Finite Group Databasebeta

← C4×#11762745 #16956153

Subgroups — C4×#11762745 #16956153

Order 4352.

1966 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
1C2×#11762745C211yesmaximal, characteristic
2C2×C4×#63225C212yesmaximal, complemented
3C2×C4×C4⋊Dic17C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic17C212yesmaximal
5#14527053C211yesmaximal, characteristic, complemented
6#14527050C212yesmaximal, complemented
7#14527048C211yesmaximal, characteristic, complemented
8#14527029C211yesmaximal, characteristic
9#14527027C212yesmaximal
10C4×#10587502C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C17C211yesmaximal, characteristic
12C22×C4⋊Dic17C2211yescharacteristic
13C22×C4⋊Dic17C2211yescharacteristic
14C22×#63225C2212yes—
15C22×#63225C2212yes—
16C22×C22⋊Dic17C2212yes—
17C22×C22⋊Dic17C2212yes—
18C22×C4×Dic17C2212yes—
19C22×C4×Dic17C2212yes—
20#11762745C418yesdirect product factor
21C4×#63225—28no—
22C4×C4⋊Dic17—24no—
23C4×C22⋊Dic17—28no—
24C2×#10587502C2212yes—
25C2×#10587502C2211yescharacteristic
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2211yescharacteristic
32C24×C4×C17C2211yescharacteristic
33C22×C22⋊C4×C17C2211yescharacteristic
34C22×C22⋊C4×C17C2211yescharacteristic
35C22×C42×C17C2211yescharacteristic
36C22×C42×C17C2211yescharacteristic
37C4×C22⋊C4×C17—24no—
38C2×C17×#95C2211yescharacteristic
39C2×C17×#95C2211yescharacteristic
40C25×C17C2311yescharacteristic
41C23×C4×C17—22no—
42C23×C4×C17—24no—
43C23×C4×C17—22no—
44C23×C4×C17—24no—
45C23×C4×C17Q814yes—
46C23×C4×C17C2311yescharacteristic
47C23×C4×C17C2311yescharacteristic
48C23×C4×C17C2311yescharacteristic
49C23×C4×C17C2311yescharacteristic
50C23×C4×C17C2311yescharacteristic
51C23×C4×C17C2311yescharacteristic
52C23×Dic17C2312yes—
53C23×Dic17C2312yes—
54C23×Dic17C2312yes—
55C23×Dic17C2312yes—
56C2×C22⋊C4×C17—22no—
57C2×C22⋊C4×C17—22no—
58C2×C22⋊C4×C17—22no—
59C2×C22⋊C4×C17—22no—
60C2×C22⋊C4×C17—22no—
61C2×C22⋊C4×C17C2×C414yes—
62C2×C42×C17—24no—
63C2×C42×C17—22no—
64C2×C42×C17—24no—
65C2×C42×C17D414yes—
66C2×C22⋊Dic17—24no—
67C2×C22⋊Dic17—24no—
68C2×C22⋊Dic17—24no—
69C2×C22⋊Dic17—24no—
70C2×C22⋊Dic17—24no—
71C2×C22⋊Dic17C2×C418yes—
72C2×C4⋊Dic17—22no—
73C2×C4⋊Dic17—22no—
74C2×C4⋊Dic17—22no—
75C2×C4⋊Dic17—24no—
76C2×C4⋊Dic17C2×C414yescomplemented
77C2×#63225—24no—
78C2×#63225—24no—
79C2×#63225—24no—
80C2×#63225—24no—
81C2×#63225—24no—
82C2×#63225C2×C418yescomplemented
83C2×C4×Dic17—24no—
84C2×C4×Dic17—24no—
85C2×C4×Dic17—24no—
86C2×C4×Dic17—24no—
87C2×C4×Dic17—24no—
88C2×C4×Dic17D418yes—
89C17×#95—22no—
90C17×#95—22no—
91#10587502—24no—
92#10587502—22no—
93#10587502—24no—
94#10587502—24no—
95#10587502—24no—
96#10587502—24no—
97#10587502—24no—
98#10587502C2×C414yescomplemented
99C24×C17—22no—
100C24×C17—21no—
101C24×C17—21no—
102C24×C17—22no—
103C24×C17—22no—
104C24×C17—22no—
