Finite Group Databasebeta

← #17958317

Subgroups — #17958317

Order 4352.

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

normal subgroups only

This group has 524 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
1#14544021C212yesmaximal, complemented
2#14543724C212yesmaximal, complemented
3#14543713C212yesmaximal, complemented
4#14531509C211yesmaximal, characteristic
5#11763777—22no—
6#11763654C2214yes—
7#11763653—22no—
8C2×#10587560C411yescharacteristic
9C2×C4×D68C411yescharacteristic
10C2×C4×D68C2211yescharacteristic
11#11762711C411yescharacteristic
12#11762711C2211yescharacteristic
13#11762687—22no—
14#11762687—22no—
15#11762675C2211yescharacteristic
16C17×#376C411yescharacteristic
17C22×D68—22no—
18C22×D68C2×C411yescharacteristic
19C22×D68C2×C411yescharacteristic
20C22×C4×D17—21no—
21C22×C4×D17D412yes—
22C2×#63242—42no—
23C2×C42×C17C2×C411yescharacteristic
24C2×C42×C17C2×C411yescharacteristic
25C2×C42×C17C2×C411yescharacteristic
26C2×#63227—22no—
27C2×#63227—21no—
28C2×#63227—22no—
29C2×#63227D412yes—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×C4⋊Dic17C2311yescharacteristic
32#10587560—22no—
33#10587560C814yescomplemented
34C4×D68—42no—
35C4×D68—42no—
36C22⋊#3624—24no—
37#10587543—42no—
38C17×#95—21no—
39C17×#95—21no—
40#10587502—22no—
41C23×D17—21no—
42C23×D17C22⋊C412yes—
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17C22⋊C411yescharacteristic
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C22×C411yescharacteristic
48C22×Dic17—21no—
49C22×Dic17C2×D412yes—
50C2×D68—21no—
51C2×D68—28no—
52C2×D68—41no—
53C2×D68—41no—
54C2×D68—41no—
55C2×D68—41no—
56C2×D68—82no—
57C2×D68—82no—
58C2×D68C2×C812yes—
59C2×D68C2×C812yescomplemented
60C2×D68M1612yes—
61C2×C4×D17—22no—
62C2×C4×D17—22no—
63C2×C4×D17—42no—
64C2×C4×D17—82no—
65C2×C4×D17—82no—
66C2×#3624—44no—
67#63242—84no—
68C42×C17—22no—
69C42×C17—21no—
70C42×C17—41no—
71C42×C17C2×C812yescomplemented
72#63227—42no—
73#63227—42no—
74#63227—82no—
75#63227—82no—
76C4⋊Dic17—41no—
77C4⋊Dic17—41no—
78#11479—171nomaximal, Sylow
79C23×C17C2×C22⋊C411yescharacteristic
80C22×D17—22no—
81C22×D17—22no—
82C22×D17—22no—
83C22×D17—42no—
84C22×D17—42no—
85C22×D17—42no—
86C22×D17—42no—
87C22×D17—41no—
88C22×D17—41no—
89C22×D17C22⋊C814yes—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—22no—
93C2×C4×C17—21no—
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—41no—
101C2×C4×C17#9912yes—
102C2×C4×C17C22×C811yescharacteristic
103C2×C4×C17C2×M1611yescharacteristic
104C2×Dic17—22no—
105C2×Dic17—42no—
106C2×Dic17—42no—
107C2×Dic17—41no—
108D68—42no—
109D68—42no—
110D68—42no—
111D68—42no—
112D68—88no—
113C4×D17—44no—
114C4×D17—82no—
115C4×D17—84no—
116#3624—84no—
117#2328—171no—
118#1459—172no—
119#1324—172no—
120#1318—172no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17C2×C22⋊C811yescharacteristic
124C22×C17C2×#9911yescharacteristic
125C22×C17#41311yescharacteristic
126C2×D17—24no—
127C2×D17—42no—
128C2×D17—42no—
129C2×D17—44no—
130C2×D17—44no—
131C2×D17—42no—
132C2×D17—82no—
133C2×D17—82no—
134C2×D17—81no—
135C2×D17—81no—
136C4×C17—22no—
137C4×C17—21no—
138C4×C17—21no—
139C4×C17—42no—
140C4×C17—41no—
141C4×C17—81no—
142Dic17—42no—
143Dic17—81no—
