Finite Group Databasebeta

← C2×#13120628 #16029944

Subgroups — C2×#13120628 #16029944

Order 3328.

3110 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88192C211yesmaximal, characteristic
2C22×#88126C211yesmaximal, characteristic, complemented
3#13120628C2116yesmaximal, direct product factor
4C2×#11718610C212yesmaximal, complemented
5C2×#11718613C212yesmaximal, complemented
6C2×#11718622C212yesmaximal, complemented
7C2×#11718620C212yesmaximal, complemented
8C2×#11718882C211yesmaximal, characteristic, complemented
9C2×#11718646C211yesmaximal, characteristic, complemented
10C2×#11718589C211yesmaximal, characteristic, complemented
11C2×#11718648C211yesmaximal, characteristic, complemented
12C2×C13×#390C211yesmaximal, characteristic, complemented
13C23×D4×C13C2211yescharacteristic
14C23×C22⋊D13C2212yes—
15C23×C4×D13C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2212yes—
18C22×C13×C22⋊C4C2212yes—
19C22×C42×C13C2211yescharacteristic
20C22×C22⋊Dic13C2212yes—
21C22×C22⋊Dic13C2212yes—
22C22×C22⋊Dic13C2212yes—
23C2×#88192—28no—
24C2×#88192C2218yes—
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2212yes—
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2212yes—
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2212yes—
34C22×C4×Dic13C2211yescharacteristic
35C2×#88126—28no—
36C2×#88126C2218yescomplemented
37C13×#390C2218yescomplemented
38#11718882C2218yescomplemented
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41C2×#88071C2212yes—
42#11718648C2218yescomplemented
43#11718646C2218yescomplemented
44#11718622C22116yescomplemented
45#11718620C22116yescomplemented
46#11718613C22116yescomplemented
47#11718610C22116yescomplemented
48#11718589C2218yescomplemented
49C25×C13C2312yes—
50C24×D13C2311yescharacteristic
51C22×D4×C13—24no—
52C22×D4×C13—24no—
53C22×D4×C13—24no—
54C22×D4×C13C2314yes—
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13—28no—
60C22×C22⋊D13—44no—
61C22×C22⋊D13—44no—
62C22×C22⋊D13C2318yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2312yes—
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C22×C4×D13—24no—
69C22×C4×D13—24no—
70C22×C4×D13D418yes—
71C22×C4×D13C2314yes—
72C2×C13×C4⋊C4—24no—
73C2×C13×C4⋊C4C2314yes—
74C2×C13×C22⋊C4—44no—
75C2×C13×C22⋊C4—44no—
76C2×C13×C22⋊C4C2318yes—
77C2×C13×C22⋊C4C2318yes—
78C2×C42×C13—24no—
79C2×C42×C13C2314yes—
80C2×C22⋊Dic13—28no—
81C2×C22⋊Dic13—44no—
82C2×C22⋊Dic13—44no—
83C2×C22⋊Dic13C2318yes—
84C2×C22⋊Dic13C2318yes—
85C2×C22⋊Dic13C2318yes—
86#88192—232no—
87C2×#6103—24no—
88C2×#6103—24no—
89C2×#6103—44no—
90C2×#6103C2314yes—
91C2×#6103C2314yes—
92C2×#6103C2318yes—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13—24no—
95C2×C4⋊Dic13—44no—
96C2×C4⋊Dic13C2314yes—
97C2×C4⋊Dic13C2314yes—
98C2×C4⋊Dic13C2318yes—
99C2×#6101—24no—
100C2×#6101—24no—
101C2×#6101—44no—
102C2×#6101C2314yes—
103C2×#6101C2314yes—
104C2×#6101C2318yes—
105C2×C4×Dic13—24no—
106C2×C4×Dic13C2314yes—
107#88126—232no—
108#88071C2318yes—
109#88071C2318yes—
110#88071C2318yes—
111C2×#2624—131nomaximal, Sylow
112C24×C13—24no—
113C24×C13—24no—
114C24×C13—24no—
115C24×C13—24no—
116C24×C13—24no—
117C24×C13—24no—
118C24×C13—24no—
119C24×C13C2414yes—
120C24×C13C2411yescharacteristic
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13C2×D414yes—
128C23×D13C2412yes—
129C2×D4×C13—28no—
130C2×D4×C13—28no—
131C2×D4×C13—28no—
