Finite Group Databasebeta

← C2×#14543632 #17950711

Subgroups — C2×#14543632 #17950711

Order 4352.

1118 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763781C211yesmaximal, characteristic
2C2×#11763752C211yesmaximal, characteristic
3#14543632C214yesmaximal, direct product factor
4C2×C4×#63227C211yesmaximal, characteristic
5C22×#63247—21no—
6C22×C22⋊#595—21no—
7#11763781—21no—
8#11763781—21no—
9#11763781C412yescomplemented
10#11763781C2212yes—
11C2×#10587543—21no—
12C2×#10587543C412yescomplemented
13#11763752—21no—
14#11763752—21no—
15#11763752C412yescomplemented
16#11763752C2212yes—
17C2×(C2×#595)⋊C4—21no—
18C2×(C2×#595)⋊C4C412yescomplemented
19C23×C4×D17C2211yescharacteristic
20C22×#63227—21no—
21C22×C4×Dic17C411yescharacteristic, complemented
22C4×#63227—21no—
23C4×#63227—21no—
24C4×#63227C412yescomplemented
25C4×#63227C2212yes—
26C2×#10587502—21no—
27C22×C42×C17C411yescharacteristic, complemented
28C24×D17D411yescharacteristic
29C23×#595—22no—
30C23×C4×C17—21no—
31C23×C4×C17C2×C411yescharacteristic
32C23×Dic17—21no—
33C23×Dic17D411yescharacteristic
34C22×C4×D17—42no—
35C22×C4×D17—42no—
36C22×C4×D17C2×C411yescharacteristic
37C22×C4×D17C2×C411yescharacteristic
38C22×C4×D17C2×C411yescharacteristic
39C22×C4×D17C2×C411yescharacteristic
40C22×C4×D17C2×C411yescharacteristic
41C22×C4×D17D411yescharacteristic
42C22×C4×D17D411yescharacteristic
43C22×C4×D17D411yescharacteristic
44C22×C4×D17D411yescharacteristic
45C22×C4×D17Q811yescharacteristic
46C22×C4×D17Q811yescharacteristic
47C22×C4×D17C2311yescharacteristic
48C2×C22⋊#595—22no—
49C2×C22⋊#595—22no—
50C2×C22⋊#595—42no—
51C2×C22⋊#595—42no—
52C2×#63247—22no—
53C2×#63247—22no—
54C2×#63247—42no—
55C2×#63247—42no—
56C22×#3624—22no—
57C2×C42×C17—21no—
58C2×C42×C17—42no—
59C2×C42×C17C2×C412yescomplemented
60C2×#63227—28no—
61C2×#63227—22no—
62C2×#63227—22no—
63C2×C4×Dic17—21no—
64C2×C4×Dic17—42no—
65C2×C4×Dic17C2×C412yescomplemented
66(C2×#595)⋊C4—22no—
67(C2×#595)⋊C4—22no—
68(C2×#595)⋊C4—22no—
69(C2×#595)⋊C4C2×C414yescomplemented
70#10587543—22no—
71#10587543—22no—
72#10587543—22no—
73#10587543C2×C414yescomplemented
74#10587502—22no—
75#10587502—22no—
76C24×C17C22⋊C411yescharacteristic
77C23×D17—22no—
78C23×D17—22no—
79C23×D17—24no—
80C23×D17—42no—
81C23×D17C22⋊C411yescharacteristic
82C23×D17C22⋊C411yescharacteristic
83C23×D17C22⋊C411yescharacteristic
84C23×D17C4⋊C411yescharacteristic
85C23×D17C4⋊C411yescharacteristic
86C23×D17C2×D411yescharacteristic
87C22×#595—24no—
88C22×#595—44no—
89C22×#595—44no—
90C22×#595—44no—
91C22×C4×C17—22no—
92C22×C4×C17—22no—
93C22×C4×C17—24no—
94C22×C4×C17—22no—
95C22×C4×C17—42no—
