Finite Group Databasebeta

← C2×#13123013 #16069293

Subgroups — C2×#13123013 #16069293

Order 3328.

1718 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
1#13123013C2116yesmaximal, direct product factor
2C2×C13⋊#401C211yesmaximal, characteristic
3C2×C13⋊#401C211yesmaximal, characteristic
4C2×#11718319C211yesmaximal, characteristic
5C2×#11718320C211yesmaximal, characteristic
6C2×#11718647C211yesmaximal, characteristic
7C2×#11718643C211yesmaximal, characteristic
8C2×#11718318C211yesmaximal, characteristic
9C2×#11718318C211yesmaximal, characteristic
10C2×#11718645C211yesmaximal, characteristic
11C2×#11718317C211yesmaximal, characteristic
12C2×#11718640C211yesmaximal, characteristic
13C2×#11718307C211yesmaximal, characteristic
14C2×#11718316C211yesmaximal, characteristic
15C2×#11718314C211yesmaximal, characteristic
16C2×C13×#400C211yesmaximal, characteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C13×#400C2218yes—
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718647C2218yes—
54#11718645C2218yes—
55#11718643C2218yes—
56#11718640C2218yes—
57C13⋊#401C2218yes—
58C13⋊#401C2218yes—
59#11718320C2218yes—
60#11718319C2218yes—
61#11718318C2218yes—
62#11718318C2218yes—
63#11718317C2218yes—
64#11718316C2218yes—
65#11718314C2218yes—
66#11718307C2218yes—
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C22×Dic26—24no—
83C22×Dic26—42no—
84C22×Dic26—42no—
85C22×Dic26C2314yes—
86C2×C13×C4⋊C4—42no—
87C2×C13×C4⋊C4—42no—
88C2×C13×C4⋊C4C2314yes—
89C2×C13×C4⋊C4C2314yes—
90C2×C4⋊Dic13—24no—
91C2×C4⋊Dic13—42no—
92C2×C4⋊Dic13—42no—
93C2×C4⋊Dic13C2314yes—
94C2×C4⋊Dic13C2314yes—
95C2×C4⋊Dic13C2314yes—
96C2×#6101—24no—
97C2×#6101—42no—
98C2×#6101—42no—
99C2×#6101—42no—
100C2×#6101—42no—
101C2×#6101—42no—
102C2×#6101C2314yes—
103C2×#6101C2314yes—
104C2×#6101C2314yes—
105C2×#6101C2314yes—
106C2×#6101C2314yes—
107C2×#6101C2314yes—
108C2×C4×Dic13—42no—
109C2×C4×Dic13C2314yes—
110C13×#95C2314yes—
111C13×#95C2314yes—
112C13×#95C2314yes—
113C13×#95C2314yes—
114C13×#95C2314yes—
115#88071C2314yes—
116#88071C2314yes—
117#88071C2314yes—
118#88071C2314yes—
119#88071C2314yes—
120#88071C2314yes—
121#88071C2314yes—
122#88071C2314yes—
123#88071C2314yes—
124#88071C2314yes—
125#88071C2314yes—
126#88071C2314yes—
127#88071C2314yes—
128#88071C2314yes—
129#88071C2314yes—
130#88071C2314yes—
131#88071C2314yes—
132C2×#2833—131nomaximal, Sylow
133C24×C13C2411yescharacteristic
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
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×C13C2412yes—
156C22×C4×C13C2412yes—
157C22×C4×C13C2412yes—
158C22×C4×C13C2412yes—
159C22×C4×C13C2412yes—
160C22×C4×C13C2412yes—
161C22×C4×C13C2412yes—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
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#4114yes—
186C22×Dic13C2412yes—
187C22×Dic13C2412yes—
188C22×Dic13C2412yes—
189C22×Dic13C2412yes—
190C22×Dic13C2412yes—
191C22×Dic13C2412yes—
192C22×Dic13C2412yes—
193C22×Dic13C2412yes—
194C2×Dic26—28no—
195C2×Dic26—44no—
196C2×Dic26—44no—
197C2×Dic26—416no—
198C13×C4⋊C4—44no—
199C13×C4⋊C4—44no—
200C4⋊Dic13—28no—
201C4⋊Dic13—44no—
202C4⋊Dic13—44no—
203#6101—28no—
204#6101—44no—
205#6101—44no—
206#6101—44no—
207#6101—44no—
208#6101—44no—
209C4×Dic13—44no—
210#2833—1316no—
211C2×#401—131no—
212C2×#401—131no—
213C2×#400—131no—
214C2×#400—131no—
215C2×#400—131no—
216C2×#400—131no—
217C2×#400D1311yescharacteristic
218C2×#398—131no—
219C2×#398—131no—
