Finite Group Databasebeta

← #16930234

Subgroups — #16930234

Order 4352.

566 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538577C211yesmaximal, characteristic
2#14531695C211yesmaximal, characteristic
3#14527348C211yesmaximal, characteristic, complemented
4#14527174C211yesmaximal, characteristic
5#14526687C211yesmaximal, characteristic, complemented
6#14526643C211yesmaximal, characteristic, complemented
7C17×#1503C211yesmaximal, characteristic, complemented
8C2×C4×D68—21no—
9C2×C4×D68C2211yescharacteristic
10#11763106—22no—
11#11763096C412yescomplemented
12#11763086C412yescomplemented
13#11762862C2211yescharacteristic
14#11762852—21no—
15#11762833C2211yescharacteristic
16#11762813—21no—
17#11762707—21no—
18#11762680—22no—
19#11762675C2211yescharacteristic
20#11762668—21no—
21#95×D17—21no—
22#11762546—22no—
23#11762536—22no—
24C17×#533C2211yescharacteristic
25C17×#431C2211yescharacteristic
26C4×C4⋊C4×C17C2211yescharacteristic
27C17×#328—21no—
28C17×#328—21no—
29C22×D68D411yescharacteristic
30C22×C4×D17—21no—
31C22×C4×D17—22no—
32C17×C4⋊Q8C2×C411yescharacteristic, complemented
33C17×C4⋊Q8C2×C411yescharacteristic, complemented
34C17×#125—21no—
35C17×C22⋊Q8—21no—
36C17×C22⋊Q8—21no—
37C4×Q8×C17—21no—
38C4×Q8×C17—21no—
39C17×#117—21no—
40C2×C4⋊C4×C17—21no—
41C2×C42×C17—21no—
42C2×C42×C17C2311yescharacteristic
43C2×#63227—22no—
44C2×#63227—21no—
45C2×C4⋊Dic17—21no—
46C2×C4⋊Dic17D411yescharacteristic
47C2×#63225—22no—
48C2×#63223—21no—
49C4×D68—21no—
50C4×D68—21no—
51C4×D68—42no—
52C4×D68—42no—
53C4×D68C2×C412yes—
54C4×D68D412yes—
55C17×C4⋊C8—21no—
56C17×C22⋊C8—21no—
57C4×C8×C17—21no—
58C17×#95D411yescharacteristic
59C17×#95D411yescharacteristic
60#10587502—22no—
61#10587502—21no—
62#10587502D412yes—
63C22⋊#3622—21no—
64#10587480—22no—
65#10587480—22no—
66#10587479—22no—
67#10587478—22no—
68C4⋊#3622—21no—
69C4⋊#3622—21no—
70C4⋊#3622C2×C412yescomplemented
71C4×#3622—21no—
72C23×D17—21no—
73C2×Q8×C17—21no—
74C2×Q8×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17C2×D411yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×Dic17—21no—
81C22×Dic17—22no—
82C2×D68—21no—
83C2×D68—21no—
84C2×D68—21no—
85C2×D68C22⋊C412yes—
86C2×D68SD1612yes—
87C2×D68Q1612yes—
88C2×C4×D17—22no—
89C2×C4×D17—22no—
90C2×C4×D17—44no—
91C2×C4×D17—44no—
92C2×C4×D17—82no—
93C2×C4×D17—82no—
94C2×C8×C17—41no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17—21no—
97C4⋊C4×C17—21no—
98C4⋊C4×C17—21no—
99C4⋊C4×C17—42no—
100C4⋊C4×C17—41no—
101C4⋊C4×C17—41no—
102C22⋊C4×C17—41no—
103C42×C17—41no—
104C42×C17—41no—
105C42×C17—41no—
106C42×C17C22×C411yescharacteristic
107C42×C17C2×D411yescharacteristic
108C42×C17#4111yescharacteristic
109C42×C17#4111yescharacteristic
110#63227—22no—
111#63227—22no—
112#63227—44no—
113C4⋊Dic17—21no—
114C4⋊Dic17—41no—
115C4⋊Dic17—41no—
116C4⋊Dic17C22⋊C412yes—
117#63225—82no—
118#63223—41no—
119#63223—41no—
120C2×#3622—22no—
121C2×#3622—41no—
122#9175—171nomaximal, Sylow