96C22×C4×C17—42no—
97C22×C4×C17C4211yescharacteristic
98C22×C4×C17C4211yescharacteristic
99C22×C4×C17C22⋊C411yescharacteristic
100C22×C4×C17C4⋊C411yescharacteristic
101C22×C4×C17C4⋊C411yescharacteristic
102C22×C4×C17C22×C411yescharacteristic
103C22×Dic17—22no—
104C22×Dic17—22no—
105C22×Dic17—24no—
106C22×Dic17—22no—
107C22×Dic17—42no—
108C22×Dic17—42no—
109C22×Dic17C22⋊C411yescharacteristic
110C22×Dic17C22⋊C411yescharacteristic
111C22×Dic17C22⋊C411yescharacteristic
112C22×Dic17C4⋊C411yescharacteristic
113C22×Dic17C4⋊C411yescharacteristic
114C22×Dic17C2×D411yescharacteristic
115C2×C4×D17—41no—
116C2×C4×D17—41no—
117C2×C4×D17—42no—
118C2×C4×D17—42no—
119C2×C4×D17—42no—
120C2×C4×D17—42no—
121C2×C4×D17—41no—
122C2×C4×D17—41no—
123C2×C4×D17—41no—
124C2×C4×D17—41no—
125C2×C4×D17—42no—
126C2×C4×D17—42no—
127C2×C4×D17—42no—
128C2×C4×D17—42no—
129C2×C4×D17—41no—
130C2×C4×D17—41no—
131C2×C4×D17C4211yescharacteristic
132C2×C4×D17C4211yescharacteristic
133C2×C4×D17C22⋊C411yescharacteristic
134C2×C4×D17C22⋊C411yescharacteristic
135C2×C4×D17C22⋊C411yescharacteristic
136C2×C4×D17C22⋊C411yescharacteristic
137C2×C4×D17C4⋊C411yescharacteristic
138C2×C4×D17C4⋊C411yescharacteristic
139C2×C4×D17C4⋊C411yescharacteristic
140C2×C4×D17C4⋊C411yescharacteristic
141C2×C4×D17C4⋊C411yescharacteristic
142C2×C4×D17C4⋊C411yescharacteristic
143C2×C4×D17C22×C411yescharacteristic
144C2×C4×D17C22×C411yescharacteristic
145C2×C4×D17C2×D411yescharacteristic
146C2×C4×D17C2×Q811yescharacteristic
147C22⋊#595—44no—
148C22⋊#595—42no—
149C22⋊#595—42no—
150#63247—44no—
151#63247—42no—
152#63247—42no—
153C2×#3624—24no—
154C2×#3624—44no—
155C42×C17—42no—
156C42×C17—42no—
157#63227—28no—
158#63227—28no—
159C4×Dic17—42no—
160C4×Dic17—42no—
161C2×#1284—171nomaximal, Sylow
162C23×C17—22no—
163C23×C17—22no—
164C23×C17#9511yescharacteristic
165C23×C17#9511yescharacteristic
166C23×C17#9912yes—
167C23×C17#9912yes—
168C23×C17C2×C22⋊C411yescharacteristic
169C22×D17—22no—
170C22×D17—22no—
171C22×D17—22no—
172C22×D17—22no—
173C22×D17—22no—
174C22×D17—22no—
175C22×D17—22no—
176C22×D17—21no—
177C22×D17—21no—
178C22×D17—21no—
179C22×D17—21no—
180C22×D17—22no—
181C22×D17—22no—
182C22×D17—22no—
183C22×D17—22no—
184C22×D17—41no—
185C22×D17—41no—
186C22×D17—41no—
187C22×D17—41no—
188C22×D17—48no—
189C22×D17—48no—
190C22×D17#9511yescharacteristic
191C22×D17#9511yescharacteristic
192C22×D17#10414yes—
193C22×D17C2×C22⋊C411yescharacteristic
194C22×D17C2×C4⋊C411yescharacteristic
195C2×#595—44no—
196C2×#595—44no—
197C2×#595—44no—
198C2×#595—88no—
199C2×C4×C17—22no—
200C2×C4×C17—22no—
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—21no—
