Finite Group Databasebeta

← #16945095

Subgroups — #16945095

Order 4352.

434 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 91 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#14528772C211yesmaximal, characteristic
2#14527125C211yesmaximal, characteristic
3#14526808C212yesmaximal, complemented
4#14526784C212yesmaximal, complemented
5C17×#2395C211yesmaximal, characteristic
6#11762866—21no—
7C2×#10587505—21no—
8#11762669—21no—
9#11762576C2212yes—
10#11762533—21no—
11#11762533C2212yes—
12C2×C4×D4×C17C2211yescharacteristic
13C2×C17×#117C411yescharacteristic, complemented
14C17×#400C411yescharacteristic, complemented
15C17×#399C2211yescharacteristic
16C17×#398C411yescharacteristic, complemented
17C17×#397—21no—
18C17×#397C2211yescharacteristic
19C17×#394—21no—
20C4×C4⋊C4×C17—21no—
21C4×C22⋊C4×C17—21no—
22C4×C22⋊C4×C17C411yescharacteristic, complemented
23C22×D4×C17D411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C4×D4×C17—41no—
27C4×D4×C17—41no—
28C17×#117—41no—
29C17×#117—41no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C22⋊C4×C17—21no—
36C2×C22⋊C4×C17—21no—
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17D411yescharacteristic
40C2×C22⋊C4×C17C2311yescharacteristic
41C2×C42×C17—21no—
42C2×C42×C17—21no—
43C2×C42×C17D411yescharacteristic
44C2×C22⋊Dic17—22no—
45C2×C4⋊Dic17—41no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95C2×C411yescharacteristic
51C17×#95C2×C411yescharacteristic
52#10587505—42no—
53#10587502—41no—
54C22⋊#3622—22no—
55C4⋊#3622—41no—
56#10587474—41no—
57C24×C17C22⋊C411yescharacteristic
58C24×C17C2×D411yescharacteristic
59C2×D4×C17—21no—
60C2×D4×C17—21no—
61C2×D4×C17—41no—
62C2×D4×C17—41no—
63C22×C4×C17—21no—
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—42no—
72C22×C4×C17—42no—
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22×C411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×Dic17—42no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—42no—
83C4⋊C4×C17—42no—
84C22⋊C4×C17—41no—
85C22⋊C4×C17—41no—
86C22⋊C4×C17—42no—
87C22⋊C4×C17—42no—
88C22⋊C4×C17—42no—
89C22⋊C4×C17—41no—
90C22⋊C4×C17—41no—
91C42×C17—21no—
92C42×C17—21no—
93C42×C17—42no—
94C42×C17—41no—
95C42×C17—41no—
96C22⋊Dic17—42no—
97C22⋊Dic17—42no—
98C4⋊Dic17—82no—
99C2×#3622—42no—
100#11822—171nomaximal, Sylow
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17C2×C22⋊C411yescharacteristic
111C23×C17AGL(1,ℤ/8)11yescharacteristic
112C23×C17#13711yescharacteristic
113D4×C17—42no—
114D4×C17—42no—
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—21no—
122C2×C4×C17—21no—
123C2×C4×C17—42no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—42no—
127C2×C4×C17—42no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
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—81no—
141C2×C4×C17#9911yescharacteristic
142C2×C4×C17#9911yescharacteristic
143C2×Dic17—82no—
144C2×Dic17—82no—
145C2×Dic17—82no—
146#3622—82no—
147#2395D1711yescharacteristic
148#1799—171no—
149#1466—171no—
150#1352—172no—
151#1344—172no—
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—21no—
156C22×C17—41no—
157C22×C17—41no—
158C22×C17—41no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—81no—
164C22×C17—81no—
165C22×C17—81no—
166C22×C17C2×#9911yescharacteristic
167C22×C17#41711yescharacteristic
168C22×C17#42111yescharacteristic
169C4×C17—21no—
170C4×C17—42no—
171C4×C17—41no—
172C4×C17—41no—
173C4×C17—41no—
174C4×C17—41no—
175C4×C17—81no—
176C4×C17—81no—
177C4×C17—81no—
178C4×C17#35212yes—
179Dic17—162no—
180C2×C4×D4C2×D1711yescharacteristic
