Finite Group Databasebeta

← #17969496

Subgroups — #17969496

Order 4352.

1318 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545261C212yesmaximal, complemented
2#14544682C212yesmaximal, complemented
3#14544647C212yesmaximal, complemented
4#14544644C212yesmaximal, complemented
5#14544613C212yesmaximal
6#14544529C212yesmaximal, complemented
7C4×#10587551C212yesmaximal, complemented
8C2×#11763290C211yesmaximal, characteristic
9C2×#10587539C2214yes—
10C2×#10587551C2214yes—
11#11763758—28no—
12#11763752C2214yes—
13#11763751C2214yes—
14C4×C22⋊#595C2214yes—
15#11763687C2214yes—
16#11763687C2214yes—
17C22×#63252C2211yescharacteristic
18#11763290—28no—
19C2×#10587573C411yescharacteristic, complemented
20C2×#10587573C411yescharacteristic, complemented
21C2×#10587579C2211yescharacteristic
22C2×#10587579C2211yescharacteristic
23C2×C4×C22⋊D17C411yescharacteristic, complemented
24C2×C4×C22⋊D17C411yescharacteristic, complemented
25C2×C4×C22⋊D17C2211yescharacteristic
26C2×C4×C22⋊D17C2211yescharacteristic
27C2×#10587612C411yescharacteristic, complemented
28C2×#10587578C411yescharacteristic, complemented
29C2×#10587578C2211yescharacteristic
30C2×C4⋊C4×D17C411yescharacteristic, complemented
31C2×C4⋊C4×D17C2211yescharacteristic
32C22×C4⋊C4×C17C411yescharacteristic, complemented
33C23×C4×C17C2×C411yescharacteristic
34C23×C4×C17C2×C411yescharacteristic
35C23×C4×C17C2×C411yescharacteristic
36C22×C22⋊D17C2×C411yescharacteristic
37C22×C22⋊D17C2311yescharacteristic
38C2×#63252—24no—
39C2×#63252—24no—
40C2×#63252—24no—
41C22×D68C2311yescharacteristic
42C22×C4×D17C2×C411yescharacteristic
43C22×C4×D17C2×C411yescharacteristic
44C22×C4×D17C2×C411yescharacteristic
45C22×C4×D17C2311yescharacteristic
46C22×C4×D17C2311yescharacteristic
47C22×C4×D17C2311yescharacteristic
48C22×Dic34C2×C411yescharacteristic
49C2×C22⋊#595C2318yes—
50C2×C4⋊#595—24no—
51C2×C4×#595—24no—
52C2×C4⋊C4×C17—24no—
53C2×C4⋊C4×C17C2×C411yescharacteristic
54C2×C4⋊C4×C17C2×C411yescharacteristic
55C2×C4⋊C4×C17C2×C411yescharacteristic
56C2×C4⋊C4×C17C2×C411yescharacteristic
57C2×C22⋊Dic17C2×C411yescharacteristic
58C2×C22⋊Dic17C2×C411yescharacteristic
59C4×C22⋊D17—24no—
60C4×C22⋊D17—24no—
61C4×C22⋊D17—24no—
62C4×C22⋊D17—24no—
63C2×#63227C2×C411yescharacteristic
64C2×#63227C2×C411yescharacteristic
65C2×#63227C2311yescharacteristic
66C2×#63227C2311yescharacteristic
67#10587612—24no—
68C2×C4⋊Dic17C2×C411yescharacteristic
69C2×C4⋊Dic17C2×C411yescharacteristic
70C2×#63225C2×C411yescharacteristic
71C2×#63225C2×C411yescharacteristic
72C2×#63225C2×C411yescharacteristic
73C2×#63225C2×C411yescharacteristic
74C2×C4×Dic17C2×C411yescharacteristic
75C2×C4×Dic17C2×C411yescharacteristic
76C2×C4×Dic17C2×C411yescharacteristic
77C2×C4×Dic17C2×C411yescharacteristic
78C2×C4×Dic17C2×C411yescharacteristic
79C2×C4×Dic17C2×C411yescharacteristic
80#10587579—24no—
81#10587579—24no—
82#10587578—24no—
83#10587578—24no—
84C4⋊C4×D17—24no—
85C4⋊C4×D17D418yes—
86#10587573—24no—
87#10587573—24no—
88#10587551—28no—
89(C2×#595)⋊C4—24no—
90(C2×#595)⋊C4—24no—
91(C2×#595)⋊C4—28no—
92#10587539—28no—
93C24×C17C22×C411yescharacteristic
