Finite Group Databasebeta

← #28362120

Subgroups — #28362120

Order 13952.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#20295681C211yesmaximal, characteristic, complemented
2#20295372C211yesmaximal, characteristic, complemented
3#20295218C211yesmaximal, characteristic, complemented
4#20294771C211yesmaximal, characteristic, complemented
5D4⋊#11724784C211yesmaximal, characteristic, complemented
6#20294753C211yesmaximal, characteristic, complemented
7#459×C109C211yesmaximal, characteristic, complemented
8C2×#13182029—21no—
9C2×#13182014—21no—
10#16812699C2211yescharacteristic
11#16812681—22no—
12#16812678—21no—
13#16812670—21no—
14C4×D436C2211yescharacteristic
15C4⋊C4×D109—21no—
16C4⋊#11724784C2211yescharacteristic
17#16812620—21no—
18#16812620—22no—
19C4×#11724784C2211yescharacteristic
20C2×D8×C109—21no—
21#127×C109C2211yescharacteristic
22C4×D4×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24#102×C109—21no—
25#13182029—42no—
26#13182029—42no—
27C2×Dic218—21no—
28C2×D436D411yescharacteristic
29C2×C22⋊D109—22no—
30C2×C4×D109—22no—
31C2×C4×D109—21no—
32#13182014—42no—
33C2×#11724784—21no—
34C2×#11724784—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109D411yescharacteristic
37C4⋊Dic109D412yes—
38#13182008—22no—
39C22⋊Dic109—22no—
40#13182006—21no—
41C2×D4×C109—21no—
42C2×D4×C109—21no—
43C2×D4×C109—21no—
44C2×D4×C109D411yescharacteristic
45C22×C4×C109—21no—
46D8×C109—42no—
47C2×C8×C109—21no—
48C4⋊C4×C109D411yescharacteristic
49C22⋊C4×C109—21no—
50C42×C109C2311yescharacteristic
51C23×C109—21no—
52C23×C109—41no—
53C22×D109—21no—
54D4×C109—21no—
55D4×C109—21no—
56D4×C109—42no—
57D4×C109—41no—
58D4×C109—41no—
59D4×C109—41no—
60D4×C109—41no—
61C2×C4×C109—21no—
62C2×C4×C109—41no—
63C2×C4×C109—41no—
64C2×C4×C109C2×D411yescharacteristic
65C2×C4×C109C2×D411yescharacteristic
66C2×C4×C109C2×D411yescharacteristic
67C22⋊D109—44no—
68C2×Dic109—21no—
69C2×Dic109—22no—
70D436—21no—
71D436D812yescomplemented
72C4×D109—44no—
73C4×D109—41no—
74C4×D109—41no—
75Dic218—41no—
76Dic218—41no—
77C8×C109—41no—
78#11724784—41no—
79#11724784—41no—
80C22×C109—41no—
81C22×C109—41no—
82C22×C109—41no—
83C22×C109—81no—
84C22×C109—81no—
85C22×C109—81no—
86C22×C109#12011yescharacteristic
87C2×D109—22no—
88C2×D109—41no—
89C2×D109—41no—
90C4×C109—21no—
91C4×C109—41no—
92C4×C109C2×D811yescharacteristic
93C4×C109#13511yescharacteristic
94C4×C109AGL(1,ℤ/8)11yescharacteristic
95C4×C109AGL(1,ℤ/8)11yescharacteristic
96Dic109—42no—
97Dic109—41no—
98C2×C109—81no—
99C2×C109—161no—
100C2×C109#44711yescharacteristic
101C2×C109#44911yescharacteristic
102C2×C109#45411yescharacteristic
103D109—42no—
104#1625—1091nomaximal, Sylow
105C109#162511yescharacteristic, complemented, Sylow
106#547—1091no—
107#486—1091no—
108#459—1091no—
109#459D10911yescharacteristic, complemented
110#332—1091no—
111D4⋊C8—1091no—
112D4⋊C8—1091no—
113C2×#41—2181no—
114C2×D8—21no—
115C2×D8—2181no—
116C4⋊Q8—1091no—
117#127C2×D10911yescharacteristic
118#123—2182no—
119C22⋊Q8—2181no—
120#121—2181no—
121C4×D4—1091no—
122C4×D4C2×D10911yescharacteristic
123C2×C4⋊C4—2181no—
124C4⋊C8—1091no—
125C4⋊C8C2×D10911yescharacteristic
126#102—21no—
127#102—2181no—
128#102—2182no—
129C4×C8—1091no—
130#41—4362no—
131#41—4362no—
132C2×Q8—2181no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—1091no—
137C2×D4—2182no—
138C2×D4C22⋊D10911yescharacteristic
139C22×C4—21no—
140C22×C4—2182no—
141C22×C4—2181no—
142D8—42no—
143D8—4362no—
144C2×C8—21no—
145C2×C8—2181no—
146C2×C8—2181no—
147C4⋊C4—1091no—
148C4⋊C4—1092no—
149C4⋊C4—2182no—
150C4⋊C4—2181no—
151C4⋊C4C22⋊D10911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2182no—
154C22⋊C4—2181no—
155C42C22×D10911yescharacteristic
156C23—21no—
157C23—41no—
158C23—2181no—
159Q8—4361no—
160Q8—4361no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—1092no—
169D4—4364no—
170D4—2181no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—4364no—
175C2×C4—4361no—
176C2×C4—4361no—
177C2×C4—2181no—
178C2×C4—2182no—
179C2×C4D4×D10911yescharacteristic
180C2×C4D4×D10911yescharacteristic
181C2×C4C2×C22⋊D10911yescharacteristic
182C8—41no—
183C8—4361no—
184C8—4361no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—4361no—
192C22—4361no—
193C22—2182no—
194C22#1681266711yescharacteristic
195C4—21no—
196C4—41no—
197C4—4361no—
198C4—4362no—
199C4D8×D10911yescharacteristic
200C4#1681271911yescharacteristic
201C4#1681272311yescharacteristic
202C4#1681272511yescharacteristic
203C2—81no—
204C2—161no—
205C2—4362no—
206C2#2029515811yescharacteristic
207C2#2029516911yescharacteristic
208C2#2029519711yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#459×C109C2
socleC22×C109#120
hypercenter#459D109
hypocenterC109#1625
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20295681C2semidirect
2. #20295372C2semidirect
3. #20295218C2semidirect
4. #20294771C2semidirect
5. D4⋊#11724784C2semidirect
6. #20294753C2semidirect
7. #459×C109C2semidirect
71. D436D8semidirect
105. C109#1625semidirect
109. #459D109semidirect

Maximal subgroups

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

subgroupindex
#202956812
#202953722
#202952182
#202947712
D4⋊#117247842
#202947532
#459×C1092
#1625109