Finite Group Databasebeta

← C2×#14530000 #17061916

Subgroups — C2×#14530000 #17061916

Order 4352.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763380C211yesmaximal, characteristic
2C2×#11762851C211yesmaximal, characteristic, complemented
3C2×#11762810C211yesmaximal, characteristic
4C22×#10587495C211yesmaximal, characteristic, complemented
5C2×#11762715C211yesmaximal, characteristic, complemented
6#14530000C218yesmaximal, direct product factor
7C2×#11762569C211yesmaximal, characteristic, complemented
8C22×C17×#104C211yesmaximal, characteristic
9C23×Dic34C2211yescharacteristic
10C22×#63223C2211yescharacteristic
11#11763380—22no—
12#11763380—22no—
13#11763380—22no—
14#11763380C2214yes—
15C2×#10587630—21no—
16C2×#10587622—21no—
17C2×#10587621—22no—
18C2×#10587610—21no—
19C2×#10587610—21no—
20C2×#10587612C2211yescharacteristic
21C22×C4⋊Dic17C2211yescharacteristic
22#11762851—22no—
23#11762851C2214yescomplemented
24C2×#10587489—21no—
25C2×#10587488—21no—
26#11762810—22no—
27#11762810C2214yes—
28C2×#10587506—21no—
29C2×#10587503—21no—
30C2×#10587495—24no—
31C2×#10587495C2214yescomplemented
32#11762715—22no—
33#11762715C2214yescomplemented
34C2×#10587502—22no—
35#11762569C2214yescomplemented
36C22×#41×C17C2211yescharacteristic
37C22×M16×C17C2211yescharacteristic
38C22×C42×C17C2211yescharacteristic
39C2×C17×#104—24no—
40C2×C17×#104C2214yes—
41C2×#41×C17—21no—
42C2×#41×C17—21no—
43C2×#41×C17—22no—
44C2×#41×C17—22no—
45C2×#41×C17—22no—
46C2×#41×C17—22no—
47C2×#41×C17D412yes—
48C2×#41×C17C2312yes—
49C22×Q8×C17D411yescharacteristic
50C22×D4×C17—21no—
51C22×D4×C17D411yescharacteristic
52C23×C4×C17—21no—
53C23×C4×C17—21no—
54C23×C4×C17C2311yescharacteristic
55C23×Dic17—21no—
56C23×Dic17D412yes—
57C22×Dic34—22no—
58C22×Dic34—21no—
59C22×Dic34—21no—
60C22×Dic34—21no—
61C22×Dic34—21no—
62C22×Dic34—22no—
63C22×Dic34—22no—
64C22×Dic34—22no—
65C22×Dic34D412yes—
66C22×Dic34C2312yes—
67C2×M16×C17—21no—
68C2×M16×C17—22no—
69C2×M16×C17D414yes—
70C2×M16×C17C2312yes—
71C22×C8×C17—21no—
72C2×C42×C17—22no—
73C2×C42×C17—22no—
74C2×C42×C17—21no—
75C2×C42×C17C2312yes—
76C2×C22⋊Dic17—22no—
77C2×C22⋊Dic17—22no—
78C2×C22⋊Dic17—21no—
79#10587630—24no—
80#10587630—24no—
81#10587622—24no—
82#10587622—24no—
83#10587621—28no—
84#10587621—28no—
85#10587612—21no—
86#10587612—21no—
87#10587612D412yes—
88#10587612C2312yes—
89C2×C4⋊Dic17—21no—
90C2×C4⋊Dic17—21no—
91C2×C4⋊Dic17—21no—
92C2×C4⋊Dic17—21no—
93C2×C4⋊Dic17—21no—
94C2×C4⋊Dic17D411yescharacteristic
95C2×C4⋊Dic17D411yescharacteristic
96C2×C4⋊Dic17C2312yes—
97#10587610—24no—
98#10587610—24no—
99#10587610—24no—
100#10587610—24no—
101C2×#63225—22no—
102C2×#63225—22no—
103C2×C4×Dic17—21no—
104C2×#63223—21no—
105C2×#63223—22no—
106C2×#63223—22no—
107C2×#63223C2312yes—
