Finite Group Databasebeta

← C2×#13119184 #16032360

Subgroups — C2×#13119184 #16032360

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
2C22×#88184C211yesmaximal, characteristic
3#13119184C2116yesmaximal, direct product factor
4C2×#11718336C212yesmaximal, complemented
5C2×#11718622C212yesmaximal, complemented
6C2×#11718649C211yesmaximal, characteristic, complemented
7C2×#11718649C211yesmaximal, characteristic, complemented
8C2×#11718618C212yesmaximal, complemented
9C2×#11718331C212yesmaximal, complemented
10C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
12C2×C13×#380C211yesmaximal, characteristic, complemented
13C24×C4×C13C2211yescharacteristic
14C23×C22⋊D13C2212yes—
15C23×D52C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2212yes—
19C22×C22⋊Dic13C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C2×#88184—28no—
22C2×#88184C2218yes—
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2212yes—
26C22×#6103C2212yes—
27C22×#6103C2212yes—
28C22×C4⋊Dic13C2212yes—
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6101C2212yes—
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2212yes—
34C2×#88144—28no—
35C2×#88144C2218yescomplemented
36C13×#380C2218yescomplemented
37C2×C13×#95C2212yes—
38C4×C22⋊Dic13C2218yescomplemented
39C2×#88071C2211yescharacteristic
40C2×#88071C2212yes—
41C2×#88071C2211yescharacteristic
42#11718649C2218yescomplemented
43#11718649C2218yescomplemented
44C4⋊C4×Dic13C2218yescomplemented
45#11718622C22116yescomplemented
46#11718618C22116yescomplemented
47#11718336C22116yescomplemented
48#11718331C22116yescomplemented
49C25×C13C2311yescharacteristic
50C24×D13C2312yes—
51C23×C4×C13—24no—
52C23×C4×C13—24no—
53C23×C4×C13—24no—
54C23×C4×C13C2314yes—
55C23×C4×C13C2312yes—
56C23×C4×C13C2312yes—
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13—28no—
60C22×C22⋊D13—28no—
61C22×C22⋊D13—44no—
62C22×C22⋊D13C2318yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C22×D52—24no—
69C22×D52—24no—
70C22×D52—24no—
71C22×D52C2314yes—
72C2×C13×C4⋊C4—24no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4C2314yes—
75C2×C13×C4⋊C4C2314yes—
76C2×C13×C22⋊C4—44no—
77C2×C13×C22⋊C4C2318yes—
78C2×C22⋊Dic13—24no—
79C2×C22⋊Dic13—24no—
80C2×C22⋊Dic13C2314yes—
81C2×C22⋊Dic13C2314yes—
82#88184—232no—
83C2×#6103—28no—
84C2×#6103—28no—
85C2×#6103—44no—
86C2×#6103—44no—
87C2×#6103—44no—
88C2×#6103C2318yes—
89C2×#6103C2318yes—
90C2×#6103C2318yes—
91C2×#6103C2318yes—
92C2×#6103C2318yes—
93C2×C4⋊Dic13—28no—
94C2×C4⋊Dic13D418yes—
95C2×C4⋊Dic13C2318yes—
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—
106C13×#95C2318yes—
107#88071C2314yes—
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#4114yes—
118C24×C13C2412yes—
119C24×C13C2411yescharacteristic
120C23×D13—24no—
121C23×D13—24no—
122C23×D13—24no—
123C23×D13—24no—
124C23×D13—24no—
125C23×D13—24no—
126C23×D13—24no—
127C23×D13C2414yes—
128C22×C4×C13—24no—
129C22×C4×C13—22no—
130C22×C4×C13—24no—
