Finite Group Databasebeta

← #16930428

Subgroups — #16930428

Order 4352.

510 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538239C211yesmaximal, characteristic
2#14528804C211yesmaximal, characteristic, complemented
3#14527280C211yesmaximal, characteristic, complemented
4#14527236C211yesmaximal, characteristic, complemented
5#14526680C211yesmaximal, characteristic, complemented
6#14526624C211yesmaximal, characteristic, complemented
7C17×#2965C211yesmaximal, characteristic, complemented
8C2×#10587636—21no—
9#11763359C2211yescharacteristic
10#11763031—21no—
11#11763024—21no—
12#11763019C411yescharacteristic, complemented
13#11763014C411yescharacteristic, complemented
14#11763009C411yescharacteristic, complemented
15#11763004C411yescharacteristic, complemented
16#11762833C2211yescharacteristic
17C2×C4⋊#3622C2211yescharacteristic
18C2×#10587508—21no—
19#11762803—21no—
20C4×C4⋊Dic17C2211yescharacteristic
21#11762568—21no—
22#11762544—22no—
23#11762538—21no—
24#11762538—21no—
25C4×#41×C17C2211yescharacteristic
26C17×#446—21no—
27C17×#436—21no—
28C17×#435—22no—
29C17×#431—21no—
30C17×#431C2211yescharacteristic
31C4×M16×C17—21no—
32C2×C4×C8×C17C2211yescharacteristic
33C2×#41×C17D411yescharacteristic
34C2×#63252—21no—
35C2×M16×C17—22no—
36C22×C8×C17—21no—
37C4×Q8×C17C2×C411yescharacteristic
38C4×Q8×C17D411yescharacteristic
39C4×D4×C17—21no—
40C4×D4×C17—21no—
41C4×D4×C17C2×C411yescharacteristic
42C4×D4×C17D411yescharacteristic
43C17×#117—21no—
44C17×#117D411yescharacteristic
45C2×C42×C17—21no—
46C2×C42×C17C2311yescharacteristic
47#10587636—42no—
48#10587636—42no—
49C2×#63231—21no—
50C2×#63230—21no—
51C2×#63229—21no—
52C2×#63228—21no—
53#10587616—21no—
54#10587616—21no—
55C2×C4⋊Dic17—21no—
56C2×C4×Dic17—21no—
57C2×#63223—21no—
58C22×#3622—21no—
59#10587561—21no—
60#10587560C2×C411yescharacteristic
61C4×D68—21no—
62C4×D68—21no—
63#10587555C2×C411yescharacteristic
64C17×C4⋊C8—22no—
65C17×C4⋊C8—21no—
66C17×C22⋊C8—22no—
67C17×C22⋊C8D412yes—
68C17×#97—22no—
69C4×C8×C17—21no—
70C4×C8×C17—21no—
71C4×C8×C17D411yescharacteristic
72C4×C8×C17D411yescharacteristic
73#10587508—42no—
74#10587502—21no—
75#10587481—21no—
76#10587481—21no—
77#10587480—21no—
78#10587480—21no—
79C4⋊#3622—21no—
80C4⋊#3622—21no—
81C4⋊#3622—21no—
82C4⋊#3622C2×C411yescharacteristic
83C4⋊#3622C2×C411yescharacteristic
84#41×C17—21no—
85#41×C17—21no—
86#41×C17—21no—
87#41×C17—21no—
88C2×Q8×C17C22⋊C411yescharacteristic
89C2×D4×C17—21no—
90C2×D4×C17C22⋊C411yescharacteristic
91C22×C4×C17—21no—
92C22×C4×C17—21no—
93C22×C4×C17—21no—
94C22×C4×C17C2×D411yescharacteristic
95C22×C4×C17C2×D411yescharacteristic
96C22×C4×C17#4111yescharacteristic
97C2×C22⋊D17—41no—
98C22×Dic17—41no—
99#63252—41no—
100#63252—41no—
101#63252—41no—
102#63252—41no—
103C2×D68—21no—
104C2×D68—21no—
105C2×D68—21no—
106C2×C4×D17—41no—
107C2×Dic34—21no—
108M16×C17—44no—
109C2×C8×C17—21no—
110C2×C8×C17—21no—
111C2×C8×C17—22no—
112C2×C8×C17—42no—
113C4⋊C4×C17—21no—
114C4⋊C4×C17—21no—
115C4⋊C4×C17C22⋊C411yescharacteristic
116C4⋊C4×C17C22⋊C411yescharacteristic
117C22⋊C4×C17—21no—
118C22⋊C4×C17—21no—
119C22⋊C4×C17—21no—
120C42×C17—21no—
121C42×C17—21no—
122C42×C17—21no—
123C42×C17C22×C411yescharacteristic
124C42×C17C2×D411yescharacteristic
125C42×C17C2×D411yescharacteristic
126C42×C17#4111yescharacteristic
127#63231—42no—
128#63230—42no—
129#63229—42no—
130#63228—42no—
131#63227—41no—
132#63227—41no—
133C4⋊Dic17—22no—
134C4⋊Dic17—21no—
135C4⋊Dic17—21no—
136C4⋊Dic17—41no—
