Finite Group Databasebeta

← C2×#14536963 #17240695

Subgroups — C2×#14536963 #17240695

Order 4352.

1718 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14536963C2116yesmaximal, direct product factor
2C2×C17⋊#401C211yesmaximal, characteristic
3C2×C17⋊#401C211yesmaximal, characteristic
4C2×#11762751C211yesmaximal, characteristic
5C2×#11762750C211yesmaximal, characteristic
6C2×#11762750C211yesmaximal, characteristic
7C2×#11762748C211yesmaximal, characteristic
8C2×#11762747C211yesmaximal, characteristic
9C2×#11762742C211yesmaximal, characteristic
10C2×#11762742C211yesmaximal, characteristic
11C2×#11762740C211yesmaximal, characteristic
12C2×#11762728C211yesmaximal, characteristic
13C2×#11762716C211yesmaximal, characteristic
14C2×#11762695C211yesmaximal, characteristic
15C2×#11762691C211yesmaximal, characteristic
16C2×C17×#395C211yesmaximal, characteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63225C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26C17⋊#401C2218yes—
27C17⋊#401C2218yes—
28#11762751C2218yes—
29#11762750C2218yes—
30#11762750C2218yes—
31#11762748C2218yes—
32#11762747C2218yes—
33#11762742C2218yes—
34#11762742C2218yes—
35#11762740C2218yes—
36#11762728C2218yes—
37#11762716C2218yes—
38#11762695C2218yes—
39#11762691C2218yes—
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C23×Q8×C17C2211yescharacteristic
60C22×C4⋊C4×C17C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C17×#395C2218yes—
64C2×C17×#95C2211yescharacteristic
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
67C22×Q8×C17—24no—
68C22×Q8×C17—42no—
69C22×Q8×C17—42no—
70C22×Q8×C17C2314yes—
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C2×C4⋊C4×C17—24no—
87C2×C4⋊C4×C17—42no—
88C2×C4⋊C4×C17—42no—
89C2×C4⋊C4×C17C2314yes—
90C2×C4⋊C4×C17C2314yes—
91C2×C4⋊C4×C17C2314yes—
92C2×C4⋊Dic17—42no—
93C2×C4⋊Dic17—42no—
94C2×C4⋊Dic17C2314yes—
95C2×C4⋊Dic17C2314yes—
96C2×#63225—24no—
97C2×#63225—42no—
98C2×#63225—42no—
99C2×#63225—42no—
100C2×#63225—42no—
101C2×#63225—42no—
102C2×#63225C2314yes—
103C2×#63225C2314yes—
104C2×#63225C2314yes—
105C2×#63225C2314yes—
106C2×#63225C2314yes—
107C2×#63225C2314yes—
108C2×C4×Dic17—42no—
109C2×C4×Dic17C2314yes—
110C17×#95C2314yes—
111C17×#95C2314yes—
112C17×#95C2314yes—
113#10587502C2314yes—
114#10587502C2314yes—
115#10587502C2314yes—
116#10587502C2314yes—
117#10587502C2314yes—
118#10587502C2314yes—
119#10587502C2314yes—
120#10587502C2314yes—
121#10587502C2314yes—
122#10587502C2314yes—
123#10587502C2314yes—
124#10587502C2314yes—
125#10587502C2314yes—
126#10587502C2314yes—
127#10587502C2314yes—
128#10587502C2314yes—
129#10587502C2314yes—
130#10587502C2314yes—
131#10587502C2314yes—
132C24×C17C2411yescharacteristic
133C2×Q8×C17—28no—
134C2×Q8×C17—44no—
135C2×Q8×C17—44no—
136C2×Q8×C17—416no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—22no—
144C22×C4×C17—22no—
145C22×C4×C17—22no—
146C22×C4×C17—22no—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—22no—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17#4114yes—
