Finite Group Databasebeta

← #16945849

Subgroups — #16945849

Order 4352.

280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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#14539412C211yesmaximal, characteristic
2#14530600C211yesmaximal, characteristic, complemented
3#14526844C212yesmaximal, complemented
4#14526824C212yesmaximal, complemented
5C17×#2153C211yesmaximal, characteristic, complemented
6#11763421C411yescharacteristic
7#11763414C411yescharacteristic
8#11763211C2211yescharacteristic
9#11763182C2211yescharacteristic
10#11763178C411yescharacteristic
11#11763174C411yescharacteristic
12#11763055—21no—
13#11763038—21no—
14#11762911—21no—
15C4×#63219—21no—
16#11762630C2212yes—
17#11762591—21no—
18#11762587—21no—
19C2×C17×M32—21no—
20C17×#405C2211yescharacteristic
21C17×#364—21no—
22C17×#364C2212yes—
23C2×M16×C17D411yescharacteristic
24C22×C8×C17D411yescharacteristic
25C17×#117C2×C411yescharacteristic
26#10587616—21no—
27#10587610—21no—
28C2×#63219—21no—
29C2×#63219—21no—
30#10587580—41no—
31#10587575—41no—
32#10587570—41no—
33#10587565—41no—
34#10587560C2×C411yescharacteristic
35C4×D68—21no—
36#10587556C2×C411yescharacteristic
37#10587556C2×C411yescharacteristic
38#10587555C2×C411yescharacteristic
39C4×Dic34—21no—
40C17×M32—22no—
41C17×M32—41no—
42C2×C16×C17—41no—
43C17×#97C2×C411yescharacteristic
44C17×#97D411yescharacteristic
45C4×C8×C17D411yescharacteristic
46C4×C8×C17C2311yescharacteristic
47#10587492—21no—
48#10587492—21no—
49#10587489—21no—
50#10587488—21no—
51#10587487—21no—
52#10587487—21no—
53#10587483—22no—
54C22×C4×C17C22⋊C411yescharacteristic
55C2×C22⋊D17—41no—
56C2×D68—21no—
57C2×D68—41no—
58C2×C4×D17—41no—
59C2×Dic34—21no—
60M16×C17—22no—
61C2×C8×C17—21no—
62C2×C8×C17—21no—
63C2×C8×C17C22⋊C411yescharacteristic
64C2×C8×C17C22⋊C411yescharacteristic
65C2×C8×C17C2×D411yescharacteristic
66C2×C8×C17C2×D411yescharacteristic
67C4⋊C4×C17—21no—
68C22⋊C4×C17—21no—
69C42×C17C22⋊C411yescharacteristic
70C42×C17C22×C411yescharacteristic
71C22⋊Dic17—41no—
72#63227—41no—
73#63227—41no—
74C4⋊Dic17—21no—
75C4⋊Dic17—21no—
76C4⋊Dic17—41no—
77#63225—41no—
78#63225—41no—
79#63225—41no—
80#63225—41no—
81C4×Dic17—41no—
82#63219—42no—
83#63219—41no—
84#63219—41no—
85C16×C17—42no—
86#63214—42no—
87#11991—171nomaximal, Sylow
88C23×C17#10011yescharacteristic
89C22×D17—41no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17#10011yescharacteristic
95C2×C4×C17C2×C22⋊C411yescharacteristic
96C22⋊D17—161no—
97C2×Dic17—41no—
98C2×Dic17—41no—
99C2×Dic17—41no—
100D68—41no—
101D68—41no—
102D68—161no—
103C4×D17—161no—
104Dic34—41no—
105Dic34—41no—
106C8×C17—21no—
107C8×C17—21no—
108C8×C17#13512yes—
109C8×C17AGL(1,ℤ/8)11yescharacteristic
110C8×C17#13711yescharacteristic
111#3174—171no—
112#2166—171no—
113#2153D1711yescharacteristic, complemented
114#1366—172no—
115#1359—172no—
116C22×C17—21no—
117C22×C17—41no—
118C22×C17C2×#10011yescharacteristic
119C2×D17—81no—
120C2×D17—81no—
121C2×D17—81no—
122C4×C17—21no—
123C4×C17—41no—
124C4×C17—41no—
125C4×C17#41611yescharacteristic
126C4×C17#41711yescharacteristic
127Dic17—81no—
128Dic17—81no—