137C4×Dic17—41no—
138C4×Dic17—41no—
139#63223—41no—
140#63223—41no—
141C2×#3622—21no—
142C2×#3622—21no—
143C2×#3622—41no—
144C2×#3622—41no—
145C2×#3622—41no—
146#9210—171nomaximal, Sylow
147C23×C17—21no—
148C23×C17#12111yescharacteristic
149C22×D17—41no—
150Q8×C17—21no—
151Q8×C17—21no—
152D4×C17—21no—
153D4×C17—21no—
154D4×C17—41no—
155D4×C17—41no—
156C2×C4×C17—21no—
157C2×C4×C17—21no—
158C2×C4×C17—21no—
159C2×C4×C17—21no—
160C2×C4×C17—21no—
161C2×C4×C17—41no—
162C2×C4×C17—42no—
163C2×C4×C17—41no—
164C2×C4×C17—41no—
165C2×C4×C17—41no—
166C2×C4×C17—41no—
167C2×C4×C17C2×C22⋊C411yescharacteristic
168C2×C4×C17C4×D411yescharacteristic
169C2×C4×C17C4×D411yescharacteristic
170C2×C4×C17#12011yescharacteristic
171C2×C4×C17#12111yescharacteristic
172C2×C4×C17#12311yescharacteristic
173C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C17#13711yescharacteristic
177C22⋊D17—81no—
178C22⋊D17—81no—
179C2×Dic17—42no—
180C2×Dic17—41no—
181C2×Dic17—81no—
182C2×Dic17—81no—
183D68—41no—
184D68—41no—
185D68—41no—
186D68—41no—
187D68—81no—
188C4×D17—81no—
189C4×D17—81no—
190Dic34—41no—
191Dic34—41no—
192C8×C17—22no—
193C8×C17—41no—
194C8×C17—42no—
195#3622—41no—
196#3622—41no—
197#3622—81no—
198#3035—171no—
199#2965D1711yescharacteristic, complemented
200#1806—171no—
201#1502—171no—
202#1492—171no—
203#1301—171no—
204#1279—171no—
205C22×C17—21no—
206C22×C17—21no—
207C22×C17—41no—
208C22×C17—41no—
209C22×C17—41no—
210C22×C17#38611yescharacteristic
211C22×C17#46811yescharacteristic
212C22×C17#46911yescharacteristic
213C2×D17—81no—
214C2×D17—81no—
215C2×D17—81no—
216C4×C17—21no—
217C4×C17—21no—
218C4×C17—21no—
219C4×C17—41no—
220C4×C17—41no—
221C4×C17—41no—
222C4×C17#41711yescharacteristic
223C4×C17#41811yescharacteristic
224C4×C17#44311yescharacteristic
225C4×C17#44411yescharacteristic
226C4×C17#46811yescharacteristic
227C4×C17#46911yescharacteristic
228Dic17—82no—
229Dic17—81no—
230C2×#135—341no—
231#532—171no—
232C4×#41C2×D1711yescharacteristic
233#464—341no—
234#463—341no—
235#462—171no—
236#461—171no—
237#460—171no—
238#459—171no—
239#446—21no—
240#436—21no—
241#435—22no—
242#431—21no—
243#431C2×D1711yescharacteristic
244#423—171no—
245C2×C4⋊C8—171no—
246C2×#104—341no—
247#416—341no—
248C4×M16—21no—
249C2×C4×C8C2×D1711yescharacteristic
250C4×C4⋊C4—171no—
251#339—341no—
252#327—342no—
253D4⋊C8—341no—
254D4⋊C8—341no—
255C2×C17—21no—
256C2×C17—21no—
257C2×C17—81no—
258C2×C17#187611yescharacteristic
259C2×C17#189511yescharacteristic
260C2×C17#190611yescharacteristic
261D17—161no—
262C2×#41—341no—
263C2×#41D6811yescharacteristic
264#135—682no—
265#135—682no—
266C2×Q16—341no—
267C2×SD16—341no—
268C2×SD16—341no—
269C2×D8—341no—
270C2×M16—22no—
271C2×M16—341no—
272C22×C8—21no—
273C22×C8—341no—
274C4⋊Q8—171no—
275#127—171no—
276#124—341no—
277#121—341no—
278#121—341no—
279C4×Q8C4×D1711yescharacteristic
280C4×Q8C22⋊D1711yescharacteristic
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—341no—
284C4×D4—341no—
285C4×D4C4×D1711yescharacteristic
286C4×D4C22⋊D1711yescharacteristic
287#117—21no—
288#117D6811yescharacteristic
289C2×C4⋊C4—341no—
290C2×C42—21no—
291C2×C42—341no—
292C2×C42C22×D1711yescharacteristic
293C4⋊C8—22no—
294C4⋊C8—21no—
295C4⋊C8—171no—
296C4⋊C8—171no—
297C4⋊C8—341no—
298C4⋊C8—341no—
299C4⋊C8—341no—
300#104—682no—
301#103—341no—
302#103—341no—
303#102—341no—
304#102—341no—
305C22⋊C8—22no—
306C22⋊C8C22⋊D1712yes—
307#97—22no—
308C4×C8—21no—
309C4×C8—21no—
310C4×C8C22⋊D1711yescharacteristic
