Finite Group Databasebeta

← C2×#14543665 #17951247

Subgroups — C2×#14543665 #17951247

Order 4352.

1226 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763780C211yesmaximal, characteristic
2C2×C4×C22⋊#595C211yesmaximal, characteristic
3#14543665C214yesmaximal, direct product factor
4C2×#11762656C211yesmaximal, characteristic
5C22×#63243C412yescomplemented
6C22×C22⋊#595—21no—
7C22×C4×#595—21no—
8#11763780—21no—
9#11763780—21no—
10#11763780C412yescomplemented
11#11763780C2212yes—
12C2×#10587543—21no—
13C2×C22⋊#3624—21no—
14C4×C22⋊#595—21no—
15C4×C22⋊#595—21no—
16C4×C22⋊#595C412yescomplemented
17C4×C22⋊#595C2212yes—
18C2×(C2×#595)⋊C4C412yescomplemented
19C23×C4×D17C2211yescharacteristic
20C22×#63227—21no—
21C22×C4×Dic17—21no—
22#11762656—21no—
23#11762656—21no—
24#11762656C412yescomplemented
25#11762656C2212yes—
26C2×#10587502C411yescharacteristic, complemented
27C2×C17×#95C411yescharacteristic, complemented
28C24×D17D411yescharacteristic
29C23×#595—22no—
30C23×C4×C17—21no—
31C23×C4×C17C2×C411yescharacteristic
32C23×Dic17—21no—
33C23×Dic17D411yescharacteristic
34C22×C4×D17—44no—
35C22×C4×D17C2×C411yescharacteristic
36C22×C4×D17C2×C411yescharacteristic
37C22×C4×D17C2×C411yescharacteristic
38C22×C4×D17C2×C411yescharacteristic
39C22×C4×D17C2×C411yescharacteristic
40C22×C4×D17D411yescharacteristic
41C22×C4×D17D411yescharacteristic
42C22×C4×D17D411yescharacteristic
43C22×C4×D17D411yescharacteristic
44C22×C4×D17Q811yescharacteristic
45C22×C4×D17Q811yescharacteristic
46C22×C4×D17C2311yescharacteristic
47C2×C22⋊#595—24no—
48C2×C22⋊#595—24no—
49C2×C22⋊#595—22no—
50C2×C22⋊#595—22no—
51C22×#3624—22no—
52C2×C4×#595—22no—
53C2×C4×#595—22no—
54C2×C4×#595—44no—
55C2×#63243—22no—
56C2×#63243—44no—
57C2×#63243C2×C414yescomplemented
58C2×#63227—28no—
59C2×#63227—22no—
60C2×#63227—22no—
61C2×C4×Dic17—22no—
62C2×C4×Dic17—22no—
63C2×C4×Dic17—44no—
64C22⋊#3624—22no—
65C22⋊#3624—22no—
66(C2×#595)⋊C4—22no—
67(C2×#595)⋊C4C2×C414yescomplemented
68#10587543—22no—
69#10587543—22no—
70C17×#95—21no—
71C17×#95C2×C412yescomplemented
72#10587502—21no—
73#10587502C2×C412yescomplemented
74C24×C17C22⋊C411yescharacteristic
75C23×D17—22no—
76C23×D17—22no—
77C23×D17—24no—
78C23×D17—42no—
79C23×D17C22⋊C411yescharacteristic
80C23×D17C22⋊C411yescharacteristic
81C23×D17C22⋊C411yescharacteristic
82C23×D17C4⋊C411yescharacteristic
83C23×D17C4⋊C411yescharacteristic
84C23×D17C2×D411yescharacteristic
85C22×#595—28no—
86C22×#595—24no—
87C22×#595—44no—
88C22×#595—44no—
89C22×C4×C17—24no—
90C22×C4×C17—22no—
91C22×C4×C17—42no—
92C22×C4×C17—42no—