181C2×#117Dic1711yescharacteristic, complemented
182#432—341no—
183C2×#99—341no—
184#400Dic1711yescharacteristic, complemented
185#399C2×D1711yescharacteristic
186#398Dic1711yescharacteristic, complemented
187#397—21no—
188#397C2×D1711yescharacteristic
189#394—21no—
190#380—341no—
191C4×C4⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4Dic1711yescharacteristic, complemented
194#342—172no—
195#323—172no—
196#323—341no—
197C2×C17—21no—
198C2×C17—21no—
199C2×C17—41no—
200C2×C17—41no—
201C2×C17—81no—
202C2×C17#151311yescharacteristic
203C2×C17C2×#35211yescharacteristic
204C2×C17#212611yescharacteristic
205C22×D4C22⋊D1711yescharacteristic
206C23×C4C2×Dic1711yescharacteristic
207C23×C4C22⋊D1711yescharacteristic
208C4×D4—41no—
209C4×D4—41no—
210#117—41no—
211#117—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—681no—
215C2×C4⋊C4C2×Dic1711yescharacteristic
216C2×C4⋊C4C2×Dic1711yescharacteristic
217C2×C4⋊C4C2×Dic1711yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—342no—
223C2×C22⋊C4C22⋊D1711yescharacteristic
224C2×C22⋊C4C22×D1711yescharacteristic
225C2×C42—21no—
226C2×C42—21no—
227C2×C42C22⋊D1711yescharacteristic
228C4⋊C8—681no—
229#99—682no—
230C22⋊C8—342no—
231#97—681no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—681no—
237#95C2×Dic1711yescharacteristic
238#95C2×Dic1711yescharacteristic
239C17#1182211yescharacteristic, complemented, Sylow
240C24C22⋊Dic1711yescharacteristic
241C24C2×C22⋊D1711yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—41no—
245C2×D4—41no—
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—42no—
255C22×C4—42no—
256C22×C4—682no—
257C22×C4C22⋊Dic1711yescharacteristic
258C22×C4C22⋊Dic1711yescharacteristic
259C22×C4C22⋊Dic1711yescharacteristic
260C22×C4C22×Dic1711yescharacteristic
261C22×C4C2×C22⋊D1711yescharacteristic
262C2×C8—682no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—1362no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—682no—
277C22⋊C4—682no—
278C42—21no—
279C42—21no—
280C42—42no—
281C42—41no—
282C42—41no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23#1058763511yescharacteristic
293C23#1058763711yescharacteristic
294C23C2×C22⋊Dic1711yescharacteristic
295D4—42no—
296D4—42no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
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—1362no—
324C2×C4—1362no—
325C2×C4—1362no—
326C2×C4#1058750511yescharacteristic
327C2×C4#1058750511yescharacteristic
328C8—1362no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C2×#1058750511yescharacteristic
344C22#1176281011yescharacteristic
345C22#1176282611yescharacteristic
346C4—21no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4—2722no—
356C4#1176259912yes—
357C2—21no—
358C2—21no—
359C2—41no—
360C2—41no—
361C2—81no—
362C2#1452732711yescharacteristic
363C2C2×#1176259911yescharacteristic
364C2#1453044911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#2395C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenter#2395D17
hypocenterC17#11822
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2395

Complements

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

NH ≅ G/Ntype
3. #14526808C2semidirect
4. #14526784C2semidirect
13. C2×C17×#117C4semidirect
14. C17×#400C4semidirect
16. C17×#398C4semidirect
22. C4×C22⋊C4×C17C4semidirect
181. C2×#117Dic17semidirect
184. #400Dic17semidirect
186. #398Dic17semidirect
193. C4×C22⋊C4Dic17semidirect
239. C17#11822semidirect

Maximal subgroups

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

subgroupindex
#145287722
#145271252
#145268082
#145267842
C17×#23952
#1182217