105C24×C17—21no—
106C24×C17—21no—
107C24×C17C22×C412yes—
108C24×C17C2×Q812yes—
109C24×C17#4112yes—
110C24×C17C2411yescharacteristic
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—21no—
115C22×C4×C17—22no—
116C22×C4×C17—22no—
117C22×C4×C17—21no—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—22no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—21no—
128C22×C4×C17—21no—
129C22×C4×C17—216no—
130C22×C4×C17—28no—
131C22×C4×C17—48no—
132C22×C4×C17—44no—
133C22×C4×C17—44no—
134C22×C4×C17C22×C412yes—
135C22×C4×C17C22×C412yes—
136C22×C4×C17C2×D414yes—
137C22×C4×C17C2×D412yes—
138C22×C4×C17C2×D412yes—
139C22×C4×C17C2×D412yes—
140C22×C4×C17C2×Q812yes—
141C22×C4×C17C2×Q812yes—
142C22×C4×C17#4112yes—
143C22×C4×C17#4112yes—
144C22×C4×C17#4112yes—
145C22×C4×C17#4114yes—
146C22×Dic17—22no—
147C22×Dic17—22no—
148C22×Dic17—22no—
149C22×Dic17—22no—
150C22×Dic17—22no—
151C22×Dic17—22no—
152C22×Dic17—22no—
153C22×Dic17—22no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17—22no—
158C22×Dic17—22no—
159C22×Dic17—22no—
160C22×Dic17—22no—
161C22×Dic17—22no—
162C22×Dic17—22no—
163C22×Dic17—22no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17C22×C414yes—
169C22×Dic17C22×C414yes—
170C22×Dic17C2×D414yes—
171C22×Dic17C2×D414yes—
172C22×Dic17#4114yes—
173C22×Dic17#4114yes—
174C22⋊C4×C17—28no—
175C22⋊C4×C17—28no—
176C42×C17—28no—
177C42×C17—44no—
178C22⋊Dic17—216no—
179C22⋊Dic17—216no—
180C4⋊Dic17—28no—
181C4⋊Dic17—28no—
182#63225—216no—
183#63225—216no—
184C4×Dic17—216no—
185C4×Dic17—48no—
186C4×#399—171nomaximal, Sylow
187C23×C17—24no—
188C23×C17—22no—
189C23×C17—24no—
190C23×C17—22no—
191C23×C17—24no—
192C23×C17—22no—
193C23×C17—24no—
194C23×C17—22no—
195C23×C17—24no—
196C23×C17—22no—
197C23×C17—24no—
198C23×C17—22no—
199C23×C17—41no—
200C23×C17—42no—
201C23×C17—41no—
202C23×C17—42no—
203C23×C17—42no—
204C23×C17—42no—
205C23×C17—42no—
206C23×C17—41no—
207C23×C17—41no—
208C23×C17—42no—
209C23×C17C4×Q814yes—
210C23×C17C23×C411yescharacteristic
211C23×C17C22×D412yes—
212C23×C17C22×D411yescharacteristic
213C23×C17C22×Q811yescharacteristic
214C23×C17C2×#4111yescharacteristic
215C23×C17C2×#4111yescharacteristic
216C23×C17C2×#4111yescharacteristic
217C23×C17C2×#4111yescharacteristic
218C23×C17C2×#4112yes—
219C23×C17C2×#4112yes—
220C23×C17C2×#4112yes—
221C2×C4×C17—24no—
222C2×C4×C17—22no—
223C2×C4×C17—22no—
224C2×C4×C17—24no—
225C2×C4×C17—22no—
226C2×C4×C17—24no—
227C2×C4×C17—24no—
228C2×C4×C17—22no—
229C2×C4×C17—22no—
230C2×C4×C17—22no—
231C2×C4×C17—22no—
232C2×C4×C17—24no—
233C2×C4×C17—22no—
234C2×C4×C17—41no—
235C2×C4×C17—42no—
236C2×C4×C17—41no—
237C2×C4×C17—42no—
238C2×C4×C17—42no—
239C2×C4×C17—42no—
240C2×C4×C17—41no—
241C2×C4×C17—41no—
242C2×C4×C17—41no—
243C2×C4×C17—41no—
244C2×C4×C17—42no—
245C2×C4×C17—416no—
246C2×C4×C17C4×D414yes—
247C2×C4×C17C22⋊Q818yes—