93C22×C4×C17—42no—
94C22×C4×C17C4211yescharacteristic
95C22×C4×C17C4211yescharacteristic
96C22×C4×C17C22⋊C411yescharacteristic
97C22×C4×C17C4⋊C411yescharacteristic
98C22×C4×C17C4⋊C411yescharacteristic
99C22×C4×C17C22×C411yescharacteristic
100C22×Dic17—24no—
101C22×Dic17—24no—
102C22×Dic17—22no—
103C22×Dic17—42no—
104C22×Dic17—42no—
105C22×Dic17C22⋊C411yescharacteristic
106C22×Dic17C22⋊C411yescharacteristic
107C22×Dic17C22⋊C411yescharacteristic
108C22×Dic17C4⋊C411yescharacteristic
109C22×Dic17C4⋊C411yescharacteristic
110C22×Dic17C2×D411yescharacteristic
111C2×C4×D17—24no—
112C2×C4×D17—24no—
113C2×C4×D17—42no—
114C2×C4×D17—42no—
115C2×C4×D17—42no—
116C2×C4×D17—42no—
117C2×C4×D17—42no—
118C2×C4×D17—42no—
119C2×C4×D17—42no—
120C2×C4×D17—42no—
121C2×C4×D17—42no—
122C2×C4×D17—42no—
123C2×C4×D17C4211yescharacteristic
124C2×C4×D17C4211yescharacteristic
125C2×C4×D17C22⋊C411yescharacteristic
126C2×C4×D17C22⋊C411yescharacteristic
127C2×C4×D17C22⋊C411yescharacteristic
128C2×C4×D17C22⋊C411yescharacteristic
129C2×C4×D17C4⋊C411yescharacteristic
130C2×C4×D17C4⋊C411yescharacteristic
131C2×C4×D17C4⋊C411yescharacteristic
132C2×C4×D17C4⋊C411yescharacteristic
133C2×C4×D17C4⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C22×C411yescharacteristic
136C2×C4×D17C22×C411yescharacteristic
137C2×C4×D17C2×D411yescharacteristic
138C2×C4×D17C2×Q811yescharacteristic
139C22⋊#595—28no—
140C22⋊#595—24no—
141C22⋊#595—24no—
142C2×#3624—24no—
143C2×#3624—44no—
144C4×#595—44no—
145C4×#595—44no—
146#63243—44no—
147#63243—44no—
148#63227—28no—
149#63227—28no—
150C4×Dic17—44no—
151C4×Dic17—44no—
152C2×#1297—171nomaximal, Sylow
153C23×C17—22no—
154C23×C17—22no—
155C23×C17#9511yescharacteristic
156C23×C17#9511yescharacteristic
157C23×C17#10412yes—
158C23×C17#10412yes—
159C23×C17C2×C22⋊C411yescharacteristic
160C22×D17—22no—
161C22×D17—22no—
162C22×D17—22no—
163C22×D17—22no—
164C22×D17—22no—
165C22×D17—22no—
166C22×D17—22no—
167C22×D17—21no—
168C22×D17—21no—
169C22×D17—21no—
170C22×D17—21no—
171C22×D17—22no—
172C22×D17—22no—
173C22×D17—22no—
174C22×D17—22no—
175C22×D17—41no—
176C22×D17—41no—
177C22×D17—41no—
178C22×D17—41no—
179C22×D17—48no—
180C22×D17—48no—
181C22×D17#9511yescharacteristic
182C22×D17#9511yescharacteristic
183C22×D17#10414yes—
184C22×D17C2×C22⋊C411yescharacteristic
185C22×D17C2×C4⋊C411yescharacteristic
186C2×#595—28no—
187C2×#595—44no—
188C2×#595—416no—
189C2×#595—44no—
190C2×C4×C17—22no—
191C2×C4×C17—22no—
192C2×C4×C17—24no—
193C2×C4×C17—41no—
194C2×C4×C17—41no—
195C2×C4×C17—41no—
196C2×C4×C17—41no—
197C2×C4×C17—48no—
198C2×C4×C17—42no—
