Finite Group Databasebeta

← #16927708

Subgroups — #16927708

Order 4352.

868 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531167C211yesmaximal, characteristic
2#14528694C211yesmaximal, characteristic
3#14526663C212yesmaximal, complemented
4#14526663C212yesmaximal, complemented
5C17×C22⋊#95C211yesmaximal, characteristic
6C2×#10587612C411yescharacteristic, complemented
7C2×#10587612C411yescharacteristic, complemented
8C2×C22⋊#3622—21no—
9C2×C22⋊#3622—21no—
10C2×C22⋊#3622C2212yes—
11#11762672—21no—
12#11762669C411yescharacteristic, complemented
13#11762669C411yescharacteristic, complemented
14#11762669C2211yescharacteristic
15#11762669C2211yescharacteristic
16#11762665—21no—
17C4×C22⋊Dic17—21no—
18C4×C22⋊Dic17—21no—
19C24×C4×C17C2211yescharacteristic
20C22×C22⋊C4×C17—21no—
21C2×C17×#95—21no—
22C2×C17×#95C2212yes—
23C25×C17D411yescharacteristic
24C23×C4×C17—24no—
25C23×C4×C17—22no—
26C23×C4×C17—42no—
27C23×C4×C17—42no—
28C23×C4×C17C2×C411yescharacteristic
29C23×C4×C17C2×C411yescharacteristic
30C23×C4×C17D411yescharacteristic
31C23×C4×C17D411yescharacteristic
32C23×C4×C17D411yescharacteristic
33C23×C4×C17C2311yescharacteristic
34C2×C22⋊C4×C17—24no—
35C2×C22⋊C4×C17—42no—
36C2×C22⋊C4×C17—42no—
37C2×C22⋊Dic17—21no—
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40C2×C22⋊Dic17—21no—
41C2×C22⋊Dic17—21no—
42C2×C22⋊Dic17—21no—
43#10587612—42no—
44#10587612—42no—
45C2×C4⋊Dic17C2×C411yescharacteristic
46C2×C4⋊Dic17C2×C411yescharacteristic
47C2×C4⋊Dic17C2×C411yescharacteristic
48C2×C4⋊Dic17C2×C411yescharacteristic
49C2×C4×Dic17—21no—
50C2×C4×Dic17—21no—
51C22×#3622—22no—
52C17×#95—24no—
53C17×#95—42no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58C22⋊#3622—24no—
59C22⋊#3622—42no—
60C22⋊#3622—42no—
61C24×C17—22no—
62C24×C17—22no—
63C24×C17—21no—
64C24×C17—21no—
65C24×C17—22no—
66C24×C17—22no—
67C24×C17—41no—
68C24×C17—41no—
69C24×C17C22⋊C411yescharacteristic
70C24×C17C22⋊C411yescharacteristic
71C24×C17C2×D411yescharacteristic
72C22×C4×C17—22no—
73C22×C4×C17—22no—
74C22×C4×C17—22no—
75C22×C4×C17—22no—
76C22×C4×C17—22no—
77C22×C4×C17—22no—
78C22×C4×C17—22no—
79C22×C4×C17—22no—
80C22×C4×C17—22no—
81C22×C4×C17—22no—
82C22×C4×C17—24no—
83C22×C4×C17—41no—
84C22×C4×C17—41no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17—41no—
88C22×C4×C17—41no—
89C22×C4×C17—41no—
90C22×C4×C17—416no—
91C22×C4×C17—42no—
92C22×C4×C17—42no—
93C22×C4×C17—42no—
94C22×C4×C17—42no—
95C22×C4×C17—42no—
96C22×C4×C17—42no—
97C22×C4×C17C22⋊C411yescharacteristic
98C22×C4×C17C22⋊C411yescharacteristic
99C22×C4×C17C22×C411yescharacteristic
100C22×C4×C17C2×D411yescharacteristic
101C22×C4×C17#4114yes—
102C22×Dic17—21no—
103C22×Dic17—21no—
104C22×Dic17—21no—
105C22×Dic17—21no—
106C22⋊C4×C17—48no—
107C22⋊Dic17—42no—
108C22⋊Dic17—42no—
109C22⋊Dic17—42no—
110C22⋊Dic17—42no—
111C22⋊Dic17—42no—
112C22⋊Dic17—41no—
113C22⋊Dic17—41no—
114C4⋊Dic17—41no—
115C4⋊Dic17—41no—
116C4⋊Dic17—41no—
117C4⋊Dic17—41no—
118C4×Dic17—42no—
119C4×Dic17—42no—
120C2×#3622—42no—
121C2×#3622—42no—
122C2×#3622—42no—
123#8715—171nomaximal, Sylow
124C23×C17—21no—
125C23×C17—21no—
126C23×C17—21no—
127C23×C17—21no—
128C23×C17—24no—
129C23×C17—24no—
130C23×C17—21no—
131C23×C17—21no—
132C23×C17—21no—
133C23×C17—21no—
134C23×C17—21no—
135C23×C17—21no—
