Finite Group Databasebeta

← C2×D17⋊#328 #17965208

Subgroups — C2×D17⋊#328 #17965208

Order 4352.

1846 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763777C211yesmaximal, characteristic
2C22×(C2×#595)⋊C4C211yesmaximal, characteristic
3C2×#11763663C212yesmaximal, complemented
4D17⋊#328C218yesmaximal, direct product factor
5C2×#11763662C212yesmaximal, complemented
6C2×C22⋊Q8×D17C211yesmaximal, characteristic
7C24×#595—21no—
8C22×#63242—21no—
9C2×#10587543C2212yes—
10#11763777—22no—
11#11763777C2214yes—
12C2×C22⋊#3624—21no—
13C2×(C2×#595)⋊C4—22no—
14C2×(C2×#595)⋊C4—21no—
15C2×(C2×#595)⋊C4C2212yes—
16C2×(C2×#595)⋊C4C2214yes—
17#11763663C2218yescomplemented
18#11763662C2218yescomplemented
19C22×Q8×D17C411yescharacteristic, complemented
20C23×C4×D17C2211yescharacteristic
21C2×#10587583C2211yescharacteristic
22C2×#10587610C411yescharacteristic, complemented
23C2×#10587582—21no—
24C2×#10587564—21no—
25C2×#10587632C2211yescharacteristic
26C22⋊Q8×D17—22no—
27C22⋊Q8×D17—22no—
28C22⋊Q8×D17C414yescomplemented
29C22⋊Q8×D17C2214yes—
30C2×C4⋊C4×D17—21no—
31C2×C4⋊C4×D17C411yescharacteristic, complemented
32C2×C22⋊C4×D17—21no—
33C2×C17×C22⋊Q8C411yescharacteristic, complemented
34C24×D17D411yescharacteristic
35C23×#595—28no—
36C23×#595—24no—
37C23×#595—22no—
38C23×#595—44no—
39C23×#595—44no—
40C22×Q8×C17C2×C411yescharacteristic, complemented
41C23×C4×C17C2×C411yescharacteristic
42C23×Dic17D411yescharacteristic
43C2×Q8×D17—22no—
44C2×Q8×D17—44no—
45C2×Q8×D17C2×C414yescomplemented
46C22×C4×D17—21no—
47C22×C4×D17—21no—
48C22×C4×D17—44no—
49C22×C4×D17C2×C411yescharacteristic
50C22×C4×D17C2×C412yes—
51C22×C4×D17D411yescharacteristic
52C22×C4×D17D412yes—
53C22×C4×D17D411yescharacteristic
54C22×C4×D17D412yes—
55C22×C4×D17C2312yes—
56C22×C4×D17C2311yescharacteristic
57C22×Dic34—21no—
58C22×Dic34C2×C411yescharacteristic, complemented
59C22×#3624—22no—
60C2×#63242—24no—
61C2×#63242—44no—
62C17×C22⋊Q8—22no—
63C17×C22⋊Q8C2×C414yescomplemented
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
66C2×C22⋊C4×C17—21no—
67C2×C22⋊Dic17—21no—
68#10587632—21no—
69#10587632—21no—
70#10587632C2×C412yescomplemented
71#10587632C2312yes—
72C2×#63227—21no—
73C2×#63227—21no—
74C2×C4⋊Dic17—21no—
75C2×C4⋊Dic17C2×C411yescharacteristic, complemented
76#10587610—22no—
77#10587610C2×C414yescomplemented
78C2×#63225—21no—
79C2×#63225—21no—
80C2×#63225—21no—
81#10587583—21no—
82#10587583—21no—
83#10587583C2×C412yescomplemented
84#10587583C2312yes—
85#10587582—24no—
86#10587582—24no—
87C4⋊C4×D17—24no—
88C4⋊C4×D17—22no—
89C4⋊C4×D17—24no—
90C4⋊C4×D17C2×C414yescomplemented
91C22⋊C4×D17—24no—
92C22⋊C4×D17—24no—
93#10587564—24no—
94#10587564—24no—
95C22⋊#3624—24no—
96(C2×#595)⋊C4—24no—
97(C2×#595)⋊C4—22no—
98(C2×#595)⋊C4C2314yes—
