Finite Group Databasebeta

← C2×#13119190 #16032366

Subgroups — C2×#13119190 #16032366

Order 3328.

3158 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
1C22×#88144C211yesmaximal, characteristic, complemented
2#13119190C2116yesmaximal, direct product factor
3C2×#11718614C212yesmaximal, complemented
4C2×#11718883C212yesmaximal, complemented
5C2×#11718882C211yesmaximal, characteristic, complemented
6C2×#11718882C211yesmaximal, characteristic, complemented
7C2×#11718882C212yesmaximal, complemented
8C2×#11718606C212yesmaximal, complemented
9C2×#11718873C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
12C22×C13×#121C211yesmaximal, characteristic
13C23×D4×C13C2211yescharacteristic
14C23×D4×C13C2212yes—
15C24×C4×C13C2211yescharacteristic
16C2×C13×#121—28no—
17C2×C13×#121C2218yes—
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C22⋊Dic13C2212yes—
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2212yes—
24C22×C22⋊Dic13C2212yes—
25C22×C22⋊Dic13C2212yes—
26C22×C22⋊Dic13C2212yes—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2212yes—
30C22×#6101C2212yes—
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2212yes—
34C2×#88144—28no—
35C2×#88144C2218yescomplemented
36#11718883C22116yescomplemented
37#11718882C2218yescomplemented
38#11718882C2218yescomplemented
39#11718882C22116yescomplemented
40#11718873C2218yescomplemented
41C4×C22⋊Dic13C2218yescomplemented
42C2×#88071C2212yes—
43C2×#88071C2211yescharacteristic
44C2×#88071C2212yes—
45C2×#88071C2211yescharacteristic
46C4⋊C4×Dic13C2218yescomplemented
47#11718614C22116yescomplemented
48#11718606C22116yescomplemented
49C25×C13C2312yes—
50C25×C13C2311yescharacteristic
51C22×D4×C13—28no—
52C22×D4×C13—28no—
53C22×D4×C13—24no—
54C22×D4×C13—24no—
55C22×D4×C13—24no—
56C22×D4×C13—44no—
57C22×D4×C13C2314yes—
58C22×D4×C13C2318yes—
59C23×C4×C13—24no—
60C23×C4×C13—24no—
61C23×C4×C13—24no—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2314yes—
64C23×C4×C13C2312yes—
65C23×C4×C13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2312yes—
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2312yes—
71C23×Dic13C2311yescharacteristic
72C13×#121—232no—
73C2×C13×C4⋊C4D418yes—
74C2×C13×C4⋊C4C2314yes—
75C2×C13×C22⋊C4—28no—
76C2×C13×C22⋊C4C2318yes—
77C2×C22⋊Dic13—24no—
78C2×C22⋊Dic13—24no—
79C2×C22⋊Dic13—28no—
80C2×C22⋊Dic13—44no—
81C2×C22⋊Dic13—44no—
82C2×C22⋊Dic13—44no—
83C2×C22⋊Dic13—44no—
84C2×C22⋊Dic13C2318yes—
85C2×C22⋊Dic13C2314yes—
86C2×C22⋊Dic13C2314yes—
87C2×C22⋊Dic13C2318yes—
88C2×C22⋊Dic13C2318yes—
89C2×C22⋊Dic13C2318yes—
90C2×C22⋊Dic13C2318yes—
91C2×C4⋊Dic13—28no—
92C2×C4⋊Dic13—24no—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13C2318yes—
95C2×C4⋊Dic13C2314yes—
96C2×C4⋊Dic13C2314yes—
97C2×#6101—28no—
98C2×#6101C2318yes—
99C2×C4×Dic13—24no—
100C2×C4×Dic13—24no—
101C2×C4×Dic13—44no—
102C2×C4×Dic13C2314yes—
103C2×C4×Dic13C2314yes—
104C2×C4×Dic13C2318yes—
105#88144—232no—
106#88071C2314yes—
107#88071C2318yes—
108#88071C2314yes—
109#88071C2318yes—
110C2×#2490—131nomaximal, Sylow
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—22no—
115C24×C13—22no—
116C24×C13—22no—
117C24×C13—24no—
118C24×C13—24no—
119C24×C13—24no—
120C24×C13—24no—
121C24×C13—24no—
122C24×C13—24no—
123C24×C13—24no—
124C24×C13#4114yes—
125C24×C13C2414yes—
126C24×C13C2412yes—
127C24×C13C2411yescharacteristic
