Finite Group Databasebeta

← #16950628

Subgroups — #16950628

Order 4352.

420 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17×#427C211yesmaximal, characteristic
2#14530394C211yesmaximal, characteristic
3#14528806C211yesmaximal, characteristic
4#14526891C211yesmaximal, characteristic, complemented
5#14526890C211yesmaximal, characteristic, complemented
6#14526889C211yesmaximal, characteristic, complemented
7C17×#1386C211yesmaximal, characteristic, complemented
8C22×C8×D17C2211yescharacteristic
9#117×D17—21no—
10C2×#10587483C2211yescharacteristic
11#11762847C2211yescharacteristic
12#11762846C411yescharacteristic, complemented
13#11762846C411yescharacteristic, complemented
14#11762845—21no—
15#11762844—21no—
16#107×D17C411yescharacteristic, complemented
17#107×D17C411yescharacteristic, complemented
18C2×#10587488C2211yescharacteristic
19#106×D17—21no—
20#11762666—21no—
21#11762588—21no—
22#11762588—21no—
23#11762571—21no—
24C2×C17×M32C2211yescharacteristic
25C17×#427C2211yescharacteristic
26C2×C17×#106C2211yescharacteristic
27C22×C4×D17D411yescharacteristic
28C22×C8×C17C2311yescharacteristic
29C17×#117—21no—
30C2×C4⋊C4×C17—21no—
31C2×#63227—41no—
32#10587612—21no—
33C2×C4⋊Dic17—21no—
34C22×#3622D411yescharacteristic
35C2×C8×D17—21no—
36C2×C8×D17—21no—
37C2×C8×D17—21no—
38C2×C8×D17—21no—
39C2×C8×D17C2×C411yescharacteristic
40C2×C8×D17C2×C411yescharacteristic
41C2×C8×D17D411yescharacteristic
42C2×C8×D17D411yescharacteristic
43#10587578—21no—
44#10587578—21no—
45C4⋊C4×D17—21no—
46C4⋊C4×D17—21no—
47C22⋊C4×D17—41no—
48#10587563—41no—
49#10587558—41no—
50C42×D17—41no—
51C17×M32—21no—
52C17×M32—21no—
53C2×C16×C17—21no—
54C17×#107C2×C411yescharacteristic
55C17×#107C2×C411yescharacteristic
56C17×#106—21no—
57C17×#106—21no—
58C17×#106—21no—
59#10587502—41no—
60#10587489C2×C411yescharacteristic
61#10587489C2×C411yescharacteristic
62#10587488—21no—
63#10587488—21no—
64#10587488—21no—
65#10587483—21no—
66#10587483—21no—
67C2×#63214—21no—
68#10587479—21no—
69#10587479—21no—
70#10587478—21no—
71#10587478—21no—
72C23×D17D811yescharacteristic
73C22×C4×C17—41no—
74C22×C4×C17C2×D411yescharacteristic
75C22×Dic17—41no—
76C22×Dic17D811yescharacteristic
77C2×C4×D17—21no—
78C2×C4×D17—21no—
79C2×C4×D17—21no—
80C2×C4×D17—21no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17C22⋊C411yescharacteristic
84C2×C4×D17C22⋊C411yescharacteristic
85C2×C4×D17SD1611yescharacteristic
86C2×C4×D17SD1611yescharacteristic
87C2×C8×C17C22×C411yescharacteristic
88C2×C8×C17C2×D411yescharacteristic
89C2×C8×C17#4111yescharacteristic
90C2×C8×C17#4111yescharacteristic
91C2×C8×C17#4111yescharacteristic
92C2×C8×C17#4111yescharacteristic
93C4⋊C4×C17—21no—
94C4⋊C4×C17—21no—
95C4⋊C4×C17—41no—
96C4⋊C4×C17—41no—
97C22⋊C4×C17—41no—
98C42×C17—41no—
99C22⋊Dic17—41no—
100#63227—41no—
101#63227—41no—
102#63227—82no—
103C4⋊Dic17—21no—
104C4⋊Dic17—21no—
105C4⋊Dic17—41no—
106C4⋊Dic17—41no—
107#63225—41no—
108#63225—41no—
109C4×Dic17—41no—
110C4×Dic17—41no—
111C4×Dic17—41no—
112C2×#3622—21no—
113C2×#3622—21no—
114C2×#3622C22⋊C411yescharacteristic
115C2×#3622C22⋊C411yescharacteristic
116C8×D17—21no—
117C8×D17—21no—
118C8×D17—21no—
119C8×D17—21no—
120C8×D17—21no—
