Finite Group Databasebeta

← #28363248

Subgroups — #28363248

Order 13952.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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#20295503C211yesmaximal, characteristic
2#20295069C211yesmaximal, characteristic
3#20295068C211yesmaximal, characteristic
4C2×#16812617C211yesmaximal, characteristic
5#20294932C211yesmaximal, characteristic
6#20294786C211yesmaximal, characteristic
7#339×C109C211yesmaximal, characteristic
8C22×Dic218C2211yescharacteristic
9C2×#13182013C2211yescharacteristic
10C4×Dic218—21no—
11C4×Dic218—21no—
12#16812664—21no—
13#16812664—21no—
14#16812658C2211yescharacteristic
15#16812655—22no—
16C2×C4⋊Dic109C2211yescharacteristic
17#16812633—21no—
18#16812632—21no—
19#16812631—21no—
20#16812630—21no—
21#16812617C414yescomplemented
22#16812606—22no—
23C2×M16×C109C2211yescharacteristic
24#117×C109C2211yescharacteristic
25C2×C42×C109C2211yescharacteristic
26C2×Dic218—21no—
27C2×Dic218—21no—
28C2×Dic218—21no—
29C2×Dic218—21no—
30C2×Dic218C2×C412yes—
31C2×Dic218Q812yes—
32C22×Dic109—21no—
33C22×Dic109D412yes—
34#13182013—21no—
35#13182013C2×C412yes—
36C2×#11724784—21no—
37C4⋊Dic109—21no—
38C4⋊Dic109—21no—
39C4⋊Dic109D411yescharacteristic
40C4⋊Dic109D411yescharacteristic
41#13182008—22no—
42#13182008—22no—
43C22⋊Dic109—21no—
44C4×Dic109—22no—
45C4×Dic109—22no—
46C4×Dic109—21no—
47C22×C4×C109—21no—
48C22×C4×C109C2311yescharacteristic
49M16×C109—21no—
50M16×C109C2×C412yes—
51C2×C8×C109—21no—
52C4⋊C4×C109D411yescharacteristic
53C4⋊C4×C109D411yescharacteristic
54C22⋊C4×C109—21no—
55C42×C109—21no—
56C42×C109—21no—
57C42×C109—21no—
58C23×C109C2×D411yescharacteristic
59C2×C4×C109—22no—
60C2×C4×C109—21no—
61C2×C4×C109—21no—
62C2×C4×C109—41no—
63C2×C4×C109—41no—
64C2×C4×C109C22×C411yescharacteristic
65C2×C4×C109C2×D411yescharacteristic
66C2×C4×C109C2×D411yescharacteristic
67C2×C4×C109C2×Q811yescharacteristic
68C2×C4×C109#4111yescharacteristic
69C2×C4×C109#4111yescharacteristic
70C2×Dic109—22no—
71C2×Dic109—22no—
72C2×Dic109—21no—
73C2×Dic109—21no—
74C2×Dic109—42no—
75C2×Dic109—41no—
76C2×Dic109C4⋊C414yes—
77Dic218—22no—
78Dic218—22no—
79Dic218—22no—
80Dic218—22no—
81C8×C109—22no—
82#11724784—22no—
83C22×C109—21no—
84C22×C109—21no—
85C22×C109C2×C4⋊C411yescharacteristic
86C22×C109#12011yescharacteristic
87C22×C109#12311yescharacteristic
88C4×C109—42no—
89C4×C109—41no—
90C4×C109—41no—
91C4×C109C4×D411yescharacteristic
92C4×C109C4×D411yescharacteristic
93C4×C109C22⋊Q811yescharacteristic
94C4×C109C22⋊Q811yescharacteristic
95Dic109—24no—
96Dic109—41no—
97Dic109—41no—
98Dic109—81no—
99C2×C109—21no—
100C2×C109—21no—
101C2×C109#38511yescharacteristic
102C2×C109#45411yescharacteristic
103C2×C109#45611yescharacteristic
104#1857—1091nomaximal, Sylow
105C109#185711yescharacteristic, complemented, Sylow
106#519—1091no—
107#428—1091no—
108#428—1091no—
109C2×#101—1091no—
110#391—1091no—
111#339—1091no—
112#339D10911yescharacteristic
113C22×Q8—1091no—
114C2×M16—1091no—
115C2×M16C2×D10911yescharacteristic
116C4×Q8—2181no—
117C4×Q8—2181no—
118C4×Q8—2181no—
119C4×Q8—2181no—
120#117—1091no—
121#117—2182no—
122#117C2×D10911yescharacteristic
123C2×C4⋊C4—1091no—
124C2×C42C2×D10911yescharacteristic
125#107—2181no—
126#107—2181no—
127#106—2181no—
128#106—2181no—
129#101—1094no—
130#95—2182no—
131C2×Q8—1092no—
132C2×Q8—1092no—
133C2×Q8—2181no—
134C2×Q8—2181no—
135C2×Q8—2181no—
136C2×Q8—2181no—
137C22×C4—21no—
138C22×C4—1092no—
139C22×C4—2181no—
140C22×C4C22×D10911yescharacteristic
141M16—21no—
142M16—1092no—
143M16—2181no—
144M16C4×D10912yes—
145C2×C8—21no—
146C2×C8—2181no—
147C4⋊C4—1091no—
148C4⋊C4—1091no—
149C4⋊C4—2182no—
150C4⋊C4—2182no—
151C4⋊C4—2181no—
152C4⋊C4—2181no—
153C4⋊C4D43611yescharacteristic
154C4⋊C4D43611yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—2181no—
157C42—21no—
158C42—21no—
159C42—21no—
160C42—2182no—
161C42—2182no—
162C42—2181no—
163C23D4×D10911yescharacteristic
164Q8—2182no—
165Q8—2182no—
166Q8—2182no—
167Q8—2182no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1094no—
174C2×C4—4362no—
175C2×C4—4361no—
176C2×C4—2181no—
177C2×C4—2181no—
178C2×C4—2182no—
179C2×C4—2182no—
180C2×C4C2×C4×D10911yescharacteristic
181C2×C4D4×D10911yescharacteristic
182C2×C4C2×D43611yescharacteristic
183C2×C4Q8×D10911yescharacteristic
184C2×C4#1318202811yescharacteristic
185C2×C4#1318202911yescharacteristic
186C8—22no—
187C8—2182no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D10911yescharacteristic
191C22#1681266911yescharacteristic
192C22#1681268111yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—8721no—
197C4—4361no—
198C4—4361no—
199C4—2184no—
200C4#1681265911yescharacteristic
201C4C4×D43611yescharacteristic
202C4#1681267711yescharacteristic
203C4#1681267911yescharacteristic
204C2—21no—
205C2—21no—
206C2#2029490011yescharacteristic
207C2#2029520011yescharacteristic
208C2#2029521011yescharacteristic
subgroupG/H
centerC22#16812669
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#339×C109C2
socleC22×C109#120
prime radicalC23×C109C2×D4
cosocleC22×C4×C109C23
hypercenter#339D109
hypocenterC109#1857
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
21. #16812617C4semidirect
105. C109#1857semidirect

Maximal subgroups

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

subgroupindex
#202955032
#202950692
#202950682
C2×#168126172
#202949322
#202947862
#339×C1092
#1857109