94C23×D17C22×C411yescharacteristic
95C23×D17C2411yescharacteristic
96C22×#595—28no—
97C22×C4×C17—22no—
98C22×C4×C17—22no—
99C22×C4×C17—22no—
100C22×C4×C17—22no—
101C22×C4×C17—22no—
102C22×C4×C17—81no—
103C22×C4×C17—81no—
104C22×C4×C17C22×C411yescharacteristic
105C22×C4×C17C22×C411yescharacteristic
106C22×C4×C17C22×C411yescharacteristic
107C22×C4×C17C22×C411yescharacteristic
108C22×C4×C17C22×C411yescharacteristic
109C22×C4×C17C22×C411yescharacteristic
110C2×C22⋊D17—22no—
111C2×C22⋊D17—22no—
112C2×C22⋊D17—22no—
113C2×C22⋊D17—22no—
114C2×C22⋊D17—22no—
115C2×C22⋊D17#4114yes—
116C22×Dic17C22×C411yescharacteristic
117C22×Dic17C22×C411yescharacteristic
118C22×Dic17C22×C411yescharacteristic
119C22×Dic17C22×C411yescharacteristic
120C22×Dic17C22×C411yescharacteristic
121C22×Dic17C22×C411yescharacteristic
122#63252—232no—
123C2×D68—22no—
124C2×D68—22no—
125C2×D68#4114yes—
126C2×C4×D17—22no—
127C2×C4×D17—22no—
128C2×C4×D17—22no—
129C2×C4×D17—22no—
130C2×C4×D17—22no—
131C2×C4×D17—22no—
132C2×C4×D17—22no—
133C2×C4×D17—81no—
134C2×C4×D17—81no—
135C2×C4×D17—81no—
136C2×C4×D17—81no—
137C2×C4×D17C2×D414yes—
138C2×C4×D17C2×D414yes—
139C2×C4×D17C2×D414yes—
140C2×Dic34—22no—
141C2×Dic34—22no—
142C2×Dic34—22no—
143C22⋊#595—28no—
144C22⋊#595—28no—
145C4⋊#595—84no—
146C4×#595—84no—
147C4⋊C4×C17—22no—
148C4⋊C4×C17—22no—
149C4⋊C4×C17—22no—
150C4⋊C4×C17C22⋊C414yes—
151C22⋊Dic17—22no—
152C22⋊Dic17—22no—
153#63227—22no—
154#63227—22no—
155#63227—22no—
156#63227—22no—
157C4⋊Dic17—22no—
158C4⋊Dic17C22⋊C414yes—
159#63225—22no—
160#63225—22no—
161#63225C22⋊C414yes—
162#63225C22⋊C414yes—
163C4×Dic17—22no—
164C4×Dic17—22no—
165C4×Dic17—22no—
166C4×Dic17—22no—
167C4×Dic17—22no—
168C4×Dic17—22no—
169#20725—171nomaximal, Sylow
170C23×C17—21no—
171C23×C17—21no—
172C23×C17—41no—
173C23×C17—41no—
174C23×C17#11712yes—
175C23×C17C23×C411yescharacteristic
176C22×D17—21no—
177C22×D17—21no—
178C22×D17—41no—
179C22×D17—41no—
180C22×D17—41no—
181C22×D17—41no—
182C22×D17#11712yes—
183C22×D17C22×D412yes—
184C22×D17C2×#4112yes—
185C22×D17C2×#4112yes—
186C2×#595—48no—
187C2×#595—48no—
188C2×#595—48no—
189C2×C4×C17—28no—
190C2×C4×C17—21no—
191C2×C4×C17—21no—
192C2×C4×C17—21no—
193C2×C4×C17—21no—
194C2×C4×C17—21no—
195C2×C4×C17—21no—
196C2×C4×C17—41no—
197C2×C4×C17—41no—
198C2×C4×C17—41no—
199C2×C4×C17—41no—
200C2×C4×C17—82no—
201C2×C4×C17—82no—
202C2×C4×C17C2×C22⋊C412yes—
203C2×C4×C17C2×C22⋊C412yes—
204C2×C4×C17C2×C22⋊C412yes—
205C2×C4×C17#11712yes—
206C22⋊D17—28no—
207C22⋊D17—28no—
208C2×Dic17—21no—
209C2×Dic17—21no—
210C2×Dic17—21no—
211C2×Dic17—21no—
212C2×Dic17—21no—
213C2×Dic17—21no—
214C2×Dic17—41no—
215C2×Dic17—41no—
216C2×Dic17—41no—
217C2×Dic17—41no—
218C2×Dic17C2×C22⋊C412yes—
219C2×Dic17C2×C22⋊C412yes—
220C2×Dic17C2×C22⋊C412yes—
221C2×Dic17#11712yes—
222D68—28no—
223C4×D17—28no—
224C4×D17—28no—
225C4×D17—44no—
226C4×D17—44no—
227C4×D17—82no—
228C4×D17—82no—
229Dic34—28no—
230C2×#520—171no—
231#2313—172no—
232#1820—172no—
233#1799—172no—
234#1799—172no—
235#1782—172no—
236C4×#99—172no—
237C4×#99—172no—
238C22×C17—21no—
239C22×C17—21no—
240C22×C17—22no—
