Finite Group Databasebeta

← #16933695

Subgroups — #16933695

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#14539109C211yesmaximal, characteristic
2#14528654C211yesmaximal, characteristic, complemented
3#14527530C211yesmaximal, characteristic, complemented
4#14527283C211yesmaximal, characteristic, complemented
5#14527280C211yesmaximal, characteristic
6#14527182C211yesmaximal, characteristic
7C17×#1481C211yesmaximal, characteristic, complemented
8#11763359C2211yescharacteristic
9#11763166—21no—
10#11763166—21no—
11#11763161C411yescharacteristic, complemented
12#11763161C411yescharacteristic, complemented
13#11763157C411yescharacteristic, complemented
14#11763157C411yescharacteristic, complemented
15#11762862C2211yescharacteristic
16#11762803—21no—
17#11762803—21no—
18C2×#10587486—21no—
19C2×C4×#3622C2211yescharacteristic
20C4×C4⋊Dic17C2211yescharacteristic
21#11762563—21no—
22#11762561—21no—
23#11762559—21no—
24#11762546—22no—
25#11762544—22no—
26#11762536—22no—
27C17×#533C2211yescharacteristic
28C17×#431C2211yescharacteristic
29C2×C17×C4⋊C8C2211yescharacteristic
30C17×Q8⋊C8—22no—
31C2×#63252—21no—
32C22×C8×C17—21no—
33C17×C4⋊Q8C2×C411yescharacteristic
34C17×C4⋊Q8C2×C411yescharacteristic
35C17×#125—21no—
36C17×C22⋊Q8—21no—
37C17×C22⋊Q8—21no—
38C4×Q8×C17—21no—
39C4×Q8×C17—21no—
40C17×#117—21no—
41C2×C42×C17C2311yescharacteristic
42#10587616—21no—
43#10587616—21no—
44C2×C4⋊Dic17—21no—
45C2×C4×Dic17—21no—
46C22×#3622D411yescharacteristic
47C22×#3622D411yescharacteristic
48#10587561—21no—
49#10587560C2×C411yescharacteristic
50C4×D68—21no—
51C4×D68—21no—
52#10587555C2×C411yescharacteristic
53C17×C4⋊C8—21no—
54C17×C4⋊C8—21no—
55C17×C4⋊C8D412yes—
56C17×C22⋊C8—21no—
57C4×C8×C17—21no—
58#10587502D412yes—
59C22⋊#3622—21no—
60#10587486—42no—
61#10587481—21no—
62#10587481—21no—
63#10587481—21no—
64#10587481—21no—
65#10587480—21no—
66#10587480—21no—
67#10587480—21no—
68#10587480—21no—
69C4⋊#3622—21no—
70C4×#3622—21no—
71C4×#3622C2×C411yescharacteristic
72C4×#3622C2×C411yescharacteristic
73C4×#3622D411yescharacteristic
74C4×#3622D411yescharacteristic
75C2×Q8×C17—21no—
76C2×Q8×C17—21no—
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17#4111yescharacteristic
80C2×C22⋊D17—41no—
81C22×Dic17—22no—
82#63252—41no—
83#63252—41no—
84#63252—41no—
85#63252—41no—
86C2×D68—21no—
87C2×D68—21no—
88C2×D68—21no—
89C2×C4×D17—41no—
90C2×Dic34—21no—
91C2×C8×C17—22no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17—21no—
97C4⋊C4×C17—21no—
98C4⋊C4×C17—21no—
99C4⋊C4×C17—41no—
100C4⋊C4×C17—41no—
101C22⋊C4×C17—41no—
102C42×C17—41no—
103C42×C17C22×C411yescharacteristic
104C42×C17C2×D411yescharacteristic
105C42×C17C2×D411yescharacteristic
106C42×C17#4111yescharacteristic
107#63227—41no—
108#63227—41no—
109C4⋊Dic17—21no—
110C4⋊Dic17—21no—
111C4⋊Dic17—42no—
112C4×Dic17—41no—
113C4×Dic17—41no—
114C2×#3622—21no—
115C2×#3622—21no—
116C2×#3622—21no—
117C2×#3622—21no—
118C2×#3622—41no—
