1681266711yescharacteristic
234C22D8×D10911yescharacteristic
235C22#1681272311yescharacteristic
236C4—21no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—8721no—
241C4—4361no—
242C4—4361no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—8721no—
247C2—4362no—
248C2#2029515811yescharacteristic
249C2#2029520211yescharacteristic
250C2#2029521511yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#480×C109C2
socleC22×C109#120
prime radical#20295584C2
hypercenter#480D109
hypocenterC109#1607
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #20295339C2semidirect
3. #20294952C2semidirect
4. #20294761C2semidirect
5. #20294760C2semidirect
6. #20294749C2semidirect
7. #480×C109C2semidirect
19. C22⋊#11724784C22semidirect
21. #16812606C22semidirect
23. C2×C4⋊C4×C109C22semidirect
26. C22⋊C8×C109C22semidirect
126. C109#1607semidirect
129. #480D109semidirect
142. C2×C4⋊C4C2×D109semidirect
150. C22⋊C8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202955842
#202953392
#202949522
#202947612
#202947602
#202947492
#480×C1092
#1607109