Finite Group Databasebeta

← C2×#14543646 #17950949

Subgroups — C2×#14543646 #17950949

Order 4352.

1130 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763777C211yesmaximal, characteristic
2C2×#11763751C211yesmaximal, characteristic
3#14543646C214yesmaximal, direct product factor
4C2×#11762668C211yesmaximal, characteristic
5C22×#63242C412yescomplemented
6C22×C4⋊#595—21no—
7C22×C22⋊#595—21no—
8C2×#10587543—21no—
9#11763777—21no—
10#11763777—21no—
11#11763777C412yescomplemented
12#11763777C2212yes—
13C2×C22⋊#3624—21no—
14#11763751—21no—
15#11763751—21no—
16#11763751C412yescomplemented
17#11763751C2212yes—
18C2×(C2×#595)⋊C4C412yescomplemented
19C23×C4×D17C2211yescharacteristic
20C22×#63225—21no—
21C22×#63227—21no—
22#11762668—21no—
23#11762668—21no—
24#11762668C412yescomplemented
25#11762668C2212yes—
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—22no—
48C2×C22⋊#595—22no—
49C2×C22⋊#595—42no—
50C2×C22⋊#595—42no—
51C22×#3624—22no—
52C2×C4⋊#595—22no—
53C2×C4⋊#595—22no—
54C2×C4⋊#595—44no—
55C2×#63242—22no—
56C2×#63242—44no—
57C2×#63242C2×C414yescomplemented
58C2×#63227—22no—
59C2×#63227—22no—
60C2×#63227—42no—
61C2×#63227—42no—
62C2×#63225—22no—
63C2×#63225—22no—
64C2×#63225—44no—
65C22⋊#3624—22no—
66C22⋊#3624—22no—
67(C2×#595)⋊C4—22no—
68(C2×#595)⋊C4C2×C414yescomplemented
69#10587543—22no—
70#10587543—22no—
71C17×#95—21no—
72C17×#95C2×C412yescomplemented
73#10587502—21no—
74#10587502C2×C412yescomplemented
75C24×C17C22⋊C411yescharacteristic
76C23×D17—42no—
77C23×D17—42no—
78C23×D17C22⋊C411yescharacteristic
79C23×D17C22⋊C411yescharacteristic
80C23×D17C22⋊C411yescharacteristic
81C23×D17C4⋊C411yescharacteristic
82C23×D17C4⋊C411yescharacteristic
83C23×D17D812yes—
84C23×D17SD1612yes—
85C23×D17SD1612yes—
86C23×D17Q1612yes—
87C23×D17C2×D411yescharacteristic
88C22×#595—24no—
89C22×#595—44no—
90C22×#595—44no—
91C22×#595—44no—
92C22×C4×C17—22no—
93C22×C4×C17—42no—
94C22×C4×C17—42no—
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—24no—
104C22×Dic17—22no—
105C22×Dic17—42no—
106C22×Dic17—42no—
107C22×Dic17—42no—
108C22×Dic17C22⋊C411yescharacteristic
109C22×Dic17C22⋊C411yescharacteristic
110C22×Dic17C22⋊C411yescharacteristic
111C22×Dic17C4⋊C411yescharacteristic
112C22×Dic17C4⋊C411yescharacteristic
113C22×Dic17C2×D411yescharacteristic
114C2×C4×D17—24no—
115C2×C4×D17—24no—
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×D17—42no—
124C2×C4×D17—42no—
125C2×C4×D17—42no—
126C2×C4×D17C4211yescharacteristic
127C2×C4×D17C4211yescharacteristic
128C2×C4×D17C22⋊C411yescharacteristic
129C2×C4×D17C22⋊C411yescharacteristic
130C2×C4×D17C22⋊C411yescharacteristic
131C2×C4×D17C22⋊C411yescharacteristic
132C2×C4×D17C4⋊C411yescharacteristic
133C2×C4×D17C4⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C4⋊C411yescharacteristic
136C2×C4×D17C4⋊C411yescharacteristic
137C2×C4×D17C4⋊C411yescharacteristic
138C2×C4×D17C22×C411yescharacteristic
139C2×C4×D17C22×C411yescharacteristic
140C2×C4×D17C2×D411yescharacteristic
141C2×C4×D17C2×Q811yescharacteristic
142C22⋊#595—44no—
143C22⋊#595—42no—