132C2×D4×C13—416no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—24no—
136C22×C4×C13—22no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13C2×D414yes—
143C22×C4×C13#4114yes—
144C22×C4×C13#4114yes—
145C22×C4×C13C2412yes—
146C22×C4×C13C2414yes—
147C22×C4×C13C2412yes—
148C22×C4×C13C2412yes—
149C2×C22⋊D13—216no—
150C2×C22⋊D13—48no—
151C2×C22⋊D13—48no—
152C2×C22⋊D13—432no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—22no—
162C22×Dic13—24no—
163C22×Dic13—24no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13C2×D414yes—
168C22×Dic13C2412yes—
169C22×Dic13C2414yes—
170C22×Dic13C2414yes—
171C22×Dic13C2412yes—
172C22×Dic13C2412yes—
173C2×C4×D13—232no—
174C2×C4×D13—28no—
175C2×C4×D13—28no—
176C2×C4×D13C2×D4116yes—
177C13×C4⋊C4—28no—
178C13×C22⋊C4—48no—
179C13×C22⋊C4—48no—
180C42×C13—28no—
181C22⋊Dic13—216no—
182C22⋊Dic13—48no—
183C22⋊Dic13—48no—
184#6103—28no—
185#6103—28no—
186#6103—48no—
187C4⋊Dic13—28no—
188C4⋊Dic13—28no—
189C4⋊Dic13—48no—
190#6101—28no—
191#6101—28no—
192#6101—48no—
193C4×Dic13—28no—
194C22×#121—131no—
195C22×#117—131no—
196#2624—1316no—
197C2×#399—132no—
198C2×#397—132no—
199C2×#394—132no—
200C2×#394—132no—
201C2×#390—131no—
202C2×#390D1311yescharacteristic, complemented
203C2×#389—131no—
204C2×#389—131no—
205C2×#380—131no—
206C23×C13—24no—
207C23×C13—24no—
208C23×C13—24no—
209C23×C13—24no—
210C23×C13—24no—
211C23×C13—24no—
212C23×C13—24no—
213C23×C13—48no—
214C23×C13—48no—
215C23×C13—48no—
216C23×C13—48no—
217C23×C13—48no—
218C23×C13—48no—
219C23×C13—48no—
220C23×C13C22×D412yes—
221C23×C13C2×#4112yes—
222C23×C13C2×#4112yes—
223C23×C13H(5,𝔽2)12yes—
224C23×C13H(5,𝔽2)12yes—
225C23×C13H(5,𝔽2)12yes—
226C23×C132−1+412yes—
227C23×C13C2511yescharacteristic
228C22×D13—28no—
229C22×D13—28no—
230C22×D13—28no—
231C22×D13—22no—
232C22×D13—22no—
233C22×D13—22no—
234C22×D13—22no—
235C22×D13—22no—
236C22×D13—22no—
237C22×D13—44no—
238C22×D13—44no—
239C22×D13—44no—
240C22×D13—44no—
241C22×D13C22×D414yes—
242D4×C13—416no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—24no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—44no—
253C2×C4×C13—44no—
254C2×C4×C13—48no—
255C2×C4×C13#123116yes—
256C2×C4×C13C22×D414yes—
257C2×C4×C13C2×#4114yes—
258C2×C4×C13C2×#4114yes—
259C22⋊D13—432no—
260C2×Dic13—28no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—24no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—44no—
276C2×Dic13—48no—
277C2×Dic13—44no—
278C2×Dic13—48no—
279C2×Dic13C22×D414yes—
280C4×D13—232no—
281C23×D4—132no—
282C23×D4C2×D1311yescharacteristic
283C24×C4—131no—
284C2×#121—138no—
285C2×#121—268no—
286C2×#117—138no—
287C2×#117—268no—
288C22×C4⋊C4—131no—
289C22×C4⋊C4—131no—
290C22×C4⋊C4—131no—
291C22×C4⋊C4—131no—
292C22×C4⋊C4—132no—
293C22×C4⋊C4—132no—
294C22×C4⋊C4C2×D1311yescharacteristic
295C22×C22⋊C4—132no—
296C22×C22⋊C4—131no—
297C22×C22⋊C4—131no—
298C22×C22⋊C4—132no—
299C22×C22⋊C4—132no—
300C22×C22⋊C4—132no—
301C22×C22⋊C4C2×D1312yes—
302C22×C22⋊C4C2×D1312yes—
303C22×C42—131no—
304C22×C42C2×D1311yescharacteristic
305#399—1316no—
306#397—1316no—
307#394—1316no—
308#394—1316no—
309#390—138no—
310#390C2×D1318yescomplemented
311#389—138no—
312#389—138no—
313#380—138no—
314C2×#95—132no—
315C2×#95—132no—
316C2×#95—132no—
317C22×C13—44no—
318C22×C13—44no—
319C22×C13—44no—
320C22×C13—44no—
321C22×C13—44no—
322C22×C13—44no—
323C22×C13—44no—
324C22×C13—816no—
