Finite Group Databasebeta

← #17050877

Subgroups — #17050877

Order 4352.

1114 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763516C211yesmaximal, characteristic
2#14531659C212yesmaximal, complemented
3#14529769C212yesmaximal, complemented
4#14529767C214yesmaximal, complemented
5#14528772C211yesmaximal, characteristic
6#14528770C212yesmaximal
7#99×Dic17C212yesmaximal
8C4×C17×#99C211yesmaximal, characteristic
9#11763516—24no—
10#11763516—22no—
11#11763516—22no—
12C2×#10587555C411yescharacteristic, complemented
13C2×#10587576C412yescomplemented
14C2×#10587610C411yescharacteristic, complemented
15C2×#10587610C2211yescharacteristic
16C2×#10587564C412yescomplemented
17C2×#10587564C2212yes—
18C2×C4×Dic34C411yescharacteristic, complemented
19C2×D4×Dic17C2212yes—
20C22×C4⋊Dic17C411yescharacteristic, complemented
21C22×C4⋊Dic17C2211yescharacteristic
22C2×#10587505C2212yes—
23#11762707—22no—
24#11762692—24no—
25#11762669C2212yes—
26#11762667C2214yes—
27C4×C4⋊Dic17—22no—
28C22⋊C4×Dic17C2214yes—
29#11762576C2212yes—
30#11762575C2214yes—
31#11762575C2214yes—
32C2×C4×D4×C17C2211yescharacteristic
33C2×C17×#99C2211yescharacteristic
34C2×C17×#99C2211yescharacteristic
35C4×C22⋊C4×C17C2212yes—
36C17×#342C2212yes—
37C22×D4×C17C2311yescharacteristic
38C23×C4×C17C2×C411yescharacteristic
39C23×C4×C17C2311yescharacteristic
40C23×Dic17C2×C412yes—
41C23×Dic17C2312yes—
42C22×Dic34C2×C411yescharacteristic
43C22×Dic34C2×C412yes—
44C4×D4×C17—22no—
45C4×D4×C17—22no—
46C2×C4⋊C4×C17C2×C411yescharacteristic
47C2×C22⋊C4×C17C2×C411yescharacteristic
48C2×C22⋊C4×C17C2312yes—
49C2×C22⋊C4×C17C2311yescharacteristic
50C2×C22⋊C4×C17C2312yes—
51C2×C42×C17—22no—
52C2×C42×C17C2×C411yescharacteristic
53C2×C22⋊Dic17C2×C412yes—
54C2×C22⋊Dic17C2314yes—
55C2×C22⋊Dic17C2312yes—
56D4×Dic17—24no—
57D4×Dic17—24no—
58C2×C4⋊Dic17—22no—
59C2×C4⋊Dic17—21no—
60C2×C4⋊Dic17—21no—
61C2×C4⋊Dic17—22no—
62C2×C4⋊Dic17C2×C412yes—
63C2×C4⋊Dic17C2×C411yescharacteristic
64C2×C4⋊Dic17C2×C412yes—
65C2×C4⋊Dic17C2×C411yescharacteristic
66C2×C4⋊Dic17C2×C412yes—
67C2×C4⋊Dic17C2×C411yescharacteristic
68C2×C4⋊Dic17D414yes—
69C2×C4⋊Dic17D412yes—
70C2×C4⋊Dic17D412yes—
71#10587610—22no—
72#10587610—22no—
73#10587610—22no—
74#10587610—22no—
75C2×#63225—24no—
76C2×#63225C2×C412yes—
77C2×#63225C2×C412yes—
78C2×#63225C2×C412yes—
79C2×C4×Dic17—24no—
80C2×C4×Dic17C2×C412yes—
81#10587576—24no—
82#10587576—24no—
83#10587564—24no—
84#10587564—24no—
85#10587564—24no—
86#10587564—24no—
87#10587555—22no—
88#10587555—22no—
89C4×Dic34—22no—
90C4×Dic34—21no—
91C4×Dic34—21no—
92C17×#99—22no—
93C17×#99Q814yescomplemented
94C17×#95—22no—
95#10587505—24no—
96#10587502—22no—
97#10587502—24no—
98#10587502—24no—
99C24×C17C22×C411yescharacteristic
100C24×C17C2411yescharacteristic
101C2×D4×C17—22no—
102C2×D4×C17—22no—
103C2×D4×C17C2×Q812yes—
104C2×D4×C17#4112yes—