108C22×#3622—21no—
109C17×#104—28no—
110#10587506—24no—
111#10587503—24no—
112#10587502—28no—
113#10587495—28no—
114#10587489—24no—
115#10587488—24no—
116C24×C17—21no—
117C24×C17C2×D411yescharacteristic
118#41×C17—24no—
119#41×C17—24no—
120#41×C17—22no—
121#41×C17—22no—
122#41×C17—22no—
123#41×C17—22no—
124#41×C17—42no—
125#41×C17—42no—
126#41×C17—42no—
127#41×C17—42no—
128C2×Q8×C17—21no—
129C2×Q8×C17—22no—
130C2×Q8×C17—22no—
131C2×Q8×C17C2×D412yes—
132C2×D4×C17—22no—
133C2×D4×C17—22no—
134C2×D4×C17—21no—
135C2×D4×C17—22no—
136C2×D4×C17—22no—
137C2×D4×C17—42no—
138C2×D4×C17—42no—
139C2×D4×C17C2×D412yes—
140C22×C4×C17—24no—
141C22×C4×C17—21no—
142C22×C4×C17—22no—
143C22×C4×C17—22no—
144C22×C4×C17—22no—
145C22×C4×C17—42no—
146C22×C4×C17—42no—
147C22×C4×C17—42no—
148C22×C4×C17—42no—
149C22×C4×C17C2×D411yescharacteristic
150C22×C4×C17C2×D411yescharacteristic
151C22×C4×C17C2×D411yescharacteristic
152C22×C4×C17C2×D411yescharacteristic
153C22×C4×C17C2×D411yescharacteristic
154C22×C4×C17C2×D412yes—
155C22×C4×C17#4112yes—
156C22×C4×C17#4112yes—
157C22×C4×C17#4112yes—
158C22×C4×C17C2411yescharacteristic
159C22×Dic17—22no—
160C22×Dic17—22no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—24no—
164C22×Dic17—24no—
165C22×Dic17—22no—
166C22×Dic17—44no—
167C22×Dic17—41no—
168C22×Dic17—41no—
169C22×Dic17C2×D414yes—
170C2×Dic34—22no—
171C2×Dic34—22no—
172C2×Dic34—24no—
173C2×Dic34—24no—
174C2×Dic34—22no—
175C2×Dic34—22no—
176C2×Dic34—22no—
177C2×Dic34—22no—
178C2×Dic34—22no—
179C2×Dic34—22no—
180C2×Dic34—42no—
181C2×Dic34—42no—
182C2×Dic34—42no—
183C2×Dic34—42no—
184C2×Dic34—42no—
185C2×Dic34—42no—
186C2×Dic34—42no—
187C2×Dic34—42no—
188M16×C17—24no—
189M16×C17—22no—
190M16×C17C2×D414yes—
191C2×C8×C17—24no—
192C2×C8×C17—22no—
193C42×C17—22no—
194C42×C17—22no—
195C42×C17—42no—
196C22⋊Dic17—28no—
197C22⋊Dic17—28no—
198C22⋊Dic17—22no—
199C22⋊Dic17—22no—
200C4⋊Dic17—21no—
201C4⋊Dic17—21no—
202C4⋊Dic17—22no—
203C4⋊Dic17—22no—
204C4⋊Dic17—41no—
205C4⋊Dic17—41no—
206C4⋊Dic17C2×D412yes—
207C4⋊Dic17C2×D412yes—
208#63225—28no—
209#63225—28no—
210C4×Dic17—22no—
211C4×Dic17—22no—
212#63223—22no—
213#63223—22no—
214#63223—42no—
215C2×#3622—22no—
216C2×#3622—42no—
217C2×#2038—171nomaximal, Sylow
218C23×C17—22no—
219C23×C17—22no—
220C23×C17—22no—
221C23×C17—42no—
222C23×C17—42no—
223C23×C17—42no—
224C23×C17#12011yescharacteristic
225C23×C17#12011yescharacteristic
226C23×C17#12112yes—
227C23×C17#12312yes—
228C23×C17C22×D411yescharacteristic
229Q8×C17—22no—
230Q8×C17—22no—
231Q8×C17—42no—
232D4×C17—22no—
233D4×C17—22no—
234D4×C17—42no—
235D4×C17—42no—
236D4×C17—44no—
237D4×C17—42no—
238C2×C4×C17—24no—
239C2×C4×C17—22no—
240C2×C4×C17—42no—
241C2×C4×C17—48no—
242C2×C4×C17—42no—
243C2×C4×C17—42no—
244C2×C4×C17—42no—
245C2×C4×C17—42no—