325C22×C13C2×#12314yes—
326C22×C13#53514yes—
327C22×C13#53714yes—
328C22×C13#54014yes—
329C22×C13#54014yes—
330C22×C13#54214yes—
331C22×C13#54214yes—
332C22×C13C23×D411yescharacteristic
333C22×C13C22×#4111yescharacteristic
334C22×C13C22×#4111yescharacteristic
335C22×C13C2×H(5,𝔽2)11yescharacteristic
336C22×C13C2×H(5,𝔽2)11yescharacteristic
337C22×C13C2×H(5,𝔽2)11yescharacteristic
338C22×C13C2×2−1+411yescharacteristic
339C2×D13—24no—
340C2×D13—24no—
341C2×D13—24no—
342C2×D13—416no—
343C2×D13—42no—
344C2×D13—42no—
345C2×D13—42no—
346C2×D13—42no—
347C4×C13—42no—
348C4×C13—42no—
349C4×C13—44no—
350C4×C13C2×#12318yes—
351Dic13—24no—
352Dic13—42no—
353Dic13—44no—
354Dic13—42no—
355Dic13—44no—
356C25—131no—
357C25C22×D1312yes—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—138no—
362C22×D4—268no—
363C22×D4—524no—
364C22×D4—524no—
365C22×D4C22×D1314yes—
366C23×C4—131no—
367C23×C4—138no—
368C23×C4—134no—
369C23×C4—131no—
370C23×C4—132no—
371C23×C4—131no—
372C23×C4—132no—
373C23×C4—264no—
374C23×C4—264no—
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1312yes—
377C23×C4C22×D1311yescharacteristic
378C23×C4C22×D1311yescharacteristic
379#121—2632no—
380#117—2632no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—134no—
384C2×C4⋊C4—134no—
385C2×C4⋊C4—134no—
386C2×C4⋊C4—138no—
387C2×C4⋊C4—138no—
388C2×C4⋊C4—264no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4—264no—
391C2×C4⋊C4—264no—
392C2×C4⋊C4—524no—
393C2×C4⋊C4—524no—
394C2×C4⋊C4C22×D1314yes—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—138no—
398C2×C22⋊C4—134no—
399C2×C22⋊C4—134no—
400C2×C22⋊C4—138no—
401C2×C22⋊C4—138no—
402C2×C22⋊C4—138no—
403C2×C22⋊C4—264no—
404C2×C22⋊C4—264no—
405C2×C22⋊C4—268no—
406C2×C22⋊C4—524no—
407C2×C22⋊C4—524no—
408C2×C22⋊C4—524no—
409C2×C22⋊C4C22×D1318yes—
410C2×C22⋊C4C22×D1318yes—
411C2×C42—24no—
412C2×C42—134no—
413C2×C42—264no—
414C2×C42C22×D1314yes—
415#95—138no—
416#95—138no—
417#95—138no—
418C2×C13—84no—
419C2×C13#262418yescomplemented
420C2×C13C22×#12311yescharacteristic
421C2×C13C2×#53511yescharacteristic
422C2×C13C2×#53711yescharacteristic
423C2×C13C2×#54011yescharacteristic
424C2×C13C2×#54011yescharacteristic
425C2×C13C2×#54211yescharacteristic
426C2×C13C2×#54211yescharacteristic
427D13—44no—
428C24—24no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—134no—
436C24—132no—
437C24—262no—
438C24—262no—
439C24—262no—
440C24—262no—
441C24—262no—
442C24—262no—
443C24C23×D1314yes—
444C24C23×D1311yescharacteristic
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—416no—
449C2×D4—2616no—
450C2×D4—528no—
451C2×D4—528no—
452C2×D4—5232no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—134no—
463C22×C4—132no—
464C22×C4—1316no—
465C22×C4—132no—
466C22×C4—134no—
467C22×C4—134no—
468C22×C4—132no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—2632no—
472C22×C4—268no—
473C22×C4—268no—
474C22×C4—264no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—264no—
478C22×C4—264no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—264no—
482C22×C4—262no—
483C22×C4—264no—
484C22×C4—264no—
485C22×C4—262no—
486C22×C4#612714yes—
487C22×C4D4×D1314yes—
488C22×C4#612914yes—
489C22×C4C23×D1312yes—
490C22×C4C23×D1314yes—
491C22×C4C23×D1312yes—
492C22×C4C23×D1312yes—
493C4⋊C4—28no—
494C4⋊C4—268no—
495C4⋊C4—268no—
496C4⋊C4—268no—
497C4⋊C4—268no—
498C4⋊C4—528no—
499C4⋊C4—528no—
