Finite Group Databasebeta

← #16020601

Subgroups — #16020601

Order 3328.

528 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 165 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#13127811C211yesmaximal, characteristic
2Q8×Dic52C211yesmaximal, characteristic, complemented
3#13117060C213yesmaximal, complemented
4#13116984C213yesmaximal, complemented
5#13116877C213yesmaximal, complemented
6C4×#88040C213yesmaximal, complemented
7Q8×C13×C16C211yesmaximal, characteristic, complemented
8#11719282—21no—
9Q8×Dic26—21no—
10C8×Q8×C13C2211yescharacteristic
11C2×#88040C2213yes—
12#11718511—23no—
13#11718504—23no—
14C4×Dic52C2213yes—
15#11718356C2213yes—
16C4×D104C2213yes—
17#11718343C2213yes—
18C13×C4⋊C16C2213yes—
19C4×C13×C16C2213yes—
20#11718101C2213yes—
21#11718101C2216yes—
22#11718097C2213yes—
23#11718095C2211yescharacteristic
24C2×#6131—41no—
25C4×Q8×C13D411yescharacteristic
26Q8×Dic13—41no—
27C2×Dic52C2311yescharacteristic
28C2×D104—23no—
29C2×D104C2313yes—
30#88149—43no—
31#88142—43no—
32#88128—23no—
33C4×D52—23no—
34#88123—23no—
35C4×Dic26—23no—
36C2×C13×C16C2311yescharacteristic
37C2×C13×C16C2313yes—
38C13×C4⋊C8D413yes—
39C4×C8×C13C2313yes—
40#88061—23no—
41#88058—23no—
42#88058C2313yes—
43#88058C2311yescharacteristic
44#88056—23no—
45#88040—26no—
46#33929—131nomaximal, Sylow
47C2×Q8×C13D811yescharacteristic
48#6131—84no—
49C2×D52—23no—
50C2×D52—43no—
51C2×D52—43no—
52C2×C4×D13—43no—
53C2×Dic26—21no—
54C2×Dic26—43no—
55C2×C8×C13C2×D413yes—
56C2×C8×C13C2411yescharacteristic
57C13×C4⋊C4D813yes—
58C42×C13C2×D413yes—
59#6103—43no—
60C4⋊Dic13—23no—
61C4⋊Dic13—21no—
62C4⋊Dic13—43no—
63#6101—43no—
64C4×Dic13—43no—
65Dic52—21no—
66Dic52#4112yescomplemented
67D104—23no—
68D104—23no—
69D104—83no—
70C13×C16—23no—
71C13×C16—21no—
72#3391—131no—
73Q8×Q16—131no—
74#2240—133no—
75#2226—133no—
76#2207—133no—
77Q8×C16D1311yescharacteristic, complemented
78C4×SD32—133no—
79C22×D13—43no—
80Q8×C13SD3214yescomplemented
81C2×C4×C13C2×D813yes—
82C2×C4×C13C2×D813yes—
83C2×C4×C13C22×D411yescharacteristic
84C2×Dic13—41no—
85C2×Dic13—43no—
86C2×Dic13—41no—
87D52—43no—
88D52—43no—
89D52—86no—
90D52—163no—
91C4×D13—86no—
92Dic26—22no—
93Dic26—41no—
94Dic26—163no—
95C8×C13—23no—
96C8×C13C2×#4111yescharacteristic
97C8×C132−1+411yescharacteristic
98Q82—261no—
99#550—261no—
100C2×SD32—133no—
101#500—133no—
102#493—133no—
103#477—263no—
104#459—263no—
105C8×Q8C2×D1311yescharacteristic
106C4×Q16—133no—
107C4×D8—133no—
108#367—133no—
109C4⋊C16C2×D1313yes—
110#358—131no—
111#357—133no—
112#357—136no—
113C4×C16C2×D1313yes—
114C22×C13C22×D811yescharacteristic
115C2×D13—83no—
116C2×D13—83no—
117C2×D13—83no—
118C4×C13—23no—
119C4×C13C2×SD3216yes—
120C4×C13#54811yescharacteristic
121C4×C13#57711yescharacteristic
122Dic13—42no—
123Dic13—81no—
124Dic13—83no—
125C2×#41—521no—
126C2×Q16—131no—
127C2×D8—133no—
128C2×D8—263no—
129C4⋊Q8—263no—
130C4⋊Q8—523no—
131#127—263no—
132#121—523no—
133C4×Q8—263no—
134C4×Q8—521no—
135C4×Q8D5211yescharacteristic
136C4×D4—263no—
137SD32—266no—
138C2×C16C22×D1311yescharacteristic
139C2×C16C22×D1313yes—
140#107—133no—
141#107—131no—
142#107—263no—
143C4⋊C8D5213yes—
144#103—263no—
145#102—263no—
146C4×C8C22×D1313yes—
147C2×C13#335811yescharacteristic
148C2×C13C22×SD3211yescharacteristic
149C2×C13#341511yescharacteristic
150D13—163no—
151#41—1044no—
152C2×Q8—261no—
153C2×Q8—523no—
154C2×Q8D10411yescharacteristic
155C2×D4—263no—
156C2×D4—523no—
157C2×D4—523no—
158C22×C4—523no—
159Q16—132no—
160Q16—261no—
161D8—263no—
162D8—263no—
163D8—1043no—
164C2×C8C2×D5213yes—
165C2×C8C23×D1311yescharacteristic
166C4⋊C4—261no—
167C4⋊C4—263no—
168C4⋊C4—523no—
169C4⋊C4—523no—
170C4⋊C4D10413yes—
171C22⋊C4—523no—
172C42—523no—
173C42C2×D5213yes—
174C16—21no—
175C16—23no—
176C13#3392911yescharacteristic, complemented, Sylow
177C23—523no—
178Q8—262no—
179Q8—521no—
180Q8—2083no—
181Q8#8804014yescomplemented
182D4—523no—
183D4—523no—
184D4—1046no—
185D4—2083no—
186C2×C4—521no—
187C2×C4—523no—
188C2×C4—521no—
189C2×C4—1046no—
190C2×C4C2×D10413yes—
191C2×C4C2×D10413yes—
192C2×C4C22×D5211yescharacteristic
193C8—23no—
194C8#8825411yescharacteristic
195C8#41×D1311yescharacteristic
196C22—1043no—
197C22—1043no—
198C22—1043no—
199C22C22×D10411yescharacteristic
200C4—23no—
201C4—522no—
202C4—1041no—
203C4—1043no—
204C4C2×#8804016yes—
205C4#1171928111yescharacteristic
206C4#1171945611yescharacteristic
207C2—2083no—
208C2#1312747211yescharacteristic
209C2C22×#8804011yescharacteristic
210C2#1312797711yescharacteristic
subgroupG/H
centerC22C22×D104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingQ8×C13×C16C2
socleC22×C13C22×D8
prime radical#13127811C2
hypercenterQ8×C16D13
hypocenterC13#33929
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ Q8×C16

Complements

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

NH ≅ G/Ntype
2. Q8×Dic52C2semidirect
3. #13117060C2semidirect
4. #13116984C2semidirect
5. #13116877C2semidirect
6. C4×#88040C2semidirect
7. Q8×C13×C16C2semidirect
66. Dic52#41semidirect
77. Q8×C16D13semidirect
80. Q8×C13SD32semidirect
176. C13#33929semidirect
181. Q8#88040semidirect

Maximal subgroups

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

subgroupindex
#131278112
Q8×Dic522
#131170602
#131169842
#131168772
C4×#880402
Q8×C13×C162
#3392913