Finite Group Databasebeta

← #16944929

Subgroups — #16944929

Order 4352.

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

normal subgroups only

This group has 460 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
1C4×#10587505C211yesmaximal, characteristic
2#14527122C211yesmaximal, characteristic
3#14526808C212yesmaximal, complemented
4#14526805C212yesmaximal, complemented
5C17×#2580C211yesmaximal, characteristic
6C2×#10587505—21no—
7#11762773—21no—
8C4×C22⋊Dic17—21no—
9#11762576C2212yes—
10#11762535—21no—
11#11762533C2212yes—
12C2×C4×Q8×C17C411yescharacteristic, complemented
13C2×C4×D4×C17C2211yescharacteristic
14C17×#399C411yescharacteristic, complemented
15C17×#399C2211yescharacteristic
16C17×#393C411yescharacteristic, complemented
17C17×#393C2211yescharacteristic
18C17×#390—21no—
19C17×#389—21no—
20C17×#385—21no—
21C17×#385—21no—
22C17×#382C411yescharacteristic, complemented
23C22×Q8×C17C2×C411yescharacteristic
24C22×D4×C17D411yescharacteristic
25C23×C4×C17D411yescharacteristic
26C23×C4×C17D411yescharacteristic
27C4×Q8×C17—41no—
28C4×Q8×C17—41no—
29C4×D4×C17—41no—
30C4×D4×C17—41no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17C2×C411yescharacteristic
36C2×C4⋊C4×C17D411yescharacteristic
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17C2×C411yescharacteristic
42C2×C22⋊C4×C17C2311yescharacteristic
43C2×C42×C17—21no—
44C2×C42×C17C2×C411yescharacteristic
45C2×C22⋊Dic17—22no—
46C2×C4×Dic17—41no—
47C2×#63223—41no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95C2×C411yescharacteristic
52C17×#95C2×C411yescharacteristic
53#10587505—24no—
54#10587502—41no—
55C22⋊#3622—22no—
56C22⋊#3622—41no—
57C24×C17C22⋊C411yescharacteristic
58C24×C17C2×D411yescharacteristic
59C2×Q8×C17—42no—
60C2×Q8×C17—41no—
61C2×D4×C17—22no—
62C2×D4×C17—22no—
63C2×D4×C17—41no—
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—81no—
73C22×C4×C17—81no—
74C22×C4×C17C22⋊C411yescharacteristic
75C22×C4×C17C22⋊C411yescharacteristic
76C22×C4×C17C22⋊C411yescharacteristic
77C22×C4×C17C22×C411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×Dic17—42no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17—41no—
84C4⋊C4×C17—42no—
85C4⋊C4×C17—81no—
86C4⋊C4×C17—81no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—41no—
89C22⋊C4×C17—42no—
90C22⋊C4×C17—42no—
91C22⋊C4×C17—81no—
92C22⋊C4×C17—81no—
93C42×C17—21no—
94C42×C17—21no—
95C42×C17—42no—
96C22⋊Dic17—24no—
97C22⋊Dic17—42no—
98C4×Dic17—82no—
99#63223—82no—
100C2×#3622—42no—
101#11784—171nomaximal, Sylow
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—21no—
107C23×C17—41no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17—41no—
111C23×C17C2×C22⋊C411yescharacteristic
112C23×C17#13712yes—
113Q8×C17—42no—
114Q8×C17—42no—
115D4×C17—44no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—22no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—42no—
124C2×C4×C17—42no—
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—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—81no—
140C2×C4×C17—81no—
141C2×C4×C17#9911yescharacteristic
142C2×C4×C17#9911yescharacteristic
143C2×C4×C17#10412yes—
144C2×Dic17—44no—
145C2×Dic17—82no—
146C2×Dic17—82no—
147#3622—82no—
148#2580D1711yescharacteristic
149C4×#99—171no—
150#1465—171no—
151#1352—172no—
152#1351—172no—
153C22×C17—21no—
154C22×C17—21no—
155C22×C17—22no—
156C22×C17—42no—
157C22×C17—42no—
158C22×C17—41no—
159C22×C17—41no—
160C22×C17—41no—
161C22×C17—41no—
162C22×C17—41no—
163C22×C17—81no—
164C22×C17—81no—
165C22×C17C2×#9911yescharacteristic
166C22×C17#41911yescharacteristic
167C22×C17C2×#10411yescharacteristic
168C4×C17—21no—
169C4×C17—21no—
