Finite Group Databasebeta

← #16933694

Subgroups — #16933694

Order 4352.

416 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14528651C211yesmaximal, characteristic, complemented
2#14527532C211yesmaximal, characteristic, complemented
3#14527283C211yesmaximal, characteristic, complemented
4#14527279C211yesmaximal, characteristic
5#14527187C211yesmaximal, characteristic, complemented
6#14527183C211yesmaximal, characteristic
7C17×#3131C211yesmaximal, characteristic
8#11762862C2211yescharacteristic
9#11762862C2211yescharacteristic
10C2×C4⋊#3622C2211yescharacteristic
11C2×#10587486—21no—
12C4×C4⋊Dic17C2211yescharacteristic
13#11762563—21no—
14#11762562—21no—
15#11762560—21no—
16#11762546—22no—
17#11762543—22no—
18Q8⋊#3622—22no—
19D4⋊#3622—22no—
20C17×#533C2211yescharacteristic
21C17×#532C2211yescharacteristic
22C17×#488—21no—
23C17×#488—21no—
24C17×#487C411yescharacteristic, complemented
25C17×#487C411yescharacteristic, complemented
26C17×#486C411yescharacteristic, complemented
27C17×#486C411yescharacteristic, complemented
28C17×#416—21no—
29C17×#416—21no—
30C2×C4×C8×C17C2211yescharacteristic
31C2×#41×C17—21no—
32C22×C8×C17D411yescharacteristic
33C22×C8×C17D411yescharacteristic
34C17×C4⋊Q8C2×C411yescharacteristic
35C17×C4⋊Q8C2×C411yescharacteristic
36C17×C4⋊Q8C2×C411yescharacteristic
37C17×#127C2×C411yescharacteristic
38C17×#125—21no—
39C17×#124—21no—
40C17×C22⋊Q8—21no—
41C17×C22⋊Q8—21no—
42C17×#121—21no—
43C17×#121—21no—
44C4×Q8×C17—21no—
45C4×Q8×C17—21no—
46C4×D4×C17—21no—
47C4×D4×C17—21no—
48C17×#117—21no—
49C2×C42×C17C2311yescharacteristic
50C2×C4⋊Dic17—21no—
51C2×C4×Dic17—21no—
52C22×#3622—21no—
53C17×#103—21no—
54C17×#103—21no—
55C17×#103—21no—
56C17×#103—21no—
57C17×#102—21no—
58C17×#102—21no—
59C17×#102—21no—
60C17×#102—21no—
61C4×C8×C17C2×C411yescharacteristic
62C4×C8×C17C2×C411yescharacteristic
63C4×C8×C17D411yescharacteristic
64C4×C8×C17D411yescharacteristic
65#10587502D412yes—
66C22⋊#3622—21no—
67C22⋊#3622—21no—
68#10587486—42no—
69C4⋊#3622—21no—
70C4⋊#3622—21no—
71C4⋊#3622—21no—
72C4⋊#3622D412yes—
73C4×#3622—21no—
74C4×#3622—21no—
75#41×C17—41no—
76#41×C17—41no—
77#41×C17—41no—
78#41×C17—41no—
79C2×Q8×C17—21no—
80C2×Q8×C17—21no—
81C2×Q8×C17—21no—
82C2×D4×C17—21no—
83C2×D4×C17—21no—
84C2×D4×C17—21no—
85C2×D4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17C2×D411yescharacteristic
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17#4111yescharacteristic
90C22×Dic17—22no—
91C2×C8×C17—21no—
92C2×C8×C17—21no—
93C2×C8×C17—21no—
94C2×C8×C17—21no—
95C2×C8×C17C22⋊C411yescharacteristic
96C2×C8×C17C22⋊C411yescharacteristic
97C2×C8×C17C22⋊C411yescharacteristic
98C2×C8×C17C22⋊C411yescharacteristic
99C4⋊C4×C17—21no—
100C4⋊C4×C17—21no—
101C4⋊C4×C17—21no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17—21no—
105C4⋊C4×C17—41no—
106C4⋊C4×C17—41no—
107C22⋊C4×C17—41no—
108C22⋊C4×C17—41no—
109C22⋊C4×C17—41no—
110C42×C17—41no—
111C42×C17C22×C411yescharacteristic
112C42×C17C2×D411yescharacteristic
