Finite Group Databasebeta

← #28363527

Subgroups — #28363527

Order 13952.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#16812732C211yesmaximal, characteristic
2#20295503C211yesmaximal, characteristic, complemented
3#20295044C211yesmaximal, characteristic
4#20295034C211yesmaximal, characteristic, complemented
5#20294999C211yesmaximal, characteristic
6#20294797C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C109C211yesmaximal, characteristic, complemented
8C2×#13182029C2211yescharacteristic
9C22×Dic218C2211yescharacteristic
10#16812732—22no—
11#16812732—22no—
12C2×Dic436C412yescomplemented
13C2×#13182018C412yescomplemented
14C2×#13182013C2211yescharacteristic
15C4×Dic218—22no—
16#16812664—22no—
17#16812658C2211yescharacteristic
18#16812655—22no—
19#16812627—22no—
20#16812622—22no—
21#16812613—22no—
22C2×M16×C109C2211yescharacteristic
23#117×C109C2211yescharacteristic
24#117×C109C2211yescharacteristic
25#13182029—21no—
26#13182029—21no—
27#13182029—21no—
28#13182029—21no—
29C2×Dic218—21no—
30C2×Dic218—21no—
31C2×Dic218—21no—
32C2×Dic218C2×C411yescharacteristic
33C2×Dic218C2×C412yes—
34C2×Dic218D412yes—
35C2×Dic218D412yes—
36C2×D436C2×C411yescharacteristic
37C2×C22⋊D109—21no—
38C22×Dic109—21no—
39C2×C4×D109—21no—
40Dic436—24no—
41#13182018—24no—
42#13182013—21no—
43#13182013—21no—
44C2×#11724784—21no—
45C4⋊Dic109—21no—
46#13182008—24no—
47C22⋊Dic109D412yes—
48C4×Dic109—24no—
49C4×Dic109—21no—
50C22×C4×C109C2311yescharacteristic
51M16×C109—21no—
52M16×C109—21no—
53C2×C8×C109C2×C412yes—
54C4⋊C4×C109—21no—
55C4⋊C4×C109—21no—
56C22⋊C4×C109—21no—
57C22⋊C4×C109—21no—
58C42×C109—21no—
59C42×C109D412yes—
60C23×C109C2×D411yescharacteristic
61C22×D109—21no—
62C2×C4×C109—22no—
63C2×C4×C109—41no—
64C2×C4×C109C22×C411yescharacteristic
65C2×C4×C109C2×D411yescharacteristic
66C2×C4×C109C2×D411yescharacteristic
67C2×C4×C109C2×D411yescharacteristic
68C2×C4×C109#4111yescharacteristic
69C2×C4×C109#4111yescharacteristic
70C22⋊D109—41no—
71C22⋊D109—41no—
72C2×Dic109—22no—
73C2×Dic109—22no—
74C2×Dic109—22no—
75C2×Dic109—21no—
76C2×Dic109—22no—
77D436—21no—
78D436—21no—
79C4×D109—41no—
80C4×D109—41no—
81Dic218—22no—
82Dic218—22no—
83Dic218—22no—
84Dic218—21no—
85Dic218—21no—
86Dic218C22⋊C414yes—
87C8×C109—22no—
88#11724784—41no—
89C22×C109—41no—
90C22×C109C4×D411yescharacteristic
91C22×C109#12011yescharacteristic
92C22×C109#12111yescharacteristic
93C2×D109—41no—
94C2×D109—81no—
95C4×C109—42no—
96C4×C109—81no—
97C4×C109C2×C22⋊C411yescharacteristic
98C4×C109C4×D411yescharacteristic
99C4×C109#12111yescharacteristic
100C4×C109#12311yescharacteristic
101Dic109—24no—
102Dic109—42no—
103Dic109—41no—
104C2×C109—21no—
105C2×C109—21no—
106C2×C109—21no—
107C2×C109#38611yescharacteristic
108D109—81no—
109#1905—1091nomaximal, Sylow
110C109#190511yescharacteristic, complemented, Sylow
111C2×#137—1091no—
112#519—1091no—
113#421—1091no—
114#419—1091no—
115#410—1091no—
116#344—1091no—
117H(3,ℤ/4)D10911yescharacteristic, complemented
118C2×#41—1091no—
119C22×Q8—1091no—
120#137—2182no—
121#137—2182no—
122C2×Q16—1092no—
123C2×SD16—1092no—
124C2×M16—1091no—
125C2×M16C2×D10911yescharacteristic
126C4×Q8—2182no—
127C4×Q8—2182no—
128#117—1091no—
129#117—2182no—
130#117C2×D10911yescharacteristic
131#117C2×D10911yescharacteristic
132#104—2182no—
133#103—2182no—
134#99—2182no—
135#41—2181no—
136#41—2181no—
137#41—2181no—
138#41—2181no—
139C2×Q8—1092no—
140C2×Q8—1091no—
141C2×Q8—1092no—
142C2×Q8—1092no—
143C2×Q8—2181no—
144C2×Q8—2181no—
145C2×Q8—2181no—
146C2×D4—1091no—
147C2×D4—2181no—
148C22×C4—2181no—
149C22×C4—2181no—
150C22×C4C22×D10911yescharacteristic
151Q16—2184no—
152SD16—2184no—
153M16—21no—
154M16—21no—
155M16—2181no—
156M16—2181no—
157C2×C8—2181no—
158C2×C8C4×D10912yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2184no—
162C4⋊C4—2181no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—1092no—
166C42—21no—
167C42—2184no—
168C42—2181no—
169C42D43612yes—
170C23—2181no—
171C23D4×D10911yescharacteristic
172Q8—1094no—
173Q8—2181no—
174Q8—2181no—
175Q8—2182no—
176Q8—2182no—
177Q8—2182no—
178D4—4361no—
179D4—4361no—
180D4—2181no—
181D4—2181no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—4361no—
185C2×C4—4361no—
186C2×C4—2181no—
187C2×C4—2182no—
188C2×C4—2182no—
189C2×C4—2182no—
190C2×C4—2182no—
191C2×C4C2×C4×D10911yescharacteristic
192C2×C4D4×D10911yescharacteristic
193C2×C4D4×D10911yescharacteristic
194C2×C4C2×D43611yescharacteristic
195C2×C4#1318202911yescharacteristic
196C2×C4#1318203011yescharacteristic
197C8—22no—
198C8—4361no—
199C22—41no—
200C22—8721no—
201C22—4361no—
202C22#1681266111yescharacteristic
203C22#1681266911yescharacteristic
204C22#1681267211yescharacteristic
205C4—42no—
206C4—81no—
207C4—4362no—
208C4—4361no—
209C4—2184no—
210C4C22⋊C4×D10911yescharacteristic
211C4C4×D43611yescharacteristic
212C4#1681267411yescharacteristic
213C4#1681268411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—8721no—
218C2#2029490411yescharacteristic
subgroupG/H
centerC2#20294904
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
FittingH(3,ℤ/4)×C109C2
socleC2×C109#386
prime radicalC2×#13182029C22
cosocleC22×C4×C109C23
hypercenterH(3,ℤ/4)D109
hypocenterC109#1905
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #20295503C2semidirect
4. #20295034C2semidirect
6. #20294797C2semidirect
7. H(3,ℤ/4)×C109C2semidirect
12. C2×Dic436C4semidirect
13. C2×#13182018C4semidirect
110. C109#1905semidirect
117. H(3,ℤ/4)D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127322
#202955032
#202950442
#202950342
#202949992
#202947972
H(3,ℤ/4)×C1092
#1905109