500C22⋊C4—48no—
501C22⋊C4—48no—
502C22⋊C4—268no—
503C22⋊C4—268no—
504C22⋊C4—2616no—
505C22⋊C4—528no—
506C22⋊C4—528no—
507C22⋊C4—528no—
508C42—28no—
509C42—268no—
510C13C2×#262411yescharacteristic, complemented, Sylow
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—48no—
519C23—48no—
520C23—48no—
521C23—48no—
522C23—48no—
523C23—48no—
524C23—48no—
525C23—134no—
526C23—268no—
527C23—268no—
528C23—268no—
529C23—262no—
530C23—262no—
531C23—262no—
532C23—262no—
533C23—262no—
534C23—262no—
535C23—524no—
536C23—524no—
537C23—524no—
538C23—524no—
539C23C2×#612712yes—
540C23C2×D4×D1312yes—
541C23C2×#612912yes—
542C23#8825112yes—
543C23#8825112yes—
544C23#8825612yes—
545C23#8825712yes—
546C23C24×D1311yescharacteristic
547D4—416no—
548D4—5232no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—48no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—134no—
562C2×C4—268no—
563C2×C4—262no—
564C2×C4—262no—
565C2×C4—2632no—
566C2×C4—264no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—264no—
574C2×C4—262no—
575C2×C4—264no—
576C2×C4—264no—
577C2×C4—262no—
578C2×C4—528no—
579C2×C4—524no—
580C2×C4—528no—
581C2×C4—524no—
582C2×C4#88137116yes—
583C2×C4C2×#612714yes—
584C2×C4C2×D4×D1314yes—
585C2×C4C2×#612914yes—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—816no—
594C22—264no—
595C22—264no—
596C22—264no—
597C22—522no—
598C22—522no—
599C22—522no—
600C22—522no—
601C22—5216no—
602C22C2×#8813714yes—
603C22#1171926614yes—
604C22#1171926714yes—
605C22#1171931214yes—
606C22#1171931314yes—
607C22#1171938714yes—
608C22#1171942414yes—
609C22C22×#612711yescharacteristic
610C22C22×D4×D1311yescharacteristic
611C22C22×#612911yescharacteristic
612C22C2×#8825111yescharacteristic
613C22C2×#8825111yescharacteristic
614C22C2×#8825611yescharacteristic
615C22C2×#8825711yescharacteristic
616C4—44no—
617C4—42no—
618C4—42no—
619C4—264no—
620C4—524no—
621C4—522no—
622C4—524no—
623C4—522no—
624C4C2×#8813718yes—
625C2—84no—
626C2—524no—
627C2#1312062818yesdirect product factor
628C2C22×#8813711yescharacteristic
629C2C2×#1171931211yescharacteristic
630C2C2×#1171931311yescharacteristic
631C2C2×#1171926711yescharacteristic
632C2C2×#1171942411yescharacteristic
633C2C2×#1171926611yescharacteristic
634C2C2×#1171938711yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#390C2
socleC24×C13C24
prime radicalC22×#88192C2
hypercenterC2×#390D13
hypocenterC13C2×#2624
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×#88126C2semidirect
3. #13120628C2direct (N × H)
4. C2×#11718610C2semidirect
5. C2×#11718613C2semidirect
6. C2×#11718622C2semidirect
7. C2×#11718620C2semidirect
8. C2×#11718882C2semidirect
9. C2×#11718646C2semidirect
10. C2×#11718589C2semidirect
11. C2×#11718648C2semidirect
12. C2×C13×#390C2semidirect
36. C2×#88126C22semidirect
37. C13×#390C22semidirect
38. #11718882C22semidirect
42. #11718648C22semidirect
43. #11718646C22semidirect
44. #11718622C22semidirect
45. #11718620C22semidirect
46. #11718613C22semidirect
47. #11718610C22semidirect
48. #11718589C22semidirect
202. C2×#390D13semidirect
310. #390C2×D13semidirect
419. C2×C13#2624semidirect
510. C13C2×#2624semidirect
627. C2#13120628direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881922
C22×#881262
#131206282
C2×#117186102
C2×#117186132
C2×#117186222
C2×#117186202
C2×#117188822
C2×#117186462
C2×#117185892
C2×#117186482
C2×C13×#3902
C2×#262413