241C22×C17—42no—
242C22×C17—42no—
243C22×C17—41no—
244C22×C17—41no—
245C22×C17C22×C22⋊C411yescharacteristic
246C22×C17C2×#11711yescharacteristic
247C22×C17C2×#11711yescharacteristic
248C2×D17—22no—
249C2×D17—22no—
250C2×D17—22no—
251C2×D17—42no—
252C2×D17—42no—
253C2×D17—42no—
254C2×D17—41no—
255C2×D17—41no—
256C2×D17—42no—
257C2×D17#52514yes—
258#595—88no—
259C4×C17—22no—
260C4×C17—22no—
261C4×C17—22no—
262C4×C17—22no—
263C4×C17—41no—
264C4×C17—41no—
265Dic17—22no—
266Dic17—22no—
267Dic17—22no—
268Dic17—22no—
269Dic17—41no—
270Dic17—41no—
271C22×#41—171no—
272#520—348no—
273C2×C4×Q8—171no—
274C2×C4×Q8—171no—
275C2×C4×D4—171no—
276C2×C4×D4—171no—
277C2×C4×D4—171no—
278C2×C4×D4—171no—
279C2×C4×D4—171no—
280C2×C4×D4—171no—
281C2×#117—171no—
282C2×#117—171no—
283C2×#117—171no—
284C22×C4⋊C4—171no—
285C22×C4⋊C4—171no—
286C22×C4⋊C4#59511yescharacteristic, complemented
287C2×#99—174no—
288C2×#99—174no—
289#387—348no—
290#381—174no—
291#380—174no—
292C4×C22⋊C4—174no—
293#342—174no—
294#342—174no—
295C2×C17—21no—
296C2×C17—21no—
297C2×C17—42no—
298C2×C17#228011yescharacteristic
299C2×C17#288311yescharacteristic
300C2×C17#288411yescharacteristic
301D17—24no—
302D17—42no—
303C2×#41—344no—
304C2×#41—344no—
305C2×#41—344no—
306C22×Q8—171no—
307C22×D4—171no—
308C22×D4—171no—
309C22×D4—171no—
310C23×C4—171no—
311C23×C4—171no—
312C23×C4—171no—
313C23×C4—171no—
314C23×C4—171no—
315C23×C4—171no—
316C23×C4C2×#59511yescharacteristic
317C23×C4C2×#59511yescharacteristic
318C23×C4C2×#59511yescharacteristic
319C4×Q8—344no—
320C4×Q8—344no—
321C4×D4—344no—
322C4×D4—344no—
323C4×D4—344no—
324C4×D4—344no—
325C4×D4—344no—
326C4×D4—344no—
327#117—344no—
328#117—344no—
329#117—344no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—171no—
332C2×C4⋊C4—171no—
333C2×C4⋊C4—171no—
334C2×C4⋊C4—178no—
335C2×C4⋊C4—171no—
336C2×C4⋊C4—171no—
337C2×C4⋊C4—171no—
338C2×C4⋊C4—344no—
339C2×C4⋊C4—344no—
340C2×C4⋊C4C2×#59511yescharacteristic
341C2×C4⋊C4C2×#59511yescharacteristic
342C2×C4⋊C4C2×#59511yescharacteristic
343C2×C4⋊C4C2×#59511yescharacteristic
344C2×C22⋊C4—171no—
345C2×C22⋊C4—171no—
346C2×C22⋊C4—171no—
347C2×C22⋊C4—171no—
348C2×C22⋊C4—171no—
349C2×C22⋊C4—171no—
350C2×C22⋊C4—178no—
351C2×C42—171no—
352C2×C42—171no—
353C2×C42—171no—
354C2×C42—171no—
355C2×C42—171no—
356C2×C42—171no—
357C2×C42—344no—
358#99—348no—
359#99—348no—
360#95—344no—
361#95—344no—
362#95—348no—
363C17#2072511yescharacteristic, complemented, Sylow
364C24—171no—
365C24—171no—
366C24C22×#59511yescharacteristic
367#41—3432no—
368C2×Q8—342no—
369C2×Q8—342no—
370C2×Q8—342no—
371C2×D4—174no—
372C2×D4—174no—
373C2×D4—342no—
374C2×D4—342no—
375C2×D4—342no—
376C2×D4—342no—
377C2×D4—342no—
378C2×D4—342no—
379C2×D4—342no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—81no—
386C22×C4—81no—
387C22×C4—171no—
388C22×C4—171no—
389C22×C4—171no—
390C22×C4—171no—
391C22×C4—174no—
392C22×C4—174no—
393C22×C4—174no—
394C22×C4—171no—
395C22×C4—171no—
396C22×C4—342no—
397C22×C4—342no—
398C22×C4—342no—
399C22×C4—342no—
400C22×C4—342no—
401C22×C4—342no—
402C22×C4—342no—
403C22×C4—348no—
404C22×C4—1361no—
405C22×C4—1361no—