204C2×C4×C17—21no—
205C2×C4×C17—21no—
206C2×C4×C17—21no—
207C2×C4×C17—24no—
208C2×C4×C17—48no—
209C2×C4×C17—42no—
210C2×C4×C17—42no—
211C2×C4×C17#9511yescharacteristic
212C2×C4×C17#9511yescharacteristic
213C2×C4×C17C2×C4211yescharacteristic
214C2×C4×C17C2×C4⋊C411yescharacteristic
215C2×Dic17—22no—
216C2×Dic17—22no—
217C2×Dic17—22no—
218C2×Dic17—22no—
219C2×Dic17—21no—
220C2×Dic17—21no—
221C2×Dic17—21no—
222C2×Dic17—21no—
223C2×Dic17—24no—
224C2×Dic17—48no—
225C2×Dic17—42no—
226C2×Dic17—42no—
227C2×Dic17#9511yescharacteristic
228C2×Dic17#9511yescharacteristic
229C2×Dic17C2×C22⋊C411yescharacteristic
230C2×Dic17C2×C4⋊C411yescharacteristic
231C4×D17—41no—
232C4×D17—41no—
233C4×D17—41no—
234C4×D17—41no—
235C4×D17—41no—
236C4×D17—41no—
237C4×D17—41no—
238C4×D17—41no—
239C4×D17—41no—
240C4×D17—41no—
241C4×D17—41no—
242C4×D17—41no—
243C4×D17—41no—
244C4×D17—41no—
245C4×D17—41no—
246C4×D17—41no—
247#3624—44no—
248C2×#407—171no—
249C2×#381—171no—
250C2×C4×C22⋊C4—171no—
251#1284—174no—
252C22×C17—24no—
253C22×C17—24no—
254C22×C17—21no—
255C22×C17—21no—
256C22×C17—21no—
257C22×C17—21no—
258C22×C17H(3,ℤ/4)12yes—
259C22×C17#33912yes—
260C22×C17#34212yes—
261C22×C17#34212yes—
262C22×C17C2×#9511yescharacteristic
263C22×C17C2×#9911yescharacteristic
264C22×C17C2×#9911yescharacteristic
265C2×D17—28no—
266C2×D17—21no—
267C2×D17—21no—
268C2×D17—21no—
269C2×D17—21no—
270C2×D17—21no—
271C2×D17—21no—
272C2×D17—21no—
273C2×D17—21no—
274C2×D17—21no—
275C2×D17—21no—
276C2×D17—42no—
277C2×D17—42no—
278C2×D17—44no—
279C2×D17—42no—
280C2×D17—42no—
281C2×D17—44no—
282C2×D17—44no—
283C2×D17#33912yes—
284C2×D17C2×#10412yes—
285#595—84no—
286C4×C17—21no—
287C4×C17—21no—
288C4×C17—21no—
289C4×C17—21no—
290C4×C17—44no—
291Dic17—21no—
292Dic17—21no—
293Dic17—21no—
294Dic17—21no—
295Dic17—44no—
296C24×C4—171no—
297C22×M16—341no—
298C22×C22⋊C4—341no—
299C22×C22⋊C4—341no—
300C22×C42—171no—
301C22×C42#59511yescharacteristic, complemented
302#407—172no—
303#407—172no—
304#407—341no—
305#407—341no—
306C2×C22⋊C8—172no—
307C2×C22⋊C8—341no—
308#381—172no—
309#381—172no—
310#381—341no—
311#381—341no—
312C4×C22⋊C4—172no—
313C4×C22⋊C4—172no—
314C4×C22⋊C4—341no—
315C4×C22⋊C4—341no—
316C2×#95—172no—
317C2×#95—341no—
318C2×#95—341no—
319C2×C17—21no—
320C2×C17—21no—
321C2×C17—22no—
322C2×C17#128414yescomplemented
323C2×C17C2×H(3,ℤ/4)11yescharacteristic
324C2×C17C2×#33911yescharacteristic
325C2×C17C2×#34211yescharacteristic
326D17—22no—
327D17—22no—
328D17—41no—
329D17—41no—
330C25—171no—
331C23×C4—21no—
332C23×C4—171no—
333C23×C4—171no—
334C23×C4—171no—
335C23×C4—171no—
336C23×C4—171no—
337C23×C4—171no—
338C23×C4—171no—
