Finite Group Databasebeta

← C2×#13120716 #16029848

Subgroups — C2×#13120716 #16029848

Order 3328.

2286 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic
2C22×C4×Dic26C211yesmaximal, characteristic
3#13120716C2116yesmaximal, direct product factor
4C2×#11718321C211yesmaximal, characteristic
5C2×#11718321C211yesmaximal, characteristic
6C2×#11718319C211yesmaximal, characteristic
7C2×#11718319C211yesmaximal, characteristic
8C2×#11718318C211yesmaximal, characteristic
9C2×#11718645C211yesmaximal, characteristic
10C2×#11718317C211yesmaximal, characteristic
11C2×#11718640C211yesmaximal, characteristic
12C2×#11718314C211yesmaximal, characteristic
13C2×#11718594C211yesmaximal, characteristic
14C2×#11718639C211yesmaximal, characteristic
15C2×#11718312C211yesmaximal, characteristic
16C2×C13×#387C211yesmaximal, characteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C2×#88143—28no—
35C2×#88143C2218yes—
36C2×C4×Dic26—28no—
37C2×C4×Dic26C2218yes—
38C13×#387C2218yes—
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718645C2218yes—
58#11718640C2218yes—
59#11718639C2218yes—
60#11718594C2218yes—
61#11718321C2218yes—
62#11718321C2218yes—
63#11718319C2218yes—
64#11718319C2218yes—
65#11718318C2218yes—
66#11718317C2218yes—
67#11718314C2218yes—
68#11718312C2218yes—
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C22×Dic26—24no—
85C22×Dic26—24no—
86C22×Dic26—24no—
87C22×Dic26C2314yes—
88C2×C13×C4⋊C4—24no—
89C2×C13×C4⋊C4—24no—
90C2×C13×C4⋊C4C2314yes—
91C2×C13×C4⋊C4C2314yes—
92C2×C42×C13—24no—
93C2×C42×C13C2314yes—
94C2×C4⋊Dic13—24no—
95C2×C4⋊Dic13—24no—
96C2×C4⋊Dic13—24no—
97C2×C4⋊Dic13C2314yes—
98C2×C4⋊Dic13C2314yes—
99C2×C4⋊Dic13C2314yes—
100C2×#6101—24no—
101C2×#6101—24no—
102C2×#6101—24no—
103C2×#6101—24no—
104C2×#6101—24no—
105C2×#6101—24no—
106C2×#6101—24no—
107C2×#6101—24no—
108C2×#6101C2314yes—
109C2×#6101C2314yes—
110C2×#6101C2314yes—
111C2×#6101C2314yes—
112C2×#6101C2314yes—
113C2×#6101C2314yes—
114C2×#6101C2314yes—
115C2×#6101C2314yes—
116C2×C4×Dic13—24no—
117C2×C4×Dic13D418yes—
118C2×C4×Dic13C2314yes—
119C2×C4×Dic13C2314yes—
120#88143—232no—
121C4×Dic26—232no—
122C13×#95C2314yes—
123C13×#95C2314yes—
124C13×#95C2314yes—
125C13×#95C2314yes—
126#88071C2314yes—
127#88071C2314yes—
128#88071C2314yes—
129#88071C2314yes—
130#88071C2314yes—
131#88071C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140C2×#2634—131nomaximal, Sylow
141C24×C13C2411yescharacteristic
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13C2×D414yes—
162C22×C4×C13#4114yes—
163C22×C4×C13C2412yes—
164C22×C4×C13C2412yes—
165C22×C4×C13C2412yes—
166C22×C4×C13C2412yes—
167C22×C4×C13C2412yes—
168C22×C4×C13C2412yes—
169C22×C4×C13C2412yes—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13C2×D414yes—
