Finite Group Databasebeta

← #17961435

Subgroups — #17961435

Order 4352.

480 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×#11763718C212yesmaximal
2#14544650C212yesmaximal, complemented
3#14543881C212yesmaximal, complemented
4#14531495C211yesmaximal, characteristic
5#11763812—22no—
6C2×#10587545C2214yes—
7#11763718—24no—
8#11763689—22no—
9C2×#10587561C2211yescharacteristic
10C2×C4×Dic34C2211yescharacteristic
11C2×C4×D68C411yescharacteristic
12#11762715C2211yescharacteristic
13#11762711C411yescharacteristic
14#11762701—22no—
15#11762683—22no—
16#11762679C411yescharacteristic
17C17×#376C411yescharacteristic
18C22×D68C2×C411yescharacteristic
19C22×C4×D17—21no—
20C22×Dic34C2311yescharacteristic
21C2×#63247—24no—
22C2×C42×C17C2×C411yescharacteristic
23C2×C42×C17C2×C411yescharacteristic
24C2×C42×C17C2×C411yescharacteristic
25C2×#63227—21no—
26C2×#63227—22no—
27C2×#63227—22no—
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17C2×C411yescharacteristic
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×#63225D412yes—
32C2×C4×Dic17D412yes—
33#10587561—22no—
34#10587561D412yes—
35#10587561Q812yes—
36C4×D68—42no—
37C4×Dic34—42no—
38#10587545—24no—
39#10587545—24no—
40#10587544—42no—
41C4⋊#3624—42no—
42C17×#95—21no—
43C17×#95—21no—
44#10587502—22no—
45C23×D17—21no—
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—21no—
52C22×Dic17C22⋊C412yes—
53C22×Dic17C2×D412yes—
54C2×D68—21no—
55C2×D68—41no—
56C2×D68—41no—
57C2×D68C4⋊C412yes—
58C2×C4×D17—42no—
59C2×C4×D17—82no—
60C2×Dic34—41no—
61C2×Dic34—41no—
62C2×Dic34C2×D411yescharacteristic
63C2×Dic34C2×Q811yescharacteristic
64C2×Dic34#4112yes—
65#63247—44no—
66#63247—44no—
67C2×#3624—44no—
68C42×C17—22no—
69C42×C17—21no—
70C42×C17—41no—
71C42×C17C4⋊C412yes—
72#63227—24no—
73#63227—24no—
74#63227—42no—
75#63227—82no—
76C4⋊Dic17—41no—
77C4⋊Dic17—41no—
78C4⋊Dic17—82no—
79#63225—42no—
80C4×Dic17—22no—
81C4×Dic17—22no—
82#12803—171nomaximal, Sylow
83C23×C17C2×C22⋊C411yescharacteristic
84C22×D17—22no—
85C22×D17—42no—
86C22×D17—42no—
87C22×D17—41no—
88C22×D17—41no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—22no—
92C2×C4×C17—21no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17#9912yes—
101C2×C4×C17C2×C4⋊C411yescharacteristic
102C2×C4×C17#11711yescharacteristic
103C2×Dic17—22no—
104C2×Dic17—22no—
105C2×Dic17—22no—
106C2×Dic17—42no—
107C2×Dic17—42no—
108C2×Dic17—41no—
109C2×Dic17#12112yes—
110C2×Dic17C22⋊Q812yes—
111D68—42no—
112D68—42no—
113C4×D17—84no—
114Dic34—41no—
115Dic34—41no—
116Dic34—42no—
117#3624—84no—
118#2326—171no—
119C2×#355—172no—
120#1801—172no—
121#1394—172no—
122C22×C17—21no—
123C22×C17—21no—
124C22×C17#38011yescharacteristic
125C22×C17C2×#9911yescharacteristic
126C22×C17#41011yescharacteristic
127C2×D17—44no—
128C2×D17—42no—
129C2×D17—82no—
130C2×D17—81no—
131C2×D17—81no—
132C4×C17—21no—
133C4×C17—21no—
134C4×C17—22no—
135C4×C17—42no—
136C4×C17—41no—
137C4×C17—81no—
138Dic17—22no—
139Dic17—22no—
140Dic17—42no—
141Dic17—81no—
