Finite Group Databasebeta

← #16945242

Subgroups — #16945242

Order 4352.

418 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 87 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#14528867C211yesmaximal, characteristic, complemented
2#14527098C211yesmaximal, characteristic, complemented
3#14526814C212yesmaximal, complemented
4#14526787C212yesmaximal, complemented
5C17×#2610C211yesmaximal, characteristic
6#11762862—21no—
7#11762773—21no—
8#11762578—21no—
9#11762578C2212yes—
10#11762535C2212yes—
11#11762533—21no—
12C2×C17×#124C411yescharacteristic
13C2×C17×#117C2211yescharacteristic
14C17×#395C2211yescharacteristic
15C17×#394C2211yescharacteristic
16C17×#393C411yescharacteristic
17C17×#392C411yescharacteristic
18C17×#390—21no—
19C17×#388—21no—
20C17×#388—21no—
21C17×#386—21no—
22C17×#376C411yescharacteristic
23C22×Q8×C17C2×C411yescharacteristic
24C22×D4×C17—21no—
25C22×D4×C17C2×C411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C17×#124—41no—
28C17×#124—41no—
29C17×#117—41no—
30C17×#117—41no—
31C2×C4⋊C4×C17—21no—
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×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17C2×C411yescharacteristic
41C2×C22⋊C4×C17D411yescharacteristic
42C2×C42×C17—21no—
43C2×C42×C17C2×C411yescharacteristic
44C2×C42×C17D411yescharacteristic
45C2×#63223—22no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95C2×C411yescharacteristic
50C17×#95C2×C411yescharacteristic
51C22⋊#3622—22no—
52C22⋊#3622—41no—
53C22⋊#3622—41no—
54C4⋊#3622—41no—
55C4×#3622—41no—
56C24×C17—21no—
57C24×C17C22⋊C411yescharacteristic
58C2×Q8×C17—41no—
59C2×Q8×C17—81no—
60C2×D4×C17—41no—
61C2×D4×C17—42no—
62C2×D4×C17—42no—
63C2×D4×C17—81no—
64C2×D4×C17—81no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—22no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
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—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—81no—
81C22⋊C4×C17—41no—
82C22⋊C4×C17—41no—
83C22⋊C4×C17—42no—
84C22⋊C4×C17—42no—
85C22⋊C4×C17—41no—
86C22⋊C4×C17—41no—
87C22⋊C4×C17—42no—
88C22⋊C4×C17—81no—
89C22⋊C4×C17—81no—
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#11851—171nomaximal, Sylow
100C23×C17—21no—
101C23×C17—21no—
102C23×C17—21no—
103C23×C17—41no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17—41no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17—41no—
111C23×C17—41no—
112C23×C17C2×C22⋊C411yescharacteristic
113Q8×C17—82no—
114D4×C17—84no—
115D4×C17—82no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—22no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—42no—
126C2×C4×C17—42no—
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—41no—
139C2×C4×C17#9911yescharacteristic
140C2×C4×C17#9911yescharacteristic
141C2×C4×C17#13512yes—
142#3622—82no—
143#3622—82no—
144#2610D1711yescharacteristic
145#1822—171no—
146#1458—171no—
147#1354—172no—
148#1345—172no—
149C22×C17—21no—
150C22×C17—21no—
151C22×C17—42no—
152C22×C17—41no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—81no—
156C22×C17—81no—
157C22×C17—81no—
158C22×C17—81no—
159C22×C17—81no—
160C22×C17—81no—
161C22×C17—81no—
162C22×C17—81no—
163C22×C17C2×#9911yescharacteristic
164C22×C17#41611yescharacteristic
165C22×C17#42111yescharacteristic
166C4×C17—22no—
167C4×C17—21no—
168C4×C17—21no—
169C4×C17—42no—
170C4×C17—41no—
171C4×C17—41no—
172C4×C17—41no—
173C4×C17—41no—
174C4×C17—81no—
175C4×C17—81no—
176C2×#124Dic1711yescharacteristic
177C2×#117C2×D1711yescharacteristic
178#431—341no—
179#407—341no—
180#395C2×D1711yescharacteristic
181#394C2×D1711yescharacteristic
182#393Dic1711yescharacteristic
183#392Dic1711yescharacteristic
184#390—21no—
185#388—21no—
186#388—21no—
187#386—21no—
188#376Dic1711yescharacteristic
189#343—172no—
190#343—341no—
191#324—172no—
192#323—341no—
193C2×C17—21no—
194C2×C17—21no—
195C2×C17—81no—
196C2×C17—161no—
197C2×C17#151611yescharacteristic
198C2×C17#212211yescharacteristic
199C2×C17#213211yescharacteristic
200C22×Q8C2×Dic1711yescharacteristic
201C22×D4—21no—
202C22×D4C2×Dic1711yescharacteristic
203C23×C4C22⋊D1711yescharacteristic
204C2×M16—342no—
205#124—41no—
206#124—41no—
207#117—41no—
208#117—41no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C22⋊D1711yescharacteristic
211C2×C4⋊C4C22×D1711yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4C2×Dic1711yescharacteristic
219C2×C22⋊C4C22⋊D1711yescharacteristic
220C2×C42—21no—
221C2×C42C2×Dic1711yescharacteristic
222C2×C42C22⋊D1711yescharacteristic
223C4⋊C8—681no—
224C22⋊C8—342no—
225C22⋊C8—681no—
226C22⋊C8—681no—
227C4×C8—681no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95C2×Dic1711yescharacteristic
232#95C2×Dic1711yescharacteristic
233C17#1185111yescharacteristic, complemented, Sylow
234C24—21no—
235C24C22⋊Dic1711yescharacteristic
236C2×Q8—41no—
237C2×Q8—81no—
238C2×D4—41no—
239C2×D4—42no—
240C2×D4—42no—
241C2×D4—81no—
242C2×D4—81no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4C22⋊Dic1711yescharacteristic
251C22×C4C22⋊Dic1711yescharacteristic
252C22×C4C22⋊Dic1711yescharacteristic
253C22×C4C22×Dic1711yescharacteristic
254C22×C4C2×C22⋊D1711yescharacteristic
255C22×C4C2×C22⋊D1711yescharacteristic
256M16—682no—
257M16—682no—
258C2×C8—682no—
259C2×C8—682no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—81no—
271C22⋊C4—81no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42—42no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C22⋊Dic1711yescharacteristic
290Q8—82no—
291D4—84no—
292D4—82no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—42no—
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—41no—
316C2×C4#1058750511yescharacteristic
317C2×C4#1058750511yescharacteristic
318C2×C4#1058763612yes—
319C8—1362no—
320C8—1362no—
321C22—21no—
322C22—21no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C2×#1058750511yescharacteristic
336C22#1176280511yescharacteristic
337C22#1176282611yescharacteristic
338C4—22no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—161no—
352C2#1452734011yescharacteristic
353C2#1453043411yescharacteristic
354C2#1453046911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2610C2
socleC22×C17C2×#99
prime radicalC17×#392C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2610D17
hypocenterC17#11851
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. #14528867C2semidirect
2. #14527098C2semidirect
3. #14526814C2semidirect
4. #14526787C2semidirect
233. C17#11851semidirect

Maximal subgroups

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

subgroupindex
#145288672
#145270982
#145268142
#145267872
C17×#26102
#1185117