Finite Group Databasebeta

← C4×#11718610 #15784748

Subgroups — C4×#11718610 #15784748

Order 3328.

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×#11718610C211yesmaximal, characteristic
2C2×C4×#6101C212yesmaximal, complemented
3C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic13C212yesmaximal
5#13113105C211yesmaximal, characteristic, complemented
6#13113102C212yesmaximal, complemented
7#13113100C211yesmaximal, characteristic, complemented
8#13113081C211yesmaximal, characteristic
9#13113079C212yesmaximal
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2212yes—
22C22×#6101C2212yes—
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2212yes—
25C4×C13×C22⋊C4—24no—
26C2×C13×#95C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C4×C22⋊Dic13—28no—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37#11718610C418yesdirect product factor
38C4×C4⋊Dic13—24no—
39C4×#6101—28no—
40C25×C13C2311yescharacteristic
41C23×C4×C13—22no—
42C23×C4×C13—24no—
43C23×C4×C13—22no—
44C23×C4×C13—24no—
45C23×C4×C13Q814yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×Dic13C2312yes—
53C23×Dic13C2312yes—
54C23×Dic13C2312yes—
55C23×Dic13C2312yes—
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4C2×C414yes—
62C2×C42×C13—24no—
63C2×C42×C13—22no—
64C2×C42×C13—24no—
65C2×C42×C13D414yes—
66C2×C22⋊Dic13—24no—
67C2×C22⋊Dic13—24no—
68C2×C22⋊Dic13—24no—
69C2×C22⋊Dic13—24no—
70C2×C22⋊Dic13—24no—
71C2×C22⋊Dic13C2×C418yes—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13—22no—
74C2×C4⋊Dic13—22no—
75C2×C4⋊Dic13—24no—
76C2×C4⋊Dic13C2×C414yescomplemented
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101—24no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101C2×C418yescomplemented
83C2×C4×Dic13—24no—
84C2×C4×Dic13—24no—
85C2×C4×Dic13—24no—
86C2×C4×Dic13—24no—
87C2×C4×Dic13—24no—
88C2×C4×Dic13D418yes—
89C13×#95—22no—
90C13×#95—22no—
91#88071—24no—
92#88071—22no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071C2×C414yescomplemented
99C4×#399—131nomaximal, Sylow
100C24×C13—22no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13—21no—
105C24×C13—21no—
106C24×C13—21no—
107C24×C13—22no—
108C24×C13C22×C412yes—
109C24×C13C2×Q812yes—
110C24×C13#4112yes—
111C24×C13C2411yescharacteristic
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—22no—
130C22×C4×C13—216no—
131C22×C4×C13—28no—
132C22×C4×C13—48no—
133C22×C4×C13—44no—
134C22×C4×C13—44no—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C22×C412yes—
137C22×C4×C13C2×D414yes—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×Q812yes—
142C22×C4×C13C2×Q812yes—
143C22×C4×C13#4112yes—
144C22×C4×C13#4112yes—
145C22×C4×C13#4112yes—
146C22×C4×C13#4114yes—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13C22×C414yes—
170C22×Dic13C22×C414yes—
171C22×Dic13C2×D414yes—
172C22×Dic13C2×D414yes—
173C22×Dic13#4114yes—
174C22×Dic13#4114yes—
175C13×C22⋊C4—28no—
176C13×C22⋊C4—28no—
177C42×C13—28no—
178C42×C13—44no—
179C22⋊Dic13—216no—
180C22⋊Dic13—216no—
181C4⋊Dic13—28no—
182C4⋊Dic13—28no—
183#6101—216no—
184#6101—216no—
185C4×Dic13—216no—
186C4×Dic13—48no—
187C2×#399—131no—
188C2×C4×C4⋊C4—131no—
189C2×C4×C4⋊C4—132no—
190C2×C4×C22⋊C4—132no—
191C2×C4×C22⋊C4D1311yescharacteristic
192#1445—132no—
193#1445—131no—
194#1444—131no—
195#1439—132no—
196#1439—131no—
197C4×#95—131no—
198C23×C13—24no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—22no—
204C23×C13—24no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—24no—
208C23×C13—22no—
209C23×C13—24no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—42no—
213C23×C13—41no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—41no—
218C23×C13—42no—
219C23×C13—41no—
220C23×C13C4×Q814yes—
221C23×C13C23×C411yescharacteristic
222C23×C13C22×D412yes—
223C23×C13C22×D411yescharacteristic
224C23×C13C22×Q811yescharacteristic
225C23×C13C2×#4111yescharacteristic
226C23×C13C2×#4112yes—
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13C2×#4112yes—
230C23×C13C2×#4111yescharacteristic