119C2×#3622C22⋊C411yescharacteristic
120C2×#3622C22⋊C411yescharacteristic
121C2×#3622C22⋊C411yescharacteristic
122C2×#3622C22⋊C411yescharacteristic
123#9754—171nomaximal, Sylow
124C23×C17#12111yescharacteristic
125C22×D17—41no—
126Q8×C17—42no—
127Q8×C17—81no—
128C2×C4×C17—22no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17C2×C22⋊C411yescharacteristic
133C2×C4×C17C4×D411yescharacteristic
134C2×C4×C17C4×D411yescharacteristic
135C2×C4×C17#12111yescharacteristic
136C2×C4×C17#12411yescharacteristic
137C2×C4×C17#12711yescharacteristic
138C2×C4×C17#13511yescharacteristic
139C2×C4×C17#13511yescharacteristic
140C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C17#13711yescharacteristic
142C22⋊D17—81no—
143C22⋊D17—81no—
144C2×Dic17—42no—
145C2×Dic17—42no—
146C2×Dic17—41no—
147C2×Dic17—42no—
148D68—41no—
149D68—41no—
150D68—42no—
151D68—81no—
152C4×D17—81no—
153C4×D17—81no—
154Dic34—41no—
155Dic34—41no—
156C8×C17—42no—
157C8×C17—81no—
158#3622—21no—
159#3622—21no—
160#3622—21no—
161#3622—21no—
162#3622—81no—
163#3131—171no—
164#1770—171no—
165#1564—171no—
166#1503—171no—
167#1502—171no—
168#1481D1711yescharacteristic, complemented
169#1480—171no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17#39011yescharacteristic
173C22×C17#46311yescharacteristic
174C22×C17#46411yescharacteristic
175C2×D17—81no—
176C2×D17—81no—
177C2×D17—81no—
178C4×C17—21no—
179C4×C17—21no—
180C4×C17—21no—
181C4×C17—81no—
182C4×C17—81no—
183C4×C17#41611yescharacteristic
184C4×C17#41711yescharacteristic
185C4×C17#44412yes—
186C4×C17#46311yescharacteristic
187C4×C17#46411yescharacteristic
188Dic17—82no—
189Dic17—81no—
190#533C2×D1711yescharacteristic
191#532—171no—
192#488—341no—
193#488—341no—
194#487—171no—
195#487—171no—
196#486—171no—
197#486—171no—
198#431—171no—
199#431C2×D1711yescharacteristic
200C2×C4⋊C8C2×D1711yescharacteristic
201#416—341no—
202#416—341no—
203C2×#97—341no—
204C2×C4×C8—171no—
205C4×C4⋊C4—171no—
206#336—341no—
207#335—341no—
208#334—341no—
209#328—342no—
210#327—342no—
211Q8⋊C8—22no—
212D4⋊C8—342no—
213C2×C17—21no—
214C2×C17—21no—
215C2×C17#197511yescharacteristic
216C2×C17#197611yescharacteristic
217C2×C17#198311yescharacteristic
218D17—161no—
219C2×#41—341no—
220C22×C8—21no—
221C22×C8—171no—
222C22×C8—171no—
223C4⋊Q8—171no—
224C4⋊Q8C4×D1711yescharacteristic
225C4⋊Q8C4×D1711yescharacteristic
226#127—171no—
227#125—21no—
228#124—341no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—341no—
232#121—341no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—341no—
236C4×D4—341no—
237#117—21no—
238C2×C4⋊C4—341no—
239C2×C42—341no—
240C2×C42C22×D1711yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—341no—
244C4⋊C8C22⋊D1712yes—
245#103—341no—
246#103—341no—
247#103—341no—
248#103—341no—
249#102—341no—
250#102—341no—
251#102—341no—
252#102—341no—
253C22⋊C8—21no—
254C22⋊C8—341no—
255#97—682no—
256C4×C8—21no—
257C4×C8—171no—
258C4×C8—171no—
