Finite Group Databasebeta

← C2×#13119191 #16032368

Subgroups — C2×#13119191 #16032368

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×#88149C211yesmaximal, characteristic
2#13119191C2116yesmaximal, direct product factor
3C2×#11718654C212yesmaximal, complemented
4C2×#11718652C212yesmaximal, complemented
5C2×#11718600C211yesmaximal, characteristic, complemented
6C2×#11718649C211yesmaximal, characteristic, complemented
7C2×#11718649C212yesmaximal, complemented
8C2×#11718651C212yesmaximal, complemented
9C2×#11718648C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
11C2×C4×#6103C211yesmaximal, characteristic, complemented
12C22×C13×#125C211yesmaximal, characteristic, complemented
13C23×D52C2211yescharacteristic
14C23×D52C2212yes—
15C23×C4×D13C2211yescharacteristic
16C2×C13×#125—28no—
17C2×C13×#125C2218yescomplemented
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2212yes—
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2212yes—
28C22×#6103C2212yes—
29C22×#6103C2212yes—
30C22×#6103C2212yes—
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2212yes—
34C2×#88149—28no—
35C2×#88149C2218yes—
36C2×#88071C2212yes—
37C2×#88071C2211yescharacteristic
38C2×#88071C2212yes—
39C2×#88071C2211yescharacteristic
40#11718654C22116yescomplemented
41#11718652C22116yescomplemented
42#11718651C22116yescomplemented
43#11718649C2218yescomplemented
44#11718649C22116yescomplemented
45#11718648C2218yescomplemented
46C4⋊C4×Dic13C2218yescomplemented
47#11718600C2218yescomplemented
48C4×#6103C2218yescomplemented
49C24×D13C2312yes—
50C24×D13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2312yes—
54C23×C4×C13C2312yes—
55C23×C4×C13C2311yescharacteristic
56C23×Dic13C2312yes—
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C22×D52—28no—
61C22×D52—28no—
62C22×D52—24no—
63C22×D52—24no—
64C22×D52—24no—
65C22×D52—44no—
66C22×D52C2314yes—
67C22×D52C2318yes—
68C22×C4×D13—24no—
69C22×C4×D13—24no—
70C22×C4×D13—24no—
71C22×C4×D13C2314yes—
72C13×#125—232no—
73C2×C13×C4⋊C4—28no—
74C2×C13×C4⋊C4—28no—
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4D418yes—
77C2×C13×C4⋊C4C2314yes—
78C2×C13×C4⋊C4C2318yes—
79C2×C13×C4⋊C4C2318yes—
80C2×C13×C4⋊C4C2314yes—
81C2×C42×C13—24no—
82C2×C42×C13C2314yes—
83C2×#6103—24no—
84C2×#6103—28no—
85C2×#6103—24no—
86C2×#6103—28no—
87C2×#6103—44no—
88C2×#6103—44no—
89C2×#6103—44no—
90C2×#6103—44no—
91C2×#6103C2318yes—
92C2×#6103C2314yes—
93C2×#6103C2314yes—
94C2×#6103C2318yes—
95C2×#6103C2318yes—
96C2×#6103C2318yes—
97C2×#6103C2318yes—
98C2×#6103C2318yes—
99C2×C4⋊Dic13—24no—
100C2×C4⋊Dic13C2314yes—
101C2×C4×Dic13—24no—
102C2×C4×Dic13—44no—
103C2×C4×Dic13C2314yes—
104C2×C4×Dic13C2318yes—
105#88149—232no—
106#88071C2314yes—
107#88071C2314yes—
108#88071C2318yes—
109#88071C2318yes—
110C2×#2490—131nomaximal, Sylow
111C24×C13C2411yescharacteristic
112C23×D13—22no—
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—22no—
116C23×D13—22no—
117C23×D13—22no—
118C23×D13—24no—
119C23×D13—24no—
120C23×D13—24no—
121C23×D13—24no—
122C23×D13—24no—
123C23×D13—24no—
124C23×D13—24no—
125C23×D13#4114yes—
126C23×D13C2414yes—
127C23×D13C2412yes—
128C22×C4×C13—24no—
129C22×C4×C13—24no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—24no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—24no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—24no—