406C22×C4—1361no—
407C22×C4—1361no—
408C22×C4C22×#59511yescharacteristic
409C22×C4C22×#59511yescharacteristic
410C22×C4C22×#59511yescharacteristic
411C22×C4C22×#59511yescharacteristic
412C22×C4C22×#59511yescharacteristic
413C22×C4C22×#59511yescharacteristic
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—174no—
418C4⋊C4—174no—
419C4⋊C4—174no—
420C4⋊C4—342no—
421C4⋊C4—342no—
422C4⋊C4—342no—
423C4⋊C4—1364no—
424C4⋊C4C22⋊#59514yes—
425C22⋊C4—342no—
426C22⋊C4—342no—
427C22⋊C4—342no—
428C22⋊C4—342no—
429C22⋊C4—342no—
430C22⋊C4—342no—
431C22⋊C4—348no—
432C22⋊C4—348no—
433C42—342no—
434C42—342no—
435C42—342no—
436C42—342no—
437C42—342no—
438C42—342no—
439C42—1364no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—172no—
445C23—172no—
446C23—172no—
447C23—172no—
448C23—341no—
449C23—341no—
450C23—681no—
451C23—681no—
452C23—681no—
453C23—681no—
454C23#1058767712yes—
455C23C23×#59511yescharacteristic
456Q8—348no—
457D4—348no—
458D4—348no—
459D4—348no—
460C2×C4—28no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—172no—
474C2×C4—172no—
475C2×C4—172no—
476C2×C4—172no—
477C2×C4—348no—
478C2×C4—348no—
479C2×C4—341no—
480C2×C4—341no—
481C2×C4—341no—
482C2×C4—341no—
483C2×C4—341no—
484C2×C4—341no—
485C2×C4—684no—
486C2×C4—684no—
487C2×C4—681no—
488C2×C4—681no—
489C2×C4—681no—
490C2×C4—681no—
491C2×C4—688no—
492C2×C4—688no—
493C2×C4—688no—
494C2×C4—1362no—
495C2×C4—1362no—
496C2×C4#1058767712yes—
497C2×C4C2×C22⋊#59512yes—
498C2×C4C2×C22⋊#59512yes—
499C2×C4C2×C22⋊#59512yes—
500C22—21no—
501C22—21no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—41no—
506C22—41no—
507C22—174no—
508C22—342no—
509C22—342no—
510C22—342no—
511C22—682no—
512C22—682no—
513C22—682no—
514C22—682no—
515C22—681no—
516C22—681no—
517C22C22×C22⋊#59511yescharacteristic
518C22C2×#1058767711yescharacteristic
519C22C2×#1058767711yescharacteristic
520C4—22no—
521C4—22no—
522C4—22no—
523C4—22no—
524C4—41no—
525C4—41no—
526C4—342no—
527C4—342no—
528C4—342no—
529C4—342no—
530C4—681no—
531C4—681no—
532C4—1368no—
533C2—21no—
534C2—21no—
535C2—42no—
536C2—344no—
537C2—682no—
538C2#1454522811yescharacteristic
539C2#1454538311yescharacteristic
540C2#1454538511yescharacteristic
subgroupG/H
centerC22C22×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C4⋊C4×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC22×#63252C22
cosocleC23×D17C24
hypercenterC22×C4⋊C4#595
hypocenterC17#20725
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14545261C2semidirect
2. #14544682C2semidirect
3. #14544647C2semidirect
4. #14544644C2semidirect
6. #14544529C2semidirect
7. C4×#10587551C2semidirect
19. C2×#10587573C4semidirect
20. C2×#10587573C4semidirect
23. C2×C4×C22⋊D17C4semidirect
24. C2×C4×C22⋊D17C4semidirect
27. C2×#10587612C4semidirect
28. C2×#10587578C4semidirect
30. C2×C4⋊C4×D17C4semidirect
32. C22×C4⋊C4×C17C4semidirect
286. C22×C4⋊C4#595semidirect
363. C17#20725semidirect

Maximal subgroups

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

subgroupindex
#145452612
#145446822
#145446472
#145446442
#145446132
#145445292
C4×#105875512
C2×#117632902
#2072517