192C22×Dic13C2×D414yes—
193C22×Dic13#4114yes—
194C22×Dic13C2412yes—
195C22×Dic13C2412yes—
196C22×Dic13C2412yes—
197C22×Dic13C2412yes—
198C22×Dic13C2412yes—
199C22×Dic13C2412yes—
200C22×Dic13C2412yes—
201C22×Dic13C2412yes—
202C2×Dic26—232no—
203C2×Dic26—28no—
204C2×Dic26—28no—
205C2×Dic26—28no—
206C13×C4⋊C4—28no—
207C13×C4⋊C4—28no—
208C42×C13—28no—
209C4⋊Dic13—28no—
210C4⋊Dic13—28no—
211C4⋊Dic13—28no—
212#6101—28no—
213#6101—28no—
214#6101—28no—
215#6101—28no—
216#6101—28no—
217#6101—28no—
218#6101—28no—
219#6101—28no—
220C4×Dic13—28no—
221C4×Dic13C2×D4116yes—
222C22×#125—131no—
223C22×C4×Q8—131no—
224#2634—1316no—
225C2×#400—131no—
226C2×#400—131no—
227C2×#400—131no—
228C2×#400—131no—
229C2×#398—131no—
230C2×#398—131no—
231C2×#395—131no—
232C2×#395—131no—
233C2×#387—131no—
234C2×#387—131no—
235C2×#387—131no—
236C2×#387D1311yescharacteristic
237C2×#383—131no—
238C23×C13C22×D412yes—
239C23×C13C2×#4112yes—
240C23×C13C2×#4112yes—
241C23×C132−1+412yes—
242C23×C132−1+412yes—
243C23×C132−1+412yes—
244C23×C132−1+412yes—
245C23×C13C2511yescharacteristic
246C2×C4×C13—28no—
247C2×C4×C13—28no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—44no—
268C2×C4×C13—44no—
269C2×C4×C13—44no—
270C2×C4×C13—44no—
271C2×C4×C13—44no—
272C2×C4×C13C22×D414yes—
273C2×C4×C13C2×#4114yes—
274C2×Dic13—28no—
275C2×Dic13—28no—
276C2×Dic13—28no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—22no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—22no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—22no—
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—22no—
296C2×Dic13—22no—
297C2×Dic13—22no—
298C2×Dic13—44no—
299C2×Dic13—44no—
300C2×Dic13—44no—
301C2×Dic13—44no—
302C2×Dic13—44no—
303C2×Dic13C22×D414yes—
304C2×Dic13C22×D414yes—
305C2×Dic13C2×#4114yes—
306Dic26—232no—
307C23×Q8—131no—
308C2×#125—138no—
309C2×#125—268no—
310C2×C4×Q8—138no—
311C2×C4×Q8—268no—
312C22×C4⋊C4—131no—
313C22×C4⋊C4—131no—
314C22×C4⋊C4—131no—
315C22×C4⋊C4—131no—
316C22×C4⋊C4—131no—
317C22×C4⋊C4—131no—
318C22×C4⋊C4—131no—
319C22×C4⋊C4—131no—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—131no—
322C22×C4⋊C4—131no—
323C22×C4⋊C4C2×D1311yescharacteristic
324C22×C4⋊C4C2×D1311yescharacteristic
325C22×C42—131no—
326C22×C42—131no—
327C22×C42C2×D1311yescharacteristic
328#400—138no—
329#400—138no—
330#400—138no—
331#400—138no—
332#398—138no—
333#398—138no—
334#395—138no—
335#395—138no—
336#387—138no—
337#387—138no—
338#387—138no—
339#387C2×D1318yes—
340#383—138no—
341C2×#95—131no—
342C2×#95—131no—
343C2×#95—131no—
344C2×#95—131no—
345C2×#95—131no—
346C2×#95—131no—
347C2×#95—131no—
348C2×#95—131no—
349C2×#95—131no—
350C2×#95—131no—
351C2×#95—131no—
352C2×#95—131no—
353C2×#95—131no—
354C2×#95—131no—
