Finite Group Databasebeta

← #16930416

Subgroups — #16930416

Order 4352.

532 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#41×#3622C211yesmaximal, characteristic, complemented
2#14528804C211yesmaximal, characteristic, complemented
3#14527279C211yesmaximal, characteristic, complemented
4#14527235C211yesmaximal, characteristic, complemented
5#14526681C211yesmaximal, characteristic, complemented
6#14526623C211yesmaximal, characteristic, complemented
7C17×#3035C211yesmaximal, characteristic
8Q8×#3622—21no—
9D4×#3622—21no—
10D4×#3622—22no—
11#11762862—21no—
12#11762862C2211yescharacteristic
13#11762833C2211yescharacteristic
14C2×#10587508—21no—
15C2×C4×#3622—21no—
16C2×C4×#3622C2211yescharacteristic
17C4×C4⋊Dic17C2211yescharacteristic
18#11762568—21no—
19#11762543—22no—
20D4⋊#3622—21no—
21D4⋊#3622—21no—
22C2×C17×#135—21no—
23C17×#532C2211yescharacteristic
24C4×#41×C17C2211yescharacteristic
25C17×#464—21no—
26C17×#463—21no—
27C17×#462C411yescharacteristic, complemented
28C17×#461C411yescharacteristic, complemented
29C17×#460C411yescharacteristic, complemented
30C17×#459C411yescharacteristic, complemented
31C2×C17×C4⋊C8C2211yescharacteristic
32C17×#416—21no—
33C2×#41×C17—21no—
34C2×#41×C17D411yescharacteristic
35C17×#135—42no—
36C17×#135—42no—
37C2×Q16×C17—21no—
38C2×SD16×C17—21no—
39C2×SD16×C17—21no—
40C2×D8×C17—21no—
41C22×C8×C17—21no—
42C17×C4⋊Q8C2×C411yescharacteristic
43C17×#127C2×C411yescharacteristic
44C17×#124—21no—
45C17×#121—21no—
46C17×#121—21no—
47C4×Q8×C17C2×C411yescharacteristic
48C4×Q8×C17D411yescharacteristic
49C4×D4×C17—21no—
50C4×D4×C17—21no—
51C4×D4×C17—21no—
52C4×D4×C17—21no—
53C4×D4×C17C2×C411yescharacteristic
54C4×D4×C17D411yescharacteristic
55C17×#117—21no—
56C17×#117D411yescharacteristic
57C2×C42×C17—21no—
58C2×C42×C17C2311yescharacteristic
59C2×C4⋊Dic17—21no—
60C2×C4×Dic17—21no—
61C2×#63223—21no—
62C22×#3622—22no—
63C22×#3622—21no—
64C17×C4⋊C8—21no—
65C17×C4⋊C8C2×C411yescharacteristic
66C17×C4⋊C8C2×C411yescharacteristic
67C17×#103—21no—
68C17×#103—21no—
69C17×#102—21no—
70C17×#102—21no—
71#10587508—42no—
72#10587502—21no—
73C22⋊#3622—22no—
74C22⋊#3622D412yes—
75C4⋊#3622—22no—
76C4⋊#3622—21no—
77C4⋊#3622—21no—
78C4⋊#3622—21no—
79C4×#3622—22no—
80C4×#3622—21no—
81C4×#3622—21no—
82C4×#3622D411yescharacteristic
83C4×#3622D411yescharacteristic
84#41×C17—21no—
85#41×C17—21no—
86#41×C17—41no—
87#41×C17—41no—
88#41×C17—41no—
89#41×C17—41no—
90#41×C17D812yes—
91#41×C17SD1612yes—
92C2×Q8×C17—21no—
93C2×Q8×C17C22⋊C411yescharacteristic
94C2×D4×C17—21no—
95C2×D4×C17—21no—
96C2×D4×C17—21no—
97C2×D4×C17—21no—
98C2×D4×C17—41no—
99C2×D4×C17C22⋊C411yescharacteristic
100C22×C4×C17—21no—
101C22×C4×C17—21no—
102C22×C4×C17—21no—
103C22×C4×C17—41no—
104C22×C4×C17C2×D411yescharacteristic
105C22×C4×C17C2×D411yescharacteristic
106C22×C4×C17#4111yescharacteristic
107C22×Dic17—41no—
108Q16×C17—42no—
109SD16×C17—42no—
110SD16×C17—42no—
111D8×C17—42no—
112C2×C8×C17—21no—
113C2×C8×C17—21no—
114C2×C8×C17—41no—
115C2×C8×C17—41no—
116C4⋊C4×C17—21no—
117C4⋊C4×C17—21no—
118C4⋊C4×C17—21no—
119C4⋊C4×C17—21no—
120C4⋊C4×C17C22⋊C411yescharacteristic
121C4⋊C4×C17C22⋊C411yescharacteristic
122C22⋊C4×C17—21no—
123C22⋊C4×C17—21no—
124C22⋊C4×C17—21no—
125C22⋊C4×C17—41no—
126C22⋊C4×C17—41no—
127C42×C17—21no—
128C42×C17—21no—
129C42×C17—21no—
130C42×C17C22×C411yescharacteristic
131C42×C17C2×D411yescharacteristic
132C42×C17C2×D411yescharacteristic
133C42×C17#4111yescharacteristic
134C4⋊Dic17—22no—
135C4⋊Dic17—41no—
136C4×Dic17—41no—
