Finite Group Databasebeta

← C2×#13131345 #16807568

Subgroups — C2×#13131345 #16807568

Order 3328.

3094 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131345C2116yesmaximal, direct product factor
2C2×#11719083C212yesmaximal, complemented
3C2×#11719082C214yesmaximal, complemented
4C2×#11719136C211yesmaximal, characteristic
5C2×#11719136C212yesmaximal
6C2×C4⋊C4×#261C212yesmaximal, complemented
7C2×C4×C22⋊#261C211yesmaximal, characteristic
8C2×C4×C22⋊#261C212yesmaximal
9C22×C4⋊C4×D13C211yesmaximal, characteristic
10C23×C4×D13C2211yescharacteristic
11C23×C4×D13C2212yes—
12C22×C22⋊#261C2211yescharacteristic
13C22×C22⋊#261C2212yes—
14C22×C22⋊#261C2211yescharacteristic
15C22×C4⋊#261C2212yes—
16C22×C4⋊#261C2214yes—
17C22×C4×#261C2212yes—
18C22×C4×#261C2214yes—
19C22×C13×C4⋊C4C411yescharacteristic, complemented
20C22×C4⋊Dic13C411yescharacteristic, complemented
21C22×#6101C412yescomplemented
22C2×C4⋊C4×D13C418yescomplemented
23C2×C4⋊C4×D13C411yescharacteristic, complemented
24C2×C4⋊C4×D13C411yescharacteristic, complemented
25C2×C4⋊C4×D13C412yescomplemented
26C2×C4⋊C4×D13C2211yescharacteristic
27C2×C4⋊C4×D13C2212yes—
28C2×C4⋊C4×D13C2211yescharacteristic
29C2×C4⋊C4×D13C2218yes—
30#11719136C22116yes—
31#11719136C2218yes—
32C4×C22⋊#261C2218yes—
33C4×C22⋊#261C22116yes—
34C2×(C2×#261)⋊C4C2212yes—
35C2×(C2×#261)⋊C4C2214yes—
36C2×(C2×#261)⋊C4C2214yes—
37C2×(C2×#261)⋊C4C2212yes—
38#11719083C22116yescomplemented
39#11719082C22132yescomplemented
40C4⋊C4×#261C22116yescomplemented
41C24×D13C2311yescharacteristic
42C23×#261C2312yes—
43C23×#261C2314yes—
44C23×#261C2312yes—
45C23×C4×C13C2×C411yescharacteristic
46C23×C4×C13C2×C412yes—
47C23×Dic13C2×C411yescharacteristic
48C23×Dic13C2×C412yes—
49C22×C4×D13—28no—
50C22×C4×D13—48no—
51C22×C4×D13C2×C411yescharacteristic
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13C2×C414yes—
54C22×C4×D13C2×C418yes—
55C22×C4×D13C2×C412yes—
56C22×C4×D13C2×C412yes—
57C22×C4×D13C2312yes—
58C22×C4×D13C2312yes—
59C22×C4×D13C2311yescharacteristic
60C22×C4×D13C2314yes—
61C22×C4×D13C2318yes—
62C22×C4×D13C2311yescharacteristic
63C2×C22⋊#261—24no—
64C2×C22⋊#261—28no—
65C2×C22⋊#261Q818yes—
66C2×C22⋊#261C2314yes—
67C2×C22⋊#261C2318yes—
68C2×C22⋊#261C2314yes—
69C2×C4⋊#261—28no—
70C2×C4⋊#261—48no—
71C2×C4⋊#261C2318yes—
72C2×C4⋊#261C23116yes—
73C2×C4×#261—28no—
74C2×C4×#261—48no—
75C2×C4×#261C2318yes—
76C2×C4×#261C23116yes—
77C2×C13×C4⋊C4C2×C412yes—
78C2×C13×C4⋊C4C2×C411yescharacteristic
79C2×C13×C4⋊C4C2×C411yescharacteristic
80C2×C13×C4⋊C4C2×C418yescomplemented
81C2×C4⋊Dic13C2×C412yes—
82C2×C4⋊Dic13C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×C4⋊Dic13C2×C418yescomplemented
85C2×#6101C2×C412yes—
86C2×#6101C2×C412yes—
87C2×#6101C2×C412yes—
88C2×#6101C2×C412yes—