144C22⋊#595—42no—
145C2×#3624—24no—
146C2×#3624—44no—
147C4⋊#595—44no—
148C4⋊#595—44no—
149#63242—44no—
150#63242—44no—
151#63227—44no—
152#63227—42no—
153#63227—42no—
154#63225—44no—
155#63225—44no—
156C2×#1289—171nomaximal, Sylow
157C23×C17—22no—
158C23×C17—22no—
159C23×C17#9511yescharacteristic
160C23×C17#9511yescharacteristic
161C23×C17#10212yes—
162C23×C17#10312yes—
163C23×C17C2×C22⋊C411yescharacteristic
164C22×D17—22no—
165C22×D17—22no—
166C22×D17—22no—
167C22×D17—22no—
168C22×D17—41no—
169C22×D17—41no—
170C22×D17—41no—
171C22×D17—41no—
172C22×D17—41no—
173C22×D17—41no—
174C22×D17—41no—
175C22×D17—44no—
176C22×D17—44no—
177C22×D17—44no—
178C22×D17—44no—
179C22×D17—41no—
180C22×D17#9511yescharacteristic
181C22×D17#9511yescharacteristic
182C22×D17#10212yes—
183C22×D17#10212yes—
184C22×D17#10212yes—
185C22×D17#10312yes—
186C22×D17#10312yes—
187C22×D17#10312yes—
188C22×D17#10612yes—
189C22×D17#10612yes—
190C22×D17#10712yes—
191C22×D17#10712yes—
192C22×D17C2×C22⋊C411yescharacteristic
193C22×D17C2×C4⋊C411yescharacteristic
194C22×D17C2×D811yescharacteristic
195C22×D17C2×SD1611yescharacteristic
196C22×D17C2×SD1611yescharacteristic
197C22×D17C2×Q1611yescharacteristic
198C2×#595—44no—
199C2×#595—44no—
200C2×#595—44no—
201C2×#595—88no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—41no—
205C2×C4×C17—41no—
206C2×C4×C17—41no—
207C2×C4×C17—41no—
208C2×C4×C17—42no—
209C2×C4×C17—42no—
210C2×C4×C17—42no—
211C2×C4×C17—84no—
212C2×C4×C17#9511yescharacteristic
213C2×C4×C17#9511yescharacteristic
214C2×C4×C17C2×C4211yescharacteristic
215C2×C4×C17C2×C4⋊C411yescharacteristic
216C2×Dic17—22no—
217C2×Dic17—22no—
218C2×Dic17—22no—
219C2×Dic17—22no—
220C2×Dic17—22no—
221C2×Dic17—42no—
222C2×Dic17—42no—
223C2×Dic17—42no—
224C2×Dic17—84no—
225C2×Dic17#9511yescharacteristic
226C2×Dic17#9511yescharacteristic
227C2×Dic17#9914yes—
228C2×Dic17C2×C22⋊C411yescharacteristic
229C2×Dic17C2×C4⋊C411yescharacteristic
230C4×D17—22no—
231C4×D17—22no—
232C4×D17—22no—
233C4×D17—22no—
234C4×D17—22no—
235C4×D17—22no—
236C4×D17—22no—
237C4×D17—22no—
238C4×D17—41no—
239C4×D17—41no—
240C4×D17—41no—
241C4×D17—41no—
242C4×D17—41no—
243C4×D17—41no—
244C4×D17—41no—
245C4×D17—41no—
246#3624—44no—
247C22×C22⋊C8—171no—
248C2×#380—171no—
249C2×#380—171no—
250#1289—174no—
251C22×C17—24no—
252C22×C17—24no—
253C22×C17—21no—
254C22×C17—21no—
255C22×C17—21no—
256C22×C17—21no—
257C22×C17H(3,ℤ/4)12yes—
258C22×C17#34012yes—
259C22×C17#34012yes—
260C22×C17#34212yes—
261C22×C17C2×#9511yescharacteristic
262C22×C17C2×#10211yescharacteristic
263C22×C17C2×#10311yescharacteristic
264C2×D17—24no—
265C2×D17—24no—
266C2×D17—24no—
267C2×D17—24no—
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—42no—
279C2×D17—42no—
280C2×D17—42no—
281C2×D17—42no—
282C2×D17—41no—
283C2×D17—41no—
284C2×D17—41no—
285C2×D17—41no—
286C2×D17#34012yes—
287C2×D17#34012yes—
288C2×D17C2×#10211yescharacteristic
289C2×D17C2×#10311yescharacteristic
290C2×D17C2×#10611yescharacteristic
291C2×D17C2×#10711yescharacteristic
292#595—84no—
293C4×C17—21no—
294C4×C17—21no—
