Finite Group Databasebeta

← #17982365

Subgroups — #17982365

Order 4352.

204 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 59 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#14546006C211yesmaximal, characteristic, complemented
2#14546005C211yesmaximal, characteristic, complemented
3#14545846C211yesmaximal, characteristic, complemented
4#14545837C211yesmaximal, characteristic, complemented
5#14545836C211yesmaximal, characteristic, complemented
6#14545804C211yesmaximal, characteristic, complemented
7#14545186C211yesmaximal, characteristic
8#11763931—21no—
9#11763930—21no—
10#11763913C2211yescharacteristic
11#11763913C2211yescharacteristic
12#11763910—21no—
13#11763909—21no—
14#11763904C2211yescharacteristic
15#11763893C2211yescharacteristic
16#11763853C2211yescharacteristic
17#11763851C2211yescharacteristic
18#11763737C411yescharacteristic
19#11763724C411yescharacteristic
20#11763723C411yescharacteristic
21#11763696C2211yescharacteristic
22#11763240C411yescharacteristic
23#10587680—21no—
24#10587678—21no—
25#10587670—41no—
26C2×#63241—41no—
27C4×#3633—21no—
28#10587666—21no—
29#10587666—21no—
30#10587666—41no—
31#10587665—41no—
32#10587665D411yescharacteristic
33#10587665D411yescharacteristic
34#10587605C2×C411yescharacteristic
35#10587598C2×C411yescharacteristic
36#10587550—21no—
37#10587548—21no—
38#10587536C2×C411yescharacteristic
39#10587536C2×C411yescharacteristic
40C8×#595C2311yescharacteristic
41#10587529C2×C411yescharacteristic
42C17×SD32C811yescharacteristic, complemented
43#10587500C811yescharacteristic, complemented
44#10587497C811yescharacteristic, complemented
45#10587471C811yescharacteristic, complemented
46C16×D17C2×C411yescharacteristic
47C2×#3633—41no—
48#63256—21no—
49#63254—21no—
50#63247—41no—
51C2×#3624—41no—
52C4×#595#4111yescharacteristic
53#63243—21no—
54#63243—21no—
55#63243—41no—
56#63242—41no—
57#63242C2×D411yescharacteristic
58#63241—21no—
59#63241—21no—
60#63241—41no—
61#63241—41no—
62Q16×C17C2×C811yescharacteristic
63D8×C17C2×C811yescharacteristic
64#63230—21no—
65#63229—21no—
66Dic68C2×C811yescharacteristic
67D136C2×C811yescharacteristic
68C8×D17C22×C411yescharacteristic
69#63216—21no—
70C16×C17C2×C811yescharacteristic
71#63214C2×C811yescharacteristic
72#12068—171nomaximal, Sylow
73C2×#595—21no—
74#3633—81no—
75Q8×C17—21no—
76D4×C17—21no—
77C22⋊D17—41no—
78C2×Dic17—41no—
79D68—21no—
80D68—41no—
81C4×D17—41no—
82C4×D17C4×D411yescharacteristic
83Dic34—21no—
84#3624—41no—
85#3624—41no—
86#3624AGL(1,ℤ/8)11yescharacteristic
87#3624AGL(1,ℤ/8)11yescharacteristic
88C8×C17C22×C811yescharacteristic
89#3622#13111yescharacteristic
90#2179—171no—
91#2171—171no—
92#2171—171no—
93#1369—171no—
94#1336—171no—
95#1336—171no—
96#1313—171no—
97C22×C17—41no—
98C2×D17—41no—
99C2×D17#44411yescharacteristic
100#595—41no—
101C4×C17—41no—
102C4×C17C8×D411yescharacteristic
103Dic17—41no—
104Dic17#44211yescharacteristic
105#508—171no—
106#504—341no—
107#504—341no—
108#443—171no—
109#443—171no—
110#368—171no—
111#364—171no—
112#364—171no—
113#359—171no—
114#359—171no—
115#350—341no—
116#350—341no—
117#346—171no—
118#346—171no—
119#322—171no—
120C2×C17—81no—
121C2×C17#158011yescharacteristic
122D17—21no—
123D17—81no—
124#135—171no—
125#135—171no—
126#131—341no—
127#131—341no—
128Q32—171no—
129SD32—171no—
130SD32#363311yescharacteristic, complemented
131D16—171no—
132M32—341no—
133M32—341no—
134M32—681no—
135M32—681no—
136C2×C16—171no—
137C2×C16—171no—
138C2×C16—171no—
139C2×C16—171no—
140C2×C16—681no—
141C2×C16—681no—
142#108—171no—
143#108—171no—
144#104—341no—
145#104—341no—
146C4×C8—171no—
147C4×C8—341no—
148C17#1206811yescharacteristic, complemented, Sylow
149#41—341no—
150#41—341no—
151Q16—171no—
152Q16C2×#363311yescharacteristic
153SD16—341no—
154SD16—341no—
155D8—171no—
156D8C2×#363311yescharacteristic
157M16—341no—
158M16—341no—
159M16—681no—
160M16—681no—
161C2×C8—171no—
162C2×C8—171no—
163C2×C8—681no—
164C2×C8—681no—
165C2×C8—681no—
166C42—171no—
167C16—171no—
168C16—341no—
169C16—341no—
170C16—341no—
171C16—681no—
172C16—681no—
173C16C2×#363311yescharacteristic
174Q8—21no—
175Q8—341no—
176D4—21no—
177D4—341no—
178D4—681no—
179D4—681no—
180C2×C4—171no—
181C2×C4—341no—
182C2×C4—681no—
183C2×C4—681no—
184C8—171no—
185C8—171no—
186C8—171no—
187C8—681no—
188C8—681no—
189C8—1361no—
190C8C22×#363311yescharacteristic
191C22—41no—
192C22—171no—
193C22—681no—
194C4—41no—
195C4—171no—
196C4—681no—
197C4—681no—
198C4D4×#363311yescharacteristic
199C2—81no—
200C2—341no—
201C2—1361no—
202C2#1454591511yescharacteristic
subgroupG/H
centerC2#14545915
commutatorC8×C17C22×C8
FrattiniC8C22×#3633
FittingC17×SD32C8
socleC2×C17#1580
prime radical#11763240C4
cosocleC8×#595C23
hypercenterSD32#3633
hypocenterC17#12068
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #14546006C2semidirect
2. #14546005C2semidirect
3. #14545846C2semidirect
4. #14545837C2semidirect
5. #14545836C2semidirect
6. #14545804C2semidirect
42. C17×SD32C8semidirect
43. #10587500C8semidirect
44. #10587497C8semidirect
45. #10587471C8semidirect
130. SD32#3633semidirect
148. C17#12068semidirect

Maximal subgroups

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

subgroupindex
#145460062
#145460052
#145458462
#145458372
#145458362
#145458042
#145451862
#1206817