Finite Group Databasebeta

← #17958209

Subgroups — #17958209

Order 4352.

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

normal subgroups only

This group has 434 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#14544018C212yesmaximal
2#14543727C212yesmaximal, complemented
3#14543726C212yesmaximal, complemented
4#14531409C211yesmaximal, characteristic
5#11763826—22no—
6#11763654C2214yes—
7#11763653—22no—
8C2×#10587578C2211yescharacteristic
9C2×#10587558C411yescharacteristic
10C2×C4⋊C4×D17C411yescharacteristic
11#11762706—22no—
12#11762683—22no—
13#11762679C2211yescharacteristic
14#11762678C2211yescharacteristic
15#11762674C411yescharacteristic
16C17×#382C411yescharacteristic
17C22×C4×D17—21no—
18C22×C4×D17C2×C411yescharacteristic
19C2×C4⋊C4×C17C2×C411yescharacteristic
20C2×C4⋊C4×C17C2×C411yescharacteristic
21C2×C42×C17C2×C411yescharacteristic
22C2×#63227—21no—
23C2×#63227D412yes—
24C2×C4⋊Dic17—22no—
25C2×C4⋊Dic17C2×C411yescharacteristic
26C2×C4⋊Dic17C2311yescharacteristic
27C2×#63225—21no—
28C2×#63225—21no—
29C2×#63225—22no—
30C2×C4×Dic17C2×C411yescharacteristic
31C2×C4×Dic17D412yes—
32#10587578—42no—
33C4⋊C4×D17—42no—
34#10587558—22no—
35#10587558C814yescomplemented
36C22⋊#3624—24no—
37#10587544—42no—
38C4×#3624—42no—
39C17×#95—22no—
40#10587502—22no—
41C23×D17C22⋊C411yescharacteristic
42C22×C4×C17—21no—
43C22×C4×C17—21no—
44C22×C4×C17C22⋊C412yes—
45C22×C4×C17C22×C411yescharacteristic
46C22×Dic17—21no—
47C22×Dic17—21no—
48C22×Dic17C22⋊C411yescharacteristic
49C22×Dic17C2×D412yes—
50C2×C4×D17—22no—
51C2×C4×D17—22no—
52C2×C4×D17—42no—
53C2×C4×D17—82no—
54C2×C4×D17C2×C812yes—
55C2×C4×D17M1612yes—
56C2×#3624—44no—
57C4⋊C4×C17—41no—
58C4⋊C4×C17—41no—
59C42×C17—21no—
60C42×C17C2×C812yes—
61#63227—24no—
62#63227—42no—
63C4⋊Dic17—41no—
64C4⋊Dic17—41no—
65C4⋊Dic17—82no—
66#63225—24no—
67#63225—42no—
68#63225—82no—
69C4×Dic17—21no—
70C4×Dic17—22no—
71C4×Dic17—22no—
72C4×Dic17C2×C812yes—
73#11450—171nomaximal, Sylow
74C23×C17C2×C22⋊C411yescharacteristic
75C22×D17—21no—
76C22×D17—21no—
77C22×D17—41no—
78C22×D17—41no—
79C22×D17C22⋊C812yes—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—22no—
83C2×C4×C17—22no—
84C2×C4×C17—41no—
85C2×C4×C17—41no—
86C2×C4×C17—42no—
87C2×C4×C17—42no—
88C2×C4×C17—41no—
89C2×C4×C17C22×C811yescharacteristic
90C2×C4×C17C2×M1611yescharacteristic
91C2×Dic17—22no—
92C2×Dic17—22no—
93C2×Dic17—41no—
94C2×Dic17—41no—
95C2×Dic17—42no—
96C2×Dic17—42no—
97C2×Dic17—41no—
98C2×Dic17C22⋊C812yes—
99C2×Dic17#9912yes—
100C2×Dic17#10112yes—
101C4×D17—24no—
102C4×D17—24no—
103C4×D17—84no—
104#3624—84no—
105#2317—171no—
106#1458—172no—
107#1325—172no—
108#1325—172no—
109C22×C17—21no—
110C22×C17—21no—
111C22×C17C2×C22⋊C811yescharacteristic
112C22×C17C2×#9911yescharacteristic
113C22×C17C2×#10111yescharacteristic
114C2×D17—22no—
115C2×D17—42no—
116C2×D17—41no—
117C2×D17—41no—
118C2×D17—42no—
119C4×C17—21no—
120C4×C17—21no—
