Finite Group Databasebeta

← #17950033

Subgroups — #17950033

Order 4352.

468 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 94 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#14544675C211yesmaximal, characteristic
2C4×C22⋊#3624C211yesmaximal, characteristic
3#14543603C212yesmaximal, complemented
4#14543602C212yesmaximal, complemented
5#14537092C211yesmaximal, characteristic
6C2×C22⋊#3624—21no—
7C2×C22⋊#3624—21no—
8C2×C4×#3624—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587576C411yescharacteristic
13C22×C4×Dic17C2211yescharacteristic
14#11762708C2211yescharacteristic
15#11762705C2211yescharacteristic
16#11762696—21no—
17#11762692—21no—
18#11762684—21no—
19#11762681—21no—
20#11762674C411yescharacteristic
21#11762669C411yescharacteristic
22C17×#380C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17D411yescharacteristic
25C23×Dic17D411yescharacteristic
26C22×#3624—22no—
27C22×#3624—22no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17C2×C411yescharacteristic
30C2×C22⋊C4×C17—21no—
31C2×C22⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17C2×C411yescharacteristic
35C2×C4⋊Dic17C2×C411yescharacteristic
36C2×#63225—21no—
37C2×#63225—21no—
38C2×C4×Dic17—42no—
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C2×C4×Dic17C2311yescharacteristic
43#10587576—42no—
44C22⋊#3624—24no—
45C22⋊#3624—42no—
46C4×#3624—42no—
47C17×#95—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53C24×C17C22⋊C411yescharacteristic
54C22×C4×C17—22no—
55C22×C4×C17—22no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—41no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—22no—
62C22×Dic17—22no—
63C22×Dic17—22no—
64C22×Dic17—22no—
65C22×Dic17—21no—
66C22×Dic17—21no—
67C22×Dic17—41no—
68C22×Dic17—41no—
69C22×Dic17C22⋊C411yescharacteristic
70C22×Dic17C22⋊C411yescharacteristic
71C22×Dic17C2×D411yescharacteristic
72C22×Dic17C2×D411yescharacteristic
73C2×#3624—24no—
74C2×#3624—42no—
75C2×#3624—42no—
76C2×#3624—42no—
77C2×#3624—42no—
78C2×#3624—42no—
79C4⋊C4×C17—22no—
80C4⋊C4×C17—41no—
81C22⋊C4×C17—42no—
82C22⋊Dic17—42no—
83C4⋊Dic17—22no—
84C4⋊Dic17—42no—
85C4⋊Dic17—42no—
86C4⋊Dic17—41no—
87#63225—42no—
88#63225—42no—
89C4×Dic17—22no—
90C4×Dic17—22no—
91C4×Dic17—41no—
92C4×Dic17—41no—
93#7671—171nomaximal, Sylow
94C23×C17—21no—
95C23×C17—21no—
96C23×C17—21no—
97C23×C17—21no—
98C23×C17—21no—
99C23×C17—21no—
100C23×C17#10412yes—
101C23×C17C2×C22⋊C411yescharacteristic
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—44no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17#10112yes—
114C2×C4×C17#13112yes—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—21no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17—21no—
122C2×Dic17—21no—
123C2×Dic17—21no—
124C2×Dic17—44no—
125C2×Dic17—44no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—41no—
132C2×Dic17#9912yes—
133C2×Dic17#13512yes—
134C2×Dic17#13512yes—
135#3624—44no—
136#3624—82no—
137#2851—171no—
138#1817—171no—
139C4×C22⋊C8—171no—
140#1271—172no—
141#1271—172no—
142C22×C17—22no—
143C22×C17—22no—
144C22×C17—22no—
145C22×C17—41no—
146C22×C17—41no—
147C22×C17—41no—
148C22×C17—41no—
149C22×C17#40811yescharacteristic
150C22×C17C2×#9911yescharacteristic
151C22×C17C2×#10111yescharacteristic
152C22×C17#41611yescharacteristic
153C22×C17#41611yescharacteristic
154C22×C17C2×#10411yescharacteristic
155C22×C17#42111yescharacteristic
156C4×C17—22no—
157C4×C17—22no—
158C4×C17—81no—
159C4×C17—81no—
160Dic17—22no—
161Dic17—22no—
162Dic17—22no—
163Dic17—41no—