131C22×C4×C13—24no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—28no—
138C22×C4×C13—28no—
139C22×C4×C13—28no—
140C22×C4×C13—416no—
141C22×C4×C13C2×D414yes—
142C22×C4×C13#4114yes—
143C22×C4×C13#4114yes—
144C22×C4×C13C2412yes—
145C22×C4×C13C2414yes—
146C22×C4×C13C2414yes—
147C22×C4×C13C2412yes—
148C2×C22⋊D13—216no—
149C2×C22⋊D13—216no—
150C2×C22⋊D13—48no—
151C2×C22⋊D13—432no—
152C22×Dic13—22no—
153C22×Dic13—24no—
154C22×Dic13—22no—
155C22×Dic13—24no—
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×Dic13C2×D418yes—
166C22×Dic13#4114yes—
167C22×Dic13C2412yes—
168C22×Dic13C2412yes—
169C22×Dic13C2412yes—
170C22×Dic13C2414yes—
171C22×Dic13C2412yes—
172C2×D52—28no—
173C2×D52—28no—
174C2×D52—28no—
175C2×D52—416no—
176C13×C4⋊C4—28no—
177C13×C4⋊C4—28no—
178C13×C22⋊C4—48no—
179C22⋊Dic13—28no—
180C22⋊Dic13—28no—
181#6103—216no—
182#6103—216no—
183#6103—48no—
184#6103—48no—
185#6103—48no—
186C4⋊Dic13—216no—
187C4⋊Dic13C2×D4116yes—
188#6101—216no—
189C4×Dic13—28no—
190C4×Dic13—28no—
191C4×Dic13—48no—
192C22×#125—131no—
193C22×#121—131no—
194#2490—1316no—
195C2×#397—132no—
196C2×#394—132no—
197C2×#390—131no—
198C2×#390—131no—
199C2×#390—132no—
200C2×#388—132no—
201C2×#380D1311yescharacteristic, complemented
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—44no—
214C23×C13—44no—
215C23×C13—44no—
216C23×C13—44no—
217C23×C13C22×D412yes—
218C23×C13C2×#4114yes—
219C23×C13C2×#4112yes—
220C23×C13C2×#4112yes—
221C23×C13C2×#4112yes—
222C23×C13C2×#4112yes—
223C23×C13H(5,𝔽2)12yes—
224C23×C13H(5,𝔽2)12yes—
225C23×C13C2511yescharacteristic
226C22×D13—24no—
227C22×D13—24no—
228C22×D13—24no—
229C22×D13—24no—
230C22×D13—24no—
231C22×D13—24no—
232C22×D13—24no—
233C22×D13—48no—
234C22×D13—48no—
235C22×D13—48no—
236C22×D13—48no—
237C22×D13—48no—
238C22×D13—48no—
239C22×D13—48no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—44no—
250C2×C4×C13—48no—
251C2×C4×C13—48no—
252C2×C4×C13—416no—
253C2×C4×C13#124116yes—
254C2×C4×C13C22×D414yes—
255C2×C4×C13C2×#4114yes—
256C2×C4×C13C2×#4114yes—
257C22⋊D13—432no—
258C2×Dic13—216no—
259C2×Dic13—28no—
260C2×Dic13—22no—
261C2×Dic13—24no—
262C2×Dic13—22no—
263C2×Dic13—24no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—44no—
274C2×Dic13—44no—
275C2×Dic13—44no—
276C2×Dic13C22×D418yes—
277C2×Dic13C2×#4114yes—
278D52—416no—
279C23×D4—132no—
280C23×D4—131no—
281C24×C4C2×D1311yescharacteristic
282C2×#125—138no—
283C2×#125—268no—
284C2×#121—138no—
285C2×#121—268no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—132no—
288C22×C4⋊C4—132no—
289C22×C4⋊C4C2×D1311yescharacteristic
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#380C2×D1318yescomplemented
309C4×C4⋊C4—138no—
310C4×C22⋊C4—138no—
311C2×#95—132no—
312C2×#95—131no—
313C2×#95—131no—
314C2×#95C2×D1312yes—
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×C13C2×#12414yes—
324C22×C13#52914yes—
325C22×C13#54014yes—
326C22×C13#54614yes—
327C22×C13#55014yes—
328C22×C13#55314yes—