89C2×#6101C2×C4116yescomplemented
90C4⋊C4×D13C2×C418yes—
91C4⋊C4×D13C2×C414yes—
92C4⋊C4×D13C2×C414yes—
93C4⋊C4×D13C2×C418yescomplemented
94C4⋊C4×D13C2×C418yescomplemented
95C4⋊C4×D13C2×C4116yescomplemented
96C4⋊C4×D13C2314yes—
97C4⋊C4×D13C2318yes—
98C4⋊C4×D13C2314yes—
99(C2×#261)⋊C4C23116yes—
100(C2×#261)⋊C4C2318yes—
101(C2×#261)⋊C4C2318yes—
102(C2×#261)⋊C4C23116yes—
103C2×#2345—131nomaximal, Sylow
104C24×C13C22×C411yescharacteristic
105C23×D13—24no—
106C23×D13—24no—
107C23×D13C22×C412yes—
108C23×D13C22×C411yescharacteristic
109C23×D13C2×Q814yes—
110C23×D13#4114yes—
111C23×D13C2412yes—
112C23×D13C2411yescharacteristic
113C22×#261—24no—
114C22×#261—24no—
115C22×#261—24no—
116C22×#261—28no—
117C22×#261—24no—
118C22×#261—28no—
119C22×#261—28no—
120C22×#261—24no—
121C22×#261C2×Q818yes—
122C22×#261C2414yes—
123C22×#261C2418yes—
124C22×#261C2414yes—
125C22×C4×C13—24no—
126C22×C4×C13—44no—
127C22×C4×C13C22×C412yes—
128C22×C4×C13C22×C412yes—
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C414yes—
131C22×C4×C13C22×C418yes—
132C22×C4×C13C22×C411yescharacteristic
133C22×Dic13—24no—
134C22×Dic13—44no—
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C412yes—
137C22×Dic13C22×C412yes—
138C22×Dic13C22×C414yes—
139C22×Dic13C22×C418yes—
140C22×Dic13C22×C411yescharacteristic
141C2×C4×D13—24no—
142C2×C4×D13—28no—
143C2×C4×D13—28no—
144C2×C4×D13—24no—
145C2×C4×D13—24no—
146C2×C4×D13—216no—
147C2×C4×D13—216no—
148C2×C4×D13—416no—
149C2×C4×D13—416no—
150C2×C4×D13—44no—
151C2×C4×D13—44no—
152C2×C4×D13C22×C412yes—
153C2×C4×D13C22×C414yes—
154C2×C4×D13C22×C414yes—
155C2×C4×D13C22×C414yes—
156C2×C4×D13C22×C414yes—
157C2×C4×D13C22×C418yes—
158C2×C4×D13C22×C418yes—
159C2×C4×D13C22×C412yes—
160C2×C4×D13#4118yes—
161C2×C4×D13C2412yes—
162C2×C4×D13C2414yes—
163C2×C4×D13C2414yes—
164C2×C4×D13C2412yes—
165C22⋊#261—28no—
166C22⋊#261—216no—
167C22⋊#261C2×Q8116yes—
168C4⋊#261—216no—
169C4⋊#261—416no—
170C4×#261—216no—
171C4×#261—416no—
172C13×C4⋊C4C22×C418yes—
173C13×C4⋊C4C22×C414yes—
174C13×C4⋊C4C22×C414yes—
175C4⋊Dic13C22×C418yes—
176C4⋊Dic13C22×C414yes—
177C4⋊Dic13C22×C414yes—
178#6101C22×C418yes—
179#6101C22×C418yes—
180#6101C22×C418yes—
181#6101C22×C418yes—
182C23×C4⋊C4—131no—
183#2345—1316no—
184C2×#389—132no—
185C2×#387—134no—
186C2×#380—131no—
187C2×#380—132no—
188C2×C4×C4⋊C4—132no—
189C2×C4×C22⋊C4—131no—
190C2×C4×C22⋊C4—132no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13C4×Q814yes—
194C23×C13C23×C412yes—
195C23×C13C23×C411yescharacteristic
196C22×D13—22no—
197C22×D13—22no—
198C22×D13—24no—
199C22×D13—24no—
200C22×D13—216no—
201C22×D13—216no—
202C22×D13—24no—
203C22×D13—24no—
204C22×D13C4×Q814yes—
205C22×D13C4×Q818yes—
206C22×D13C23×C412yes—
207C22×D13C23×C411yescharacteristic
208C22×D13C22×Q814yes—