139C22×C4×C13C2×D418yes—
140C22×C4×C13C2×D414yes—
141C22×C4×C13#4114yes—
142C22×C4×C13#4114yes—
143C22×C4×C13C2412yes—
144C22×C4×C13C2412yes—
145C22×C4×C13C2414yes—
146C22×C4×C13C2414yes—
147C22×C4×C13C2412yes—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—24no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—24no—
157C22×Dic13—24no—
158C22×Dic13—22no—
159C22×Dic13#4114yes—
160C22×Dic13C2412yes—
161C22×Dic13C2412yes—
162C22×Dic13C2414yes—
163C22×Dic13C2412yes—
164C2×D52—216no—
165C2×D52—216no—
166C2×D52—28no—
167C2×D52—28no—
168C2×D52—28no—
169C2×D52—48no—
170C2×D52—432no—
171C2×D52—416no—
172C2×C4×D13—28no—
173C2×C4×D13—28no—
174C2×C4×D13—28no—
175C2×C4×D13—416no—
176C13×C4⋊C4—216no—
177C13×C4⋊C4—216no—
178C13×C4⋊C4—28no—
179C13×C4⋊C4C2×D4116yes—
180C42×C13—28no—
181#6103—28no—
182#6103—216no—
183#6103—28no—
184#6103—216no—
185#6103—48no—
186#6103—48no—
187#6103—48no—
188#6103—48no—
189C4⋊Dic13—28no—
190C4×Dic13—28no—
191C4×Dic13—48no—
192C22×#125D1311yescharacteristic, complemented
193C22×#121—131no—
194#2490—1316no—
195C2×#397—132no—
196C2×#394—132no—
197C2×#390—131no—
198C2×#390—132no—
199C2×#390—131no—
200C2×#388—132no—
201C2×#380—131no—
202C2×C4×C4⋊C4—131no—
203C2×C4×C22⋊C4—131no—
204C23×C13C22×D412yes—
205C23×C13C2×#4112yes—
206C23×C13C2×#4112yes—
207C23×C13C2×#4112yes—
208C23×C13C2×#4112yes—
209C23×C13H(5,𝔽2)12yes—
210C23×C13H(5,𝔽2)12yes—
211C23×C13C2511yescharacteristic
212C22×D13—28no—
213C22×D13—28no—
214C22×D13—28no—
215C22×D13—22no—
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—22no—
220C22×D13—22no—
221C22×D13—24no—
222C22×D13—24no—
223C22×D13—24no—
224C22×D13—24no—
225C22×D13—24no—
226C22×D13—24no—
227C22×D13—24no—
228C22×D13—44no—
229C22×D13—44no—
230C22×D13—44no—
231C22×D13—44no—
232C22×D13—48no—
233C22×D13—48no—
234C22×D13—48no—
235C22×D13—48no—
236C22×D13—48no—
237C22×D13—48no—
238C22×D13—48no—
239C22×D13C2×#4114yes—
240C2×C4×C13—216no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—24no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—24no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—24no—
252C2×C4×C13—44no—
253C2×C4×C13—44no—
254C2×C4×C13—48no—
255C2×C4×C13#124116yes—
256C2×C4×C13C22×D418yes—
257C2×C4×C13C22×D414yes—
258C2×C4×C13C2×#4114yes—
259C2×C4×C13C2×#4114yes—
260C2×Dic13—28no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—24no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—24no—
270C2×Dic13—24no—
271C2×Dic13—22no—
272C2×Dic13—44no—
273C2×Dic13—48no—
274C2×Dic13—44no—
275C2×Dic13C2×#4114yes—
276D52—432no—
277D52—416no—
278C4×D13—416no—
279C23×D4—131no—
280C23×D4—132no—
281C24×C4—131no—
282C2×#125—28no—
283C2×#125C2×D1318yescomplemented
284C2×#121—138no—
285C2×#121—268no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4C2×D1312yes—
288C22×C4⋊C4C2×D1312yes—
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C4⋊C4C2×D1311yescharacteristic
291C22×C22⋊C4—131no—
292C22×C22⋊C4—132no—
293C22×C22⋊C4—131no—
294C22×C22⋊C4—132no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4—132no—
297C22×C22⋊C4—132no—
298C22×C22⋊C4—132no—
299C22×C42—131no—
300C22×C42—132no—
301C22×C42C2×D1311yescharacteristic
302#397—1316no—
303#394—1316no—
304#390—138no—
305#390—1316no—
306#390—138no—