170C4×C17—22no—
171C4×C17—42no—
172C4×C17—41no—
173C4×C17—41no—
174C4×C17—41no—
175C4×C17—81no—
176C4×C17—81no—
177C4×C17—81no—
178Dic17—84no—
179C2×C4×Q8Dic1711yescharacteristic, complemented
180C2×C4×D4C2×D1711yescharacteristic
181C2×#99—341no—
182#407—341no—
183#399Dic1711yescharacteristic, complemented
184#399C2×D1711yescharacteristic
185#393Dic1711yescharacteristic, complemented
186#393C2×D1711yescharacteristic
187#390—21no—
188#389—21no—
189#385—21no—
190#385—21no—
191#382Dic1711yescharacteristic, complemented
192C4×C22⋊C4—341no—
193#342—172no—
194#324—341no—
195#323—172no—
196C2×C17—21no—
197C2×C17—21no—
198C2×C17—42no—
199C2×C17—81no—
200C2×C17#150811yescharacteristic
201C2×C17#212011yescharacteristic
202C2×C17#212711yescharacteristic
203C22×Q8C2×Dic1711yescharacteristic
204C22×D4C22⋊D1711yescharacteristic
205C23×C4C22⋊D1711yescharacteristic
206C23×C4C22⋊D1711yescharacteristic
207C2×M16—681no—
208C4×Q8—41no—
209C4×Q8—41no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C2×Dic1711yescharacteristic
217C2×C4⋊C4C22⋊D1711yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—342no—
223C2×C22⋊C4C2×Dic1711yescharacteristic
224C2×C22⋊C4C22×D1711yescharacteristic
225C2×C42—21no—
226C2×C42—681no—
227C2×C42C2×Dic1711yescharacteristic
228#99—344no—
229C22⋊C8—342no—
230C22⋊C8—681no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—681no—
235#95C2×Dic1711yescharacteristic
236#95C2×Dic1711yescharacteristic
237C17#1178411yescharacteristic, complemented, Sylow
238C24C22⋊Dic1711yescharacteristic
239C24C2×C22⋊D1711yescharacteristic
240C2×Q8—42no—
241C2×Q8—41no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—682no—
256C22×C4C22⋊Dic1711yescharacteristic
257C22×C4C22⋊Dic1711yescharacteristic
258C22×C4C22⋊Dic1711yescharacteristic
259C22×C4C22×Dic1711yescharacteristic
260C22×C4C2×C22⋊D1711yescharacteristic
261M16—1362no—
262C2×C8—682no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—81no—
275C22⋊C4—81no—
276C22⋊C4—344no—
277C22⋊C4—682no—
278C42—21no—
279C42—21no—
280C42—42no—
281C42—1362no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23#1058762812yes—
292C23C2×C22⋊Dic1711yescharacteristic
293Q8—42no—
294Q8—42no—
295D4—44no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
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—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—684no—
322C2×C4—1362no—
323C2×C4—1362no—
324C2×C4#1058750511yescharacteristic
325C2×C4#1058750511yescharacteristic
326C2×C4#1058750812yes—
327C8—1362no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22C2×#1058750511yescharacteristic
341C22#1176281811yescharacteristic
342C22C2×#1058750811yescharacteristic
343C4—22no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—1364no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—81no—
358C2#1452730411yescharacteristic
359C2#1453042511yescharacteristic
360C2#1453045311yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#2580C2
socleC22×C17C2×#99
prime radicalC22×D4×C17D4
cosocleC2×C22⋊C4×C17C23
hypercenter#2580D17
hypocenterC17#11784
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2580

Complements

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

NH ≅ G/Ntype
3. #14526808C2semidirect
4. #14526805C2semidirect
12. C2×C4×Q8×C17C4semidirect
14. C17×#399C4semidirect
16. C17×#393C4semidirect
22. C17×#382C4semidirect
179. C2×C4×Q8Dic17semidirect
183. #399Dic17semidirect
185. #393Dic17semidirect
191. #382Dic17semidirect
237. C17#11784semidirect

Maximal subgroups

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

subgroupindex
C4×#105875052
#145271222
#145268082
#145268052
C17×#25802
#1178417