355C2×#95C2×D1311yescharacteristic
356C2×#95C2×D1311yescharacteristic
357C2×#95C2×D1311yescharacteristic
358C2×#95C2×D1311yescharacteristic
359C22×C13#52514yes—
360C22×C13#53614yes—
361C22×C13#53614yes—
362C22×C13#54114yes—
363C22×C13#54114yes—
364C22×C13#54114yes—
365C22×C13#54114yes—
366C22×C13C23×D411yescharacteristic
367C22×C13C22×#4111yescharacteristic
368C22×C13C22×#4111yescharacteristic
369C22×C13C2×2−1+411yescharacteristic
370C22×C13C2×2−1+411yescharacteristic
371C22×C13C2×2−1+411yescharacteristic
372C22×C13C2×2−1+411yescharacteristic
373C4×C13—24no—
374C4×C13—24no—
375C4×C13—42no—
376C4×C13—42no—
377C4×C13—42no—
378C4×C13—42no—
379C4×C13—42no—
380Dic13—24no—
381Dic13—24no—
382Dic13—24no—
383Dic13—42no—
384Dic13—42no—
385Dic13—42no—
386Dic13—42no—
387Dic13—42no—
388C22×Q8—134no—
389C22×Q8—264no—
390C22×Q8—264no—
391C22×Q8—264no—
392C23×C4—131no—
393C23×C4—131no—
394C23×C4—131no—
395C23×C4—131no—
396C23×C4—131no—
397C23×C4—131no—
398C23×C4—131no—
399C23×C4—131no—
400C23×C4C22×D1311yescharacteristic
401C23×C4C22×D1311yescharacteristic
402C23×C4C22×D1311yescharacteristic
403C23×C4C22×D1311yescharacteristic
404C23×C4C22×D1311yescharacteristic
405C23×C4C22×D1311yescharacteristic
406C23×C4C22×D1311yescharacteristic
407#125—2632no—
408C4×Q8—2632no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—134no—
412C2×C4⋊C4—134no—
413C2×C4⋊C4—134no—
414C2×C4⋊C4—134no—
415C2×C4⋊C4—134no—
416C2×C4⋊C4—134no—
417C2×C4⋊C4—134no—
418C2×C4⋊C4—134no—
419C2×C4⋊C4—134no—
420C2×C4⋊C4—134no—
421C2×C4⋊C4—134no—
422C2×C4⋊C4—264no—
423C2×C4⋊C4—264no—
424C2×C4⋊C4—264no—
425C2×C4⋊C4—264no—
426C2×C4⋊C4—264no—
427C2×C4⋊C4—264no—
428C2×C4⋊C4—264no—
429C2×C4⋊C4—264no—
430C2×C4⋊C4—264no—
431C2×C4⋊C4—264no—
432C2×C4⋊C4—264no—
433C2×C4⋊C4C22×D1314yes—
434C2×C4⋊C4C22×D1314yes—
435C2×C42—24no—
436C2×C42—138no—
437C2×C42—134no—
438C2×C42—134no—
439C2×C42—264no—
440C2×C42C22×D1314yes—
441#95—134no—
442#95—134no—
443#95—134no—
444#95—134no—
445#95—134no—
446#95—134no—
447#95—134no—
448#95—134no—
449#95—134no—
450#95—134no—
451#95—134no—
452#95—134no—
453#95—134no—
454#95—134no—
455#95C22×D1314yes—
456#95C22×D1314yes—
457#95C22×D1314yes—
458#95C22×D1314yes—
459C2×C13#263418yescomplemented
460C2×C13C2×#52511yescharacteristic
461C2×C13C2×#53611yescharacteristic
462C2×C13C2×#53611yescharacteristic
463C2×C13C2×#54111yescharacteristic
464C2×C13C2×#54111yescharacteristic
465C2×C13C2×#54111yescharacteristic
466C2×C13C2×#54111yescharacteristic
467C24C23×D1311yescharacteristic
468C2×Q8—268no—
469C2×Q8—268no—
470C2×Q8—2632no—
471C2×Q8—268no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—134no—
492C22×C4—134no—
493C22×C4—134no—
494C22×C4—132no—
495C22×C4—132no—
496C22×C4—132no—
497C22×C4—132no—
498C22×C4—132no—
