Finite Group Databasebeta

← #16945413

Subgroups — #16945413

Order 4352.

416 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14530395C211yesmaximal, characteristic, complemented
2#14528813C211yesmaximal, characteristic, complemented
3#14526796C212yesmaximal, complemented
4#14526793C212yesmaximal, complemented
5C17×#3050C211yesmaximal, characteristic
6C2×#10587483—21no—
7C2×#10587489—21no—
8#11762669—21no—
9C22⋊#63214—21no—
10C22⋊#63214C2212yes—
11#11762572C2212yes—
12C2×C17×#135C411yescharacteristic, complemented
13C23×C8×C17C2211yescharacteristic
14C17×#525—21no—
15C17×#467C411yescharacteristic, complemented
16C17×#467C2211yescharacteristic
17C17×#466C411yescharacteristic, complemented
18C17×#466C2211yescharacteristic
19C17×#465—21no—
20C17×#465—21no—
21C17×#427C411yescharacteristic, complemented
22C17×#416—21no—
23C2×#41×C17—21no—
24C23×C4×C17D411yescharacteristic
25C17×#135—42no—
26C2×Q16×C17C2×C411yescharacteristic
27C2×SD16×C17—21no—
28C2×D8×C17C2×C411yescharacteristic
29C22×C8×C17—42no—
30C22×C8×C17C2×C411yescharacteristic
31C22×C8×C17C2×C411yescharacteristic
32C22×C8×C17D411yescharacteristic
33C22×C8×C17D411yescharacteristic
34C22×C8×C17D411yescharacteristic
35C22×C8×C17C2311yescharacteristic
36C17×#123—41no—
37C17×C22⋊Q8—21no—
38C17×C22⋊Q8—21no—
39C17×#121—21no—
40C17×#121—21no—
41C17×#120—41no—
42C4×D4×C17—41no—
43C4×D4×C17—41no—
44C17×#117—21no—
45C2×C22⋊Dic17—41no—
46C2×C4⋊Dic17—22no—
47C17×#107C2×C411yescharacteristic
48C17×#107C2×C411yescharacteristic
49C17×#106—21no—
50C17×#103—21no—
51C17×#103—21no—
52C17×#102—21no—
53C17×#102—21no—
54#10587502—41no—
55#10587489—42no—
56#10587483—42no—
57C2×#63214—22no—
58C24×C17D811yescharacteristic
59#41×C17—42no—
60#41×C17—42no—
61C2×Q8×C17—21no—
62C2×D4×C17—21no—
63C2×D4×C17—41no—
64C2×D4×C17—41no—
65C2×D4×C17—41no—
66C22×C4×C17—41no—
67C22×C4×C17—41no—
68C22×C4×C17—41no—
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17D811yescharacteristic
72C22×C4×C17SD1611yescharacteristic
73C22×C4×C17SD1611yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×Dic17—42no—
76Q16×C17—41no—
77SD16×C17—42no—
78D8×C17—41no—
79C2×C8×C17—22no—
80C2×C8×C17—22no—
81C2×C8×C17—22no—
82C2×C8×C17—41no—
83C2×C8×C17—41no—
84C2×C8×C17—41no—
85C2×C8×C17C22⋊C411yescharacteristic
86C2×C8×C17C22⋊C411yescharacteristic
87C2×C8×C17C22×C411yescharacteristic
88C2×C8×C17C2×D411yescharacteristic
89C4⋊C4×C17—21no—
90C4⋊C4×C17—21no—
91C4⋊C4×C17—41no—
92C4⋊C4×C17—41no—
93C22⋊C4×C17—41no—
94C22⋊C4×C17—41no—
95C22⋊C4×C17—41no—
96C22⋊C4×C17—41no—
97C22⋊C4×C17—41no—
98C42×C17—41no—
99C22⋊Dic17—82no—
100C4⋊Dic17—42no—
101C4⋊Dic17—42no—
102#63214—42no—
103#11890—171nomaximal, Sylow
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17#10211yescharacteristic
110C23×C17#10211yescharacteristic
111C23×C17C2×D811yescharacteristic
112Q8×C17—41no—
113Q8×C17—41no—
114D4×C17—41no—
115D4×C17—41no—
116D4×C17—82no—
117D4×C17—82no—
118D4×C17—81no—
119D4×C17—81no—
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—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—82no—
133C2×C4×C17#10211yescharacteristic
134C2×C4×C17#10211yescharacteristic
135C2×C4×C17C2×C22⋊C411yescharacteristic
136C2×C4×C17C2×SD1611yescharacteristic
137C2×Dic17—82no—
138C2×Dic17—82no—
139C2×Dic17—82no—
140C8×C17—21no—
141C8×C17—21no—
142C8×C17—21no—
143C8×C17#9912yes—
144#3050D1711yescharacteristic
145#2112—171no—
146#1808—171no—
147#1348—172no—
148#1347—172no—
149C22×C17—21no—
150C22×C17—21no—
151C22×C17—21no—
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—21no—
156C22×C17—21no—
157C22×C17—42no—
158C22×C17—42no—
159C22×C17—81no—
160C22×C17—81no—
161C22×C17—81no—
162C22×C17C2×#10211yescharacteristic
163C22×C17#50911yescharacteristic
164C22×C17#51011yescharacteristic
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—21no—
168C4×C17—81no—
169C4×C17—81no—
170C4×C17—81no—
171C4×C17C2×#9911yescharacteristic
172C4×C17#42111yescharacteristic
