Finite Group Databasebeta

← #16945130

Subgroups — #16945130

Order 4352.

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

normal subgroups only

This group has 416 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#14528780C211yesmaximal, characteristic, complemented
2#14527128C211yesmaximal, characteristic, complemented
3#14526811C212yesmaximal, complemented
4#14526787C212yesmaximal
5C17×#2398C211yesmaximal, characteristic
6#11762866—21no—
7#11762833—21no—
8C2×#10587507—21no—
9#11762578C2212yes—
10#11762535—21no—
11#11762535C2212yes—
12C2×C4×Q8×C17C2211yescharacteristic
13C2×C4×D4×C17C411yescharacteristic
14C17×#400C411yescharacteristic
15C17×#400C2211yescharacteristic
16C17×#397—21no—
17C17×#394C411yescharacteristic
18C17×#394C2211yescharacteristic
19C17×#393—21no—
20C4×C22⋊C4×C17—21no—
21C4×C22⋊C4×C17—21no—
22C17×#376C411yescharacteristic
23C22×Q8×C17D411yescharacteristic
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17—21no—
26C4×Q8×C17—41no—
27C4×Q8×C17—41no—
28C4×D4×C17—41no—
29C4×D4×C17—41no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C4⋊C4×C17C2311yescharacteristic
34C2×C22⋊C4×C17—21no—
35C2×C22⋊C4×C17—21no—
36C2×C22⋊C4×C17—21no—
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C42×C17—21no—
40C2×C42×C17C2×C411yescharacteristic
41C2×C42×C17D411yescharacteristic
42C2×C42×C17D411yescharacteristic
43C2×#63223—22no—
44C17×#95—21no—
45C17×#95—21no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95C2×C411yescharacteristic
50C17×#95C2×C411yescharacteristic
51#10587507—42no—
52C22⋊#3622—22no—
53C4⋊#3622—41no—
54C4⋊#3622—41no—
55C4⋊#3622—41no—
56#10587474—41no—
57C24×C17—21no—
58C2×Q8×C17—21no—
59C2×Q8×C17—21no—
60C2×Q8×C17—41no—
61C2×Q8×C17—41no—
62C2×D4×C17—41no—
63C2×D4×C17—42no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—42no—
68C22×C4×C17—42no—
69C22×C4×C17—41no—
70C22×C4×C17—41no—
71C22×C4×C17C22⋊C411yescharacteristic
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—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C22⋊C4×C17—42no—
83C22⋊C4×C17—42no—
84C22⋊C4×C17—42no—
85C22⋊C4×C17—42no—
86C22⋊C4×C17—41no—
87C22⋊C4×C17—41no—
88C42×C17—21no—
89C42×C17—21no—
90C42×C17—21no—
91C42×C17—21no—
92C42×C17—21no—
93C42×C17—21no—
94C42×C17—42no—
95#63223—42no—
96#63223—42no—
97C2×#3622—42no—
98C2×#3622—42no—
99#11829—171nomaximal, Sylow
100C23×C17—22no—
101C23×C17—41no—
102C23×C17—41no—
103C23×C17—41no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17C2×C22⋊C411yescharacteristic
108Q8×C17—42no—
109Q8×C17—42no—
110D4×C17—42no—
111D4×C17—42no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—22no—
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—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—41no—
136C2×C4×C17—82no—
137C2×C4×C17—82no—
138C2×C4×C17#9911yescharacteristic
139C2×C4×C17#9911yescharacteristic
140C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C17#13711yescharacteristic
142#3622—82no—
143#3622—82no—
144#2398D1711yescharacteristic
145#1801—171no—
146#1467—171no—
147#1353—172no—
148#1345—172no—
149C22×C17—21no—
150C22×C17—21no—
151C22×C17—42no—
152C22×C17—42no—
153C22×C17—42no—
154C22×C17—81no—
155C22×C17—81no—
156C22×C17—81no—
157C22×C17—81no—
158C22×C17C2×#9911yescharacteristic
159C22×C17#41711yescharacteristic
160C22×C17#42111yescharacteristic
161C4×C17—21no—
162C4×C17—21no—
163C4×C17—21no—
164C4×C17—41no—
165C4×C17—41no—
166C4×C17—41no—
167C4×C17—41no—
168C4×C17—41no—
169C4×C17—81no—
170C4×C17—81no—
171C4×C17—81no—
172C4×C17#35512yes—
173C2×C4×Q8C2×D1711yescharacteristic
174C2×C4×D4Dic1711yescharacteristic
175#432—341no—
176#423—341no—
177C2×#101—341no—
178#400Dic1711yescharacteristic
179#400C2×D1711yescharacteristic
180#397—21no—
181#394Dic1711yescharacteristic
182#394C2×D1711yescharacteristic
183#393—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4—21no—
186#376Dic1711yescharacteristic
187#343—172no—
188#324—172no—
189#324—341no—
190C2×C17—21no—
191C2×C17—21no—
192C2×C17—82no—
193C2×C17#151311yescharacteristic
194C2×C17#212011yescharacteristic
195C2×C17C2×#35511yescharacteristic
196C22×Q8C22⋊D1711yescharacteristic
197C22×D4C2×Dic1711yescharacteristic
198C23×C4—21no—
199C2×M16—342no—
200C4×Q8—41no—
201C4×Q8—41no—
202C4×D4—41no—
203C4×D4—41no—
204C2×C4⋊C4C2×Dic1711yescharacteristic
205C2×C4⋊C4C2×Dic1711yescharacteristic
206C2×C4⋊C4C22⋊D1711yescharacteristic
207C2×C4⋊C4C22×D1711yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42—21no—
214C2×C42C2×Dic1711yescharacteristic
215C2×C42C22⋊D1711yescharacteristic
216C2×C42C22⋊D1711yescharacteristic
217C4⋊C8—681no—
218C4⋊C8—681no—
219C4⋊C8—681no—
220#101—682no—
221C22⋊C8—342no—
222#97—681no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95C2×Dic1711yescharacteristic
229#95C2×Dic1711yescharacteristic
230C17#1182911yescharacteristic, complemented, Sylow
231C24—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×D4—41no—
237C2×D4—42no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4C22⋊Dic1711yescharacteristic
246C22×C4C22⋊Dic1711yescharacteristic
247C22×C4C22⋊Dic1711yescharacteristic
248C22×C4C22⋊Dic1711yescharacteristic
249C22×C4C22×Dic1711yescharacteristic
250C22×C4C2×C22⋊D1711yescharacteristic
251C22×C4C2×C22⋊D1711yescharacteristic
252M16—682no—
253M16—682no—
254C2×C8—682no—
255C2×C8—682no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—42no—
273C23—22no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×C22⋊Dic1711yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—42no—
284D4—42no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
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—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4#1058750511yescharacteristic
312C2×C4#1058750511yescharacteristic
313C2×C4#1058763511yescharacteristic
314C2×C4#1058763711yescharacteristic
315C8—1362no—
316C8—1362no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22C2×#1058750511yescharacteristic
327C22#1176281011yescharacteristic
328C22#1176282611yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4#1176260612yes—
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1452732711yescharacteristic
345C2#1453042511yescharacteristic
346C2C2×#1176260611yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2398C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2398D17
hypocenterC17#11829
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. #14528780C2semidirect
2. #14527128C2semidirect
3. #14526811C2semidirect
230. C17#11829semidirect

Maximal subgroups

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

subgroupindex
#145287802
#145271282
#145268112
#145267872
C17×#23982
#1182917