Finite Group Databasebeta

← #17038595

Subgroups — #17038595

Order 4352.

766 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×Dic17C211yesmaximal, characteristic
2#14531429C212yesmaximal
3#14529646C211yesmaximal, characteristic
4#14529517C211yesmaximal, characteristic
5#14529515C211yesmaximal, characteristic
6#14529477C212yesmaximal
7#14529471C212yesmaximal
8#107×Dic17C211yesmaximal, characteristic
9#14528616C212yesmaximal
10#14528470C211yesmaximal, characteristic
11C17×#1969C211yesmaximal, characteristic
12C2×Q8×Dic17C2212yes—
13Q16×Dic17C418yescomplemented
14C2×#10587489C2211yescharacteristic
15C2×#10587489C2211yescharacteristic
16C2×#10587506C2212yes—
17C2×#10587506C2212yes—
18C2×#10587474C2211yescharacteristic
19C2×#10587486C2211yescharacteristic
20C2×#10587486C2211yescharacteristic
21C2×C8×Dic17C2211yescharacteristic
22C2×C8×Dic17C2211yescharacteristic
23#11762716C2212yes—
24#11762707C2212yes—
25#11762705C2212yes—
26#11762694—22no—
27#11762692—22no—
28#11762676—22no—
29#11762673—22no—
30C4⋊C4×Dic17C2212yes—
31#11762655C2211yescharacteristic
32#11762572C2212yes—
33#11762571C2212yes—
34#11762571C2212yes—
35C22×Q16×C17C2211yescharacteristic
36C2×C17×#107C2211yescharacteristic
37C2×C17×#103C2212yes—
38C2×C4×C8×C17C2211yescharacteristic
39C17×#391C2212yes—
40C22×Q8×C17C2312yes—
41C2×Q16×C17—22no—
42C2×Q16×C17—22no—
43C2×Q16×C17C2×C414yes—
44C22×C8×C17C2311yescharacteristic
45C22×C8×C17C2311yescharacteristic
46C2×C4⋊C4×C17C2312yes—
47C2×C42×C17C2311yescharacteristic
48Q8×Dic17—24no—
49Q8×Dic17C2×C418yes—
50C2×C4⋊Dic17—22no—
51C2×C4⋊Dic17C2312yes—
52C2×C4⋊Dic17C2312yes—
53C2×#63225—22no—
54C2×#63225—22no—
55C2×C4×Dic17—22no—
56C2×C4×Dic17—22no—
57C2×C4×Dic17C2311yescharacteristic
58C2×C4×Dic17C2311yescharacteristic
59C22×#3622C2311yescharacteristic
60C22×#3622C2311yescharacteristic
61C17×#107—22no—
62C17×#103—24no—
63C4×C8×C17—22no—
64C17×#95—22no—
65C17×#95—22no—
66#10587506—24no—
67#10587506C2×C418yes—
68#10587502—22no—
69#10587502—22no—
70#10587502—22no—
71#10587502—22no—
72#10587502—22no—
73#10587502D411yescharacteristic
74#10587502D411yescharacteristic
75#10587502D411yescharacteristic
76#10587502D411yescharacteristic
77#10587489—22no—
78#10587489C2×C414yes—
79#10587486—22no—
80#10587486—22no—
81C8×Dic17—22no—
82C8×Dic17C2×C414yes—
83#10587474—22no—
84C2×Q8×C17—22no—
85C2×Q8×C17—22no—
86C2×Q8×C17—22no—
87C2×Q8×C17—22no—
88C2×Q8×C17—22no—
89C2×Q8×C17C22×C414yes—
90C22×C4×C17—22no—
91C22×C4×C17—22no—
92C22×C4×C17C2×D411yescharacteristic
93C22×C4×C17C2×D411yescharacteristic
94C22×C4×C17C2411yescharacteristic
95C22×Dic17—22no—
96C22×Dic17—22no—
97C22×Dic17C2×D411yescharacteristic
98C22×Dic17C2×D411yescharacteristic
99C22×Dic17C2×D411yescharacteristic
100C22×Dic17C2×D411yescharacteristic
101Q16×C17—28no—
102C2×C8×C17—21no—
103C2×C8×C17—21no—
104C2×C8×C17C22×C412yes—
105C2×C8×C17#4112yes—
106C2×C8×C17#4112yes—
107C2×C8×C17#4112yes—
108C4⋊C4×C17—22no—
109C4⋊C4×C17—22no—
110C42×C17—21no—
111C42×C17—21no—
112C4⋊Dic17—22no—
113C4⋊Dic17—28no—
114C4⋊Dic17—22no—
115C4⋊Dic17—22no—
116C4⋊Dic17C22×C414yes—
117#63225—82no—
118#63225—82no—
119C4×Dic17—21no—
120C4×Dic17—21no—
