Finite Group Databasebeta

← #16948534

Subgroups — #16948534

Order 4352.

236 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 65 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#14531036C211yesmaximal, characteristic, complemented
2#14530603C211yesmaximal, characteristic
3#14528150C211yesmaximal, characteristic
4#14528146C211yesmaximal, characteristic
5#14526855C211yesmaximal, characteristic, complemented
6#14526834C211yesmaximal, characteristic, complemented
7C17×#1362C211yesmaximal, characteristic, complemented
8C2×#10587500—21no—
9C2×#10587500—21no—
10C2×C16×D17—21no—
11#11763189C2211yescharacteristic
12#11763090—21no—
13#11763086—21no—
14C8×D68C2211yescharacteristic
15#11762588—21no—
16C4×#63214C2211yescharacteristic
17#11762562C2211yescharacteristic
18#11762555—21no—
19#11762554—21no—
20C17×#494C2211yescharacteristic
21C17×C4⋊C16C2211yescharacteristic
22C17×#335C2211yescharacteristic
23C2×Q16×C17—21no—
24C2×Q16×C17—21no—
25C17×C4⋊Q8—21no—
26C2×Dic68—21no—
27C2×Dic68—21no—
28C2×C8×D17—21no—
29C4×D68D411yescharacteristic
30#10587555—21no—
31C2×C16×C17—21no—
32C17×C4⋊C8—21no—
33C4×C8×C17C2311yescharacteristic
34#10587500—42no—
35#10587500—42no—
36#10587492—41no—
37#10587491—21no—
38#10587489—41no—
39C2×#63214D411yescharacteristic
40C2×#63214D411yescharacteristic
41#10587480—41no—
42#10587478—41no—
43C4⋊#3622—21no—
44C4⋊#3622D411yescharacteristic
45C16×D17—42no—
46C2×Q8×C17—41no—
47C2×D68D811yescharacteristic
48C2×C4×D17—21no—
49C2×Dic34—41no—
50Q16×C17—41no—
51Q16×C17—41no—
52Q16×C17—81no—
53C2×C8×C17—41no—
54C2×C8×C17C2×D411yescharacteristic
55C2×C8×C17#4111yescharacteristic
56C4⋊C4×C17—41no—
57C4⋊C4×C17—41no—
58C42×C17C2×D411yescharacteristic
59#63227—21no—
60C4⋊Dic17—41no—
61C4⋊Dic17—41no—
62C4⋊Dic17D811yescharacteristic
63C2×#3622—21no—
64C2×#3622—41no—
65Dic68—41no—
66Dic68—41no—
67Dic68—81no—
68C8×D17—41no—
69C8×D17—41no—
70C16×C17—41no—
71#63214—21no—
72#63214D812yes—
73#12431—171nomaximal, Sylow
74C22×D17—21no—
75Q8×C17—81no—
76Q8×C17—81no—
77C2×C4×C17—81no—
78C2×C4×C17#12111yescharacteristic
79C2×C4×C17C2×D811yescharacteristic
80C2×C4×C17#13511yescharacteristic
81C2×Dic17—21no—
82C2×Dic17—81no—
83D68—21no—
84D68Q3212yescomplemented
85C4×D17—41no—
86C4×D17—41no—
87Dic34—81no—
88Dic34—81no—
89C8×C17—21no—
90C8×C17—81no—
91C8×C17C2×D811yescharacteristic
92C8×C17AGL(1,ℤ/8)11yescharacteristic
93#3622—41no—
94#3622—81no—
95#2247—171no—
96D4×C16—171no—
97#1669—171no—
98#1669—171no—
99#1371—171no—
100#1362—171no—
101#1362D1711yescharacteristic, complemented
102C22×C17#46611yescharacteristic
103C2×D17—22no—
104C2×D17—41no—
105C2×D17—41no—
106C4×C17—21no—
107C4×C17—161no—
108C4×C17#45911yescharacteristic
109C4×C17#47211yescharacteristic
110C4×C17C2×Q3211yescharacteristic
