Finite Group Databasebeta

← #17948792

Subgroups — #17948792

Order 4352.

248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 58 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#14544668C211yesmaximal, characteristic
2#14544666C211yesmaximal, characteristic
3#14530397C211yesmaximal, characteristic
4D17⋊#108—21no—
5#11763819—21no—
6#11763795—21no—
7#11763788—21no—
8#11763678C412yescomplemented
9#11763677C412yes—
10C2×#10587587C2211yescharacteristic
11C2×#10587483C411yescharacteristic, complemented
12#11762588—21no—
13#11762588—21no—
14C22×C16×C17C411yescharacteristic, complemented
15C2×#63252D411yescharacteristic
16#10587677—22no—
17D17⋊M16—22no—
18C22×C8×C17C2×C411yescharacteristic
19C2×#63223Q811yescharacteristic
20#10587587—41no—
21#10587587—41no—
22C2×#63218C2×C411yescharacteristic
23C2×#63218C2×C411yescharacteristic
24C2×C8×D17D411yescharacteristic
25C2×C8×D17D411yescharacteristic
26#10587553—41no—
27#10587551—41no—
28#10587545—41no—
29#10587539—41no—
30#10587536—41no—
31#10587535—41no—
32#10587534—41no—
33#10587533—41no—
34C2×C16×C17—21no—
35C2×C16×C17—41no—
36#10587483—41no—
37C2×#63214—21no—
38C22×C4×C17C4⋊C411yescharacteristic
39C2×C22⋊D17D811yescharacteristic
40C2×C22⋊D17Q1611yescharacteristic
41#63252—41no—
42#63252—41no—
43C2×D68SD1611yescharacteristic
44C2×C4×D17C22⋊C411yescharacteristic
45C2×C4×D17C22⋊C411yescharacteristic
46C2×Dic34SD1611yescharacteristic
47C22⋊#595—42no—
48#63247—42no—
49C4⋊#595—42no—
50C4×#595—42no—
51#63243—42no—
52#63242—42no—
53C2×C8×C17—21no—
54C2×C8×C17—21no—
55C2×C8×C17C4211yescharacteristic
56C2×C8×C17C22⋊C411yescharacteristic
57#63223—41no—
58C2×#3622C4⋊C411yescharacteristic
59C2×#3622C4⋊C411yescharacteristic
60#63218—41no—
61#63218—41no—
62C8×D17—21no—
63C8×D17—21no—
64C8×D17—21no—
65C8×D17—21no—
66C16×C17—41no—
67#63214—41no—
68#7227—171nomaximal, Sylow
69C23×C17#10711yescharacteristic
70C22×D17#10211yescharacteristic
71C22×D17#10311yescharacteristic
72C2×#595—82no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17#9511yescharacteristic
76C2×C4×C17#10611yescharacteristic
77C22⋊D17—41no—
78C22⋊D17—41no—
79C2×Dic17#10211yescharacteristic
80C2×Dic17#10311yescharacteristic
81D68—41no—
82C4×D17—21no—
83C4×D17—21no—
84C4×D17—21no—
85C4×D17—21no—
86Dic34—41no—
87#3624—82no—
88C8×C17—21no—
89C8×C17#9911yescharacteristic
90C8×C17#9911yescharacteristic
91#3622—21no—
92#3622—21no—
93#2113—171no—
94#1813—171no—
95#1812—171no—
96C22×C17—21no—
97C22×C17—41no—
98C22×C17#34011yescharacteristic
99C2×D17—21no—
100C2×D17—21no—
101C2×D17—41no—
102C2×D17—41no—
103#595—162no—
104C4×C17—21no—
105C4×C17H(3,ℤ/4)11yescharacteristic
106C4×C17#34211yescharacteristic
107Dic17—21no—
108Dic17—21no—
109C2×#131—171no—
110C2×M32—171no—
111C22×C16#59511yescharacteristic, complemented
112C2×#108—341no—
113#427—341no—
114#413—341no—
115#410—341no—
116C22⋊C16—341no—
117C22⋊C16—341no—
118#338—172no—
119H(3,ℤ/4)—172no—
120C2×C17—21no—
121C2×C17—41no—
122C2×C17#128911yescharacteristic
123D17—41no—
124D17—41no—
125C2×#41—171no—
126#131—681no—
127#131—681no—
128C2×M16—171no—
129C2×M16—171no—
130C2×M16—171no—
131C2×M16—342no—
132C22×C8—171no—
133C22×C8—171no—
134C22×C8C2×#59511yescharacteristic
135#117—342no—
136M32—681no—
137C2×C16—21no—
138C2×C16—41no—
139C2×C16—341no—
140#108—681no—
141#108—681no—
142#107—681no—
143#106—681no—
144#101—681no—
145#100—681no—
146#99—681no—
147#99—681no—
148C17#722711yescharacteristic, complemented, Sylow
149#41—681no—
150#41—681no—
151C2×Q8—171no—
152C2×D4—171no—
153C2×D4—171no—
154C2×D4—171no—
155C22×C4—171no—
156C22×C4—171no—
157C22×C4C4⋊#59511yescharacteristic
158M16—681no—
159M16—681no—
160M16—681no—
161M16—682no—
162M16—682no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—171no—
166C2×C8—171no—
167C2×C8—341no—
168C2×C8—341no—
169C2×C8—341no—
170C2×C8—341no—
171C2×C8—682no—
172C2×C8C4×#59511yescharacteristic
173C2×C8C22⋊#59511yescharacteristic
174C4⋊C4—682no—
175C22⋊C4—682no—
176C42—682no—
177C16—41no—
178C16—681no—
179C23—171no—
180C23—171no—
181C23#1058753411yescharacteristic
182Q8—681no—
183D4—681no—
184D4—681no—
185D4—681no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—171no—
189C2×C4—171no—
190C2×C4—341no—
191C2×C4—341no—
192C2×C4—341no—
193C2×C4—341no—
194C2×C4—1362no—
195C2×C4#1058753311yescharacteristic
196C2×C4(C2×#595)⋊C411yescharacteristic
197C8—21no—
198C8—341no—
199C8—341no—
200C8—1362no—
201C8#1058753911yescharacteristic
202C8#1058755111yescharacteristic
203C22—21no—
204C22—41no—
205C22—341no—
206C22—341no—
207C22—681no—
208C22—681no—
209C22#1176368311yescharacteristic
210C4—21no—
211C4—2722no—
212C4—341no—
213C4—341no—
214C4#1176367711yescharacteristic
215C4#1176368711yescharacteristic
216C2—21no—
217C2—41no—
218C2—681no—
219C2—681no—
220C2#1454364711yescharacteristic
subgroupG/H
centerC4#11763677
commutatorC2×C8×C17C42
FrattiniC22×C8C2×#595
FittingC22×C16×C17C4
socleC2×C17#1289
prime radicalC2×#63252D4
cosocleC2×#10587587C22
hypercenterC22×C16#595
hypocenterC17#7227
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
8. #11763678C4semidirect
11. C2×#10587483C4semidirect
14. C22×C16×C17C4semidirect
111. C22×C16#595semidirect
148. C17#7227semidirect

Maximal subgroups

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

subgroupindex
#145446682
#145446662
#145303972
#722717