Finite Group Databasebeta

← #31779795

Subgroups — #31779795

Order 17536.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#22578032C211yesmaximal, characteristic
2#22577733C211yesmaximal, characteristic
3#22577334C211yesmaximal, characteristic
4#22577141C211yesmaximal, characteristic
5#22577140C211yesmaximal, characteristic
6#22577128C211yesmaximal, characteristic
7#483×C137C211yesmaximal, characteristic
8#17984087—21no—
9#17984086—21no—
10#17984078—21no—
11#17984078—21no—
12#17984067C2211yescharacteristic
13#17984065—21no—
14#17984044—21no—
15C2×#14555489—21no—
16C2×#14555489C2211yescharacteristic
17#17984019—21no—
18#17984011—21no—
19C22⋊#11764040C2211yescharacteristic
20#17983995—21no—
21#17983995C2211yescharacteristic
22C22⋊Q8×C137C2211yescharacteristic
23C2×C4⋊C4×C137C2211yescharacteristic
24#106×C137—21no—
25#103×C137—21no—
26C22⋊C8×C137C2211yescharacteristic
27C2×Dic274—21no—
28C2×Dic274D411yescharacteristic
29C22×Dic137—21no—
30C22×Dic137D411yescharacteristic
31C22×Dic137D411yescharacteristic
32C2×#11764040—21no—
33C4⋊Dic137—21no—
34C4⋊Dic137D411yescharacteristic
35#14555489—21no—
36#14555489—21no—
37#14555489—21no—
38#14555489—21no—
39#14555489—21no—
40#14555489—21no—
41#14555489—21no—
42#14555489—42no—
43C22⋊Dic137—21no—
44C4×Dic137—21no—
45C4×Dic137—21no—
46C2×Q8×C137D411yescharacteristic
47C22×C4×C137—21no—
48C22×C4×C137C2311yescharacteristic
49C2×C8×C137—21no—
50C4⋊C4×C137—21no—
51C4⋊C4×C137—21no—
52C4⋊C4×C137—21no—
53C4⋊C4×C137D411yescharacteristic
54C22⋊C4×C137—21no—
55Dic274—41no—
56Dic274—81no—
57C2×Dic137—21no—
58C2×Dic137—21no—
59C2×Dic137—22no—
60C2×Dic137—21no—
61C2×Dic137—21no—
62C2×Dic137—21no—
63C2×Dic137—41no—
64C2×Dic137—41no—
65C2×Dic137—41no—
66C2×Dic137SD1612yes—
67#11764040—41no—
68C23×C137C2×D411yescharacteristic
69Q8×C137—41no—
70C2×C4×C137—21no—
71C2×C4×C137—21no—
72C2×C4×C137—41no—
73C2×C4×C137—41no—
74C2×C4×C137—41no—
75C2×C4×C137—41no—
76C2×C4×C137C2×D411yescharacteristic
77C2×C4×C137C2×D411yescharacteristic
78C8×C137—41no—
79C22×C137—21no—
80C22×C137—21no—
81C22×C137#12011yescharacteristic
82C22×C137C2×SD1611yescharacteristic
83C22×C137#13711yescharacteristic
84C4×C137—21no—
85C4×C137—21no—
86C4×C137—41no—
87C4×C137—41no—
88C4×C137—81no—
89Dic137—22no—
90Dic137—42no—
91Dic137—41no—
92Dic137—41no—
93Dic137—41no—
94C2×C137—21no—
95C2×C137—21no—
96C2×C137#44811yescharacteristic
97C2×C137#45611yescharacteristic
98C2×C137#45811yescharacteristic
99C137#161111yescharacteristic, complemented, Sylow
100#1611—1371nomaximal, Sylow
101#544—1371no—
102#483—1371no—
103#483D13711yescharacteristic
104#398—1371no—
105#328—1371no—
106#328—1371no—
107#324—1371no—
108C4⋊Q8—2741no—
109C4⋊Q8—2741no—
110#125—2741no—
111#125—2741no—
112C22⋊Q8—2741no—
113C22⋊Q8—1371no—
114C22⋊Q8C2×D13711yescharacteristic
115#117—2741no—
116C2×C4⋊C4—2741no—
117C2×C4⋊C4—1371no—
118C2×C4⋊C4C2×D13711yescharacteristic
119#106—21no—
120#106—2741no—
121#103—21no—
122#103—2741no—
123C22⋊C8—1371no—
124C22⋊C8C2×D13711yescharacteristic
125#95—2741no—
126#95—1371no—
127C2×Q8—2741no—
128C2×Q8—1371no—
129C2×Q8C22⋊D13711yescharacteristic
130C22×C4—21no—
131C22×C4—2741no—
132C22×C4—1371no—
133C22×C4—1371no—
134C22×C4C22×D13711yescharacteristic
135C2×C8—21no—
136C2×C8—2741no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—2741no—
141C4⋊C4—2741no—
142C4⋊C4—2741no—
143C4⋊C4—2741no—
144C4⋊C4—2741no—
145C4⋊C4—2741no—
146C4⋊C4—2741no—
147C4⋊C4—2741no—
148C4⋊C4—5482no—
149C4⋊C4—1371no—
150C4⋊C4C22⋊D13711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2741no—
153C42—2741no—
154C42—2741no—
155C23D4×D13711yescharacteristic
156Q8—41no—
157Q8—5481no—
158Q8—10961no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—2741no—
166C2×C4—2741no—
167C2×C4—2742no—
168C2×C4—2741no—
169C2×C4—2741no—
170C2×C4—2741no—
171C2×C4—5481no—
172C2×C4—5481no—
173C2×C4—5481no—
174C2×C4—1372no—
175C2×C4D4×D13711yescharacteristic
176C2×C4C2×C22⋊D13711yescharacteristic
177C8—41no—
178C8—5481no—
179C22—21no—
180C22—21no—
181C22#1798405611yescharacteristic
182C22SD16×D13711yescharacteristic
183C22#1798411711yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—81no—
189C4—2742no—
190C4—5482no—
191C4—5481no—
192C4—5481no—
193C4—5481no—
194C2—21no—
195C2—21no—
196C2#2257754011yescharacteristic
197C2#2257758411yescharacteristic
198C2#2257759211yescharacteristic
subgroupG/H
centerC22#17984056
commutator, cosocleC22×C4×C137C23
FrattiniC22×C4C22×D137
Fitting#483×C137C2
socleC22×C137#120
prime radicalC23×C137C2×D4
hypercenter#483D137
hypocenterC137#1611
LCSG ▷ C22×C4×C137 ▷ C22×C137 ▷ C137
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
99. C137#1611semidirect

Maximal subgroups

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

subgroupindex
#225780322
#225777332
#225773342
#225771412
#225771402
#225771282
#483×C1372
#1611137