220C2×#398—131no—
221C2×#395—131no—
222C2×#395—131no—
223C2×#391—131no—
224C2×#387—131no—
225C2×#387—131no—
226C23×C13C2×#4112yes—
227C23×C13H(5,𝔽2)12yes—
228C23×C13H(5,𝔽2)12yes—
229C23×C132−1+412yes—
230C23×C132−1+412yes—
231C23×C132−1+412yes—
232C23×C132−1+412yes—
233C23×C13C2511yescharacteristic
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
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—44no—
256C2×C4×C13—44no—
257C2×C4×C13—44no—
258C2×C4×C13—44no—
259C2×C4×C13—44no—
260C2×C4×C13—44no—
261C2×C4×C13—44no—
262C2×Dic13—28no—
263C2×Dic13—22no—
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—22no—
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—22no—
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—44no—
287C2×Dic13—44no—
288C2×Dic13—44no—
289C2×Dic13—44no—
290C2×Dic13—44no—
291C2×Dic13—44no—
292C2×Dic13—44no—
293C2×Dic13C2×#4114yes—
294Dic26—416no—
295C23×Q8—131no—
296C22×C4⋊C4—131no—
297C22×C4⋊C4—131no—
298C22×C4⋊C4—131no—
299C22×C4⋊C4—131no—
300C22×C4⋊C4—131no—
301C22×C4⋊C4—131no—
302C22×C4⋊C4—131no—
303C22×C4⋊C4—131no—
304C22×C4⋊C4—131no—
305C22×C4⋊C4C2×D1311yescharacteristic
306C22×C4⋊C4C2×D1311yescharacteristic
307C22×C42—131no—
308#401—138no—
309#401—138no—
310#400—138no—
311#400—138no—
312#400—138no—
313#400—138no—
314#400C2×D1318yes—
315#398—138no—
316#398—138no—
317#398—138no—
318#395—138no—
319#395—138no—
320#391—138no—
321#387—138no—
322#387—138no—
323C2×#95—131no—
324C2×#95—131no—
325C2×#95—131no—
326C2×#95—131no—
327C2×#95—131no—
328C2×#95—131no—
329C2×#95—131no—
330C2×#95—131no—
331C2×#95—131no—
332C2×#95—131no—
333C2×#95—131no—
334C2×#95—131no—
335C2×#95—131no—
336C2×#95—131no—
337C2×#95—131no—
338C2×#95—131no—
339C2×#95—131no—
340C2×#95C2×D1311yescharacteristic
341C2×#95C2×D1311yescharacteristic
342C2×#95C2×D1311yescharacteristic
343C2×#95C2×D1311yescharacteristic
344C2×#95C2×D1311yescharacteristic
345C22×C13#53814yes—
346C22×C13#54114yes—
347C22×C13#54114yes—
348C22×C13#56314yes—
349C22×C13#56314yes—
350C22×C13#56314yes—
351C22×C13#56314yes—
352C22×C13C22×#4111yescharacteristic
353C22×C13C2×H(5,𝔽2)11yescharacteristic
354C22×C13C2×H(5,𝔽2)11yescharacteristic
355C22×C13C2×2−1+411yescharacteristic
356C22×C13C2×2−1+411yescharacteristic
357C22×C13C2×2−1+411yescharacteristic
358C22×C13C2×2−1+411yescharacteristic
359C4×C13—42no—
360C4×C13—42no—
361C4×C13—42no—
362C4×C13—42no—
363C4×C13—42no—
364C4×C13—42no—
365C4×C13—42no—
366Dic13—24no—
367Dic13—42no—
368Dic13—42no—
369Dic13—42no—
370Dic13—42no—
371Dic13—42no—
372Dic13—42no—
373Dic13—42no—
374C22×Q8—134no—
375C22×Q8—264no—
376C22×Q8—522no—
377C22×Q8—522no—
378C23×C4—131no—
379C23×C4—131no—
380C23×C4—131no—
381C23×C4—131no—
382C23×C4—131no—
383C23×C4—131no—
384C23×C4—131no—
385C23×C4—131no—
386C23×C4C22×D1311yescharacteristic
387C23×C4C22×D1311yescharacteristic
388C23×C4C22×D1311yescharacteristic
389C23×C4C22×D1311yescharacteristic
390C23×C4C22×D1311yescharacteristic
391C23×C4C22×D1311yescharacteristic
392C23×C4C22×D1311yescharacteristic
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—134no—
396C2×C4⋊C4—134no—
397C2×C4⋊C4—134no—
398C2×C4⋊C4—134no—
399C2×C4⋊C4—134no—
400C2×C4⋊C4—134no—
401C2×C4⋊C4—134no—
402C2×C4⋊C4—134no—
403C2×C4⋊C4—134no—
404C2×C4⋊C4—264no—
405C2×C4⋊C4—264no—
406C2×C4⋊C4—522no—
407C2×C4⋊C4—522no—
408C2×C4⋊C4—522no—
409C2×C4⋊C4—522no—
410C2×C4⋊C4—522no—
411C2×C4⋊C4—522no—
412C2×C4⋊C4—522no—
413C2×C4⋊C4C22×D1314yes—
