Finite Group Databasebeta

← #17949059

Subgroups — #17949059

Order 4352.

342 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 56 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#14544644C211yesmaximal, characteristic
2#14544043C211yesmaximal, characteristic
3#14529081C211yesmaximal, characteristic
4#11763830—21no—
5C2×#10587551C412yes—
6#11763751—21no—
7#11763687—21no—
8#11763653—21no—
9#11763652C412yescomplemented
10C2×C4×C22⋊D17C2211yescharacteristic
11C2×C22⋊#3622C411yescharacteristic, complemented
12C2×#10587491—21no—
13#11762563—21no—
14C22×M16×C17C411yescharacteristic, complemented
15C23×C4×C17C2×C411yescharacteristic
16C22×C22⋊D17C2×C411yescharacteristic
17C22×C4×D17D411yescharacteristic
18C2×C22⋊#595—22no—
19C2×C4⋊#595—41no—
20C2×M16×C17—42no—
21C2×M16×C17—41no—
22C22×C8×C17—21no—
23C2×C22⋊Dic17C2×C411yescharacteristic
24C4×C22⋊D17—41no—
25C4×C22⋊D17—41no—
26C2×#63227D411yescharacteristic
27C2×#63225Q811yescharacteristic
28C2×C4×Dic17D411yescharacteristic
29C22×#3622—21no—
30C22⋊#3624—22no—
31#10587551—42no—
32(C2×#595)⋊C4—41no—
33#10587542—41no—
34C4⋊#3624—41no—
35C22⋊#3622—41no—
36#10587491—42no—
37C24×C17C4211yescharacteristic
38C23×D17C22⋊C411yescharacteristic
39C22×#595—42no—
40C22×C4×C17—21no—
41C22×C4×C17—21no—
42C22×C4×C17—41no—
43C22×C4×C17—41no—
44C22×C4×C17C22⋊C411yescharacteristic
45C22×C4×C17C4⋊C411yescharacteristic
46C2×C22⋊D17—21no—
47C2×C22⋊D17—21no—
48C2×C22⋊D17—41no—
49C2×C22⋊D17—41no—
50C22×Dic17C22⋊C411yescharacteristic
51C22×Dic17C4⋊C411yescharacteristic
52C22×Dic17C4⋊C411yescharacteristic
53C2×C4×D17—21no—
54C2×C4×D17—21no—
55C2×C4×D17—41no—
56C2×C4×D17—41no—
57C22⋊#595—42no—
58C22⋊#595—42no—
59C2×#3624—42no—
60C4⋊#595—81no—
61C4⋊#595—81no—
62M16×C17—42no—
63M16×C17—42no—
64C2×C8×C17—22no—
65C2×C8×C17—41no—
66C2×C8×C17—41no—
67C22⋊Dic17—41no—
68#63227—41no—
69#63225—41no—
70C4×Dic17—21no—
71C4×Dic17—21no—
72C2×#3622—41no—
73C2×#3622—41no—
74C2×#3622—41no—
75#7320—171nomaximal, Sylow
76C23×C17—21no—
77C23×C17—21no—
78C23×C17—21no—
79C23×C17—41no—
80C23×C17—41no—
81C23×C17#9511yescharacteristic
82C22×D17—21no—
83C22×D17—21no—
84C22×D17—41no—
85C22×D17—41no—
86C22×D17#10011yescharacteristic
87C22×D17#10111yescharacteristic
88C2×#595—82no—
89C2×#595—82no—
90C2×#595—82no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—42no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17#9911yescharacteristic
99C2×C4×C17#9911yescharacteristic
100C22⋊D17—42no—
101C22⋊D17—42no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—41no—
108C2×Dic17—41no—
109C4×D17—41no—
110C4×D17—41no—
111C4×D17—81no—
112#3624—82no—
113C8×C17—42no—
114#3622—81no—
115#1870—171no—
116#1799—171no—
117#1466—171no—
118C22×C17—21no—
119C22×C17—21no—
120C22×C17—41no—
121C22×C17—41no—
122C22×C17—41no—
123C22×C17—81no—
124C22×C17—81no—
125C22×C17#34211yescharacteristic
126C22×C17#34311yescharacteristic
127C22×C17#34411yescharacteristic
128C2×D17—21no—
129C2×D17—21no—
130C2×D17—41no—
131C2×D17—41no—
132C2×D17—41no—
133C2×D17—41no—
134C2×D17—81no—
135#595—162no—
136C4×C17—21no—
137C4×C17—41no—
138C4×C17AΣL(1,𝔽16)11yescharacteristic
139C4×C17#35211yescharacteristic
140Dic17—41no—
141Dic17—41no—
142Dic17—41no—
