Finite Group Databasebeta

← #17950236

Subgroups — #17950236

Order 4352.

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

normal subgroups only

This group has 494 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#14544676C211yesmaximal, characteristic
2#14544641C211yesmaximal, characteristic
3#14543605C214yesmaximal, complemented
4#14537137C211yesmaximal, characteristic
5C2×#10587544—21no—
6C2×#10587543—21no—
7C2×#10587543—21no—
8#11763675—21no—
9#11763675C2212yes—
10#11763675C2212yes—
11C2×#10587555C411yescharacteristic
12C2×#10587583C412yes—
13C2×C42×D17C2211yescharacteristic
14#11762714C2212yes—
15#11762708—21no—
16#11762708—21no—
17#11762666—21no—
18#11762666—21no—
19C17×#384C411yescharacteristic
20C22×C4×D17C2×C411yescharacteristic
21C22×C4×D17D411yescharacteristic
22C22×C4×D17D411yescharacteristic
23C22×Dic34C2×C412yes—
24C22×#3624—22no—
25C22×#3624—22no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17C2×C412yes—
29C2×C42×C17C2×C411yescharacteristic
30C2×#63227—22no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—22no—
34C2×C4×Dic17D411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36C2×C4×Dic17C2311yescharacteristic
37#10587583—44no—
38C42×D17—42no—
39#10587555—42no—
40#10587544—42no—
41#10587543—42no—
42#10587543—42no—
43#10587502—22no—
44#10587502—22no—
45C23×D17C22⋊C411yescharacteristic
46C22×C4×C17—22no—
47C22×C4×C17C22⋊C411yescharacteristic
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C22×C411yescharacteristic
50C22×Dic17—22no—
51C22×Dic17C22⋊C411yescharacteristic
52C22×Dic17C2×D411yescharacteristic
53C22×Dic17C2×D411yescharacteristic
54C2×C4×D17—22no—
55C2×C4×D17—22no—
56C2×C4×D17—22no—
57C2×C4×D17—22no—
58C2×C4×D17—41no—
59C2×C4×D17—41no—
60C2×C4×D17—41no—
61C2×C4×D17—41no—
62C2×C4×D17SD1612yes—
63C2×C4×D17Q1612yes—
64C2×Dic34—24no—
65C2×Dic34—42no—
66C2×Dic34—42no—
67C2×#3624—42no—
68C2×#3624—42no—
69C2×#3624—42no—
70C2×#3624—42no—
71C2×#3624—42no—
72C2×#3624—42no—
73C4⋊C4×C17—42no—
74C4⋊C4×C17—42no—
75C4⋊C4×C17—42no—
76C42×C17—22no—
77#63227—44no—
78C4⋊Dic17—42no—
79C4⋊Dic17—42no—
80C4⋊Dic17—44no—
81C4×Dic17—22no—
82C4×Dic17—41no—
83C4×Dic17—41no—
84#7727—171nomaximal, Sylow
85C23×C17C2×C22⋊C411yescharacteristic
86C22×D17—21no—
87C22×D17—21no—
88C22×D17—21no—
89C22×D17—21no—
90C22×D17—21no—
91C22×D17—21no—
92C22×D17#10312yes—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—42no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17#9912yes—
103C2×C4×C17#10312yes—
104C2×C4×C17#13112yes—
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—42no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17#10012yes—
115C2×Dic17C2×SD1611yescharacteristic
116C2×Dic17C2×Q1611yescharacteristic
117C2×Dic17#13712yes—
118C4×D17—42no—
119C4×D17—42no—
120C4×D17—44no—
121C4×D17—44no—
122Dic34—84no—
123#3624—82no—
124#3624—82no—
125#2857—171no—
126#1817—171no—
127#1797—171no—
128#1272—174no—
129C22×C17#40811yescharacteristic
130C22×C17C2×#9911yescharacteristic
131C22×C17C2×#10011yescharacteristic
132C22×C17C2×#10311yescharacteristic
133C22×C17#41911yescharacteristic
134C22×C17#42111yescharacteristic
135C22×C17#42111yescharacteristic
136C2×D17—22no—
137C2×D17—22no—
138C2×D17—22no—
139C2×D17—41no—
140C2×D17—41no—
141C2×D17—41no—
142C2×D17—41no—
143C4×C17—22no—
144C4×C17—22no—
145C4×C17—22no—
146C4×C17—82no—
147Dic17—22no—
148Dic17—22no—
149Dic17—21no—
150Dic17—21no—
151Dic17—82no—
