Finite Group Databasebeta

← #28362340

Subgroups — #28362340

Order 13952.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#20295768C211yesmaximal, characteristic
2#20295420C211yesmaximal, characteristic, complemented
3#20295386C211yesmaximal, characteristic, complemented
4#20295385C211yesmaximal, characteristic, complemented
5#20294765C211yesmaximal, characteristic, complemented
6#20294765C211yesmaximal, characteristic, complemented
7#329×C109C211yesmaximal, characteristic, complemented
8C2×Dic436—21no—
9C2×#13182018—21no—
10#16812699C2211yescharacteristic, complemented
11#16812688—21no—
12#16812687C2211yescharacteristic
13#16812687C2211yescharacteristic
14#16812685—21no—
15#16812685—21no—
16#16812669—21no—
17#16812669—21no—
18#16812667—21no—
19#16812624—21no—
20#16812623—21no—
21#16812621—21no—
22#16812620—21no—
23#16812610C2211yescharacteristic, complemented
24#124×C109C2211yescharacteristic
25#97×C109C2211yescharacteristic, complemented
26#97×C109C2211yescharacteristic, complemented
27C23×D109—21no—
28C2×Dic218—21no—
29C2×Dic218D411yescharacteristic
30C2×Dic218D411yescharacteristic
31C2×D436—21no—
32C2×D436D411yescharacteristic
33C2×D436D411yescharacteristic
34C2×C22⋊D109—21no—
35C2×C22⋊D109—21no—
36Dic436—42no—
37#13182018—42no—
38C2×#11724784—21no—
39C4⋊Dic109—21no—
40C4⋊Dic109—21no—
41C22⋊Dic109—21no—
42#13182006—21no—
43#13182006—21no—
44#13182006—21no—
45#13182006—21no—
46#13182006—21no—
47#13182006—21no—
48C4×Dic109—21no—
49C2×Q8×C109D411yescharacteristic
50C2×D4×C109D411yescharacteristic
51C2×C8×C109—21no—
52C2×C8×C109—21no—
53C22⋊C4×C109—21no—
54C22⋊C4×C109—21no—
55C42×C109C2311yescharacteristic
56C23×C109—21no—
57C22×D109—21no—
58C22×D109—21no—
59C22×D109—81no—
60C22×D109—81no—
61C22×D109—81no—
62Q8×C109—41no—
63D4×C109—41no—
64C2×C4×C109—21no—
65C2×C4×C109C2×D411yescharacteristic
66C2×C4×C109C2×D411yescharacteristic
67C2×C4×C109C2×D411yescharacteristic
68C22⋊D109—81no—
69C22⋊D109—81no—
70C2×Dic109—21no—
71C2×Dic109—21no—
72C2×Dic109—41no—
73D436—41no—
74D436—41no—
75D436—81no—
76Dic218—41no—
77Dic218—41no—
78Dic218—41no—
79Dic218—41no—
80C8×C109—22no—
81C8×C109—41no—
82#11724784—41no—
83C22×C109—41no—
84C22×C109—41no—
85C22×C109—41no—
86C22×C109#12011yescharacteristic
87C2×D109—41no—
88C2×D109—41no—
89C2×D109—41no—
90C2×D109—41no—
91C2×D109—41no—
92C2×D109—41no—
93C2×D109—84no—
94C4×C109—21no—
95C4×C109—21no—
96C4×C109—21no—
97C4×C109—41no—
98Dic109—41no—
99Dic109—41no—
100Dic109—81no—
101C2×C109—81no—
102C2×C109#45311yescharacteristic
103C2×C109#45511yescharacteristic
104C2×C109#45511yescharacteristic
105D109—81no—
106D109—81no—
107#1659—1091nomaximal, Sylow
108C109#165911yescharacteristic, complemented, Sylow
109H(3,𝔽4)—1091no—
110#497—1091no—
111#489—1091no—
112#489—1091no—
113#329—1091no—
114#329—1091no—
115#329D10911yescharacteristic, complemented
116C2×Q16—2181no—
117C2×SD16—2181no—
118C4⋊Q8—1091no—
119#124—1091no—
120#124—1091no—
121#124—2181no—
122#124—2181no—
123#124—2181no—
124#124C2×D10911yescharacteristic
125#120—2181no—
126#120—2181no—
127#120—2181no—
128#103—2181no—
129#103—2181no—
130#102—2181no—
131#102—2181no—
132#97—1091no—
133#97C2×D10911yescharacteristic, complemented
134#97C2×D10911yescharacteristic, complemented
135C24—2181no—
136C2×Q8—1091no—
137C2×Q8—1091no—
138C2×Q8—2181no—
139C2×Q8D43611yescharacteristic
140C2×D4—1091no—
141C2×D4—1091no—
142C2×D4—2181no—
143C2×D4—2181no—
144C2×D4—2181no—
145C2×D4D43611yescharacteristic
146Q16—4362no—
147SD16—4362no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—2181no—
151C4⋊C4—2181no—
152C4⋊C4—2181no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—2181no—
156C22⋊C4—2181no—
157C22⋊C4—2181no—
158C22⋊C4—2181no—
159C22⋊C4—2181no—
160C22⋊C4—2181no—
161C22⋊C4—2181no—
162C42—2181no—
163C42C22×D10911yescharacteristic
164C23—21no—
165C23—8721no—
166C23—8721no—
167C23—8721no—
168C23—2181no—
169C23—2181no—
170Q8—41no—
171Q8—4361no—
172Q8—4361no—
173Q8—4361no—
174Q8—4361no—
175D4—41no—
176D4—8721no—
177D4—8721no—
178D4—8721no—
179D4—4361no—
180D4—4361no—
181C2×C4—21no—
182C2×C4—4361no—
183C2×C4—2181no—
184C2×C4—2181no—
185C2×C4D4×D10911yescharacteristic
186C2×C4D4×D10911yescharacteristic
187C2×C4C2×D43611yescharacteristic
188C8—22no—
189C8—41no—
190C8—4361no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—8724no—
195C22—4361no—
196C22—4361no—
197C22—4361no—
198C22—4361no—
199C22—4361no—
200C22—4361no—
201C22#1681266911yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—8721no—
207C4—4361no—
208C4—4361no—
209C2—81no—
210C2—8721no—
211C2—8721no—
212C2#2029519511yescharacteristic
213C2#2029520511yescharacteristic
214C2#2029520611yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#329×C109C2
socleC22×C109#120
prime radical#20295768C2
hypercenter#329D109
hypocenterC109#1659
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20295420C2semidirect
3. #20295386C2semidirect
4. #20295385C2semidirect
5. #20294765C2semidirect
6. #20294765C2semidirect
7. #329×C109C2semidirect
10. #16812699C22semidirect
23. #16812610C22semidirect
25. #97×C109C22semidirect
26. #97×C109C22semidirect
108. C109#1659semidirect
115. #329D109semidirect
133. #97C2×D109semidirect
134. #97C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202957682
#202954202
#202953862
#202953852
#202947652
#329×C1092
#1659109