Finite Group Databasebeta

← #16937769

Subgroups — #16937769

Order 4352.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14533733C211yesmaximal, characteristic
2#14529745C211yesmaximal, characteristic, complemented
3#14529547C211yesmaximal, characteristic, complemented
4#14528785C211yesmaximal, characteristic
5C2×#11762554C211yesmaximal, characteristic, complemented
6C2×#11762538C211yesmaximal, characteristic
7C17×#1279C211yesmaximal, characteristic, complemented
8C2×#10587555C2211yescharacteristic
9C2×#10587583—21no—
10C2×#10587583—21no—
11C2×C4×D68C2211yescharacteristic
12C2×#10587479—21no—
13C2×C4⋊#3622C2211yescharacteristic
14C2×#10587492—21no—
15#11762746—22no—
16#11762711—21no—
17#11762679—21no—
18#11762679C2211yescharacteristic
19#11762572—21no—
20#11762572—22no—
21#11762571—21no—
22#11762554—22no—
23#11762538—22no—
24C2×C17×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C17C2211yescharacteristic
26C4×C4⋊C4×C17C2211yescharacteristic
27C22×D68D411yescharacteristic
28C22×C4×D17—21no—
29C22×Dic34—21no—
30C22×C8×C17—21no—
31C22×C8×C17—21no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C42×C17—21no—
35C2×C42×C17C2311yescharacteristic
36C2×#63227—22no—
37C2×#63227—22no—
38C2×#63227—21no—
39C2×C4⋊Dic17—22no—
40C2×C4⋊Dic17—22no—
41C2×C4⋊Dic17—21no—
42C2×C4⋊Dic17—21no—
43C2×C4⋊Dic17—21no—
44C2×C4⋊Dic17—21no—
45C2×C4⋊Dic17D412yes—
46C2×C4⋊Dic17D411yescharacteristic
47C22×#3622—21no—
48#10587583—42no—
49#10587583—42no—
50#10587583—42no—
51#10587583—42no—
52C4×D68—21no—
53C4×D68—21no—
54C4×D68—21no—
55C4×D68—21no—
56#10587555—21no—
57#10587555—21no—
58#10587555—21no—
59#10587555—21no—
60C17×C4⋊C8—21no—
61C17×C4⋊C8—21no—
62C4×C8×C17—21no—
63C4×C8×C17—21no—
64C17×#95—21no—
65#10587492—42no—
66#10587479—42no—
67C4⋊#3622—21no—
68C4⋊#3622D412yes—
69C23×D17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17C2×D411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×Dic17—22no—
76C22×Dic17—21no—
77C22×Dic17—41no—
78C2×D68—21no—
79C2×D68—21no—
80C2×D68—21no—
81C2×D68—21no—
82C2×D68—21no—
83C2×D68SD1612yes—
84C2×C4×D17—41no—
85C2×C4×D17—41no—
86C2×C4×D17—41no—
87C2×C4×D17—41no—
88C2×C4×D17—41no—
89C2×C4×D17—41no—
90C2×Dic34—41no—
91C2×Dic34—41no—
92C2×Dic34—41no—
93C2×Dic34—41no—
94C2×Dic34—41no—
95C2×Dic34—41no—
96C2×C8×C17—22no—
97C2×C8×C17—41no—
98C2×C8×C17—41no—
99C2×C8×C17—41no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17D812yes—
105C4⋊C4×C17SD1612yes—
106C42×C17—41no—
107C42×C17—41no—
108C42×C17C2×D411yescharacteristic
109C42×C17#4111yescharacteristic
110C42×C17#4111yescharacteristic
111C42×C17#4111yescharacteristic
112#63227—44no—
113#63227—44no—
114#63227—41no—
115#63227—41no—
116C4⋊Dic17—22no—
117C4⋊Dic17—21no—
118C4⋊Dic17—22no—
119C4⋊Dic17—21no—
120C4⋊Dic17—44no—
121C4⋊Dic17—44no—
122C4⋊Dic17—41no—
123C4⋊Dic17—41no—
124C4⋊Dic17—42no—
125C4⋊Dic17—41no—
126C4⋊Dic17—41no—
127C4⋊Dic17—41no—
128C4⋊Dic17—41no—
129C2×#3622—22no—
130C2×#3622—41no—
131C2×#3622—41no—
132#10420—171nomaximal, Sylow
133C23×C17#12011yescharacteristic
134C22×D17—22no—
135C22×D17—41no—
136C22×D17—41no—
137C22×D17—41no—
138C22×D17—41no—
139C22×D17—41no—
140C22×D17—41no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—22no—
144C2×C4×C17—22no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17#12111yescharacteristic
150C2×C4×C17#12111yescharacteristic
151C2×C4×C17#12111yescharacteristic