248C2×C4×C17C22⋊Q814yes—
249C2×C4×C17#12318yes—
250C2×C4×C17#12314yes—
251C2×C4×C17#12714yes—
252C2×Dic17—24no—
253C2×Dic17—24no—
254C2×Dic17—24no—
255C2×Dic17—24no—
256C2×Dic17—24no—
257C2×Dic17—24no—
258C2×Dic17—24no—
259C2×Dic17—24no—
260C2×Dic17—24no—
261C2×Dic17—24no—
262C2×Dic17—24no—
263C2×Dic17—24no—
264C2×Dic17—24no—
265C2×Dic17—24no—
266C2×Dic17—24no—
267C2×Dic17—42no—
268C2×Dic17—42no—
269C2×Dic17—42no—
270C2×Dic17—42no—
271C2×Dic17—42no—
272C2×Dic17—42no—
273C2×Dic17—42no—
274C2×Dic17—42no—
275C2×Dic17—42no—
276C2×Dic17—42no—
277C2×Dic17—42no—
278C2×Dic17—42no—
279C2×Dic17C4×D418yes—
280C2×#399—171no—
281C2×C4×C4⋊C4—171no—
282C2×C4×C4⋊C4—172no—
283C2×C4×C22⋊C4—172no—
284C2×C4×C22⋊C4D1711yescharacteristic
285#1445—172no—
286#1445—171no—
287#1444—171no—
288#1439—172no—
289#1439—171no—
290C4×#95—171no—
291C22×C17—28no—
292C22×C17—24no—
293C22×C17—42no—
294C22×C17—42no—
295C22×C17—42no—
296C22×C17—44no—
297C22×C17—42no—
298C22×C17—44no—
299C22×C17—42no—
300C22×C17—42no—
301C22×C17—44no—
302C22×C17C2×C4×D412yes—
303C22×C17C2×C4×D411yescharacteristic
304C22×C17C2×C4×Q811yescharacteristic
305C22×C17C4×#4112yes—
306C22×C17C4×#4111yescharacteristic
307C22×C17C2×C22⋊Q812yes—
308C22×C17C2×C22⋊Q811yescharacteristic
309C22×C17C2×#12311yescharacteristic
310C22×C17C2×#12312yes—
311C22×C17#52511yescharacteristic
312C22×C17#52512yes—
313C22×C17#52512yes—
314C22×C17#52511yescharacteristic
315C22×C17#52912yes—
316C22×C17#52912yes—
317C22×C17#52912yes—
318C22×C17#52912yes—
319C22×C17#52911yescharacteristic
320C22×C17C2×#12711yescharacteristic
321C22×C17#53211yescharacteristic
322C22×C17#53212yes—
323C22×C17#53312yes—
324C22×C17#53311yescharacteristic
325C4×C17—24no—
326C4×C17—42no—
327C4×C17—42no—
328C4×C17—42no—
329C4×C17—42no—
330C4×C17#39918yescomplemented
331Dic17—28no—
332Dic17—44no—
333Dic17—44no—
334Dic17—44no—
335C24×C4C2×D1711yescharacteristic
336C22×C4⋊C4—172no—
337C22×C4⋊C4—171no—
338C22×C4⋊C4—172no—
339C22×C4⋊C4—171no—
340C22×C22⋊C4—172no—
341C22×C22⋊C4—172no—
342C22×C22⋊C4C2×D1711yescharacteristic
343C22×C22⋊C4C2×D1711yescharacteristic
344C22×C42—172no—
345C22×C42—172no—
346C22×C42C2×D1711yescharacteristic
347C22×C42C2×D1711yescharacteristic
348#399—178no—
349C4×C4⋊C4—348no—
350C4×C4⋊C4—344no—
351C4×C22⋊C4—24no—
352C4×C22⋊C4—348no—
353C2×#95—171no—
354C2×#95—172no—
355C2×#95—171no—
356C2×#95—172no—
357C2×#95—172no—
358C2×#95—172no—
359C2×#95—172no—
360C2×#95—172no—
361C2×#95C2×D1711yescharacteristic
362C2×#95C2×D1711yescharacteristic
363C2×C17—44no—
364C2×C17C4×#12311yescharacteristic
365C2×C17C4×#12312yes—
366C2×C17C4×C22⋊Q812yes—
367C2×C17C4×C22⋊Q811yescharacteristic
368C2×C17C4×#12711yescharacteristic
369C2×C17C2×#39911yescharacteristic
370C2×C17#239511yescharacteristic
371C2×C17#239512yes—
372C2×C17#239611yescharacteristic
373C2×C17#239612yes—