121C4×Dic17—28no—
122C4×Dic17—82no—
123C4×Dic17C22×C412yes—
124C4×Dic17#4112yes—
125C2×#3622—21no—
126C2×#3622—21no—
127C2×#3622—21no—
128C2×#3622—21no—
129C2×#3622C22×C412yes—
130C2×#3622#4112yes—
131#21281—171nomaximal, Sylow
132C23×C17C22×D411yescharacteristic
133Q8×C17—24no—
134Q8×C17—24no—
135Q8×C17—42no—
136Q8×C17—42no—
137C2×C4×C17—24no—
138C2×C4×C17—21no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—21no—
144C2×C4×C17—42no—
145C2×C4×C17—42no—
146C2×C4×C17—42no—
147C2×C4×C17—42no—
148C2×C4×C17—42no—
149C2×C4×C17C23×C411yescharacteristic
150C2×C4×C17C2×#4111yescharacteristic
151C2×C4×C17C2×#4111yescharacteristic
152C2×C4×C17C2×#4111yescharacteristic
153C2×C4×C17C2×#4111yescharacteristic
154C2×C4×C17C2×#4111yescharacteristic
155C2×Dic17—21no—
156C2×Dic17—21no—
157C2×Dic17—21no—
158C2×Dic17—21no—
159C2×Dic17—24no—
160C2×Dic17—21no—
161C2×Dic17—21no—
162C2×Dic17—21no—
163C2×Dic17—21no—
164C2×Dic17—21no—
165C2×Dic17—21no—
166C2×Dic17—42no—
167C2×Dic17—42no—
168C2×Dic17—42no—
169C2×Dic17—42no—
170C2×Dic17—42no—
171C2×Dic17C4×D412yes—
172C2×Dic17C4×D412yes—
173C8×C17—22no—
174C8×C17#11714yes—
175#3622—22no—
176#3622—22no—
177C2×C4×Q16—171no—
178#2320—172no—
179#1969—171no—
180#1969D1711yescharacteristic
181#1942—171no—
182#1942—171no—
183#1935—172no—
184#1935—172no—
185C4×#107—171no—
186#1763—172no—
187#1726—171no—
188C22×C17C2×C4×D411yescharacteristic
189C22×C17#53211yescharacteristic
190C22×C17#53211yescharacteristic
191C22×C17#57611yescharacteristic
192C22×C17#57811yescharacteristic
193C22×C17#57811yescharacteristic
194C22×C17#57811yescharacteristic
195C4×C17—41no—
196C4×C17—41no—
197C4×C17—44no—
198C4×C17—82no—
199C4×C17C2×#11711yescharacteristic
200C4×C17C4×#4111yescharacteristic
201C4×C17#52911yescharacteristic
202C4×C17#52911yescharacteristic
203Dic17—22no—
204Dic17—22no—
205Dic17—41no—
206Dic17—41no—
207Dic17—44no—
208Dic17—82no—
209C22×Q16C2×D1711yescharacteristic
210C2×C4×Q8—172no—
211C4×Q16—178no—
212C2×#107—171no—
213C2×#107—171no—
214C2×#107C2×D1711yescharacteristic
215C2×#103—172no—
216C2×#103—172no—
217C2×#103C2×D1712yes—
218C2×#97—171no—
219C2×#97—171no—
220C2×#97—171no—
221C2×C4×C8—171no—
222C2×C4×C8—171no—
223C2×C4×C8C2×D1711yescharacteristic
224#391—172no—
225#391C2×D1712yes—
226#389—172no—
227#389—172no—
228#387—342no—
229#387—342no—
230#383—342no—
231#382—342no—
232C4×C4⋊C4—172no—
233#376—171no—
234#340—172no—
235#340—172no—
236#340—172no—
237C2×C17#229311yescharacteristic
238C2×C17#295011yescharacteristic
239C2×C17#295111yescharacteristic
240C2×C17#317511yescharacteristic
241C2×C17#317511yescharacteristic
242C2×C17#317711yescharacteristic
243C2×C17#317711yescharacteristic
244C22×Q8C22×D1712yes—
245C2×Q16—22no—
246C2×Q16—22no—
247C2×Q16C4×D1714yes—
248C22×C8—171no—
249C22×C8—171no—
250C22×C8C22×D1711yescharacteristic
251C22×C8C22×D1711yescharacteristic
252C4×Q8—178no—
253C4×Q8—344no—
254C2×C4⋊C4—172no—
255C2×C4⋊C4—172no—
256C2×C4⋊C4—342no—
257C2×C4⋊C4—342no—
258C2×C4⋊C4—342no—
259C2×C4⋊C4C22×D1712yes—
260C2×C42—171no—
261C2×C42—171no—
262C2×C42—342no—
263C2×C42—342no—
264C2×C42C22×D1711yescharacteristic
265#107—22no—
266#107—174no—
267#107—342no—
