Finite Group Databasebeta

← C2×#14544182 #17965240

Subgroups — C2×#14544182 #17965240

Order 4352.

1554 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763781C211yesmaximal, characteristic
2C2×C4×C22⋊#595C211yesmaximal, characteristic
3#14544182C218yesmaximal, direct product factor
4C2×#11763663C212yesmaximal, complemented
5C2×#11763662C212yesmaximal, complemented
6C2×C22⋊Q8×D17C211yesmaximal, characteristic
7C22×#63247—21no—
8C22×C22⋊#595—21no—
9C22×C4×#595—21no—
10#11763781—22no—
11#11763781C2214yes—
12C2×#10587543—21no—
13C2×#10587543C2212yes—
14C4×C22⋊#595—22no—
15C4×C22⋊#595C2214yes—
16C2×(C2×#595)⋊C4C2212yes—
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—22no—
36C22×Q8×C17C2×C411yescharacteristic
37C23×C4×C17C2×C411yescharacteristic
38C23×Dic17D411yescharacteristic
39C2×Q8×D17—22no—
40C2×Q8×D17—44no—
41C2×Q8×D17C2×C414yescomplemented
42C22×C4×D17—21no—
43C22×C4×D17—21no—
44C22×C4×D17—44no—
45C22×C4×D17C2×C411yescharacteristic
46C22×C4×D17C2×C412yes—
47C22×C4×D17D411yescharacteristic
48C22×C4×D17D412yes—
49C22×C4×D17D411yescharacteristic
50C22×C4×D17D412yes—
51C22×C4×D17C2311yescharacteristic
52C22×C4×D17C2312yes—
53C22×Dic34—21no—
54C22×Dic34C2×C411yescharacteristic
55C2×C22⋊#595—28no—
56C2×C22⋊#595—24no—
57C2×#63247—24no—
58C2×#63247—44no—
59C22×#3624—22no—
60C2×C4×#595—24no—
61C2×C4×#595—44no—
62C17×C22⋊Q8—22no—
63C17×C22⋊Q8C2×C414yescomplemented
64C2×C4⋊C4×C17—21no—
65C2×C4⋊C4×C17C2×C411yescharacteristic
66C2×C22⋊C4×C17—21no—
67C2×C22⋊Dic17—21no—
68#10587632—21no—
69#10587632—21no—
70#10587632C2×C412yes—
71#10587632C2312yes—
72C2×#63227—21no—
73C2×#63227—21no—
74C2×C4⋊Dic17—21no—
75C2×C4⋊Dic17C2×C411yescharacteristic
76#10587610—22no—
77#10587610C2×C414yescomplemented
78C2×#63225—21no—
79C2×#63225—21no—
80C2×#63225—21no—
81#10587583—21no—
82#10587583—21no—
83#10587583C2×C412yes—
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—
95(C2×#595)⋊C4—22no—
96(C2×#595)⋊C4C2314yes—
97#10587543—24no—
98#10587543—22no—
99#10587543C2314yes—
100C24×C17C22⋊C411yescharacteristic
101C23×D17—24no—
102C23×D17—24no—
103C23×D17—42no—
104C23×D17C22⋊C412yes—
105C23×D17C22⋊C411yescharacteristic
106C23×D17C2×D412yes—
107C23×D17C2×D411yescharacteristic
108C22×#595—28no—
109C22×#595—24no—
110C22×#595—44no—
111C22×#595—44no—
112C2×Q8×C17—21no—
113C2×Q8×C17—42no—
114C2×Q8×C17C22×C412yes—
115C22×C4×C17—21no—
116C22×C4×C17—21no—
117C22×C4×C17—42no—
118C22×C4×C17C22⋊C411yescharacteristic
119C22×C4×C17C22⋊C412yes—
120C22×C4×C17C22×C411yescharacteristic
121C22×C4×C17C22×C412yes—
122C22×Dic17—24no—
123C22×Dic17—21no—
124C22×Dic17—21no—
125C22×Dic17C22⋊C412yes—
126C22×Dic17C22⋊C411yescharacteristic
127C22×Dic17C2×D411yescharacteristic
128C22×Dic17C2×D412yes—
129Q8×D17—48no—
130Q8×D17—48no—
131C2×C4×D17—24no—
132C2×C4×D17—24no—
133C2×C4×D17—24no—
134C2×C4×D17—24no—
135C2×C4×D17—44no—
136C2×C4×D17—44no—
137C2×C4×D17—44no—
