Finite Group Databasebeta

← #16929950

Subgroups — #16929950

Order 4352.

530 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762866C211yesmaximal, characteristic
2#14528546C211yesmaximal, characteristic
3C2×#11762551C212yesmaximal, complemented
4#14526665C212yesmaximal, complemented
5C17×#2851C211yesmaximal, characteristic
6#11762866—24no—
7C2×C4⋊#3622—21no—
8C2×C22⋊#3622—21no—
9C2×C22⋊#3622—21no—
10C2×#10587474C2212yes—
11C2×#10587474C2212yes—
12#11762564—21no—
13#11762551—24no—
14C2×C17×#125C2211yescharacteristic
15C22×C42×C17C2211yescharacteristic
16C17×#389C411yescharacteristic
17C17×#389C411yescharacteristic
18C17×#387—21no—
19C17×#387—21no—
20C17×#385—21no—
21C17×#385—21no—
22C17×#382C2211yescharacteristic
23C17×#380C411yescharacteristic
24C17×#380C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C17×#125—22no—
29C17×#125—22no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17C2×C411yescharacteristic
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C42×C17—22no—
41C2×C42×C17—22no—
42C2×C42×C17C2×C411yescharacteristic
43C2×C42×C17D411yescharacteristic
44C2×C42×C17D411yescharacteristic
45C2×C42×C17C2311yescharacteristic
46C22×#3622—22no—
47C22×#3622—22no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C17×#95—21no—
54C22⋊#3622—24no—
55C22⋊#3622—24no—
56C4⋊#3622—24no—
57#10587474—22no—
58#10587474—22no—
59#10587474—22no—
60#10587474D414yes—
61C24×C17C22⋊C411yescharacteristic
62C22×C4×C17—22no—
63C22×C4×C17—22no—
64C22×C4×C17—22no—
65C22×C4×C17—21no—
66C22×C4×C17—22no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—41no—
73C22×C4×C17—41no—
74C22×C4×C17—41no—
75C22×C4×C17—41no—
76C22×C4×C17C22⋊C411yescharacteristic
77C22×C4×C17C22⋊C411yescharacteristic
78C22×C4×C17C22⋊C411yescharacteristic
79C22×C4×C17C22×C411yescharacteristic
80C22×C4×C17C2×D411yescharacteristic
81C22×C4×C17C2×D411yescharacteristic
82C4⋊C4×C17—22no—
83C4⋊C4×C17—22no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—42no—
87C4⋊C4×C17—42no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—42no—
90C4⋊C4×C17—41no—
91C22⋊C4×C17—42no—
92C22⋊C4×C17—42no—
93C42×C17—22no—
94C42×C17—21no—
95C42×C17—22no—
96C42×C17—21no—
97C42×C17C2×D412yes—
98C42×C17#4112yes—
99C2×#3622—24no—
100C2×#3622—24no—
101C2×#3622—42no—
102C2×#3622—42no—
103C2×#3622—42no—
104C2×#3622—42no—
105#9125—171nomaximal, Sylow
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17#10412yes—
113C23×C17C2×C22⋊C411yescharacteristic
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—44no—
129C2×C4×C17—44no—
130C2×C4×C17—42no—
131C2×C4×C17—42no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—41no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17#10112yes—
145C2×C4×C17C4×D412yes—
146C2×C4×C17#12011yescharacteristic
147C2×C4×C17#12112yes—
148C2×C4×C17#12311yescharacteristic
149#3622—44no—
150#3622—44no—
151C2×#432—171no—
152#2851D1711yescharacteristic
153#1749—171no—
154C2×#330—172no—
155#1295—172no—
156C22×C17—22no—
157C22×C17—22no—
158C22×C17—22no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17#38611yescharacteristic
164C22×C17C2×#10111yescharacteristic
165C22×C17#41311yescharacteristic
166C22×C17C2×#10411yescharacteristic
167C22×C17#42111yescharacteristic
168C22×C17#42111yescharacteristic
169C22×C17#42111yescharacteristic
170C4×C17—22no—
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—22no—
174C4×C17—22no—
175C4×C17—41no—
176C4×C17—41no—