164Dic17—81no—
165Dic17—81no—
166C2×#125—171no—
167C22×C42—171no—
168C2×C22⋊C8—341no—
169C2×C22⋊C8—341no—
170C2×C4×C8—341no—
171#389—171no—
172#389—171no—
173#387—341no—
174#387—341no—
175#385—341no—
176#385—341no—
177#382—171no—
178#380—171no—
179#380#59511yescharacteristic
180#336—172no—
181#336—172no—
182#336—341no—
183C2×C17—42no—
184C2×C17#147211yescharacteristic
185C2×C17#148211yescharacteristic
186C2×C17#149411yescharacteristic
187C2×C17#150111yescharacteristic
188C2×C17#151611yescharacteristic
189C2×C17#152811yescharacteristic
190C2×C17#154411yescharacteristic
191C23×C4—171no—
192C23×C4—171no—
193C23×C4C2×#59511yescharacteristic
194C22×C8—342no—
195C22×C8—342no—
196#125—682no—
197C2×C4⋊C4—171no—
198C2×C4⋊C4—171no—
199C2×C4⋊C4—341no—
200C2×C4⋊C4—341no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4C2×#59511yescharacteristic
204C2×C4⋊C4C2×#59511yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—341no—
207C2×C42—171no—
208C2×C42—171no—
209C2×C42—171no—
210C2×C42—171no—
211C2×C42—682no—
212C22⋊C8—344no—
213C22⋊C8—682no—
214C4×C8—682no—
215#95—21no—
216#95—341no—
217#95—341no—
218#95—341no—
219#95—341no—
220#95—341no—
221C17#767111yescharacteristic, complemented, Sylow
222C24C22⋊#59511yescharacteristic
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—41no—
228C22×C4—171no—
229C22×C4—171no—
230C22×C4—171no—
231C22×C4—171no—
232C22×C4—342no—
233C22×C4—342no—
234C22×C4—342no—
235C22×C4—342no—
236C22×C4—341no—
237C22×C4—341no—
238C22×C4—681no—
239C22×C4—681no—
240C22×C4C22⋊#59511yescharacteristic
241C22×C4C22×#59511yescharacteristic
242C2×C8—344no—
243C2×C8—682no—
244C2×C8—682no—
245C2×C8—682no—
246C2×C8—682no—
247C2×C8—682no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—342no—
251C4⋊C4—681no—
252C4⋊C4—682no—
253C4⋊C4—682no—
254C4⋊C4—682no—
255C4⋊C4—682no—
256C22⋊C4—42no—
257C22⋊C4—682no—
258C42—342no—
259C42—342no—
260C42—681no—
261C42—681no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#1058754812yes—
269C23C2×C22⋊#59511yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—44no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—172no—
282C2×C4—172no—
283C2×C4—172no—
284C2×C4—341no—
285C2×C4—341no—
286C2×C4—341no—
287C2×C4—341no—
288C2×C4—341no—
289C2×C4—341no—
290C2×C4—341no—
291C2×C4—341no—
292C2×C4—341no—
293C2×C4—684no—
294C2×C4—684no—
295C2×C4—681no—
296C2×C4—681no—
297C2×C4—681no—
298C2×C4—681no—
299C2×C4—681no—
300C2×C4—681no—
301C2×C4#1058754512yes—
302C2×C4#1058767812yes—
303C8—684no—
304C8—1362no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22#1176378211yescharacteristic
313C22D17⋊#9911yescharacteristic
314C22C2×#1058754511yescharacteristic
315C22#1176379911yescharacteristic
316C22#1176379911yescharacteristic
317C22C2×#1058754811yescharacteristic
318C22#1176380811yescharacteristic
319C4—22no—
320C4—22no—
321C4—81no—
322C4—81no—
323C4—342no—
324C4—342no—
325C4—342no—
326C4—681no—
327C4—1361no—
328C4—1361no—
329C2—42no—
330C2#1454406311yescharacteristic
331C2#1454409711yescharacteristic
332C2#1454413511yescharacteristic
333C2#1454416011yescharacteristic
334C2#1454421111yescharacteristic
335C2#1454424611yescharacteristic
336C2#1454428911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#380#595
hypocenterC17#7671
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543603C2semidirect
4. #14543602C2semidirect
221. C17#7671semidirect

Maximal subgroups

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

subgroupindex
#145446752
C4×C22⋊#36242
#145436032
#145436022
#145370922
#767117