137C4×Dic17—41no—
138#63223—41no—
139#63223—41no—
140C2×#3622—21no—
141C2×#3622—22no—
142C2×#3622—21no—
143C2×#3622—42no—
144C2×#3622—44no—
145C2×#3622—41no—
146#9208—171nomaximal, Sylow
147C23×C17—21no—
148C23×C17—41no—
149C23×C17#12111yescharacteristic
150Q8×C17—21no—
151Q8×C17—41no—
152Q8×C17—41no—
153Q8×C17#10212yes—
154D4×C17—22no—
155D4×C17—22no—
156D4×C17—21no—
157D4×C17—41no—
158D4×C17—41no—
159D4×C17—41no—
160D4×C17—41no—
161D4×C17—81no—
162D4×C17—81no—
163D4×C17—81no—
164D4×C17#10212yes—
165C2×C4×C17—21no—
166C2×C4×C17—21no—
167C2×C4×C17—21no—
168C2×C4×C17—22no—
169C2×C4×C17—22no—
170C2×C4×C17—21no—
171C2×C4×C17—21no—
172C2×C4×C17—41no—
173C2×C4×C17—42no—
174C2×C4×C17—41no—
175C2×C4×C17—41no—
176C2×C4×C17—41no—
177C2×C4×C17—81no—
178C2×C4×C17—81no—
179C2×C4×C17C2×C22⋊C411yescharacteristic
180C2×C4×C17C4×D411yescharacteristic
181C2×C4×C17C4×D411yescharacteristic
182C2×C4×C17#12011yescharacteristic
183C2×C4×C17#12111yescharacteristic
184C2×C4×C17#12311yescharacteristic
185C2×C4×C17C2×D811yescharacteristic
186C2×C4×C17C2×SD1611yescharacteristic
187C2×C4×C17#13511yescharacteristic
188C2×C4×C17#13511yescharacteristic
189C2×Dic17—42no—
190C2×Dic17—81no—
191C2×Dic17—81no—
192C8×C17—41no—
193C8×C17—41no—
194#3622—22no—
195#3622—42no—
196#3622—41no—
197#3622—81no—
198#3035D1711yescharacteristic
199C8×#41—171no—
200#1806—171no—
201#1502—171no—
202#1492—171no—
203#1301—171no—
204#1279—171no—
205C22×C17—21no—
206C22×C17—21no—
207C22×C17—22no—
208C22×C17—41no—
209C22×C17—41no—
210C22×C17—81no—
211C22×C17—81no—
212C22×C17—81no—
213C22×C17#38611yescharacteristic
214C22×C17#46511yescharacteristic
215C22×C17#46611yescharacteristic
216C4×C17—21no—
217C4×C17—22no—
218C4×C17—21no—
219C4×C17—21no—
220C4×C17—41no—
221C4×C17—41no—
222C4×C17—81no—
223C4×C17C2×#10211yescharacteristic
224C4×C17#41611yescharacteristic
225C4×C17#44311yescharacteristic
226C4×C17#44411yescharacteristic
227C4×C17#46511yescharacteristic
228C4×C17#46611yescharacteristic
229Dic17—82no—
230C2×#135—21no—
231#532C2×D1711yescharacteristic
232C4×#41C2×D1711yescharacteristic
233#464—21no—
234#463—21no—
235#462Dic1711yescharacteristic, complemented
236#461Dic1711yescharacteristic, complemented
237#460Dic1711yescharacteristic, complemented
238#459Dic1711yescharacteristic, complemented
239C8×Q8—341no—
240C8×D4—342no—
241C8×D4—341no—
242#431—171no—
243#431—341no—
244#423—171no—
245C2×C4⋊C8C2×D1711yescharacteristic
246C2×#104—341no—
247#416—21no—
248C2×C4×C8—171no—
249C2×C4×C8—341no—
250C4×C4⋊C4—171no—
251#339—341no—
252#327—342no—
253D4⋊C8—341no—
254D4⋊C8—341no—
255C2×C17—21no—
256C2×C17—21no—
257C2×C17—42no—
258C2×C17—161no—
259C2×C17#187611yescharacteristic
260C2×C17#189311yescharacteristic
261C2×C17#190611yescharacteristic
262C2×#41—21no—
263C2×#41C22⋊D1711yescharacteristic
264#135—42no—
265#135—42no—
266C2×Q16—21no—
267C2×SD16—21no—
268C2×SD16—21no—
269C2×D8—21no—
270C2×M16—341no—
271C22×C8—21no—
272C22×C8—342no—
273C22×C8—341no—
274C4⋊Q8C2×Dic1711yescharacteristic
275#127C2×Dic1711yescharacteristic
276#124—21no—
277#121—21no—
278#121—21no—
279C4×Q8C2×Dic1711yescharacteristic
280C4×Q8C22⋊D1711yescharacteristic
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4C2×Dic1711yescharacteristic
286C4×D4C22⋊D1711yescharacteristic
287#117—21no—
288#117C22⋊D1711yescharacteristic
289C2×C4⋊C4—341no—
290C2×C42—21no—
291C2×C42—341no—
292C2×C42C22×D1711yescharacteristic
293C4⋊C8—21no—
294C4⋊C8—342no—
295C4⋊C8—341no—
296C4⋊C8—341no—
297C4⋊C8—341no—
