Finite Group Databasebeta

← C2×#14532644 #17202596

Subgroups — C2×#14532644 #17202596

Order 4352.

2486 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587575C211yesmaximal, characteristic
2C22×C4×Dic34C211yesmaximal, characteristic
3#14532644C2116yesmaximal, direct product factor
4C2×#11762751C211yesmaximal, characteristic
5C2×#11762749C211yesmaximal, characteristic
6C2×#11762743C211yesmaximal, characteristic
7C2×#11762742C211yesmaximal, characteristic
8C2×#11762713C211yesmaximal, characteristic
9C2×#11762713C211yesmaximal, characteristic
10C2×#11762707C211yesmaximal, characteristic
11C2×#11762706C211yesmaximal, characteristic
12C2×#11762704C211yesmaximal, characteristic
13C2×#11762704C211yesmaximal, characteristic
14C2×#11762691C211yesmaximal, characteristic
15C2×#11762660C211yesmaximal, characteristic
16C2×C17×#387C211yesmaximal, characteristic
17C23×Dic34C2211yescharacteristic
18C2×#10587575—28no—
19C2×#10587575C2218yes—
20C2×C4×Dic34—28no—
21C2×C4×Dic34C2218yes—
22C22×C4⋊Dic17C2211yescharacteristic
23C22×C4⋊Dic17C2211yescharacteristic
24C22×C4⋊Dic17C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63225C2211yescharacteristic
33C22×#63225C2211yescharacteristic
34C22×#63225C2211yescharacteristic
35C22×C4×Dic17C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38C22×C4×Dic17C2211yescharacteristic
39#11762751C2218yes—
40#11762749C2218yes—
41#11762743C2218yes—
42#11762742C2218yes—
43#11762713C2218yes—
44#11762713C2218yes—
45#11762707C2218yes—
46#11762706C2218yes—
47#11762704C2218yes—
48#11762704C2218yes—
49#11762691C2218yes—
50#11762660C2218yes—
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60C2×#10587502C2211yescharacteristic
61C22×C4⋊C4×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C42×C17C2211yescharacteristic
64C17×#387C2218yes—
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C22×Dic34—24no—
85C22×Dic34—24no—
86C22×Dic34Q818yes—
87C22×Dic34C2314yes—
88C2×C4⋊C4×C17—24no—
89C2×C4⋊C4×C17—24no—
90C2×C4⋊C4×C17C2314yes—
91C2×C4⋊C4×C17C2314yes—
92C2×C42×C17—24no—
93C2×C42×C17C2314yes—
94C2×C4⋊Dic17—24no—
95C2×C4⋊Dic17—24no—
96C2×C4⋊Dic17—24no—
97C2×C4⋊Dic17C2314yes—
98C2×C4⋊Dic17C2314yes—
99C2×C4⋊Dic17C2314yes—
100C2×#63225—24no—
101C2×#63225—24no—
102C2×#63225—24no—
103C2×#63225—24no—
104C2×#63225—24no—
105C2×#63225—24no—
106C2×#63225—24no—
107C2×#63225—24no—
108C2×#63225—24no—
109C2×#63225D418yes—
110C2×#63225C2314yes—
111C2×#63225C2314yes—
112C2×#63225C2314yes—
113C2×#63225C2314yes—
114C2×#63225C2314yes—
115C2×#63225C2314yes—
116C2×#63225C2314yes—
117C2×#63225C2314yes—
118C2×#63225C2314yes—