158C22×C4×C17C2412yes—
159C22×C4×C17C2412yes—
160C22×C4×C17C2412yes—
161C22×C4×C17C2412yes—
162C22×C4×C17C2412yes—
163C22×C4×C17C2412yes—
164C22×C4×C17C2412yes—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17—22no—
171C22×Dic17—22no—
172C22×Dic17—22no—
173C22×Dic17—22no—
174C22×Dic17—22no—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17C2412yes—
190C22×Dic17C2412yes—
191C22×Dic17C2412yes—
192C22×Dic17C2412yes—
193C22×Dic17C2412yes—
194C22×Dic17C2412yes—
195C22×Dic17C2412yes—
196C22×Dic17C2412yes—
197C4⋊C4×C17—28no—
198C4⋊C4×C17—44no—
199C4⋊C4×C17—44no—
200C4⋊Dic17—44no—
201C4⋊Dic17—44no—
202#63225—28no—
203#63225—44no—
204#63225—44no—
205#63225—44no—
206#63225—44no—
207#63225—44no—
208C4×Dic17—44no—
209C2×#2833—171nomaximal, Sylow
210C23×C17C2×#4112yes—
211C23×C17H(5,𝔽2)12yes—
212C23×C17H(5,𝔽2)12yes—
213C23×C172−1+412yes—
214C23×C172−1+412yes—
215C23×C172−1+412yes—
216C23×C172−1+412yes—
217C23×C17C2511yescharacteristic
218Q8×C17—416no—
219C2×C4×C17—28no—
220C2×C4×C17—22no—
221C2×C4×C17—22no—
222C2×C4×C17—22no—
223C2×C4×C17—22no—
224C2×C4×C17—22no—
225C2×C4×C17—22no—
226C2×C4×C17—22no—
227C2×C4×C17—22no—
228C2×C4×C17—22no—
229C2×C4×C17—22no—
230C2×C4×C17—22no—
231C2×C4×C17—22no—
232C2×C4×C17—22no—
233C2×C4×C17—22no—
234C2×C4×C17—22no—
235C2×C4×C17—22no—
236C2×C4×C17—22no—
237C2×C4×C17—22no—
238C2×C4×C17—22no—
239C2×C4×C17—22no—
240C2×C4×C17—44no—
241C2×C4×C17—44no—
242C2×C4×C17—44no—
243C2×C4×C17—44no—
244C2×C4×C17—44no—
245C2×C4×C17—44no—
246C2×C4×C17C2×#4114yes—
247C2×Dic17—22no—
248C2×Dic17—22no—
249C2×Dic17—22no—
250C2×Dic17—22no—
251C2×Dic17—22no—
252C2×Dic17—22no—
253C2×Dic17—22no—
254C2×Dic17—22no—
255C2×Dic17—22no—
256C2×Dic17—22no—
257C2×Dic17—22no—
258C2×Dic17—22no—
259C2×Dic17—22no—
260C2×Dic17—22no—
261C2×Dic17—22no—
262C2×Dic17—22no—
263C2×Dic17—22no—
264C2×Dic17—22no—
265C2×Dic17—22no—
266C2×Dic17—22no—
267C2×Dic17—22no—
268C2×Dic17—22no—
269C2×Dic17—22no—
270C2×Dic17—22no—
271C2×Dic17—44no—
272C2×Dic17—44no—
273C2×Dic17—44no—
274C2×Dic17—44no—
275C2×Dic17—44no—
276C2×Dic17—44no—
277C2×Dic17—44no—
278C2×Dic17—44no—
279#2833—1716no—
280C2×#401—171no—
281C2×#401—171no—
282C2×#400—171no—
283C2×#400—171no—
284C2×#400—171no—
285C2×#400—171no—
286C2×#400—171no—
287C2×#398—171no—
288C2×#398—171no—
289C2×#398—171no—
290C2×#395—171no—
291C2×#395D1711yescharacteristic
292C2×#391—171no—
293C2×#387—171no—
294C2×#387—171no—
295C22×C17#53814yes—
296C22×C17#54114yes—
297C22×C17#54114yes—
298C22×C17#56314yes—
299C22×C17#56314yes—
300C22×C17#56314yes—
301C22×C17#56314yes—
302C22×C17C22×#4111yescharacteristic
303C22×C17C2×H(5,𝔽2)11yescharacteristic
304C22×C17C2×H(5,𝔽2)11yescharacteristic
305C22×C17C2×2−1+411yescharacteristic
306C22×C17C2×2−1+411yescharacteristic
307C22×C17C2×2−1+411yescharacteristic
308C22×C17C2×2−1+411yescharacteristic
309C4×C17—24no—
310C4×C17—42no—
311C4×C17—42no—
312C4×C17—42no—
313C4×C17—42no—
314C4×C17—42no—
315C4×C17—42no—
316Dic17—42no—
317Dic17—42no—
318Dic17—42no—
319Dic17—42no—
320Dic17—42no—
321Dic17—42no—
