Finite Group Databasebeta

← #16947592

Subgroups — #16947592

Order 4352.

310 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 71 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#14530979C212yesmaximal
2#14530272C211yesmaximal, characteristic
3#14526796C212yesmaximal
4#14526724C211yesmaximal, characteristic
5C17×#3249C211yesmaximal, characteristic
6C2×#10587489C2211yescharacteristic
7#11762707—21no—
8#11762636—22no—
9#11762613—22no—
10C22⋊#63214C2212yes—
11#11762572—21no—
12#11762572C2211yescharacteristic
13C17×#533—21no—
14C17×#477—22no—
15C17×#467—21no—
16C17×#467C2212yes—
17C17×#462—22no—
18C2×C17×C4⋊C8C2211yescharacteristic
19C2×Q16×C17—21no—
20C2×Q16×C17D412yes—
21C22×C8×C17D411yescharacteristic
22C22×C8×C17C2311yescharacteristic
23C17×C4⋊Q8—21no—
24C17×C4⋊Q8—21no—
25C17×#125—41no—
26C17×C22⋊Q8—22no—
27C17×C22⋊Q8—41no—
28C4×Q8×C17—22no—
29C4×Q8×C17—41no—
30C17×#117—41no—
31C2×C42×C17D411yescharacteristic
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×#63225—41no—
35C17×#107—21no—
36C17×#107D412yes—
37C17×C4⋊C8—22no—
38C17×#103—22no—
39C17×#103—22no—
40#10587502—41no—
41#10587489—22no—
42C2×#63214—22no—
43C2×Q8×C17—22no—
44C2×Q8×C17—41no—
45C22×C4×C17D811yescharacteristic
46C22×C4×C17D811yescharacteristic
47C22×C4×C17C2×D411yescharacteristic
48C22×Dic17—41no—
49C22×Dic17—41no—
50Q16×C17—42no—
51Q16×C17—81no—
52C2×C8×C17—21no—
53C2×C8×C17—41no—
54C2×C8×C17—41no—
55C2×C8×C17C2×D412yes—
56C4⋊C4×C17—22no—
57C4⋊C4×C17—42no—
58C4⋊C4×C17—41no—
59C4⋊C4×C17—41no—
60C4⋊C4×C17—41no—
61C4⋊C4×C17—42no—
62C22⋊C4×C17—42no—
63C42×C17—21no—
64C42×C17—21no—
65C42×C17—42no—
66C4⋊Dic17—22no—
67C4⋊Dic17—41no—
68C4⋊Dic17—41no—
69C4⋊Dic17—41no—
70#63225—82no—
71#63214—42no—
72#12289—171nomaximal, Sylow
73C23×C17C2×D811yescharacteristic
74Q8×C17—42no—
75Q8×C17—42no—
76Q8×C17—82no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—41no—
83C2×C4×C17—42no—
84C2×C4×C17—42no—
85C2×C4×C17SD3212yes—
86C2×C4×C17#12011yescharacteristic
87C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
88C2×Dic17—42no—
89C2×Dic17—81no—
90C2×Dic17—81no—
91C2×Dic17—81no—
92C2×Dic17—81no—
93C2×Dic17—81no—
94C8×C17—22no—
95C8×C17—41no—
96#3249D1711yescharacteristic
97#2235—172no—
98#2086—171no—
99#1348—172no—
100#1322—171no—
101C22×C17—21no—
102C22×C17—21no—
103C22×C17#44711yescharacteristic
104C22×C17C2×SD3211yescharacteristic
105C22×C17#51011yescharacteristic
106C4×C17—21no—
107C4×C17—22no—
108C4×C17—41no—
109C4×C17—82no—
110C4×C17—82no—
111C4×C17#45611yescharacteristic
112C4×C17#45811yescharacteristic
113Dic17—82no—
114Dic17—161no—
115#533—21no—
116#477—22no—
117#467—21no—
118#467C2×D1712yes—
119#462—22no—
120C2×#107—171no—
121C2×C4⋊C8C2×D1711yescharacteristic
122#389—341no—
123#367—342no—
124#358—342no—
125C22⋊C16—172no—
126#340—171no—
127#340—341no—
128C2×C17—21no—
129C2×C17—21no—
130C2×C17#161011yescharacteristic
131C2×C17#218511yescharacteristic
132C2×C17#219111yescharacteristic
133C2×Q16—21no—
134C2×Q16C22⋊D1712yes—
135C22×C8C22⋊D1711yescharacteristic
136C22×C8C22×D1711yescharacteristic
137C4⋊Q8—21no—
138C4⋊Q8—21no—
139#125—41no—
140C22⋊Q8—22no—
141C22⋊Q8—41no—
142C4×Q8—22no—
143C4×Q8—41no—
144#117—41no—
145C2×C4⋊C4—341no—
146C2×C4⋊C4—341no—
147C2×C4⋊C4—681no—
148C2×C42C22⋊D1711yescharacteristic
149C2×C16—342no—
150#107—21no—
151#107—342no—
152#107C22⋊D1712yes—
153C4⋊C8—22no—
154#103—22no—
155#103—22no—
156#95—681no—
157C17#1228911yescharacteristic, complemented, Sylow
158C2×Q8—22no—
159C2×Q8—41no—
160C22×C4—681no—
161C22×C4—681no—
162C22×C4#6322811yescharacteristic
163C22×C4#6322811yescharacteristic
164C22×C4C2×C22⋊D1711yescharacteristic
165Q16—42no—
166Q16—81no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8C2×C22⋊D1712yes—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—41no—
176C4⋊C4—42no—
177C4⋊C4—342no—
178C4⋊C4—681no—
179C4⋊C4—681no—
180C4⋊C4—681no—
181C4⋊C4—1362no—
182C22⋊C4—42no—
183C42—21no—
184C42—21no—
185C42—42no—
186C16—682no—
187C23C2×#6322811yescharacteristic
188Q8—42no—
189Q8—42no—
190Q8—82no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—682no—
200C2×C4—1361no—
201C2×C4—1361no—
202C2×C4—1361no—
203C2×C4—1361no—
204C2×C4—1361no—
205C2×C4#1058749912yes—
206C2×C4#1058761811yescharacteristic
207C2×C4#1058763911yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1176294311yescharacteristic
213C22C2×#1058749911yescharacteristic
214C22#1176325011yescharacteristic
215C4—21no—
216C4—22no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—2721no—
221C4—1362no—
222C4#1176299211yescharacteristic
223C4#1176299911yescharacteristic
224C2—21no—
225C2—21no—
226C2#1452778711yescharacteristic
227C2#1453070111yescharacteristic
228C2#1453073511yescharacteristic
subgroupG/H
centerC22#11762943
commutator, cosocleC22×C8×C17C23
FrattiniC22×C8C22×D17
FittingC17×#3249C2
socleC22×C17#447
prime radicalC23×C17C2×D8
hypercenter#3249D17
hypocenterC17#12289
LCSG ▷ C22×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #3249

Complements

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

NH ≅ G/Ntype
157. C17#12289semidirect

Maximal subgroups

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

subgroupindex
#145309792
#145302722
#145267962
#145267242
C17×#32492
#1228917