152C2×C4⋊Q8—171no—
153C2×C22⋊Q8—172no—
154C22×C42—171no—
155C2×C4⋊C8—341no—
156C2×C22⋊C8—341no—
157C2×C22⋊C8—341no—
158#391—172no—
159#389—341no—
160#389—341no—
161#384#59511yescharacteristic
162#380—341no—
163#380—341no—
164#336—172no—
165#336—172no—
166#336—341no—
167C2×C17#147111yescharacteristic
168C2×C17#148111yescharacteristic
169C2×C17#149711yescharacteristic
170C2×C17#151111yescharacteristic
171C2×C17#152011yescharacteristic
172C2×C17#153611yescharacteristic
173C2×C17#154811yescharacteristic
174D17—42no—
175C22×Q8—172no—
176C23×C4—171no—
177C23×C4—171no—
178C23×C4—171no—
179C22×C8—342no—
180C22×C8—342no—
181C4⋊Q8—682no—
182C22⋊Q8—684no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—342no—
186C2×C4⋊C4—341no—
187C2×C4⋊C4—341no—
188C2×C4⋊C4C2×#59512yes—
189C2×C22⋊C4—342no—
190C2×C42—171no—
191C2×C42—171no—
192C2×C42—171no—
193C2×C42—682no—
194C2×C42C2×#59511yescharacteristic
195C4⋊C8—682no—
196C22⋊C8—682no—
197C22⋊C8—682no—
198#95—342no—
199#95—342no—
200C17#772711yescharacteristic, complemented, Sylow
201C24—171no—
202C2×Q8—344no—
203C2×Q8—682no—
204C2×Q8—682no—
205C22×C4—22no—
206C22×C4—171no—
207C22×C4—171no—
208C22×C4—171no—
209C22×C4—172no—
210C22×C4—172no—
211C22×C4—342no—
212C22×C4—342no—
213C22×C4—342no—
214C22×C4—342no—
215C22×C4—342no—
216C22×C4—681no—
217C22×C4—681no—
218C22×C4—681no—
219C22×C4—681no—
220C22×C4C22⋊#59511yescharacteristic
221C22×C4C22⋊#59511yescharacteristic
222C22×C4C22×#59511yescharacteristic
223C2×C8—682no—
224C2×C8—682no—
225C2×C8—682no—
226C2×C8—682no—
227C2×C8—682no—
228C2×C8—682no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—682no—
233C4⋊C4—684no—
234C4⋊C4—682no—
235C22⋊C4—684no—
236C42—22no—
237C42—342no—
238C42—681no—
239C42—681no—
240C23—172no—
241C23—341no—
242C23—341no—
243C23—341no—
244C23—341no—
245C23—341no—
246C23—341no—
247C23C2×C22⋊#59511yescharacteristic
248Q8—1364no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—172no—
259C2×C4—171no—
260C2×C4—171no—
261C2×C4—172no—
262C2×C4—341no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—341no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—682no—
269C2×C4—682no—
270C2×C4—684no—
271C2×C4—684no—
272C2×C4—682no—
273C2×C4—682no—
274C2×C4—682no—
275C2×C4#1058753912yes—
276C2×C4#1058754912yes—
277C2×C4#1058768012yes—
278C8—1362no—
279C8—1362no—
280C22—342no—
281C22—342no—
282C22—342no—
283C22—681no—
284C22—681no—
285C22—681no—
286C22—681no—
287C22#1176378411yescharacteristic
288C22C2×#1058753911yescharacteristic
289C22D17⋊#10011yescharacteristic
290C22C2×#1058754911yescharacteristic
291C22#1176380211yescharacteristic
292C22#1176380711yescharacteristic
293C22#1176380711yescharacteristic
294C4—22no—
295C4—22no—
296C4—22no—
297C4—82no—
298C4—342no—
299C4—341no—
300C4—341no—
301C4—342no—
302C4—1362no—
303C2—682no—
304C2#1454406111yescharacteristic
305C2#1454409411yescharacteristic
306C2#1454414811yescharacteristic
307C2#1454419211yescharacteristic
308C2#1454422311yescharacteristic
309C2#1454427311yescharacteristic
310C2#1454429811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#384C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#384#595
hypocenterC17#7727
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #14543605C2semidirect
200. C17#7727semidirect

Maximal subgroups

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

subgroupindex
#145446762
#145446412
#145436052
#145371372
#772717