199C2×C4×C17—42no—
200C2×C4×C17#9511yescharacteristic
201C2×C4×C17#9511yescharacteristic
202C2×C4×C17C2×C4211yescharacteristic
203C2×C4×C17C2×C4⋊C411yescharacteristic
204C2×Dic17—22no—
205C2×Dic17—22no—
206C2×Dic17—22no—
207C2×Dic17—22no—
208C2×Dic17—22no—
209C2×Dic17—24no—
210C2×Dic17—48no—
211C2×Dic17—42no—
212C2×Dic17—42no—
213C2×Dic17#9511yescharacteristic
214C2×Dic17#9511yescharacteristic
215C2×Dic17#9914yes—
216C2×Dic17C2×C22⋊C411yescharacteristic
217C2×Dic17C2×C4⋊C411yescharacteristic
218C4×D17—22no—
219C4×D17—22no—
220C4×D17—22no—
221C4×D17—22no—
222C4×D17—22no—
223C4×D17—22no—
224C4×D17—22no—
225C4×D17—22no—
226C4×D17—41no—
227C4×D17—41no—
228C4×D17—41no—
229C4×D17—41no—
230C4×D17—41no—
231C4×D17—41no—
232C4×D17—41no—
233C4×D17—41no—
234#3624—44no—
235C2×#407—171no—
236C2×C4×C22⋊C4—171no—
237C2×C4×C22⋊C4—171no—
238#1297—174no—
239C22×C17—24no—
240C22×C17—24no—
241C22×C17—21no—
242C22×C17—21no—
243C22×C17—21no—
244C22×C17—21no—
245C22×C17#33912yes—
246C22×C17#33912yes—
247C22×C17#33912yes—
248C22×C17#34212yes—
249C22×C17C2×#9511yescharacteristic
250C22×C17C2×#10411yescharacteristic
251C22×C17C2×#10411yescharacteristic
252C2×D17—28no—
253C2×D17—21no—
254C2×D17—21no—
255C2×D17—21no—
256C2×D17—21no—
257C2×D17—21no—
258C2×D17—21no—
259C2×D17—21no—
260C2×D17—21no—
261C2×D17—21no—
262C2×D17—21no—
263C2×D17—42no—
264C2×D17—42no—
265C2×D17—44no—
266C2×D17—42no—
267C2×D17—42no—
268C2×D17—44no—
269C2×D17—44no—
270C2×D17#33912yes—
271C2×D17C2×#10412yes—
272#595—48no—
273C4×C17—21no—
274C4×C17—21no—
275C4×C17—21no—
276C4×C17—21no—
277C4×C17—44no—
278Dic17—21no—
279Dic17—21no—
280Dic17—44no—
281Dic17#34212yes—
282Dic17C2×#9912yes—
283C24×C4—171no—
284C22×M16—172no—
285C22×C22⋊C4—341no—
286C22×C22⋊C4—341no—
287C22×C42—341no—
288C22×C42—341no—
289#407—172no—
290#407—172no—
291#407—341no—
292#407—341no—
293C2×C22⋊C8—341no—
294C2×C22⋊C8—341no—
295C4×C22⋊C4—172no—
296C4×C22⋊C4—172no—
297C4×C22⋊C4—172no—
298C4×C22⋊C4—172no—
299C4×C22⋊C4—341no—
300C4×C22⋊C4—341no—
301C4×C22⋊C4—341no—
302C4×C22⋊C4—341no—
303C2×#95—172no—
304C2×#95—171no—
305C2×#95#59511yescharacteristic, complemented
306C2×C17—21no—
307C2×C17—21no—
308C2×C17—22no—
309C2×C17#129714yescomplemented
310C2×C17C2×#33911yescharacteristic
311C2×C17C2×#33911yescharacteristic
312C2×C17C2×#34211yescharacteristic
313D17—22no—
314D17—22no—
315D17—41no—
316D17—41no—
317C25—171no—
318C23×C4—21no—
319C23×C4—171no—
320C23×C4—171no—
321C23×C4—171no—
322C23×C4—171no—
323C23×C4—171no—
324C23×C4—171no—
325C23×C4—171no—
326C23×C4—171no—
327C23×C4—171no—
