Finite Group Databasebeta

← #28362047

Subgroups — #28362047

Order 13952.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#20295613C211yesmaximal, characteristic
2#20295357C211yesmaximal, characteristic, complemented
3#20295337C211yesmaximal, characteristic, complemented
4#20294953C211yesmaximal, characteristic, complemented
5#20294762C211yesmaximal, characteristic, complemented
6#20294749C211yesmaximal, characteristic, complemented
7#327×C109C211yesmaximal, characteristic, complemented
8#16812694—21no—
9#16812685—21no—
10#16812683—21no—
11#16812678C2211yescharacteristic
12#16812671—21no—
13#16812667—21no—
14D4×Dic109—21no—
15C2×C4⋊Dic109C2211yescharacteristic
16C2×#13182006—21no—
17C2×#13182006C2211yescharacteristic
18#16812632—21no—
19#16812631—21no—
20#16812624—21no—
21#16812620—21no—
22C22⋊#11724784C2211yescharacteristic
23#16812606—21no—
24#121×C109C2211yescharacteristic
25C22⋊C8×C109C2211yescharacteristic
26#95×C109C2211yescharacteristic
27C23×D109D411yescharacteristic
28C2×Dic218D411yescharacteristic
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C22×Dic109—21no—
32C22×Dic109—21no—
33C22×Dic109D411yescharacteristic
34C2×#11724784—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109—21no—
37C4⋊Dic109—21no—
38C4⋊Dic109D411yescharacteristic
39#13182008—21no—
40C22⋊Dic109—21no—
41C22⋊Dic109—21no—
42#13182006—21no—
43#13182006—21no—
44#13182006—21no—
45#13182006—21no—
46#13182006—42no—
47C4×Dic109—21no—
48C2×D4×C109—21no—
49C2×D4×C109D411yescharacteristic
50C22×C4×C109—21no—
51C22×C4×C109C2311yescharacteristic
52C2×C8×C109—21no—
53C4⋊C4×C109D411yescharacteristic
54C22⋊C4×C109—21no—
55C23×C109—21no—
56C23×C109C2×D411yescharacteristic
57C22×D109—21no—
58C22×D109—21no—
59C22×D109—21no—
60C22×D109—41no—
61C22×D109—41no—
62D4×C109—41no—
63D4×C109—41no—
64D4×C109—41no—
65C2×C4×C109—21no—
66C2×C4×C109—41no—
67C2×C4×C109—41no—
68C2×C4×C109—41no—
69C2×C4×C109—41no—
70C2×C4×C109C2×D411yescharacteristic
71C2×C4×C109C2×D411yescharacteristic
72C22⋊D109—81no—
73C22⋊D109—81no—
74C2×Dic109—21no—
75C2×Dic109—21no—
76C2×Dic109—21no—
77C2×Dic109—41no—
78C2×Dic109—41no—
79C2×Dic109—41no—
80C2×Dic109—41no—
81C2×Dic109—81no—
82Dic218—41no—
83C8×C109—41no—
84#11724784—41no—
85C22×C109—21no—
86C22×C109—21no—
87C22×C109—41no—
88C22×C109—41no—
89C22×C109—41no—
90C22×C109#12011yescharacteristic
91C22×C109#13511yescharacteristic
92C22×C109AGL(1,ℤ/8)11yescharacteristic
93C2×D109—42no—
94C2×D109—41no—
95C2×D109—41no—
96C2×D109—41no—
97C2×D109—81no—
98C4×C109—21no—
99C4×C109—21no—
100C4×C109—41no—
101C4×C109—81no—
102Dic109—41no—
103Dic109—41no—
104Dic109—41no—
105Dic109—81no—
106C2×C109—21no—
107C2×C109—21no—
108C2×C109—81no—
109C2×C109#44911yescharacteristic
110C2×C109#45511yescharacteristic
111C2×C109#45811yescharacteristic
112D109—81no—
113#1612—1091nomaximal, Sylow
114C109#161211yescharacteristic, complemented, Sylow
115#538—1091no—
116#483—1091no—
117#480—1091no—
118#397—1091no—
119#328—1091no—
120#327D10911yescharacteristic, complemented
121#323—1091no—
122#126—2181no—
123#124—2181no—
124#123—2181no—
125C22⋊Q8—1091no—
126#121—2181no—
127#121C2×D10911yescharacteristic
128#120—2181no—
129C4×D4—2181no—
130C2×C4⋊C4—1091no—
131C2×C22⋊C4—1091no—
132C2×C22⋊C4—2181no—
133#107—2181no—
134#106—2181no—
135#103—2181no—
136#102—2181no—
137C22⋊C8—1091no—
138C22⋊C8C2×D10911yescharacteristic
139#95—2181no—
140#95C2×D10911yescharacteristic
141C24—1091no—
142C2×Q8—1091no—
143C2×D4—21no—
144C2×D4—2181no—
145C2×D4—2181no—
146C2×D4D43611yescharacteristic
147C22×C4—21no—
148C22×C4—1091no—
149C22×C4—2181no—
150C22×C4—2181no—
151C22×C4C22×D10911yescharacteristic
152C2×C8—21no—
153C2×C8—2181no—
154C4⋊C4—1091no—
155C4⋊C4—2181no—
156C4⋊C4—2181no—
157C4⋊C4—2181no—
158C4⋊C4—2181no—
159C4⋊C4D43611yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—4362no—
162C22⋊C4—2181no—
163C22⋊C4—2181no—
164C22⋊C4—2181no—
165C22⋊C4—2181no—
166C22⋊C4—2181no—
167C22⋊C4—2181no—
168C42—2181no—
169C23—21no—
170C23—4361no—
171C23—4361no—
172C23—2181no—
173C23—2181no—
174C23—2181no—
175C23D4×D10911yescharacteristic
176Q8—4361no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—8721no—
181D4—8721no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—8721no—
188C2×C4—4361no—
189C2×C4—4361no—
190C2×C4—4361no—
191C2×C4—4361no—
192C2×C4—2181no—
193C2×C4—2181no—
194C2×C4—2181no—
195C2×C4D4×D10911yescharacteristic
196C2×C4C2×D43611yescharacteristic
197C8—41no—
198C8—4361no—
199C22—21no—
200C22—21no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—8721no—
205C22—4362no—
206C22—4361no—
207C22—4361no—
208C22—4361no—
209C22#1681266911yescharacteristic
210C22#1681272011yescharacteristic
211C22#1681272311yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—8721no—
217C4—4361no—
218C4—4361no—
219C4—4361no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—8721no—
224C2#2029517211yescharacteristic
225C2#2029520511yescharacteristic
226C2#2029521711yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#327×C109C2
socleC22×C109#120
prime radical#20295613C2
hypercenter#327D109
hypocenterC109#1612
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20295357C2semidirect
3. #20295337C2semidirect
4. #20294953C2semidirect
5. #20294762C2semidirect
6. #20294749C2semidirect
7. #327×C109C2semidirect
114. C109#1612semidirect
120. #327D109semidirect

Maximal subgroups

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

subgroupindex
#202956132
#202953572
#202953372
#202949532
#202947622
#202947492
#327×C1092
#1612109