Finite Group Databasebeta

← C2×#14543684 #17951553

Subgroups — C2×#14543684 #17951553

Order 4352.

986 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763780C211yesmaximal, characteristic
2C2×#11763751C211yesmaximal, characteristic
3#14543684C214yesmaximal, direct product factor
4C2×#11762772C211yesmaximal, characteristic
5C22×#63243—21no—
6C22×C4⋊#595—21no—
7C22×C22⋊#595C412yes—
8#11763780—21no—
9#11763780—21no—
10#11763780C412yescomplemented
11#11763780C2212yes—
12C2×#10587543—21no—
13C2×C22⋊#3624C412yescomplemented
14#11763751—21no—
15#11763751—21no—
16#11763751C412yes—
17#11763751C2212yes—
18C2×(C2×#595)⋊C4—21no—
19C23×C4×D17C2211yescharacteristic
20C22×#63223C411yescharacteristic, complemented
21#11762772—21no—
22#11762772—21no—
23#11762772C412yescomplemented
24#11762772C2212yes—
25C2×#10587491—21no—
26C2×#10587491—21no—
27C22×M16×C17C411yescharacteristic, complemented
28C24×D17C2×C411yescharacteristic
29C23×#595—22no—
30C23×C4×C17C2×C411yescharacteristic
31C23×Dic17C2×C411yescharacteristic
32C22×C4×D17—42no—
33C22×C4×D17—42no—
34C22×C4×D17C2×C411yescharacteristic
35C22×C4×D17C2×C411yescharacteristic
36C22×C4×D17C2×C411yescharacteristic
37C22×C4×D17D411yescharacteristic
38C22×C4×D17D411yescharacteristic
39C22×C4×D17D411yescharacteristic
40C22×C4×D17D411yescharacteristic
41C22×C4×D17D411yescharacteristic
42C22×C4×D17D411yescharacteristic
43C22×C4×D17Q811yescharacteristic
44C22×C4×D17Q811yescharacteristic
45C22×C4×D17C2311yescharacteristic
46C2×C22⋊#595—22no—
47C2×C22⋊#595—44no—
48C2×C22⋊#595C2×C414yes—
49C22×#3624—22no—
50C2×C4⋊#595—22no—
51C2×C4⋊#595—22no—
52C2×C4⋊#595—42no—
53C2×C4⋊#595—42no—
54C2×#63243—22no—
55C2×#63243—22no—
56C2×#63243—42no—
57C2×#63243—42no—
58C2×M16×C17—21no—
59C2×M16×C17—42no—
60C2×M16×C17C2×C412yescomplemented
61C22×C8×C17—21no—
62C2×#63223—21no—
63C2×#63223—42no—
64C2×#63223C2×C412yescomplemented
65C22×#3622—21no—
66C22⋊#3624—22no—
67C22⋊#3624C2×C414yescomplemented
68(C2×#595)⋊C4—22no—
69(C2×#595)⋊C4—22no—
70#10587543—22no—
71#10587543—22no—
72#10587491—22no—
73#10587491—22no—
74#10587491—22no—
75#10587491—22no—
76C24×C17C4211yescharacteristic
77C23×D17—22no—
78C23×D17—22no—
79C23×D17—42no—
80C23×D17—42no—
81C23×D17C4211yescharacteristic
82C23×D17C22⋊C411yescharacteristic
83C23×D17C22⋊C411yescharacteristic
84C23×D17C4⋊C411yescharacteristic
85C23×D17C4⋊C411yescharacteristic
86C23×D17C22×C411yescharacteristic
87C22×#595—24no—
88C22×#595—44no—
89C22×#595—44no—
90C22×#595—44no—
91C22×C4×C17—22no—
92C22×C4×C17—22no—
93C22×C4×C17C4211yescharacteristic
94C22×C4×C17C22⋊C411yescharacteristic
95C22×C4×C17C22⋊C411yescharacteristic
96C22×C4×C17C4⋊C411yescharacteristic
97C22×C4×C17C4⋊C411yescharacteristic
98C22×C4×C17C22×C411yescharacteristic
99C22×Dic17—42no—
100C22×Dic17C4211yescharacteristic
101C22×Dic17C22⋊C411yescharacteristic
102C22×Dic17C22⋊C411yescharacteristic
103C22×Dic17C4⋊C411yescharacteristic
104C22×Dic17C4⋊C411yescharacteristic
105C22×Dic17C22×C411yescharacteristic
106C2×C4×D17—22no—
107C2×C4×D17—22no—
108C2×C4×D17—22no—
109C2×C4×D17—22no—
110C2×C4×D17—42no—
111C2×C4×D17—42no—
112C2×C4×D17—41no—
113C2×C4×D17—41no—
114C2×C4×D17—42no—