209C22×D13C22×Q812yes—
210C22×D13C2×#4114yes—
211C22×D13C2×#4114yes—
212C22×D13C2×#4112yes—
213C22×D13H(5,𝔽2)14yes—
214C22×D13C2511yescharacteristic
215C2×#261—216no—
216C2×#261—24no—
217C2×#261—24no—
218C2×#261—24no—
219C2×#261—28no—
220C2×#261—24no—
221C2×#261—28no—
222C2×#261—28no—
223C2×#261—24no—
224C2×#261—48no—
225C2×#261—416no—
226C2×#261C22×Q818yes—
227C2×C4×C13—22no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—28no—
231C2×C4×C13—48no—
232C2×C4×C13#11714yes—
233C2×C4×C13C23×C414yes—
234C2×C4×C13C23×C414yes—
235C2×C4×C13C23×C412yes—
236C2×C4×C13C23×C412yes—
237C2×Dic13—22no—
238C2×Dic13—24no—
239C2×Dic13—24no—
240C2×Dic13—28no—
241C2×Dic13—48no—
242C2×Dic13#11714yes—
243C2×Dic13C23×C412yes—
244C2×Dic13C23×C414yes—
245C2×Dic13C23×C414yes—
246C2×Dic13C23×C412yes—
247C4×D13—24no—
248C4×D13—28no—
249C4×D13—28no—
250C4×D13—24no—
251C4×D13—28no—
252C4×D13—28no—
253C4×D13—28no—
254C4×D13—28no—
255C4×D13—48no—
256C4×D13—48no—
257C4×D13#11718yes—
258C4×D13C2×#4118yes—
259C24×C4—131no—
260C24×C4—132no—
261C22×C4⋊C4—132no—
262C22×C4⋊C4—131no—
263C22×C4⋊C4—132no—
264C22×C4⋊C4—131no—
265C22×C4⋊C4—131no—
266C22×C4⋊C4—131no—
267C22×C4⋊C4—132no—
268C22×C4⋊C4—131no—
269C22×C4⋊C4—138no—
270C22×C4⋊C4—138no—
271C22×C4⋊C4—132no—
272C22×C4⋊C4—134no—
273C22×C4⋊C4#26111yescharacteristic, complemented
274C22×C22⋊C4—131no—
275C22×C22⋊C4—131no—
276C22×C22⋊C4—132no—
277C22×C42—132no—
278C22×C42—134no—
279#389—1316no—
280#387—1332no—
281#380—1316no—
282#380—138no—
283C4×C4⋊C4—1316no—
284C4×C22⋊C4—138no—
285C4×C22⋊C4—1316no—
286C2×#95—132no—
287C2×#95—134no—
288C2×#95—134no—
289C2×#95—132no—
290C22×C13—28no—
291C22×C13—22no—
292C22×C13—22no—
293C22×C13C2×#11712yes—
294C22×C13C2×C4×Q814yes—
295C22×C13C2×C4×Q812yes—
296C22×C13#51812yes—
297C22×C13C24×C411yescharacteristic
298C2×D13—28no—
299C2×D13—22no—
300C2×D13—22no—
301C2×D13—216no—
302C2×D13—28no—
303C2×D13—28no—
304C2×D13C2×#11712yes—
305C2×D13C2×C4×Q814yes—
306C2×D13C2×C4×Q812yes—
307C2×D13#51812yes—
308C2×D13#55318yes—
309C2×D13#55418yes—
310C2×D13C23×Q811yescharacteristic
311C2×D13C22×#4111yescharacteristic
312C2×D13C22×#4112yes—
313C2×D13C2×H(5,𝔽2)12yes—
314#261—28no—
315#261—44no—
316#261—48no—
317C4×C13—22no—
318C4×C13—24no—
319C4×C13—24no—
320C4×C13C2×#11714yes—
321Dic13—22no—
322Dic13—24no—
323Dic13—24no—
324Dic13C2×#11714yes—
325C25—131no—
326C23×C4—131no—
327C23×C4—132no—
328C23×C4—131no—
329C23×C4—132no—
330C23×C4—132no—
331C23×C4—131no—
332C23×C4—132no—
333C23×C4—134no—
334C23×C4—131no—
335C23×C4—134no—
336C23×C4—131no—
337C23×C4—138no—
338C23×C4—132no—
339C23×C4—132no—
340C23×C4—138no—
341C23×C4—132no—
342C23×C4—134no—
343C23×C4—268no—
344C23×C4—528no—
345C23×C4C2×#26111yescharacteristic
346C23×C4C2×#26112yes—
347C2×C4⋊C4—132no—
