Finite Group Databasebeta

← #16922845

Subgroups — #16922845

Order 4352.

494 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14528852C211yesmaximal, characteristic
2#14528478C211yesmaximal, characteristic
3#14526610C212yesmaximal, complemented
4#14526607C212yesmaximal, complemented
5C17×#2855C211yesmaximal, characteristic
6C22×#63223—21no—
7C2×C22⋊#3622—21no—
8#11762564—21no—
9#11762564—21no—
10#11762564C2212yes—
11#11762564C2212yes—
12C2×C17×C22⋊Q8C411yescharacteristic
13C22×C42×C17C2211yescharacteristic
14C17×#391C411yescharacteristic
15C17×#391C2211yescharacteristic
16C17×#389C411yescharacteristic
17C17×#389C2211yescharacteristic
18C17×#387—21no—
19C17×#387—21no—
20C17×#385—21no—
21C17×#381—21no—
22C17×#380C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C17×C22⋊Q8—42no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C22⋊C4×C17—21no—
35C2×C22⋊C4×C17—21no—
36C2×C42×C17—42no—
37C2×C42×C17C2×C411yescharacteristic
38C2×C42×C17D411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C2×C42×C17C2311yescharacteristic
41C2×#63223—24no—
42C2×#63223—42no—
43C2×#63223—42no—
44C22×#3622—22no—
45C22×#3622—22no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C22⋊#3622—42no—
54C24×C17C22⋊C411yescharacteristic
55C2×Q8×C17—22no—
56C2×Q8×C17—41no—
57C2×Q8×C17—41no—
58C22×C4×C17—22no—
59C22×C4×C17—22no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—22no—
63C22×C4×C17—22no—
64C22×C4×C17—22no—
65C22×C4×C17—22no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—41no—
71C22×C4×C17—41no—
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22×C411yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C4⋊C4×C17—22no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—42no—
82C4⋊C4×C17—42no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C22⋊C4×C17—42no—
86C22⋊C4×C17—42no—
87C42×C17—41no—
88C42×C17—41no—
89C42×C17—41no—
90C42×C17—41no—
91#63223—48no—
92C2×#3622—24no—
93C2×#3622—42no—
94C2×#3622—42no—
95C2×#3622—42no—
96C2×#3622—42no—
97C2×#3622—42no—
98#7695—171nomaximal, Sylow
99C23×C17—21no—
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17#9912yes—
106C23×C17C2×C22⋊C411yescharacteristic
107Q8×C17—82no—
108C2×C4×C17—24no—
109C2×C4×C17—24no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
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—44no—
125C2×C4×C17—44no—
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—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17#10412yes—
139C2×C4×C17#13112yes—
140C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C17#13712yes—
142C2×C4×C17#13711yescharacteristic
143#3622—44no—
144#3622—82no—
145#2855D1711yescharacteristic
146#1817—171no—
147#1728—171no—
148#1272—172no—
149#1271—172no—
150C22×C17—22no—
151C22×C17—22no—
152C22×C17—22no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—41no—
156C22×C17—41no—
157C22×C17#40811yescharacteristic
158C22×C17C2×#9911yescharacteristic
159C22×C17#41311yescharacteristic
160C22×C17#41711yescharacteristic
161C22×C17#41911yescharacteristic
162C22×C17C2×#10411yescharacteristic
163C22×C17#42111yescharacteristic
164C4×C17—22no—
165C4×C17—21no—
166C4×C17—22no—
167C4×C17—21no—
168C4×C17—22no—
169C4×C17—41no—
170C4×C17—41no—
171C4×C17—81no—
172C4×C17—81no—
173C4×C17—81no—
174C4×C17—81no—
175C22×M16—341no—
176C2×C22⋊Q8Dic1711yescharacteristic
177C22×C42C2×D1711yescharacteristic
178C2×C22⋊C8—341no—
179#391Dic1711yescharacteristic
180#391C2×D1711yescharacteristic
181#389Dic1711yescharacteristic
182#389C2×D1711yescharacteristic
183#387—21no—
184#387—21no—
185#385—21no—
186#381—21no—
187#380Dic1711yescharacteristic
188#336—172no—
189#336—172no—
190#336—341no—
191#336—341no—
192C2×C17—42no—
193C2×C17#146811yescharacteristic
194C2×C17#148511yescharacteristic
195C2×C17#149511yescharacteristic
196C2×C17#150411yescharacteristic
197C2×C17#151111yescharacteristic
198C2×C17#152911yescharacteristic
199C2×C17#155911yescharacteristic
200C22×Q8C2×Dic1711yescharacteristic
201C23×C4C2×Dic1711yescharacteristic
202C23×C4C22⋊D1711yescharacteristic
203C23×C4C22⋊D1711yescharacteristic
204C2×M16—344no—
205C2×M16—682no—
206C2×M16—682no—
207C22×C8—342no—
208C22×C8—342no—
209C22⋊Q8—42no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×Dic1711yescharacteristic
214C2×C4⋊C4C2×Dic1711yescharacteristic
215C2×C4⋊C4C2×Dic1711yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C42—42no—
219C2×C42C2×Dic1711yescharacteristic
220C2×C42C22⋊D1711yescharacteristic
221C2×C42C22⋊D1711yescharacteristic
222C2×C42C22×D1711yescharacteristic
223C22⋊C8—682no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C17#769511yescharacteristic, complemented, Sylow
232C24C22⋊Dic1711yescharacteristic
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4C22⋊Dic1711yescharacteristic
251C22×C4C22⋊Dic1711yescharacteristic
252C22×C4C22⋊Dic1711yescharacteristic
253C22×C4C22×Dic1711yescharacteristic
254C22×C4C2×C22⋊D1711yescharacteristic
255C22×C4C2×C22⋊D1711yescharacteristic
256M16—688no—
257C2×C8—344no—
258C2×C8—682no—
259C2×C8—682no—
260C2×C8—682no—
261C2×C8—682no—
262C2×C8—682no—
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C42—41no—
273C42—41no—
274C42—41no—
275C42—41no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23#1058750512yes—
283C23C2×C22⋊Dic1711yescharacteristic
284Q8—82no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4#1058750812yes—
316C2×C4#1058762812yes—
317C2×C4#1058763412yes—
318C2×C4#1058763511yescharacteristic
319C2×C4#1058763711yescharacteristic
320C8—684no—
321C8—1362no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22#1176277611yescharacteristic
330C22C2×#1058750511yescharacteristic
331C22#1176279311yescharacteristic
332C22#1176281011yescharacteristic
333C22#1176281811yescharacteristic
334C22C2×#1058750811yescharacteristic
335C22#1176282611yescharacteristic
336C4—21no—
337C4—22no—
338C4—21no—
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C2—42no—
348C2#1452713211yescharacteristic
349C2#1452720511yescharacteristic
350C2#1452724911yescharacteristic
351C2#1452728811yescharacteristic
352C2#1452731711yescharacteristic
353C2#1452739111yescharacteristic
354C2#1452751411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic17
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2855C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2855D17
hypocenterC17#7695
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
3. #14526610C2semidirect
4. #14526607C2semidirect
231. C17#7695semidirect

Maximal subgroups

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

subgroupindex
#145288522
#145284782
#145266102
#145266072
C17×#28552
#769517