Finite Group Databasebeta

← #17950097

Subgroups — #17950097

Order 4352.

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

normal subgroups only

This group has 410 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#14544569C211yesmaximal, characteristic
2C4×C4⋊#3624C211yesmaximal, characteristic
3#14543604C212yesmaximal
4#14543603C212yesmaximal
5#14537163C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C4⋊#3624—21no—
8C2×#10587542—21no—
9C2×C4×#3624—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12#11762716C411yescharacteristic
13#11762716C2211yescharacteristic
14#11762708C411yescharacteristic
15#11762707C411yescharacteristic
16#11762705C2211yescharacteristic
17#11762696—21no—
18#11762694—21no—
19#11762691—21no—
20#11762676—21no—
21C42×Dic17C2211yescharacteristic
22C17×#391C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C22×#3624—22no—
25C22×#3624—22no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C42×C17C2×C411yescharacteristic
28C2×C4⋊Dic17—21no—
29C2×C4⋊Dic17C2×C411yescharacteristic
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×#63225—21no—
32C2×#63225—21no—
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36C2×C4×Dic17D411yescharacteristic
37C2×C4×Dic17D411yescharacteristic
38C2×C4×Dic17C2311yescharacteristic
39#10587544—24no—
40#10587542—42no—
41C4⋊#3624—24no—
42C4×#3624—42no—
43C17×#95—21no—
44C17×#95—21no—
45#10587502—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52C2×Q8×C17—22no—
53C2×Q8×C17—41no—
54C2×Q8×C17—41no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×Dic17—21no—
61C22×Dic17—21no—
62C22×Dic17C22⋊C411yescharacteristic
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C2×#3624—24no—
67C2×#3624—24no—
68C2×#3624—42no—
69C2×#3624—42no—
70C2×#3624—42no—
71C2×#3624—42no—
72C4⋊C4×C17—41no—
73C42×C17—22no—
74C4⋊Dic17—22no—
75C4⋊Dic17—42no—
76C4⋊Dic17—41no—
77#63225—42no—
78#63225—41no—
79#63225—41no—
80C4×Dic17—22no—
81C4×Dic17—22no—
82C4×Dic17—21no—
83C4×Dic17—21no—
84C4×Dic17—41no—
85C4×Dic17—41no—
86C4×Dic17SD1612yes—
87C4×Dic17Q1612yes—
88#7689—171nomaximal, Sylow
89C23×C17C2×C22⋊C411yescharacteristic
90Q8×C17—82no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17#10312yes—
104C2×C4×C17#10412yes—
105C2×C4×C17#13112yes—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17#10312yes—
121C2×Dic17#10412yes—
122C2×Dic17C2×SD1611yescharacteristic
123C2×Dic17C2×Q1611yescharacteristic
124C2×Dic17AGL(1,ℤ/8)11yescharacteristic
125C2×Dic17#13711yescharacteristic
126#3624—44no—
127#3624—44no—
128#2863—171no—
129#1767—171no—
130C4×C4⋊C8—171no—
131#1272—172no—
132#1271—172no—
133C22×C17#40811yescharacteristic
134C22×C17#41011yescharacteristic
135C22×C17#41311yescharacteristic
136C22×C17C2×#10311yescharacteristic
137C22×C17#41711yescharacteristic
138C22×C17C2×#10411yescharacteristic
139C22×C17C2×#10411yescharacteristic
140C4×C17—22no—
141C4×C17—22no—
142C4×C17—22no—
143C4×C17—81no—
144C4×C17—81no—
145Dic17—22no—
146Dic17—21no—
147Dic17—21no—
148Dic17—21no—
149Dic17—21no—
150Dic17—22no—
151Dic17—81no—
152Dic17—81no—
153C2×C4⋊C8—341no—
154C2×C4⋊C8—341no—
155C2×#97—341no—
156C2×C4×C8—341no—
157#391—171no—
158#391—171no—
159#391#59511yescharacteristic
160#389—171no—
161#389—171no—
162#389—171no—
163#387—341no—
164#387—341no—
165#387—341no—
166#383—341no—
167C43—171no—
168#336—172no—
169#336—172no—
170C2×C17#147311yescharacteristic
171C2×C17#148311yescharacteristic
172C2×C17#149311yescharacteristic
173C2×C17#150311yescharacteristic
174C2×C17#150911yescharacteristic
175C2×C17#152411yescharacteristic
176C2×C17#155011yescharacteristic
177C22×Q8C2×#59511yescharacteristic
178C22×C8—342no—
179C22×C8—342no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4—171no—
182C2×C4⋊C4—341no—
183C2×C4⋊C4—341no—
184C2×C4⋊C4—341no—
185C2×C4⋊C4C2×#59511yescharacteristic
186C2×C42—171no—
187C2×C42—171no—
188C2×C42—171no—
189C2×C42—171no—
190C2×C42—171no—
191C2×C42—171no—
192C2×C42C2×#59511yescharacteristic
193C4⋊C8—344no—
194C4⋊C8—344no—
195#97—682no—
196C4×C8—682no—
197#95—21no—
198#95—21no—
199#95—341no—
200#95—341no—
201#95—341no—
202#95—341no—
203#95—341no—
204#95—341no—
205#95—341no—
206C17#768911yescharacteristic, complemented, Sylow
207C2×Q8—22no—
208C2×Q8—41no—
209C2×Q8—41no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—171no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—171no—
216C22×C4—341no—
217C22×C4—341no—
218C22×C4C22⋊#59511yescharacteristic
219C22×C4C22⋊#59511yescharacteristic
220C22×C4C22×#59511yescharacteristic
221C2×C8—344no—
222C2×C8—344no—
223C2×C8—682no—
224C2×C8—682no—
225C2×C8—682no—
226C2×C8—682no—
227C4⋊C4—41no—
228C4⋊C4—342no—
229C4⋊C4—681no—
230C4⋊C4—681no—
231C4⋊C4—681no—
232C4⋊C4—682no—
233C4⋊C4—682no—
234C42—22no—
235C42—172no—
236C42—172no—
237C42—341no—
238C42—342no—
239C42—341no—
240C42—342no—
241C42—681no—
242C42—681no—
243C23C2×C22⋊#59511yescharacteristic
244Q8—82no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—171no—
258C2×C4—172no—
259C2×C4—171no—
260C2×C4—171no—
261C2×C4—171no—
262C2×C4—172no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—341no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—341no—
271C2×C4—681no—
272C2×C4—681no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4#1058754912yes—
278C2×C4#1058755012yes—
279C2×C4#1058767812yes—
280C8—684no—
281C8—684no—
282C22#1176378211yescharacteristic
283C22#1176378911yescharacteristic
284C22#1176379511yescharacteristic
285C22C2×#1058754911yescharacteristic
286C22#1176380011yescharacteristic
287C22D17⋊#10411yescharacteristic
288C22C2×#1058755011yescharacteristic
289C4—22no—
290C4—22no—
291C4—22no—
292C4—81no—
293C4—81no—
294C4—341no—
295C4—341no—
296C4—341no—
297C4—341no—
298C4—342no—
299C4—342no—
300C4—1361no—
301C4—1361no—
302C2#1454406611yescharacteristic
303C2#1454410111yescharacteristic
304C2#1454413211yescharacteristic
305C2#1454416811yescharacteristic
306C2#1454418511yescharacteristic
307C2#1454423611yescharacteristic
308C2#1454430111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#391C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#391#595
hypocenterC17#7689
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
206. C17#7689semidirect

Maximal subgroups

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

subgroupindex
#145445692
C4×C4⋊#36242
#145436042
#145436032
#145371632
#768917