129Dic17—81no—
130#541—171no—
131#540—171no—
132C2×M32—21no—
133#499—171no—
134#492—171no—
135#491—171no—
136#490—171no—
137#468—341no—
138#465—341no—
139#440—341no—
140C4×SD16—341no—
141#405C2×D1711yescharacteristic
142#364—21no—
143#364—172no—
144#364C2×D1712yes—
145#349—341no—
146#347—341no—
147C2×C17—21no—
148C2×C17—41no—
149C2×C17#155111yescharacteristic
150D17—161no—
151C2×SD16—341no—
152C2×SD16—341no—
153C2×M16D6811yescharacteristic
154C22×C8C22⋊D1711yescharacteristic
155C4⋊Q8—171no—
156#127—171no—
157#126—681no—
158#125—171no—
159#125—171no—
160#125—681no—
161#123—681no—
162C22⋊Q8—341no—
163#121—341no—
164#121—681no—
165C4×Q8—341no—
166C4×D4—341no—
167#117C4×D1711yescharacteristic
168M32—22no—
169M32—41no—
170M32—342no—
171C2×C16—41no—
172#107—341no—
173#106—341no—
174#103—341no—
175#103—341no—
176#102—341no—
177#102—341no—
178#97C4×D1711yescharacteristic
179#97D6811yescharacteristic
180C4×C8C22⋊D1711yescharacteristic
181C4×C8C22×D1711yescharacteristic
182C17#1199111yescharacteristic, complemented, Sylow
183C2×Q8—341no—
184C2×D4—341no—
185C2×D4—681no—
186C2×D4—681no—
187C22×C4—681no—
188C22×C4#6322711yescharacteristic
189SD16—682no—
190SD16—681no—
191SD16—681no—
192M16—22no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8#6322711yescharacteristic
196C2×C8#6322711yescharacteristic
197C2×C8C2×D6811yescharacteristic
198C2×C8C2×C22⋊D1711yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—341no—
201C4⋊C4—341no—
202C4⋊C4—681no—
203C4⋊C4—681no—
204C4⋊C4—681no—
205C4⋊C4—681no—
206C4⋊C4—681no—
207C22⋊C4—21no—
208C22⋊C4—681no—
209C22⋊C4—681no—
210C22⋊C4—681no—
211C42—681no—
212C42#6322711yescharacteristic
213C42C2×C4×D1711yescharacteristic
214C16—42no—
215C16—682no—
216C23—681no—
217C23#1058749411yescharacteristic
218Q8—681no—
219Q8—681no—
220D4—2721no—
221D4—2721no—
222D4—681no—
223D4—681no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—2721no—
229C2×C4—681no—
230C2×C4—681no—
231C2×C4—681no—
232C2×C4#1058749411yescharacteristic
233C2×C4C2×#6322711yescharacteristic
234C8—21no—
235C8—21no—
236C8#1058759012yes—
237C8#1058761811yescharacteristic
238C8#1058762811yescharacteristic
239C22—21no—
240C22—41no—
241C22—1361no—
242C22—1361no—
243C22—1361no—
244C22C2×#1058749411yescharacteristic
245C4—21no—
246C4—41no—
247C4—41no—
248C4—1361no—
249C4—1361no—
250C4—1361no—
251C4#1176280611yescharacteristic
252C4#1176280811yescharacteristic
253C2—21no—
254C2—41no—
255C2—2721no—
256C2#1452747711yescharacteristic
subgroupG/H
centerC2#14527477
commutatorC42×C17C22×C4
FrattiniC4×C8C22×D17
FittingC17×#2153C2
socleC2×C17#1551
prime radical#11763414C4
cosocleC4×C8×C17C23
hypercenter#2153D17
hypocenterC17#11991
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2153

Complements

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

NH ≅ G/Ntype
2. #14530600C2semidirect
3. #14526844C2semidirect
4. #14526824C2semidirect
5. C17×#2153C2semidirect
113. #2153D17semidirect
182. C17#11991semidirect

Maximal subgroups

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

subgroupindex
#145394122
#145306002
#145268442
#145268242
C17×#21532
#1199117