Finite Group Databasebeta

← #16946319

Subgroups — #16946319

Order 4352.

220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#10587471C211yesmaximal, characteristic
2#14527680C211yesmaximal, characteristic, complemented
3#14527668C211yesmaximal, characteristic
4#14526747C211yesmaximal, characteristic, complemented
5#14526744C211yesmaximal, characteristic
6#14526700C211yesmaximal, characteristic, complemented
7C17×#1371C211yesmaximal, characteristic, complemented
8C2×#10587471C411yescharacteristic
9#11762936—21no—
10C4×Dic68C2211yescharacteristic
11C4×D136C2211yescharacteristic
12#11762886—21no—
13#11762637C411yescharacteristic
14#11762614C411yescharacteristic
15#11762611C411yescharacteristic
16C4×#63214C2211yescharacteristic
17#11762539—21no—
18#11762536—21no—
19C8×#3622C2211yescharacteristic
20C4×C16×C17C2211yescharacteristic
21C17×#335C2211yescharacteristic
22C17×#335C2211yescharacteristic
23C2×Dic68C2×C411yescharacteristic
24C2×D136C2×C411yescharacteristic
25C2×#63218—41no—
26C4×D68—21no—
27C4×Dic34—21no—
28C2×C16×C17C2×C411yescharacteristic
29C2×C16×C17C2×C411yescharacteristic
30C17×C4⋊C8—21no—
31C17×C4⋊C8—21no—
32C4×C8×C17C2311yescharacteristic
33#10587492—21no—
34#10587491—41no—
35#10587489C2×C411yescharacteristic
36#10587489C2×C411yescharacteristic
37#10587487—21no—
38#10587486—41no—
39#10587485—41no—
40C2×#63214—21no—
41C4×#3622D411yescharacteristic
42C4×#3622D411yescharacteristic
43#10587471—22no—
44C2×D68—21no—
45C2×C4×D17—41no—
46C2×Dic34—21no—
47C2×C8×C17—41no—
48C2×C8×C17—41no—
49C2×C8×C17C22×C411yescharacteristic
50C2×C8×C17#4111yescharacteristic
51C42×C17C2×D411yescharacteristic
52#63227—41no—
53C4⋊Dic17—21no—
54C4⋊Dic17—21no—
55#63225—41no—
56C4×Dic17—41no—
57C2×#3622—21no—
58C2×#3622D811yescharacteristic
59C2×#3622D811yescharacteristic
60Dic68—21no—
61Dic68—21no—
62D136—21no—
63D136—21no—
64#63218—82no—
65C16×C17—21no—
66C16×C17M1612yescomplemented
67#63214—22no—
68#12084—171nomaximal, Sylow
69C22×D17—41no—
70C2×C4×C17C4×D411yescharacteristic
71C2×C4×C17C2×D811yescharacteristic
72C2×C4×C17#13511yescharacteristic
73C2×Dic17—41no—
74C2×Dic17—41no—
75C2×Dic17—41no—
76D68—41no—
77D68—41no—
78C4×D17—81no—
79C4×D17—81no—
80Dic34—41no—
81Dic34—41no—
82C8×C17—21no—
83C8×C17—81no—
84C8×C17—81no—
85C8×C17C2×M1611yescharacteristic
86C8×C17#13111yescharacteristic
87#3622—21no—
88#3622—21no—
89#3622—41no—
90C4×SD32—171no—
91#1591—171no—
92#1589—171no—
93#1371D1711yescharacteristic, complemented
94#1332—171no—
95#1331—171no—
96#1311—171no—
97C22×C17C4×D811yescharacteristic
98C2×D17—81no—
99C2×D17—81no—
100C2×D17—81no—
101C4×C17—21no—
102C4×C17#43611yescharacteristic
103C4×C17#44311yescharacteristic
104C4×C17#50911yescharacteristic
105C4×C17#51011yescharacteristic
106Dic17—81no—
107Dic17—81no—
108Dic17—81no—
109C2×SD32—171no—