136C23×C17—21no—
137C23×C17—21no—
138C23×C17—21no—
139C23×C17—21no—
140C23×C17—21no—
141C23×C17—21no—
142C23×C17—44no—
143C23×C17—44no—
144C23×C17—44no—
145C23×C17—44no—
146C23×C17—42no—
147C23×C17—42no—
148C23×C17—42no—
149C23×C17—42no—
150C23×C17#9912yes—
151C23×C17#10412yes—
152C23×C17C2×C22⋊C411yescharacteristic
153C23×C17#12312yes—
154C23×C17#13512yes—
155C23×C17AGL(1,ℤ/8)11yescharacteristic
156C23×C17#13711yescharacteristic
157C2×C4×C17—28no—
158C2×C4×C17—21no—
159C2×C4×C17—21no—
160C2×C4×C17—21no—
161C2×C4×C17—21no—
162C2×C4×C17—21no—
163C2×C4×C17—21no—
164C2×C4×C17—21no—
165C2×C4×C17—21no—
166C2×C4×C17—21no—
167C2×C4×C17—44no—
168C2×C4×C17—44no—
169C2×C4×C17—44no—
170C2×C4×C17—44no—
171C2×C4×C17—44no—
172C2×C4×C17—44no—
173C2×C4×C17—44no—
174C2×C4×C17—44no—
175C2×C4×C17—82no—
176C2×C4×C17—82no—
177C2×C4×C17—82no—
178C2×C4×C17—82no—
179C2×C4×C17#9912yes—
180C2×C4×C17#11712yes—
181C2×C4×C17#12312yes—
182C2×Dic17—41no—
183C2×Dic17—41no—
184C2×Dic17—41no—
185C2×Dic17—41no—
186C2×Dic17—41no—
187C2×Dic17—41no—
188C2×Dic17—41no—
189C2×Dic17—41no—
190C2×Dic17—41no—
191C2×Dic17—41no—
192C2×Dic17—41no—
193C2×Dic17—41no—
194#3622—82no—
195#2280—171no—
196#1779—171no—
197C22⋊#95D1711yescharacteristic
198#1294—172no—
199#1294—172no—
200C22×C17—22no—
201C22×C17—22no—
202C22×C17—22no—
203C22×C17—21no—
204C22×C17—21no—
205C22×C17—21no—
206C22×C17—21no—
207C22×C17—22no—
208C22×C17—22no—
209C22×C17—22no—
210C22×C17—22no—
211C22×C17—22no—
212C22×C17—22no—
213C22×C17—22no—
214C22×C17—48no—
215C22×C17—48no—
216C22×C17—41no—
217C22×C17—41no—
218C22×C17—41no—
219C22×C17—41no—
220C22×C17—41no—
221C22×C17—41no—
222C22×C17—41no—
223C22×C17—41no—
224C22×C17#38111yescharacteristic
225C22×C17C2×#9911yescharacteristic
226C22×C17C2×#9911yescharacteristic
227C22×C17#41611yescharacteristic
228C22×C17#41711yescharacteristic
229C22×C17C2×#10411yescharacteristic
230C22×C17#42111yescharacteristic
231C22×C17#48212yes—
232C22×C17#48512yes—
233C4×C17—22no—
234C4×C17—22no—
235C4×C17—22no—
236C4×C17—41no—
237C4×C17—84no—
238Dic17—81no—
239Dic17—81no—
240Dic17—81no—
241Dic17—81no—
242C24×C4C2×D1711yescharacteristic
243C2×#117—171no—
244C2×#117—171no—
245C22×C22⋊C4—21no—
246C2×C22⋊C8—172no—
247C2×C22⋊C8—341no—
248C2×C22⋊C8—341no—
249#381—341no—
250#380—171no—
251#380—171no—
252#380—171no—
253#380—171no—
254#379—341no—
255C4×C22⋊C4—341no—
256C4×C22⋊C4—341no—
257C2×#95—21no—
258C2×#95C2×D1712yes—
259C2×C17—22no—
260C2×C17—22no—
261C2×C17—42no—
262C2×C17—42no—
263C2×C17#150111yescharacteristic
264C2×C17#150411yescharacteristic
265C2×C17#151311yescharacteristic
266C2×C17#151611yescharacteristic
267C2×C17#181911yescharacteristic
268C2×C17#182511yescharacteristic
269C2×C17#182611yescharacteristic
270C25C22⋊D1711yescharacteristic
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4C4×D1711yescharacteristic
276C23×C4C4×D1711yescharacteristic
277C23×C4D6811yescharacteristic
278C23×C4D6811yescharacteristic
279C23×C4C22⋊D1711yescharacteristic
280C23×C4C22×D1711yescharacteristic
281C22×C8—342no—
282#117—682no—
283#117—682no—
284C2×C4⋊C4—171no—
285C2×C4⋊C4—171no—
286C2×C4⋊C4—171no—
287C2×C4⋊C4—171no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—341no—
292C2×C22⋊C4—341no—
293C2×C22⋊C4—341no—
294C2×C22⋊C4—341no—
295C2×C22⋊C4—341no—