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×C13C2×#12414yes—
316C22×C13#52914yes—
317C22×C13#54014yes—
318C22×C13#54614yes—
319C22×C13#55014yes—
320C22×C13#55314yes—
321C22×C13#55314yes—
322C22×C13C23×D411yescharacteristic
323C22×C13C22×#4111yescharacteristic
324C22×C13C22×#4111yescharacteristic
325C22×C13C22×#4111yescharacteristic
326C22×C13C22×#4111yescharacteristic
327C22×C13C2×H(5,𝔽2)11yescharacteristic
328C22×C13C2×H(5,𝔽2)11yescharacteristic
329C2×D13—24no—
330C2×D13—24no—
331C2×D13—24no—
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—42no—
336C2×D13—416no—
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—28no—
346C4×C13—42no—
347C4×C13—42no—
348C4×C13—44no—
349C4×C13C2×#12418yes—
350Dic13—24no—
351Dic13—42no—
352Dic13—44no—
353Dic13—42no—
354C25—131no—
355C25—132no—
356C22×D4—134no—
357C22×D4—138no—
358C22×D4—268no—
359C22×D4—264no—
360C22×D4—264no—
361C22×D4—268no—
362C22×D4—264no—
363C22×D4—524no—
364C23×C4—131no—
365C23×C4—132no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4—134no—
369C23×C4—264no—
370C23×C4—264no—
371C23×C4—264no—
372C23×C4C22×D1312yes—
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1312yes—
376C23×C4C22×D1311yescharacteristic
377#125—232no—
378#121—2632no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4C22⋊D1318yes—
385C2×C4⋊C4C22×D1314yes—
386C2×C4⋊C4C22×D1318yes—
387C2×C4⋊C4C22×D1318yes—
388C2×C4⋊C4C22×D1314yes—
389C2×C22⋊C4—138no—
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—268no—
401C2×C22⋊C4—524no—
402C2×C22⋊C4—524no—
403C2×C22⋊C4—524no—
404C2×C22⋊C4—524no—
405C2×C42—24no—
406C2×C42—134no—
407C2×C42—138no—
408C2×C42—264no—
409C2×C42—524no—
410C2×C42C22×D1314yes—
411#95—134no—
412#95—134no—
413#95—138no—
414#95—138no—
415C2×C13#249018yescomplemented
416C2×C13C22×#12411yescharacteristic
417C2×C13C2×#52911yescharacteristic
418C2×C13C2×#54011yescharacteristic
419C2×C13C2×#54611yescharacteristic
420C2×C13C2×#55011yescharacteristic
421C2×C13C2×#55311yescharacteristic
422C2×C13C2×#55311yescharacteristic
423D13—44no—
424D13—84no—
425C24—134no—
426C24—132no—
427C24—134no—
428C24—262no—
429C24—262no—
430C24—262no—
431C24—262no—
432C24—262no—
433C24—262no—
434C24—264no—
435C24—264no—
436C24—264no—
437C24—264no—
438C24—264no—
439C24—264no—
440C24—264no—
441C24C23×D1311yescharacteristic
442C2×D4—2616no—
443C2×D4—268no—
444C2×D4—268no—
445C2×D4—2616no—
446C2×D4—268no—
447C2×D4—528no—
448C2×D4—5232no—
449C2×D4—5216no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—134no—
462C22×C4—132no—
463C22×C4—132no—
464C22×C4—132no—
465C22×C4—134no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—264no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—264no—
474C22×C4—262no—
475C22×C4—264no—
476C22×C4—262no—
477C22×C4—268no—
478C22×C4—268no—
479C22×C4—268no—
480C22×C4—5216no—
481C22×C4#613114yes—
482C22×C4#613114yes—
483C22×C4C2×C22⋊D1318yes—
484C22×C4C2×C22⋊D1314yes—
485C22×C4C23×D1312yes—
486C22×C4C23×D1312yes—
487C22×C4C23×D1314yes—
488C22×C4C23×D1314yes—
489C22×C4C23×D1312yes—
490C4⋊C4—216no—
491C4⋊C4—216no—
492C4⋊C4—28no—
493C4⋊C4—268no—
494C4⋊C4C2×C22⋊D13116yes—
495C22⋊C4—268no—
496C22⋊C4—2616no—
497C22⋊C4—268no—
498C22⋊C4—2616no—
499C22⋊C4—528no—
500C22⋊C4—528no—
501C22⋊C4—528no—
502C22⋊C4—528no—
503C42—28no—
504C42—268no—
