Finite Group Databasebeta

← #28362122

Subgroups — #28362122

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#20295679C211yesmaximal, characteristic, complemented
2#20295374C211yesmaximal, characteristic, complemented
3#20295222C211yesmaximal, characteristic, complemented
4#20295222C211yesmaximal, characteristic, complemented
5#20294753C211yesmaximal, characteristic, complemented
6#20294753C211yesmaximal, characteristic, complemented
7#332×C109C211yesmaximal, characteristic, complemented
8C2×#13182030—21no—
9C2×D872—21no—
10C2×D872—21no—
11#16812696C2211yescharacteristic
12#16812684—22no—
13#16812675—21no—
14#16812674—21no—
15C4×D436C2211yescharacteristic
16C4×D436C2211yescharacteristic
17C4⋊C4×D109—21no—
18#16812621—21no—
19#16812621—21no—
20#16812619—22no—
21C4×#11724784C2211yescharacteristic
22C4⋊Q8×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24C4⋊C8×C109C2211yescharacteristic
25#13182030—42no—
26#13182030—42no—
27C2×D436—22no—
28C2×D436—21no—
29C2×D436—21no—
30C2×D436—21no—
31C2×D436D411yescharacteristic
32C2×D436D411yescharacteristic
33C2×C4×D109—22no—
34C2×C4×D109—21no—
35C2×C4×D109—21no—
36D872—42no—
37D872—42no—
38C2×#11724784—21no—
39C4⋊Dic109D411yescharacteristic
40C4⋊Dic109D411yescharacteristic
41#13182008—22no—
42#13182006—22no—
43#13182006—21no—
44#13182006—21no—
45C2×Q8×C109—21no—
46C2×C8×C109—21no—
47C2×C8×C109—21no—
48C4⋊C4×C109—21no—
49C4⋊C4×C109D412yes—
50C42×C109C2311yescharacteristic
51C22×D109—21no—
52C22×D109—21no—
53C22×D109—41no—
54Q8×C109—41no—
55Q8×C109—41no—
56C2×C4×C109—22no—
57C2×C4×C109C2×D411yescharacteristic
58C2×C4×C109C2×D411yescharacteristic
59C2×C4×C109C2×D411yescharacteristic
60C2×Dic109—21no—
61C2×Dic109—21no—
62D436—21no—
63D436—21no—
64D436—21no—
65D436—42no—
66D436—44no—
67D436—41no—
68D436—41no—
69D436—41no—
70D436—41no—
71D436D812yescomplemented
72C4×D109—44no—
73C4×D109—41no—
74C4×D109—41no—
75C4×D109—41no—
76C4×D109—41no—
77C8×C109—41no—
78C8×C109—41no—
79#11724784—41no—
80C22×C109#12011yescharacteristic
81C2×D109—22no—
82C2×D109—41no—
83C2×D109—41no—
84C2×D109—41no—
85C2×D109—41no—
86C2×D109—41no—
87C2×D109—81no—
88C2×D109—81no—
89C2×D109—81no—
90C4×C109—21no—
91C4×C109—42no—
92C4×C109C2×D811yescharacteristic
93C4×C109#13511yescharacteristic
94C4×C109AGL(1,ℤ/8)11yescharacteristic
95C4×C109AGL(1,ℤ/8)11yescharacteristic
96Dic109—41no—
97Dic109—41no—
98C2×C109#44711yescharacteristic
99C2×C109#44911yescharacteristic
100C2×C109#45411yescharacteristic
101D109—42no—
102D109—81no—
103D109—161no—
104#1625—1091nomaximal, Sylow
105C109#162511yescharacteristic, complemented, Sylow
106#547—1091no—
107#486—1091no—
108#459—1091no—
109#459—1091no—
110#332D10911yescharacteristic, complemented
111D4⋊C8—1091no—
112D4⋊C8—1091no—
113C2×#41—2181no—
114C2×D8—2181no—
115C2×D8—2181no—
116C4⋊Q8C2×D10911yescharacteristic
117#127—1091no—
118#123—2182no—
119C22⋊Q8—2181no—
120#121—2181no—
121C4×D4—1091no—
122C4×D4—1091no—
123C2×C4⋊C4—2181no—
124C4⋊C8C2×D10911yescharacteristic
125C4⋊C8C2×D10911yescharacteristic
126#102—2181no—
127#102—2181no—
128#102—2182no—
129C4×C8—1091no—
130#41—4362no—
131#41—4362no—
132C2×Q8—21no—
133C2×D4—1091no—
134C2×D4—1091no—
135C2×D4—2182no—
136C2×D4—2181no—
137C2×D4—2181no—
138C2×D4—2181no—
139C22×C4—2182no—
140C22×C4—2181no—
141C22×C4—2181no—
142D8—4362no—
143D8—4362no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—2181no—
147C4⋊C4—21no—
148C4⋊C4—1091no—
149C4⋊C4—1091no—
150C4⋊C4—2182no—
151C4⋊C4D43612yes—
152C22⋊C4—2182no—
153C22⋊C4—2181no—
154C22⋊C4—2181no—
155C42C22×D10911yescharacteristic
156C23—4361no—
157C23—2181no—
158C23—2181no—
159Q8—41no—
160Q8—41no—
161D4—1092no—
162D4—4362no—
163D4—4364no—
164D4—4361no—
165D4—4361no—
166D4—4361no—
167D4—4361no—
168D4—2181no—
169D4—2181no—
170D4—2181no—
171C2×C4—22no—
172C2×C4—4364no—
173C2×C4—4361no—
174C2×C4—4361no—
175C2×C4—4361no—
176C2×C4—4361no—
177C2×C4—2181no—
178C2×C4—2181no—
179C2×C4D4×D10911yescharacteristic
180C2×C4D4×D10911yescharacteristic
181C2×C4C2×D43611yescharacteristic
182C8—41no—
183C8—41no—
184C8—4361no—
185C22—8721no—
186C22—8721no—
187C22—8721no—
188C22—4361no—
189C22—4361no—
190C22—4361no—
191C22—4361no—
192C22—4361no—
193C22—2182no—
194C22#1681266911yescharacteristic
195C4—21no—
196C4—42no—
197C4—4361no—
198C4—4361no—
199C4D8×D10911yescharacteristic
200C4#1681272211yescharacteristic
201C4#1681272611yescharacteristic
202C4#1681272611yescharacteristic
203C2—8721no—
204C2—4362no—
205C2—17441no—
206C2#2029516111yescharacteristic
207C2#2029517411yescharacteristic
208C2#2029520111yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#332×C109C2
socleC22×C109#120
hypercenter#332D109
hypocenterC109#1625
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #20295679C2semidirect
2. #20295374C2semidirect
3. #20295222C2semidirect
4. #20295222C2semidirect
5. #20294753C2semidirect
6. #20294753C2semidirect
7. #332×C109C2semidirect
71. D436D8semidirect
105. C109#1625semidirect
110. #332D109semidirect

Maximal subgroups

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

subgroupindex
#202956792
#202953742
#202952222
#202947532
#332×C1092
#1625109