Finite Group Databasebeta

← #28362048

Subgroups — #28362048

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#20295614C211yesmaximal, characteristic
2#20295357C211yesmaximal, characteristic, complemented
3#20295340C211yesmaximal, characteristic, complemented
4#20294951C211yesmaximal, characteristic, complemented
5#20294764C211yesmaximal, characteristic, complemented
6#20294761C211yesmaximal, characteristic, complemented
7#323×C109C211yesmaximal, characteristic, complemented
8#16812692—21no—
9#16812685—21no—
10#16812681—21no—
11#16812678C2211yescharacteristic
12#16812673C2211yescharacteristic
13#16812672—21no—
14#16812668—21no—
15C4×C22⋊D109—21no—
16C2×C4⋊Dic109C2211yescharacteristic
17C2×C22⋊Dic109—21no—
18#16812633—21no—
19#16812631—21no—
20#16812624—21no—
21#16812621—21no—
22#16812606—21no—
23#16812606C2211yescharacteristic
24C2×C22⋊C4×C109C2211yescharacteristic
25C22⋊C8×C109C2211yescharacteristic
26C22⋊C8×C109C2211yescharacteristic
27C2×Dic218D411yescharacteristic
28C2×D436D411yescharacteristic
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C2×C22⋊D109—21no—
32C22×Dic109—21no—
33C22×Dic109—21no—
34C2×C4×D109—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109—21no—
37C4⋊Dic109D411yescharacteristic
38C4⋊Dic109D411yescharacteristic
39#13182008—21no—
40#13182008—21no—
41C22⋊Dic109—21no—
42C22⋊Dic109—21no—
43C22⋊Dic109—21no—
44C22⋊Dic109—42no—
45#13182006—21no—
46#13182006—21no—
47C4×Dic109—21no—
48C24×C109D411yescharacteristic
49C22×C4×C109D411yescharacteristic
50C22×C4×C109C2311yescharacteristic
51C2×C8×C109—21no—
52C2×C8×C109—21no—
53C22⋊C4×C109—21no—
54C22⋊C4×C109—21no—
55C23×C109—21no—
56C23×C109—21no—
57C23×C109—21no—
58C23×C109—41no—
59C23×C109—41no—
60C23×C109C2×D411yescharacteristic
61C22×D109—21no—
62C2×C4×C109—21no—
63C2×C4×C109—41no—
64C2×C4×C109—41no—
65C2×C4×C109C2×D411yescharacteristic
66C2×C4×C109C2×D411yescharacteristic
67C22⋊D109—41no—
68C22⋊D109—41no—
69C22⋊D109—81no—
70C22⋊D109—81no—
71C2×Dic109—21no—
72C2×Dic109—21no—
73C2×Dic109—21no—
74C2×Dic109—41no—
75C2×Dic109—41no—
76C2×Dic109—41no—
77C2×Dic109—41no—
78C2×Dic109—41no—
79C2×Dic109—41no—
80D436—41no—
81C4×D109—81no—
82Dic218—41no—
83C8×C109—41no—
84C8×C109—41no—
85C22×C109—21no—
86C22×C109—21no—
87C22×C109—42no—
88C22×C109—41no—
89C22×C109—41no—
90C22×C109—41no—
91C22×C109—81no—
92C22×C109#12011yescharacteristic
93C22×C109#13511yescharacteristic
94C22×C109AGL(1,ℤ/8)11yescharacteristic
95C2×D109—41no—
96C2×D109—41no—
97C2×D109—41no—
98C4×C109—21no—
99C4×C109—21no—
100C4×C109—41no—
101Dic109—41no—
102Dic109—41no—
103Dic109—41no—
104Dic109—81no—
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#327—1091no—
121#323D10911yescharacteristic, complemented
122#126—2181no—
123#124—2181no—
124#123—2181no—
125C22⋊Q8—1091no—
126#121—1091no—
127#121—2181no—
128#120—2181no—
129C4×D4—2181no—
130C2×C4⋊C4—1091no—
131C2×C22⋊C4—2181no—
132C2×C22⋊C4C2×D10911yescharacteristic
133#107—2181no—
134#106—2181no—
135#103—2181no—
136#102—2181no—
137C22⋊C8C2×D10911yescharacteristic
138C22⋊C8C2×D10911yescharacteristic
139#95—1091no—
140#95—2181no—
141C24D43611yescharacteristic
142C2×Q8—1091no—
143C2×D4—1091no—
144C2×D4—2181no—
145C2×D4—2181no—
146C2×D4—2181no—
147C22×C4—2181no—
148C22×C4—2181no—
149C22×C4—2181no—
150C22×C4D43611yescharacteristic
151C22×C4C22×D10911yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C4⋊C4—1091no—
155C4⋊C4—1091no—
156C4⋊C4—2181no—
157C4⋊C4—2181no—
158C4⋊C4—2181no—
159C4⋊C4—2181no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—4362no—
163C22⋊C4—2181no—
164C22⋊C4—2181no—
165C22⋊C4—2181no—
166C22⋊C4—2181no—
167C22⋊C4—2181no—
168C42—2181no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—2181no—
175C23C2×D43611yescharacteristic
176Q8—4361no—
177D4—8721no—
178D4—8721no—
179D4—4361no—
180D4—4361no—
181D4—4361no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—8721no—
186C2×C4—4361no—
187C2×C4—4361no—
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×C4D4×D10911yescharacteristic
197C8—41no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—4361no—
207C22—4361no—
208C22—4361no—
209C22#1681266911yescharacteristic
210C22#1681272111yescharacteristic
211C22#1681272711yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—8721no—
216C4—8721no—
217C4—4361no—
218C4—4361no—
219C4—4361no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—8721no—
224C2#2029517311yescharacteristic
225C2#2029520611yescharacteristic
226C2#2029521711yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#323×C109C2
socleC22×C109#120
prime radical#20295614C2
hypercenter#323D109
hypocenterC109#1612
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #20295357C2semidirect
3. #20295340C2semidirect
4. #20294951C2semidirect
5. #20294764C2semidirect
6. #20294761C2semidirect
7. #323×C109C2semidirect
114. C109#1612semidirect
121. #323D109semidirect

Maximal subgroups

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

subgroupindex
#202956142
#202953572
#202953402
#202949512
#202947642
#202947612
#323×C1092
#1612109