329C22×C13#55314yes—
330C22×C13C23×D411yescharacteristic
331C22×C13C22×#4111yescharacteristic
332C22×C13C22×#4111yescharacteristic
333C22×C13C22×#4111yescharacteristic
334C22×C13C22×#4111yescharacteristic
335C22×C13C2×H(5,𝔽2)11yescharacteristic
336C22×C13C2×H(5,𝔽2)11yescharacteristic
337C2×D13—44no—
338C2×D13—44no—
339C2×D13—44no—
340C2×D13—44no—
341C2×D13—44no—
342C2×D13—44no—
343C2×D13—44no—
344C2×D13—816no—
345C4×C13—42no—
346C4×C13—44no—
347C4×C13—44no—
348C4×C13C2×#12418yes—
349Dic13—28no—
350Dic13—24no—
351Dic13—42no—
352Dic13—42no—
353Dic13—42no—
354C25—132no—
355C25C22×D1311yescharacteristic
356C22×D4—138no—
357C22×D4—134no—
358C22×D4—268no—
359C22×D4—268no—
360C22×D4—264no—
361C22×D4—264no—
362C22×D4—264no—
363C22×D4—524no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—131no—
368C23×C4—132no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4C22×D1314yes—
373C23×C4C22×D1312yes—
374C23×C4C22×D1312yes—
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1311yescharacteristic
377#125—2632no—
378#121—2632no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—138no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—138no—
384C2×C4⋊C4—138no—
385C2×C4⋊C4—268no—
386C2×C4⋊C4—268no—
387C2×C4⋊C4C22×D1314yes—
388C2×C4⋊C4C22×D1314yes—
389C2×C22⋊C4—44no—
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—268no—
398C2×C22⋊C4—268no—
399C2×C22⋊C4—264no—
400C2×C22⋊C4—264no—
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#95C22×D1318yes—
415C2×C13—44no—
416C2×C13#249018yescomplemented
417C2×C13C22×#12411yescharacteristic
418C2×C13C2×#52911yescharacteristic
419C2×C13C2×#54011yescharacteristic
420C2×C13C2×#54611yescharacteristic
421C2×C13C2×#55011yescharacteristic
422C2×C13C2×#55311yescharacteristic
423C2×C13C2×#55311yescharacteristic
424D13—84no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—134no—
432C24—264no—
433C24—264no—
434C24—264no—
435C24—264no—
436C24—264no—
437C24—264no—
438C24—264no—
439C24#613114yes—
440C24C23×D1312yes—
441C24C23×D1311yescharacteristic
442C2×D4—2616no—
443C2×D4—2616no—
444C2×D4—268no—
445C2×D4—268no—
446C2×D4—268no—
447C2×D4—528no—
448C2×D4—5232no—
449C2×D4—5216no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—416no—
463C22×C4—138no—
464C22×C4—134no—
465C22×C4—132no—
466C22×C4—134no—
467C22×C4—132no—
468C22×C4—132no—
469C22×C4—132no—
470C22×C4—262no—
471C22×C4—264no—
472C22×C4—262no—
473C22×C4—264no—
474C22×C4—262no—
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#612714yes—
484C22×C4D4×D1314yes—
485C22×C4#612914yes—
486C22×C4C23×D1312yes—
487C22×C4C23×D1314yes—
488C22×C4C23×D1314yes—
489C22×C4C23×D1312yes—
490C4⋊C4—28no—
491C4⋊C4—28no—
492C4⋊C4—1316no—
493C4⋊C4—2616no—
494C4⋊C4—2616no—
495C22⋊C4—48no—
496C22⋊C4—2616no—
497C22⋊C4—2616no—
498C22⋊C4—268no—
499C22⋊C4—268no—
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—44no—
517C23—44no—
518C23—44no—
519C23—44no—
520C23—264no—
521C23—264no—
522C23—264no—
523C23—264no—
