Finite Group Databasebeta

← #28362136

Subgroups — #28362136

Order 13952.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#20295691C211yesmaximal, characteristic, complemented
2#20295374C211yesmaximal, characteristic, complemented
3#20295227C211yesmaximal, characteristic, complemented
4#20295222C211yesmaximal, characteristic
5#20294756C211yesmaximal, characteristic, complemented
6#20294753C211yesmaximal, characteristic, complemented
7#332×C109C211yesmaximal, characteristic, complemented
8C2×Q8×D109—21no—
9C2×#13182018—21no—
10C2×D872—21no—
11#16812698—21no—
12#16812696C2211yescharacteristic
13#16812677—22no—
14#16812675—21no—
15C4×Dic218C2211yescharacteristic
16C4×D436C2211yescharacteristic
17#16812661—21no—
18#16812621—21no—
19#16812621—21no—
20#16812619—22no—
21C4×#11724784C2211yescharacteristic
22C4⋊Q8×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24C4⋊C8×C109C2211yescharacteristic
25C2×Dic218—22no—
26C2×Dic218D411yescharacteristic
27Q8×D109—42no—
28Q8×D109—42no—
29C2×D436—21no—
30C2×D436—21no—
31C2×D436—21no—
32C2×D436D411yescharacteristic
33C2×C4×D109—22no—
34C2×C4×D109—21no—
35#13182018—42no—
36D872—42no—
37C2×#11724784—21no—
38C4⋊Dic109D411yescharacteristic
39C4⋊Dic109D411yescharacteristic
40#13182008—22no—
41#13182008—21no—
42#13182006—22no—
43#13182006—21no—
44C4×Dic109—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—41no—
53Q8×C109—41no—
54Q8×C109—41no—
55C2×C4×C109—22no—
56C2×C4×C109C2×D411yescharacteristic
57C2×C4×C109C2×D411yescharacteristic
58C2×C4×C109C2×D411yescharacteristic
59C2×Dic109—21no—
60C2×Dic109—21no—
61C2×Dic109—21no—
62D436—21no—
63D436—42no—
64D436—41no—
65D436—41no—
66D436—41no—
67D436—41no—
68D436SD1612yescomplemented
69C4×D109—44no—
70C4×D109—41no—
71C4×D109—41no—
72Dic218—21no—
73Dic218—44no—
74Dic218D812yescomplemented
75C8×C109—41no—
76C8×C109—41no—
77#11724784—41no—
78C22×C109#12011yescharacteristic
79C2×D109—22no—
80C2×D109—41no—
81C2×D109—41no—
82C2×D109—81no—
83C2×D109—81no—
84C2×D109—81no—
85C4×C109—21no—
86C4×C109—42no—
87C4×C109C2×D811yescharacteristic
88C4×C109C2×SD1611yescharacteristic
89C4×C109AGL(1,ℤ/8)11yescharacteristic
90C4×C109#13711yescharacteristic
91Dic109—22no—
92Dic109—41no—
93Dic109—41no—
94C2×C109#44711yescharacteristic
95C2×C109#44811yescharacteristic
96C2×C109#45411yescharacteristic
97D109—42no—
98D109—161no—
99#1627—1091nomaximal, Sylow
100C109#162711yescharacteristic, complemented, Sylow
101D4×Q8—1091no—
102#486—1091no—
103#460—1091no—
104#459—1091no—
105#332D10911yescharacteristic, complemented
106Q8⋊C8—1091no—
107D4⋊C8—1091no—
108C22×Q8—2181no—
109C2×SD16—2181no—
110C2×D8—2181no—
111C4⋊Q8—2181no—
112C4⋊Q8C2×D10911yescharacteristic
113#127—1091no—
114C22⋊Q8—2181no—
115C22⋊Q8—2182no—
116C4×Q8—1091no—
117C4×D4—1091no—
118C4×D4—2181no—
119C4⋊C8C2×D10911yescharacteristic
120C4⋊C8C2×D10911yescharacteristic
121#102—2181no—
122#102—2181no—
123#102—2182no—
124C4×C8—1091no—
125C2×Q8—21no—
126C2×Q8—1091no—
127C2×Q8—4362no—
128C2×Q8—4362no—
129C2×Q8—2182no—
130C2×D4—1091no—
131C2×D4—2181no—
132C2×D4—2181no—
133C2×D4—2181no—
134C22×C4—2182no—
135C22×C4—2181no—
136SD16—4362no—
137D8—4362no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—2181no—
141C4⋊C4—21no—
142C4⋊C4—1091no—
143C4⋊C4—1091no—
144C4⋊C4—2182no—
145C4⋊C4—2181no—
146C4⋊C4D43612yes—
147C22⋊C4—2182no—
148C22⋊C4—2181no—
149C42—2181no—
150C42C22×D10911yescharacteristic
151C23—4361no—
152C23—2181no—
153Q8—41no—
154Q8—41no—
155Q8—1092no—
156Q8—4364no—
157Q8—2181no—
158D4—1092no—
159D4—4362no—
160D4—4361no—
161D4—4361no—
162D4—4361no—
163D4—4361no—
164D4—2181no—
165C2×C4—22no—
166C2×C4—4364no—
167C2×C4—4361no—
168C2×C4—4361no—
169C2×C4—2181no—
170C2×C4—2181no—
171C2×C4—2181no—
172C2×C4D4×D10911yescharacteristic
173C2×C4D4×D10911yescharacteristic
174C2×C4C2×D43611yescharacteristic
175C8—41no—
176C8—41no—
177C8—4361no—
178C22—8721no—
179C22—8721no—
180C22—8721no—
181C22—4361no—
182C22—4361no—
183C22—2182no—
184C22#1681266911yescharacteristic
185C4—21no—
186C4—42no—
187C4—4361no—
188C4—4361no—
189C4—2182no—
190C4D8×D10911yescharacteristic
191C4SD16×D10911yescharacteristic
192C4#1681272611yescharacteristic
193C4#1681273111yescharacteristic
194C2—4362no—
195C2—17441no—
196C2#2029516111yescharacteristic
197C2#2029516611yescharacteristic
198C2#2029520111yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#332×C109C2
socleC22×C109#120
prime radical#20295222C2
hypercenter#332D109
hypocenterC109#1627
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. #20295691C2semidirect
2. #20295374C2semidirect
3. #20295227C2semidirect
5. #20294756C2semidirect
6. #20294753C2semidirect
7. #332×C109C2semidirect
68. D436SD16semidirect
74. Dic218D8semidirect
100. C109#1627semidirect
105. #332D109semidirect

Maximal subgroups

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

subgroupindex
#202956912
#202953742
#202952272
#202952222
#202947562
#202947532
#332×C1092
#1627109