143C22×M16#59511yescharacteristic, complemented
144C2×C4×D4—171no—
145#432—341no—
146C2×#99—172no—
147C2×C22⋊C8—171no—
148C2×C22⋊C8—341no—
149#380—341no—
150#342—341no—
151#336—341no—
152#323—172no—
153#323—341no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17—81no—
157C2×C17#130511yescharacteristic
158C2×C17#139011yescharacteristic
159C2×C17#139111yescharacteristic
160D17—41no—
161D17—41no—
162C22×D4—171no—
163C23×C4—171no—
164C23×C4C2×#59511yescharacteristic
165C2×M16—42no—
166C2×M16—41no—
167C22×C8—21no—
168C22×C8—341no—
169C4×D4—681no—
170C4×D4—681no—
171C2×C4⋊C4—171no—
172C2×C4⋊C4—681no—
173C2×C22⋊C4—171no—
174C2×C22⋊C4—171no—
175C2×C22⋊C4—342no—
176C2×C42—171no—
177C4⋊C8—681no—
178#99—682no—
179C22⋊C8—342no—
180C22⋊C8—682no—
181C22⋊C8—681no—
182#97—681no—
183#95—681no—
184C17#732011yescharacteristic, complemented, Sylow
185C24—171no—
186C24C4×#59511yescharacteristic
187C2×D4—341no—
188C2×D4—341no—
189C2×D4—681no—
190C2×D4—681no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—171no—
196C22×C4—171no—
197C22×C4—171no—
198C22×C4—341no—
199C22×C4—341no—
200C22×C4—681no—
201C22×C4—681no—
202C22×C4—682no—
203C22×C4C4⋊#59511yescharacteristic
204C22×C4C22⋊#59511yescharacteristic
205M16—42no—
206M16—42no—
207C2×C8—22no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—681no—
211C2×C8—681no—
212C2×C8—682no—
213C2×C8—681no—
214C4⋊C4—681no—
215C4⋊C4—1361no—
216C4⋊C4—1361no—
217C22⋊C4—681no—
218C22⋊C4—681no—
219C22⋊C4—682no—
220C22⋊C4—682no—
221C42—341no—
222C42—341no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23—171no—
229C23—171no—
230C23—341no—
231C23—341no—
232C23—681no—
233C23—681no—
234C23(C2×#595)⋊C411yescharacteristic
235D4—682no—
236D4—682no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—341no—
245C2×C4—341no—
246C2×C4—341no—
247C2×C4—341no—
248C2×C4—341no—
249C2×C4—681no—
250C2×C4—681no—
251C2×C4—681no—
252C2×C4—681no—
253C2×C4—1361no—
254C2×C4—1362no—
255C2×C4—1362no—
256C2×C4—1362no—
257C2×C4#1058753911yescharacteristic
258C2×C4#1058755111yescharacteristic
259C8—42no—
260C8—1361no—
261C8—1362no—
262C22—21no—
263C22—21no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22—81no—
268C22—81no—
269C22—341no—
270C22—341no—
271C22—681no—
272C22—681no—
273C22—681no—
274C22—681no—
275C22—1361no—
276C22#1176368711yescharacteristic
277C22#1176368811yescharacteristic
278C22#1176369211yescharacteristic
279C4—21no—
280C4—41no—
281C4—2722no—
282C4—681no—
283C4—681no—
284C4—681no—
285C4#1176370911yescharacteristic
286C4#1176371111yescharacteristic
287C2—21no—
288C2—21no—
289C2—81no—
290C2—681no—
291C2—681no—
292C2#1454368411yescharacteristic
293C2#1454386811yescharacteristic
294C2#1454387311yescharacteristic
subgroupG/H
centerC22#11763687
commutatorC24×C17C42
FrattiniC23×C4C2×#595
FittingC22×M16×C17C4
socleC22×C17#342
prime radicalC22×C22⋊D17C2×C4
cosocleC2×C4×C22⋊D17C22
hypercenterC22×M16#595
hypocenterC17#7320
LCSG ▷ C24×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
9. #11763652C4semidirect
11. C2×C22⋊#3622C4semidirect
14. C22×M16×C17C4semidirect
143. C22×M16#595semidirect
184. C17#7320semidirect

Maximal subgroups

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

subgroupindex
#145446442
#145440432
#145290812
#732017