99#10587543—22no—
100#10587543C2314yes—
101C24×C17C22⋊C411yescharacteristic
102C23×D17—24no—
103C23×D17—24no—
104C23×D17C22⋊C412yes—
105C23×D17C22⋊C411yescharacteristic
106C23×D17SD1614yes—
107C23×D17Q1614yes—
108C23×D17C2×D412yes—
109C23×D17C2×D411yescharacteristic
110C22×#595—28no—
111C22×#595—216no—
112C22×#595—24no—
113C22×#595—44no—
114C22×#595—432no—
115C22×#595—48no—
116C22×#595—44no—
117C22×#595—48no—
118C2×Q8×C17—21no—
119C2×Q8×C17—42no—
120C2×Q8×C17C22×C412yescomplemented
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—42no—
124C22×C4×C17C22⋊C411yescharacteristic
125C22×C4×C17C22⋊C412yes—
126C22×C4×C17C22×C411yescharacteristic
127C22×C4×C17C22×C412yes—
128C22×Dic17—21no—
129C22×Dic17—21no—
130C22×Dic17—42no—
131C22×Dic17C22⋊C411yescharacteristic
132C22×Dic17C22⋊C412yes—
133C22×Dic17C2×D411yescharacteristic
134C22×Dic17C2×D412yes—
135Q8×D17—48no—
136Q8×D17—48no—
137C2×C4×D17—24no—
138C2×C4×D17—24no—
139C2×C4×D17—24no—
140C2×C4×D17—24no—
141C2×C4×D17—44no—
142C2×C4×D17—44no—
143C2×C4×D17—44no—
144C2×C4×D17—44no—
145C2×C4×D17—42no—
146C2×C4×D17—42no—
147C2×C4×D17—44no—
148C2×C4×D17—44no—
149C2×C4×D17C22⋊C412yes—
150C2×C4×D17C22⋊C412yes—
151C2×C4×D17C22⋊C412yes—
152C2×C4×D17C22×C412yes—
153C2×C4×D17C22×C411yescharacteristic
154C2×C4×D17C2×D412yes—
155C2×C4×D17C2×D412yes—
156C2×C4×D17C2×D411yescharacteristic
157C2×C4×D17C2×D411yescharacteristic
158C2×C4×D17C2411yescharacteristic
159C2×Dic34—21no—
160C2×Dic34—24no—
161C2×Dic34—44no—
162C2×Dic34—42no—
163C2×Dic34C22×C412yescomplemented
164C2×#3624—24no—
165C2×#3624—44no—
166#63242—48no—
167C4⋊C4×C17—21no—
168C4⋊C4×C17—24no—
169C4⋊C4×C17C22×C412yescomplemented
170C22⋊C4×C17—24no—
171C22⋊Dic17—24no—
172#63227—22no—
173#63227—22no—
174#63227—22no—
175#63227—22no—
176C4⋊Dic17—21no—
177C4⋊Dic17—22no—
178C4⋊Dic17—22no—
179C4⋊Dic17C22×C412yescomplemented
180#63225—24no—
181#63225—22no—
182#63225—24no—
183#63225—22no—
184C22×#328—171nomaximal, Sylow
185C23×C17—22no—
186C23×C17—22no—
187C23×C17#10314yes—
188C23×C17C2×C22⋊C412yes—
189C23×C17C2×C22⋊C411yescharacteristic
190C22×D17—22no—
191C22×D17—22no—
192C22×D17—216no—
193C22×D17—216no—
194C22×D17—24no—
195C22×D17—24no—
196C22×D17—24no—
197C22×D17—24no—
198C22×D17#9914yes—
199C22×D17#10318yes—
200C22×D17#10314yes—
201C22×D17#10414yes—
202C22×D17C2×C22⋊C411yescharacteristic
203C22×D17C2×C22⋊C412yes—
204C22×D17C2×SD1612yes—
205C22×D17C2×SD1614yes—
206C22×D17C2×Q1612yes—
207C22×D17C2×Q1614yes—
208C22×D17C22×D411yescharacteristic
209C2×#595—28no—
210C2×#595—44no—
211C2×#595—416no—
212C2×#595—432no—
213C2×#595—44no—
214Q8×C17—42no—
215Q8×C17—42no—
216C2×C4×C17—22no—
217C2×C4×C17—22no—
218C2×C4×C17—22no—
219C2×C4×C17—22no—
220C2×C4×C17—42no—
221C2×C4×C17—42no—