138C2×C4×D17—44no—
139C2×C4×D17—42no—
140C2×C4×D17—42no—
141C2×C4×D17—44no—
142C2×C4×D17—44no—
143C2×C4×D17C22⋊C412yes—
144C2×C4×D17C22⋊C412yes—
145C2×C4×D17C22⋊C412yes—
146C2×C4×D17C22×C412yes—
147C2×C4×D17C22×C411yescharacteristic
148C2×C4×D17C2×D412yes—
149C2×C4×D17C2×D411yescharacteristic
150C2×C4×D17C2×D412yes—
151C2×C4×D17C2×D411yescharacteristic
152C2×C4×D17C2411yescharacteristic
153C2×Dic34—21no—
154C2×Dic34—24no—
155C2×Dic34—44no—
156C2×Dic34—42no—
157C2×Dic34C22×C412yes—
158C22⋊#595—216no—
159#63247—48no—
160C2×#3624—24no—
161C2×#3624—44no—
162C4×#595—48no—
163C4⋊C4×C17—21no—
164C4⋊C4×C17—24no—
165C4⋊C4×C17C22×C412yes—
166C22⋊C4×C17—24no—
167C22⋊Dic17—24no—
168#63227—22no—
169#63227—22no—
170#63227—22no—
171#63227—22no—
172C4⋊Dic17—21no—
173C4⋊Dic17—22no—
174C4⋊Dic17—22no—
175C4⋊Dic17C22×C412yes—
176#63225—24no—
177#63225—22no—
178#63225—24no—
179#63225—22no—
180C2×#1508—171nomaximal, Sylow
181C23×C17—22no—
182C23×C17—22no—
183C23×C17—22no—
184C23×C17C2×C22⋊C412yes—
185C23×C17C2×C22⋊C411yescharacteristic
186C22×D17—22no—
187C22×D17—22no—
188C22×D17—22no—
189C22×D17—22no—
190C22×D17—24no—
191C22×D17—24no—
192C22×D17—24no—
193C22×D17—24no—
194C22×D17—42no—
195C22×D17—42no—
196C22×D17—416no—
197C22×D17#10414yes—
198C22×D17C2×C22⋊C411yescharacteristic
199C22×D17C2×C22⋊C412yes—
200C22×D17#13714yes—
201C22×D17C22×D411yescharacteristic
202C2×#595—28no—
203C2×#595—44no—
204C2×#595—416no—
205C2×#595—44no—
206Q8×C17—42no—
207Q8×C17—42no—
208C2×C4×C17—22no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—42no—
213C2×C4×C17—42no—
214C2×C4×C17—42no—
215C2×C4×C17—42no—
216C2×C4×C17C2×C22⋊C412yes—
217C2×C4×C17C2×C22⋊C411yescharacteristic
218C2×C4×C17C23×C411yescharacteristic
219C2×Dic17—22no—
220C2×Dic17—24no—
221C2×Dic17—24no—
222C2×Dic17—22no—
223C2×Dic17—22no—
224C2×Dic17—42no—
225C2×Dic17—42no—
226C2×Dic17#9914yes—
227C2×Dic17C2×C22⋊C411yescharacteristic
228C2×Dic17C2×C22⋊C412yes—
229C2×Dic17C22×D411yescharacteristic
230C4×D17—24no—
231C4×D17—24no—
232C4×D17—24no—
233C4×D17—24no—
234C4×D17—42no—
235C4×D17—41no—
236C4×D17—41no—
237C4×D17—42no—
238C4×D17—41no—
239C4×D17—41no—
240C4×D17—48no—
241C4×D17—48no—
242Dic34—42no—
243Dic34—48no—
244Dic34—42no—
245#3624—44no—
246C22×C22⋊Q8—171no—
247C2×#407—171no—
248C2×C4×C22⋊C4—171no—
249#1508—178no—
250C2×#328—172no—
251C2×#328—172no—
252C22×C17—22no—
253C22×C17—22no—
254C22×C17—22no—
255C22×C17—44no—
256C22×C17C2×#9912yes—
257C22×C17#41912yes—
258C22×C17C2×#10412yes—
259C22×C17C22×C22⋊C411yescharacteristic
260C2×D17—22no—
261C2×D17—21no—
262C2×D17—21no—
263C2×D17—22no—
264C2×D17—21no—
265C2×D17—21no—
266C2×D17—28no—
267C2×D17—28no—
268C2×D17—48no—
269C2×D17—48no—
270C2×D17#41912yes—
271C2×D17C2×#10414yes—
272C2×D17C2×#13712yes—
273#595—48no—
274C4×C17—21no—
275C4×C17—21no—
276C4×C17—22no—
277C4×C17—42no—
278C4×C17—42no—
279Dic17—21no—
280Dic17—21no—
281Dic17—42no—
