Finite Group Databasebeta

← #16947653

Subgroups — #16947653

Order 4352.

324 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 55 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#14539608C211yesmaximal, characteristic
2#14531003C212yesmaximal, complemented
3#14526777C212yesmaximal, complemented
4#14526720C211yesmaximal, characteristic
5C17×#2091C211yesmaximal, characteristic
6C2×#10587610—21no—
7#11763140—22no—
8#11763067—21no—
9#11763067C2212yes—
10#11762967—22no—
11#11762633—22no—
12#11762624—22no—
13#11762591C2212yes—
14C17×#430—21no—
15C17×#430C2211yescharacteristic
16C17×#407—21no—
17C17×#407C2211yescharacteristic
18C17×#338C2211yescharacteristic
19C23×C4×C17D411yescharacteristic
20C22×Dic34—21no—
21C2×M16×C17—21no—
22C2×M16×C17—21no—
23C2×M16×C17D411yescharacteristic
24C2×M16×C17C2311yescharacteristic
25C2×C22⋊Dic17—41no—
26C2×C4⋊Dic17—21no—
27#10587610—22no—
28#10587610—22no—
29#10587610—41no—
30#10587610—41no—
31C2×#63225—41no—
32C2×Dic68—21no—
33C2×Dic68D412yes—
34C17×#108—22no—
35C17×#108—42no—
36C17×C22⋊C8—22no—
37C17×C22⋊C8—42no—
38#10587488—21no—
39#10587488D412yes—
40#10587487—22no—
41#10587487—22no—
42#10587483—22no—
43C24×C17SD1611yescharacteristic
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17—41no—
47C22×C4×C17—41no—
48C22×C4×C17SD1611yescharacteristic
49C22×C4×C17C2×D411yescharacteristic
50C22×Dic17—41no—
51C22×Dic17—41no—
52C2×Dic34—22no—
53C2×Dic34—41no—
54C2×Dic34—81no—
55C2×Dic34—81no—
56M16×C17—41no—
57M16×C17—41no—
58M16×C17—41no—
59M16×C17—41no—
60M16×C17—41no—
61M16×C17—41no—
62C2×C8×C17—22no—
63C2×C8×C17—21no—
64C2×C8×C17—41no—
65C2×C8×C17C2×D412yes—
66C22⋊Dic17—42no—
67C22⋊Dic17—42no—
68C4⋊Dic17—22no—
69C4⋊Dic17—41no—
70#63225—42no—
71#63225—42no—
72Dic68—42no—
73Dic68—81no—
74#63214—42no—
75#12299—171nomaximal, Sylow
76C23×C17—21no—
77C23×C17—41no—
78C23×C17—42no—
79C23×C17C2×SD1611yescharacteristic
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—41no—
84C2×C4×C17—41no—
85C2×C4×C17—41no—
86C2×C4×C17—81no—
87C2×C4×C17#12011yescharacteristic
88C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—82no—
92C2×Dic17—82no—
93Dic34—42no—
94Dic34—42no—
95Dic34—82no—
96C8×C17—22no—
97C8×C17—42no—
98C8×C17—41no—
99C8×C17—81no—
100#3195—171no—
101#2239—172no—
102#2091D1711yescharacteristic
103#1342—172no—
104#1320—171no—
105C22×C17—22no—
106C22×C17—21no—
107C22×C17—41no—
108C22×C17—41no—
109C22×C17—42no—
110C22×C17—41no—
111C22×C17—81no—
112C22×C17#45011yescharacteristic
113C4×C17—21no—
114C4×C17—41no—
115C4×C17#45311yescharacteristic
116C4×C17#45811yescharacteristic
117Dic17—82no—
118Dic17—82no—
119C2×C22⋊Q8—341no—
120#483—342no—
121#470—172no—
122#470—341no—
123#451—342no—
124#430—21no—
125#430C2×D1711yescharacteristic
126#407—21no—
127#407C2×D1711yescharacteristic
128#365—342no—
129#362—342no—
130#349—172no—
131#338C2×D1711yescharacteristic
132C2×C17—21no—
133C2×C17—42no—
134C2×C17—41no—
135C2×C17#161311yescharacteristic
136C22×Q8—341no—
137C23×C4C22⋊D1711yescharacteristic
138C2×Q16—172no—
139C2×Q16—341no—
140C2×M16—21no—
141C2×M16—21no—
142C2×M16C22⋊D1711yescharacteristic
143C2×M16C22×D1711yescharacteristic
144C22⋊Q8—342no—
145C22⋊Q8—342no—
146C22⋊Q8—681no—
147C22⋊Q8—681no—
148C2×C4⋊C4—341no—
149C2×C4⋊C4—681no—
150C2×C22⋊C4—681no—
151M32—342no—
152#108—22no—
153#108—42no—
154#106—172no—
155#106—341no—
156#103—342no—
157#103—342no—
158C22⋊C8—22no—
159C22⋊C8—42no—
160C17#1229911yescharacteristic, complemented, Sylow
161C24#6323011yescharacteristic
162C2×Q8—342no—
163C2×Q8—681no—
164C2×Q8—1361no—
165C2×Q8—1361no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—681no—
171C22×C4—681no—
172C22×C4#6323011yescharacteristic
173C22×C4C2×C22⋊D1711yescharacteristic
174Q16—682no—
175Q16—1361no—
176M16—41no—
177M16—41no—
178M16—41no—
179M16—41no—
180M16—41no—
181M16—41no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8D4×D1712yes—
186C4⋊C4—342no—
187C4⋊C4—681no—
188C4⋊C4—682no—
189C4⋊C4—682no—
190C22⋊C4—682no—
191C22⋊C4—682no—
192C16—682no—
193C23—21no—
194C23—41no—
195C23—42no—
196C23C2×#6323011yescharacteristic
197Q8—682no—
198Q8—682no—
199Q8—1362no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—81no—
207C2×C4—682no—
208C2×C4—682no—
209C2×C4—1362no—
210C2×C4—1362no—
211C2×C4#1058762311yescharacteristic
212C2×C4#1058763511yescharacteristic
213C8—22no—
214C8—42no—
215C8—41no—
216C8—81no—
217C22—22no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22#1176295911yescharacteristic
225C4—21no—
226C4—41no—
227C4—1362no—
228C4—1362no—
229C4#1176297611yescharacteristic
230C4#1176299811yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1452780311yescharacteristic
subgroupG/H
centerC2#14527803
commutator, cosocleC2×M16×C17C23
FrattiniC2×M16C22×D17
FittingC17×#2091C2
socleC2×C17#1613
prime radicalC24×C17SD16
hypercenter#2091D17
hypocenterC17#12299
LCSG ▷ C2×M16×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2091

Complements

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

NH ≅ G/Ntype
2. #14531003C2semidirect
3. #14526777C2semidirect
160. C17#12299semidirect

Maximal subgroups

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

subgroupindex
#145396082
#145310032
#145267772
#145267202
C17×#20912
#1229917