348C2×C4⋊C4—132no—
349C2×C4⋊C4—132no—
350C2×C4⋊C4—132no—
351C2×C4⋊C4—1316no—
352C2×C4⋊C4—132no—
353C2×C4⋊C4—131no—
354C2×C4⋊C4—131no—
355C2×C4⋊C4—138no—
356C2×C4⋊C4—134no—
357C2×C4⋊C4—134no—
358C2×C4⋊C4—138no—
359C2×C4⋊C4—1316no—
360C2×C4⋊C4—138no—
361C2×C4⋊C4—138no—
362C2×C4⋊C4—134no—
363C2×C4⋊C4—138no—
364C2×C4⋊C4—134no—
365C2×C4⋊C4—138no—
366C2×C4⋊C4—1316no—
367C2×C4⋊C4—268no—
368C2×C4⋊C4—528no—
369C2×C4⋊C4C2×#26112yes—
370C2×C4⋊C4C2×#26111yescharacteristic
371C2×C4⋊C4C2×#26111yescharacteristic
372C2×C4⋊C4C2×#26118yescomplemented
373C2×C22⋊C4—134no—
374C2×C22⋊C4—138no—
375C2×C22⋊C4—134no—
376C2×C22⋊C4—138no—
377C2×C22⋊C4—264no—
378C2×C22⋊C4—268no—
379C2×C42—138no—
380C2×C42—1316no—
381C2×C42—268no—
382C2×C42—528no—
383#95—138no—
384#95—1316no—
385#95—1316no—
386#95—138no—
387C2×C13—24no—
388C2×C13#234514yescomplemented
389C2×C13C22×#11711yescharacteristic
390C2×C13C22×C4×Q811yescharacteristic
391C2×C13C2×#51811yescharacteristic
392D13—24no—
393D13#234514yescomplemented
394D13C2×#55312yes—
395D13C2×#55412yes—
396C24—131no—
397C24—134no—
398C24—134no—
399C24—132no—
400C24—132no—
401C24—131no—
402C24—264no—
403C24—264no—
404C24C22×#26111yescharacteristic
405C22×C4—24no—
406C22×C4—44no—
407C22×C4—131no—
408C22×C4—138no—
409C22×C4—132no—
410C22×C4—132no—
411C22×C4—134no—
412C22×C4—138no—
413C22×C4—134no—
414C22×C4—131no—
415C22×C4—132no—
416C22×C4—132no—
417C22×C4—138no—
418C22×C4—132no—
419C22×C4—134no—
420C22×C4—134no—
421C22×C4—134no—
422C22×C4—132no—
423C22×C4—134no—
424C22×C4—134no—
425C22×C4—134no—
426C22×C4—138no—
427C22×C4—138no—
428C22×C4—134no—
429C22×C4—138no—
430C22×C4—264no—
431C22×C4—2616no—
432C22×C4—2616no—
433C22×C4—268no—
434C22×C4—268no—
435C22×C4—264no—
436C22×C4—264no—
437C22×C4—264no—
438C22×C4—264no—
439C22×C4—264no—
440C22×C4—264no—
441C22×C4—268no—
442C22×C4—264no—
443C22×C4—268no—
444C22×C4—268no—
445C22×C4—264no—
446C22×C4—524no—
447C22×C4—524no—
448C22×C4—5216no—
449C22×C4—5216no—
450C22×C4—524no—
451C22×C4C22×#26114yes—
452C22×C4C22×#26111yescharacteristic
453C22×C4C22×#26112yes—
454C22×C4C22×#26112yes—
455C22×C4C22×#26118yes—
456C22×C4C22×#26111yescharacteristic
457C4⋊C4—138no—
458C4⋊C4—138no—
459C4⋊C4—138no—
460C4⋊C4—138no—
461C4⋊C4—138no—
462C4⋊C4—134no—
463C4⋊C4—134no—
464C4⋊C4—2616no—
465C4⋊C4—5216no—
466C4⋊C4C22×#26118yes—
467C4⋊C4C22×#26114yes—
468C4⋊C4C22×#26114yes—
469C22⋊C4—1316no—
470C22⋊C4—268no—
471C22⋊C4—2616no—
472C42—2616no—
473C42—5216no—
474C13C2×#234511yescharacteristic, complemented, Sylow
475C23—22no—
476C23—22no—
477C23—134no—
478C23—134no—
479C23—132no—
480C23—132no—
481C23—131no—
482C23—131no—
483C23—134no—
484C23—134no—
485C23—138no—
486C23—134no—
487C23—132no—
488C23—264no—
489C23—264no—
490C23—264no—
491C23—264no—
492C23—2616no—