121C4×C17—42no—
122C4×C17—42no—
123C4×C17—81no—
124Dic17—42no—
125Dic17—42no—
126Dic17—81no—
127Dic17#32414yes—
128C2×#117—171no—
129C2×#117—171no—
130C22×C4⋊C4—171no—
131#431—342no—
132#389—342no—
133#385—342no—
134#384—171no—
135#384—171no—
136#382—171no—
137#382#59511yescharacteristic
138#324—174no—
139#323—342no—
140C2×C17—21no—
141C2×C17—21no—
142C2×C17C2×#32411yescharacteristic
143C2×C17#212811yescharacteristic
144C2×C17#213511yescharacteristic
145D17—42no—
146C23×C4—171no—
147C23×C4—341no—
148#117—174no—
149#117—342no—
150#117—682no—
151C2×C4⋊C4—171no—
152C2×C4⋊C4—171no—
153C2×C4⋊C4—341no—
154C2×C4⋊C4—341no—
155C2×C4⋊C4—342no—
156C2×C4⋊C4—342no—
157C2×C4⋊C4—682no—
158C2×C4⋊C4C2×#59511yescharacteristic
159C2×C4⋊C4C2×#59511yescharacteristic
160C2×C22⋊C4—172no—
161C2×C22⋊C4—341no—
162C2×C42—171no—
163C2×C42—172no—
164C2×C42C2×#59511yescharacteristic
165C4⋊C8—682no—
166C22⋊C8—344no—
167C4×C8—682no—
168#95—22no—
169#95—342no—
170C17#1145011yescharacteristic, complemented, Sylow
171C24—171no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—171no—
175C22×C4—172no—
176C22×C4—172no—
177C22×C4—172no—
178C22×C4—342no—
179C22×C4—342no—
180C22×C4—341no—
181C22×C4—341no—
182C22×C4—682no—
183C22×C4—1362no—
184C22×C4C22⋊#59512yes—
185C22×C4C22×#59511yescharacteristic
186C2×C8—684no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—344no—
190C4⋊C4—681no—
191C4⋊C4—681no—
192C4⋊C4—682no—
193C4⋊C4—1362no—
194C4⋊C4—1362no—
195C22⋊C4—344no—
196C22⋊C4—682no—
197C42—21no—
198C42—172no—
199C42—342no—
200C42—342no—
201C42—341no—
202C42#6324212yes—
203C23—172no—
204C23—341no—
205C23—341no—
206C23—681no—
207C23—681no—
208C23C2×C22⋊#59511yescharacteristic
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—172no—
219C2×C4—172no—
220C2×C4—172no—
221C2×C4—344no—
222C2×C4—344no—
223C2×C4—342no—
224C2×C4—342no—
225C2×C4—681no—
226C2×C4—681no—
227C2×C4—682no—
228C2×C4—682no—
229C2×C4—681no—
230C2×C4—1364no—
231C2×C4C2×#6324211yescharacteristic
232C2×C4D17⋊M1611yescharacteristic
233C8—1364no—
234C22—21no—
235C22—21no—
236C22—342no—
237C22—682no—
238C22—682no—
239C22—681no—
240C22—681no—
241C22#1176377711yescharacteristic
242C22D17⋊#9911yescharacteristic
243C22D17⋊#10111yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—81no—
249C4—174no—
250C4—682no—
251C4—682no—
252C4—1361no—
253C2—21no—
254C2—21no—
255C2—682no—
256C2#1454401311yescharacteristic
257C2#1454506411yescharacteristic
258C2#1454508711yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC22×C17C2×#99
prime radicalC23×D17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenter#382#595
hypocenterC17#11450
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #14543727C2semidirect
3. #14543726C2semidirect
35. #10587558C8semidirect
170. C17#11450semidirect

Maximal subgroups

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

subgroupindex
#145440182
#145437272
#145437262
#145314092
#1145017