123C23×C17#12011yescharacteristic
124C22×D17—22no—
125C22×D17—22no—
126C22×D17—22no—
127C22×D17—42no—
128C22×D17—42no—
129Q8×C17—81no—
130Q8×C17—81no—
131C2×C4×C17—22no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17C2×C22⋊C411yescharacteristic
142C2×C4×C17C4×D411yescharacteristic
143C2×C4×C17C4×D411yescharacteristic
144C2×C4×C17#12111yescharacteristic
145C2×C4×C17#12111yescharacteristic
146C2×C4×C17#12311yescharacteristic
147C2×C4×C17C2×SD1611yescharacteristic
148C2×C4×C17C2×Q1611yescharacteristic
149C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C17#13711yescharacteristic
151C2×Dic17—22no—
152C2×Dic17—42no—
153C2×Dic17—42no—
154C2×Dic17—42no—
155C2×Dic17—42no—
156D68—22no—
157D68—22no—
158D68—22no—
159D68#10314yes—
160C4×D17—82no—
161C4×D17—82no—
162C4×D17—88no—
163C8×C17—81no—
164#3622—42no—
165#3622—81no—
166#3077—171no—
167#2349—171no—
168#1518—171no—
169#1503D1711yescharacteristic, complemented
170#1478—171no—
171#1303—171no—
172#1286—171no—
173C22×C17—21no—
174C22×C17—21no—
175C22×C17#38611yescharacteristic
176C22×C17#45011yescharacteristic
177C22×C17#45111yescharacteristic
178C2×D17—24no—
179C2×D17—44no—
180C2×D17—44no—
181C2×D17—42no—
182C2×D17—42no—
183C4×C17—21no—
184C4×C17—21no—
185C4×C17—21no—
186C4×C17—21no—
187C4×C17—42no—
188C4×C17—81no—
189C4×C17—81no—
190C4×C17—81no—
191C4×C17C2×#10311yescharacteristic
192C4×C17#41711yescharacteristic
193C4×C17#48311yescharacteristic
194C4×C17#48411yescharacteristic
195Dic17—42no—
196Dic17—82no—
197#533C2×D1711yescharacteristic
198C2×C4×D4—171no—
199C2×C4×D4—341no—
200#478—342no—
201#476—172no—
202#474—172no—
203#431—171no—
204#431C2×D1711yescharacteristic
205#428—341no—
206#423—171no—
207#418—341no—
208#389—341no—
209#385—342no—
210#382—171no—
211#380—341no—
212C4×C4⋊C4C2×D1711yescharacteristic
213C2×#95—341no—
214#328—21no—
215#328—21no—
216#328—342no—
217D4⋊C8—342no—
218C2×C17—21no—
219C2×C17—21no—
220C2×C17#187211yescharacteristic
221C2×C17#190411yescharacteristic
222C2×C17#190611yescharacteristic
223D17—44no—
224C22×D4—171no—
225C23×C4—342no—
226C23×C4—341no—
227C2×M16—341no—
228C4⋊Q8C4×D1711yescharacteristic, complemented
229C4⋊Q8C4×D1711yescharacteristic, complemented
230#125—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—172no—
236C4×D4—172no—
237C4×D4—341no—
238C4×D4—341no—
239C4×D4—682no—
240C4×D4—682no—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—171no—
244C2×C4⋊C4—341no—
245C2×C4⋊C4—342no—
246C2×C22⋊C4—341no—
247C2×C22⋊C4—342no—
248C2×C42—21no—
249C2×C42C22×D1711yescharacteristic
250#107—342no—
251#106—342no—
252C4⋊C8—21no—
253C4⋊C8—172no—
254C4⋊C8—341no—
255C4⋊C8—341no—
256#102—342no—
257#102—342no—
258C22⋊C8—21no—
259C22⋊C8—341no—
260C4×C8—21no—
261C4×C8—341no—
262#95—172no—
263#95—342no—
264#95—341no—
265#95C22⋊D1711yescharacteristic
266#95C22⋊D1711yescharacteristic
267C17#917511yescharacteristic, complemented, Sylow