231C23×C13C2×#4112yes—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—24no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—42no—
246C2×C4×C13—41no—
247C2×C4×C13—42no—
248C2×C4×C13—41no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—42no—
255C2×C4×C13—41no—
256C2×C4×C13—416no—
257C2×C4×C13C4×D414yes—
258C2×C4×C13C22⋊Q818yes—
259C2×C4×C13C22⋊Q814yes—
260C2×C4×C13#12318yes—
261C2×C4×C13#12314yes—
262C2×C4×C13#12714yes—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—24no—
271C2×Dic13—24no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13—24no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13C4×D418yes—
291C24×C4C2×D1311yescharacteristic
292C22×C4⋊C4—132no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—132no—
295C22×C4⋊C4—131no—
296C22×C22⋊C4—132no—
297C22×C22⋊C4—132no—
298C22×C22⋊C4C2×D1311yescharacteristic
299C22×C22⋊C4C2×D1311yescharacteristic
300C22×C42—132no—
301C22×C42—132no—
302C22×C42C2×D1311yescharacteristic
303C22×C42C2×D1311yescharacteristic
304#399—138no—
305C4×C4⋊C4—268no—
306C4×C4⋊C4—264no—
307C4×C22⋊C4—24no—
308C4×C22⋊C4—268no—
309C2×#95—131no—
310C2×#95—132no—
311C2×#95—131no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95—132no—
315C2×#95—132no—
316C2×#95—132no—
317C2×#95C2×D1311yescharacteristic
318C2×#95C2×D1311yescharacteristic
319C22×C13—28no—
320C22×C13—24no—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—44no—
325C22×C13—42no—
326C22×C13—44no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—44no—
330C22×C13C2×C4×D411yescharacteristic
331C22×C13C2×C4×D412yes—
332C22×C13C2×C4×Q811yescharacteristic
333C22×C13C4×#4111yescharacteristic
334C22×C13C4×#4112yes—
335C22×C13C2×C22⋊Q812yes—
336C22×C13C2×C22⋊Q811yescharacteristic
337C22×C13C2×#12312yes—
338C22×C13C2×#12311yescharacteristic
339C22×C13#52511yescharacteristic
340C22×C13#52512yes—
341C22×C13#52512yes—
342C22×C13#52511yescharacteristic
343C22×C13#52911yescharacteristic
344C22×C13#52912yes—
345C22×C13#52912yes—
346C22×C13#52912yes—
347C22×C13#52912yes—
348C22×C13C2×#12711yescharacteristic
349C22×C13#53212yes—
350C22×C13#53211yescharacteristic
351C22×C13#53311yescharacteristic
352C22×C13#53312yes—
353C4×C13—24no—
354C4×C13—42no—
355C4×C13—42no—
356C4×C13—42no—
357C4×C13—42no—
358C4×C13#39918yescomplemented
359Dic13—28no—
360Dic13—44no—
361Dic13—44no—
362Dic13—44no—
363C25C22×D1311yescharacteristic
364C23×C4—22no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—132no—
369C23×C4—132no—
370C23×C4—132no—
371C23×C4—132no—
372C23×C4Dic2614yes—
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1311yescharacteristic
377C23×C4C22×D1311yescharacteristic
378C23×C4C22×D1311yescharacteristic
379C2×C4⋊C4—138no—
380C2×C4⋊C4—134no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—264no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—264no—
385C2×C4⋊C4—264no—
386C2×C4⋊C4—264no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—262no—
389C2×C4⋊C4—262no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—138no—
396C2×C22⋊C4—264no—
397C2×C22⋊C4—264no—
398C2×C22⋊C4—264no—
399C2×C22⋊C4—264no—
400C2×C22⋊C4—264no—
401C2×C22⋊C4C4×D1314yes—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—138no—
406C2×C42—264no—
407C2×C42—264no—
408C2×C42—264no—
409C2×C42—264no—
410C2×C42—264no—
411C2×C42C22⋊D1314yes—
412#95—22no—
413#95—22no—
414#95—134no—
415#95—264no—
416#95—264no—
417#95—264no—
418#95—264no—
419#95—264no—
420#95—262no—
421#95—264no—
422C2×C13—44no—
423C2×C13C4×#12311yescharacteristic
424C2×C13C4×#12312yes—
425C2×C13C4×C22⋊Q812yes—
426C2×C13C4×C22⋊Q811yescharacteristic
427C2×C13C4×#12711yescharacteristic
428C2×C13C2×#39911yescharacteristic
429C2×C13#239511yescharacteristic
430C2×C13#239512yes—
431C2×C13#239611yescharacteristic
432C2×C13#239612yes—
433C2×C13#239711yescharacteristic
434C24—21no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24C2×Dic2612yes—
443C24C2×C4×D1312yes—
444C24#612712yes—
445C24C23×D1311yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
