Finite Group Databasebeta

← #28362082

Subgroups — #28362082

Order 13952.

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

normal subgroups only

This group has 240 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#20295362C211yesmaximal, characteristic, complemented
3#20295345C211yesmaximal, characteristic, complemented
4#20294962C211yesmaximal, 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×#13182008—21no—
18C2×C22⋊Dic109—21no—
19#16812633—21no—
20#16812631—21no—
21#16812624—21no—
22#16812621—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—
41#13182008—42no—
42C22⋊Dic109—21no—
43C22⋊Dic109—21no—
44C22⋊Dic109—21no—
45C22⋊Dic109—42no—
46#13182006—21no—
47#13182006—21no—
48C4×Dic109—21no—
49C24×C109D411yescharacteristic
50C22×C4×C109D411yescharacteristic
51C22×C4×C109C2311yescharacteristic
52C2×C8×C109—21no—
53C2×C8×C109—21no—
54C22⋊C4×C109—21no—
55C22⋊C4×C109—21no—
56C23×C109—21no—
57C23×C109—21no—
58C23×C109—21no—
59C23×C109—41no—
60C23×C109—41no—
61C23×C109C2×D411yescharacteristic
62C22×D109—21no—
63C2×C4×C109—21no—
64C2×C4×C109—41no—
65C2×C4×C109—41no—
66C2×C4×C109C2×D411yescharacteristic
67C2×C4×C109C2×D411yescharacteristic
68C22⋊D109—41no—
69C22⋊D109—41no—
70C22⋊D109—81no—
71C22⋊D109—81no—
72C2×Dic109—22no—
73C2×Dic109—21no—
74C2×Dic109—21no—
75C2×Dic109—21no—
76C2×Dic109—41no—
77C2×Dic109—41no—
78C2×Dic109—41no—
79C2×Dic109—41no—
80C2×Dic109—41no—
81D436—41no—
82C4×D109—81no—
83Dic218—41no—
84C8×C109—41no—
85C8×C109—41no—
86C22×C109—21no—
87C22×C109—21no—
88C22×C109—42no—
89C22×C109—41no—
90C22×C109—41no—
91C22×C109—41no—
92C22×C109—81no—
93C22×C109#12011yescharacteristic
94C22×C109#13511yescharacteristic
95C22×C109#13711yescharacteristic
96C2×D109—41no—
97C2×D109—41no—
98C2×D109—41no—
99C4×C109—21no—
100C4×C109—21no—
101C4×C109—41no—
102Dic109—42no—
103Dic109—41no—
104Dic109—41no—
105Dic109—41no—
106Dic109—81no—
107C2×C109—21no—
108C2×C109—21no—
109C2×C109—81no—
110C2×C109#45211yescharacteristic
111C2×C109#45311yescharacteristic
112C2×C109#45811yescharacteristic
113D109—81no—
114#1618—1091nomaximal, Sylow
115C109#161811yescharacteristic, complemented, Sylow
116#538—1091no—
117#484—1091no—
118#481—1091no—
119#399—1091no—
120#328—1091no—
121#327—1091no—
122#323D10911yescharacteristic, complemented
123#126—2181no—
124#124—2181no—
125#123—2181no—
126C22⋊Q8—1091no—
127#121—1091no—
128#121—2181no—
129#120—2181no—
130C4×D4—2181no—
131C2×C4⋊C4—1091no—
132C2×C4⋊C4—2181no—
133C2×C22⋊C4—2181no—
134C2×C22⋊C4C2×D10911yescharacteristic
135#107—2181no—
136#106—2181no—
137#103—2181no—
138#102—2181no—
139C22⋊C8C2×D10911yescharacteristic
140C22⋊C8C2×D10911yescharacteristic
141#95—1091no—
142C24D43611yescharacteristic
143C2×Q8—1091no—
144C2×D4—1091no—
145C2×D4—2181no—
146C2×D4—2181no—
147C2×D4—2181no—
148C22×C4—2181no—
149C22×C4—2181no—
150C22×C4—2181no—
151C22×C4D43611yescharacteristic
152C22×C4C22×D10911yescharacteristic
153C2×C8—21no—
154C2×C8—21no—
155C4⋊C4—1091no—
156C4⋊C4—1091no—
157C4⋊C4—4362no—
158C4⋊C4—2181no—
159C4⋊C4—2181no—
160C4⋊C4—2181no—
161C4⋊C4—2181no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—4362no—
165C22⋊C4—2181no—
166C22⋊C4—2181no—
167C22⋊C4—2181no—
168C22⋊C4—2181no—
169C22⋊C4—2181no—
170C42—2181no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—41no—
175C23—41no—
176C23—2181no—
177C23C2×D43611yescharacteristic
178Q8—4361no—
179D4—8721no—
180D4—8721no—
181D4—4361no—
182D4—4361no—
183D4—4361no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—8721no—
188C2×C4—4361no—
189C2×C4—4361no—
190C2×C4—4361no—
191C2×C4—4361no—
192C2×C4—4361no—
193C2×C4—2182no—
194C2×C4—2181no—
195C2×C4—2181no—
196C2×C4—2181no—
197C2×C4D4×D10911yescharacteristic
198C2×C4D4×D10911yescharacteristic
199C8—41no—
200C8—41no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—4361no—
209C22—4361no—
210C22—4361no—
211C22#1681266911yescharacteristic
212C22#1681272111yescharacteristic
213C22#1681273211yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—8721no—
218C4—4362no—
219C4—4361no—
220C4—4361no—
221C4—4361no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—8721no—
226C2#2029519011yescharacteristic
227C2#2029519611yescharacteristic
228C2#2029521711yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#323×C109C2
socleC22×C109#120
prime radical#20295614C2
hypercenter#323D109
hypocenterC109#1618
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. #20295362C2semidirect
3. #20295345C2semidirect
4. #20294962C2semidirect
5. #20294764C2semidirect
6. #20294761C2semidirect
7. #323×C109C2semidirect
115. C109#1618semidirect
122. #323D109semidirect

Maximal subgroups

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

subgroupindex
#202956142
#202953622
#202953452
#202949622
#202947642
#202947612
#323×C1092
#1618109