298C4⋊C8C2×Dic1711yescharacteristic
299C4⋊C8C2×Dic1711yescharacteristic
300#104—682no—
301#103—21no—
302#103—21no—
303#102—21no—
304#102—21no—
305C22⋊C8—172no—
306C22⋊C8—342no—
307C4×C8—171no—
308C4×C8—171no—
309C4×C8—342no—
310C4×C8—341no—
311C4×C8—341no—
312#95—341no—
313C17#920811yescharacteristic, complemented, Sylow
314#41—21no—
315#41—21no—
316#41—41no—
317#41—41no—
318#41—41no—
319#41—41no—
320#41#6322812yes—
321#41#6322912yes—
322C2×Q8—21no—
323C2×Q8C22⋊Dic1711yescharacteristic
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4C22⋊Dic1711yescharacteristic
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—41no—
334C22×C4—681no—
335C22×C4D4×D1711yescharacteristic
336C22×C4#6325411yescharacteristic
337C22×C4C2×C22⋊D1711yescharacteristic
338Q16—42no—
339SD16—42no—
340SD16—42no—
341D8—42no—
342M16—681no—
343M16—681no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—341no—
349C2×C8—341no—
350C2×C8—342no—
351C2×C8—682no—
352C2×C8—684no—
353C2×C8—681no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—342no—
359C4⋊C4—681no—
360C4⋊C4C22⋊Dic1711yescharacteristic
361C4⋊C4C22⋊Dic1711yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42—681no—
371C42—681no—
372C42D4×D1711yescharacteristic
373C42#6325411yescharacteristic
374C42C22×Dic1711yescharacteristic
375C42C2×C22⋊D1711yescharacteristic
376C23—21no—
377C23—41no—
378C23#1058762511yescharacteristic
379Q8—21no—
380Q8—41no—
381Q8—41no—
382Q8#1058750312yes—
383D4—22no—
384D4—22no—
385D4—21no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—81no—
391D4—81no—
392D4—81no—
393D4#1058750312yes—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—682no—
409C2×C4—1361no—
410C2×C4—1361no—
411C2×C4C2×#6322811yescharacteristic
412C2×C4C2×#6322911yescharacteristic
413C2×C4D4×Dic1711yescharacteristic
414C2×C4D4×Dic1711yescharacteristic
415C2×C4#1058762111yescharacteristic
416C2×C4#1058762311yescharacteristic
417C2×C4#1058762511yescharacteristic
418C2×C4#1058763611yescharacteristic
419C2×C4#1058763611yescharacteristic
420C2×C4C2×C22⋊Dic1711yescharacteristic
421C8—41no—
422C8—41no—
423C8—342no—
424C8—681no—
425C8—682no—
426C8—1361no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22#1176268911yescharacteristic
436C22#1176303611yescharacteristic
437C22#1176304311yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—81no—
445C4—1362no—
446C4C2×#1058750311yescharacteristic
447C4#1176280511yescharacteristic
448C4#1176292611yescharacteristic
449C4#1176293111yescharacteristic
450C4#1176303611yescharacteristic
451C4#1176304311yescharacteristic
452C2—21no—
453C2—21no—
454C2—42no—
455C2—161no—
456C2#1452911311yescharacteristic
457C2#1452921311yescharacteristic
458C2#1452928711yescharacteristic
subgroupG/H
centerC2×C4#10587625
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
Fitting, prime radicalC17×#3035C2
socleC22×C17#386
cosocleC2×C42×C17C23
hypercenter#3035D17
hypocenterC17#9208
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #41×#3622C2semidirect
2. #14528804C2semidirect
3. #14527279C2semidirect
4. #14527235C2semidirect
5. #14526681C2semidirect
6. #14526623C2semidirect
27. C17×#462C4semidirect
28. C17×#461C4semidirect
29. C17×#460C4semidirect
30. C17×#459C4semidirect
235. #462Dic17semidirect
236. #461Dic17semidirect
237. #460Dic17semidirect
238. #459Dic17semidirect
313. C17#9208semidirect

Maximal subgroups

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

subgroupindex
#41×#36222
#145288042
#145272792
#145272352
#145266812
#145266232
C17×#30352
#920817