493C23—2616no—
494C23—262no—
495C23—262no—
496C23Q8×#26114yes—
497C23C23×#26112yes—
498C23C23×#26111yescharacteristic
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—48no—
504C2×C4—134no—
505C2×C4—132no—
506C2×C4—138no—
507C2×C4—138no—
508C2×C4—138no—
509C2×C4—132no—
510C2×C4—134no—
511C2×C4—134no—
512C2×C4—268no—
513C2×C4—268no—
514C2×C4—268no—
515C2×C4—264no—
516C2×C4—264no—
517C2×C4—268no—
518C2×C4—268no—
519C2×C4—268no—
520C2×C4—264no—
521C2×C4—264no—
522C2×C4—2616no—
523C2×C4—262no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—268no—
527C2×C4—264no—
528C2×C4—268no—
529C2×C4—264no—
530C2×C4—268no—
531C2×C4—268no—
532C2×C4—264no—
533C2×C4—528no—
534C2×C4—528no—
535C2×C4—528no—
536C2×C4—528no—
537C2×C4—5216no—
538C2×C4#8823714yes—
539C2×C4C23×#26112yes—
540C2×C4C23×#26114yes—
541C2×C4C23×#26114yes—
542C2×C4C23×#26112yes—
543C22—22no—
544C22—22no—
545C22—28no—
546C22—132no—
547C22—132no—
548C22—132no—
549C22—131no—
550C22—131no—
551C22—132no—
552C22—132no—
553C22—138no—
554C22—138no—
555C22—134no—
556C22—268no—
557C22—268no—
558C22—2616no—
559C22—262no—
560C22—262no—
561C22—268no—
562C22C2×#8823712yes—
563C22#1171962312yes—
564C22C2×Q8×#26114yes—
565C22C2×Q8×#26112yes—
566C22C24×#26111yescharacteristic
567C4—22no—
568C4—24no—
569C4—24no—
570C4—134no—
571C4—268no—
572C4—262no—
573C4—264no—
574C4—264no—
575C4—524no—
576C4—528no—
577C4C2×#8823714yes—
578C2—24no—
579C2—132no—
580C2—132no—
581C2—134no—
582C2—264no—
583C2#1313134514yesdirect product factor
584C2C22×#8823711yescharacteristic
585C2C22×Q8×#26111yescharacteristic
586C2C2×#1171962311yescharacteristic
subgroupG/H
centerC23C23×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC22×D13C25
hypercenterC22×C4⋊C4#261
hypocenterC13C2×#2345
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13131345C2direct (N × H)
2. C2×#11719083C2semidirect
3. C2×#11719082C2semidirect
6. C2×C4⋊C4×#261C2semidirect
19. C22×C13×C4⋊C4C4semidirect
20. C22×C4⋊Dic13C4semidirect
21. C22×#6101C4semidirect
22. C2×C4⋊C4×D13C4semidirect
23. C2×C4⋊C4×D13C4semidirect
24. C2×C4⋊C4×D13C4semidirect
25. C2×C4⋊C4×D13C4semidirect
38. #11719083C22semidirect
39. #11719082C22semidirect
40. C4⋊C4×#261C22semidirect
80. C2×C13×C4⋊C4C2×C4semidirect
84. C2×C4⋊Dic13C2×C4semidirect
89. C2×#6101C2×C4semidirect
93. C4⋊C4×D13C2×C4semidirect
94. C4⋊C4×D13C2×C4semidirect
95. C4⋊C4×D13C2×C4semidirect
273. C22×C4⋊C4#261semidirect
372. C2×C4⋊C4C2×#261semidirect
388. C2×C13#2345semidirect
393. D13#2345semidirect
474. C13C2×#2345semidirect
583. C2#13131345direct (N × H)

Maximal subgroups

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

subgroupindex
#131313452
C2×#117190832
C2×#117190822
C2×#117191362
C2×C4⋊C4×#2612
C2×C4×C22⋊#2612
C22×C4⋊C4×D132
C2×#234513