Finite Group Databasebeta

← #17958648

Subgroups — #17958648

Order 4352.

350 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 70 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#14544047C211yesmaximal, characteristic
2#14544027C211yesmaximal, characteristic
3#14543726C212yesmaximal
4#14543725C212yesmaximal
5#14533977C211yesmaximal, characteristic
6#11763829—21no—
7#11763825—21no—
8#11763654—21no—
9#11763654—21no—
10#11763654C2212yes—
11#11763654C2212yes—
12C2×#10587576C411yescharacteristic
13C2×Q8×Dic17C2211yescharacteristic
14#11762741—21no—
15#11762741—21no—
16#11762716C411yescharacteristic
17#11762692—21no—
18#11762692—21no—
19#11762679C2211yescharacteristic
20#11762674C2211yescharacteristic
21C4×#63225C411yescharacteristic
22C17×#391C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C2×C4⋊C4×C17C2×C411yescharacteristic
25C2×C42×C17C2×C411yescharacteristic
26Q8×Dic17—41no—
27Q8×Dic17—41no—
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×C4⋊Dic17D411yescharacteristic
33C2×C4⋊Dic17D411yescharacteristic
34C2×C4⋊Dic17C2311yescharacteristic
35C2×#63225—21no—
36C2×#63225—21no—
37C2×C4×Dic17C2×C411yescharacteristic
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41#10587576—41no—
42#10587576—41no—
43C22⋊#3624—22no—
44C22⋊#3624—22no—
45#10587544—41no—
46#10587542—41no—
47C4⋊#3624—41no—
48C4×#3624—41no—
49C17×#95—21no—
50C17×#95—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56C2×Q8×C17—22no—
57C2×Q8×C17—22no—
58C2×Q8×C17—41no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22×C411yescharacteristic
64C22×Dic17—21no—
65C22×Dic17—21no—
66C22×Dic17C22⋊C411yescharacteristic
67C22×Dic17C22⋊C411yescharacteristic
68C22×Dic17C2×D411yescharacteristic
69C22×Dic17C2×D411yescharacteristic
70C2×#3624—42no—
71C2×#3624—42no—
72C4⋊C4×C17—41no—
73C42×C17—22no—
74C4⋊Dic17—41no—
75C4⋊Dic17—41no—
76C4⋊Dic17—41no—
77C4⋊Dic17—42no—
78C4⋊Dic17—42no—
79C4⋊Dic17—42no—
80C4⋊Dic17—41no—
81#63225—42no—
82#63225—41no—
83#63225—41no—
84C4×Dic17—21no—
85C4×Dic17—21no—
86C4×Dic17—21no—
87C4×Dic17—21no—
88C4×Dic17—21no—
89C4×Dic17—21no—
90C4×Dic17—22no—
91#11571—171nomaximal, Sylow
92C23×C17C2×C22⋊C411yescharacteristic
93Q8×C17—44no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—22no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—42no—
105C2×C4×C17—41no—
106C2×C4×C17#10112yes—
107C2×C4×C17#13112yes—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17#9911yescharacteristic
122C2×Dic17#9911yescharacteristic
123#3624—82no—
124#3624—82no—
125#2565—171no—
126#1467—171no—
127#1461—171no—
128#1325—172no—
129#1324—172no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17#40811yescharacteristic
133C22×C17C2×#9911yescharacteristic
134C22×C17C2×#10111yescharacteristic
135C4×C17—22no—
136C4×C17—22no—
137C4×C17—42no—
138C4×C17—41no—
139C4×C17—81no—
140Dic17—21no—
141Dic17—21no—
142Dic17—41no—
143Dic17—41no—
144Dic17—41no—
145Dic17—81no—
146Dic17—81no—
147C2×#125—171no—
148C2×C4×Q8—171no—
149#432—341no—
150#431—341no—
151#398—341no—
152#398—341no—
153#391—171no—
154#391#59511yescharacteristic
155#387—341no—
156#387—341no—
157#384—171no—
158#382—171no—
159C4×C4⋊C4—171no—
160#324—172no—
161#324—172no—
162#324—341no—
163#324—341no—
164C2×C17—21no—
165C2×C17—21no—
166C2×C17#147211yescharacteristic
167C2×C17#212611yescharacteristic
168C2×C17#213311yescharacteristic
169C22×Q8C2×#59511yescharacteristic
170#125—681no—
171#125—681no—
172C4×Q8—681no—
173C4×Q8—681no—
174C2×C4⋊C4—171no—
175C2×C4⋊C4—171no—
176C2×C4⋊C4—171no—
177C2×C4⋊C4—171no—
178C2×C4⋊C4—341no—
179C2×C4⋊C4—341no—
180C2×C4⋊C4—341no—
181C2×C4⋊C4—341no—
182C2×C4⋊C4—341no—
183C2×C4⋊C4C2×#59511yescharacteristic
184C2×C42—171no—
185C2×C42—171no—
186C2×C42—171no—
187C2×C42—171no—
188C2×C42C2×#59511yescharacteristic
189C4⋊C8—681no—
190C4⋊C8—681no—
191C22⋊C8—342no—
192C22⋊C8—342no—
193#97—681no—
194C4×C8—681no—
195#95—21no—
196#95—21no—
197#95—341no—
198#95—341no—
199#95—341no—
200#95—341no—
201#95—341no—
202C17#1157111yescharacteristic, complemented, Sylow
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—171no—
209C22×C4—171no—
210C22×C4—171no—
211C22×C4—171no—
212C22×C4—341no—
213C22×C4—341no—
214C22×C4C22⋊#59511yescharacteristic
215C22×C4C22⋊#59511yescharacteristic
216C22×C4C22×#59511yescharacteristic
217C2×C8—682no—
218C2×C8—682no—
219C4⋊C4—41no—
220C4⋊C4—681no—
221C4⋊C4—681no—
222C4⋊C4—681no—
223C4⋊C4—681no—
224C4⋊C4—682no—
225C4⋊C4—682no—
226C4⋊C4—682no—
227C4⋊C4—681no—
228C4⋊C4—681no—
229C4⋊C4—682no—
230C42—22no—
231C42—341no—
232C42—341no—
233C42—341no—
234C42—341no—
235C42—341no—
236C42—341no—
237C42—342no—
238C23C2×C22⋊#59511yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—171no—
253C2×C4—171no—
254C2×C4—341no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—681no—
258C2×C4—681no—
259C2×C4—681no—
260C2×C4—681no—
261C2×C4—681no—
262C2×C4—681no—
263C2×C4—681no—
264C2×C4—681no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4#1058754512yes—
268C2×C4#1058767812yes—
269C8—1362no—
270C8—1362no—
271C22—21no—
272C22—21no—
273C22#1176378211yescharacteristic
274C22D17⋊#9911yescharacteristic
275C22C2×#1058754511yescharacteristic
276C4—22no—
277C4—22no—
278C4—42no—
279C4—41no—
280C4—81no—
281C4—341no—
282C4—341no—
283C4—681no—
284C4—681no—
285C4—681no—
286C4—1361no—
287C4—1361no—
288C2—21no—
289C2—21no—
290C2#1454406311yescharacteristic
291C2#1454505811yescharacteristic
292C2#1454508011yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenter#391#595
hypocenterC17#11571
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
202. C17#11571semidirect

Maximal subgroups

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

subgroupindex
#145440472
#145440272
#145437262
#145437252
#145339772
#1157117