Finite Group Databasebeta

← #16948761

Subgroups — #16948761

Order 4352.

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

normal subgroups only

This group has 224 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#14528174C211yesmaximal, characteristic
4#14528146C211yesmaximal, characteristic
5#14526857C211yesmaximal, characteristic, complemented
6#14526838C211yesmaximal, characteristic, complemented
7C17×#1362C211yesmaximal, characteristic, complemented
8C2×C16×D17—21no—
9#11763214C2211yescharacteristic
10#11763086—21no—
11#11763015—21no—
12C8×D68C2211yescharacteristic
13#11762613—21no—
14#11762613—21no—
15#11762588—21no—
16C4×#63214C2211yescharacteristic
17#11762562C2211yescharacteristic
18#11762556—21no—
19#11762555—21no—
20C17×#494C2211yescharacteristic
21C17×C4⋊C16C2211yescharacteristic
22C17×#335C2211yescharacteristic
23C2×Q16×C17—21no—
24C2×Q16×C17—21no—
25C17×C4⋊Q8—21no—
26C2×#63219—41no—
27C2×C8×D17—21no—
28C4×D68D411yescharacteristic
29#10587555—21no—
30C2×C16×C17—21no—
31C17×C4⋊C8—21no—
32C4×C8×C17C2311yescharacteristic
33#10587491—21no—
34#10587489—21no—
35#10587489—21no—
36#10587487—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—
63#63219—82no—
64C8×D17—41no—
65C8×D17—41no—
66C16×C17—41no—
67#63214—21no—
68#63214—21no—
69#12470—171nomaximal, Sylow
70C22×D17—21no—
71Q8×C17—81no—
72Q8×C17—81no—
73C2×C4×C17—81no—
74C2×C4×C17#12111yescharacteristic
75C2×C4×C17C2×D811yescharacteristic
76C2×C4×C17#13511yescharacteristic
77C2×Dic17—21no—
78C2×Dic17—81no—
79D68—21no—
80D68SD3212yes—
81C4×D17—41no—
82C4×D17—41no—
83Dic34—81no—
84Dic34—81no—
85C8×C17—21no—
86C8×C17—81no—
87C8×C17#13511yescharacteristic
88C8×C17AGL(1,ℤ/8)11yescharacteristic
89#3622—41no—
90#3622—81no—
91#2241—171no—
92D4×C16—171no—
93#1673—171no—
94#1669—171no—
95#1372—171no—
96#1364—171no—
97#1362D1711yescharacteristic, complemented
98C22×C17#46611yescharacteristic
99C2×D17—22no—
100C2×D17—41no—
101C2×D17—41no—
102C4×C17—21no—
103C4×C17—161no—
104C4×C17#46311yescharacteristic
105C4×C17#47111yescharacteristic
106C4×C17C2×SD3211yescharacteristic
107C4×C17#50811yescharacteristic
108Dic17—41no—
109Dic17—161no—
110C22×C16—341no—
111#500—171no—
112#494C2×D1711yescharacteristic
113#474—341no—
114#461—341no—
115C8×D4—171no—
116C4⋊C16C2×D1711yescharacteristic
117#358—341no—
118#358—341no—
119C22⋊C16—341no—
120C4×C16—171no—
121#335—171no—
122#335C2×D1711yescharacteristic
123#332—341no—
124#332—341no—
125C2×C17#168111yescharacteristic
126C2×C17#221711yescharacteristic
127C2×C17#222211yescharacteristic
128D17—42no—
129C2×Q16—21no—
130C2×Q16—21no—
131C2×SD16—681no—
132C22×C8—341no—
133C4⋊Q8—21no—
134C4⋊Q8—341no—
135C4×D4—171no—
136C2×C16—21no—
137C2×C16—171no—
138C2×C16—171no—
139C2×C16—682no—
140#107—341no—
141#107—341no—
142#107—681no—
143C4⋊C8—21no—
144C4⋊C8—171no—
145C4⋊C8—341no—
146#103—681no—
147#102—681no—
148C22⋊C8—341no—
149C4×C8C22×D1711yescharacteristic
150C17#1247011yescharacteristic, complemented, Sylow
151C2×Q8—41no—
152C2×Q8—681no—
153C2×D4—171no—
154C22×C4—341no—
155Q16—41no—
156Q16—41no—
157Q16—81no—
158SD16—1362no—
159C2×C8—41no—
160C2×C8—341no—
161C2×C8—681no—
162C2×C8—681no—
163C2×C8—681no—
164C2×C8#6325211yescharacteristic
165C2×C8D4×D1711yescharacteristic
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—171no—
169C4⋊C4—681no—
170C4⋊C4—681no—
171C22⋊C4—341no—
172C42D4×D1711yescharacteristic
173C16—41no—
174C16—341no—
175C16—341no—
176C23—341no—
177Q8—81no—
178Q8—81no—
179Q8—1361no—
180Q8—1361no—
181D4—172no—
182D4—341no—
183C2×C4—81no—
184C2×C4—341no—
185C2×C4—681no—
186C2×C4—681no—
187C2×C4—1361no—
188C2×C4#1058757011yescharacteristic
189C2×C4D8×D1711yescharacteristic
190C2×C4#1058760211yescharacteristic
191C8—21no—
192C8—81no—
193C8—681no—
194C8—1361no—
195C8#1058759711yescharacteristic
196C8#1058760211yescharacteristic
197C22—342no—
198C22—681no—
199C22—681no—
200C22#1176304411yescharacteristic
201C4—21no—
202C4—161no—
203C4—2721no—
204C4—681no—
205C4#1176302311yescharacteristic
206C4#1176307111yescharacteristic
207C4SD32×D1711yescharacteristic
208C4#1176324211yescharacteristic
209C2—682no—
210C2#1452822011yescharacteristic
211C2#1453088311yescharacteristic
212C2#1453090811yescharacteristic
subgroupG/H
centerC22#11763044
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1362C2
socleC22×C17#466
prime radicalC2×D68D8
hypercenter#1362D17
hypocenterC17#12470
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. #14526857C2semidirect
6. #14526838C2semidirect
7. C17×#1362C2semidirect
97. #1362D17semidirect
150. C17#12470semidirect

Maximal subgroups

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

subgroupindex
#145310112
#145306032
#145281742
#145281462
#145268572
#145268382
C17×#13622
#1247017