121C8×D17—21no—
122C8×D17—21no—
123C8×D17—21no—
124C16×C17—41no—
125#63214—41no—
126#12870—171nomaximal, Sylow
127C23×C17C2×D811yescharacteristic
128C22×D17—21no—
129C22×D17—21no—
130C22×D17—22no—
131C22×D17—41no—
132C22×D17#10211yescharacteristic
133C22×D17#10211yescharacteristic
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17—81no—
139C2×C4×C17C2×C22⋊C411yescharacteristic
140C2×C4×C17#12311yescharacteristic
141C2×C4×C17#12311yescharacteristic
142C2×C4×C17C2×SD1611yescharacteristic
143C2×C4×C17#13711yescharacteristic
144C2×C4×C17#13711yescharacteristic
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—41no—
148C2×Dic17—41no—
149C2×Dic17—81no—
150C2×Dic17—81no—
151C2×Dic17—81no—
152C2×Dic17#10211yescharacteristic
153C2×Dic17#10211yescharacteristic
154C4×D17—21no—
155C4×D17—21no—
156C4×D17—21no—
157C4×D17—21no—
158C4×D17—21no—
159C4×D17—21no—
160C4×D17—21no—
161C4×D17—21no—
162C4×D17—82no—
163C4×D17—82no—
164C8×C17#11711yescharacteristic
165C8×C17#11711yescharacteristic
166C8×C17#12311yescharacteristic
167C8×C17#12311yescharacteristic
168#3622—21no—
169#3622—21no—
170C2×#427—171no—
171#2112—171no—
172#1807—171no—
173#1386—171no—
174#1386—171no—
175#1386—171no—
176#1386D1711yescharacteristic, complemented
177C22×C17—21no—
178C22×C17—21no—
179C22×C17C2×#10211yescharacteristic
180C22×C17#48011yescharacteristic
181C22×C17#48011yescharacteristic
182C2×D17—21no—
183C2×D17—21no—
184C2×D17—21no—
185C2×D17—21no—
186C2×D17—21no—
187C2×D17—42no—
188C2×D17—42no—
189C2×D17#36012yes—
190C4×C17—81no—
191C4×C17—81no—
192C4×C17—161no—
193C4×C17#38111yescharacteristic
194C4×C17#41911yescharacteristic
195C4×C17#48311yescharacteristic
196C4×C17#48311yescharacteristic
197Dic17—21no—
198Dic17—21no—
199Dic17—81no—
200Dic17—81no—
201Dic17—161no—
202C23×C8—171no—
203C2×#117—341no—
204C2×M32—171no—
205C2×M32C2×D1711yescharacteristic
206#427—171no—
207#427—171no—
208#427—171no—
209#427—341no—
210#427—341no—
211#427C2×D1711yescharacteristic
212C2×#107—171no—
213C2×#107—171no—
214C2×#106—171no—
215C2×#106—341no—
216C2×#106C2×D1711yescharacteristic
217#380—341no—
218C22⋊C16—341no—
219C22⋊C16—341no—
220#340—341no—
221C2×C17—21no—
222C2×C17—21no—
223C2×C17#182311yescharacteristic
224C2×C17C2×#36011yescharacteristic
225C2×C17#214511yescharacteristic
226D17—22no—
227D17—41no—
228C23×C4—171no—
229C22×C8—171no—
230C22×C8—171no—
231C22×C8—171no—
232C22×C8—171no—
233C22×C8—171no—
234C22×C8—341no—
235C22×C8—341no—
236C22×C8—341no—
237C22×C8—341no—
238C22×C8C22×D1711yescharacteristic
239#117—21no—
240#117—341no—
241#117—341no—
242#117—341no—
243#117—681no—
244#117—681no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—341no—
247C2×C4⋊C4—341no—
248C2×C4⋊C4—341no—
249C2×C22⋊C4—681no—
250C2×C22⋊C4—681no—
251C2×C42—681no—
252M32—21no—
253M32—21no—
254M32—341no—
255M32—341no—
256C2×C16—21no—
257C2×C16—341no—
258#107—171no—
259#107—171no—
260#107—341no—
261#107—341no—
262#107C4×D1711yescharacteristic
263#107C4×D1711yescharacteristic
264#106—21no—
265#106—21no—
266#106—21no—
267#106—341no—
268#106—341no—
269#106—341no—
270#106—341no—
271#106—341no—
272#95—681no—
273C17#1287011yescharacteristic, complemented, Sylow
274C24—171no—
