Finite Group Databasebeta

← #28362296

Subgroups — #28362296

Order 13952.

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

normal subgroups only

This group has 234 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
2#20295422C211yesmaximal, characteristic, complemented
3#20295312C211yesmaximal, characteristic, complemented
4#20295232C211yesmaximal, characteristic
5#20294756C211yesmaximal, characteristic, complemented
6#20294753C211yesmaximal, characteristic
7#332×C109C211yesmaximal, characteristic, complemented
8C2×Q8×D109—21no—
9C2×#13182018—21no—
10#16812699C2211yescharacteristic
11#16812698—21no—
12#16812677—22no—
13#16812675—21no—
14C4×Dic218C2211yescharacteristic
15C4×D436C2211yescharacteristic
16#16812661—21no—
17#16812631—21no—
18#16812630—22no—
19#16812624—21no—
20#16812624—21no—
21C4×#11724784C2211yescharacteristic
22C4⋊Q8×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24C4⋊C8×C109C2211yescharacteristic
25C2×Dic218—22no—
26C2×Dic218—21no—
27C2×Dic218D411yescharacteristic
28Q8×D109—42no—
29Q8×D109—42no—
30C2×D436D411yescharacteristic
31C2×C4×D109—22no—
32C2×C4×D109—21no—
33#13182018—42no—
34C2×#11724784—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109—21no—
37C4⋊Dic109D411yescharacteristic
38C4⋊Dic109D411yescharacteristic
39#13182008—22no—
40#13182008—21no—
41#13182006—22no—
42#13182006—21no—
43C4×Dic109—21no—
44C2×Q8×C109—21no—
45C2×C8×C109—21no—
46C2×C8×C109—21no—
47C4⋊C4×C109—21no—
48C4⋊C4×C109D412yes—
49C42×C109C2311yescharacteristic
50C22×D109—21no—
51Q8×C109—41no—
52Q8×C109—41no—
53C2×C4×C109—22no—
54C2×C4×C109C2×D411yescharacteristic
55C2×C4×C109C2×D411yescharacteristic
56C2×C4×C109C2×D411yescharacteristic
57C2×Dic109—21no—
58C2×Dic109—21no—
59C2×Dic109—21no—
60C2×Dic109—41no—
61D436—21no—
62D436SD1612yes—
63C4×D109—44no—
64C4×D109—41no—
65C4×D109—41no—
66Dic218—21no—
67Dic218—44no—
68Dic218—41no—
69Dic218—41no—
70Dic218SD1612yescomplemented
71C8×C109—41no—
72C8×C109—41no—
73#11724784—22no—
74C22×C109#12011yescharacteristic
75C2×D109—22no—
76C2×D109—41no—
77C2×D109—41no—
78C4×C109—21no—
79C4×C109—42no—
80C4×C109C2×SD1611yescharacteristic
81C4×C109C2×SD1611yescharacteristic
82C4×C109AGL(1,ℤ/8)11yescharacteristic
83C4×C109#13711yescharacteristic
84Dic109—22no—
85Dic109—41no—
86Dic109—41no—
87Dic109—81no—
88C2×C109#44811yescharacteristic
89C2×C109#45011yescharacteristic
90C2×C109#45611yescharacteristic
91D109—42no—
92#1651—1091nomaximal, Sylow
93C109#165111yescharacteristic, complemented, Sylow
94D4×Q8—1091no—
95#498—1091no—
96#475—1091no—
97#461—1091no—
98#332D10911yescharacteristic, complemented
99Q8⋊C8—1091no—
100D4⋊C8—1091no—
101C22×Q8—2181no—
102C2×SD16—2181no—
103C4⋊Q8—1091no—
104C4⋊Q8—2181no—
105C4⋊Q8C2×D10911yescharacteristic
106C22⋊Q8—2181no—
107C22⋊Q8—2182no—
108C4×Q8—1091no—
109C4×D4—1091no—
110C4×D4—2181no—
111#106—2181no—
112#106—2182no—
113C4⋊C8C2×D10911yescharacteristic
114C4⋊C8C2×D10911yescharacteristic
115#103—2181no—
116#103—2181no—
117C4×C8—1091no—
118C2×Q8—21no—
119C2×Q8—1091no—
120C2×Q8—4362no—
121C2×Q8—4362no—
122C2×Q8—2182no—
123C2×Q8—2181no—
124C2×D4—1091no—
125C22×C4—2182no—
126C22×C4—2181no—
127SD16—4362no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—2181no—
131C4⋊C4—21no—
132C4⋊C4—1091no—
133C4⋊C4—1091no—
134C4⋊C4—2182no—
135C4⋊C4—2181no—
136C4⋊C4—2181no—
137C4⋊C4—2181no—
138C4⋊C4D43612yes—
139C22⋊C4—2182no—
140C22⋊C4—2181no—
141C42—2181no—
142C42C22×D10911yescharacteristic
143C23—2181no—
144Q8—41no—
145Q8—41no—
146Q8—1092no—
147Q8—4364no—
148Q8—4361no—
149Q8—4361no—
150Q8—2181no—
151D4—1092no—
152D4—2181no—
153C2×C4—22no—
154C2×C4—4364no—
155C2×C4—4361no—
156C2×C4—4361no—
157C2×C4—4361no—
158C2×C4—2181no—
159C2×C4—2181no—
160C2×C4—2181no—
161C2×C4D4×D10911yescharacteristic
162C2×C4D4×D10911yescharacteristic
163C2×C4C2×D43611yescharacteristic
164C8—41no—
165C8—41no—
166C8—2182no—
167C22—4361no—
168C22—4361no—
169C22—2182no—
170C22#1681266911yescharacteristic
171C4—21no—
172C4—42no—
173C4—8721no—
174C4—4361no—
175C4—4361no—
176C4—2182no—
177C4SD16×D10911yescharacteristic
178C4SD16×D10911yescharacteristic
179C4#1681272311yescharacteristic
180C4#1681273111yescharacteristic
181C2—4362no—
182C2#2029516611yescharacteristic
183C2#2029517811yescharacteristic
184C2#2029521111yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#332×C109C2
socleC22×C109#120
prime radicalC2×D436D4
hypercenter#332D109
hypocenterC109#1651
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #20295422C2semidirect
3. #20295312C2semidirect
5. #20294756C2semidirect
7. #332×C109C2semidirect
70. Dic218SD16semidirect
93. C109#1651semidirect
98. #332D109semidirect

Maximal subgroups

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

subgroupindex
#202956912
#202954222
#202953122
#202952322
#202947562
#202947532
#332×C1092
#1651109