105C22×C4×C17—22no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—22no—
109C22×C4×C17—42no—
110C22×C4×C17—42no—
111C22×C4×C17C22×C411yescharacteristic
112C22×C4×C17C22×C411yescharacteristic
113C22×C4×C17C22×C411yescharacteristic
114C22×C4×C17C22×C411yescharacteristic
115C22×C4×C17C22×C411yescharacteristic
116C22×C4×C17C2×D412yes—
117C22×C4×C17C2×D412yes—
118C22×Dic17—22no—
119C22×Dic17—22no—
120C22×Dic17—24no—
121C22×Dic17—82no—
122C22×Dic17—82no—
123C22×Dic17C22×C412yes—
124C22×Dic17C22×C412yes—
125C22×Dic17C22×C412yes—
126C22×Dic17C22×C412yes—
127C22×Dic17C2×D414yes—
128C22×Dic17C2×D414yes—
129C2×Dic34—21no—
130C2×Dic34—21no—
131C2×Dic34—24no—
132C2×Dic34—42no—
133C2×Dic34—82no—
134C4⋊C4×C17—22no—
135C22⋊C4×C17—22no—
136C22⋊C4×C17—22no—
137C22⋊C4×C17—22no—
138C22⋊C4×C17—22no—
139C22⋊C4×C17—22no—
140C22⋊C4×C17C2×Q814yes—
141C42×C17—21no—
142C42×C17—21no—
143C42×C17—44no—
144C22⋊Dic17—24no—
145C22⋊Dic17—24no—
146C22⋊Dic17—24no—
147C22⋊Dic17—24no—
148C4⋊Dic17—21no—
149C4⋊Dic17—21no—
150C4⋊Dic17—24no—
151C4⋊Dic17—22no—
152C4⋊Dic17—22no—
153C4⋊Dic17—44no—
154C4⋊Dic17C22⋊C412yes—
155C4⋊Dic17C22⋊C411yescharacteristic
156C4⋊Dic17C22⋊C411yescharacteristic
157C4⋊Dic17C22⋊C412yes—
158C4⋊Dic17C22⋊C412yes—
159C4⋊Dic17C22⋊C414yes—
160C4⋊Dic17C22⋊C414yes—
161#63225—24no—
162#63225—22no—
163#63225—22no—
164#63225—24no—
165#63225—84no—
166C4×Dic17—22no—
167C4×Dic17—22no—
168C4×Dic17—84no—
169#22513—171nomaximal, Sylow
170C23×C17—21no—
171C23×C17—21no—
172C23×C17—41no—
173C23×C17—41no—
174C23×C17—41no—
175C23×C17—41no—
176C23×C17C4×Q812yes—
177C23×C17C23×C411yescharacteristic
178C23×C17C22×D412yes—
179C23×C17C22×Q811yescharacteristic
180C23×C17C2×#4111yescharacteristic
181C23×C172−1+412yes—
182D4×C17—24no—
183D4×C17—24no—
184C2×C4×C17—21no—
185C2×C4×C17—21no—
186C2×C4×C17—24no—
187C2×C4×C17—22no—
188C2×C4×C17—21no—
189C2×C4×C17—21no—
190C2×C4×C17—24no—
191C2×C4×C17—41no—
192C2×C4×C17—42no—
193C2×C4×C17—42no—
194C2×C4×C17—42no—
195C2×C4×C17—42no—
196C2×C4×C17—42no—
197C2×C4×C17—41no—
198C2×C4×C17—41no—
199C2×C4×C17—42no—
200C2×C4×C17—42no—
201C2×C4×C17—42no—
202C2×C4×C17C2×C22⋊C411yescharacteristic
203C2×C4×C17C2×C22⋊C412yes—
204C2×C4×C17C2×C22⋊C411yescharacteristic
205C2×C4×C17C4×Q812yes—
206C2×Dic17—22no—
207C2×Dic17—22no—
208C2×Dic17—42no—
209C2×Dic17—42no—
210C2×Dic17—44no—
211C2×Dic17—44no—
212C2×Dic17—42no—
213C2×Dic17—42no—
214C2×Dic17—44no—
215C2×Dic17—44no—
216C2×Dic17—44no—
217C2×Dic17—82no—
218C2×Dic17—82no—
219C2×Dic17C2×C22⋊C414yes—
220C2×Dic17C2×C22⋊C412yes—
221C2×Dic17C2×C22⋊C412yes—
222Dic34—42no—
223Dic34—42no—
224Dic34—84no—
225C2×#554—171no—
226#2345—172no—
227#1996—172no—
228#1996—174no—
229#1799—172no—
230#1799—171no—
231C4×#99—172no—
232C4×#99D1711yescharacteristic
233C22×C17—22no—
234C22×C17—21no—
235C22×C17—22no—
236C22×C17—21no—
237C22×C17—22no—
238C22×C17—41no—
239C22×C17—41no—
240C22×C17—42no—
241C22×C17—42no—