295C4×C17—21no—
296C4×C17—21no—
297C4×C17—82no—
298Dic17—21no—
299Dic17—21no—
300Dic17—82no—
301Dic17#34212yes—
302Dic17C2×#9912yes—
303C24×C4—171no—
304C23×C8—172no—
305C22×C4⋊C4—341no—
306C22×C4⋊C4—341no—
307C22×C22⋊C4—341no—
308C22×C22⋊C4—341no—
309C2×C22⋊C8—172no—
310C2×C22⋊C8—172no—
311C2×C22⋊C8—341no—
312C2×C22⋊C8—341no—
313C2×C22⋊C8—341no—
314C2×C22⋊C8—341no—
315#380—172no—
316#380—172no—
317#380—172no—
318#380—172no—
319#380—341no—
320#380—341no—
321#380—341no—
322#380—341no—
323C2×#95—172no—
324C2×#95—171no—
325C2×#95#59511yescharacteristic, complemented
326C2×C17—21no—
327C2×C17—22no—
328C2×C17—21no—
329C2×C17#128914yescomplemented
330C2×C17C2×H(3,ℤ/4)11yescharacteristic
331C2×C17C2×#34011yescharacteristic
332C2×C17C2×#34211yescharacteristic
333D17—21no—
334D17—22no—
335D17—22no—
336D17—21no—
337D17—21no—
338D17—21no—
339C25—171no—
340C23×C4—21no—
341C23×C4—171no—
342C23×C4—171no—
343C23×C4—171no—
344C23×C4—171no—
345C23×C4—171no—
346C23×C4—171no—
347C23×C4—171no—
348C23×C4—171no—
349C23×C4—171no—
350C23×C4—171no—
351C23×C4—171no—
352C23×C4—171no—
353C23×C4—171no—
354C23×C4—342no—
355C23×C4—341no—
356C23×C4—684no—
357C23×C4C2×#59511yescharacteristic
358C22×C8—174no—
359C22×C8—342no—
360C22×C8—342no—
361C22×C8—684no—
362C2×C4⋊C4—342no—
363C2×C4⋊C4—342no—
364C2×C4⋊C4—342no—
365C2×C4⋊C4—342no—
366C2×C4⋊C4—684no—
367C2×C4⋊C4—684no—
368C2×C22⋊C4—342no—
369C2×C22⋊C4—342no—
370C2×C22⋊C4—342no—
371C2×C22⋊C4—342no—
372C2×C22⋊C4—682no—
373C2×C22⋊C4—682no—
374C2×C22⋊C4—682no—
375C2×C22⋊C4—682no—
376C22⋊C8—342no—
377C22⋊C8—342no—
378C22⋊C8—342no—
379C22⋊C8—342no—
380#95—21no—
381#95—174no—
382#95—172no—
383#95—342no—
384#95—341no—
385#95C2×#59512yescomplemented
386C17C2×#128911yescharacteristic, complemented, Sylow
387C24—171no—
388C24—171no—
389C24—171no—
390C24—171no—
391C24—171no—
392C24—171no—
393C24—172no—
394C24—172no—
395C24—172no—
396C24—172no—
397C24—682no—
398C24—682no—
399C24C22⋊#59511yescharacteristic
400C22×C4—22no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
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—171no—
419C22×C4—171no—
420C22×C4—171no—
421C22×C4—171no—
422C22×C4—171no—
423C22×C4—171no—
424C22×C4—171no—
425C22×C4—171no—
426C22×C4—171no—
427C22×C4—344no—
428C22×C4—344no—
429C22×C4—344no—
430C22×C4—344no—
431C22×C4—342no—
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—682no—
442C22×C4—682no—
443C22×C4—682no—
444C22×C4—684no—
445C22×C4—684no—
446C22×C4—684no—
447C22×C4—682no—
448C22×C4C4×#59511yescharacteristic
449C22×C4C4×#59511yescharacteristic
450C22×C4C4⋊#59511yescharacteristic
451C22×C4C4⋊#59511yescharacteristic
452C22×C4C22⋊#59511yescharacteristic
453C22×C4C22×#59511yescharacteristic
454C2×C8—344no—
455C2×C8—684no—
456C2×C8—684no—
457C2×C8—684no—
458C4⋊C4—684no—
459C4⋊C4—684no—
460C4⋊C4—684no—
461C4⋊C4—684no—
462C22⋊C4—682no—
463C22⋊C4—684no—
464C22⋊C4—682no—
465C22⋊C4—682no—
466C22⋊C4—682no—
467C22⋊C4—684no—
468C23—22no—
469C23—22no—
470C23—171no—
471C23—171no—
472C23—171no—
473C23—171no—
474C23—172no—
475C23—172no—
476C23—172no—