339C23×C4—171no—
340C23×C4—171no—
341C23×C4—171no—
342C23×C4—171no—
343C23×C4—171no—
344C23×C4—171no—
345C23×C4—341no—
346C23×C4—342no—
347C23×C4—682no—
348C23×C4—682no—
349C23×C4C2×#59511yescharacteristic
350C2×M16—342no—
351C2×M16—342no—
352C2×M16—682no—
353C2×M16—682no—
354C22×C8—342no—
355C2×C22⋊C4—342no—
356C2×C22⋊C4—342no—
357C2×C22⋊C4—348no—
358C2×C22⋊C4—342no—
359C2×C22⋊C4—342no—
360C2×C22⋊C4—682no—
361C2×C22⋊C4—682no—
362C2×C42—21no—
363C2×C42—42no—
364C2×C42—172no—
365C2×C42—341no—
366C2×C42—682no—
367C2×C42C2×#59512yescomplemented
368C22⋊C8—174no—
369C22⋊C8—342no—
370C22⋊C8—342no—
371C22⋊C8—342no—
372#95—174no—
373#95—342no—
374#95—342no—
375#95—342no—
376#95—342no—
377#95—342no—
378C17C2×#128411yescharacteristic, complemented, Sylow
379C24—171no—
380C24—171no—
381C24—171no—
382C24—171no—
383C24—171no—
384C24—171no—
385C24—344no—
386C24—342no—
387C24—342no—
388C24—682no—
389C24C22⋊#59511yescharacteristic
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—42no—
395C22×C4—42no—
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—171no—
408C22×C4—171no—
409C22×C4—171no—
410C22×C4—171no—
411C22×C4—171no—
412C22×C4—171no—
413C22×C4—171no—
414C22×C4—171no—
415C22×C4—171no—
416C22×C4—171no—
417C22×C4—171no—
418C22×C4—342no—
419C22×C4—342no—
420C22×C4—344no—
421C22×C4—342no—
422C22×C4—344no—
423C22×C4—681no—
424C22×C4—681no—
425C22×C4—681no—
426C22×C4—681no—
427C22×C4—681no—
428C22×C4—681no—
429C22×C4—681no—
430C22×C4—681no—
431C22×C4—682no—
432C22×C4—682no—
433C22×C4—682no—
434C22×C4—682no—
435C22×C4—682no—
436C22×C4—682no—
437C22×C4—682no—
438C22×C4—682no—
439C22×C4—682no—
440C22×C4—682no—
441C22×C4—684no—
442C22×C4—684no—
443C22×C4—684no—
444C22×C4C4×#59511yescharacteristic
445C22×C4C4×#59511yescharacteristic
446C22×C4C4⋊#59511yescharacteristic
447C22×C4C4⋊#59511yescharacteristic
448C22×C4C22⋊#59511yescharacteristic
449C22×C4C22×#59511yescharacteristic
450M16—682no—
451M16—682no—
452M16—684no—
453C2×C8—344no—
454C2×C8—684no—
455C22⋊C4—348no—
456C22⋊C4—348no—
457C22⋊C4—682no—
458C22⋊C4—682no—
459C22⋊C4—684no—
460C42—42no—
461C42—42no—
462C42—682no—
463C42—682no—
464C23—22no—
465C23—22no—
466C23—171no—
467C23—171no—
468C23—174no—
469C23—171no—
470C23—171no—
471C23—342no—
472C23—342no—
473C23—342no—
474C23—342no—
475C23—342no—
476C23—342no—
477C23—341no—
478C23—341no—
479C23—341no—
480C23—341no—
481C23—342no—
482C23—342no—
483C23—342no—
484C23—342no—
485C23—342no—
486C23—681no—
487C23—681no—
488C23—681no—
489C23—681no—
490C23—688no—
491C23—688no—
492C23#1058753912yes—
493C23(C2×#595)⋊C411yescharacteristic
494C23(C2×#595)⋊C411yescharacteristic
