Finite Group Databasebeta

← #17952090

Subgroups — #17952090

Order 4352.

528 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 118 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#14544501C212yesmaximal, complemented
2C2×#11763664C212yesmaximal
3#14543660C212yesmaximal, complemented
4C4×#10587622C211yesmaximal, characteristic
5C2×#10587542C2214yes—
6#11763675—22no—
7#11763675—22no—
8#11763664C418yescomplemented
9C2×#10587622C2211yescharacteristic
10C2×C4×Dic34C411yescharacteristic
11#11762714C411yescharacteristic
12#11762712C411yescharacteristic
13#11762703—22no—
14#11762674C2211yescharacteristic
15C4×C22⋊Dic17—22no—
16C42×Dic17C2211yescharacteristic
17C2×C4×D4×C17C411yescharacteristic
18C22×D4×C17C2×C411yescharacteristic
19C23×C4×C17—21no—
20C22×Dic34C2×C411yescharacteristic
21C22×#3624—24no—
22C4×D4×C17—42no—
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C22⋊C4×C17—21no—
25C2×C42×C17C2×C411yescharacteristic
26C2×C22⋊Dic17—22no—
27C2×C22⋊Dic17—22no—
28#10587622—22no—
29#10587622C2×C414yes—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×#63225—21no—
32C2×C4×Dic17—21no—
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17D412yes—
35C2×C4×Dic17D412yes—
36C2×C4×Dic17C2311yescharacteristic
37C4×Dic34—42no—
38#10587542—24no—
39#10587542C2×C418yescomplemented
40#10587502—22no—
41#10587502—22no—
42C24×C17—21no—
43C2×D4×C17—21no—
44C2×D4×C17—41no—
45C2×D4×C17—41no—
46C2×D4×C17C4212yes—
47C22×C4×C17—21no—
48C22×C4×C17—44no—
49C22×C4×C17—42no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—21no—
54C22×Dic17—21no—
55C22×Dic17C22⋊C412yes—
56C22×Dic17C2×D412yes—
57C2×Dic34—21no—
58C2×Dic34—41no—
59C2×Dic34—41no—
60C2×Dic34C4212yes—
61C2×#3624—28no—
62C2×#3624—44no—
63C2×#3624—44no—
64C4⋊C4×C17—41no—
65C22⋊C4×C17—42no—
66C42×C17—22no—
67C22⋊Dic17—28no—
68C22⋊Dic17—44no—
69C4⋊Dic17—41no—
70#63225—42no—
71C4×Dic17—41no—
72C4×Dic17—42no—
73C4×Dic17—42no—
74C4×Dic17—42no—
75C4×Dic17C22×C412yes—
76C4×Dic17#4112yes—
77#8224—171nomaximal, Sylow
78C23×C17—22no—
79C23×C17—41no—
80C23×C17—41no—
81C23×C17—42no—
82C23×C17—42no—
83C23×C17C2×C22⋊C411yescharacteristic
84D4×C17—42no—
85D4×C17—42no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—22no—
89C2×C4×C17—21no—
90C2×C4×C17—22no—
91C2×C4×C17—41no—
92C2×C4×C17—42no—
93C2×C4×C17—84no—
94C2×C4×C17#10012yes—
95C2×C4×C17C2×C4211yescharacteristic
96C2×C4×C17#11711yescharacteristic
97C2×Dic17—22no—
98C2×Dic17—22no—
99C2×Dic17—22no—
100C2×Dic17—22no—
101C2×Dic17—22no—
102C2×Dic17—22no—
103C2×Dic17—41no—
104C2×Dic17—41no—
105C2×Dic17—41no—
106C2×Dic17—42no—
107C2×Dic17C4×D414yes—
108Dic34—42no—
109Dic34—42no—
110#3624—48no—
111C4×#124—171no—
112#1745—172no—
113C2×#329—172no—
114#1295—172no—
115C22×C17—42no—
116C22×C17—44no—
117C22×C17—81no—
118C22×C17—81no—
119C22×C17—82no—
120C22×C17C4×C22⋊C411yescharacteristic
121C22×C17C2×#10011yescharacteristic
122C22×C17#41311yescharacteristic
123C22×C17#42112yes—
124C22×C17#42112yes—
125C4×C17—21no—
126C4×C17—21no—
127C4×C17—22no—
128C4×C17—41no—
129C4×C17—81no—
130Dic17—24no—