282Dic17—42no—
283Dic17C2×#9914yes—
284C23×Q8—171no—
285C24×C4—171no—
286C22×M16—341no—
287C2×C22⋊Q8—171no—
288C2×C22⋊Q8—171no—
289C2×C22⋊Q8—174no—
290C2×C22⋊Q8—174no—
291C2×C22⋊Q8—171no—
292C2×C22⋊Q8—341no—
293C2×C22⋊Q8—341no—
294C2×C22⋊Q8—342no—
295C2×C22⋊Q8—342no—
296C2×C22⋊Q8#59511yescharacteristic, complemented
297C22×C4⋊C4—171no—
298C22×C4⋊C4—341no—
299C22×C22⋊C4—341no—
300C22×C22⋊C4—341no—
301C22×C42—341no—
302#407—174no—
303#407—342no—
304C2×C22⋊C8—172no—
305C2×C22⋊C8—341no—
306C4×C22⋊C4—174no—
307C4×C22⋊C4—342no—
308C2×#95—172no—
309#328—178no—
310#328—178no—
311C2×C17—42no—
312C2×C17#150814yescomplemented
313C2×C17C22×#9911yescharacteristic
314C2×C17C2×#41911yescharacteristic
315C2×C17C22×#10411yescharacteristic
316D17—22no—
317D17—22no—
318D17—24no—
319C25—171no—
320C22×Q8—174no—
321C22×Q8—171no—
322C22×Q8—341no—
323C22×Q8—342no—
324C22×Q8—684no—
325C22×Q8C2×#59511yescharacteristic
326C23×C4—171no—
327C23×C4—171no—
328C23×C4—171no—
329C23×C4—171no—
330C23×C4—172no—
331C23×C4—172no—
332C23×C4—172no—
333C23×C4—171no—
334C23×C4—172no—
335C23×C4—341no—
336C23×C4—341no—
337C23×C4—342no—
338C23×C4—684no—
339C23×C4C2×#59511yescharacteristic
340C2×M16—344no—
341C2×M16—684no—
342C22×C8—342no—
343C22⋊Q8—22no—
344C22⋊Q8—172no—
345C22⋊Q8—172no—
346C22⋊Q8—174no—
347C22⋊Q8—172no—
348C22⋊Q8—172no—
349C22⋊Q8—344no—
350C22⋊Q8—344no—
351C22⋊Q8—344no—
352C22⋊Q8—344no—
353C22⋊Q8—341no—
354C22⋊Q8—341no—
355C22⋊Q8—341no—
356C22⋊Q8—341no—
357C22⋊Q8—342no—
358C22⋊Q8C2×#59514yescomplemented
359C2×C4⋊C4—21no—
360C2×C4⋊C4—171no—
361C2×C4⋊C4—174no—
362C2×C4⋊C4—342no—
363C2×C4⋊C4—344no—
364C2×C4⋊C4—344no—
365C2×C4⋊C4—341no—
366C2×C4⋊C4—341no—
367C2×C4⋊C4—341no—
368C2×C4⋊C4—341no—
369C2×C4⋊C4C2×#59511yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—344no—
372C2×C22⋊C4—344no—
373C2×C22⋊C4—341no—
374C2×C22⋊C4—341no—
375C2×C22⋊C4—344no—
376C2×C22⋊C4—348no—
377C2×C22⋊C4—341no—
378C2×C42—344no—
379C2×C42—684no—
380C22⋊C8—174no—
381C22⋊C8—342no—
382C22⋊C8—344no—
383#95—174no—
384#95—342no—
385C17C2×#150811yescharacteristic, complemented, Sylow
386C24—171no—
387C24—171no—
388C24—172no—
389C24—172no—
390C24—344no—
391C24—344no—
392C24—682no—
393C24C22⋊#59511yescharacteristic
394C2×Q8—21no—
395C2×Q8—42no—
396C2×Q8—172no—
397C2×Q8—344no—
398C2×Q8—341no—
399C2×Q8—682no—
400C2×Q8—684no—
401C2×Q8—688no—
402C2×Q8—688no—
403C2×Q8C22×#59512yes—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—42no—
407C22×C4—171no—
408C22×C4—172no—
409C22×C4—172no—
410C22×C4—171no—
411C22×C4—172no—
412C22×C4—172no—
413C22×C4—172no—
414C22×C4—172no—
415C22×C4—172no—
416C22×C4—171no—
417C22×C4—172no—
418C22×C4—171no—
419C22×C4—171no—
420C22×C4—171no—
421C22×C4—344no—
422C22×C4—344no—
423C22×C4—344no—
424C22×C4—344no—
425C22×C4—344no—
426C22×C4—344no—
427C22×C4—348no—
428C22×C4—341no—
429C22×C4—341no—
430C22×C4—682no—
431C22×C4—682no—
432C22×C4—684no—