115C2×C4×D17—41no—
116C2×C4×D17—41no—
117C2×C4×D17—41no—
118C2×C4×D17—41no—
119C2×C4×D17—42no—
120C2×C4×D17—41no—
121C2×C4×D17—41no—
122C2×C4×D17—42no—
123C2×C4×D17—42no—
124C2×C4×D17C22⋊C411yescharacteristic
125C2×C4×D17C22⋊C411yescharacteristic
126C2×C4×D17C22⋊C411yescharacteristic
127C2×C4×D17C22⋊C411yescharacteristic
128C2×C4×D17C22⋊C411yescharacteristic
129C2×C4×D17C22⋊C411yescharacteristic
130C2×C4×D17C4⋊C411yescharacteristic
131C2×C4×D17C4⋊C411yescharacteristic
132C2×C4×D17C4⋊C411yescharacteristic
133C2×C4×D17C4⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C4⋊C411yescharacteristic
136C2×C4×D17C2×D411yescharacteristic
137C2×C4×D17C2×D411yescharacteristic
138C2×C4×D17C2×D411yescharacteristic
139C2×C4×D17C2×Q811yescharacteristic
140C22⋊#595—44no—
141C22⋊#595—44no—
142C2×#3624—24no—
143C2×#3624—44no—
144C4⋊#595—44no—
145C4⋊#595—42no—
146C4⋊#595—42no—
147#63243—44no—
148#63243—42no—
149#63243—42no—
150M16×C17—42no—
151M16×C17—42no—
152C2×C8×C17—22no—
153C2×C8×C17—42no—
154#63223—42no—
155#63223—42no—
156C2×#3622—22no—
157C2×#3622—42no—
158C2×#1305—171nomaximal, Sylow
159C23×C17—22no—
160C23×C17—22no—
161C23×C17—22no—
162C23×C17#9511yescharacteristic
163C23×C17#9511yescharacteristic
164C23×C17C2×C4211yescharacteristic
165C22×D17—22no—
166C22×D17—22no—
167C22×D17—22no—
168C22×D17—22no—
169C22×D17—22no—
170C22×D17—22no—
171C22×D17—22no—
172C22×D17—21no—
173C22×D17—21no—
174C22×D17—21no—
175C22×D17—21no—
176C22×D17—41no—
177C22×D17—41no—
178C22×D17—41no—
179C22×D17—41no—
180C22×D17—41no—
181C22×D17—41no—
182C22×D17—41no—
183C22×D17—41no—
184C22×D17—48no—
185C22×D17—48no—
186C22×D17#9511yescharacteristic
187C22×D17#9511yescharacteristic
188C22×D17#10012yes—
189C22×D17#10112yes—
190C22×D17C2×C22⋊C411yescharacteristic
191C22×D17C2×C4⋊C411yescharacteristic
192C2×#595—44no—
193C2×#595—44no—
194C2×#595—44no—
195C2×#595—88no—
196C2×C4×C17—22no—
197C2×C4×C17—22no—
198C2×C4×C17—22no—
199C2×C4×C17—21no—
200C2×C4×C17—21no—
201C2×C4×C17—21no—
202C2×C4×C17—21no—
203C2×C4×C17#9511yescharacteristic
204C2×C4×C17#9511yescharacteristic
205C2×C4×C17#9912yes—
206C2×C4×C17#9912yes—
207C2×C4×C17C2×C22⋊C411yescharacteristic
208C2×C4×C17C2×C4⋊C411yescharacteristic
209C2×Dic17—22no—
210C2×Dic17—22no—
211C2×Dic17—41no—
212C2×Dic17—41no—
213C2×Dic17—41no—
214C2×Dic17—41no—
215C2×Dic17#9511yescharacteristic
216C2×Dic17#9511yescharacteristic
217C2×Dic17C2×C22⋊C411yescharacteristic
218C2×Dic17C2×C4⋊C411yescharacteristic
219C4×D17—22no—
220C4×D17—22no—
221C4×D17—22no—
222C4×D17—22no—
223C4×D17—21no—
224C4×D17—21no—
225C4×D17—21no—
226C4×D17—21no—
227C4×D17—21no—
228C4×D17—21no—
229C4×D17—21no—
230C4×D17—21no—
231C4×D17—41no—
232C4×D17—41no—
233C4×D17—41no—
234C4×D17—41no—
235C4×D17—41no—
236C4×D17—41no—
237C4×D17—41no—
238C4×D17—41no—
239#3624—44no—
240C8×C17—42no—
241#3622—42no—
242C2×#407—171no—
243C2×#407—171no—
244C2×#380—171no—
245#1305—174no—
246C22×C17—21no—
247C22×C17—21no—
248C22×C17—21no—
249C22×C17—21no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—44no—
253C22×C17#34212yes—
254C22×C17#34312yes—
255C22×C17#34412yes—
256C22×C17C2×#9511yescharacteristic
257C2×D17—24no—
258C2×D17—24no—
