Finite Group Databasebeta

← #16945105

Subgroups — #16945105

Order 4352.

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

normal subgroups only

This group has 464 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#14528772C211yesmaximal, characteristic, complemented
2#14527125C211yesmaximal, characteristic, complemented
3#14526808C212yesmaximal, complemented
4#14526781C212yesmaximal, complemented
5C17×#2635C211yesmaximal, characteristic
6#11762866—21no—
7C2×#10587505—21no—
8#11762669—21no—
9#11762576C2212yes—
10#11762533—21no—
11#11762533C2212yes—
12C2×C17×#121C411yescharacteristic, complemented
13C2×C4×D4×C17C2211yescharacteristic
14C17×#400C411yescharacteristic, complemented
15C17×#399C2211yescharacteristic
16C17×#394—21no—
17C17×#394C411yescharacteristic, complemented
18C17×#392—21no—
19C17×#392C2211yescharacteristic
20C17×#388—21no—
21C17×#386—21no—
22C17×#381C411yescharacteristic, complemented
23C22×D4×C17—21no—
24C22×D4×C17—21no—
25C22×D4×C17C2×C411yescharacteristic
26C22×D4×C17D411yescharacteristic
27C23×C4×C17C2×C411yescharacteristic
28C23×C4×C17D411yescharacteristic
29C17×#121—41no—
30C17×#121—41no—
31C4×D4×C17—41no—
32C4×D4×C17—41no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17C2×C411yescharacteristic
36C2×C22⋊C4×C17—21no—
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17D411yescharacteristic
43C2×C22⋊C4×C17C2311yescharacteristic
44C2×C42×C17D411yescharacteristic
45C2×C22⋊Dic17—22no—
46C2×C4⋊Dic17—41no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95C2×C411yescharacteristic
51C17×#95C2×C411yescharacteristic
52#10587505—42no—
53#10587502—41no—
54C22⋊#3622—22no—
55C4⋊#3622—41no—
56#10587474—41no—
57C24×C17—21no—
58C24×C17C22⋊C411yescharacteristic
59C24×C17C2×D411yescharacteristic
60C2×D4×C17—21no—
61C2×D4×C17—21no—
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C2×D4×C17—41no—
65C2×D4×C17—42no—
66C2×D4×C17—41no—
67C2×D4×C17—41no—
68C2×D4×C17—81no—
69C2×D4×C17—81no—
70C2×D4×C17—81no—
71C2×D4×C17—81no—
72C2×D4×C17—81no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—81no—
81C22×C4×C17—81no—
82C22×C4×C17C22⋊C411yescharacteristic
83C22×C4×C17C22⋊C411yescharacteristic
84C22×C4×C17C22⋊C411yescharacteristic
85C22×C4×C17C22×C411yescharacteristic
86C22×C4×C17C2×D411yescharacteristic
87C22×Dic17—42no—
88C4⋊C4×C17—41no—
89C4⋊C4×C17—41no—
90C4⋊C4×C17—81no—
91C22⋊C4×C17—41no—
92C22⋊C4×C17—41no—
93C22⋊C4×C17—42no—
94C22⋊C4×C17—41no—
95C22⋊C4×C17—41no—
96C22⋊C4×C17—81no—
97C22⋊C4×C17—81no—
98C22⋊C4×C17—81no—
99C22⋊C4×C17—81no—
100C42×C17—21no—
101C42×C17—21no—
102C22⋊Dic17—42no—
103C22⋊Dic17—42no—
104C4⋊Dic17—82no—
105C2×#3622—42no—
106#11824—171nomaximal, Sylow
107C23×C17—21no—
108C23×C17—21no—
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—41no—
113C23×C17—41no—
114C23×C17—41no—
115C23×C17—41no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—41no—
119C23×C17—41no—
120C23×C17—41no—
121C23×C17—41no—
122C23×C17—41no—
123C23×C17C2×C22⋊C411yescharacteristic
124C23×C17AGL(1,ℤ/8)11yescharacteristic
125C23×C17#13711yescharacteristic
126D4×C17—42no—
127D4×C17—42no—
128D4×C17—82no—
129D4×C17—82no—
130D4×C17—82no—
131D4×C17—84no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—41no—
139C2×C4×C17—42no—
140C2×C4×C17—41no—
141C2×C4×C17—41no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—41no—
150C2×C4×C17—41no—
151C2×C4×C17—41no—
152C2×C4×C17—81no—
153C2×C4×C17—81no—
154C2×C4×C17—81no—
155C2×C4×C17#9911yescharacteristic
156C2×C4×C17#9911yescharacteristic
157C2×Dic17—82no—
158C2×Dic17—82no—
159C2×Dic17—82no—
160#3622—82no—
161#2635D1711yescharacteristic
162#1799—171no—
163#1466—171no—
164#1352—172no—
165#1343—172no—
166C22×C17—21no—
167C22×C17—21no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—81no—
178C22×C17—81no—
179C22×C17—81no—
180C22×C17—81no—
181C22×C17—81no—
182C22×C17—81no—
183C22×C17—81no—
184C22×C17—81no—
185C22×C17—81no—
