Finite Group Databasebeta

← #17958306

Subgroups — #17958306

Order 4352.

460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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#14544027C212yesmaximal, complemented
2#14543725C212yesmaximal, complemented
3#14543713C212yesmaximal
4#14531327C211yesmaximal, characteristic
5#11763825—22no—
6#11763654—22no—
7#11763654C2214yes—
8C2×#10587633C411yescharacteristic
9C2×Q8×Dic17C2211yescharacteristic
10C2×#10587579C411yescharacteristic
11#11762711C2211yescharacteristic
12#11762701—22no—
13#11762674C2211yescharacteristic
14#11762656—22no—
15C42×Dic17C411yescharacteristic
16C17×#391C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C22×D68C2×C411yescharacteristic
19C22×C4×D17—21no—
20C2×C4⋊C4×C17C2×C411yescharacteristic
21C2×C42×C17C2×C411yescharacteristic
22#10587633—22no—
23#10587633C814yescomplemented
24Q8×Dic17—41no—
25Q8×Dic17—41no—
26C2×#63227—22no—
27C2×#63227—21no—
28C2×#63227—22no—
29C2×C4⋊Dic17D412yes—
30C2×C4⋊Dic17C2311yescharacteristic
31C2×C4×Dic17—21no—
32C2×C4×Dic17—21no—
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17C2×C411yescharacteristic
35C2×C4×Dic17D412yes—
36#10587579—41no—
37#10587579—41no—
38C22⋊#3624—24no—
39C4⋊#3624—42no—
40C4×#3624—42no—
41C17×#95—22no—
42#10587502—22no—
43C23×D17—21no—
44C2×Q8×C17—41no—
45C2×Q8×C17—41no—
46C2×Q8×C17C2×C812yes—
47C2×Q8×C17M1612yes—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17C22⋊C412yes—
51C22×C4×C17C22×C411yescharacteristic
52C22×Dic17—21no—
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D412yes—
56C2×D68—21no—
57C2×D68—41no—
58C2×D68—41no—
59C2×D68C2×C812yes—
60C2×C4×D17—44no—
61C2×C4×D17—41no—
62C2×C4×D17—41no—
63C2×#3624—44no—
64C4⋊C4×C17—41no—
65C42×C17—41no—
66#63227—28no—
67#63227—42no—
68#63227—44no—
69C4⋊Dic17—42no—
70C4⋊Dic17—41no—
71C4×Dic17—21no—
72C4×Dic17—22no—
73C4×Dic17—22no—
74C4×Dic17—21no—
75C4×Dic17—21no—
76C4×Dic17—42no—
77C4×Dic17—42no—
78C4×Dic17C2×C812yes—
79#11476—171nomaximal, Sylow
80C23×C17C2×C22⋊C411yescharacteristic
81C22×D17—22no—
82C22×D17—42no—
83C22×D17—42no—
84C22×D17—41no—
85C22×D17—41no—
86Q8×C17—42no—
87Q8×C17—42no—
88C2×C4×C17—21no—
89C2×C4×C17—22no—
90C2×C4×C17—21no—
91C2×C4×C17—22no—
92C2×C4×C17—22no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—42no—
96C2×C4×C17—41no—
97C2×C4×C17C22⋊C814yes—
98C2×C4×C17C22×C811yescharacteristic
99C2×C4×C17C2×M1611yescharacteristic
100C2×Dic17—22no—
101C2×Dic17—22no—
102C2×Dic17—22no—
103C2×Dic17—21no—
104C2×Dic17—41no—
105C2×Dic17—41no—
106C2×Dic17—41no—
107C2×Dic17—42no—
108C2×Dic17#9911yescharacteristic
109C2×Dic17#9911yescharacteristic
110D68—42no—
111D68—42no—
112C4×D17—82no—
113C4×D17—82no—
114#3624—84no—
115C4×#124—171no—
116#1461—172no—
117#1324—172no—
118#1318—172no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17C2×C22⋊C811yescharacteristic
122C22×C17C2×#9911yescharacteristic
123C22×C17#41311yescharacteristic
124C2×D17—44no—
125C2×D17—42no—
126C2×D17—82no—
127C2×D17—81no—
128C2×D17—81no—
129C4×C17—21no—
130C4×C17—21no—
131C4×C17—24no—
132C4×C17—42no—