246C2×C4×C17—44no—
247C2×C4×C17#12011yescharacteristic
248C2×C4×C17#12011yescharacteristic
249C2×C4×C17#12112yes—
250C2×C4×C17#12112yes—
251C2×C4×C17#12112yes—
252C2×C4×C17#12112yes—
253C2×C4×C17#12112yes—
254C2×C4×C17#12312yes—
255C2×C4×C17#12312yes—
256C2×C4×C17#12312yes—
257C2×C4×C17#12412yes—
258C2×C4×C17#12412yes—
259C2×C4×C17C22×D411yescharacteristic
260C2×C4×C17C22×D411yescharacteristic
261C2×C4×C17C22×D411yescharacteristic
262C2×C4×C17C2×#4111yescharacteristic
263C2×C4×C17C2×#4111yescharacteristic
264C2×C4×C17C2×#4111yescharacteristic
265C2×Dic17—22no—
266C2×Dic17—22no—
267C2×Dic17—24no—
268C2×Dic17—24no—
269C2×Dic17—24no—
270C2×Dic17—44no—
271C2×Dic17—44no—
272C2×Dic17—42no—
273C2×Dic17—42no—
274C2×Dic17—44no—
275C2×Dic17—42no—
276C2×Dic17—82no—
277C2×Dic17—82no—
278Dic34—42no—
279Dic34—42no—
280Dic34—42no—
281Dic34—42no—
282Dic34—44no—
283Dic34—44no—
284C8×C17—24no—
285#3622—42no—
286C2×#536—171no—
287C2×#428—171no—
288C22×#104D1711yescharacteristic
289C2×#417—171no—
290C22×#101—171no—
291C2×#391—171no—
292#2038—178no—
293C2×#339—171no—
294C22×C17—21no—
295C22×C17—21no—
296C22×C17—21no—
297C22×C17—21no—
298C22×C17—24no—
299C22×C17—24no—
300C22×C17—42no—
301C22×C17—42no—
302C22×C17—42no—
303C22×C17—84no—
304C22×C17#39412yes—
305C22×C17#39412yes—
306C22×C17#45412yes—
307C22×C17#45612yes—
308C22×C17C2×#12011yescharacteristic
309C22×C17C2×#12111yescharacteristic
310C22×C17C2×#12311yescharacteristic
311C4×C17—44no—
312C4×C17—42no—
313C4×C17#39412yes—
314C4×C17#39412yes—
315C4×C17C2×#12111yescharacteristic
316C4×C17C2×#12111yescharacteristic
317C4×C17C2×#12311yescharacteristic
318C4×C17C2×#12411yescharacteristic
319Dic17—44no—
320Dic17—42no—
321Dic17—42no—
322Dic17—82no—
323C22×#41C2×D1711yescharacteristic
324C23×Q8—171no—
325C22×M16—171no—
326C22×M16C2×D1711yescharacteristic
327#536—174no—
328#536—342no—
329#536—342no—
330#536—342no—
331C2×C4⋊Q8—341no—
332C2×#124—341no—
333C2×#123—342no—
334C2×C22⋊Q8—341no—
335C2×C22⋊Q8—341no—
336C2×#117—171no—
337C22×C4⋊C4—171no—
338C22×C42C2×D1711yescharacteristic
339#428—174no—
340#428—342no—
341C2×#107—341no—
342C2×#106—341no—
343C2×#104—24no—
344C2×#104C2×D1714yes—
345#417—174no—
346#417—342no—
347C2×#103—341no—
348C2×#102—341no—
349C2×#101—174no—
350C2×#101—344no—
351#391—174no—
352#391—342no—
353C2×#95—342no—
354#339—174no—
355C2×C17—21no—
356C2×C17—21no—
357C2×C17—22no—
358C2×C17—82no—
359C2×C17#203814yescomplemented
360C2×C17C2×#39411yescharacteristic
361C2×C17C2×#45411yescharacteristic
362C2×C17C2×#45611yescharacteristic
363C2×#41—21no—
364C2×#41—21no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41D6812yes—
370C2×#41C22×D1712yes—
371C22×Q8—172no—
372C22×Q8—172no—
373C22×Q8—341no—
374C22×Q8—341no—
375C22×Q8—342no—
376C22×Q8—341no—