259C2×D17—21no—
260C2×D17—21no—
261C2×D17—21no—
262C2×D17—21no—
263C2×D17—21no—
264C2×D17—21no—
265C2×D17—21no—
266C2×D17—21no—
267C2×D17—21no—
268C2×D17—21no—
269C2×D17—42no—
270C2×D17—42no—
271C2×D17—44no—
272C2×D17—44no—
273C2×D17—42no—
274C2×D17—42no—
275C2×D17—44no—
276C2×D17#34312yes—
277C2×D17C2×#10011yescharacteristic
278C2×D17C2×#10111yescharacteristic
279#595—84no—
280C4×C17—21no—
281C4×C17—21no—
282C4×C17#34212yes—
283C4×C17C2×#9911yescharacteristic
284C4×C17C2×#9911yescharacteristic
285Dic17—21no—
286Dic17—21no—
287Dic17—21no—
288Dic17—21no—
289C24×C4—171no—
290C22×M16—171no—
291C22×M16—341no—
292C22×M16#59511yescharacteristic, complemented
293C22×C4⋊C4—341no—
294C22×C22⋊C4—172no—
295#407—172no—
296#407—172no—
297#407—172no—
298#407—172no—
299#407—341no—
300#407—341no—
301#407—341no—
302#407—341no—
303C2×C22⋊C8—172no—
304C2×C22⋊C8—341no—
305C2×C22⋊C8—341no—
306C2×C22⋊C8—341no—
307#380—172no—
308#380—172no—
309#380—341no—
310#380—341no—
311C2×#95—341no—
312C2×C17—41no—
313C2×C17—41no—
314C2×C17#130514yescomplemented
315C2×C17C2×#34211yescharacteristic
316C2×C17C2×#34311yescharacteristic
317C2×C17C2×#34411yescharacteristic
318D17—21no—
319D17—22no—
320D17—21no—
321D17—41no—
322D17—41no—
323C25—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—171no—
333C23×C4—171no—
334C23×C4—171no—
335C23×C4—171no—
336C23×C4—171no—
337C23×C4—342no—
338C23×C4—682no—
339C23×C4—682no—
340C23×C4C2×#59511yescharacteristic
341C2×M16—21no—
342C2×M16—42no—
343C2×M16—172no—
344C2×M16—342no—
345C2×M16—342no—
346C2×M16—341no—
347C2×M16—682no—
348C2×M16—682no—
349C2×M16—682no—
350C2×M16C2×#59512yescomplemented
351C22×C8—21no—
352C22×C8—342no—
353C22×C8—341no—
354C2×C4⋊C4—342no—
355C2×C4⋊C4—342no—
356C2×C4⋊C4—682no—
357C2×C4⋊C4—682no—
358C2×C22⋊C4—174no—
359C2×C22⋊C4—342no—
360C2×C22⋊C4—684no—
361C22⋊C8—174no—
362C22⋊C8—342no—
363C22⋊C8—342no—
364C22⋊C8—342no—
365C22⋊C8—342no—
366C22⋊C8—342no—
367C22⋊C8—342no—
368C22⋊C8—342no—
369#95—342no—
370#95—342no—
371C17C2×#130511yescharacteristic, complemented, Sylow
372C24—171no—
373C24—171no—
374C24—171no—
375C24—171no—
376C24—171no—
377C24—171no—
378C24—342no—
379C24—342no—
380C24—682no—
381C24—682no—
382C24C4×#59511yescharacteristic
383C22×C4—22no—
384C22×C4—22no—
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—171no—
403C22×C4—171no—
404C22×C4—171no—
405C22×C4—171no—
406C22×C4—171no—
407C22×C4—342no—
408C22×C4—342no—
409C22×C4—342no—
410C22×C4—342no—
411C22×C4—344no—
412C22×C4—681no—
413C22×C4—681no—
414C22×C4—681no—
415C22×C4—681no—
416C22×C4—681no—
417C22×C4—681no—
418C22×C4—681no—
419C22×C4—681no—
420C22×C4—682no—
421C22×C4—682no—
422C22×C4—682no—
423C22×C4—682no—
424C22×C4—682no—
425C22×C4—682no—
426C22×C4—682no—
427C22×C4—684no—
428C22×C4—684no—
429C22×C4—684no—
430C22×C4C4×#59511yescharacteristic
431C22×C4C4⋊#59511yescharacteristic
432C22×C4C4⋊#59511yescharacteristic
433C22×C4C22⋊#59511yescharacteristic
434C22×C4C22⋊#59511yescharacteristic
435C22×C4C22×#59511yescharacteristic
436M16—42no—
437M16—42no—
438M16—682no—
439M16—682no—
440M16—682no—
441M16—684no—
442M16—682no—
443C2×C8—22no—
444C2×C8—42no—
445C2×C8—344no—
446C2×C8—342no—