133C4×C17—81no—
134Dic17—21no—
135Dic17—42no—
136Dic17—42no—
137Dic17—41no—
138Dic17#35512yes—
139C2×#124—171no—
140C2×C4×Q8—171no—
141C2×C4×D4—171no—
142#431—342no—
143#391#59511yescharacteristic
144#390—171no—
145#388—342no—
146#382—171no—
147C4×C22⋊C4—342no—
148C43—171no—
149#324—174no—
150#324—342no—
151C2×C17—21no—
152C2×C17—21no—
153C2×C17#145911yescharacteristic
154C2×C17#212611yescharacteristic
155C2×C17C2×#35511yescharacteristic
156D17—82no—
157C22×Q8C2×#59511yescharacteristic
158C22×D4—171no—
159C23×C4—341no—
160#124—174no—
161#124—342no—
162C4×Q8—681no—
163C4×Q8—681no—
164C4×D4—681no—
165C4×D4—681no—
166C2×C4⋊C4—172no—
167C2×C4⋊C4—171no—
168C2×C4⋊C4C2×#59511yescharacteristic
169C2×C22⋊C4—342no—
170C2×C22⋊C4—341no—
171C2×C22⋊C4—342no—
172C2×C42—171no—
173C2×C42—172no—
174C2×C42—171no—
175C2×C42—341no—
176C2×C42—341no—
177C2×C42C2×#59511yescharacteristic
178C4⋊C8—682no—
179C22⋊C8—344no—
180C4×C8—682no—
181#95—22no—
182#95—342no—
183C17#1147611yescharacteristic, complemented, Sylow
184C24—341no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8#6324212yes—
188C2×Q8#6324312yes—
189C2×D4—172no—
190C2×D4—341no—
191C2×D4—681no—
192C2×D4—681no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—171no—
196C22×C4—171no—
197C22×C4—172no—
198C22×C4—341no—
199C22×C4—681no—
200C22×C4—681no—
201C22×C4—684no—
202C22×C4C22⋊#59512yes—
203C22×C4C22×#59511yescharacteristic
204C2×C8—684no—
205C4⋊C4—41no—
206C4⋊C4—681no—
207C4⋊C4—682no—
208C22⋊C4—348no—
209C22⋊C4—684no—
210C22⋊C4—682no—
211C42—41no—
212C42—172no—
213C42—342no—
214C42—342no—
215C42—341no—
216C42—341no—
217C42—341no—
218C42—682no—
219C42—682no—
220C23—342no—
221C23—682no—
222C23—682no—
223C23—681no—
224C23—681no—
225C23C2×C22⋊#59511yescharacteristic
226Q8—42no—
227Q8—42no—
228D4—682no—
229D4—682no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—171no—
240C2×C4—171no—
241C2×C4—342no—
242C2×C4—342no—
243C2×C4—341no—
244C2×C4—342no—
245C2×C4—681no—
246C2×C4—681no—
247C2×C4—681no—
248C2×C4—682no—
249C2×C4—1362no—
250C2×C4—1362no—
251C2×C4#1058754314yes—
252C2×C4C2×#6324211yescharacteristic
253C2×C4C2×#6324311yescharacteristic
254C8—1364no—
255C22—21no—
256C22—21no—
257C22—684no—
258C22—682no—
259C22—1362no—
260C22—1361no—
261C22—1361no—
262C22C2×#1058754311yescharacteristic
263C22D17⋊#9911yescharacteristic
264C22#1176379611yescharacteristic
265C4—21no—
266C4—21no—
267C4—24no—
268C4—42no—
269C4—81no—
270C4—172no—
271C4—341no—
272C4—682no—
273C4—682no—
274C4—681no—
275C2—21no—
276C2—21no—
277C2—1362no—
278C2#1454402211yescharacteristic
279C2#1454505811yescharacteristic
280C2D17⋊#35511yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC22×C17C2×#99
prime radicalC22×D68C2×C4
cosocleC2×C4⋊Dic17C23
hypercenter#391#595
hypocenterC17#11476
LCSG ▷ C2×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
1. #14544027C2semidirect
2. #14543725C2semidirect
23. #10587633C8semidirect
183. C17#11476semidirect

Maximal subgroups

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

subgroupindex
#145440272
#145437252
#145437132
#145313272
#1147617