242C22×C17—42no—
243C22×C17—41no—
244C22×C17—41no—
245C22×C17C22×C22⋊C411yescharacteristic
246C22×C17C2×C4×Q811yescharacteristic
247C22×C17#51911yescharacteristic
248C22×C17#54812yes—
249C22×C17D4×Q812yes—
250C4×C17—22no—
251C4×C17—21no—
252C4×C17—22no—
253C4×C17—44no—
254C4×C17—41no—
255C4×C17—41no—
256C4×C17—82no—
257C4×C17#41012yes—
258Dic17—24no—
259Dic17—22no—
260Dic17—22no—
261Dic17—42no—
262Dic17—42no—
263Dic17—84no—
264#554—342no—
265#554—344no—
266#554—342no—
267C2×C4⋊Q8—171no—
268C2×#125—172no—
269C2×C22⋊Q8—171no—
270C2×C22⋊Q8—171no—
271C2×C22⋊Q8—172no—
272C2×C22⋊Q8—172no—
273C2×C4×Q8—171no—
274C2×C4×D4—172no—
275C2×C4×D4C2×D1711yescharacteristic
276C22×C4⋊C4—171no—
277C22×C4⋊C4—171no—
278C2×#99—172no—
279C2×#99C2×D1711yescharacteristic
280C2×#99C2×D1711yescharacteristic
281#389—342no—
282#387—344no—
283#380—172no—
284#380—174no—
285C4×C4⋊C4—342no—
286C4×C22⋊C4—174no—
287C4×C22⋊C4C2×D1712yes—
288#342—174no—
289#342—172no—
290#342—174no—
291#342C2×D1712yes—
292C2×C17—22no—
293C2×C17—22no—
294C2×C17—21no—
295C2×C17—21no—
296C2×C17—42no—
297C2×C17Q8×C22⋊C411yescharacteristic
298C2×C17C2×#41011yescharacteristic
299C2×C17#288311yescharacteristic
300C22×Q8—171no—
301C22×Q8—172no—
302C22×D4C22×D1711yescharacteristic
303C23×C4—172no—
304C23×C4—172no—
305C23×C4C4×D1711yescharacteristic
306C23×C4C22×D1711yescharacteristic
307C4⋊Q8—342no—
308C4⋊Q8—342no—
309#125—344no—
310#125—344no—
311C22⋊Q8—344no—
312C22⋊Q8—344no—
313C22⋊Q8—344no—
314C22⋊Q8—344no—
315C22⋊Q8—342no—
316C22⋊Q8—342no—
317C22⋊Q8—342no—
318C22⋊Q8—342no—
319C4×Q8—342no—
320C4×Q8—341no—
321C4×Q8—341no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—344no—
325C4×D4—344no—
326C2×C4⋊C4—171no—
327C2×C4⋊C4—172no—
328C2×C4⋊C4—171no—
329C2×C4⋊C4—172no—
330C2×C4⋊C4—174no—
331C2×C4⋊C4—172no—
332C2×C4⋊C4—172no—
333C2×C4⋊C4—171no—
334C2×C4⋊C4—172no—
335C2×C4⋊C4—172no—
336C2×C4⋊C4—172no—
337C2×C4⋊C4—172no—
338C2×C4⋊C4—342no—
339C2×C4⋊C4—341no—
340C2×C4⋊C4—341no—
341C2×C4⋊C4—342no—
342C2×C4⋊C4—344no—
343C2×C4⋊C4C4×D1711yescharacteristic
344C2×C22⋊C4—172no—
345C2×C22⋊C4—172no—
346C2×C22⋊C4—174no—
347C2×C22⋊C4C4×D1711yescharacteristic
348C2×C22⋊C4C22×D1712yes—
349C2×C22⋊C4C22×D1711yescharacteristic
350C2×C22⋊C4C22×D1712yes—
351C2×C42—22no—
352C2×C42—172no—
353C2×C42—344no—
354C2×C42C4×D1711yescharacteristic
355#99—22no—
356#99—344no—
357#99Dic3414yescomplemented
358#95—22no—
359#95—344no—
360#95—344no—
361#95—342no—
362C17#2251311yescharacteristic, complemented, Sylow
363C24C2×C4×D1711yescharacteristic
364C24C23×D1711yescharacteristic
365C2×Q8—344no—
366C2×Q8—341no—
367C2×Q8—341no—
368C2×Q8—682no—
369C2×Q8—1362no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4C2×Dic3412yes—
373C2×D4#6325212yes—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—172no—
381C22×C4—172no—
382C22×C4—174no—
383C22×C4—174no—
384C22×C4—172no—
385C22×C4—172no—
386C22×C4—342no—
