Finite Group Databasebeta

← #17953580

Subgroups — #17953580

Order 4352.

554 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 100 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#14544511C212yesmaximal
2#14543660C212yesmaximal, complemented
3#14543660C212yesmaximal, complemented
4D17×#382C211yesmaximal, characteristic
5C2×#10587543—22no—
6C2×#10587542C2214yes—
7#11763675—22no—
8C2×C4⋊C4×D17C411yescharacteristic
9C2×C4⋊C4×D17C411yescharacteristic
10C2×C42×D17C2211yescharacteristic
11#11762675C411yescharacteristic
12#11762674C2211yescharacteristic
13#11762674C2211yescharacteristic
14#11762673—22no—
15#95×D17—22no—
16C17×#382C411yescharacteristic
17C22×C4×D17—21no—
18C22×C4×D17—21no—
19C22×C4×D17C2×C411yescharacteristic
20C22×C4×D17D412yes—
21C22×#3624—24no—
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C42×C17C2×C411yescharacteristic
25C2×C4⋊Dic17C2×C411yescharacteristic
26C2×C4⋊Dic17C2×C411yescharacteristic
27C2×#63225—21no—
28C2×#63225—21no—
29C2×C4×Dic17D412yes—
30C2×C4×Dic17C2311yescharacteristic
31C4⋊C4×D17—42no—
32C4⋊C4×D17—42no—
33C42×D17—24no—
34#10587543—28no—
35#10587542—28no—
36C17×#95—22no—
37#10587502—22no—
38#10587502—22no—
39#10587502—22no—
40C23×D17C22⋊C411yescharacteristic
41C22×C4×C17—21no—
42C22×C4×C17—21no—
43C22×C4×C17C22⋊C412yes—
44C22×C4×C17C22×C411yescharacteristic
45C22×Dic17—21no—
46C22×Dic17—21no—
47C22×Dic17C22⋊C411yescharacteristic
48C22×Dic17C2×D412yes—
49C2×C4×D17—22no—
50C2×C4×D17—22no—
51C2×C4×D17—22no—
52C2×C4×D17—24no—
53C2×C4×D17—24no—
54C2×C4×D17—42no—
55C2×C4×D17—44no—
56C2×C4×D17—42no—
57C2×C4×D17—42no—
58C2×C4×D17—44no—
59C2×#3624—28no—
60C2×#3624—44no—
61C2×#3624—44no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—41no—
64C42×C17—22no—
65C4⋊Dic17—41no—
66C4⋊Dic17—41no—
67#63225—42no—
68#63225—42no—
69C4×Dic17—24no—
70C4×Dic17#4114yes—
71#8718—171nomaximal, Sylow
72C23×C17C2×C22⋊C411yescharacteristic
73C22×D17—21no—
74C22×D17—21no—
75C22×D17—22no—
76C22×D17#10012yes—
77C22×D17#10414yes—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—22no—
81C2×C4×C17—22no—
82C2×C4×C17—22no—
83C2×C4×C17—41no—
84C2×C4×C17—41no—
85C2×C4×C17—42no—
86C2×C4×C17—42no—
87C2×C4×C17#11712yes—
88C2×Dic17—21no—
89C2×Dic17—21no—
90C2×Dic17—22no—
91C2×Dic17—22no—
92C2×Dic17—41no—
93C2×Dic17—41no—
94C2×Dic17—42no—
95C2×Dic17—42no—
96C2×Dic17#10112yes—
97C2×Dic17#12314yes—
98C4×D17—28no—
99C4×D17—48no—
100C4×D17—84no—
101C4×D17—84no—
102#3624—48no—
103C2×#382—171no—
104#1749—172no—
105#1295—172no—
106#1295—172no—
107C22×C17#38111yescharacteristic
108C22×C17C2×#10011yescharacteristic
109C22×C17C2×#10111yescharacteristic
110C22×C17C2×#10412yes—
111C22×C17#42112yes—
112C2×D17—22no—
113C2×D17—24no—
114C2×D17—24no—
115C2×D17—22no—
116C2×D17#32914yes—