447C2×C8—684no—
448C2×C8—682no—
449C4⋊C4—682no—
450C4⋊C4—682no—
451C4⋊C4—684no—
452C22⋊C4—684no—
453C22⋊C4—684no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—171no—
458C23—171no—
459C23—172no—
460C23—172no—
461C23—171no—
462C23—171no—
463C23—341no—
464C23—341no—
465C23—342no—
466C23—341no—
467C23—342no—
468C23—341no—
469C23—342no—
470C23—342no—
471C23—342no—
472C23—342no—
473C23—342no—
474C23—681no—
475C23—681no—
476C23—681no—
477C23—681no—
478C23—681no—
479C23—681no—
480C23—681no—
481C23—681no—
482C23—688no—
483C23—688no—
484C23(C2×#595)⋊C411yescharacteristic
485C23(C2×#595)⋊C411yescharacteristic
486C23C2×C4×#59511yescharacteristic
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—171no—
495C2×C4—171no—
496C2×C4—171no—
497C2×C4—171no—
498C2×C4—342no—
499C2×C4—342no—
500C2×C4—341no—
501C2×C4—341no—
502C2×C4—341no—
503C2×C4—341no—
504C2×C4—341no—
505C2×C4—341no—
506C2×C4—341no—
507C2×C4—341no—
508C2×C4—342no—
509C2×C4—342no—
510C2×C4—342no—
511C2×C4—342no—
512C2×C4—681no—
513C2×C4—681no—
514C2×C4—681no—
515C2×C4—681no—
516C2×C4—681no—
517C2×C4—681no—
518C2×C4—681no—
519C2×C4—681no—
520C2×C4—681no—
521C2×C4—681no—
522C2×C4—681no—
523C2×C4—681no—
524C2×C4—684no—
525C2×C4—684no—
526C2×C4—684no—
527C2×C4—1368no—
528C2×C4#1058753912yes—
529C2×C4(C2×#595)⋊C411yescharacteristic
530C2×C4(C2×#595)⋊C411yescharacteristic
531C2×C4#1058755112yes—
532C2×C4C2×C4⋊#59511yescharacteristic
533C2×C4C2×C22⋊#59511yescharacteristic
534C8—42no—
535C8—684no—
536C8—682no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—44no—
544C22—171no—
545C22—172no—
546C22—171no—
547C22—344no—
548C22—344no—
549C22—341no—
550C22—341no—
551C22—341no—
552C22—341no—
553C22—341no—
554C22—341no—
555C22—341no—
556C22—341no—
557C22—341no—
558C22—341no—
559C22—682no—
560C22—682no—
561C22—684no—
562C22—682no—
563C22—684no—
564C22—682no—
565C22—684no—
566C22#1176368712yes—
567C22#1176368812yes—
568C22#1176369212yes—
569C22C2×(C2×#595)⋊C411yescharacteristic
570C4—21no—
571C4—21no—
572C4—341no—
573C4—341no—
574C4—341no—
575C4—341no—
576C4—1364no—
577C4#1176368712yes—
578C4C2×#1058755111yescharacteristic
579C4C2×#1058753911yescharacteristic
580C2—41no—
581C2—41no—
582C2—341no—
583C2—342no—
584C2—341no—
585C2—681no—
586C2—681no—
587C2#1454368414yesdirect product factor
588C2C2×#1176368711yescharacteristic
589C2C2×#1176368811yescharacteristic
590C2C2×#1176369211yescharacteristic
subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC23×C17C2×C42
FrattiniC22×C4C22×#595
FittingC22×M16×C17C4
socleC23×C17#95
prime radicalC24×D17C2×C4
cosocleC22×C4×D17C23
hypercenterC22×M16#595
hypocenterC17C2×#1305
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #14543684C2direct (N × H)
10. #11763780C4semidirect
13. C2×C22⋊#3624C4semidirect
20. C22×#63223C4semidirect
23. #11762772C4semidirect
27. C22×M16×C17C4semidirect
60. C2×M16×C17C2×C4semidirect
64. C2×#63223C2×C4semidirect
67. C22⋊#3624C2×C4semidirect
292. C22×M16#595semidirect
314. C2×C17#1305semidirect
350. C2×M16C2×#595semidirect
371. C17C2×#1305semidirect
587. C2#14543684direct (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×#117637512
#145436842
C2×#117627722
C2×#130517