Finite Group Databasebeta

← #17958313

Subgroups — #17958313

Order 4352.

428 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544026C212yesmaximal
2#14543726C212yesmaximal
3#14543715C212yesmaximal
4C4×#10587555C211yesmaximal, characteristic
5#11763826—22no—
6#11763655—22no—
7#11763654C2214yes—
8C2×#10587555C411yescharacteristic
9C2×C4×Dic34C411yescharacteristic
10C2×C4×Dic34C2211yescharacteristic
11#11762715C411yescharacteristic
12#11762715C2211yescharacteristic
13#11762707—22no—
14#11762679C2211yescharacteristic
15C4×C4⋊Dic17—22no—
16C43×C17C411yescharacteristic
17C22×Dic34C2×C411yescharacteristic
18C22×Dic34C2×C411yescharacteristic
19C2×C42×C17—21no—
20C2×C42×C17—21no—
21C2×C42×C17C2×C411yescharacteristic
22C2×C42×C17C2×C411yescharacteristic
23C2×C42×C17C2×C411yescharacteristic
24C2×C4⋊Dic17—22no—
25C2×C4⋊Dic17—22no—
26C2×C4⋊Dic17C2×C411yescharacteristic
27C2×C4⋊Dic17C2311yescharacteristic
28C2×#63225—21no—
29C2×#63225D412yes—
30C2×C4×Dic17—21no—
31C2×C4×Dic17D412yes—
32#10587555—22no—
33#10587555C814yescomplemented
34C4×Dic34—41no—
35C4×Dic34—41no—
36C4×Dic34—41no—
37C4×Dic34—41no—
38C22⋊#3624—24no—
39#10587544—42no—
40C4×#3624—42no—
41#10587502—22no—
42#10587502—22no—
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17C22⋊C411yescharacteristic
46C22×C4×C17C22⋊C411yescharacteristic
47C22×C4×C17C22×C411yescharacteristic
48C22×Dic17—21no—
49C22×Dic17—21no—
50C22×Dic17C22⋊C412yes—
51C22×Dic17C2×D412yes—
52C2×Dic34—21no—
53C2×Dic34—41no—
54C2×Dic34—41no—
55C2×Dic34—41no—
56C2×Dic34—41no—
57C2×Dic34C2×C812yes—
58C2×Dic34C2×C812yes—
59C2×Dic34M1612yes—
60C2×#3624—44no—
61C42×C17—24no—
62C42×C17—21no—
63C42×C17—21no—
64C42×C17—21no—
65C42×C17—41no—
66C42×C17—42no—
67C42×C17C2×C812yes—
68C4⋊Dic17—28no—
69C4⋊Dic17—41no—
70C4⋊Dic17—44no—
71C4⋊Dic17—41no—
72#63225—42no—
73#63225—42no—
74C4×Dic17—22no—
75C4×Dic17—22no—
76C4×Dic17—41no—
77C4×Dic17—41no—
78#11478—171nomaximal, Sylow
79C23×C17C2×C22⋊C411yescharacteristic
80C2×C4×C17—22no—
81C2×C4×C17—22no—
82C2×C4×C17—22no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—21no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17#9911yescharacteristic
92C2×C4×C17#9911yescharacteristic
93C2×C4×C17C22×C811yescharacteristic
94C2×C4×C17C2×M1611yescharacteristic
95C2×Dic17—22no—
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—22no—
99C2×Dic17—41no—
100C2×Dic17—41no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103C2×Dic17—41no—
104C2×Dic17C22⋊C814yes—
105Dic34—42no—
106Dic34—42no—
107Dic34—42no—
108Dic34—42no—
109#3624—84no—
110C4×C4⋊Q8—171no—
111#1461—172no—
112#1325—172no—
113#1319—172no—
114C22×C17—21no—
115C22×C17—21no—
116C22×C17C2×C22⋊C811yescharacteristic
117C22×C17C2×#9911yescharacteristic
118C22×C17#41311yescharacteristic
119C4×C17—24no—
120C4×C17—21no—
121C4×C17—21no—
122C4×C17—21no—
123C4×C17—42no—
124C4×C17—41no—