377C22×Q8—341no—
378C22×Q8—342no—
379C22×Q8—342no—
380C22×Q8—342no—
381C22×Q8D6811yescharacteristic
382C22×D4—21no—
383C22×D4D6811yescharacteristic
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—172no—
387C23×C4—341no—
388C23×C4C22×D1711yescharacteristic
389C2×M16—21no—
390C2×M16—22no—
391C2×M16—172no—
392C2×M16—341no—
393C2×M16—342no—
394C2×M16—342no—
395C2×M16C22⋊D1714yes—
396C2×M16C22×D1712yes—
397C22×C8—21no—
398C22×C8—341no—
399C4⋊Q8—344no—
400C4⋊Q8—344no—
401#124—344no—
402#124—344no—
403#123—348no—
404#123—348no—
405C22⋊Q8—344no—
406C22⋊Q8—344no—
407C22⋊Q8—344no—
408C22⋊Q8—344no—
409#117—172no—
410#117—172no—
411#117—341no—
412#117—341no—
413C2×C4⋊C4—171no—
414C2×C4⋊C4—171no—
415C2×C4⋊C4—172no—
416C2×C4⋊C4—342no—
417C2×C4⋊C4—342no—
418C2×C4⋊C4—341no—
419C2×C4⋊C4—341no—
420C2×C4⋊C4—341no—
421C2×C4⋊C4—341no—
422C2×C4⋊C4—341no—
423C2×C22⋊C4—342no—
424C2×C22⋊C4—342no—
425C2×C22⋊C4—341no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—21no—
429C2×C42—341no—
430C2×C42C22×D1712yes—
431#107—344no—
432#106—344no—
433#104—28no—
434#103—344no—
435#102—344no—
436#101—348no—
437#95—348no—
438C17C2×#203811yescharacteristic, complemented, Sylow
439C24—21no—
440C24D4×D1711yescharacteristic
441#41—22no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—24no—
446#41—24no—
447#41—42no—
448#41—42no—
449#41—42no—
450#41—42no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—342no—
455C2×Q8—342no—
456C2×Q8—342no—
457C2×Q8—342no—
458C2×Q8—342no—
459C2×Q8—342no—
460C2×Q8—342no—
461C2×Q8—342no—
462C2×Q8—344no—
463C2×Q8—344no—
464C2×Q8—682no—
465C2×Q8—682no—
466C2×Q8—682no—
467C2×Q8—682no—
468C2×Q8—682no—
469C2×Q8—682no—
470C2×Q8—682no—
471C2×Q8—682no—
472C2×Q8C2×D6812yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4C2×D6812yes—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—174no—
491C22×C4—342no—
492C22×C4—341no—
493C22×C4—341no—
494C22×C4—342no—
495C22×C4—344no—
496C22×C4—344no—
497C22×C4—342no—
498C22×C4—684no—
499C22×C4—681no—
500C22×C4—681no—
501C22×C4C2×D6811yescharacteristic
502C22×C4C2×D6811yescharacteristic
503C22×C4#6325212yes—
504C22×C4D4×D1711yescharacteristic
505C22×C4D4×D1711yescharacteristic
506C22×C4D4×D1711yescharacteristic
507C22×C4#6325412yes—
508C22×C4#6325412yes—
509C22×C4C2×C22⋊D1712yes—
510C22×C4C23×D1711yescharacteristic
511M16—22no—
512M16—24no—
513M16—342no—
514M16—342no—
515M16—682no—
516M16C2×C22⋊D1714yes—
517C2×C8—22no—
518C2×C8—24no—
519C2×C8—342no—
520C2×C8—682no—
521C4⋊C4—172no—
522C4⋊C4—172no—
523C4⋊C4—348no—
524C4⋊C4—348no—
525C4⋊C4—341no—
526C4⋊C4—341no—
527C4⋊C4—342no—
528C4⋊C4—342no—
529C4⋊C4—681no—
530C4⋊C4—681no—
531C22⋊C4—348no—
532C22⋊C4—348no—
533C22⋊C4—342no—
534C22⋊C4—342no—
535C42—22no—
536C42—22no—
537C42—42no—
538C42—342no—
