Finite Group Databasebeta

← #16944855

Subgroups — #16944855

Order 4352.

462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#11762578C211yesmaximal, characteristic
2#14527114C211yesmaximal, characteristic
3#14526814C212yesmaximal, complemented
4#14526790C212yesmaximal, complemented
5C17×#2583C211yesmaximal, characteristic
6C22×#63223—21no—
7#11762773—21no—
8#11762578—21no—
9#11762578C2212yes—
10#11762535—21no—
11#11762535C2212yes—
12C2×C17×C22⋊Q8C411yescharacteristic
13C22×C4⋊C4×C17C2211yescharacteristic
14C17×#398C411yescharacteristic
15C17×#398C2211yescharacteristic
16C17×#395C411yescharacteristic
17C17×#395C2211yescharacteristic
18C17×#389—21no—
19C17×#389—21no—
20C17×#385—21no—
21C17×#385—21no—
22C4×C22⋊C4×C17C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C17×C22⋊Q8—41no—
28C17×C22⋊Q8—41no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—41no—
35C2×C4⋊C4×C17—41no—
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C4⋊C4×C17D411yescharacteristic
39C2×C4⋊C4×C17D411yescharacteristic
40C2×C4⋊C4×C17C2311yescharacteristic
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C42×C17—21no—
44C2×#63223—24no—
45C2×#63223—22no—
46C2×#63223—41no—
47C2×#63223—42no—
48C2×#63223—41no—
49C22×#3622—41no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C17×#95—21no—
54C17×#95C2×C411yescharacteristic
55C17×#95C2×C411yescharacteristic
56C22⋊#3622—22no—
57C22⋊#3622—41no—
58C24×C17C22⋊C411yescharacteristic
59C2×Q8×C17—41no—
60C2×Q8×C17—81no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—22no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—81no—
75C22×C4×C17—81no—
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—41no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—41no—
87C4⋊C4×C17—42no—
88C4⋊C4×C17—42no—
89C4⋊C4×C17—41no—
90C4⋊C4×C17—41no—
91C4⋊C4×C17—81no—
92C4⋊C4×C17—81no—
93C22⋊C4×C17—24no—
94C22⋊C4×C17—41no—
95C22⋊C4×C17—41no—
96C42×C17—81no—
97#63223—24no—
98#63223—44no—
99#63223—42no—
100#63223—82no—
101C2×#3622—44no—
102C2×#3622—42no—
103C2×#3622—42no—
104#11768—171nomaximal, Sylow
105C23×C17—22no—
106C23×C17—21no—
107C23×C17—21no—
108C23×C17—41no—
109C23×C17#9911yescharacteristic
110C23×C17#9911yescharacteristic
111C23×C17C2×C22⋊C411yescharacteristic
112Q8×C17—82no—
113C2×C4×C17—22no—
114C2×C4×C17—22no—
115C2×C4×C17—22no—
116C2×C4×C17—22no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—22no—
122C2×C4×C17—22no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—42no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
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—81no—
143C2×C4×C17—81no—
144C2×C4×C17—81no—
145C2×C4×C17#10412yes—
146C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C17#13711yescharacteristic
148#3622—44no—
149#3622—82no—
150#2583D1711yescharacteristic
151C2×#343—171no—
152#1463—171no—
153#1354—172no—
154#1346—172no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—21no—
158C22×C17—21no—
159C22×C17—21no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17—42no—
163C22×C17—42no—
164C22×C17#35612yes—
165C22×C17C2×#9911yescharacteristic
166C22×C17#41711yescharacteristic
167C22×C17C2×#10411yescharacteristic
168C4×C17—21no—
169C4×C17—22no—
170C4×C17—21no—
171C4×C17—42no—
172C4×C17—42no—
173C4×C17—41no—
174C4×C17—41no—
175C4×C17—41no—
176C4×C17—41no—
177C4×C17—81no—
178C4×C17—81no—
179C22×M16—341no—
180C2×C22⋊Q8Dic1711yescharacteristic
181C22×C4⋊C4C2×D1711yescharacteristic
182#407—341no—
183#398Dic1711yescharacteristic
184#398C2×D1711yescharacteristic
185#395Dic1711yescharacteristic
186#395C2×D1711yescharacteristic
187#389—21no—
188#389—21no—
189#385—21no—
190#385—21no—
191C4×C22⋊C4Dic1711yescharacteristic
192#343—172no—
193#343—341no—
194#324—172no—
195#324—341no—
196C2×C17—21no—
197C2×C17—21no—
198C2×C17—22no—
199C2×C17—41no—
200C2×C17#150411yescharacteristic
201C2×C17#212111yescharacteristic
202C2×C17C2×#35611yescharacteristic
203C22×Q8C2×Dic1711yescharacteristic
204C23×C4C2×Dic1711yescharacteristic
205C23×C4C22⋊D1711yescharacteristic
206C23×C4C22⋊D1711yescharacteristic
207C2×M16—344no—
208C2×M16—342no—
209C2×M16—681no—
210C2×M16—682no—
211C2×M16—681no—
212C22×C8—681no—
213C22⋊Q8—41no—
214C22⋊Q8—41no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4C2×Dic1711yescharacteristic
223C2×C4⋊C4C2×Dic1711yescharacteristic
224C2×C4⋊C4C22⋊D1711yescharacteristic
225C2×C4⋊C4C22⋊D1711yescharacteristic
226C2×C4⋊C4C22×D1711yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C42—21no—
230C22⋊C8—342no—
231C22⋊C8—681no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95C2×Dic1711yescharacteristic
237#95C2×Dic1711yescharacteristic
238C17#1176811yescharacteristic, complemented, Sylow
239C24C22⋊Dic1711yescharacteristic
240C2×Q8—41no—
241C2×Q8—81no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4C22⋊Dic1711yescharacteristic
258C22×C4C22⋊Dic1711yescharacteristic
259C22×C4C22⋊Dic1711yescharacteristic
260C22×C4C22×Dic1711yescharacteristic
261C22×C4C2×C22⋊D1711yescharacteristic
262C22×C4C2×C22⋊D1711yescharacteristic
263M16—344no—
264M16—684no—
265M16—682no—
266M16—1362no—
267C2×C8—684no—
268C2×C8—682no—
269C2×C8—682no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—81no—
280C4⋊C4—81no—
281C22⋊C4—24no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—81no—
285C23—21no—
286C23—21no—
287C23—22no—
288C23—41no—
289C23#1058750511yescharacteristic
290C23#1058750511yescharacteristic
291C23C2×C22⋊Dic1711yescharacteristic
292Q8—82no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4#1058750812yes—
326C2×C4#1058763511yescharacteristic
327C2×C4#1058763711yescharacteristic
328C8—684no—
329C8—1362no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22#1176260812yes—
340C22C2×#1058750511yescharacteristic
341C22#1176281011yescharacteristic
342C22C2×#1058750811yescharacteristic
343C4—21no—
344C4—22no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—81no—
353C4—81no—
354C2—21no—
355C2—21no—
356C2—22no—
357C2—41no—
358C2#1452728811yescharacteristic
359C2#1453043011yescharacteristic
360C2C2×#1176260811yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2583C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2583D17
hypocenterC17#11768
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
3. #14526814C2semidirect
4. #14526790C2semidirect
238. C17#11768semidirect

Maximal subgroups

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

subgroupindex
C2×#117625782
#145271142
#145268142
#145267902
C17×#25832
#1176817