125C4×C17#35612yes—
126Dic17—24no—
127Dic17—42no—
128Dic17—42no—
129Dic17—81no—
130C2×C4⋊Q8—171no—
131C2×C4×Q8—171no—
132C2×C4×Q8—171no—
133#431—342no—
134#391—171no—
135#391—171no—
136#389—342no—
137#384—171no—
138C4×C4⋊C4—342no—
139C43#59511yescharacteristic
140#324—174no—
141#324—342no—
142C2×C17—21no—
143C2×C17—21no—
144C2×C17#145911yescharacteristic
145C2×C17#212611yescharacteristic
146C2×C17C2×#35611yescharacteristic
147C22×Q8—171no—
148C22×Q8—171no—
149C4⋊Q8—174no—
150C4⋊Q8—342no—
151C4×Q8—681no—
152C4×Q8—681no—
153C4×Q8—681no—
154C4×Q8—681no—
155C2×C4⋊C4—172no—
156C2×C4⋊C4—171no—
157C2×C4⋊C4—171no—
158C2×C4⋊C4—342no—
159C2×C4⋊C4—342no—
160C2×C4⋊C4—341no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—172no—
164C2×C42—341no—
165C2×C42C2×#59511yescharacteristic
166C2×C42C2×#59511yescharacteristic
167C2×C42C2×#59511yescharacteristic
168C4⋊C8—682no—
169C22⋊C8—344no—
170C4×C8—682no—
171#95—342no—
172#95—342no—
173C17#1147811yescharacteristic, complemented, Sylow
174C2×Q8—172no—
175C2×Q8—172no—
176C2×Q8—172no—
177C2×Q8—341no—
178C2×Q8—681no—
179C2×Q8—681no—
180C2×Q8—681no—
181C2×Q8—681no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—172no—
185C22×C4—172no—
186C22×C4—341no—
187C22×C4—341no—
188C22×C4C22⋊#59511yescharacteristic
189C22×C4C22⋊#59511yescharacteristic
190C22×C4C22×#59511yescharacteristic
191C2×C8—684no—
192C4⋊C4—348no—
193C4⋊C4—682no—
194C4⋊C4—681no—
195C4⋊C4—681no—
196C4⋊C4—682no—
197C4⋊C4—684no—
198C42—24no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—41no—
203C42—42no—
204C42—342no—
205C42—342no—
206C42—681no—
207C42—681no—
208C42#6324212yes—
209C23C2×C22⋊#59511yescharacteristic
210Q8—682no—
211Q8—682no—
212Q8—682no—
213Q8—682no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—174no—
226C2×C4—342no—
227C2×C4—342no—
228C2×C4—342no—
229C2×C4—342no—
230C2×C4—681no—
231C2×C4—681no—
232C2×C4—682no—
233C2×C4—682no—
234C2×C4—681no—
235C2×C4#1058753911yescharacteristic
236C2×C4#1058753911yescharacteristic
237C2×C4C2×#6324211yescharacteristic
238C2×C4D17⋊M1611yescharacteristic
239C8—1364no—
240C22—21no—
241C22—21no—
242C22#1176377711yescharacteristic
243C22C2×#1058753911yescharacteristic
244C22#1176379511yescharacteristic
245C4—24no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—41no—
251C4—344no—
252C4—682no—
253C4—682no—
254C4—1361no—
255C4#1176372012yes—
256C2—21no—
257C2—21no—
258C2#1454402111yescharacteristic
259C2#1454505711yescharacteristic
260C2C2×#1176372011yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC43×C17C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC43#595
hypocenterC17#11478
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
33. #10587555C8semidirect
173. C17#11478semidirect

Maximal subgroups

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

subgroupindex
#145440262
#145437262
#145437152
C4×#105875552
#1147817