222C2×C4×C17—42no—
223C2×C4×C17—42no—
224C2×C4×C17C2×C22⋊C412yes—
225C2×C4×C17C2×C22⋊C411yescharacteristic
226C2×C4×C17C23×C411yescharacteristic
227C2×Dic17—22no—
228C2×Dic17—22no—
229C2×Dic17—22no—
230C2×Dic17—22no—
231C2×Dic17—42no—
232C2×Dic17—42no—
233C2×Dic17—42no—
234C2×Dic17—42no—
235C2×Dic17C2×C22⋊C412yes—
236C2×Dic17C2×C22⋊C411yescharacteristic
237C2×Dic17C22×D411yescharacteristic
238C4×D17—24no—
239C4×D17—24no—
240C4×D17—24no—
241C4×D17—24no—
242C4×D17—42no—
243C4×D17—41no—
244C4×D17—41no—
245C4×D17—42no—
246C4×D17—41no—
247C4×D17—41no—
248C4×D17—48no—
249C4×D17—48no—
250Dic34—48no—
251Dic34—42no—
252Dic34—42no—
253#3624—44no—
254C22×C22⋊Q8—171no—
255C22×C22⋊C8—171no—
256C22×#95—171no—
257C2×#328—172no—
258C2×#328—178no—
259C2×#328—172no—
260C22×C17—22no—
261C22×C17—22no—
262C22×C17—28no—
263C22×C17C2×#9912yes—
264C22×C17C2×#10314yes—
265C22×C17C2×#10312yes—
266C22×C17C2×#10412yes—
267C22×C17C22×C22⋊C411yescharacteristic
268C2×D17—21no—
269C2×D17—21no—
270C2×D17—21no—
271C2×D17—21no—
272C2×D17—24no—
273C2×D17—24no—
274C2×D17—28no—
275C2×D17—216no—
276C2×D17—28no—
277C2×D17#328116yescomplemented
278C2×D17C2×#9914yes—
279C2×D17C2×#10312yes—
280C2×D17C2×#10314yes—
281C2×D17C2×#10414yes—
282C2×D17C22×SD1611yescharacteristic
283C2×D17C22×Q1611yescharacteristic
284#595—48no—
285C4×C17—21no—
286C4×C17—21no—
287C4×C17—22no—
288C4×C17—42no—
289C4×C17—42no—
290Dic17—21no—
291Dic17—22no—
292Dic17—21no—
293Dic17—42no—
294Dic17—42no—
295C23×Q8—171no—
296C24×C4—171no—
297C24×C4—341no—
298C23×C8—341no—
299C2×C22⋊Q8—171no—
300C2×C22⋊Q8—171no—
301C2×C22⋊Q8—174no—
302C2×C22⋊Q8—174no—
303C2×C22⋊Q8—171no—
304C2×C22⋊Q8—341no—
305C2×C22⋊Q8—341no—
306C2×C22⋊Q8—342no—
307C2×C22⋊Q8—342no—
308C2×C22⋊Q8#59511yescharacteristic, complemented
309C22×C4⋊C4—171no—
310C22×C4⋊C4—341no—
311C22×C22⋊C4—341no—
312C2×C22⋊C8—174no—
313C2×C22⋊C8—172no—
314C2×C22⋊C8—341no—
315C2×C22⋊C8—342no—
316C2×#95—172no—
317C2×#95—174no—
318C2×#95—341no—
319C2×#95—342no—
320#328—178no—
321#328—178no—
322C2×C17—24no—
323C2×C17C2×#32814yescomplemented
324C2×C17C22×#9911yescharacteristic
325C2×C17C22×#10311yescharacteristic
326C2×C17C22×#10411yescharacteristic
327D17—21no—
328D17—21no—
329D17—22no—
330D17C2×#32818yescomplemented
331C25—171no—
332C22×Q8—174no—
333C22×Q8—171no—
334C22×Q8—341no—
335C22×Q8—342no—
336C22×Q8—684no—
337C22×Q8C2×#59511yescharacteristic, complemented
338C23×C4—171no—
339C23×C4—171no—
340C23×C4—171no—
341C23×C4—171no—
342C23×C4—172no—
343C23×C4—172no—
344C23×C4—172no—
345C23×C4—171no—
346C23×C4—172no—
347C23×C4—341no—
348C23×C4—341no—
349C23×C4—344no—
350C23×C4—342no—
351C23×C4—348no—
352C23×C4—684no—
353C23×C4—684no—
354C23×C4—684no—
355C23×C4C2×#59511yescharacteristic
356C22×C8—344no—
357C22×C8—342no—