328C23×C4—171no—
329C23×C4—171no—
330C23×C4—171no—
331C23×C4—171no—
332C23×C4—342no—
333C23×C4—341no—
334C23×C4—684no—
335C23×C4C2×#59511yescharacteristic
336C2×M16—174no—
337C2×M16—342no—
338C2×M16—684no—
339C22×C8—342no—
340C2×C22⋊C4—342no—
341C2×C22⋊C4—342no—
342C2×C22⋊C4—348no—
343C2×C22⋊C4—342no—
344C2×C22⋊C4—342no—
345C2×C22⋊C4—344no—
346C2×C22⋊C4—344no—
347C2×C42—342no—
348C2×C42—342no—
349C2×C42—342no—
350C2×C42—342no—
351C2×C42—684no—
352C2×C42—684no—
353C22⋊C8—342no—
354C22⋊C8—342no—
355C22⋊C8—342no—
356C22⋊C8—342no—
357#95—21no—
358#95—174no—
359#95—172no—
360#95—342no—
361#95—341no—
362#95C2×#59512yescomplemented
363C17C2×#129711yescharacteristic, complemented, Sylow
364C24—171no—
365C24—171no—
366C24—171no—
367C24—171no—
368C24—171no—
369C24—171no—
370C24—344no—
371C24—342no—
372C24—342no—
373C24—682no—
374C24C22⋊#59511yescharacteristic
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—171no—
381C22×C4—171no—
382C22×C4—171no—
383C22×C4—171no—
384C22×C4—171no—
385C22×C4—171no—
386C22×C4—171no—
387C22×C4—171no—
388C22×C4—171no—
389C22×C4—171no—
390C22×C4—171no—
391C22×C4—171no—
392C22×C4—171no—
393C22×C4—171no—
394C22×C4—171no—
395C22×C4—171no—
396C22×C4—171no—
397C22×C4—171no—
398C22×C4—171no—
399C22×C4—171no—
400C22×C4—171no—
401C22×C4—171no—
402C22×C4—344no—
403C22×C4—344no—
404C22×C4—344no—
405C22×C4—344no—
406C22×C4—344no—
407C22×C4—348no—
408C22×C4—342no—
409C22×C4—682no—
410C22×C4—682no—
411C22×C4—682no—
412C22×C4—682no—
413C22×C4—682no—
414C22×C4—682no—
415C22×C4—682no—
416C22×C4—682no—
417C22×C4—682no—
418C22×C4—682no—
419C22×C4—682no—
420C22×C4—684no—
421C22×C4—684no—
422C22×C4—682no—
423C22×C4C4×#59511yescharacteristic
424C22×C4C4×#59511yescharacteristic
425C22×C4C4⋊#59511yescharacteristic
426C22×C4C4⋊#59511yescharacteristic
427C22×C4C22⋊#59511yescharacteristic
428C22×C4C22×#59511yescharacteristic
429M16—684no—
430M16—684no—
431C2×C8—344no—
432C2×C8—684no—
433C22⋊C4—348no—
434C22⋊C4—348no—
435C22⋊C4—344no—
436C22⋊C4—344no—
437C22⋊C4—348no—
438C42—684no—
439C42—684no—
440C42—684no—
441C42—684no—
442C23—22no—
443C23—22no—
444C23—171no—
445C23—171no—
446C23—174no—
447C23—171no—
448C23—171no—
449C23—342no—
450C23—342no—
451C23—342no—
452C23—342no—
453C23—342no—
454C23—342no—
455C23—341no—
456C23—341no—
457C23—341no—
458C23—341no—
459C23—342no—
460C23—342no—
461C23—342no—
462C23—342no—
463C23—342no—
464C23—681no—
465C23—681no—
466C23—681no—
467C23—681no—
468C23—688no—
469C23—688no—
470C23(C2×#595)⋊C411yescharacteristic
471C23(C2×#595)⋊C411yescharacteristic
472C23#1058754812yes—
473C23#1058755012yes—