113C42×C17C2×D411yescharacteristic
114C42×C17#4111yescharacteristic
115C4⋊Dic17—42no—
116C4×Dic17—41no—
117C4×Dic17—41no—
118C2×#3622—22no—
119C2×#3622—41no—
120C2×#3622—41no—
121C2×#3622—41no—
122C2×#3622—41no—
123#9754—171nomaximal, Sylow
124C23×C17—41no—
125C23×C17#12111yescharacteristic
126Q8×C17—41no—
127Q8×C17—41no—
128Q8×C17—42no—
129Q8×C17—81no—
130D4×C17—41no—
131D4×C17—41no—
132D4×C17—42no—
133D4×C17—81no—
134D4×C17—81no—
135D4×C17—81no—
136C2×C4×C17—22no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—81no—
142C2×C4×C17—81no—
143C2×C4×C17C2×C22⋊C411yescharacteristic
144C2×C4×C17C4×D411yescharacteristic
145C2×C4×C17C4×D411yescharacteristic
146C2×C4×C17#12111yescharacteristic
147C2×C4×C17#12411yescharacteristic
148C2×C4×C17#12711yescharacteristic
149C2×C4×C17#13511yescharacteristic
150C2×C4×C17#13511yescharacteristic
151C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C17#13711yescharacteristic
153C2×Dic17—42no—
154C2×Dic17—42no—
155C2×Dic17—42no—
156C8×C17—21no—
157C8×C17—21no—
158C8×C17—21no—
159C8×C17—21no—
160#3622—42no—
161#3622—81no—
162#3622—81no—
163#3131D1711yescharacteristic
164#1770—171no—
165#1564—171no—
166#1503—171no—
167#1502—171no—
168#1481—171no—
169#1480—171no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—81no—
173C22×C17—81no—
174C22×C17—81no—
175C22×C17#39011yescharacteristic
176C22×C17#46311yescharacteristic
177C22×C17#46411yescharacteristic
178C4×C17—21no—
179C4×C17—21no—
180C4×C17—21no—
181C4×C17—81no—
182C4×C17—81no—
183C4×C17—81no—
184C4×C17#41611yescharacteristic
185C4×C17#41711yescharacteristic
186C4×C17#44412yes—
187C4×C17#46311yescharacteristic
188C4×C17#46411yescharacteristic
189Dic17—82no—
190#533C2×D1711yescharacteristic
191#532C2×D1711yescharacteristic
192#488—21no—
193#488—21no—
194#487Dic1711yescharacteristic, complemented
195#487Dic1711yescharacteristic, complemented
196#486Dic1711yescharacteristic, complemented
197#486Dic1711yescharacteristic, complemented
198#431—171no—
199#431—171no—
200C2×C4⋊C8—171no—
201#416—21no—
202#416—21no—
203C2×#97—341no—
204C2×C4×C8C2×D1711yescharacteristic
205C4×C4⋊C4—171no—
206#336—341no—
207#335—341no—
208#334—341no—
209#328—342no—
210#327—342no—
211Q8⋊C8—342no—
212D4⋊C8—342no—
213C2×C17—21no—
214C2×C17—21no—
215C2×C17—161no—
216C2×C17#197511yescharacteristic
217C2×C17#197611yescharacteristic
218C2×C17#198311yescharacteristic
219C2×#41—21no—
220C22×C8—341no—
221C22×C8C22⋊D1711yescharacteristic
222C22×C8C22⋊D1711yescharacteristic
223C4⋊Q8C2×Dic1711yescharacteristic
224C4⋊Q8C2×Dic1711yescharacteristic
225C4⋊Q8C2×Dic1711yescharacteristic
226#127C2×Dic1711yescharacteristic
227#125—21no—
228#124—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—21no—
232#121—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—21no—
236C4×D4—21no—
237#117—21no—
238C2×C4⋊C4—341no—
239C2×C42—341no—
240C2×C42C22×D1711yescharacteristic
241C4⋊C8—172no—
242C4⋊C8—341no—
243C4⋊C8—341no—
244C4⋊C8—341no—
245#103—21no—
246#103—21no—