128C2×D4×C13—216no—
129C2×D4×C13—216no—
130C2×D4×C13—28no—
131C2×D4×C13—28no—
132C2×D4×C13—28no—
133C2×D4×C13—48no—
134C2×D4×C13—432no—
135C2×D4×C13—416no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—28no—
142C22×C4×C13—28no—
143C22×C4×C13—28no—
144C22×C4×C13—416no—
145C22×C4×C13C2×D418yes—
146C22×C4×C13C2×D414yes—
147C22×C4×C13#4114yes—
148C22×C4×C13#4114yes—
149C22×C4×C13C2412yes—
150C22×C4×C13C2414yes—
151C22×C4×C13C2412yes—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—24no—
157C22×Dic13—22no—
158C22×Dic13—24no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—24no—
162C22×Dic13—22no—
163C22×Dic13—24no—
164C22×Dic13—24no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—24no—
168C22×Dic13—22no—
169C22×Dic13#4114yes—
170C22×Dic13C2412yes—
171C22×Dic13C2414yes—
172C22×Dic13C2412yes—
173C22×Dic13C2412yes—
174C22×Dic13C2414yes—
175C22×Dic13C2412yes—
176C13×C4⋊C4C2×D4116yes—
177C13×C22⋊C4—216no—
178C22⋊Dic13—28no—
179C22⋊Dic13—28no—
180C22⋊Dic13—216no—
181C22⋊Dic13—48no—
182C22⋊Dic13—48no—
183C22⋊Dic13—48no—
184C22⋊Dic13—48no—
185C4⋊Dic13—216no—
186C4⋊Dic13—28no—
187C4⋊Dic13—28no—
188#6101—216no—
189C4×Dic13—28no—
190C4×Dic13—28no—
191C4×Dic13—48no—
192C22×#125—131no—
193C22×#121D1311yescharacteristic
194#2490—1316no—
195C2×#397—132no—
196C2×#394—132no—
197C2×#390—132no—
198C2×#390—131no—
199C2×#390—131no—
200C2×#388—132no—
201C2×#380—131no—
202C2×C4×C4⋊C4—131no—
203C2×C4×C22⋊C4—131no—
204C23×C13—28no—
205C23×C13—28no—
206C23×C13—28no—
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—24no—
214C23×C13—24no—
215C23×C13—24no—
216C23×C13—24no—
217C23×C13—24no—
218C23×C13—24no—
219C23×C13—24no—
220C23×C13—44no—
221C23×C13—44no—
222C23×C13—44no—
223C23×C13—44no—
224C23×C13—48no—
225C23×C13—48no—
226C23×C13—48no—
227C23×C13—48no—
228C23×C13—48no—
229C23×C13—48no—
230C23×C13—48no—
231C23×C13C22×D412yes—
232C23×C13C2×#4114yes—
233C23×C13C2×#4112yes—
234C23×C13C2×#4112yes—
235C23×C13C2×#4112yes—
236C23×C13C2×#4112yes—
237C23×C13H(5,𝔽2)12yes—
238C23×C13H(5,𝔽2)12yes—
239C23×C13C2511yescharacteristic
240D4×C13—432no—
241D4×C13—416no—
242C2×C4×C13—216no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—44no—
249C2×C4×C13—416no—
250C2×C4×C13#124116yes—
251C2×C4×C13C22×D418yes—
252C2×C4×C13C22×D414yes—
253C2×C4×C13C2×#4114yes—
254C2×C4×C13C2×#4114yes—
255C2×Dic13—28no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—24no—
266C2×Dic13—22no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—24no—
272C2×Dic13—22no—
273C2×Dic13—48no—
274C2×Dic13—44no—
275C2×Dic13—44no—
276C2×Dic13—48no—
277C2×Dic13—44no—
278C2×Dic13C2×#4114yes—
279C23×D4C2×D1311yescharacteristic
280C23×D4C2×D1312yes—
281C24×C4C2×D1311yescharacteristic
282C2×#125—138no—
283C2×#125—268no—
284C2×#121—28no—
285C2×#121C2×D1318yes—
286C22×C4⋊C4—132no—
287C22×C4⋊C4—132no—
288C22×C4⋊C4—131no—
289C22×C4⋊C4—131no—
290C22×C4⋊C4C2×D1311yescharacteristic
291C22×C22⋊C4—131no—
292C22×C22⋊C4—131no—
293C22×C22⋊C4—132no—
294C22×C22⋊C4—132no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4—132no—
297C22×C22⋊C4—132no—
298C22×C22⋊C4C2×D1312yes—
299C22×C42—131no—
300C22×C42—131no—
301C22×C42—132no—
302#397—1316no—
303#394—1316no—
304#390—138no—
305#390—138no—
306#390—1316no—
307#388—1316no—
308#380—138no—
309C4×C4⋊C4—138no—
310C4×C22⋊C4—138no—
311C2×#95—132no—
312C2×#95—131no—
313C2×#95—132no—