111C4×C17#50811yescharacteristic
112Dic17—41no—
113Dic17—161no—
114C2×Q32—341no—
115C2×Q32—341no—
116C22×C16—341no—
117#494—171no—
118#494C2×D1711yescharacteristic
119#474—341no—
120#474—341no—
121C8×D4—171no—
122C4⋊C16C2×D1711yescharacteristic
123C22⋊C16—341no—
124C4×C16—171no—
125#335—171no—
126#335C2×D1711yescharacteristic
127#332—341no—
128#332—341no—
129C2×C17#166711yescharacteristic
130C2×C17#221611yescharacteristic
131C2×C17#222211yescharacteristic
132D17—42no—
133C2×Q16—21no—
134C2×Q16—21no—
135C2×Q16—341no—
136C2×Q16—341no—
137C22×C8—341no—
138C4⋊Q8—21no—
139C4⋊Q8—341no—
140C4×D4—171no—
141Q32—682no—
142Q32—682no—
143C2×C16—21no—
144C2×C16—171no—
145C2×C16—171no—
146C2×C16—682no—
147#107—681no—
148#107—681no—
149C4⋊C8—21no—
150C4⋊C8—171no—
151C4⋊C8—341no—
152#102—681no—
153#102—681no—
154C22⋊C8—341no—
155C4×C8C22×D1711yescharacteristic
156C17#1243111yescharacteristic, complemented, Sylow
157C2×Q8—41no—
158C2×Q8—681no—
159C2×D4—171no—
160C22×C4—341no—
161Q16—41no—
162Q16—41no—
163Q16—81no—
164Q16—681no—
165Q16—681no—
166Q16—1361no—
167C2×C8—41no—
168C2×C8—341no—
169C2×C8—681no—
170C2×C8—681no—
171C2×C8—681no—
172C2×C8#6325211yescharacteristic
173C2×C8D4×D1711yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—171no—
177C4⋊C4—681no—
178C4⋊C4—681no—
179C22⋊C4—341no—
180C42D4×D1711yescharacteristic
181C16—41no—
182C16—172no—
183C16—341no—
184C23—341no—
185Q8—81no—
186Q8—81no—
187Q8—1361no—
188Q8—1361no—
189D4—172no—
190D4—341no—
191C2×C4—81no—
192C2×C4—341no—
193C2×C4—681no—
194C2×C4—681no—
195C2×C4—1361no—
196C2×C4#1058757011yescharacteristic
197C2×C4D8×D1711yescharacteristic
198C2×C4#1058760211yescharacteristic
199C8—21no—
200C8—81no—
201C8—681no—
202C8—1361no—
203C8D8×D1711yescharacteristic
204C8#1058760011yescharacteristic
205C22—342no—
206C22—681no—
207C22—681no—
208C22#1176304411yescharacteristic
209C4—21no—
210C4—161no—
211C4—2721no—
212C4—681no—
213C4#1176300311yescharacteristic
214C4#1176307811yescharacteristic
215C4Q32×D1711yescharacteristic
216C4#1176324011yescharacteristic
217C2—682no—
218C2#1452813811yescharacteristic
219C2#1453087411yescharacteristic
220C2#1453090811yescharacteristic
subgroupG/H
centerC22#11763044
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1362C2
socleC22×C17#466
prime radicalC2×D68D8
hypercenter#1362D17
hypocenterC17#12431
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. #14531036C2semidirect
5. #14526855C2semidirect
6. #14526834C2semidirect
7. C17×#1362C2semidirect
84. D68Q32semidirect
101. #1362D17semidirect
156. C17#12431semidirect

Maximal subgroups

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

subgroupindex
#145310362
#145306032
#145281502
#145281462
#145268552
#145268342
C17×#13622
#1243117