259C4×C8—171no—
260C4×C8—171no—
261C4×C8—341no—
262#95—172no—
263C17#975411yescharacteristic, complemented, Sylow
264#41—681no—
265#41—681no—
266#41—681no—
267#41—681no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—341no—
271C2×D4—341no—
272C2×D4—341no—
273C2×D4—341no—
274C2×D4—681no—
275C22×C4—342no—
276C22×C4—681no—
277C22×C4#6325211yescharacteristic
278C22×C4D4×D1711yescharacteristic
279C22×C4D4×D1711yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—171no—
285C2×C8—171no—
286C2×C8—171no—
287C2×C8—171no—
288C2×C8—341no—
289C2×C8—341no—
290C2×C8—341no—
291C2×C8—341no—
292C2×C8—681no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—341no—
300C4⋊C4—341no—
301C4⋊C4—682no—
302C22⋊C4—41no—
303C22⋊C4—681no—
304C22⋊C4—681no—
305C42—41no—
306C42—681no—
307C42—681no—
308C42C2×C4×D1711yescharacteristic
309C42D4×D1711yescharacteristic
310C42#6325411yescharacteristic
311C42C2×C22⋊D1711yescharacteristic
312C23—681no—
313C23#1058757011yescharacteristic
314Q8—42no—
315Q8—81no—
316Q8—681no—
317Q8—681no—
318D4—681no—
319D4—681no—
320D4—682no—
321D4—1361no—
322D4—1361no—
323D4—1361no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—682no—
329C2×C4—682no—
330C2×C4—681no—
331C2×C4—682no—
332C2×C4—1361no—
333C2×C4—1361no—
334C2×C4C22⋊C4×D1711yescharacteristic
335C2×C4#1058756711yescharacteristic
336C2×C4#1058757111yescharacteristic
337C2×C4#1058760011yescharacteristic
338C2×C4#1058760211yescharacteristic
339C2×C4#1058760411yescharacteristic
340C2×C4#1058760511yescharacteristic
341C2×C4C4×C22⋊D1711yescharacteristic
342C2×C4#1058762511yescharacteristic
343C2×C4#1058762611yescharacteristic
344C8—42no—
345C8—81no—
346C8—341no—
347C8—341no—
348C8—341no—
349C8—341no—
350C8—1361no—
351C22—21no—
352C22—21no—
353C22—1361no—
354C22—1361no—
355C22—1361no—
356C22#1176270911yescharacteristic
357C22#1176302711yescharacteristic
358C22#1176303411yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—1362no—
365C4—1361no—
366C4#1176280411yescharacteristic
367C4#1176280911yescharacteristic
368C4#1176292912yes—
369C4#1176302611yescharacteristic
370C4#1176303311yescharacteristic
371C2—21no—
372C2—21no—
373C2—2721no—
374C2#1452967611yescharacteristic
375C2#1452968111yescharacteristic
376C2#1452971311yescharacteristic
subgroupG/H
centerC2×C4#10587625
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1481C2
socleC22×C17#390
prime radical#11763359C22
cosocleC2×C42×C17C23
hypercenter#1481D17
hypocenterC17#9754
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #14528654C2semidirect
3. #14527530C2semidirect
4. #14527283C2semidirect
7. C17×#1481C2semidirect
11. #11763161C4semidirect
12. #11763161C4semidirect
13. #11763157C4semidirect
14. #11763157C4semidirect
168. #1481D17semidirect
263. C17#9754semidirect

Maximal subgroups

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

subgroupindex
#145391092
#145286542
#145275302
#145272832
#145272802
#145271822
C17×#14812
#975417