119C2×#63225C2314yes—
120C2×C4×Dic17—24no—
121C2×C4×Dic17—24no—
122C2×C4×Dic17—24no—
123C2×C4×Dic17—24no—
124C2×C4×Dic17C2314yes—
125C2×C4×Dic17C2314yes—
126C2×C4×Dic17C2314yes—
127C2×C4×Dic17C2314yes—
128#10587575—232no—
129C4×Dic34—232no—
130C17×#95C2314yes—
131C17×#95C2314yes—
132C17×#95C2314yes—
133C17×#95C2314yes—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138#10587502C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144C24×C17C2411yescharacteristic
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—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17C2×D414yes—
164C22×C4×C17C2×Q814yes—
165C22×C4×C17#4114yes—
166C22×C4×C17C2412yes—
167C22×C4×C17C2412yes—
168C22×C4×C17C2412yes—
169C22×C4×C17C2412yes—
170C22×C4×C17C2412yes—
171C22×C4×C17C2412yes—
172C22×C4×C17C2412yes—
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×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17C2×D414yes—
192C22×Dic17C2×D414yes—
193C22×Dic17C2×Q814yes—
194C22×Dic17C2×Q814yes—
195C22×Dic17#4114yes—
196C22×Dic17#4114yes—
197C22×Dic17C2412yes—
198C22×Dic17C2412yes—
199C22×Dic17C2412yes—
200C22×Dic17C2412yes—
201C22×Dic17C2412yes—
202C22×Dic17C2412yes—
203C22×Dic17C2412yes—
204C22×Dic17C2412yes—
205C2×Dic34—232no—
206C2×Dic34—28no—
207C2×Dic34—28no—
208C2×Dic34C2×Q8116yes—
209C4⋊C4×C17—28no—
210C4⋊C4×C17—28no—
211C42×C17—28no—
212C4⋊Dic17—28no—
213C4⋊Dic17—28no—
214C4⋊Dic17—28no—
215#63225—28no—
216#63225—28no—
217#63225—28no—
218#63225—28no—
219#63225—28no—
220#63225—28no—
221#63225—28no—
222#63225—28no—
223#63225—28no—
224#63225C2×D4116yes—
225C4×Dic17—28no—
226C4×Dic17—28no—
227C4×Dic17—28no—
228C4×Dic17—28no—
229C2×#2453—171nomaximal, Sylow
230C23×C17C22×D412yes—
231C23×C17C22×Q812yes—
232C23×C17C2×#4112yes—
233C23×C17C2×#4112yes—
234C23×C17C2×#4112yes—
235C23×C172−1+412yes—
236C23×C172−1+412yes—
237C23×C17C2511yescharacteristic
238C2×C4×C17—28no—
239C2×C4×C17—28no—
240C2×C4×C17—28no—
241C2×C4×C17—22no—
242C2×C4×C17—22no—
243C2×C4×C17—22no—
244C2×C4×C17—22no—
245C2×C4×C17—22no—
246C2×C4×C17—22no—
247C2×C4×C17—22no—
248C2×C4×C17—22no—
249C2×C4×C17—22no—
250C2×C4×C17—22no—
251C2×C4×C17—22no—
252C2×C4×C17—22no—
253C2×C4×C17—22no—
254C2×C4×C17—22no—
255C2×C4×C17—22no—
256C2×C4×C17—22no—
257C2×C4×C17—22no—
258C2×C4×C17—22no—
259C2×C4×C17—44no—
260C2×C4×C17—44no—
261C2×C4×C17—44no—
262C2×C4×C17—44no—
263C2×C4×C17C22×D414yes—
264C2×C4×C17C22×Q814yes—
265C2×C4×C17C2×#4114yes—
266C2×Dic17—28no—
267C2×Dic17—28no—
268C2×Dic17—28no—
269C2×Dic17—22no—
270C2×Dic17—22no—
271C2×Dic17—22no—
272C2×Dic17—22no—
273C2×Dic17—22no—
274C2×Dic17—22no—
275C2×Dic17—22no—