322Dic17—42no—
323Dic17—42no—
324C23×Q8C2×D1711yescharacteristic
325C22×C4⋊C4—171no—
326C22×C4⋊C4—171no—
327C22×C4⋊C4—171no—
328C22×C4⋊C4—171no—
329C22×C4⋊C4—171no—
330C22×C4⋊C4—171no—
331C22×C4⋊C4—171no—
332C22×C4⋊C4—171no—
333C22×C4⋊C4C2×D1711yescharacteristic
334C22×C4⋊C4C2×D1711yescharacteristic
335C22×C4⋊C4C2×D1711yescharacteristic
336C22×C42—171no—
337#401—178no—
338#401—178no—
339#400—178no—
340#400—178no—
341#400—178no—
342#400—178no—
343#400—178no—
344#398—178no—
345#398—178no—
346#398—178no—
347#395—178no—
348#395C2×D1718yes—
349#391—178no—
350#387—178no—
351#387—178no—
352C2×#95—171no—
353C2×#95—171no—
354C2×#95—171no—
355C2×#95—171no—
356C2×#95—171no—
357C2×#95—171no—
358C2×#95—171no—
359C2×#95—171no—
360C2×#95—171no—
361C2×#95—171no—
362C2×#95—171no—
363C2×#95—171no—
364C2×#95—171no—
365C2×#95—171no—
366C2×#95—171no—
367C2×#95—171no—
368C2×#95—171no—
369C2×#95—171no—
370C2×#95—171no—
371C2×#95C2×D1711yescharacteristic
372C2×#95C2×D1711yescharacteristic
373C2×#95C2×D1711yescharacteristic
374C2×C17#283318yescomplemented
375C2×C17C2×#53811yescharacteristic
376C2×C17C2×#54111yescharacteristic
377C2×C17C2×#54111yescharacteristic
378C2×C17C2×#56311yescharacteristic
379C2×C17C2×#56311yescharacteristic
380C2×C17C2×#56311yescharacteristic
381C2×C17C2×#56311yescharacteristic
382C22×Q8—24no—
383C22×Q8—42no—
384C22×Q8—42no—
385C22×Q8C22×D1714yes—
386C23×C4—171no—
387C23×C4—171no—
388C23×C4—171no—
389C23×C4—171no—
390C23×C4—171no—
391C23×C4—171no—
392C23×C4—171no—
393C23×C4—171no—
394C23×C4C22×D1711yescharacteristic
395C23×C4C22×D1711yescharacteristic
396C23×C4C22×D1711yescharacteristic
397C23×C4C22×D1711yescharacteristic
398C23×C4C22×D1711yescharacteristic
399C23×C4C22×D1711yescharacteristic
400C23×C4C22×D1711yescharacteristic
401C2×C4⋊C4—24no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—174no—
405C2×C4⋊C4—174no—
406C2×C4⋊C4—174no—
407C2×C4⋊C4—174no—
408C2×C4⋊C4—174no—
409C2×C4⋊C4—174no—
410C2×C4⋊C4—174no—
411C2×C4⋊C4—174no—
412C2×C4⋊C4—344no—
413C2×C4⋊C4—682no—
414C2×C4⋊C4—682no—
415C2×C4⋊C4—682no—
416C2×C4⋊C4—682no—
417C2×C4⋊C4—682no—
418C2×C4⋊C4—682no—
419C2×C4⋊C4—682no—
420C2×C4⋊C4C22×D1714yes—
421C2×C4⋊C4C22×D1714yes—
422C2×C4⋊C4C22×D1714yes—
423C2×C42—174no—
424C2×C42—682no—
425#95—174no—
426#95—174no—
427#95—174no—
428#95—174no—
429#95—174no—
430#95—174no—
431#95—174no—
432#95—174no—
433#95—174no—
434#95—174no—
435#95—174no—
436#95—174no—
437#95—174no—
438#95—174no—
439#95—174no—
440#95—174no—
441#95—174no—
442#95—174no—
443#95—174no—
444#95C22×D1714yes—
445#95C22×D1714yes—
446#95C22×D1714yes—
447C17C2×#283311yescharacteristic, complemented, Sylow
448C24C23×D1711yescharacteristic
449C2×Q8—28no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—416no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—172no—
474C22×C4—172no—
475C22×C4—172no—
476C22×C4—172no—
477C22×C4—172no—
478C22×C4—172no—
479C22×C4—172no—
480C22×C4—172no—
481C22×C4—342no—
482C22×C4—342no—
483C22×C4—342no—
484C22×C4—342no—