144C2×#127—171no—
145C2×C4×D4—171no—
146C2×C4×D4—171no—
147C2×C22⋊C8—342no—
148#390—171no—
149#390—171no—
150#386—342no—
151#386—342no—
152#382—171no—
153#376#59511yescharacteristic
154#324—174no—
155#323—342no—
156C2×C17—21no—
157C2×C17—21no—
158C2×C17#145911yescharacteristic
159C2×C17#212711yescharacteristic
160C2×C17#213411yescharacteristic
161D17—44no—
162D17—82no—
163C22×D4—171no—
164C22×D4—171no—
165C22×D4—342no—
166C23×C4—172no—
167C23×C4—341no—
168C22×C8—682no—
169#127—174no—
170#127—342no—
171C4×D4—682no—
172C4×D4—682no—
173C2×C4⋊C4—171no—
174C2×C4⋊C4—171no—
175C2×C22⋊C4—172no—
176C2×C22⋊C4—341no—
177C2×C22⋊C4—342no—
178C2×C22⋊C4—342no—
179C2×C42C2×#59511yescharacteristic
180C2×C42C2×#59511yescharacteristic
181C2×C42C2×#59511yescharacteristic
182C22⋊C8—344no—
183C22⋊C8—682no—
184#95—21no—
185#95—21no—
186#95—342no—
187C17#1147911yescharacteristic, complemented, Sylow
188C24—172no—
189C24—341no—
190C2×D4—172no—
191C2×D4—172no—
192C2×D4—172no—
193C2×D4—348no—
194C2×D4—341no—
195C2×D4—681no—
196C2×D4—681no—
197C2×D4—681no—
198C2×D4—681no—
199C2×D4—1362no—
200C2×D4—1362no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—172no—
204C22×C4—342no—
205C22×C4—342no—
206C22×C4—341no—
207C22×C4—682no—
208C22×C4—1362no—
209C22×C4—1362no—
210C22×C4C22⋊#59511yescharacteristic
211C22×C4C22⋊#59511yescharacteristic
212C22×C4C22×#59511yescharacteristic
213C2×C8—684no—
214C2×C8—1364no—
215C4⋊C4—681no—
216C4⋊C4—681no—
217C22⋊C4—682no—
218C22⋊C4—682no—
219C22⋊C4—1362no—
220C22⋊C4—1362no—
221C42—21no—
222C42—22no—
223C42—41no—
224C42#6324212yescomplemented
225C23—174no—
226C23—342no—
227C23—342no—
228C23—342no—
229C23—682no—
230C23—682no—
231C23—682no—
232C23—682no—
233C23—681no—
234C23—681no—
235C23C2×C22⋊#59511yescharacteristic
236D4—682no—
237D4—682no—
238D4—682no—
239D4—682no—
240D4—1368no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—342no—
253C2×C4—684no—
254C2×C4—682no—
255C2×C4—682no—
256C2×C4—681no—
257C2×C4—1362no—
258C2×C4—1364no—
259C2×C4#1058753912yes—
260C2×C4C2×#6324211yescharacteristic
261C2×C4D17⋊M1611yescharacteristic
262C8—1364no—
263C22—21no—
264C22—21no—
265C22—344no—
266C22—684no—
267C22—684no—
268C22—682no—
269C22—682no—
270C22—682no—
271C22—1362no—
272C22—1362no—
273C22—1361no—
274C22—1361no—
275C22#1176377711yescharacteristic
276C22C2×#1058753911yescharacteristic
277C22#1176379511yescharacteristic
278C4—21no—
279C4—21no—
280C4—22no—
281C4—42no—
282C4—41no—
283C4—81no—
284C4—682no—
285C4—1361no—
286C2—21no—
287C2—21no—
288C2—684no—
289C2—1362no—
290C2#1454402111yescharacteristic
291C2#1454506111yescharacteristic
292C2#1454508511yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#376C4
socleC22×C17C2×#99
prime radicalC2×#10587560C4
cosocleC2×C4⋊Dic17C23
hypercenter#376#595
hypocenterC17#11479
LCSG ▷ C2×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
1. #14544021C2semidirect
2. #14543724C2semidirect
3. #14543713C2semidirect
33. #10587560C8semidirect
59. C2×D68C2×C8semidirect
71. C42×C17C2×C8semidirect
187. C17#11479semidirect
224. C42#63242semidirect

Maximal subgroups

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

subgroupindex
#145440212
#145437242
#145437132
#145315092
#1147917