276C2×Dic17—22no—
277C2×Dic17—22no—
278C2×Dic17—22no—
279C2×Dic17—22no—
280C2×Dic17—22no—
281C2×Dic17—22no—
282C2×Dic17—22no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—22no—
286C2×Dic17—22no—
287C2×Dic17—44no—
288C2×Dic17—44no—
289C2×Dic17—44no—
290C2×Dic17—44no—
291C2×Dic17C22⋊Q8116yes—
292C2×Dic17C22×D414yes—
293C2×Dic17C22×D414yes—
294C2×Dic17C22×Q814yes—
295C2×Dic17C22×Q814yes—
296C2×Dic17C2×#4114yes—
297C2×Dic17C2×#4114yes—
298Dic34—232no—
299C22×#125—171no—
300C22×C4×Q8—171no—
301#2453—1716no—
302C2×#400—171no—
303C2×#400—171no—
304C2×#398—171no—
305C2×#398—171no—
306C2×#391—171no—
307C2×#391—171no—
308C2×#389—171no—
309C2×#389—171no—
310C2×#389—171no—
311C2×#389—171no—
312C2×#387—171no—
313C2×#387D1711yescharacteristic
314C2×C4×C4⋊C4—171no—
315C22×C17C2×C22⋊Q814yes—
316C22×C17#52914yes—
317C22×C17#54114yes—
318C22×C17#54714yes—
319C22×C17#54814yes—
320C22×C17#55714yes—
321C22×C17#55714yes—
322C22×C17C23×D411yescharacteristic
323C22×C17C23×Q811yescharacteristic
324C22×C17C22×#4111yescharacteristic
325C22×C17C22×#4111yescharacteristic
326C22×C17C22×#4111yescharacteristic
327C22×C17C2×2−1+411yescharacteristic
328C22×C17C2×2−1+411yescharacteristic
329C4×C17—24no—
330C4×C17—24no—
331C4×C17—24no—
332C4×C17—42no—
333C4×C17—42no—
334C4×C17—42no—
335C4×C17—42no—
336Dic17—24no—
337Dic17—24no—
338Dic17—24no—
339Dic17—42no—
340Dic17—42no—
341Dic17—42no—
342Dic17—42no—
343Dic17C2×C22⋊Q818yes—
344C23×Q8—171no—
345C2×#125—178no—
346C2×#125—348no—
347C2×C4×Q8—178no—
348C2×C4×Q8—348no—
349C22×C4⋊C4—171no—
350C22×C4⋊C4—171no—
351C22×C4⋊C4—171no—
352C22×C4⋊C4—171no—
353C22×C4⋊C4—171no—
354C22×C4⋊C4—171no—
355C22×C4⋊C4—171no—
356C22×C4⋊C4—171no—
357C22×C4⋊C4—171no—
358C22×C4⋊C4—171no—
359C22×C4⋊C4—171no—
360C22×C4⋊C4—171no—
361C22×C4⋊C4—171no—
362C22×C4⋊C4C2×D1711yescharacteristic
363C22×C4⋊C4C2×D1711yescharacteristic
364C22×C42—171no—
365C22×C42—171no—
366C22×C42—171no—
367C22×C42—171no—
368C22×C42C2×D1711yescharacteristic
369#400—178no—
370#400—178no—
371#398—178no—
372#398—178no—
373#391—178no—
374#391—178no—
375#389—178no—
376#389—178no—
377#389—178no—
378#389—178no—
379#387—178no—
380#387C2×D1718yes—
381C4×C4⋊C4—178no—
382C2×#95—171no—
383C2×#95—171no—
384C2×#95—171no—
385C2×#95—171no—
386C2×#95—171no—
387C2×#95—171no—
388C2×#95—171no—
389C2×#95—171no—
390C2×#95—171no—
391C2×#95—171no—
392C2×#95C2×D1711yescharacteristic
393C2×#95C2×D1711yescharacteristic
394C2×#95C2×D1711yescharacteristic
395C2×#95C2×D1711yescharacteristic
396C2×C17#245318yescomplemented
397C2×C17C22×C22⋊Q811yescharacteristic
398C2×C17C2×#52911yescharacteristic
