Finite Group Databasebeta

← #28364191

Subgroups — #28364191

Order 13952.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#20295654C211yesmaximal, characteristic
2#20295035C211yesmaximal, characteristic
3#20294933C211yesmaximal, characteristic
4#20294794C211yesmaximal, characteristic
5#20294787C211yesmaximal, characteristic
6#20294785C211yesmaximal, characteristic
7#419×C109C211yesmaximal, characteristic
8C2×#13182013C2211yescharacteristic
9#16812699—21no—
10#16812698—21no—
11#16812691—21no—
12#16812690—21no—
13#16812676—22no—
14#16812658C2211yescharacteristic
15C2×C4⋊Dic109C2211yescharacteristic
16C2×C4×Dic109C2211yescharacteristic
17#16812623—21no—
18#16812623—21no—
19#16812606—22no—
20C22×Q8×C109C2211yescharacteristic
21C2×M16×C109C2211yescharacteristic
22#117×C109C2211yescharacteristic
23#103×C109—21no—
24#103×C109—21no—
25C2×Dic218—22no—
26C22×Dic109—21no—
27C22×Dic109D412yes—
28#13182013—21no—
29#13182013—21no—
30C2×#11724784—21no—
31C4⋊Dic109—22no—
32C4⋊Dic109—21no—
33C4⋊Dic109—21no—
34C4⋊Dic109D411yescharacteristic
35C4⋊Dic109D411yescharacteristic
36#13182008—22no—
37#13182008—22no—
38C22⋊Dic109—21no—
39C4×Dic109—21no—
40C4×Dic109—21no—
41C4×Dic109—21no—
42C2×Q8×C109—21no—
43C2×Q8×C109—21no—
44C2×Q8×C109—21no—
45C2×Q8×C109—21no—
46C2×Q8×C109—21no—
47C2×Q8×C109Q812yescomplemented
48C22×C4×C109—21no—
49C22×C4×C109C2311yescharacteristic
50M16×C109—21no—
51M16×C109—21no—
52C2×C8×C109—21no—
53C4⋊C4×C109D411yescharacteristic
54C4⋊C4×C109D411yescharacteristic
55C22⋊C4×C109—21no—
56C42×C109—21no—
57C23×C109C2×D411yescharacteristic
58Q8×C109—22no—
59Q8×C109—22no—
60Q8×C109—41no—
61Q8×C109—41no—
62C2×C4×C109—21no—
63C2×C4×C109—21no—
64C2×C4×C109—22no—
65C2×C4×C109—41no—
66C2×C4×C109—41no—
67C2×C4×C109C2×D411yescharacteristic
68C2×C4×C109C2×D411yescharacteristic
69C2×C4×C109C2×Q811yescharacteristic
70C2×C4×C109#4111yescharacteristic
71C2×C4×C109#4111yescharacteristic
72C2×C4×C109#4111yescharacteristic
73C2×Dic109—22no—
74C2×Dic109—21no—
75C2×Dic109—21no—
76C2×Dic109—22no—
77C2×Dic109—41no—
78C2×Dic109—41no—
79C2×Dic109—42no—
80Dic218—82no—
81C8×C109—41no—
82#11724784—41no—
83C22×C109—21no—
84C22×C109—21no—
85C22×C109#12011yescharacteristic
86C22×C109C22⋊Q811yescharacteristic
87C22×C109#12411yescharacteristic
88C4×C109—42no—
89C4×C109—41no—
90C4×C109—41no—
91C4×C109C22⋊Q811yescharacteristic
92C4×C109C22⋊Q811yescharacteristic
93C4×C109#12411yescharacteristic
94C4×C109#12411yescharacteristic
95Dic109—42no—
96Dic109—41no—
97Dic109—42no—
98Dic109—41no—
99C2×C109—21no—
100C2×C109—21no—
101C2×C109#39311yescharacteristic
102C2×C109#45511yescharacteristic
103C2×C109#45611yescharacteristic
104#2028—1091nomaximal, Sylow
105C109#202811yescharacteristic, complemented, Sylow
106#544—1091no—
107#419—1091no—
108#419D10911yescharacteristic
109#391—1091no—
110#343—1091no—
111#339—1091no—
112#339—1091no—
113C22×Q8C2×D10911yescharacteristic
114C2×M16—1091no—
115C2×M16C2×D10911yescharacteristic
116C4⋊Q8—2181no—
117C4⋊Q8—2181no—
118#125—2181no—
119#125—2181no—
120C22⋊Q8—2182no—
121#117—1091no—
122#117C2×D10911yescharacteristic
123C2×C4⋊C4—1091no—
124C2×C42—1091no—
125#103—21no—
126#103—21no—
127#103—2181no—
128#103—2181no—
129#95—2182no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—2182no—
136C2×Q8Dic21812yescomplemented
137C22×C4—21no—
138C22×C4—1092no—
139C22×C4—2181no—
140C22×C4C22×D10911yescharacteristic
141M16—21no—
142M16—21no—
143M16—2181no—
144M16—2181no—
145C2×C8—21no—
146C2×C8—2181no—
147C4⋊C4—1091no—
148C4⋊C4—1091no—
149C4⋊C4—2182no—
150C4⋊C4—2182no—
151C4⋊C4—2182no—
152C4⋊C4—2181no—
153C4⋊C4—2181no—
154C4⋊C4C22⋊D10911yescharacteristic
155C4⋊C4C22⋊D10911yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—2181no—
158C42—21no—
159C42—2181no—
160C42—2181no—
161C42—2181no—
162C23D4×D10911yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—8722no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—4361no—
174C2×C4—4361no—
175C2×C4—4362no—
176C2×C4—2182no—
177C2×C4—2181no—
178C2×C4—2181no—
179C2×C4—2182no—
180C2×C4D4×D10911yescharacteristic
181C2×C4C2×C22⋊D10911yescharacteristic
182C2×C4C2×Dic21811yescharacteristic
183C2×C4#1318202811yescharacteristic
184C2×C4#1318202811yescharacteristic
185C2×C4#1318202911yescharacteristic
186C8—41no—
187C8—4361no—
188C22—21no—
189C22—21no—
190C22#1681266711yescharacteristic
191C22#1681267611yescharacteristic
192C22#1681268511yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—4362no—
197C4—4362no—
198C4—4361no—
199C4—4361no—
200C4#1681267611yescharacteristic
201C4#1681267811yescharacteristic
202C4#1681268511yescharacteristic
203C4#1681268611yescharacteristic
204C2—21no—
205C2—21no—
206C2#2029493811yescharacteristic
207C2#2029520211yescharacteristic
208C2#2029520711yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#419×C109C2
socleC22×C109#120
prime radicalC23×C109C2×D4
hypercenter#419D109
hypocenterC109#2028
LCSG ▷ C22×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C109Q8semidirect
105. C109#2028semidirect
136. C2×Q8Dic218semidirect

Maximal subgroups

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

subgroupindex
#202956542
#202950352
#202949332
#202947942
#202947872
#202947852
#419×C1092
#2028109