505C42—528no—
506C13C2×#249011yescharacteristic, complemented, Sylow
507C23—134no—
508C23—268no—
509C23—262no—
510C23—262no—
511C23—262no—
512C23—262no—
513C23—262no—
514C23—268no—
515C23—262no—
516C23—268no—
517C23—264no—
518C23—264no—
519C23—264no—
520C23—264no—
521C23—264no—
522C23—264no—
523C23—264no—
524C23—524no—
525C23—524no—
526C23—524no—
527C23—524no—
528C23—528no—
529C23—528no—
530C23—528no—
531C23—528no—
532C23—528no—
533C23—528no—
534C23—528no—
535C23C2×#613112yes—
536C23C2×#613112yes—
537C23#41×D1312yes—
538C23#41×D1312yes—
539C23#8825612yes—
540C23#8825612yes—
541C23C22×C22⋊D1312yes—
542C23C24×D1311yescharacteristic
543D4—5232no—
544D4—5216no—
545C2×C4—216no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—48no—
560C2×C4—134no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—268no—
564C2×C4—262no—
565C2×C4—264no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—524no—
574C2×C4—524no—
575C2×C4—528no—
576C2×C4—5216no—
577C2×C4#88201116yes—
578C2×C4C2×#613114yes—
579C2×C4C2×#613114yes—
580C2×C4C22×C22⋊D1318yes—
581C2×C4C22×C22⋊D1314yes—
582C22—264no—
583C22—264no—
584C22—264no—
585C22—522no—
586C22—522no—
587C22—522no—
588C22—522no—
589C22—5216no—
590C22—524no—
591C22—524no—
592C22—524no—
593C22—524no—
594C22—524no—
595C22—524no—
596C22—524no—
597C22—10416no—
598C22#1171939614yes—
599C22#1171940014yes—
600C22#1171940014yes—
601C22#1171940314yes—
602C22C2×#8820114yes—
603C22#1171953414yes—
604C22#1171953914yes—
605C22C22×#613111yescharacteristic
606C22C22×#613111yescharacteristic
607C22C2×#41×D1311yescharacteristic
608C22C2×#41×D1311yescharacteristic
609C22C2×#8825611yescharacteristic
610C22C2×#8825611yescharacteristic
611C22C23×C22⋊D1311yescharacteristic
612C4—28no—
613C4—42no—
614C4—42no—
615C4—44no—
616C4—264no—
617C4—524no—
618C4—522no—
619C4—522no—
620C4C2×#8820118yes—
621C2—524no—
622C2—1044no—
623C2#1311919118yesdirect product factor
624C2C22×#8820111yescharacteristic
625C2C2×#1171939611yescharacteristic
626C2C2×#1171940311yescharacteristic
627C2C2×#1171953411yescharacteristic
628C2C2×#1171953911yescharacteristic
629C2C2×#1171940011yescharacteristic
630C2C2×#1171940011yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#125C2
socleC24×C13C24
prime radicalC22×#88149C2
hypercenterC22×#125D13
hypocenterC13C2×#2490
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #13119191C2direct (N × H)
3. C2×#11718654C2semidirect
4. C2×#11718652C2semidirect
5. C2×#11718600C2semidirect
6. C2×#11718649C2semidirect
7. C2×#11718649C2semidirect
8. C2×#11718651C2semidirect
9. C2×#11718648C2semidirect
10. C2×C4⋊C4×Dic13C2semidirect
11. C2×C4×#6103C2semidirect
12. C22×C13×#125C2semidirect
17. C2×C13×#125C22semidirect
40. #11718654C22semidirect
41. #11718652C22semidirect
42. #11718651C22semidirect
43. #11718649C22semidirect
44. #11718649C22semidirect
45. #11718648C22semidirect
46. C4⋊C4×Dic13C22semidirect
47. #11718600C22semidirect
48. C4×#6103C22semidirect
192. C22×#125D13semidirect
283. C2×#125C2×D13semidirect
415. C2×C13#2490semidirect
506. C13C2×#2490semidirect
623. C2#13119191direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881492
#131191912
C2×#117186542
C2×#117186522
C2×#117186002
C2×#117186492
C2×#117186512
C2×#117186482
C2×C4⋊C4×Dic132
C2×C4×#61032
C22×C13×#1252
C2×#249013