399C2×C17C2×#54111yescharacteristic
400C2×C17C2×#54711yescharacteristic
401C2×C17C2×#54811yescharacteristic
402C2×C17C2×#55711yescharacteristic
403C2×C17C2×#55711yescharacteristic
404C22×Q8—178no—
405C22×Q8—174no—
406C22×Q8—344no—
407C22×Q8—344no—
408C23×C4—171no—
409C23×C4—171no—
410C23×C4—171no—
411C23×C4—171no—
412C23×C4—171no—
413C23×C4—171no—
414C23×C4—171no—
415C23×C4—171no—
416C23×C4C22×D1711yescharacteristic
417C23×C4C22×D1711yescharacteristic
418C23×C4C22×D1711yescharacteristic
419C23×C4C22×D1711yescharacteristic
420C23×C4C22×D1711yescharacteristic
421C23×C4C22×D1711yescharacteristic
422C23×C4C22×D1711yescharacteristic
423#125—3432no—
424C4×Q8—3432no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—178no—
428C2×C4⋊C4—174no—
429C2×C4⋊C4—174no—
430C2×C4⋊C4—174no—
431C2×C4⋊C4—174no—
432C2×C4⋊C4—174no—
433C2×C4⋊C4—174no—
434C2×C4⋊C4—174no—
435C2×C4⋊C4—174no—
436C2×C4⋊C4—174no—
437C2×C4⋊C4—174no—
438C2×C4⋊C4—174no—
439C2×C4⋊C4—174no—
440C2×C4⋊C4—174no—
441C2×C4⋊C4—344no—
442C2×C4⋊C4—344no—
443C2×C4⋊C4—344no—
444C2×C4⋊C4—344no—
445C2×C4⋊C4—344no—
446C2×C4⋊C4—344no—
447C2×C4⋊C4—344no—
448C2×C4⋊C4—344no—
449C2×C4⋊C4—344no—
450C2×C4⋊C4—344no—
451C2×C4⋊C4—344no—
452C2×C4⋊C4—344no—
453C2×C4⋊C4C22×D1714yes—
454C2×C4⋊C4C22×D1714yes—
455C2×C42—24no—
456C2×C42—174no—
457C2×C42—174no—
458C2×C42—174no—
459C2×C42—174no—
460C2×C42—344no—
461C2×C42—344no—
462C2×C42—344no—
463C2×C42—344no—
464C2×C42C22×D1714yes—
465#95—174no—
466#95—174no—
467#95—174no—
468#95—174no—
469#95—174no—
470#95—174no—
471#95—174no—
472#95—174no—
473#95—174no—
474#95—174no—
475#95C22×D1714yes—
476#95C22×D1714yes—
477#95C22×D1714yes—
478#95C22×D1714yes—
479C17C2×#245311yescharacteristic, complemented, Sylow
480C24C23×D1711yescharacteristic
481C2×Q8—1716no—
482C2×Q8—348no—
483C2×Q8—3432no—
484C2×Q8—348no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—174no—
504C22×C4—174no—
505C22×C4—174no—
506C22×C4—172no—
507C22×C4—174no—
508C22×C4—174no—
509C22×C4—174no—
510C22×C4—172no—
511C22×C4—172no—
512C22×C4—172no—
513C22×C4—172no—
514C22×C4—172no—
515C22×C4—172no—
516C22×C4—172no—
517C22×C4—342no—
518C22×C4—342no—
519C22×C4—342no—
520C22×C4—342no—
521C22×C4—342no—
522C22×C4—342no—
523C22×C4—342no—
524C22×C4—342no—
525C22×C4—342no—
526C22×C4—342no—
527C22×C4—342no—
528C22×C4—342no—
529C22×C4—342no—
530C22×C4—342no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4#6325214yes—
536C22×C4D4×D1714yes—
537C22×C4Q8×D1714yes—
538C22×C4C23×D1712yes—
539C22×C4C23×D1712yes—
540C22×C4C23×D1712yes—
541C22×C4C23×D1712yes—
542C22×C4C23×D1712yes—
543C22×C4C23×D1712yes—
