Finite Group Databasebeta

← #16945257

Subgroups — #16945257

Order 4352.

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

normal subgroups only

This group has 412 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#14528864C211yesmaximal, characteristic
2C2×#11762535C211yesmaximal, characteristic
3#14526814C212yesmaximal, complemented
4#14526790C212yesmaximal, complemented
5C17×#2583C211yesmaximal, characteristic
6#11762773—21no—
7C2×C22⋊#3622—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—22no—
45C22×#3622—41no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95C2×C411yescharacteristic
51C17×#95C2×C411yescharacteristic
52C22⋊#3622—22no—
53C22⋊#3622—41no—
54C22⋊#3622—41no—
55C22⋊#3622—41no—
56C24×C17C22⋊C411yescharacteristic
57C2×Q8×C17—41no—
58C2×Q8×C17—81no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—22no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—41no—
71C22×C4×C17—81no—
72C22×C4×C17—81no—
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22×C411yescharacteristic
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—42no—
85C4⋊C4×C17—42no—
86C4⋊C4×C17—42no—
87C4⋊C4×C17—81no—
88C4⋊C4×C17—81no—
89C22⋊C4×C17—24no—
90C22⋊C4×C17—41no—
91C22⋊C4×C17—41no—
92C42×C17—81no—
93#63223—42no—
94#63223—42no—
95C2×#3622—42no—
96C2×#3622—42no—
97C2×#3622—82no—
98#11854—171nomaximal, Sylow
99C23×C17—22no—
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—41no—
103C23×C17#9911yescharacteristic
104C23×C17#9911yescharacteristic
105C23×C17C2×C22⋊C411yescharacteristic
106Q8×C17—82no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—22no—
110C2×C4×C17—22no—
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—42no—
119C2×C4×C17—42no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
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—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17#13512yes—
139#3622—82no—
140#3622—82no—
141#2583D1711yescharacteristic
142#1821—171no—
143C2×#324—171no—
144#1354—172no—
145#1346—172no—
146C22×C17—21no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17—21no—
150C22×C17—21no—
151C22×C17—21no—
152C22×C17—21no—
153C22×C17—42no—
154C22×C17—42no—
155C22×C17#35612yes—
156C22×C17C2×#9911yescharacteristic
157C22×C17#41611yescharacteristic
158C22×C17#42111yescharacteristic
159C4×C17—22no—
160C4×C17—42no—
161C4×C17—42no—
162C4×C17—41no—
163C4×C17—41no—
164C4×C17—41no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—81no—
168C4×C17—81no—
169C2×C22⋊Q8Dic1711yescharacteristic
170C22×C4⋊C4C2×D1711yescharacteristic
171#407—341no—
172C2×C22⋊C8—341no—
173#398Dic1711yescharacteristic
174#398C2×D1711yescharacteristic
175#395Dic1711yescharacteristic
176#395C2×D1711yescharacteristic
177#389—21no—
178#389—21no—
179#385—21no—
180#385—21no—
181C4×C22⋊C4Dic1711yescharacteristic
182#343—172no—
183#343—341no—
184#324—172no—
185#324—341no—
186C2×C17—21no—
187C2×C17—21no—
188C2×C17—22no—
189C2×C17—41no—
190C2×C17#151611yescharacteristic
191C2×C17#212111yescharacteristic
192C2×C17C2×#35611yescharacteristic
193C22×Q8C2×Dic1711yescharacteristic
194C23×C4C2×Dic1711yescharacteristic
195C23×C4C22⋊D1711yescharacteristic
196C23×C4C22⋊D1711yescharacteristic
197C2×M16—342no—
198C22×C8—681no—
199C22⋊Q8—41no—
200C22⋊Q8—41no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4C2×Dic1711yescharacteristic
209C2×C4⋊C4C2×Dic1711yescharacteristic
210C2×C4⋊C4C22⋊D1711yescharacteristic
211C2×C4⋊C4C22⋊D1711yescharacteristic
212C2×C4⋊C4C22×D1711yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C42—21no—
216C22⋊C8—342no—
217C22⋊C8—681no—
218C22⋊C8—681no—
219C22⋊C8—681no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95C2×Dic1711yescharacteristic
225#95C2×Dic1711yescharacteristic
226C17#1185411yescharacteristic, complemented, Sylow
227C24C22⋊Dic1711yescharacteristic
228C2×Q8—41no—
229C2×Q8—81no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4C22⋊Dic1711yescharacteristic
245C22×C4C22⋊Dic1711yescharacteristic
246C22×C4C22⋊Dic1711yescharacteristic
247C22×C4C22×Dic1711yescharacteristic
248C22×C4C2×C22⋊D1711yescharacteristic
249C22×C4C2×C22⋊D1711yescharacteristic
250M16—682no—
251M16—682no—
252C2×C8—682no—
253C2×C8—682no—
254C2×C8—1362no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C22⋊C4—24no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—81no—
269C23—21no—
270C23—21no—
271C23—22no—
272C23—41no—
273C23#1058750511yescharacteristic
274C23#1058750511yescharacteristic
275C23C2×C22⋊Dic1711yescharacteristic
276Q8—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
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—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4#1058763612yes—
309C8—1362no—
310C8—1362no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—42no—
319C22—42no—
320C22#1176260812yes—
321C22C2×#1058750511yescharacteristic
322C22#1176280511yescharacteristic
323C22#1176282611yescharacteristic
324C4—22no—
325C4—42no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—41no—
338C2#1452734011yescharacteristic
339C2#1453043011yescharacteristic
340C2C2×#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#11854
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
226. C17#11854semidirect

Maximal subgroups

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

subgroupindex
#145288642
C2×#117625352
#145268142
#145267902
C17×#25832
#1185417