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—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—216no—
465C22×C4—28no—
466C22×C4—48no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—134no—
470C22×C4—134no—
471C22×C4—134no—
472C22×C4—134no—
473C22×C4—134no—
474C22×C4—134no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4C2×Dic2612yes—
498C22×C4C2×Dic2612yes—
499C22×C4C2×C4×D1312yes—
500C22×C4C2×C4×D1312yes—
501C22×C4#612712yes—
502C22×C4#612712yes—
503C22×C4#612712yes—
504C22×C4D4×D1314yes—
505C22×C4#612914yes—
506C22×C4C2×C22⋊D1312yes—
507C22×C4C2×C22⋊D1312yes—
508C22×C4C2×C22⋊D1312yes—
509C4⋊C4—2616no—
510C4⋊C4—2616no—
511C4⋊C4—268no—
512C4⋊C4—268no—
513C22⋊C4—28no—
514C22⋊C4—28no—
515C22⋊C4—2616no—
516C22⋊C4—2616no—
517C42—28no—
518C42—44no—
519C42—2616no—
520C42—528no—
521C13C4×#39911yescharacteristic, complemented, Sylow
522C23—22no—
523C23—22no—
524C23—22no—
525C23—24no—
526C23—24no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—42no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—41no—
543C23—41no—
544C23C4×Dic2614yes—
545C23C22×Dic2611yescharacteristic
546C23C22×C4×D1311yescharacteristic
547C23C2×#612711yescharacteristic
548C23C2×#612711yescharacteristic
549C23C2×#612711yescharacteristic
550C23C2×#612711yescharacteristic
551C23C2×D4×D1312yes—
552C23C2×#612912yes—
553C23#41×D1312yes—
554C23#41×D1312yes—
555C23C22×C22⋊D1311yescharacteristic
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—416no—
581C2×C4—138no—
582C2×C4—264no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—264no—
588C2×C4—264no—
589C2×C4—264no—
590C2×C4—264no—
591C2×C4—264no—
592C2×C4—264no—
593C2×C4—264no—
594C2×C4—264no—
595C2×C4—264no—
596C2×C4—264no—
597C2×C4—522no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4—522no—
601C2×C4—522no—
602C2×C4—522no—
603C2×C4—522no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4—522no—
609C2×C4#8813218yes—
610C2×C4#8813718yes—
611C2×C4#8817814yes—
612C2×C4C4×C22⋊D1314yes—
613C2×C4#8818914yes—
614C2×C4#8819414yes—
615C22—28no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—44no—
620C22—42no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—44no—
625C22—42no—
626C22C2×C4×Dic2611yescharacteristic
627C22#1171917511yescharacteristic
628C22C4×#612711yescharacteristic
629C22#1171918411yescharacteristic
630C22C2×#8813212yes—
631C22C2×#8813712yes—
632C22#1171922212yes—
633C22#1171923312yes—
634C22C4×#612912yes—
635C22#1171924312yes—
636C22#1171924312yes—
637C22C4×D4×D1312yes—
638C22#1171925212yes—
639C22#1171925212yes—
640C22#1171925312yes—
641C22#1171926212yes—
642C22C2×#8817811yescharacteristic
643C22C2×C4×C22⋊D1311yescharacteristic
644C22#1171949611yescharacteristic
645C22C2×#8818911yescharacteristic
646C22C2×#8819411yescharacteristic
647C22#1171953311yescharacteristic
648C22#1171953711yescharacteristic
649C4—24no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—42no—
654C4—268no—
655C4—524no—
656C4—524no—
657C4—524no—
658C4#1171861018yesdirect product factor
659C2—44no—
660C2C4×#8818911yescharacteristic
661C2C4×#8813712yes—
662C2C4×#8813212yes—
663C2C4×#8817811yescharacteristic
664C2C4×#8819411yescharacteristic
665C2C2×#1171861011yescharacteristic
666C2#1311809511yescharacteristic
667C2#1311809712yes—
668C2#1311810411yescharacteristic
669C2#1311811012yes—
670C2#1311811511yescharacteristic
subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C4×#399
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6101C2semidirect
3. C2×C4×C4⋊Dic13C2semidirect
5. #13113105C2semidirect
6. #13113102C2semidirect
7. #13113100C2semidirect
10. C4×#88071C2semidirect
37. #11718610C4direct (N × H)
76. C2×C4⋊Dic13C2×C4semidirect
82. C2×#6101C2×C4semidirect
98. #88071C2×C4semidirect
358. C4×C13#399semidirect
521. C13C4×#399semidirect
658. C4#11718610direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186102
C2×C4×#61012
C2×C4×C4⋊Dic132
C2×C4×C22⋊Dic132
#131131052
#131131022
#131131002
#131130812
#131130792
C4×#880712
C2×C4×C13×C22⋊C42
C4×#39913