387C22×C4—342no—
388C22×C4—344no—
389C22×C4—1362no—
390C22×C4—1362no—
391C22×C4C2×C4×D1711yescharacteristic
392C22×C4C2×C4×D1711yescharacteristic
393C22×C4C2×C4×D1711yescharacteristic
394C22×C4C2×C4×D1711yescharacteristic
395C22×C4C2×C4×D1711yescharacteristic
396C22×C4D4×D1712yes—
397C22×C4D4×D1712yes—
398C4⋊C4—22no—
399C4⋊C4—172no—
400C4⋊C4—171no—
401C4⋊C4—171no—
402C4⋊C4—174no—
403C4⋊C4—174no—
404C4⋊C4—172no—
405C4⋊C4—172no—
406C4⋊C4—342no—
407C4⋊C4—342no—
408C4⋊C4—344no—
409C4⋊C4—342no—
410C4⋊C4—342no—
411C4⋊C4—344no—
412C4⋊C4—341no—
413C4⋊C4—341no—
414C4⋊C4—344no—
415C4⋊C4—684no—
416C4⋊C4—1364no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—344no—
423C22⋊C4—344no—
424C22⋊C4—344no—
425C22⋊C4—344no—
426C22⋊C4C2×Dic3414yes—
427C42—21no—
428C42—21no—
429C42—44no—
430C42—342no—
431C42—342no—
432C42—1364no—
433C23—21no—
434C23—21no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23C4×Dic3412yes—
440C23C22×Dic3411yescharacteristic
441C23C22×C4×D1711yescharacteristic
442C23C2×#6325211yescharacteristic
443C23C2×D4×D1712yes—
444C23#1058769712yes—
445Q8—682no—
446Q8—682no—
447Q8—1364no—
448D4—24no—
449D4—24no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—172no—
469C2×C4—172no—
470C2×C4—174no—
471C2×C4—342no—
472C2×C4—342no—
473C2×C4—684no—
474C2×C4—684no—
475C2×C4—682no—
476C2×C4—682no—
477C2×C4—682no—
478C2×C4—682no—
479C2×C4—684no—
480C2×C4—684no—
481C2×C4—684no—
482C2×C4—1362no—
483C2×C4—1362no—
484C2×C4C4×Dic3412yes—
485C2×C4C22⋊C4×D1711yescharacteristic
486C2×C4C22⋊C4×D1712yes—
487C2×C4C22⋊C4×D1711yescharacteristic
488C22—22no—
489C22—21no—
490C22—22no—
491C22—21no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—41no—
499C22—41no—
500C22C2×C22⋊C4×D1711yescharacteristic
501C22C2×C4×Dic3411yescharacteristic
502C22#1176328611yescharacteristic
503C22#1176346812yes—
504C22D4×Dic3412yes—
505C4—21no—
506C4—22no—
507C4—22no—
508C4—44no—
509C4—41no—
510C4—41no—
511C4—82no—
512C4—342no—
513C4—342no—
514C4—344no—
515C4—682no—
516C4—682no—
517C4—1364no—
518C4#1176278112yes—
519C2—22no—
520C2—22no—
521C2—21no—
522C2—21no—
523C2—42no—
524C2C22⋊C4×Dic3411yescharacteristic
525C2C2×#1176278111yescharacteristic
526C2#1453724311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC4×C17×#99C2
socleC22×C17C22×C22⋊C4
prime radicalC22×D4×C17C23
cosocleC24×C17C24
hypercenterC4×#99D17
hypocenterC17#22513
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #14531659C2semidirect
3. #14529769C2semidirect
4. #14529767C2semidirect
12. C2×#10587555C4semidirect
13. C2×#10587576C4semidirect
14. C2×#10587610C4semidirect
16. C2×#10587564C4semidirect
18. C2×C4×Dic34C4semidirect
20. C22×C4⋊Dic17C4semidirect
93. C17×#99Q8semidirect
357. #99Dic34semidirect
362. C17#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#117635162
#145316592
#145297692
#145297672
#145287722
#145287702
#99×Dic172
C4×C17×#992
#2251317