499C22×C4—132no—
500C22×C4—132no—
501C22×C4—132no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—262no—
517C22×C4—262no—
518C22×C4—262no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4—262no—
522C22×C4—262no—
523C22×C4#612714yes—
524C22×C4D4×D1314yes—
525C22×C4C23×D1312yes—
526C22×C4C23×D1312yes—
527C22×C4C23×D1312yes—
528C22×C4C23×D1312yes—
529C22×C4C23×D1312yes—
530C22×C4C23×D1312yes—
531C22×C4C23×D1312yes—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—268no—
535C4⋊C4—268no—
536C4⋊C4—268no—
537C4⋊C4—268no—
538C4⋊C4—268no—
539C4⋊C4—268no—
540C4⋊C4—268no—
541C4⋊C4—268no—
542C4⋊C4—268no—
543C4⋊C4—268no—
544C4⋊C4—268no—
545C42—28no—
546C42—1316no—
547C42—268no—
548C13C2×#263411yescharacteristic, complemented, Sylow
549C23C2×#612712yes—
550C23C2×D4×D1312yes—
551C23#8825412yes—
552C23#41×D1312yes—
553C23#8825712yes—
554C23#8825712yes—
555C23#8825712yes—
556C23C24×D1311yescharacteristic
557Q8—2632no—
558C2×C4—28no—
559C2×C4—28no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—134no—
585C2×C4—134no—
586C2×C4—134no—
587C2×C4—268no—
588C2×C4—268no—
589C2×C4—268no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—262no—
608C2×C4—262no—
609C2×C4—262no—
610C2×C4—262no—
611C2×C4—524no—
612C2×C4—524no—
613C2×C4—524no—
614C2×C4—524no—
615C2×C4—524no—
616C2×C4C2×#612714yes—
617C2×C4C2×D4×D1314yes—
618C22#1171922314yes—
619C22#1171925214yes—
620C22#1171928814yes—
621C22#1171933314yes—
622C22#1171935314yes—
623C22#1171940114yes—
624C22#1171940614yes—
625C22C22×#612711yescharacteristic
626C22C22×D4×D1311yescharacteristic
627C22C2×#8825411yescharacteristic
628C22C2×#41×D1311yescharacteristic
629C22C2×#8825711yescharacteristic
630C22C2×#8825711yescharacteristic
631C22C2×#8825711yescharacteristic
632C4—24no—
633C4—24no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—264no—
640C4—264no—
641C4—264no—
642C4—522no—
643C4—522no—
644C4—522no—
645C4—522no—
646C4—522no—
647C2#1312071618yesdirect product factor
648C2C2×#1171925211yescharacteristic
649C2C2×#1171935311yescharacteristic
650C2C2×#1171933311yescharacteristic
651C2C2×#1171940611yescharacteristic
652C2C2×#1171928811yescharacteristic
653C2C2×#1171940111yescharacteristic
654C2C2×#1171922311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#387C2
socle, prime radicalC24×C13C24
hypercenterC2×#387D13
hypocenterC13C2×#2634
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #13120716C2direct (N × H)
459. C2×C13#2634semidirect
548. C13C2×#2634semidirect
647. C2#13120716direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881432
C22×C4×Dic262
#131207162
C2×#117183212
C2×#117183192
C2×#117183182
C2×#117186452
C2×#117183172
C2×#117186402
C2×#117183142
C2×#117185942
C2×#117186392
C2×#117183122
C2×C13×#3872
C2×#263413