247#103—21no—
248#103—21no—
249#102—21no—
250#102—21no—
251#102—21no—
252#102—21no—
253C22⋊C8—341no—
254C22⋊C8—341no—
255#97—682no—
256C4×C8—341no—
257C4×C8—341no—
258C4×C8C2×Dic1711yescharacteristic
259C4×C8C2×Dic1711yescharacteristic
260C4×C8C22⋊D1711yescharacteristic
261C4×C8C22⋊D1711yescharacteristic
262#95—172no—
263C17#975411yescharacteristic, complemented, Sylow
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—342no—
277C22×C4D4×D1711yescharacteristic
278C22×C4#6325411yescharacteristic
279C22×C4C2×C22⋊D1711yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—342no—
285C2×C8—681no—
286C2×C8—681no—
287C2×C8—681no—
288C2×C8—681no—
289C2×C8C22⋊Dic1711yescharacteristic
290C2×C8C22⋊Dic1711yescharacteristic
291C2×C8C22⋊Dic1711yescharacteristic
292C2×C8C22⋊Dic1711yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—682no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—41no—
306C42—681no—
307C42—681no—
308C42D4×D1711yescharacteristic
309C42#6325411yescharacteristic
310C42C22×Dic1711yescharacteristic
311C42C2×C22⋊D1711yescharacteristic
312C23—41no—
313C23#1058762411yescharacteristic
314Q8—41no—
315Q8—41no—
316Q8—42no—
317Q8—81no—
318D4—41no—
319D4—41no—
320D4—42no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—682no—
332C2×C4—682no—
333C2×C4—682no—
334C2×C4D4×Dic1711yescharacteristic
335C2×C4D4×Dic1711yescharacteristic
336C2×C4#1058762211yescharacteristic
337C2×C4#1058762411yescharacteristic
338C2×C4#1058762611yescharacteristic
339C2×C4#1058763511yescharacteristic
340C2×C4#1058763611yescharacteristic
341C2×C4#1058763611yescharacteristic
342C2×C4#1058763711yescharacteristic
343C2×C4C2×C22⋊Dic1711yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C8—682no—
349C8—1361no—
350C8—1361no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1176271211yescharacteristic
357C22#1176302111yescharacteristic
358C22#1176302811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—1362no—
366C4#1176280511yescharacteristic
367C4#1176281011yescharacteristic
368C4#1176293112yes—
369C4#1176302111yescharacteristic
370C4#1176302811yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2#1452967811yescharacteristic
375C2#1452968311yescharacteristic
376C2#1452971711yescharacteristic
subgroupG/H
centerC2×C4#10587624
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#3131C2
socleC22×C17#390
prime radicalC17×#532C22
cosocleC2×C42×C17C23
hypercenter#3131D17
hypocenterC17#9754
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #14528651C2semidirect
2. #14527532C2semidirect
3. #14527283C2semidirect
5. #14527187C2semidirect
24. C17×#487C4semidirect
25. C17×#487C4semidirect
26. C17×#486C4semidirect
27. C17×#486C4semidirect
194. #487Dic17semidirect
195. #487Dic17semidirect
196. #486Dic17semidirect
197. #486Dic17semidirect
263. C17#9754semidirect

Maximal subgroups

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

subgroupindex
#145286512
#145275322
#145272832
#145272792
#145271872
#145271832
C17×#31312
#975417