268C24—341no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×D4—172no—
272C2×D4—172no—
273C2×D4—172no—
274C2×D4—341no—
275C2×D4—341no—
276C2×D4—341no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—341no—
280C22×C4—342no—
281C22×C4—342no—
282C22×C4—342no—
283C22×C4—684no—
284C22×C4—684no—
285C22×C4—1362no—
286C22×C4—1362no—
287C22×C4D4×D1711yescharacteristic
288C22×C4D4×D1711yescharacteristic
289C22×C4C2×C22⋊D1711yescharacteristic
290M16—681no—
291M16—681no—
292C2×C8—41no—
293C2×C8—342no—
294C2×C8—681no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—172no—
303C4⋊C4—341no—
304C4⋊C4—681no—
305C4⋊C4—681no—
306C4⋊C4—1362no—
307C22⋊C4—41no—
308C22⋊C4—342no—
309C22⋊C4—342no—
310C22⋊C4—684no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42C2×C4×D1711yescharacteristic
315C42#6325211yescharacteristic
316C42D4×D1711yescharacteristic
317C42#6325411yescharacteristic
318C23—342no—
319C23—342no—
320C23—342no—
321C23—682no—
322C23—682no—
323C23#1058762311yescharacteristic
324Q8—81no—
325Q8—81no—
326D4—174no—
327D4—342no—
328D4—342no—
329D4—342no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—342no—
341C2×C4—682no—
342C2×C4—682no—
343C2×C4—682no—
344C2×C4—682no—
345C2×C4—1362no—
346C2×C4—1362no—
347C2×C4—1368no—
348C2×C4C22⋊C4×D1711yescharacteristic
349C2×C4#1058756711yescharacteristic
350C2×C4#1058756911yescharacteristic
351C2×C4#1058757011yescharacteristic
352C2×C4SD16×D1711yescharacteristic
353C2×C4#1058760011yescharacteristic
354C2×C4Q16×D1711yescharacteristic
355C2×C4#1058760411yescharacteristic
356C2×C4C4×C22⋊D1711yescharacteristic
357C2×C4#1058762411yescharacteristic
358C8—81no—
359C8—682no—
360C8—1361no—
361C22—21no—
362C22—21no—
363C22—344no—
364C22—684no—
365C22—684no—
366C22—682no—
367C22—682no—
368C22#1176268511yescharacteristic
369C22#1176295811yescharacteristic
370C22#1176296311yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—682no—
380C4—1362no—
381C4#103×D1711yescharacteristic
382C4#1176280911yescharacteristic
383C4#1176313811yescharacteristic
384C4#1176314311yescharacteristic
385C2—21no—
386C2—21no—
387C2—684no—
388C2#1452908811yescharacteristic
389C2#1452927411yescharacteristic
390C2#1452928811yescharacteristic
subgroupG/H
centerC22#11762685
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1503C2
socleC22×C17#386
prime radicalC22×D68D4
cosocleC2×C42×C17C23
hypercenter#1503D17
hypocenterC17#9175
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
3. #14527348C2semidirect
5. #14526687C2semidirect
6. #14526643C2semidirect
7. C17×#1503C2semidirect
11. #11763096C4semidirect
12. #11763086C4semidirect
32. C17×C4⋊Q8C2×C4semidirect
33. C17×C4⋊Q8C2×C4semidirect
70. C4⋊#3622C2×C4semidirect
169. #1503D17semidirect
228. C4⋊Q8C4×D17semidirect
229. C4⋊Q8C4×D17semidirect
267. C17#9175semidirect

Maximal subgroups

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

subgroupindex
#145385772
#145316952
#145273482
#145271742
#145266872
#145266432
C17×#15032
#917517