152C2×C4×C17#12311yescharacteristic
153C2×C4×C17#12311yescharacteristic
154C2×C4×C17#12411yescharacteristic
155C2×C4×C17C2×D811yescharacteristic
156C2×C4×C17C2×SD1611yescharacteristic
157C2×C4×C17C2×SD1611yescharacteristic
158C2×C4×C17#13511yescharacteristic
159C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C17#13711yescharacteristic
162C2×C4×C17#13711yescharacteristic
163C2×Dic17—42no—
164C2×Dic17—41no—
165C2×Dic17—42no—
166C2×Dic17—41no—
167C2×Dic17—42no—
168C2×Dic17—41no—
169C2×Dic17—81no—
170C2×Dic17—81no—
171C2×Dic17—81no—
172D68—22no—
173D68—22no—
174D68—41no—
175D68—41no—
176C4×D17—81no—
177C4×D17—81no—
178C4×D17—81no—
179C4×D17—81no—
180Dic34—81no—
181Dic34—81no—
182Dic34—81no—
183Dic34—81no—
184C8×C17—42no—
185C8×C17—81no—
186#3622—42no—
187#2542—171no—
188#1990—171no—
189#1948—171no—
190#1802—171no—
191C2×#332—171no—
192C2×D4⋊C8—171no—
193#1279D1711yescharacteristic, complemented
194C22×C17#39411yescharacteristic
195C22×C17#44711yescharacteristic
196C22×C17#44811yescharacteristic
197C22×C17#45011yescharacteristic
198C22×C17#45211yescharacteristic
199C22×C17#45411yescharacteristic
200C22×C17#45611yescharacteristic
201C2×D17—42no—
202C2×D17—42no—
203C2×D17—42no—
204C2×D17—81no—
205C2×D17—81no—
206C2×D17—81no—
207C2×D17—81no—
208C4×C17—21no—
209C4×C17—21no—
210C4×C17—42no—
211C4×C17—42no—
212C4×C17#45911yescharacteristic
213C4×C17#46011yescharacteristic
214C4×C17#46511yescharacteristic
215C4×C17#47011yescharacteristic
216C4×C17#48311yescharacteristic
217C4×C17#48511yescharacteristic
218C4×C17#48611yescharacteristic
219C4×C17#49011yescharacteristic
220Dic17—82no—
221Dic17—81no—
222Dic17—161no—
223C2×C4⋊Q8—171no—
224C2×C22⋊Q8—341no—
225C2×C22⋊Q8—341no—
226C2×C4×D4—171no—
227C2×#106—341no—
228C2×C4⋊C8—171no—
229C2×C4⋊C8C2×D1711yescharacteristic
230C2×#102—341no—
231C2×C4×C8C2×D1711yescharacteristic
232#399—342no—
233#390—341no—
234#384—171no—
235#384—341no—
236C4×C4⋊C4C2×D1711yescharacteristic
237#340—341no—
238#340—342no—
239#340—341no—
240#332—342no—
241D4⋊C8—342no—
242C2×C17#162711yescharacteristic
243C2×C17#163511yescharacteristic
244C2×C17#164711yescharacteristic
245C2×C17#165111yescharacteristic
246C2×C17#203511yescharacteristic
247C2×C17#203811yescharacteristic
248C2×C17#204111yescharacteristic
249D17—82no—
250C22×Q8—341no—
251C22×D4—171no—
252C23×C4—341no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—341no—
256C4⋊Q8—341no—
257C4⋊Q8—341no—
258C4⋊Q8—341no—
259C4⋊Q8—341no—
260C22⋊Q8—682no—
261C22⋊Q8—682no—
262C22⋊Q8—682no—
263C22⋊Q8—682no—
264C4×D4—341no—
265C4×D4—341no—
266C4×D4—341no—
267C4×D4—341no—
268C2×C4⋊C4—171no—
269C2×C4⋊C4—172no—
270C2×C4⋊C4—342no—
271C2×C4⋊C4—342no—
272C2×C4⋊C4—341no—
273C2×C4⋊C4—341no—
274C2×C4⋊C4—341no—
275C2×C4⋊C4—341no—
276C2×C4⋊C4D6811yescharacteristic
277C2×C4⋊C4D6811yescharacteristic
278C2×C22⋊C4—342no—
279C2×C22⋊C4—342no—
280C2×C22⋊C4—341no—
281C2×C42—21no—
282C2×C42C22×D1711yescharacteristic
283#106—682no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8—172no—
287C4⋊C8—341no—
288#102—682no—
289C4×C8—21no—
290C4×C8—21no—
291#95—21no—
292C17#1042011yescharacteristic, complemented, Sylow
293C24—341no—
294C2×Q8—681no—
295C2×Q8—681no—
296C2×Q8—681no—
297C2×Q8—681no—
298C2×Q8—681no—
299C2×Q8—681no—
300C2×D4—172no—
301C2×D4—341no—
302C2×D4—341no—
303C2×D4—341no—
304C2×D4—341no—
305C2×D4—341no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—342no—