358C22×C8—684no—
359C22⋊Q8—22no—
360C22⋊Q8—172no—
361C22⋊Q8—172no—
362C22⋊Q8—174no—
363C22⋊Q8—172no—
364C22⋊Q8—172no—
365C22⋊Q8—344no—
366C22⋊Q8—344no—
367C22⋊Q8—344no—
368C22⋊Q8—344no—
369C22⋊Q8—341no—
370C22⋊Q8—341no—
371C22⋊Q8—341no—
372C22⋊Q8—341no—
373C22⋊Q8—342no—
374C22⋊Q8C2×#59514yescomplemented
375C2×C4⋊C4—21no—
376C2×C4⋊C4—171no—
377C2×C4⋊C4—174no—
378C2×C4⋊C4—342no—
379C2×C4⋊C4—344no—
380C2×C4⋊C4—344no—
381C2×C4⋊C4—341no—
382C2×C4⋊C4—341no—
383C2×C4⋊C4—341no—
384C2×C4⋊C4—341no—
385C2×C4⋊C4C2×#59511yescharacteristic, complemented
386C2×C22⋊C4—21no—
387C2×C22⋊C4—344no—
388C2×C22⋊C4—344no—
389C2×C22⋊C4—341no—
390C2×C22⋊C4—341no—
391C2×C22⋊C4—341no—
392C22⋊C8—174no—
393C22⋊C8—342no—
394C22⋊C8—344no—
395#95—174no—
396#95—342no—
397#95—344no—
398C17C22×#32811yescharacteristic, complemented, Sylow
399C24—171no—
400C24—172no—
401C24—172no—
402C24—171no—
403C24—174no—
404C24—174no—
405C24—344no—
406C24—344no—
407C24C22⋊#59511yescharacteristic
408C2×Q8—21no—
409C2×Q8—42no—
410C2×Q8—172no—
411C2×Q8—344no—
412C2×Q8—341no—
413C2×Q8—682no—
414C2×Q8—684no—
415C2×Q8—688no—
416C2×Q8—688no—
417C2×Q8C22×#59512yescomplemented
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—42no—
421C22×C4—171no—
422C22×C4—171no—
423C22×C4—172no—
424C22×C4—172no—
425C22×C4—172no—
426C22×C4—172no—
427C22×C4—172no—
428C22×C4—172no—
429C22×C4—172no—
430C22×C4—171no—
431C22×C4—172no—
432C22×C4—171no—
433C22×C4—171no—
434C22×C4—171no—
435C22×C4—344no—
436C22×C4—344no—
437C22×C4—344no—
438C22×C4—344no—
439C22×C4—344no—
440C22×C4—3416no—
441C22×C4—348no—
442C22×C4—341no—
443C22×C4—341no—
444C22×C4—682no—
445C22×C4—682no—
446C22×C4—684no—
447C22×C4—684no—
448C22×C4—684no—
449C22×C4—684no—
450C22×C4—684no—
451C22×C4—684no—
452C22×C4—682no—
453C22×C4—688no—
454C22×C4—684no—
455C22×C4—688no—
456C22×C4—6832no—
457C22×C4—684no—
458C22×C4C22⋊#59511yescharacteristic
459C22×C4C22⋊#59512yes—
460C22×C4C22×#59511yescharacteristic
461C22×C4C22×#59512yes—
462C2×C8—344no—
463C2×C8—688no—
464C2×C8—684no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—172no—
468C4⋊C4—344no—
469C4⋊C4—342no—
470C4⋊C4—342no—
471C4⋊C4—342no—
472C4⋊C4—342no—
473C4⋊C4—341no—
474C4⋊C4—344no—
475C4⋊C4C22×#59512yescomplemented
476C22⋊C4—24no—
477C22⋊C4—342no—
478C22⋊C4—342no—
479C22⋊C4—342no—
480C22⋊C4—342no—
481C22⋊C4—344no—
482C23—22no—
483C23—22no—
484C23—174no—
485C23—174no—
486C23—174no—
487C23—172no—
488C23—174no—
489C23—172no—
490C23—178no—
491C23—174no—
492C23—172no—
493C23—171no—
494C23—171no—
495C23—344no—
496C23—344no—
497C23—3416no—
498C23—344no—
499C23—344no—
500C23—3416no—
501C23—342no—
502C23—342no—
503C23#1058754914yes—
504C23C2×C22⋊#59512yes—
505C23C2×C22⋊#59511yescharacteristic
506Q8—42no—
507Q8—42no—
508Q8—682no—