539C42—342no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23#1058756811yescharacteristic
547C23#1058756811yescharacteristic
548C23#1058756912yes—
549C23#1058762412yes—
550C23C2×D4×D1711yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—42no—
554Q8—684no—
555Q8—684no—
556Q8—682no—
557Q8—682no—
558Q8—682no—
559Q8—682no—
560D4—22no—
561D4—22no—
562D4—44no—
563D4—42no—
564D4—42no—
565D4—42no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—42no—
569C2×C4—48no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—342no—
576C2×C4—342no—
577C2×C4—344no—
578C2×C4—344no—
579C2×C4—344no—
580C2×C4—684no—
581C2×C4—684no—
582C2×C4—682no—
583C2×C4—682no—
584C2×C4—684no—
585C2×C4—682no—
586C2×C4—1362no—
587C2×C4—1362no—
588C2×C4#1058756811yescharacteristic
589C2×C4#1058756811yescharacteristic
590C2×C4#1058756912yes—
591C2×C4#1058757112yes—
592C2×C4#1058757112yes—
593C2×C4#1058757212yes—
594C2×C4#1058757212yes—
595C2×C4#1058761612yes—
596C2×C4#1058761612yes—
597C2×C4#1058762412yes—
598C2×C4#1058762512yes—
599C2×C4#1058762512yes—
600C2×C4C22×D6811yescharacteristic
601C2×C4C2×#6325211yescharacteristic
602C2×C4C2×D4×D1711yescharacteristic
603C2×C4C2×#6325411yescharacteristic
604C2×C4C2×#6325411yescharacteristic
605C2×C4C22×C22⋊D1711yescharacteristic
606C8—24no—
607C8—682no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—24no—
613C22—24no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—84no—
618C22#1176272512yes—
619C22#1176272512yes—
620C22#1176298312yes—
621C22#1176299312yes—
622C22C2×#1058756811yescharacteristic
623C22C2×#1058762411yescharacteristic
624C22C2×#1058756911yescharacteristic
625C4—44no—
626C4—42no—
627C4—682no—
628C4—682no—
629C4—684no—
630C4—1362no—
631C4#1176272512yes—
632C4#1176272512yes—
633C4C2×#1058762511yescharacteristic
634C4C2×#1058761611yescharacteristic
635C4C2×#1058757211yescharacteristic
636C4C2×#1058757111yescharacteristic
637C2—21no—
638C2—22no—
639C2—21no—
640C2—82no—
641C2#1453000014yesdirect product factor
642C2C2×#1176272511yescharacteristic
643C2C2×#1176298311yescharacteristic
644C2C2×#1176299311yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×#104C2
socleC23×C17#120
prime radicalC22×#41×C17C22
hypercenterC22×#104D17
hypocenterC17C2×#2038
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#11762851C2semidirect
4. C22×#10587495C2semidirect
5. C2×#11762715C2semidirect
6. #14530000C2direct (N × H)
7. C2×#11762569C2semidirect
23. #11762851C22semidirect
31. C2×#10587495C22semidirect
33. #11762715C22semidirect
35. #11762569C22semidirect
359. C2×C17#2038semidirect
438. C17C2×#2038semidirect
641. C2#14530000direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117633802
C2×#117628512
C2×#117628102
C22×#105874952
C2×#117627152
#145300002
C2×#117625692
C22×C17×#1042
C2×#203817