142C2×#124—171no—
143C2×C4×Q8—171no—
144C2×C4×D4—171no—
145#423—342no—
146C2×#101—174no—
147#391—171no—
148#390—171no—
149#388—342no—
150#385—342no—
151#384—171no—
152#376#59511yescharacteristic
153#355—344no—
154#343—342no—
155C2×C17—21no—
156C2×C17—21no—
157C2×C17#179911yescharacteristic
158C2×C17#213311yescharacteristic
159C2×C17#213411yescharacteristic
160D17—82no—
161C22×Q8—171no—
162C22×D4—171no—
163C23×C4—341no—
164C2×M16—344no—
165#124—172no—
166#124—172no—
167#124—342no—
168C4×Q8—682no—
169C4×D4—682no—
170C2×C4⋊C4—172no—
171C2×C4⋊C4—171no—
172C2×C4⋊C4—171no—
173C2×C4⋊C4—342no—
174C2×C22⋊C4—342no—
175C2×C22⋊C4—341no—
176C2×C22⋊C4—342no—
177C2×C42—172no—
178C2×C42C2×#59511yescharacteristic
179C2×C42C2×#59511yescharacteristic
180C2×C42C2×#59511yescharacteristic
181C4⋊C8—682no—
182C4⋊C8—682no—
183#101—344no—
184#101—344no—
185#95—21no—
186#95—21no—
187#95—342no—
188C17#1280311yescharacteristic, complemented, Sylow
189C24—341no—
190C2×Q8—171no—
191C2×Q8—171no—
192C2×Q8—172no—
193C2×Q8—681no—
194C2×Q8—681no—
195C2×D4—172no—
196C2×D4—341no—
197C2×D4—681no—
198C2×D4—681no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—172no—
202C22×C4—172no—
203C22×C4—341no—
204C22×C4—682no—
205C22×C4—1362no—
206C22×C4C22⋊#59511yescharacteristic
207C22×C4C22⋊#59511yescharacteristic
208C22×C4C22×#59511yescharacteristic
209M16—684no—
210M16—684no—
211C2×C8—684no—
212C4⋊C4—682no—
213C4⋊C4—681no—
214C4⋊C4—681no—
215C4⋊C4—1362no—
216C22⋊C4—344no—
217C22⋊C4—344no—
218C22⋊C4—682no—
219C22⋊C4—1362no—
220C42—21no—
221C42—22no—
222C42—41no—
223C42—342no—
224C42—342no—
225C42C4⋊#59512yes—
226C23—342no—
227C23—682no—
228C23—682no—
229C23—681no—
230C23—681no—
231C23C2×C22⋊#59511yescharacteristic
232Q8—681no—
233Q8—681no—
234Q8—682no—
235D4—682no—
236D4—682no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—172no—
249C2×C4—172no—
250C2×C4—342no—
251C2×C4—342no—
252C2×C4—342no—
253C2×C4—682no—
254C2×C4—682no—
255C2×C4—681no—
256C2×C4—1364no—
257C2×C4#1058753912yes—
258C2×C4C2×C4⋊#59511yescharacteristic
259C2×C4#1058767711yescharacteristic
260C8—1364no—
261C22—21no—
262C22—21no—
263C22—684no—
264C22—682no—
265C22—1362no—
266C22—1361no—
267C22—1361no—
268C22#1176375111yescharacteristic
269C22C2×#1058753911yescharacteristic
270C22#1176378811yescharacteristic
271C4—21no—
272C4—21no—
273C4—22no—
274C4—42no—
275C4—41no—
276C4—81no—
277C4—342no—
278C4—342no—
279C4—682no—
280C4—1361no—
281C2—21no—
282C2—21no—
283C2—1362no—
284C2#1454464511yescharacteristic
285C2#1454508111yescharacteristic
286C2#1454508511yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#376C4
socleC22×C17C2×#99
prime radicalC22×D68C2×C4
cosocleC22×Dic34C23
hypercenter#376#595
hypocenterC17#12803
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #14544650C2semidirect
3. #14543881C2semidirect
188. C17#12803semidirect

Maximal subgroups

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

subgroupindex
C2×#117637182
#145446502
#145438812
#145314952
#1280317