Finite Group Databasebeta

← #16020596

Subgroups — #16020596

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
1Q8×Dic52C211yesmaximal, characteristic, complemented
2#13117059C213yesmaximal, complemented
3#13116983C213yesmaximal, complemented
4#13116873C213yesmaximal, complemented
5Q8×#6090C211yesmaximal, characteristic, complemented
6C4×#88067C213yesmaximal, complemented
7C13×#3391C211yesmaximal, characteristic
8C13×#550—21no—
9Q8×Dic26—21no—
10C13×#493C2213yes—
11C13×#459—23no—
12C8×Q8×C13C2211yescharacteristic
13C4×C13×D8C2213yes—
14C2×#88067C2213yes—
15#11718511—23no—
16C4×Dic52C2213yes—
17#11718343C2213yes—
18#11718154C2213yes—
19#11718154C2216yes—
20#11718084C2211yescharacteristic
21#11718082C2213yes—
22C4⋊#6090C2213yes—
23C4×#6090C2213yes—
24C2×C13×#41—41no—
25C2×C13×D8—23no—
26C2×C13×D8C2313yes—
27C13×#127—23no—
28C13×#121—43no—
29C4×Q8×C13D411yescharacteristic
30C4×D4×C13—23no—
31Q8×Dic13—41no—
32C2×Dic52C2311yescharacteristic
33#88142—43no—
34#88123—23no—
35C4×Dic26—23no—
36C13×#107C2311yescharacteristic
37C13×C4⋊C8D413yes—
38C13×#102—23no—
39C4×C8×C13C2313yes—
40#88067—26no—
41#88058—23no—
42#88058C2313yes—
43#88056—23no—
44C2×#6090C2311yescharacteristic
45C2×#6090C2313yes—
46#33929—131nomaximal, Sylow
47C13×#41—84no—
48C2×Q8×C13D811yescharacteristic
49C2×D4×C13—23no—
50C2×D4×C13—43no—
51C2×D4×C13—43no—
52C22×C4×C13—43no—
53C2×Dic26—21no—
54C2×Dic26—43no—
55C13×D8—23no—
56C13×D8—23no—
57C13×D8—83no—
58C2×C8×C13C2×D413yes—
59C2×C8×C13C2411yescharacteristic
60C13×C4⋊C4—21no—
61C13×C4⋊C4D813yes—
62C13×C22⋊C4—43no—
63C42×C13C2×D413yes—
64C4⋊Dic13—23no—
65C4⋊Dic13—43no—
66#6101—43no—
67C4×Dic13—43no—
68Dic52—21no—
69Dic52#4112yescomplemented
70#6090—23no—
71#6090—21no—
72#3391D1311yescharacteristic
73Q8×Q16—131no—
74#2240—133no—
75#2226—133no—
76#2207—133no—
77Q8×C16—131no—
78C4×SD32—133no—
79C23×C13—43no—
80Q8×C13SD3214yescomplemented
81D4×C13—43no—
82D4×C13—43no—
83D4×C13—86no—
84D4×C13—163no—
85C2×C4×C13—41no—
86C2×C4×C13—86no—
87C2×C4×C13C2×D813yes—
88C2×C4×C13C2×D813yes—
89C2×C4×C13C22×D411yescharacteristic
90C2×Dic13—41no—
91C2×Dic13—43no—
92Dic26—22no—
93Dic26—41no—
94Dic26—163no—
95C8×C13—23no—
96C8×C13C2×#4111yescharacteristic
97C8×C132−1+411yescharacteristic
98Q82—261no—
99#550—21no—
100C2×SD32—133no—
101#500—133no—
102#493C2×D1313yes—
103#477—263no—
104#459—23no—
105C8×Q8C2×D1311yescharacteristic
106C4×Q16—133no—
107C4×D8C2×D1313yes—
108#367—133no—
109C4⋊C16—133no—
110#358—131no—
111#357—133no—
112#357—136no—
113C4×C16—133no—
114C22×C13—83no—
115C22×C13—83no—
116C22×C13—83no—
117C22×C13C22×D811yescharacteristic
118C4×C13—23no—
119C4×C13—81no—
120C4×C13C2×SD3216yes—
121C4×C13#54811yescharacteristic
122C4×C13#57711yescharacteristic
123Dic13—42no—
124Dic13—83no—
125C2×#41—41no—
126C2×Q16—131no—
127C2×D8—23no—
128C2×D8C22×D1313yes—
129C4⋊Q8—263no—
130C4⋊Q8—523no—
131#127—23no—
132#121—43no—
133C4×Q8—263no—
134C4×Q8—521no—
135C4×Q8C22⋊D1311yescharacteristic
136C4×D4—23no—
137SD32—266no—
138C2×C16—131no—
139C2×C16—133no—
140#107—133no—
141#107—263no—
142#107C22×D1311yescharacteristic
143C4⋊C8C22⋊D1313yes—
144#103—263no—
145#102—23no—
146C4×C8C22×D1313yes—
147C2×C13—163no—
148C2×C13#335811yescharacteristic
149C2×C13C22×SD3211yescharacteristic
150C2×C13#341511yescharacteristic
151#41—84no—
152C2×Q8—261no—
153C2×Q8—523no—
154C2×Q8#610411yescharacteristic
155C2×D4—23no—
156C2×D4—43no—
157C2×D4—43no—
158C22×C4—43no—
159Q16—132no—
160Q16—261no—
161D8—23no—
162D8—23no—
163D8—83no—
164C2×C8C2×C22⋊D1313yes—
165C2×C8C23×D1311yescharacteristic
166C4⋊C4—21no—
167C4⋊C4—263no—
168C4⋊C4—523no—
169C4⋊C4—523no—
170C4⋊C4#610413yes—
171C22⋊C4—43no—
172C42—523no—
173C42C2×C22⋊D1313yes—
174C16—263no—
175C16—261no—
176C13#3392911yescharacteristic, complemented, Sylow
177C23—43no—
178Q8—262no—
179Q8—521no—
180Q8—2083no—
181Q8#8806714yescomplemented
182D4—43no—
183D4—43no—
184D4—86no—
185D4—163no—
186C2×C4—41no—
187C2×C4—86no—
188C2×C4—521no—
189C2×C4—523no—
190C2×C4C2×#610413yes—
191C2×C4C2×#610413yes—
192C2×C4C22×C22⋊D1311yescharacteristic
193C8—23no—
194C8#41×D1311yescharacteristic
195C8#8825711yescharacteristic
196C22—83no—
197C22—83no—
198C22—83no—
199C22C22×#610411yescharacteristic
200C4—23no—
201C4—81no—
202C4—522no—
203C4—1043no—
204C4C2×#8806716yes—
205C4#1171953611yescharacteristic
206C4#1171954111yescharacteristic
207C2—163no—
208C2#1312746711yescharacteristic
209C2C22×#8806711yescharacteristic
210C2#1312797511yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
Fitting, prime radicalC13×#3391C2
socleC22×C13C22×D8
hypercenter#3391D13
hypocenterC13#33929
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3391

Complements

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

NH ≅ G/Ntype
1. Q8×Dic52C2semidirect
2. #13117059C2semidirect
3. #13116983C2semidirect
4. #13116873C2semidirect
5. Q8×#6090C2semidirect
6. C4×#88067C2semidirect
69. Dic52#41semidirect
80. Q8×C13SD32semidirect
176. C13#33929semidirect
181. Q8#88067semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic522
#131170592
#131169832
#131168732
Q8×#60902
C4×#880672
C13×#33912
#3392913