311C4×C8C22⋊D1711yescharacteristic
312#95—341no—
313C17#921011yescharacteristic, complemented, Sylow
314#41—21no—
315#41—21no—
316#41—21no—
317#41—21no—
318#41—681no—
319#41—681no—
320#41—681no—
321#41—681no—
322C2×Q8—341no—
323C2×Q8#6322711yescharacteristic
324C2×D4—21no—
325C2×D4—341no—
326C2×D4—341no—
327C2×D4—341no—
328C2×D4—681no—
329C2×D4#6322711yescharacteristic
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—681no—
334C22×C4—681no—
335C22×C4C2×D6811yescharacteristic
336C22×C4#6325211yescharacteristic
337C22×C4C2×C22⋊D1711yescharacteristic
338Q16—682no—
339SD16—682no—
340SD16—682no—
341D8—682no—
342M16—44no—
343M16—681no—
344M16—681no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—42no—
349C2×C8—341no—
350C2×C8—341no—
351C2×C8—681no—
352C2×C8—681no—
353C2×C8—681no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—342no—
357C4⋊C4—341no—
358C4⋊C4—341no—
359C4⋊C4—681no—
360C4⋊C4#6322711yescharacteristic
361C4⋊C4#6322711yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—681no—
366C22⋊C4—681no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42—681no—
371C42—681no—
372C42C2×C4×D1711yescharacteristic
373C42#6325211yescharacteristic
374C42C2×C22⋊D1711yescharacteristic
375C42C2×C22⋊D1711yescharacteristic
376C23—21no—
377C23—681no—
378C23#1058761611yescharacteristic
379Q8—21no—
380Q8—21no—
381Q8—681no—
382Q8—681no—
383D4—21no—
384D4—21no—
385D4—41no—
386D4—41no—
387D4—681no—
388D4—681no—
389D4—681no—
390D4—681no—
391D4—1361no—
392D4—1361no—
393D4—1361no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—682no—
406C2×C4—681no—
407C2×C4—1361no—
408C2×C4—1361no—
409C2×C4—1361no—
410C2×C4—1361no—
411C2×C4#1058759411yescharacteristic
412C2×C4#1058759411yescharacteristic
413C2×C4#1058759411yescharacteristic
414C2×C4#1058759511yescharacteristic
415C2×C4C2×#6322711yescharacteristic
416C2×C4C4×C22⋊D1711yescharacteristic
417C2×C4C4×C22⋊D1711yescharacteristic
418C2×C4#1058761511yescharacteristic
419C2×C4#1058761611yescharacteristic
420C2×C4#1058763911yescharacteristic
421C8—22no—
422C8—41no—
423C8—42no—
424C8—681no—
425C8—681no—
426C8—1361no—
427C22—21no—
428C22—21no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—1361no—
433C22—1361no—
434C22—1361no—
435C22#1176268811yescharacteristic
436C22#1176305511yescharacteristic
437C22#1176306211yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—41no—
443C4—41no—
444C4—1362no—
445C4—1361no—
446C4#1176281111yescharacteristic
447C4#1176281511yescharacteristic
448C4#1176292411yescharacteristic
449C4#1176292911yescharacteristic
450C4#1176305511yescharacteristic
451C4#1176306211yescharacteristic
452C2—21no—
453C2—21no—
454C2—81no—
455C2—2721no—
456C2#1452911111yescharacteristic
457C2#1452922211yescharacteristic
458C2#1452928511yescharacteristic
subgroupG/H
centerC2×C4#10587616
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2965C2
socleC22×C17#386
prime radical#14538239C2
cosocleC2×C42×C17C23
hypercenter#2965D17
hypocenterC17#9210
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #14528804C2semidirect
3. #14527280C2semidirect
4. #14527236C2semidirect
5. #14526680C2semidirect
6. #14526624C2semidirect
7. C17×#2965C2semidirect
12. #11763019C4semidirect
13. #11763014C4semidirect
14. #11763009C4semidirect
15. #11763004C4semidirect
199. #2965D17semidirect
313. C17#9210semidirect

Maximal subgroups

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

subgroupindex
#145382392
#145288042
#145272802
#145272362
#145266802
#145266242
C17×#29652
#921017