485C22×C4—342no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—342no—
489C22×C4—342no—
490C22×C4—342no—
491C22×C4—342no—
492C22×C4—342no—
493C22×C4—342no—
494C22×C4—342no—
495C22×C4—342no—
496C22×C4—342no—
497C22×C4—342no—
498C22×C4—342no—
499C22×C4—342no—
500C22×C4—342no—
501C22×C4—342no—
502C22×C4—342no—
503C22×C4—342no—
504C22×C4—342no—
505C22×C4#6325414yes—
506C22×C4C23×D1712yes—
507C22×C4C23×D1712yes—
508C22×C4C23×D1712yes—
509C22×C4C23×D1712yes—
510C22×C4C23×D1712yes—
511C22×C4C23×D1712yes—
512C22×C4C23×D1712yes—
513C4⋊C4—28no—
514C4⋊C4—44no—
515C4⋊C4—44no—
516C4⋊C4—348no—
517C4⋊C4—684no—
518C4⋊C4—684no—
519C4⋊C4—684no—
520C4⋊C4—684no—
521C4⋊C4—684no—
522C4⋊C4—684no—
523C4⋊C4—684no—
524C42—684no—
525C23C2×#6325412yes—
526C23#1058769112yes—
527C23#1058769112yes—
528C23#1058769412yes—
529C23#1058769412yes—
530C23#1058769412yes—
531C23#1058769712yes—
532C23C24×D1711yescharacteristic
533Q8—416no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—28no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—342no—
562C2×C4—342no—
563C2×C4—342no—
564C2×C4—342no—
565C2×C4—342no—
566C2×C4—342no—
567C2×C4—342no—
568C2×C4—342no—
569C2×C4—342no—
570C2×C4—342no—
571C2×C4—342no—
572C2×C4—342no—
573C2×C4—342no—
574C2×C4—342no—
575C2×C4—342no—
576C2×C4—342no—
577C2×C4—342no—
578C2×C4—342no—
579C2×C4—342no—
580C2×C4—342no—
581C2×C4—342no—
582C2×C4—342no—
583C2×C4—342no—
584C2×C4—342no—
585C2×C4—684no—
586C2×C4—684no—
587C2×C4—684no—
588C2×C4—684no—
589C2×C4—684no—
590C2×C4—684no—
591C2×C4—684no—
592C2×C4—684no—
593C2×C4C2×#6325414yes—
594C22#1176339414yes—
595C22#1176341914yes—
596C22#1176342014yes—
597C22#1176355814yes—
598C22#1176355814yes—
599C22#1176356014yes—
600C22#1176356014yes—
601C22C22×#6325411yescharacteristic
602C22C2×#1058769111yescharacteristic
603C22C2×#1058769111yescharacteristic
604C22C2×#1058769711yescharacteristic
605C22C2×#1058769411yescharacteristic
606C22C2×#1058769411yescharacteristic
607C22C2×#1058769411yescharacteristic
608C4—24no—
609C4—42no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—42no—
614C4—42no—
615C4—682no—
616C4—682no—
617C4—682no—
618C4—682no—
619C4—682no—
620C4—682no—
621C4—682no—
622C4—682no—
623C2#1453696318yesdirect product factor
624C2C2×#1176339411yescharacteristic
625C2C2×#1176341911yescharacteristic
626C2C2×#1176342011yescharacteristic
627C2C2×#1176355811yescharacteristic
628C2C2×#1176355811yescharacteristic
629C2C2×#1176356011yescharacteristic
630C2C2×#1176356011yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#395C2
socle, prime radicalC24×C17C24
hypercenterC2×#395D17
hypocenterC17C2×#2833
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. #14536963C2direct (N × H)
374. C2×C17#2833semidirect
447. C17C2×#2833semidirect
623. C2#14536963direct (N × H)

Maximal subgroups

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

subgroupindex
#145369632
C2×C17⋊#4012
C2×#117627512
C2×#117627502
C2×#117627482
C2×#117627472
C2×#117627422
C2×#117627402
C2×#117627282
C2×#117627162
C2×#117626952
C2×#117626912
C2×C17×#3952
C2×#283317