177C4×C17—81no—
178C4×C17—81no—
179C4×C17—81no—
180C4×C17—81no—
181C2×#125C2×D1711yescharacteristic
182C22×C42C2×D1711yescharacteristic
183#432—344no—
184C2×C4⋊C8—341no—
185C2×C22⋊C8—341no—
186C2×C22⋊C8—341no—
187C2×#97—172no—
188C2×#97—172no—
189#389Dic1711yescharacteristic
190#389Dic1711yescharacteristic
191#387—21no—
192#387—21no—
193#385—21no—
194#385—21no—
195#382C2×D1711yescharacteristic
196#380Dic1711yescharacteristic
197#380Dic1711yescharacteristic
198#336—341no—
199#330—344no—
200C2×C17—42no—
201C2×C17#152811yescharacteristic
202C2×C17#153211yescharacteristic
203C2×C17#153511yescharacteristic
204C2×C17#153711yescharacteristic
205C2×C17#187111yescharacteristic
206C2×C17#189711yescharacteristic
207C2×C17#190111yescharacteristic
208C23×C4C2×Dic1711yescharacteristic
209C23×C4C22⋊D1711yescharacteristic
210C23×C4C22⋊D1711yescharacteristic
211C22×C8—342no—
212C22×C8—342no—
213#125—22no—
214#125—22no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C2×Dic1711yescharacteristic
220C2×C4⋊C4C2×Dic1711yescharacteristic
221C2×C4⋊C4C2×Dic1711yescharacteristic
222C2×C4⋊C4C2×Dic1711yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42C2×Dic1711yescharacteristic
228C2×C42C22⋊D1711yescharacteristic
229C2×C42C22⋊D1711yescharacteristic
230C2×C42C22×D1711yescharacteristic
231C4⋊C8—344no—
232C22⋊C8—344no—
233C22⋊C8—344no—
234#97—174no—
235#97—342no—
236#97—342no—
237#97—342no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244C17#912511yescharacteristic, complemented, Sylow
245C24C22⋊Dic1711yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4C22⋊Dic1711yescharacteristic
261C22×C4C22⋊Dic1711yescharacteristic
262C22×C4C22⋊Dic1711yescharacteristic
263C22×C4C22×Dic1711yescharacteristic
264C22×C4C2×C22⋊D1711yescharacteristic
265C22×C4C2×C22⋊D1711yescharacteristic
266C2×C8—344no—
267C2×C8—344no—
268C2×C8—682no—
269C2×C8—682no—
270C2×C8—682no—
271C2×C8—682no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—22no—
284C42—21no—
285C42—21no—
286C42—22no—
287C42D4×D1712yes—
288C42#6325412yes—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#1058750812yes—
296C23C2×C22⋊Dic1711yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4#1058750712yes—
328C2×C4D4×Dic1712yes—
329C2×C4#1058762111yescharacteristic
330C2×C4#1058762311yescharacteristic
331C2×C4#1058762512yes—
332C8—684no—
333C8—684no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22#1176268911yescharacteristic
342C22C2×#1058750711yescharacteristic
343C22#1176279311yescharacteristic
344C22C2×#1058750811yescharacteristic
345C22#1176282611yescharacteristic
346C22#1176282611yescharacteristic
347C22#1176282611yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—81no—
359C2—42no—
360C2#1452738611yescharacteristic
361C2#1452740411yescharacteristic
362C2#1452741511yescharacteristic
363C2#1452742211yescharacteristic
364C2#1452908711yescharacteristic
365C2#1452923311yescharacteristic
366C2#1452925311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic17
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2851C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2851D17
hypocenterC17#9125
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. C2×#11762551C2semidirect
4. #14526665C2semidirect
244. C17#9125semidirect

Maximal subgroups

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

subgroupindex
C2×#117628662
#145285462
C2×#117625512
#145266652
C17×#28512
#912517