477C23—172no—
478C23—171no—
479C23—172no—
480C23—171no—
481C23—171no—
482C23—172no—
483C23—171no—
484C23—172no—
485C23—172no—
486C23—172no—
487C23—172no—
488C23—342no—
489C23—342no—
490C23—342no—
491C23—342no—
492C23—681no—
493C23—681no—
494C23—681no—
495C23—681no—
496C23—684no—
497C23—684no—
498C23—684no—
499C23—684no—
500C23—681no—
501C23—681no—
502C23—681no—
503C23—681no—
504C23(C2×#595)⋊C411yescharacteristic
505C23(C2×#595)⋊C411yescharacteristic
506C23#1058754712yes—
507C23#1058754912yes—
508C23C2×C22⋊#59511yescharacteristic
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—84no—
519C2×C4—171no—
520C2×C4—171no—
521C2×C4—174no—
522C2×C4—171no—
523C2×C4—171no—
524C2×C4—342no—
525C2×C4—342no—
526C2×C4—342no—
527C2×C4—342no—
528C2×C4—342no—
529C2×C4—342no—
530C2×C4—342no—
531C2×C4—342no—
532C2×C4—342no—
533C2×C4—342no—
534C2×C4—342no—
535C2×C4—342no—
536C2×C4—342no—
537C2×C4—681no—
538C2×C4—681no—
539C2×C4—681no—
540C2×C4—681no—
541C2×C4—681no—
542C2×C4—681no—
543C2×C4—681no—
544C2×C4—681no—
545C2×C4—682no—
546C2×C4—682no—
547C2×C4—684no—
548C2×C4—684no—
549C2×C4—684no—
550C2×C4—682no—
551C2×C4—1364no—
552C2×C4—1368no—
553C2×C4(C2×#595)⋊C411yescharacteristic
554C2×C4(C2×#595)⋊C411yescharacteristic
555C2×C4C2×C4×#59511yescharacteristic
556C2×C4C2×C4⋊#59511yescharacteristic
557C8—684no—
558C22—24no—
559C22—24no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—171no—
565C22—172no—
566C22—172no—
567C22—171no—
568C22—171no—
569C22—171no—
570C22—344no—
571C22—344no—
572C22—344no—
573C22—344no—
574C22—341no—
575C22—341no—
576C22—341no—
577C22—341no—
578C22—341no—
579C22—341no—
580C22—341no—
581C22—341no—
582C22—681no—
583C22—682no—
584C22—681no—
585C22—681no—
586C22—682no—
587C22—681no—
588C22—682no—
589C22—682no—
590C22—682no—
591C22—682no—
592C22#1176367612yes—
593C22#1176368212yes—
594C22#1176368212yes—
595C22#1176368612yes—
596C22C2×(C2×#595)⋊C411yescharacteristic
597C22C2×#1058754711yescharacteristic
598C22C2×#1058754911yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—82no—
604C4—172no—
605C4—172no—
606C4—341no—
607C4—341no—
608C4—1362no—
609C4—1364no—
610C2—21no—
611C2—21no—
612C2—22no—
613C2—341no—
614C2—342no—
615C2—342no—
616C2—341no—
617C2—341no—
618C2—341no—
619C2#1454364614yesdirect product factor
620C2C2×#1176367611yescharacteristic
621C2C2×#1176368211yescharacteristic
622C2C2×#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×#1289
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #14543646C2direct (N × H)
5. C22×#63242C4semidirect
11. #11763777C4semidirect
16. #11763751C4semidirect
18. C2×(C2×#595)⋊C4C4semidirect
24. #11762668C4semidirect
26. C2×#10587502C4semidirect
27. C2×C17×#95C4semidirect
57. C2×#63242C2×C4semidirect
68. (C2×#595)⋊C4C2×C4semidirect
72. C17×#95C2×C4semidirect
74. #10587502C2×C4semidirect
325. C2×#95#595semidirect
329. C2×C17#1289semidirect
385. #95C2×#595semidirect
386. C17C2×#1289semidirect
619. C2#14543646direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637772
C2×#117637512
#145436462
C2×#117626682
C2×#128917