509Q8—682no—
510Q8—688no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—171no—
520C2×C4—171no—
521C2×C4—172no—
522C2×C4—344no—
523C2×C4—344no—
524C2×C4—344no—
525C2×C4—344no—
526C2×C4—342no—
527C2×C4—342no—
528C2×C4—348no—
529C2×C4—342no—
530C2×C4—342no—
531C2×C4—681no—
532C2×C4—681no—
533C2×C4—682no—
534C2×C4—682no—
535C2×C4—681no—
536C2×C4—681no—
537C2×C4—688no—
538C2×C4—688no—
539C2×C4—682no—
540C2×C4—682no—
541C2×C4—684no—
542C2×C4—6832no—
543C2×C4—6816no—
544C2×C4—684no—
545C2×C4—682no—
546C2×C4—682no—
547C2×C4C2×C22⋊#59512yes—
548C2×C4C2×C22⋊#59511yescharacteristic
549C2×C4C23×#59511yescharacteristic
550C8—684no—
551C22—22no—
552C22—28no—
553C22—22no—
554C22—174no—
555C22—1716no—
556C22—174no—
557C22—174no—
558C22—171no—
559C22—171no—
560C22—172no—
561C22—348no—
562C22—3416no—
563C22—348no—
564C22—341no—
565C22—341no—
566C22—344no—
567C22—344no—
568C22—341no—
569C22—341no—
570C22D17⋊#9912yes—
571C22C2×#1058754914yes—
572C22C2×#1058754912yes—
573C22D17⋊#10412yes—
574C22C22×C22⋊#59511yescharacteristic
575C4—21no—
576C4—22no—
577C4—21no—
578C4—42no—
579C4—42no—
580C4—341no—
581C4—342no—
582C4—341no—
583C4—688no—
584C4—682no—
585C4—682no—
586C2—24no—
587C2—178no—
588C2—341no—
589C2—341no—
590C2—342no—
591C2D17⋊#32814yesdirect product factor
592C2C2×D17⋊#9911yescharacteristic
593C2C22×#1058754911yescharacteristic
594C2C2×D17⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×C22⋊Q8C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC2×C4×D17C24
hypercenterC2×C22⋊Q8#595
hypocenterC17C22×#328
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#11763663C2semidirect
4. D17⋊#328C2direct (N × H)
5. C2×#11763662C2semidirect
17. #11763663C22semidirect
18. #11763662C22semidirect
19. C22×Q8×D17C4semidirect
22. C2×#10587610C4semidirect
28. C22⋊Q8×D17C4semidirect
31. C2×C4⋊C4×D17C4semidirect
33. C2×C17×C22⋊Q8C4semidirect
40. C22×Q8×C17C2×C4semidirect
45. C2×Q8×D17C2×C4semidirect
58. C22×Dic34C2×C4semidirect
63. C17×C22⋊Q8C2×C4semidirect
65. C2×C4⋊C4×C17C2×C4semidirect
70. #10587632C2×C4semidirect
75. C2×C4⋊Dic17C2×C4semidirect
77. #10587610C2×C4semidirect
83. #10587583C2×C4semidirect
90. C4⋊C4×D17C2×C4semidirect
120. C2×Q8×C17C22×C4semidirect
163. C2×Dic34C22×C4semidirect
169. C4⋊C4×C17C22×C4semidirect
179. C4⋊Dic17C22×C4semidirect
277. C2×D17#328semidirect
308. C2×C22⋊Q8#595semidirect
323. C2×C17C2×#328semidirect
330. D17C2×#328semidirect
337. C22×Q8C2×#595semidirect
374. C22⋊Q8C2×#595semidirect
385. C2×C4⋊C4C2×#595semidirect
398. C17C22×#328semidirect
417. C2×Q8C22×#595semidirect
475. C4⋊C4C22×#595semidirect
591. C2D17⋊#328direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637772
C22×(C2×#595)⋊C42
C2×#117636632
D17⋊#3282
C2×#117636622
C2×C22⋊Q8×D172
C22×#32817