474C23C2×C22⋊#59511yescharacteristic
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—48no—
484C2×C4—42no—
485C2×C4—171no—
486C2×C4—171no—
487C2×C4—174no—
488C2×C4—171no—
489C2×C4—171no—
490C2×C4—342no—
491C2×C4—342no—
492C2×C4—342no—
493C2×C4—342no—
494C2×C4—342no—
495C2×C4—342no—
496C2×C4—342no—
497C2×C4—342no—
498C2×C4—342no—
499C2×C4—342no—
500C2×C4—342no—
501C2×C4—342no—
502C2×C4—342no—
503C2×C4—344no—
504C2×C4—348no—
505C2×C4—681no—
506C2×C4—681no—
507C2×C4—681no—
508C2×C4—681no—
509C2×C4—681no—
510C2×C4—681no—
511C2×C4—681no—
512C2×C4—681no—
513C2×C4—682no—
514C2×C4—688no—
515C2×C4—684no—
516C2×C4—684no—
517C2×C4—6816no—
518C2×C4—682no—
519C2×C4(C2×#595)⋊C411yescharacteristic
520C2×C4(C2×#595)⋊C411yescharacteristic
521C2×C4C2×C4×#59511yescharacteristic
522C2×C4C2×C4⋊#59511yescharacteristic
523C8—684no—
524C22—24no—
525C22—24no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—172no—
531C22—172no—
532C22—348no—
533C22—341no—
534C22—341no—
535C22—341no—
536C22—341no—
537C22—341no—
538C22—341no—
539C22—341no—
540C22—341no—
541C22—341no—
542C22—341no—
543C22—682no—
544C22—682no—
545C22—682no—
546C22—682no—
547C22—684no—
548C22—684no—
549C22—684no—
550C22#1176367912yes—
551C22#1176367912yes—
552C22#1176368012yes—
553C22#1176368612yes—
554C22C2×(C2×#595)⋊C411yescharacteristic
555C22C2×#1058754811yescharacteristic
556C22C2×#1058755011yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—44no—
562C4—172no—
563C4—172no—
564C4—341no—
565C4—341no—
566C4—684no—
567C4—688no—
568C2—21no—
569C2—21no—
570C2—22no—
571C2—342no—
572C2—342no—
573C2—681no—
574C2—681no—
575C2#1454366514yesdirect product factor
576C2C2×#1176367911yescharacteristic
577C2C2×#1176368011yescharacteristic
578C2C2×#1176368611yescharacteristic
subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC2×C17×#95C4
socleC23×C17#95
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC2×#95#595
hypocenterC17C2×#1297
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #14543665C2direct (N × H)
5. C22×#63243C4semidirect
10. #11763780C4semidirect
16. C4×C22⋊#595C4semidirect
18. C2×(C2×#595)⋊C4C4semidirect
24. #11762656C4semidirect
26. C2×#10587502C4semidirect
27. C2×C17×#95C4semidirect
57. C2×#63243C2×C4semidirect
67. (C2×#595)⋊C4C2×C4semidirect
71. C17×#95C2×C4semidirect
73. #10587502C2×C4semidirect
305. C2×#95#595semidirect
309. C2×C17#1297semidirect
362. #95C2×#595semidirect
363. C17C2×#1297semidirect
575. C2#14543665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637802
C2×C4×C22⋊#5952
#145436652
C2×#117626562
C2×#129717