268#103—24no—
269#103—178no—
270#103—344no—
271#97—342no—
272#97—342no—
273#97—342no—
274C4×C8—22no—
275C4×C8—174no—
276C4×C8—342no—
277#95—22no—
278#95—22no—
279#95—171no—
280#95—171no—
281#95—171no—
282#95—171no—
283#95—342no—
284#95—342no—
285#95—342no—
286#95—342no—
287#95—342no—
288C17#2128111yescharacteristic, complemented, Sylow
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8C2×C4×D1714yes—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—171no—
298C22×C4—171no—
299C22×C4—171no—
300C22×C4—171no—
301C22×C4—342no—
302C22×C4—342no—
303C22×C4D4×D1711yescharacteristic
304C22×C4D4×D1711yescharacteristic
305C22×C4C23×D1711yescharacteristic
306Q16—28no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—172no—
310C2×C8—172no—
311C2×C8—341no—
312C2×C8—341no—
313C2×C8—341no—
314C2×C8—341no—
315C2×C8C2×C4×D1712yes—
316C2×C8#6325412yes—
317C2×C8#6325412yes—
318C2×C8#6325412yes—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—174no—
322C4⋊C4—348no—
323C4⋊C4—342no—
324C4⋊C4—342no—
325C4⋊C4—342no—
326C4⋊C4—1362no—
327C4⋊C4—1362no—
328C42—21no—
329C42—21no—
330C42—172no—
331C42—172no—
332C42—348no—
333C42—341no—
334C42—341no—
335C42—1362no—
336C23C2×D4×D1711yescharacteristic
337Q8—24no—
338Q8—24no—
339Q8—42no—
340Q8—42no—
341C2×C4—24no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—172no—
354C2×C4—172no—
355C2×C4—341no—
356C2×C4—341no—
357C2×C4—341no—
358C2×C4—341no—
359C2×C4—344no—
360C2×C4—341no—
361C2×C4—341no—
362C2×C4—341no—
363C2×C4—341no—
364C2×C4—341no—
365C2×C4—341no—
366C2×C4—682no—
367C2×C4—682no—
368C2×C4—682no—
369C2×C4—682no—
370C2×C4—682no—
371C2×C4C22×C4×D1711yescharacteristic
372C2×C4C2×#6325411yescharacteristic
373C2×C4C2×#6325411yescharacteristic
374C2×C4C2×#6325411yescharacteristic
375C2×C4#41×D1711yescharacteristic
376C2×C4#41×D1711yescharacteristic
377C8—22no—
378C8—342no—
379C8—342no—
380C8#1058756314yes—
381C22C4×D4×D1711yescharacteristic
382C22#1176335411yescharacteristic
383C22#1176335711yescharacteristic
384C22#1176361111yescharacteristic
385C22#1176362211yescharacteristic
386C22#1176362211yescharacteristic
387C22#1176362311yescharacteristic
388C4—41no—
389C4—41no—
390C4—44no—
391C4—82no—
392C4—342no—
393C4—342no—
394C4—681no—
395C4—681no—
396C4—684no—
397C4—1362no—
398C4C2×#1058756311yescharacteristic
399C4C4×#6325411yescharacteristic
400C4#1176333811yescharacteristic
401C4#1176334011yescharacteristic
402C2#1453124611yescharacteristic
403C2#1453764711yescharacteristic
404C2#1453765911yescharacteristic
405C2#1453942011yescharacteristic
406C2#1453942411yescharacteristic
407C2#1453943611yescharacteristic
408C2#1453944011yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1969C2
socle, prime radicalC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenter#1969D17
hypocenterC17#21281
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1969

Complements

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

NH ≅ G/Ntype
13. Q16×Dic17C4semidirect
288. C17#21281semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×Dic172
#145314292
#145296462
#145295172
#145295152
#145294772
#145294712
#107×Dic172
#145286162
#145284702
C17×#19692
#2128117