314C2×#95—131no—
315C22×C13—24no—
316C22×C13—24no—
317C22×C13—24no—
318C22×C13—42no—
319C22×C13—42no—
320C22×C13—42no—
321C22×C13—42no—
322C22×C13—416no—
323C22×C13—44no—
324C22×C13—44no—
325C22×C13—44no—
326C22×C13—44no—
327C22×C13—44no—
328C22×C13—44no—
329C22×C13—44no—
330C22×C13—816no—
331C22×C13C2×#12414yes—
332C22×C13#52914yes—
333C22×C13#54014yes—
334C22×C13#54614yes—
335C22×C13#55014yes—
336C22×C13#55314yes—
337C22×C13#55314yes—
338C22×C13C23×D411yescharacteristic
339C22×C13C22×#4111yescharacteristic
340C22×C13C22×#4111yescharacteristic
341C22×C13C22×#4111yescharacteristic
342C22×C13C22×#4111yescharacteristic
343C22×C13C2×H(5,𝔽2)11yescharacteristic
344C22×C13C2×H(5,𝔽2)11yescharacteristic
345C4×C13—28no—
346C4×C13—42no—
347C4×C13C2×#12418yes—
348Dic13—24no—
349Dic13—44no—
350Dic13—42no—
351Dic13—42no—
352Dic13—44no—
353Dic13—42no—
354C25C22×D1312yes—
355C25C22×D1311yescharacteristic
356C22×D4—28no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—28no—
360C22×D4—24no—
361C22×D4—44no—
362C22×D4C22×D1314yes—
363C22×D4C22×D1318yes—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—131no—
368C23×C4—132no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—132no—
372C23×C4—131no—
373C23×C4C22×D1314yes—
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1312yes—
376C23×C4C22×D1311yescharacteristic
377#125—2632no—
378#121—232no—
379C2×C4⋊C4—138no—
380C2×C4⋊C4—134no—
381C2×C4⋊C4—138no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—268no—
385C2×C4⋊C4—268no—
386C2×C4⋊C4—264no—
387C2×C4⋊C4C22⋊D1318yes—
388C2×C4⋊C4C22×D1314yes—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—134no—
391C2×C22⋊C4—134no—
392C2×C22⋊C4—138no—
393C2×C22⋊C4—138no—
394C2×C22⋊C4—138no—
395C2×C22⋊C4—138no—
396C2×C22⋊C4—138no—
397C2×C22⋊C4—264no—
398C2×C22⋊C4—268no—
399C2×C22⋊C4—264no—
400C2×C22⋊C4—524no—
401C2×C22⋊C4—524no—
402C2×C22⋊C4—524no—
403C2×C22⋊C4—524no—
404C2×C22⋊C4C22×D1318yes—
405C2×C42—134no—
406C2×C42—134no—
407C2×C42—138no—
408C2×C42—264no—
409C2×C42—264no—
410C2×C42—524no—
411#95—134no—
412#95—134no—
413#95—138no—
414#95—138no—
415C2×C13—44no—
416C2×C13—84no—
417C2×C13#249018yescomplemented
418C2×C13C22×#12411yescharacteristic
419C2×C13C2×#52911yescharacteristic
420C2×C13C2×#54011yescharacteristic
421C2×C13C2×#54611yescharacteristic
422C2×C13C2×#55011yescharacteristic
423C2×C13C2×#55311yescharacteristic
424C2×C13C2×#55311yescharacteristic
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—24no—
438C24#612914yes—
439C24C23×D1314yes—
440C24C23×D1312yes—
441C24C23×D1311yescharacteristic
442C2×D4—216no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—216no—
446C2×D4—28no—
447C2×D4—48no—
448C2×D4—432no—
449C2×D4—416no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—416no—
459C22×C4—134no—
460C22×C4—132no—
461C22×C4—132no—
462C22×C4—134no—
463C22×C4—132no—
464C22×C4—132no—
465C22×C4—134no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—264no—
472C22×C4—264no—
473C22×C4—262no—
474C22×C4—264no—
475C22×C4—262no—
476C22×C4—264no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—264no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—264no—
483C22×C4#612914yes—
484C22×C4#612914yes—
485C22×C4C2×C22⋊D1318yes—
486C22×C4C2×C22⋊D1314yes—
487C22×C4C23×D1312yes—
488C22×C4C23×D1314yes—
489C22×C4C23×D1312yes—
490C4⋊C4—268no—
491C4⋊C4—2616no—