414C2×C4⋊C4C22×D1314yes—
415C2×C42—134no—
416C2×C42—522no—
417#95—134no—
418#95—134no—
419#95—134no—
420#95—134no—
421#95—134no—
422#95—134no—
423#95—134no—
424#95—134no—
425#95—134no—
426#95—134no—
427#95—134no—
428#95—134no—
429#95—134no—
430#95—134no—
431#95—134no—
432#95—134no—
433#95—134no—
434#95C22×D1314yes—
435#95C22×D1314yes—
436#95C22×D1314yes—
437#95C22×D1314yes—
438#95C22×D1314yes—
439C2×C13#283318yescomplemented
440C2×C13C2×#53811yescharacteristic
441C2×C13C2×#54111yescharacteristic
442C2×C13C2×#54111yescharacteristic
443C2×C13C2×#56311yescharacteristic
444C2×C13C2×#56311yescharacteristic
445C2×C13C2×#56311yescharacteristic
446C2×C13C2×#56311yescharacteristic
447C24C23×D1311yescharacteristic
448C2×Q8—268no—
449C2×Q8—524no—
450C2×Q8—524no—
451C2×Q8—5216no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—134no—
474C22×C4—132no—
475C22×C4—132no—
476C22×C4—132no—
477C22×C4—132no—
478C22×C4—132no—
479C22×C4—132no—
480C22×C4—132no—
481C22×C4—132no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4C23×D1312yes—
506C22×C4C23×D1312yes—
507C22×C4C23×D1312yes—
508C22×C4C23×D1312yes—
509C22×C4C23×D1312yes—
510C22×C4C23×D1312yes—
511C22×C4C23×D1312yes—
512C4⋊C4—44no—
513C4⋊C4—44no—
514C4⋊C4—268no—
515C4⋊C4—268no—
516C4⋊C4—524no—
517C4⋊C4—524no—
518C4⋊C4—524no—
519C4⋊C4—524no—
520C4⋊C4—524no—
521C4⋊C4—524no—
522C4⋊C4—524no—
523C42—524no—
524C13C2×#283311yescharacteristic, complemented, Sylow
525C23#8825112yes—
526C23#8825412yes—
527C23#41×D1312yes—
528C23#8825612yes—
529C23#8825712yes—
530C23#8825712yes—
531C23#8825712yes—
532C23C24×D1311yescharacteristic
533Q8—5216no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—134no—
563C2×C4—268no—
564C2×C4—262no—
565C2×C4—262no—
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—262no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—524no—
588C2×C4—524no—
589C2×C4—524no—
590C2×C4—524no—
591C2×C4—524no—
592C2×C4—524no—
593C2×C4—524no—
594C22#1171935114yes—
595C22#1171935614yes—
596C22#1171938314yes—
597C22#1171940114yes—
598C22#1171940414yes—
599C22#1171940614yes—
600C22#1171941714yes—
601C22C2×#8825111yescharacteristic
602C22C2×#8825411yescharacteristic
603C22C2×#41×D1311yescharacteristic
604C22C2×#8825611yescharacteristic
605C22C2×#8825711yescharacteristic
606C22C2×#8825711yescharacteristic
607C22C2×#8825711yescharacteristic
608C4—42no—
609C4—42no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—42no—
614C4—42no—
615C4—264no—
616C4—522no—
617C4—522no—
618C4—522no—
619C4—522no—
620C4—522no—
621C4—522no—
622C4—522no—
623C2#1312301318yesdirect product factor
624C2C2×#1171938311yescharacteristic
625C2C2×#1171940611yescharacteristic
626C2C2×#1171940111yescharacteristic
627C2C2×#1171935111yescharacteristic
628C2C2×#1171941711yescharacteristic
629C2C2×#1171935611yescharacteristic
630C2C2×#1171940411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#400C2
socle, prime radicalC24×C13C24
hypercenterC2×#400D13
hypocenterC13C2×#2833
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #13123013C2direct (N × H)
439. C2×C13#2833semidirect
524. C13C2×#2833semidirect
623. C2#13123013direct (N × H)

Maximal subgroups

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

subgroupindex
#131230132
C2×C13⋊#4012
C2×#117183192
C2×#117183202
C2×#117186472
C2×#117186432
C2×#117183182
C2×#117186452
C2×#117183172
C2×#117186402
C2×#117183072
C2×#117183162
C2×#117183142
C2×C13×#4002
C2×#283313