495C23#1058755112yes—
496C23C2×C22⋊#59511yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—48no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—171no—
510C2×C4—171no—
511C2×C4—171no—
512C2×C4—171no—
513C2×C4—341no—
514C2×C4—341no—
515C2×C4—341no—
516C2×C4—341no—
517C2×C4—342no—
518C2×C4—342no—
519C2×C4—342no—
520C2×C4—342no—
521C2×C4—344no—
522C2×C4—681no—
523C2×C4—681no—
524C2×C4—681no—
525C2×C4—681no—
526C2×C4—681no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4—681no—
530C2×C4—681no—
531C2×C4—681no—
532C2×C4—681no—
533C2×C4—681no—
534C2×C4—681no—
535C2×C4—681no—
536C2×C4—681no—
537C2×C4—681no—
538C2×C4—688no—
539C2×C4—682no—
540C2×C4—682no—
541C2×C4—684no—
542C2×C4—684no—
543C2×C4—684no—
544C2×C4—1368no—
545C2×C4(C2×#595)⋊C411yescharacteristic
546C2×C4(C2×#595)⋊C411yescharacteristic
547C2×C4C2×C4×#59511yescharacteristic
548C2×C4C2×C4⋊#59511yescharacteristic
549C8—684no—
550C22—24no—
551C22—24no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—172no—
557C22—172no—
558C22—348no—
559C22—341no—
560C22—341no—
561C22—341no—
562C22—341no—
563C22—341no—
564C22—341no—
565C22—341no—
566C22—341no—
567C22—341no—
568C22—341no—
569C22—682no—
570C22—682no—
571C22—682no—
572C22—682no—
573C22—684no—
574C22—684no—
575C22—684no—
576C22#1176367612yes—
577C22#1176368012yes—
578C22#1176368712yes—
579C22#1176368712yes—
580C22C2×(C2×#595)⋊C411yescharacteristic
581C22C2×#1058755111yescharacteristic
582C22C2×#1058753911yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—44no—
588C4—341no—
589C4—341no—
590C4—341no—
591C4—341no—
592C4—684no—
593C4—1364no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—342no—
598C2—342no—
599C2—681no—
600C2—681no—
601C2#1454363214yesdirect product factor
602C2C2×#1176367611yescharacteristic
603C2C2×#1176368011yescharacteristic
604C2C2×#1176368711yescharacteristic
subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC23×C17#95
prime radicalC24×D17D4
cosocleC22×C4×D17C23
hypercenterC22×C42#595
hypocenterC17C2×#1284
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
3. #14543632C2direct (N × H)
9. #11763781C4semidirect
12. C2×#10587543C4semidirect
15. #11763752C4semidirect
18. C2×(C2×#595)⋊C4C4semidirect
21. C22×C4×Dic17C4semidirect
24. C4×#63227C4semidirect
27. C22×C42×C17C4semidirect
59. C2×C42×C17C2×C4semidirect
65. C2×C4×Dic17C2×C4semidirect
69. (C2×#595)⋊C4C2×C4semidirect
73. #10587543C2×C4semidirect
301. C22×C42#595semidirect
322. C2×C17#1284semidirect
367. C2×C42C2×#595semidirect
378. C17C2×#1284semidirect
601. C2#14543632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637812
C2×#117637522
#145436322
C2×C4×#632272
C2×#128417