492C4⋊C4—2616no—
493C4⋊C4—268no—
494C4⋊C4C2×C22⋊D13116yes—
495C22⋊C4—216no—
496C22⋊C4—268no—
497C22⋊C4—2616no—
498C22⋊C4—268no—
499C22⋊C4—528no—
500C22⋊C4—528no—
501C22⋊C4—528no—
502C22⋊C4—528no—
503C42—268no—
504C42—268no—
505C42—528no—
506C13C2×#249011yescharacteristic, complemented, Sylow
507C23—28no—
508C23—28no—
509C23—28no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—48no—
528C23—48no—
529C23—48no—
530C23—48no—
531C23—48no—
532C23—48no—
533C23—48no—
534C23C2×#612914yes—
535C23C2×#612912yes—
536C23C2×#612912yes—
537C23C2×#612912yes—
538C23#8825112yes—
539C23#41×D1312yes—
540C23#8825612yes—
541C23C22×C22⋊D1312yes—
542C23C24×D1311yescharacteristic
543D4—432no—
544D4—416no—
545C2×C4—216no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—44no—
552C2×C4—416no—
553C2×C4—134no—
554C2×C4—268no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—264no—
561C2×C4—264no—
562C2×C4—262no—
563C2×C4—262no—
564C2×C4—264no—
565C2×C4—264no—
566C2×C4—262no—
567C2×C4—264no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—264no—
572C2×C4—524no—
573C2×C4—524no—
574C2×C4—528no—
575C2×C4—524no—
576C2×C4—528no—
577C2×C4#88190116yes—
578C2×C4C2×#612914yes—
579C2×C4C2×#612914yes—
580C2×C4C22×C22⋊D1318yes—
581C2×C4C22×C22⋊D1314yes—
582C22—24no—
583C22—24no—
584C22—24no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—416no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—816no—
598C22#1171930514yes—
599C22#1171931914yes—
600C22#1171932314yes—
601C22#1171932414yes—
602C22C2×#8819014yes—
603C22#1171951114yes—
604C22#1171953914yes—
605C22C22×#612911yescharacteristic
606C22C22×#612911yescharacteristic
607C22C22×#612911yescharacteristic
608C22C2×#8825111yescharacteristic
609C22C2×#41×D1311yescharacteristic
610C22C2×#8825611yescharacteristic
611C22C23×C22⋊D1311yescharacteristic
612C4—28no—
613C4—42no—
614C4—264no—
615C4—524no—
616C4—522no—
617C4—522no—
618C4—524no—
619C4—522no—
620C4C2×#8819018yes—
621C2—44no—
622C2—84no—
623C2#1311919018yesdirect product factor
624C2C22×#8819011yescharacteristic
625C2C2×#1171930511yescharacteristic
626C2C2×#1171932411yescharacteristic
627C2C2×#1171951111yescharacteristic
628C2C2×#1171953911yescharacteristic
629C2C2×#1171931911yescharacteristic
630C2C2×#1171932311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
Fitting, prime radicalC22×C13×#121C2
socleC24×C13C24
hypercenterC22×#121D13
hypocenterC13C2×#2490
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#88144C2semidirect
2. #13119190C2direct (N × H)
3. C2×#11718614C2semidirect
4. C2×#11718883C2semidirect
5. C2×#11718882C2semidirect
6. C2×#11718882C2semidirect
7. C2×#11718882C2semidirect
8. C2×#11718606C2semidirect
9. C2×#11718873C2semidirect
10. C2×C4⋊C4×Dic13C2semidirect
11. C2×C4×C22⋊Dic13C2semidirect
35. C2×#88144C22semidirect
36. #11718883C22semidirect
37. #11718882C22semidirect
38. #11718882C22semidirect
39. #11718882C22semidirect
40. #11718873C22semidirect
41. C4×C22⋊Dic13C22semidirect
46. C4⋊C4×Dic13C22semidirect
47. #11718614C22semidirect
48. #11718606C22semidirect
417. C2×C13#2490semidirect
506. C13C2×#2490semidirect
623. C2#13119190direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881442
#131191902
C2×#117186142
C2×#117188832
C2×#117188822
C2×#117186062
C2×#117188732
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
C22×C13×#1212
C2×#249013