374C2×C17#239711yescharacteristic
375C25C22×D1711yescharacteristic
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—172no—
381C23×C4—172no—
382C23×C4—172no—
383C23×C4—172no—
384C23×C4Dic3414yes—
385C23×C4C22×D1711yescharacteristic
386C23×C4C22×D1711yescharacteristic
387C23×C4C22×D1711yescharacteristic
388C23×C4C22×D1711yescharacteristic
389C23×C4C22×D1711yescharacteristic
390C23×C4C22×D1711yescharacteristic
391C2×C4⋊C4—178no—
392C2×C4⋊C4—174no—
393C2×C4⋊C4—344no—
394C2×C4⋊C4—344no—
395C2×C4⋊C4—344no—
396C2×C4⋊C4—344no—
397C2×C4⋊C4—344no—
398C2×C4⋊C4—344no—
399C2×C4⋊C4—342no—
400C2×C4⋊C4—342no—
401C2×C4⋊C4—342no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—178no—
408C2×C22⋊C4—344no—
409C2×C22⋊C4—344no—
410C2×C22⋊C4—344no—
411C2×C22⋊C4—344no—
412C2×C22⋊C4—344no—
413C2×C22⋊C4C4×D1714yes—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—178no—
418C2×C42—344no—
419C2×C42—344no—
420C2×C42—344no—
421C2×C42—344no—
422C2×C42—344no—
423C2×C42C22⋊D1714yes—
424#95—22no—
425#95—22no—
426#95—174no—
427#95—344no—
428#95—344no—
429#95—344no—
430#95—344no—
431#95—344no—
432#95—342no—
433#95—344no—
434C17C4×#39911yescharacteristic, complemented, Sylow
435C24—21no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24C2×Dic3412yes—
444C24C2×C4×D1712yes—
445C24#6325212yes—
446C24C23×D1711yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
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—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—216no—
466C22×C4—28no—
467C22×C4—48no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—174no—
471C22×C4—174no—
472C22×C4—174no—
473C22×C4—174no—
474C22×C4—174no—
475C22×C4—174no—
476C22×C4—342no—
477C22×C4—342no—
478C22×C4—342no—
479C22×C4—342no—
480C22×C4—342no—
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×C4C2×Dic3412yes—
499C22×C4C2×Dic3412yes—
500C22×C4C2×C4×D1712yes—
501C22×C4C2×C4×D1712yes—
502C22×C4#6325212yes—
503C22×C4#6325212yes—
504C22×C4#6325212yes—
505C22×C4D4×D1714yes—
506C22×C4#6325414yes—
507C22×C4C2×C22⋊D1712yes—
508C22×C4C2×C22⋊D1712yes—
509C22×C4C2×C22⋊D1712yes—
510C4⋊C4—3416no—
511C4⋊C4—3416no—
512C4⋊C4—348no—
513C4⋊C4—348no—
514C22⋊C4—28no—
515C22⋊C4—28no—
516C22⋊C4—3416no—
517C22⋊C4—3416no—
518C42—28no—
519C42—44no—
520C42—3416no—
521C42—688no—
522C23—24no—
523C23—22no—
524C23—24no—
525C23—22no—
526C23—24no—
527C23—22no—
528C23—24no—
529C23—22no—
530C23—24no—
531C23—22no—
532C23—24no—
533C23—22no—
534C23—41no—
535C23—42no—
536C23—41no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—41no—
542C23—41no—
543C23—42no—
544C23C4×Dic3414yes—
545C23C22×Dic3411yescharacteristic
546C23C22×C4×D1711yescharacteristic
547C23C2×#6325211yescharacteristic
548C23C2×#6325211yescharacteristic
549C23C2×#6325211yescharacteristic
550C23C2×#6325211yescharacteristic
551C23C2×D4×D1712yes—
552C23C2×#6325412yes—