433C22×C4—684no—
434C22×C4—684no—
435C22×C4—684no—
436C22×C4—684no—
437C22×C4—684no—
438C22×C4—684no—
439C22×C4—684no—
440C22×C4C22⋊#59511yescharacteristic
441C22×C4C22⋊#59512yes—
442C22×C4C22×#59511yescharacteristic
443C22×C4C22×#59512yes—
444M16—688no—
445C2×C8—344no—
446C2×C8—684no—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—172no—
450C4⋊C4—344no—
451C4⋊C4—342no—
452C4⋊C4—342no—
453C4⋊C4—342no—
454C4⋊C4—342no—
455C4⋊C4—341no—
456C4⋊C4—344no—
457C4⋊C4C22×#59512yes—
458C22⋊C4—24no—
459C22⋊C4—342no—
460C22⋊C4—342no—
461C22⋊C4—342no—
462C22⋊C4—342no—
463C22⋊C4—3416no—
464C22⋊C4—344no—
465C42—688no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—174no—
470C23—174no—
471C23—171no—
472C23—171no—
473C23—172no—
474C23—344no—
475C23—344no—
476C23—344no—
477C23—344no—
478C23—342no—
479C23—342no—
480C23—342no—
481C23—342no—
482C23—682no—
483C23—682no—
484C23—6816no—
485C23C2×C22⋊#59512yes—
486C23C2×C22⋊#59511yescharacteristic
487Q8—42no—
488Q8—42no—
489Q8—682no—
490Q8—682no—
491Q8—688no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—174no—
501C2×C4—172no—
502C2×C4—171no—
503C2×C4—171no—
504C2×C4—344no—
505C2×C4—344no—
506C2×C4—344no—
507C2×C4—344no—
508C2×C4—344no—
509C2×C4—344no—
510C2×C4—342no—
511C2×C4—348no—
512C2×C4—342no—
513C2×C4—342no—
514C2×C4—681no—
515C2×C4—681no—
516C2×C4—682no—
517C2×C4—682no—
518C2×C4—681no—
519C2×C4—681no—
520C2×C4—688no—
521C2×C4—688no—
522C2×C4—684no—
523C2×C4—684no—
524C2×C4—6816no—
525C2×C4—682no—
526C2×C4—682no—
527C2×C4C2×C22⋊#59512yes—
528C2×C4C2×C22⋊#59511yescharacteristic
529C2×C4C23×#59511yescharacteristic
530C8—684no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—44no—
535C22—174no—
536C22—172no—
537C22—172no—
538C22—341no—
539C22—341no—
540C22—348no—
541C22—348no—
542C22—341no—
543C22—342no—
544C22—341no—
545C22—342no—
546C22—688no—
547C22—688no—
548C22D17⋊#9912yes—
549C22#1176380212yes—
550C22D17⋊#10412yes—
551C22C22×C22⋊#59511yescharacteristic
552C4—21no—
553C4—22no—
554C4—21no—
555C4—42no—
556C4—42no—
557C4—174no—
558C4—341no—
559C4—341no—
560C4—688no—
561C4—682no—
562C4—682no—
563C2—42no—
564C2—342no—
565C2—344no—
566C2—342no—
567C2#1454418214yesdirect product factor
568C2C2×D17⋊#9911yescharacteristic
569C2C2×#1176380211yescharacteristic
570C2C2×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
hypocenterC17C2×#1508
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. #14544182C2direct (N × H)
4. C2×#11763663C2semidirect
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
41. C2×Q8×D17C2×C4semidirect
63. C17×C22⋊Q8C2×C4semidirect
77. #10587610C2×C4semidirect
90. C4⋊C4×D17C2×C4semidirect
296. C2×C22⋊Q8#595semidirect
312. C2×C17#1508semidirect
358. C22⋊Q8C2×#595semidirect
385. C17C2×#1508semidirect
567. C2#14544182direct (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×C4×C22⋊#5952
#145441822
C2×#117636632
C2×#117636622
C2×C22⋊Q8×D172
C2×#150817