524C23—264no—
525C23—264no—
526C23—264no—
527C23—528no—
528C23—528no—
529C23—528no—
530C23—528no—
531C23—528no—
532C23—528no—
533C23—528no—
534C23C2×#612712yes—
535C23C2×D4×D1312yes—
536C23C2×#612912yes—
537C23#8825112yes—
538C23C2×#613114yes—
539C23C2×#613112yes—
540C23#41×D1312yes—
541C23#8825612yes—
542C23C24×D1311yescharacteristic
543D4—5232no—
544D4—5216no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—44no—
555C2×C4—48no—
556C2×C4—48no—
557C2×C4—416no—
558C2×C4—138no—
559C2×C4—134no—
560C2×C4—268no—
561C2×C4—2616no—
562C2×C4—262no—
563C2×C4—264no—
564C2×C4—262no—
565C2×C4—264no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—524no—
576C2×C4—524no—
577C2×C4—524no—
578C2×C4#88139116yes—
579C2×C4C2×#612714yes—
580C2×C4C2×D4×D1314yes—
581C2×C4C2×#612914yes—
582C22—24no—
583C22—24no—
584C22—24no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—416no—
590C22—524no—
591C22—524no—
592C22—524no—
593C22—524no—
594C22—524no—
595C22—524no—
596C22—524no—
597C22—10416no—
598C22C2×#8813914yes—
599C22#1171921914yes—
600C22#1171923514yes—
601C22#1171930414yes—
602C22#1171932414yes—
603C22#1171932914yes—
604C22#1171933514yes—
605C22C22×#612711yescharacteristic
606C22C22×D4×D1311yescharacteristic
607C22C22×#612911yescharacteristic
608C22C2×#8825111yescharacteristic
609C22C22×#613111yescharacteristic
610C22C2×#41×D1311yescharacteristic
611C22C2×#8825611yescharacteristic
612C4—44no—
613C4—44no—
614C4—42no—
615C4—268no—
616C4—264no—
617C4—522no—
618C4—522no—
619C4—522no—
620C4C2×#8813918yes—
621C2—44no—
622C2—1044no—
623C2#1311918418yesdirect product factor
624C2C22×#8813911yescharacteristic
625C2C2×#1171932911yescharacteristic
626C2C2×#1171932411yescharacteristic
627C2C2×#1171933511yescharacteristic
628C2C2×#1171930411yescharacteristic
629C2C2×#1171923511yescharacteristic
630C2C2×#1171921911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC22×#88184C2
hypercenterC2×#380D13
hypocenterC13C2×#2490
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#88144C2semidirect
3. #13119184C2direct (N × H)
4. C2×#11718336C2semidirect
5. C2×#11718622C2semidirect
6. C2×#11718649C2semidirect
7. C2×#11718649C2semidirect
8. C2×#11718618C2semidirect
9. C2×#11718331C2semidirect
10. C2×C4⋊C4×Dic13C2semidirect
11. C2×C4×C22⋊Dic13C2semidirect
12. C2×C13×#380C2semidirect
35. C2×#88144C22semidirect
36. C13×#380C22semidirect
38. C4×C22⋊Dic13C22semidirect
42. #11718649C22semidirect
43. #11718649C22semidirect
44. C4⋊C4×Dic13C22semidirect
45. #11718622C22semidirect
46. #11718618C22semidirect
47. #11718336C22semidirect
48. #11718331C22semidirect
201. C2×#380D13semidirect
308. #380C2×D13semidirect
416. C2×C13#2490semidirect
506. C13C2×#2490semidirect
623. C2#13119184direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881442
C22×#881842
#131191842
C2×#117183362
C2×#117186222
C2×#117186492
C2×#117186182
C2×#117183312
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
C2×C13×#3802
C2×#249013