309C22×C4—341no—
310C22×C4—681no—
311C22×C4—681no—
312C22×C4—681no—
313C22×C4—681no—
314C22×C4—681no—
315C22×C4—681no—
316C22×C4—681no—
317C22×C4C2×D6811yescharacteristic
318C22×C4D4×D1711yescharacteristic
319C22×C4D4×D1711yescharacteristic
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—342no—
327C2×C8—681no—
328C2×C8—681no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—341no—
332C4⋊C4—342no—
333C4⋊C4—341no—
334C4⋊C4—342no—
335C4⋊C4—684no—
336C4⋊C4—684no—
337C4⋊C4—682no—
338C4⋊C4—681no—
339C4⋊C4—681no—
340C4⋊C4—681no—
341C4⋊C4—681no—
342C4⋊C4—681no—
343C4⋊C4—681no—
344C4⋊C4#6321912yes—
345C4⋊C4D13612yes—
346C22⋊C4—684no—
347C22⋊C4—684no—
348C22⋊C4—681no—
349C22⋊C4—681no—
350C42—41no—
351C42—41no—
352C42#6325211yescharacteristic
353C42#6325211yescharacteristic
354C42D4×D1711yescharacteristic
355C42#6325611yescharacteristic
356C23—342no—
357C23—681no—
358C23—681no—
359C23—681no—
360C23—681no—
361C23—681no—
362C23—681no—
363C23#1058756811yescharacteristic
364Q8—1361no—
365Q8—1361no—
366Q8—1361no—
367Q8—1361no—
368D4—342no—
369D4—342no—
370D4—681no—
371D4—681no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—682no—
381C2×C4—681no—
382C2×C4—682no—
383C2×C4—681no—
384C2×C4—681no—
385C2×C4—682no—
386C2×C4—1361no—
387C2×C4—1361no—
388C2×C4—1361no—
389C2×C4—1361no—
390C2×C4—1361no—
391C2×C4—1361no—
392C2×C4—1361no—
393C2×C4#1058756111yescharacteristic
394C2×C4#1058757011yescharacteristic
395C2×C4#1058757011yescharacteristic
396C2×C4#1058758011yescharacteristic
397C2×C4#1058758011yescharacteristic
398C2×C4#1058758111yescharacteristic
399C2×C4C2×#6321911yescharacteristic
400C2×C4C2×D13611yescharacteristic
401C2×C4#1058759411yescharacteristic
402C2×C4#1058759411yescharacteristic
403C2×C4#1058759811yescharacteristic
404C2×C4SD16×D1711yescharacteristic
405C2×C4#1058760111yescharacteristic
406C2×C4#1058760411yescharacteristic
407C8—42no—
408C8—81no—
409C8—682no—
410C22—682no—
411C22—682no—
412C22—682no—
413C22—1361no—
414C22—1361no—
415C22—1361no—
416C22—1361no—
417C22#1176272711yescharacteristic
418C22#1176294511yescharacteristic
419C22#1176294911yescharacteristic
420C22#1176296211yescharacteristic
421C22#1176297211yescharacteristic
422C22#1176298311yescharacteristic
423C22#1176299311yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—2721no—
429C4—1361no—
430C4—1362no—
431C4#1176300511yescharacteristic
432C4#1176301011yescharacteristic
433C4#1176303711yescharacteristic
434C4#1176306611yescharacteristic
435C4#1176314111yescharacteristic
436C4#1176315211yescharacteristic
437C4#1176315611yescharacteristic
438C4#1176317411yescharacteristic
439C2—1362no—
440C2#1452788911yescharacteristic
441C2#1452793711yescharacteristic
442C2#1452802111yescharacteristic
443C2#1452805011yescharacteristic
444C2#1452998311yescharacteristic
445C2#1453000411yescharacteristic
446C2#1453001911yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1279C2
socleC23×C17#120
prime radicalC22×D68D4
hypercenter#1279D17
hypocenterC17#10420
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #14529745C2semidirect
3. #14529547C2semidirect
5. C2×#11762554C2semidirect
7. C17×#1279C2semidirect
193. #1279D17semidirect
292. C17#10420semidirect

Maximal subgroups

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

subgroupindex
#145337332
#145297452
#145295472
#145287852
C2×#117625542
C2×#117625382
C17×#12792
#1042017