275C22×C4—41no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—171no—
279C22×C4—171no—
280C22×C4—171no—
281C22×C4—341no—
282C22×C4—341no—
283C22×C4—341no—
284C22×C4—341no—
285C22×C4—681no—
286C22×C4—681no—
287C22×C4—681no—
288C22×C4D4×D1711yescharacteristic
289C2×C8—171no—
290C2×C8—171no—
291C2×C8—341no—
292C2×C8—341no—
293C2×C8—341no—
294C2×C8—341no—
295C2×C8—341no—
296C2×C8—341no—
297C2×C8—341no—
298C2×C8—341no—
299C2×C8—341no—
300C2×C8—341no—
301C2×C8C2×C4×D1711yescharacteristic
302C2×C8#6325211yescharacteristic
303C2×C8#6325211yescharacteristic
304C2×C8D4×D1711yescharacteristic
305C2×C8#6325411yescharacteristic
306C2×C8#6325611yescharacteristic
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—341no—
312C4⋊C4—341no—
313C4⋊C4—681no—
314C4⋊C4—681no—
315C4⋊C4—681no—
316C4⋊C4—681no—
317C22⋊C4—41no—
318C22⋊C4—681no—
319C22⋊C4—681no—
320C22⋊C4—681no—
321C22⋊C4—1362no—
322C42—41no—
323C42—681no—
324C42—681no—
325C42—681no—
326C16—41no—
327C16—681no—
328C23—171no—
329C23—171no—
330C23—342no—
331C23—341no—
332C23—341no—
333C23—681no—
334C23D8×D1711yescharacteristic
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—171no—
341C2×C4—171no—
342C2×C4—341no—
343C2×C4—341no—
344C2×C4—341no—
345C2×C4—341no—
346C2×C4—341no—
347C2×C4—341no—
348C2×C4—341no—
349C2×C4—341no—
350C2×C4—341no—
351C2×C4—341no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4—1362no—
355C2×C4—1362no—
356C2×C4—1361no—
357C2×C4—1361no—
358C2×C4—1361no—
359C2×C4C22⋊C4×D1711yescharacteristic
360C2×C4#1058756911yescharacteristic
361C2×C4#1058758011yescharacteristic
362C2×C4SD16×D1711yescharacteristic
363C2×C4#1058760111yescharacteristic
364C2×C4#1058760411yescharacteristic
365C8—341no—
366C8—341no—
367C8#1058755811yescharacteristic
368C8#1058756911yescharacteristic
369C8#1058757811yescharacteristic
370C8#1058758011yescharacteristic
371C22—21no—
372C22—21no—
373C22—172no—
374C22—341no—
375C22—341no—
376C22—341no—
377C22—341no—
378C22—341no—
379C22—682no—
380C22—682no—
381C22#102×D1711yescharacteristic
382C22#1176312111yescharacteristic
383C22#1176312411yescharacteristic
384C4—81no—
385C4—81no—
386C4—161no—
387C4—2721no—
388C4—341no—
389C4—341no—
390C4—1361no—
391C4—1361no—
392C4#1176267111yescharacteristic
393C4#1176281611yescharacteristic
394C4#1176313811yescharacteristic
395C4#1176314111yescharacteristic
396C2—21no—
397C2—21no—
398C2—342no—
399C2—681no—
400C2#1452886911yescharacteristic
401C2D17×#36011yescharacteristic
402C2#1453051811yescharacteristic
subgroupG/H
centerC22#102×D17
commutatorC2×C8×C17C22×C4
FrattiniC22×C8C22×D17
FittingC17×#1386C2
socleC22×C17C2×#102
prime radicalC23×D17D8
cosocleC22×C8×C17C23
hypercenter#1386D17
hypocenterC17#12870
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
4. #14526891C2semidirect
5. #14526890C2semidirect
6. #14526889C2semidirect
7. C17×#1386C2semidirect
12. #11762846C4semidirect
13. #11762846C4semidirect
16. #107×D17C4semidirect
17. #107×D17C4semidirect
176. #1386D17semidirect
273. C17#12870semidirect

Maximal subgroups

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

subgroupindex
D17×#4272
#145303942
#145288062
#145268912
#145268902
#145268892
C17×#13862
#1287017