296C2×C22⋊C4—341no—
297C2×C42—341no—
298C2×C42—341no—
299C22⋊C8—344no—
300C22⋊C8—682no—
301C22⋊C8—682no—
302#95—24no—
303#95—42no—
304#95—341no—
305#95—341no—
306#95—341no—
307#95—341no—
308C17#871511yescharacteristic, complemented, Sylow
309C24—22no—
310C24—22no—
311C24—21no—
312C24—21no—
313C24—22no—
314C24—22no—
315C24—41no—
316C24—41no—
317C24#6322711yescharacteristic
318C24#6322711yescharacteristic
319C24C2×C22⋊D1711yescharacteristic
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—416no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—341no—
346C22×C4—341no—
347C22×C4—341no—
348C22×C4—341no—
349C22×C4#6322711yescharacteristic
350C22×C4#6322711yescharacteristic
351C22×C4C2×C4×D1711yescharacteristic
352C22×C4C2×D6811yescharacteristic
353C22×C4#6325414yes—
354C2×C8—682no—
355C2×C8—682no—
356C2×C8—682no—
357C4⋊C4—681no—
358C4⋊C4—681no—
359C4⋊C4—681no—
360C4⋊C4—681no—
361C22⋊C4—48no—
362C22⋊C4—682no—
363C22⋊C4—682no—
364C22⋊C4—682no—
365C22⋊C4—682no—
366C22⋊C4—681no—
367C22⋊C4—681no—
368C22⋊C4—682no—
369C42—682no—
370C42—682no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—24no—
376C23—24no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—44no—
390C23—44no—
391C23—44no—
392C23—44no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23#1058747612yes—
398C23#1058747712yes—
399C23C2×#6322711yescharacteristic
400C23#1058761811yescharacteristic
401C23#1058762112yes—
402C23#1058762811yescharacteristic
403C23#1058763612yes—
404C2×C4—28no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—681no—
427C2×C4—681no—
428C2×C4—681no—
429C2×C4—681no—
430C2×C4—681no—
431C2×C4—681no—
432C2×C4—681no—
433C2×C4—681no—
434C2×C4—681no—
435C2×C4—681no—
436C2×C4—681no—
437C2×C4—681no—
438C2×C4#1058747712yes—
439C2×C4#1058756312yes—
440C2×C4#1058757212yes—
441C8—1362no—
442C22—22no—
443C22—21no—
444C22—21no—
445C22—22no—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—48no—
457C22—48no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22#1176267011yescharacteristic
467C22C2×#1058747711yescharacteristic
468C22C2×#1058747711yescharacteristic
469C22#1176280311yescharacteristic
470C22#1176280811yescharacteristic
471C22C2×#1058747611yescharacteristic
472C22#1176282711yescharacteristic
473C22#1176313012yes—
474C22#1176314712yes—
475C4—22no—
476C4—22no—
477C4—22no—
478C4—41no—
479C4—84no—
480C4—1361no—
481C4—1361no—
482C4—1361no—
483C4—1361no—
484C2—22no—
485C2—22no—
486C2—42no—
487C2—42no—
488C2#1452727311yescharacteristic
489C2#1452728611yescharacteristic
490C2#1452732511yescharacteristic
491C2#1452733811yescharacteristic
492C2#1452885611yescharacteristic
493C2#1452887611yescharacteristic
494C2#1452888411yescharacteristic
subgroupG/H
centerC23C2×#63227
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×C22⋊#95C2
socleC23×C17C2×C22⋊C4
prime radicalC25×C17D4
cosocleC23×C4×C17C23
hypercenterC22⋊#95D17
hypocenterC17#8715
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. #14526663C2semidirect
4. #14526663C2semidirect
6. C2×#10587612C4semidirect
7. C2×#10587612C4semidirect
12. #11762669C4semidirect
13. #11762669C4semidirect
308. C17#8715semidirect

Maximal subgroups

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

subgroupindex
#145311672
#145286942
#145266632
C17×C22⋊#952
#871517