544C22×C4C23×D1712yes—
545C4⋊C4—28no—
546C4⋊C4—28no—
547C4⋊C4—1716no—
548C4⋊C4—348no—
549C4⋊C4—348no—
550C4⋊C4—348no—
551C4⋊C4—348no—
552C4⋊C4—348no—
553C4⋊C4—348no—
554C4⋊C4—348no—
555C4⋊C4—348no—
556C4⋊C4—348no—
557C4⋊C4—348no—
558C4⋊C4—348no—
559C4⋊C4—348no—
560C42—28no—
561C42—348no—
562C42—348no—
563C42—348no—
564C42—348no—
565C23C2×#6325212yes—
566C23C2×D4×D1712yes—
567C23C2×Q8×D1712yes—
568C23#41×D1712yes—
569C23#41×D1712yes—
570C23#1058769712yes—
571C23#1058769712yes—
572C23C24×D1711yescharacteristic
573Q8—3432no—
574C2×C4—28no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—1716no—
600C2×C4—174no—
601C2×C4—174no—
602C2×C4—174no—
603C2×C4—174no—
604C2×C4—174no—
605C2×C4—174no—
606C2×C4—348no—
607C2×C4—348no—
608C2×C4—348no—
609C2×C4—342no—
610C2×C4—342no—
611C2×C4—342no—
612C2×C4—342no—
613C2×C4—342no—
614C2×C4—342no—
615C2×C4—342no—
616C2×C4—342no—
617C2×C4—342no—
618C2×C4—342no—
619C2×C4—342no—
620C2×C4—342no—
621C2×C4—342no—
622C2×C4—342no—
623C2×C4—342no—
624C2×C4—342no—
625C2×C4—342no—
626C2×C4—342no—
627C2×C4—684no—
628C2×C4—684no—
629C2×C4—684no—
630C2×C4—684no—
631C2×C4C2×#6325214yes—
632C2×C4C2×D4×D1714yes—
633C2×C4C2×Q8×D1714yes—
634C22C22⋊Q8×D1714yes—
635C22#1176333714yes—
636C22#1176341614yes—
637C22#1176345714yes—
638C22#1176346814yes—
639C22#1176353614yes—
640C22#1176353714yes—
641C22C22×D4×D1711yescharacteristic
642C22C22×Q8×D1711yescharacteristic
643C22C2×#41×D1711yescharacteristic
644C22C2×#41×D1711yescharacteristic
645C22C22×#6325211yescharacteristic
646C22C2×#1058769711yescharacteristic
647C22C2×#1058769711yescharacteristic
648C4—24no—
649C4—24no—
650C4—24no—
651C4—42no—
652C4—42no—
653C4—42no—
654C4—42no—
655C4—178no—
656C4—344no—
657C4—344no—
658C4—344no—
659C4—682no—
660C4—682no—
661C4—682no—
662C4—682no—
663C2#1453264418yesdirect product factor
664C2C2×C22⋊Q8×D1711yescharacteristic
665C2C2×#1176333711yescharacteristic
666C2C2×#1176341611yescharacteristic
667C2C2×#1176345711yescharacteristic
668C2C2×#1176346811yescharacteristic
669C2C2×#1176353611yescharacteristic
670C2C2×#1176353711yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#387C2
socle, prime radicalC24×C17C24
hypercenterC2×#387D17
hypocenterC17C2×#2453
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #14532644C2direct (N × H)
396. C2×C17#2453semidirect
479. C17C2×#2453semidirect
663. C2#14532644direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875752
C22×C4×Dic342
#145326442
C2×#117627512
C2×#117627492
C2×#117627432
C2×#117627422
C2×#117627132
C2×#117627072
C2×#117627062
C2×#117627042
C2×#117626912
C2×#117626602
C2×C17×#3872
C2×#245317