117C4×C17—22no—
118C4×C17—42no—
119C4×C17—81no—
120C4×C17—81no—
121Dic17—22no—
122Dic17—24no—
123Dic17—81no—
124Dic17—81no—
125C22×C4⋊C4—171no—
126C22×C4⋊C4—171no—
127C22×C42—171no—
128C2×C22⋊C8—342no—
129C2×#97—174no—
130#382—171no—
131#382—171no—
132#382—171no—
133#382—342no—
134#382#59511yescharacteristic
135C2×#95—342no—
136#336—342no—
137C2×C17C2×#32911yescharacteristic
138C2×C17#152812yes—
139C2×C17#153311yescharacteristic
140C2×C17#182111yescharacteristic
141C2×C17#182612yes—
142D17—24no—
143C23×C4—171no—
144C23×C4—172no—
145C23×C4—341no—
146C23×C4—341no—
147C22×C8—344no—
148C2×C4⋊C4—171no—
149C2×C4⋊C4—171no—
150C2×C4⋊C4—341no—
151C2×C4⋊C4—341no—
152C2×C4⋊C4—682no—
153C2×C4⋊C4—682no—
154C2×C4⋊C4C2×#59511yescharacteristic
155C2×C4⋊C4C2×#59511yescharacteristic
156C2×C42—171no—
157C2×C42—172no—
158C2×C42—344no—
159C2×C42C2×#59511yescharacteristic
160C22⋊C8—348no—
161#97—348no—
162#95—22no—
163#95—342no—
164#95—342no—
165#95—342no—
166C17#871811yescharacteristic, complemented, Sylow
167C24—171no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—171no—
171C22×C4—172no—
172C22×C4—342no—
173C22×C4—344no—
174C22×C4—342no—
175C22×C4—344no—
176C22×C4—342no—
177C22×C4—341no—
178C22×C4—341no—
179C22×C4—682no—
180C22×C4—682no—
181C22×C4—682no—
182C22×C4—684no—
183C22×C4—684no—
184C22×C4C22⋊#59512yes—
185C22×C4C22×#59511yescharacteristic
186C2×C8—348no—
187C2×C8—684no—
188C2×C8—684no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—681no—
192C4⋊C4—681no—
193C4⋊C4—682no—
194C4⋊C4—682no—
195C42—22no—
196C42—174no—
197C42—344no—
198C23—172no—
199C23—174no—
200C23—341no—
201C23—341no—
202C23—342no—
203C23C2×C22⋊#59511yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—174no—
214C2×C4—172no—
215C2×C4—348no—
216C2×C4—341no—
217C2×C4—341no—
218C2×C4—342no—
219C2×C4—342no—
220C2×C4—688no—
221C2×C4—681no—
222C2×C4—681no—
223C2×C4—682no—
224C2×C4—682no—
225C2×C4—1364no—
226C2×C4—1364no—
227C2×C4#1058767712yes—
228C8—688no—
229C22—174no—
230C22—342no—
231C22—344no—
232C22—344no—
233C22—342no—
234C22#1176375211yescharacteristic
235C22D17⋊#10011yescharacteristic
236C22D17⋊#10111yescharacteristic
237C22D17⋊#10412yes—
238C22#1176380612yes—
239C4—22no—
240C4—42no—
241C4—81no—
242C4—81no—
243C4—342no—
244C4—344no—
245C4—1361no—
246C4—1361no—
247C2—344no—
248C2D17⋊#32911yescharacteristic
249C2#1454424712yes—
250C2#1454426411yescharacteristic
251C2#1454468411yescharacteristic
252C2#1454469212yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#8718
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #14543660C2semidirect
3. #14543660C2semidirect
166. C17#8718semidirect

Maximal subgroups

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

subgroupindex
#145445112
#145436602
D17×#3822
#871817