131Dic17—42no—
132Dic17—42no—
133Dic17—81no—
134C2×#124—171no—
135C2×C4×Q8—171no—
136C2×C4×D4#59511yescharacteristic
137C2×#97—174no—
138#391—171no—
139#390—171no—
140#388—342no—
141#382—171no—
142C4×C22⋊C4—342no—
143C43—171no—
144#336—342no—
145#336—342no—
146#329—178no—
147C2×C17—82no—
148C2×C17#153311yescharacteristic
149C2×C17#153512yes—
150C2×C17#153611yescharacteristic
151C2×C17C4×#10011yescharacteristic
152C2×C17#175912yes—
153C22×Q8—171no—
154C22×D4C2×#59511yescharacteristic
155C23×C4—21no—
156C22×C8—344no—
157#124—174no—
158#124—342no—
159C4×Q8—682no—
160C4×D4—42no—
161C2×C4⋊C4—171no—
162C2×C4⋊C4—341no—
163C2×C4⋊C4C2×#59511yescharacteristic
164C2×C22⋊C4—21no—
165C2×C22⋊C4—342no—
166C2×C22⋊C4—342no—
167C2×C42—171no—
168C2×C42—172no—
169C2×C42—172no—
170C2×C42—171no—
171C2×C42—341no—
172C2×C42C2×#59511yescharacteristic
173#97—178no—
174#97—344no—
175#95—342no—
176#95—342no—
177C17#822411yescharacteristic, complemented, Sylow
178C24—21no—
179C2×Q8—172no—
180C2×Q8—341no—
181C2×Q8—681no—
182C2×Q8—681no—
183C2×D4—21no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4C4×#59512yes—
187C22×C4—21no—
188C22×C4—44no—
189C22×C4—42no—
190C22×C4—172no—
191C22×C4—172no—
192C22×C4—341no—
193C22×C4—341no—
194C22×C4C22⋊#59511yescharacteristic
195C22×C4C22⋊#59511yescharacteristic
196C22×C4C22×#59511yescharacteristic
197C2×C8—348no—
198C2×C8—684no—
199C2×C8—684no—
200C4⋊C4—41no—
201C4⋊C4—681no—
202C4⋊C4—682no—
203C22⋊C4—42no—
204C22⋊C4—348no—
205C22⋊C4—684no—
206C42—22no—
207C42—172no—
208C42—172no—
209C42—681no—
210C42—682no—
211C42—682no—
212C42—682no—
213C23—22no—
214C23—41no—
215C23—41no—
216C23—42no—
217C23—42no—
218C23C2×C22⋊#59511yescharacteristic
219Q8—682no—
220Q8—682no—
221D4—42no—
222D4—42no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—174no—
232C2×C4—342no—
233C2×C4—342no—
234C2×C4—342no—
235C2×C4—342no—
236C2×C4—342no—
237C2×C4—342no—
238C2×C4—681no—
239C2×C4—681no—
240C2×C4—681no—
241C2×C4—682no—
242C2×C4#1058755312yes—
243C2×C4C2×C4×#59511yescharacteristic
244C2×C4#1058767711yescharacteristic
245C8—688no—
246C22—42no—
247C22—44no—
248C22—81no—
249C22—82no—
250C22—81no—
251C22C4×C22⋊#59511yescharacteristic
252C22C2×#1058755311yescharacteristic
253C22#1176379511yescharacteristic
254C22#1176380612yes—
255C22#1176380712yes—
256C4—22no—
257C4—21no—
258C4—21no—
259C4—41no—
260C4—81no—
261C4—344no—
262C4—682no—
263C4—682no—
264C4—1361no—
265C2—82no—
266C2#1454426311yescharacteristic
267C2#1454426812yes—
268C2#1454427211yescharacteristic
269C2C4×#1058755311yescharacteristic
270C2#1454454712yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC22×D4×C17C2×C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×D4#595
hypocenterC17#8224
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14544501C2semidirect
3. #14543660C2semidirect
8. #11763664C4semidirect
39. #10587542C2×C4semidirect
177. C17#8224semidirect

Maximal subgroups

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

subgroupindex
#145445012
C2×#117636642
#145436602
C4×#105876222
#822417