Finite Group Databasebeta

← #16948754

Subgroups — #16948754

Order 4352.

218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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#14531011C211yesmaximal, characteristic, complemented
2#14530603C211yesmaximal, characteristic
3#14528184C211yesmaximal, characteristic
4#14528146C211yesmaximal, characteristic
5#14526855C211yesmaximal, characteristic, complemented
6#14526841C211yesmaximal, characteristic, complemented
7C17×#1362C211yesmaximal, characteristic, complemented
8C2×C16×D17—21no—
9#11763214C2211yescharacteristic
10#11763100—21no—
11#11763086—21no—
12C8×D68C2211yescharacteristic
13#11762613—21no—
14#11762613—21no—
15#11762588—21no—
16C4×#63214C2211yescharacteristic
17#11762562C2211yescharacteristic
18#11762557—21no—
19#11762555—21no—
20C17×#494C2211yescharacteristic
21C17×C4⋊C16C2211yescharacteristic
22C17×#335C2211yescharacteristic
23C2×Q16×C17—21no—
24C2×Q16×C17—21no—
25C17×C4⋊Q8—21no—
26C2×C8×D17—21no—
27C4×D68D411yescharacteristic
28#10587555—21no—
29C2×C16×C17—21no—
30C17×C4⋊C8—21no—
31C4×C8×C17C2311yescharacteristic
32#10587492—41no—
33#10587491—21no—
34#10587489—21no—
35#10587489—21no—
36#10587488—41no—
37C2×#63214D411yescharacteristic
38C2×#63214D411yescharacteristic
39#10587480—41no—
40#10587478—41no—
41C4⋊#3622—21no—
42C4⋊#3622D411yescharacteristic
43C16×D17—42no—
44C2×Q8×C17—41no—
45C2×D68D811yescharacteristic
46C2×C4×D17—21no—
47C2×Dic34—41no—
48Q16×C17—41no—
49Q16×C17—41no—
50Q16×C17—81no—
51C2×C8×C17—41no—
52C2×C8×C17C2×D411yescharacteristic
53C2×C8×C17#4111yescharacteristic
54C4⋊C4×C17—41no—
55C4⋊C4×C17—41no—
56C42×C17C2×D411yescharacteristic
57#63227—21no—
58C4⋊Dic17—41no—
59C4⋊Dic17—41no—
60C4⋊Dic17D811yescharacteristic
61C2×#3622—21no—
62C2×#3622—41no—
63C8×D17—41no—
64C8×D17—41no—
65C16×C17—41no—
66#63214—21no—
67#63214—21no—
68#12469—171nomaximal, Sylow
69C22×D17—21no—
70Q8×C17—81no—
71Q8×C17—81no—
72C2×C4×C17—81no—
73C2×C4×C17#12111yescharacteristic
74C2×C4×C17C2×D811yescharacteristic
75C2×C4×C17#13511yescharacteristic
76C2×Dic17—21no—
77C2×Dic17—81no—
78D68—21no—
79D68Q3212yes—
80C4×D17—41no—
81C4×D17—41no—
82Dic34—161no—
83C8×C17—21no—
84C8×C17—81no—
85C8×C17#13511yescharacteristic
86C8×C17AGL(1,ℤ/8)11yescharacteristic
87#3622—41no—
88#3622—81no—
89#2241—171no—
90D4×C16—171no—
91#1675—171no—
92#1669—171no—
93#1371—171no—
94#1365—171no—
95#1362D1711yescharacteristic, complemented
96C22×C17#46611yescharacteristic
97C2×D17—22no—
98C2×D17—41no—
99C2×D17—41no—
100C4×C17—21no—
101C4×C17—161no—
102C4×C17#46311yescharacteristic
103C4×C17#47111yescharacteristic
104C4×C17C2×Q3211yescharacteristic
105C4×C17#50811yescharacteristic
106Dic17—41no—
107Dic17—161no—
108C22×C16—341no—
109#500—171no—
110#494C2×D1711yescharacteristic
111#476—341no—
112#474—341no—
113C8×D4—171no—
114C4⋊C16C2×D1711yescharacteristic
115#358—341no—
116#358—341no—
117C22⋊C16—341no—
118C4×C16—171no—
119#335—171no—
120#335C2×D1711yescharacteristic
121#333—341no—
122#332—341no—
123C2×C17#168111yescharacteristic
124C2×C17#221611yescharacteristic
125C2×C17#222311yescharacteristic
126D17—42no—
127C2×Q16—21no—
128C2×Q16—21no—
129C22×C8—341no—
130C4⋊Q8—21no—
131C4⋊Q8—341no—
132C4×D4—171no—
133C2×C16—21no—
134C2×C16—171no—
135C2×C16—171no—
136C2×C16—682no—
137#107—341no—
138#107—341no—
139#107—681no—
140#106—681no—
141C4⋊C8—21no—
142C4⋊C8—171no—
143C4⋊C8—341no—
144#102—681no—
145#102—681no—
146C22⋊C8—341no—
147C4×C8C22×D1711yescharacteristic
148C17#1246911yescharacteristic, complemented, Sylow
149C2×Q8—41no—
150C2×Q8—681no—
151C2×D4—171no—
152C22×C4—341no—
153Q16—41no—
154Q16—41no—
155Q16—81no—
156C2×C8—41no—
157C2×C8—341no—
158C2×C8—681no—
159C2×C8—681no—
160C2×C8—681no—
161C2×C8#6325211yescharacteristic
162C2×C8D4×D1711yescharacteristic
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—171no—
166C4⋊C4—681no—
167C4⋊C4—681no—
168C22⋊C4—341no—
169C42D4×D1711yescharacteristic
170C16—41no—
171C16—341no—
172C16—341no—
173C23—341no—
174Q8—81no—
175Q8—81no—
176Q8—2721no—
177D4—172no—
178D4—341no—
179C2×C4—81no—
180C2×C4—341no—
181C2×C4—681no—
182C2×C4—681no—
183C2×C4—1361no—
184C2×C4#1058757011yescharacteristic
185C2×C4D8×D1711yescharacteristic
186C2×C4#1058760211yescharacteristic
187C8—21no—
188C8—81no—
189C8—681no—
190C8—1361no—
191C8#1058759711yescharacteristic
192C8#1058760211yescharacteristic
193C22—342no—
194C22—681no—
195C22—681no—
196C22#1176304411yescharacteristic
197C4—21no—
198C4—161no—
199C4—2721no—
200C4—681no—
201C4#1176302311yescharacteristic
202C4#1176307111yescharacteristic
203C4Q32×D1711yescharacteristic
204C4#1176324011yescharacteristic
205C2—682no—
206C2#1452822011yescharacteristic
207C2#1453087411yescharacteristic
208C2#1453091711yescharacteristic
subgroupG/H
centerC22#11763044
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1362C2
socleC22×C17#466
prime radicalC2×D68D8
hypercenter#1362D17
hypocenterC17#12469
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #14531011C2semidirect
5. #14526855C2semidirect
6. #14526841C2semidirect
7. C17×#1362C2semidirect
95. #1362D17semidirect
148. C17#12469semidirect

Maximal subgroups

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

subgroupindex
#145310112
#145306032
#145281842
#145281462
#145268552
#145268412
C17×#13622
#1246917