173Dic17—162no—
174C2×#135Dic1711yescharacteristic, complemented
175C23×C8C2×D1711yescharacteristic
176#525—21no—
177C2×M32—341no—
178#467Dic1711yescharacteristic, complemented
179#467C2×D1711yescharacteristic
180#466Dic1711yescharacteristic, complemented
181#466C2×D1711yescharacteristic
182#465—21no—
183#465—21no—
184#427Dic1711yescharacteristic, complemented
185C2×#107—341no—
186#416—21no—
187#380—341no—
188C22⋊C16—172no—
189C22⋊C16—341no—
190#340—172no—
191C2×C17—21no—
192C2×C17—21no—
193C2×C17—41no—
194C2×C17—41no—
195C2×C17—161no—
196C2×C17#151911yescharacteristic
197C2×C17#213911yescharacteristic
198C2×C17#214511yescharacteristic
199C2×#41—21no—
200C23×C4C22⋊D1711yescharacteristic
201#135—42no—
202C2×Q16C2×Dic1711yescharacteristic
203C2×SD16—21no—
204C2×D8C2×Dic1711yescharacteristic
205C22×C8—42no—
206C22×C8C2×Dic1711yescharacteristic
207C22×C8C2×Dic1711yescharacteristic
208C22×C8C22⋊D1711yescharacteristic
209C22×C8C22⋊D1711yescharacteristic
210C22×C8C22⋊D1711yescharacteristic
211C22×C8C22×D1711yescharacteristic
212#123—41no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215#121—21no—
216#121—21no—
217#120—41no—
218C4×D4—41no—
219C4×D4—41no—
220#117—21no—
221C2×C4⋊C4—342no—
222C2×C22⋊C4—681no—
223M32—682no—
224C2×C16—342no—
225#107—682no—
226#107C2×Dic1711yescharacteristic
227#107C2×Dic1711yescharacteristic
228#106—21no—
229#103—21no—
230#103—21no—
231#102—21no—
232#102—21no—
233#95—681no—
234C17#1189011yescharacteristic, complemented, Sylow
235C24#6322811yescharacteristic
236#41—42no—
237#41—42no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—682no—
247C22×C4#6322811yescharacteristic
248C22×C4#6322911yescharacteristic
249C22×C4#6322911yescharacteristic
250C22×C4C22⋊Dic1711yescharacteristic
251C22×C4C22⋊Dic1711yescharacteristic
252C22×C4C2×C22⋊D1711yescharacteristic
253Q16—41no—
254SD16—42no—
255D8—41no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8C22⋊Dic1711yescharacteristic
263C2×C8C22⋊Dic1711yescharacteristic
264C2×C8C22×Dic1711yescharacteristic
265C2×C8C2×C22⋊D1711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—682no—
271C4⋊C4—682no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—1362no—
278C42—41no—
279C16—682no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23#1058750311yescharacteristic
286C23#1058750311yescharacteristic
287C23C2×#6322811yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—41no—
291D4—41no—
292D4—82no—
293D4—82no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—82no—
309C2×C4—1362no—
310C2×C4—1362no—
311C2×C4—1362no—
312C2×C4#1058750311yescharacteristic
313C2×C4#1058750311yescharacteristic
314C2×C4C2×#6322911yescharacteristic
315C2×C4C2×C22⋊Dic1711yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8#1058750512yes—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C2×#1058750311yescharacteristic
334C22#1176324411yescharacteristic
335C22#1176324911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—2722no—
343C4C2×#1058750511yescharacteristic
344C4#1176282611yescharacteristic
345C2—21no—
346C2—21no—
347C2—41no—
348C2—41no—
349C2—161no—
350C2#1452735211yescharacteristic
351C2#1453049611yescharacteristic
352C2#1453052011yescharacteristic
subgroupG/H
centerC22C2×#10587503
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
Fitting, prime radicalC17×#3050C2
socleC22×C17C2×#102
cosocleC22×C8×C17C23
hypercenter#3050D17
hypocenterC17#11890
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. #14530395C2semidirect
2. #14528813C2semidirect
3. #14526796C2semidirect
4. #14526793C2semidirect
12. C2×C17×#135C4semidirect
15. C17×#467C4semidirect
17. C17×#466C4semidirect
21. C17×#427C4semidirect
174. C2×#135Dic17semidirect
178. #467Dic17semidirect
180. #466Dic17semidirect
184. #427Dic17semidirect
234. C17#11890semidirect

Maximal subgroups

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

subgroupindex
#145303952
#145288132
#145267962
#145267932
C17×#30502
#1189017