186C22×C17—81no—
187C22×C17C2×#9911yescharacteristic
188C22×C17#41711yescharacteristic
189C22×C17#42111yescharacteristic
190C4×C17—21no—
191C4×C17—21no—
192C4×C17—41no—
193C4×C17—41no—
194C4×C17—41no—
195C4×C17—41no—
196C4×C17—81no—
197C4×C17—81no—
198C4×C17—81no—
199Dic17—162no—
200C2×#121Dic1711yescharacteristic, complemented
201C2×C4×D4C2×D1711yescharacteristic
202#432—341no—
203C2×#99—341no—
204#400Dic1711yescharacteristic, complemented
205#399C2×D1711yescharacteristic
206#394—21no—
207#394Dic1711yescharacteristic, complemented
208#392—21no—
209#392C2×D1711yescharacteristic
210#388—21no—
211#386—21no—
212#381Dic1711yescharacteristic, complemented
213#380—341no—
214#342—172no—
215#323—172no—
216#323—341no—
217C2×C17—21no—
218C2×C17—21no—
219C2×C17—41no—
220C2×C17—41no—
221C2×C17—81no—
222C2×C17—161no—
223C2×C17#151311yescharacteristic
224C2×C17#212111yescharacteristic
225C2×C17#212811yescharacteristic
226C22×D4—21no—
227C22×D4—21no—
228C22×D4C2×Dic1711yescharacteristic
229C22×D4C22⋊D1711yescharacteristic
230C23×C4C2×Dic1711yescharacteristic
231C23×C4C22⋊D1711yescharacteristic
232#121—41no—
233#121—41no—
234C4×D4—41no—
235C4×D4—41no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—681no—
238C2×C4⋊C4C2×Dic1711yescharacteristic
239C2×C4⋊C4C2×Dic1711yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—342no—
247C2×C22⋊C4C22⋊D1711yescharacteristic
248C2×C22⋊C4C22×D1711yescharacteristic
249C2×C42C22⋊D1711yescharacteristic
250C4⋊C8—681no—
251#99—682no—
252C22⋊C8—342no—
253#97—681no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—681no—
258#95C2×Dic1711yescharacteristic
259#95C2×Dic1711yescharacteristic
260C17#1182411yescharacteristic, complemented, Sylow
261C24—21no—
262C24C22⋊Dic1711yescharacteristic
263C24C2×C22⋊D1711yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—81no—
273C2×D4—81no—
274C2×D4—81no—
275C2×D4—81no—
276C2×D4—81no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—81no—
285C22×C4—81no—
286C22×C4—682no—
287C22×C4C22⋊Dic1711yescharacteristic
288C22×C4C22⋊Dic1711yescharacteristic
289C22×C4C22⋊Dic1711yescharacteristic
290C22×C4C22×Dic1711yescharacteristic
291C22×C4C2×C22⋊D1711yescharacteristic
292C2×C8—682no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—81no—
296C4⋊C4—1362no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C22⋊C4—682no—
307C22⋊C4—682no—
308C42—21no—
309C42—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23#1058763511yescharacteristic
327C23#1058763711yescharacteristic
328C23C2×C22⋊Dic1711yescharacteristic
329D4—42no—
330D4—42no—
331D4—82no—
332D4—82no—
333D4—82no—
334D4—84no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—1362no—
359C2×C4—1362no—
360C2×C4—1362no—
361C2×C4#1058750511yescharacteristic
362C2×C4#1058750511yescharacteristic
363C8—1362no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22C2×#1058750511yescharacteristic
386C22#1176281011yescharacteristic
387C22#1176282611yescharacteristic
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—2722no—
398C2—21no—
399C2—21no—
400C2—41no—
401C2—41no—
402C2—81no—
403C2—161no—
404C2#1452732711yescharacteristic
405C2#1453043011yescharacteristic
406C2#1453045611yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
Fitting, prime radicalC17×#2635C2
socleC22×C17C2×#99
cosocleC2×C22⋊C4×C17C23
hypercenter#2635D17
hypocenterC17#11824
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. #14528772C2semidirect
2. #14527125C2semidirect
3. #14526808C2semidirect
4. #14526781C2semidirect
12. C2×C17×#121C4semidirect
14. C17×#400C4semidirect
17. C17×#394C4semidirect
22. C17×#381C4semidirect
200. C2×#121Dic17semidirect
204. #400Dic17semidirect
207. #394Dic17semidirect
212. #381Dic17semidirect
260. C17#11824semidirect

Maximal subgroups

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

subgroupindex
#145287722
#145271252
#145268082
#145267812
C17×#26352
#1182417