Finite Group Databasebeta

← #16948898

Subgroups — #16948898

Order 4352.

226 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 61 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#14530918C211yesmaximal, characteristic
2#14530830C211yesmaximal, characteristic
3#14528382C211yesmaximal, characteristic, complemented
4#14527668C211yesmaximal, characteristic
5#14526853C211yesmaximal, characteristic, complemented
6#14526832C211yesmaximal, characteristic, complemented
7C17×#1364C211yesmaximal, characteristic, complemented
8C2×#10587471—21no—
9#11763205—21no—
10#11763189C2211yescharacteristic
11#11763159—21no—
12C4×D136C2211yescharacteristic
13#11762886—21no—
14#11762634—21no—
15C4⋊#63214C2211yescharacteristic
16#11762614—21no—
17#11762609—21no—
18#11762536—21no—
19C8×#3622C2211yescharacteristic
20C17×#500C2211yescharacteristic
21C17×C4⋊C16C2211yescharacteristic
22C17×#335C2211yescharacteristic
23C17×C4⋊Q8—21no—
24C2×Dic68—21no—
25C2×Dic68—21no—
26C2×D136D411yescharacteristic
27C2×#63218—41no—
28C4×D68—21no—
29#10587555—21no—
30C2×C16×C17—21no—
31C17×#107—21no—
32C17×#107—21no—
33C17×C4⋊C8—21no—
34C4×C8×C17C2311yescharacteristic
35#10587506—41no—
36#10587506—41no—
37#10587492—21no—
38#10587491—41no—
39#10587489D411yescharacteristic
40C2×#63214—21no—
41#10587479—42no—
42C4×#3622D411yescharacteristic
43C4×#3622D411yescharacteristic
44#10587471—42no—
45C2×Q8×C17—41no—
46C2×D68—21no—
47C2×C4×D17—41no—
48C2×Dic34—41no—
49C2×C8×C17—41no—
50C2×C8×C17C2×D411yescharacteristic
51C2×C8×C17#4111yescharacteristic
52C4⋊C4×C17—41no—
53C4⋊C4×C17—41no—
54C42×C17C2×D411yescharacteristic
55#63227—41no—
56C4⋊Dic17—21no—
57C4⋊Dic17—41no—
58C4⋊Dic17—41no—
59C2×#3622—21no—
60C2×#3622D811yescharacteristic
61C2×#3622D811yescharacteristic
62Dic68—41no—
63Dic68—41no—
64Dic68—81no—
65D136—21no—
66D136—21no—
67#63218—82no—
68C16×C17—41no—
69#63214—41no—
70#12489—171nomaximal, Sylow
71C22×D17—41no—
72Q8×C17—81no—
73Q8×C17—81no—
74C2×C4×C17—81no—
75C2×C4×C17#12111yescharacteristic
76C2×C4×C17C2×D811yescharacteristic
77C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
78C2×Dic17—41no—
79C2×Dic17—81no—
80D68—41no—
81D68—41no—
82C4×D17—81no—
83C4×D17—81no—
84Dic34—81no—
85Dic34—81no—
86C8×C17—21no—
87C8×C17—81no—
88C8×C17AGL(1,ℤ/8)11yescharacteristic
89C8×C17#13711yescharacteristic
90#3622—22no—
91#3622—21no—
92#3622—21no—
93#2224—171no—
94#2208—171no—
95#1707—171no—
96#1589—171no—
97#1370—171no—
98#1364D1711yescharacteristic, complemented
99#1362—171no—
100C22×C17#45911yescharacteristic
101C2×D17—81no—
102C2×D17—81no—
103C2×D17—81no—
104C4×C17—21no—
105C4×C17—161no—
106C4×C17#46811yescharacteristic
107C4×C17#47111yescharacteristic
108C4×C17#50811yescharacteristic
109C4×C17#50911yescharacteristic
110Dic17—81no—
111Dic17—161no—
112C2×SD32—341no—
113#500C2×D1711yescharacteristic
114#498—341no—
115#494—171no—
116#487—341no—
117C4×D8—171no—
118#436—341no—
119#366—341no—
120C4⋊C16—171no—
121C4⋊C16C2×D1711yescharacteristic
122#358—341no—
123#357—341no—
124#335C2×D1711yescharacteristic
125D4⋊C8—341no—
126C82—171no—
127C2×C17#168511yescharacteristic
128C2×C17#221011yescharacteristic
129C2×C17#221411yescharacteristic
130D17—161no—
131C2×Q16—341no—
132C2×Q16—341no—
133C2×D8—171no—
134C2×M16—681no—
135C4⋊Q8—21no—
136C4⋊Q8—341no—
137C4×D4—341no—
138SD32—682no—
139C2×C16—21no—
140C2×C16—341no—
141#107—21no—
142#107—21no—
143#107—171no—
144#106—682no—
145C4⋊C8—21no—
146#103—681no—
147#103—681no—
148#102—341no—
149C22⋊C8—681no—
150C4×C8—171no—
151C4×C8—171no—
152C4×C8C22×D1711yescharacteristic
153C17#1248911yescharacteristic, complemented, Sylow
154C2×Q8—41no—
155C2×Q8—681no—
156C2×D4—341no—
157C22×C4—681no—
158Q16—681no—
159Q16—681no—
160Q16—1361no—
161D8—341no—
162D8—341no—
163M16—1362no—
164C2×C8—41no—
165C2×C8—171no—
166C2×C8—171no—
167C2×C8—341no—
168C2×C8#6325211yescharacteristic
169C2×C8D4×D1711yescharacteristic
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—341no—
173C4⋊C4—681no—
174C4⋊C4—681no—
175C22⋊C4—681no—
176C42D4×D1711yescharacteristic
177C16—41no—
178C16—681no—
179C23—681no—
180Q8—81no—
181Q8—81no—
182Q8—1361no—
183Q8—1361no—
184D4—681no—
185D4—681no—
186C2×C4—81no—
187C2×C4—681no—
188C2×C4—1361no—
189C2×C4—1361no—
190C2×C4—1361no—
191C2×C4#1058757011yescharacteristic
192C2×C4D8×D1711yescharacteristic
193C2×C4#1058760011yescharacteristic
194C8—21no—
195C8—81no—
196C8—342no—
197C8—341no—
198C8—341no—
199C8#1058760011yescharacteristic
200C8#1058760411yescharacteristic
201C22—1361no—
202C22—1361no—
203C22—1361no—
204C22#1176300311yescharacteristic
205C4—21no—
206C4—161no—
207C4—2721no—
208C4—1361no—
209C4#1176305811yescharacteristic
210C4#1176307511yescharacteristic
211C4#1176324011yescharacteristic
212C4#1176324311yescharacteristic
213C2—2721no—
214C2#1452825211yescharacteristic
215C2#1453083811yescharacteristic
216C2#1453086411yescharacteristic
subgroupG/H
centerC22#11763003
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1364C2
socleC22×C17#459
prime radicalC2×D136D4
hypercenter#1364D17
hypocenterC17#12489
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
3. #14528382C2semidirect
5. #14526853C2semidirect
6. #14526832C2semidirect
7. C17×#1364C2semidirect
98. #1364D17semidirect
153. C17#12489semidirect

Maximal subgroups

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

subgroupindex
#145309182
#145308302
#145283822
#145276682
#145268532
#145268322
C17×#13642
#1248917