Finite Group Databasebeta

← #16944835

Subgroups — #16944835

Order 4352.

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

normal subgroups only

This group has 446 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#14526811C212yesmaximal, complemented
4#14526790C212yesmaximal, complemented
5C17×#2484C211yesmaximal, characteristic
6C22×#63223—21no—
7#11762773—21no—
8#11762578—21no—
9#11762578C2212yes—
10#11762535—21no—
11#11762535C2212yes—
12C2×C17×#117C411yescharacteristic
13C22×C4⋊C4×C17C2211yescharacteristic
14C17×#400C411yescharacteristic
15C17×#400C2211yescharacteristic
16C17×#398C411yescharacteristic
17C17×#398C2211yescharacteristic
18C17×#387—21no—
19C17×#387—21no—
20C17×#385—21no—
21C17×#381—21no—
22C17×#381C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C17×#117—41no—
27C17×#117—41no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—41no—
31C2×C4⋊C4×C17—41no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C4⋊C4×C17D411yescharacteristic
37C2×C4⋊C4×C17C2311yescharacteristic
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C42×C17—21no—
41C2×#63223—24no—
42C2×#63223—22no—
43C2×#63223—41no—
44C2×#63223—42no—
45C2×#63223—41no—
46C22×#3622—41no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
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
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—22no—
62C22×C4×C17—21no—
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—21no—
72C22×C4×C17—42no—
73C22×C4×C17—42no—
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22⋊C411yescharacteristic
77C22×C4×C17C22×C411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—41no—
86C4⋊C4×C17—42no—
87C4⋊C4×C17—41no—
88C4⋊C4×C17—41no—
89C22⋊C4×C17—42no—
90C22⋊C4×C17—41no—
91C22⋊C4×C17—41no—
92C42×C17—42no—
93#63223—24no—
94#63223—44no—
95#63223—42no—
96#63223—82no—
97C2×#3622—44no—
98C2×#3622—42no—
99C2×#3622—42no—
100#11764—171nomaximal, Sylow
101C23×C17—22no—
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—41no—
105C23×C17#9911yescharacteristic
106C23×C17#9911yescharacteristic
107C23×C17C2×C22⋊C411yescharacteristic
108C2×C4×C17—22no—
109C2×C4×C17—22no—
110C2×C4×C17—22no—
111C2×C4×C17—22no—
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—42no—
121C2×C4×C17—42no—
122C2×C4×C17—42no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
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—81no—
139C2×C4×C17#10412yes—
140C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C17#13711yescharacteristic
142#3622—44no—
143#3622—82no—
144#2484D1711yescharacteristic
145C2×#343—171no—
146#1463—171no—
147#1353—172no—
148#1346—172no—
149C22×C17—21no—
150C22×C17—21no—
151C22×C17—21no—
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—21no—
156C22×C17—42no—
157C22×C17—42no—
158C22×C17#35212yes—
159C22×C17C2×#9911yescharacteristic
160C22×C17#41711yescharacteristic
161C22×C17C2×#10411yescharacteristic
162C4×C17—21no—
163C4×C17—22no—
164C4×C17—21no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—41no—
168C4×C17—41no—
169C4×C17—81no—
170C4×C17—81no—
171C4×C17—81no—
172C4×C17—81no—
173C22×M16—341no—
174C2×#117Dic1711yescharacteristic
175C22×C4⋊C4C2×D1711yescharacteristic
176#407—341no—
177#400Dic1711yescharacteristic
178#400C2×D1711yescharacteristic
179#398Dic1711yescharacteristic
180#398C2×D1711yescharacteristic
181#387—21no—
182#387—21no—
183#385—21no—
184#381—21no—
185#381Dic1711yescharacteristic
186#343—172no—
187#343—341no—
188#324—172no—
189#324—341no—
190C2×C17—21no—
191C2×C17—21no—
192C2×C17—22no—
193C2×C17—41no—
194C2×C17#150411yescharacteristic
195C2×C17C2×#35211yescharacteristic
196C2×C17#213311yescharacteristic
197C23×C4C2×Dic1711yescharacteristic
198C23×C4C22⋊D1711yescharacteristic
199C23×C4C22⋊D1711yescharacteristic
200C2×M16—344no—
201C2×M16—342no—
202C2×M16—681no—
203C2×M16—682no—
204C2×M16—681no—
205C22×C8—681no—
206#117—41no—
207#117—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4C2×Dic1711yescharacteristic
213C2×C4⋊C4C2×Dic1711yescharacteristic
214C2×C4⋊C4C2×Dic1711yescharacteristic
215C2×C4⋊C4C22⋊D1711yescharacteristic
216C2×C4⋊C4C22⋊D1711yescharacteristic
217C2×C4⋊C4C22×D1711yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C42—21no—
221C22⋊C8—342no—
222C22⋊C8—681no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95C2×Dic1711yescharacteristic
231#95C2×Dic1711yescharacteristic
232C17#1176411yescharacteristic, complemented, Sylow
233C24C22⋊Dic1711yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4C22⋊Dic1711yescharacteristic
250C22×C4C22⋊Dic1711yescharacteristic
251C22×C4C22⋊Dic1711yescharacteristic
252C22×C4C22×Dic1711yescharacteristic
253C22×C4C2×C22⋊D1711yescharacteristic
254C22×C4C2×C22⋊D1711yescharacteristic
255M16—344no—
256M16—684no—
257M16—682no—
258M16—1362no—
259C2×C8—684no—
260C2×C8—682no—
261C2×C8—682no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42—42no—
275C23—21no—
276C23—21no—
277C23—22no—
278C23—41no—
279C23#1058750511yescharacteristic
280C23#1058750511yescharacteristic
281C23C2×C22⋊Dic1711yescharacteristic
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4#1058750812yes—
314C2×C4#1058763511yescharacteristic
315C2×C4#1058763711yescharacteristic
316C8—684no—
317C8—1362no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22#1176259912yes—
328C22C2×#1058750511yescharacteristic
329C22#1176281011yescharacteristic
330C22C2×#1058750811yescharacteristic
331C4—21no—
332C4—22no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—81no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—41no—
346C2#1452728811yescharacteristic
347C2C2×#1176259911yescharacteristic
348C2#1453047311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2484C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2484D17
hypocenterC17#11764
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
3. #14526811C2semidirect
4. #14526790C2semidirect
232. C17#11764semidirect

Maximal subgroups

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

subgroupindex
C2×#117625782
#145271142
#145268112
#145267902
C17×#24842
#1176417