553C23#41×D1712yes—
554C23#41×D1712yes—
555C23C22×C22⋊D1711yescharacteristic
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—416no—
581C2×C4—178no—
582C2×C4—344no—
583C2×C4—344no—
584C2×C4—344no—
585C2×C4—344no—
586C2×C4—344no—
587C2×C4—344no—
588C2×C4—344no—
589C2×C4—344no—
590C2×C4—344no—
591C2×C4—344no—
592C2×C4—344no—
593C2×C4—344no—
594C2×C4—344no—
595C2×C4—344no—
596C2×C4—344no—
597C2×C4—682no—
598C2×C4—682no—
599C2×C4—682no—
600C2×C4—682no—
601C2×C4—682no—
602C2×C4—682no—
603C2×C4—682no—
604C2×C4—682no—
605C2×C4—682no—
606C2×C4—682no—
607C2×C4—682no—
608C2×C4—682no—
609C2×C4#1058756418yes—
610C2×C4#1058756918yes—
611C2×C4#1058761014yes—
612C2×C4C4×C22⋊D1714yes—
613C2×C4#1058762114yes—
614C2×C4#1058762614yes—
615C22—28no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—44no—
621C22—42no—
622C22—44no—
623C22—42no—
624C22—42no—
625C22—44no—
626C22C4×D4×D1712yes—
627C22C2×C4×C22⋊D1711yescharacteristic
628C22C2×C4×Dic3411yescharacteristic
629C22C4×#6325412yes—
630C22C4×#6325211yescharacteristic
631C22C2×#1058756412yes—
632C22C2×#1058761011yescharacteristic
633C22C2×#1058762111yescharacteristic
634C22C2×#1058756912yes—
635C22#1176331611yescharacteristic
636C22#1176331812yes—
637C22#1176331812yes—
638C22#1176332011yescharacteristic
639C22#1176333712yes—
640C22#1176333912yes—
641C22#1176333912yes—
642C22#1176334112yes—
643C22#1176334311yescharacteristic
644C22C2×#1058762611yescharacteristic
645C22#1176335511yescharacteristic
646C22#1176335612yes—
647C22#1176336212yes—
648C22#1176336611yescharacteristic
649C4—24no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—42no—
654C4—348no—
655C4—684no—
656C4—684no—
657C4—684no—
658C4#1176274518yesdirect product factor
659C2—44no—
660C2C4×#1058762111yescharacteristic
661C2C4×#1058756912yes—
662C2C4×#1058756412yes—
663C2C4×#1058761011yescharacteristic
664C2C4×#1058762611yescharacteristic
665C2C2×#1176274511yescharacteristic
666C2#1453204311yescharacteristic
667C2#1453204512yes—
668C2#1453205211yescharacteristic
669C2#1453205812yes—
670C2#1453206311yescharacteristic
subgroupG/H
centerC23×C4C22×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C4×C22⋊C4×C17C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C4×#399
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#63225C2semidirect
3. C2×C4×C4⋊Dic17C2semidirect
5. #14527053C2semidirect
6. #14527050C2semidirect
7. #14527048C2semidirect
10. C4×#10587502C2semidirect
20. #11762745C4direct (N × H)
76. C2×C4⋊Dic17C2×C4semidirect
82. C2×#63225C2×C4semidirect
98. #10587502C2×C4semidirect
330. C4×C17#399semidirect
434. C17C4×#399semidirect
658. C4#11762745direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117627452
C2×C4×#632252
C2×C4×C4⋊Dic172
C2×C4×C22⋊Dic172
#145270532
#145270502
#145270482
#145270292
#145270272
C4×#105875022
C2×C4×C22⋊C4×C172
C4×#39917