Finite Group Databasebeta

← #28362067

Subgroups — #28362067

Order 13952.

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

normal subgroups only

This group has 246 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#20295603C211yesmaximal, characteristic
2#20295344C211yesmaximal, characteristic, complemented
3#20294964C211yesmaximal, characteristic, complemented
4#20294761C211yesmaximal, characteristic, complemented
5#20294760C211yesmaximal, characteristic, complemented
6#20294751C211yesmaximal, characteristic, complemented
7#481×C109C211yesmaximal, characteristic, complemented
8C2×#13182028—21no—
9#16812677—21no—
10#16812676—21no—
11#16812673C2211yescharacteristic
12#16812672—21no—
13#16812671—21no—
14#16812671—21no—
15C2×#13182008C2211yescharacteristic
16#16812630—21no—
17#16812619—21no—
18C22⋊#11724784C2211yescharacteristic
19#16812606—21no—
20#16812606—21no—
21#16812606C2211yescharacteristic
22#121×C109C2211yescharacteristic
23C2×C4⋊C4×C109C2211yescharacteristic
24#106×C109—21no—
25#102×C109—21no—
26C22⋊C8×C109C2211yescharacteristic
27#13182028—42no—
28#13182028—42no—
29C2×Dic218—21no—
30C2×D436D411yescharacteristic
31C2×C22⋊D109—21no—
32C2×C22⋊D109—21no—
33C2×C22⋊D109—21no—
34C22×Dic109—21no—
35C22×Dic109—21no—
36C22×Dic109D411yescharacteristic
37C22×Dic109D411yescharacteristic
38C2×C4×D109—21no—
39C2×#11724784—21no—
40C4⋊Dic109D411yescharacteristic
41#13182008—21no—
42#13182008—21no—
43#13182008—21no—
44C22⋊Dic109—21no—
45#13182006—21no—
46#13182006—21no—
47C2×D4×C109—21no—
48C2×D4×C109D411yescharacteristic
49C22×C4×C109—21no—
50C22×C4×C109C2311yescharacteristic
51C2×C8×C109—21no—
52C4⋊C4×C109—21no—
53C4⋊C4×C109—21no—
54C4⋊C4×C109D411yescharacteristic
55C22⋊C4×C109—21no—
56C23×C109—21no—
57C23×C109C2×D411yescharacteristic
58C22×D109—21no—
59D4×C109—41no—
60D4×C109—41no—
61D4×C109—41no—
62C2×C4×C109—21no—
63C2×C4×C109—41no—
64C2×C4×C109—42no—
65C2×C4×C109—41no—
66C2×C4×C109C2×D411yescharacteristic
67C2×C4×C109C2×D411yescharacteristic
68C22⋊D109—42no—
69C22⋊D109—41no—
70C22⋊D109—41no—
71C22⋊D109—81no—
72C2×Dic109—21no—
73C2×Dic109—21no—
74C2×Dic109—21no—
75C2×Dic109—21no—
76C2×Dic109—42no—
77C2×Dic109—41no—
78C2×Dic109—41no—
79C2×Dic109—41no—
80C2×Dic109—41no—
81C2×Dic109SD1612yes—
82D436—41no—
83C4×D109—42no—
84Dic218—42no—
85C8×C109—41no—
86#11724784—41no—
87C22×C109—21no—
88C22×C109—21no—
89C22×C109—41no—
90C22×C109—41no—
91C22×C109—41no—
92C22×C109#12011yescharacteristic
93C22×C109C2×SD1611yescharacteristic
94C22×C109AGL(1,ℤ/8)11yescharacteristic
95C2×D109—41no—
96C2×D109—41no—
97C2×D109—41no—
98C4×C109—21no—
99C4×C109—21no—
100C4×C109—41no—
101C4×C109—81no—
102Dic109—22no—
103Dic109—41no—
104Dic109—41no—
105Dic109—81no—
106C2×C109—21no—
107C2×C109—21no—
108C2×C109—81no—
109C2×C109#45011yescharacteristic
110C2×C109#45411yescharacteristic
111C2×C109#45811yescharacteristic
112D109—81no—
113#1616—1091nomaximal, Sylow
114C109#161611yescharacteristic, complemented, Sylow
115#537—1091no—
116#481—1091no—
117#481D10911yescharacteristic, complemented
118#400—1091no—
119#327—1091no—
120#327—1091no—
121#324—1091no—
122C2×#41—2181no—
123C22⋊Q8—2181no—
124C22⋊Q8—2181no—
125#121—1091no—
126#121—2181no—
127#121—2181no—
128#121—2181no—
129#121C2×D10911yescharacteristic
130C2×C4⋊C4—1091no—
131C2×C4⋊C4C2×D10911yescharacteristic
132#106—21no—
133#106—2181no—
134#102—21no—
135#102—2181no—
136C22⋊C8—1091no—
137C22⋊C8C2×D10911yescharacteristic
138#95—1091no—
139#95—2181no—
140#95—2181no—
141#41—4362no—
142#41—4362no—
143C2×Q8—2181no—
144C2×D4—21no—
145C2×D4—1091no—
146C2×D4—2181no—
147C2×D4—2181no—
148C2×D4—2181no—
149C2×D4C22⋊D10911yescharacteristic
150C22×C4—21no—
151C22×C4—1091no—
152C22×C4—1091no—
153C22×C4—2181no—
154C22×C4—2181no—
155C22×C4—2181no—
156C22×C4C22×D10911yescharacteristic
157C2×C8—21no—
158C2×C8—2181no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1091no—
162C4⋊C4—2181no—
163C4⋊C4—2181no—
164C4⋊C4—2181no—
165C4⋊C4C22⋊D10911yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—2181no—
168C22⋊C4—2181no—
169C22⋊C4—2181no—
170C23—21no—
171C23—2181no—
172C23D4×D10911yescharacteristic
173Q8—4362no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—8721no—
178D4—4361no—
179D4—4361no—
180D4—4361no—
181D4—4362no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—41no—
186C2×C4—1092no—
187C2×C4—4362no—
188C2×C4—4361no—
189C2×C4—4361no—
190C2×C4—4361no—
191C2×C4—4362no—
192C2×C4—4361no—
193C2×C4—2181no—
194C2×C4—2181no—
195C2×C4—2181no—
196C2×C4—2181no—
197C2×C4D4×D10911yescharacteristic
198C2×C4C2×C22⋊D10911yescharacteristic
199C8—41no—
200C8—4361no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—4361no—
207C22—4361no—
208C22—4361no—
209C22#1681266711yescharacteristic
210C22SD16×D10911yescharacteristic
211C22#1681272611yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—8721no—
217C4—4361no—
218C4—4361no—
219C4—2182no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—8721no—
224C2#2029517511yescharacteristic
225C2#2029519711yescharacteristic
226C2#2029521511yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#481×C109C2
socleC22×C109#120
prime radical#20295603C2
hypercenter#481D109
hypocenterC109#1616
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #20295344C2semidirect
3. #20294964C2semidirect
4. #20294761C2semidirect
5. #20294760C2semidirect
6. #20294751C2semidirect
7. #481×C109C2semidirect
114. C109#1616semidirect
117. #481D109semidirect

Maximal subgroups

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

subgroupindex
#202956032
#202953442
#202949642
#202947612
#202947602
#202947512
#481×C1092
#1616109