110#446—341no—
111C4×Q16—171no—
112C4×D8—171no—
113#436—341no—
114#367—171no—
115#358—171no—
116#357—171no—
117C4×C16—171no—
118C4×C16C2×D1711yescharacteristic
119#335C2×D1711yescharacteristic
120#335C2×D1711yescharacteristic
121Q8⋊C8—341no—
122D4⋊C8—341no—
123C82—171no—
124C2×C17#158911yescharacteristic
125C2×C17#217511yescharacteristic
126C2×C17#217911yescharacteristic
127D17—161no—
128C2×Q16—171no—
129C2×D8—171no—
130C2×M16—681no—
131C4×Q8—341no—
132C4×D4—341no—
133SD32—342no—
134C2×C16—341no—
135C2×C16C4×D1711yescharacteristic
136C2×C16C4×D1711yescharacteristic
137#107—171no—
138#107—171no—
139C4⋊C8—21no—
140C4⋊C8—21no—
141C4⋊C8—681no—
142#103—341no—
143#102—341no—
144C22⋊C8—681no—
145#97—681no—
146C4×C8—171no—
147C4×C8—171no—
148C4×C8C22×D1711yescharacteristic
149C17#1208411yescharacteristic, complemented, Sylow
150C2×Q8—341no—
151C2×D4—341no—
152C22×C4—681no—
153Q16—341no—
154Q16—341no—
155D8—341no—
156D8—341no—
157M16—1362no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—171no—
161C2×C8—171no—
162C2×C8—341no—
163C2×C8C2×C4×D1711yescharacteristic
164C2×C8#6325611yescharacteristic
165C4⋊C4—341no—
166C4⋊C4—341no—
167C4⋊C4—681no—
168C22⋊C4—681no—
169C42—681no—
170C42D4×D1711yescharacteristic
171C16—21no—
172C16—342no—
173C16#6321812yescomplemented
174C23—681no—
175Q8—681no—
176Q8—681no—
177D4—681no—
178D4—681no—
179C2×C4—681no—
180C2×C4—681no—
181C2×C4—681no—
182C2×C4—1361no—
183C2×C4—1361no—
184C2×C4#1058757911yescharacteristic
185C2×C4D8×D1711yescharacteristic
186C2×C4#1058760511yescharacteristic
187C8—21no—
188C8—81no—
189C8—81no—
190C8—341no—
191C8—341no—
192C8—681no—
193C8C2×#6321811yescharacteristic
194C8#1058759311yescharacteristic
195C22—1361no—
196C22—1361no—
197C22—1361no—
198C22#1176289111yescharacteristic
199C4—21no—
200C4—1361no—
201C4—1361no—
202C4—1361no—
203C4#1176288611yescharacteristic
204C4#1176292511yescharacteristic
205C4#1176324311yescharacteristic
206C4#1176325111yescharacteristic
207C2—2721no—
208C2#1452766811yescharacteristic
209C2#1453064711yescharacteristic
210C2#1453066911yescharacteristic
subgroupG/H
centerC2×C4D8×D17
commutatorC2×C8×C17C22×C4
FrattiniC4×C8C22×D17
FittingC17×#1371C2
socleC22×C17C4×D8
prime radicalC2×D136C2×C4
cosocleC4×C8×C17C23
hypercenter#1371D17
hypocenterC17#12084
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1371

Complements

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

NH ≅ G/Ntype
2. #14527680C2semidirect
4. #14526747C2semidirect
6. #14526700C2semidirect
7. C17×#1371C2semidirect
66. C16×C17M16semidirect
93. #1371D17semidirect
149. C17#12084semidirect
173. C16#63218semidirect

Maximal subgroups

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

subgroupindex
C4×#105874712
#145276802
#145276682
#145267472
#145267442
#145267002
C17×#13712
#1208417