Finite Group Databasebeta

← C2×#13120642 #16029266

Subgroups — C2×#13120642 #16029266

Order 3328.

4142 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D13C211yesmaximal, characteristic
3#13120642C2116yesmaximal, direct product factor
4C2×#11718653C211yesmaximal, characteristic, complemented
5C2×#11718609C212yesmaximal, complemented
6C2×#11718655C212yesmaximal, complemented
7C2×#11718334C211yesmaximal, characteristic, complemented
8C2×#11718608C211yesmaximal, characteristic, complemented
9C2×#11718650C212yesmaximal, complemented
10C2×#11718328C211yesmaximal, characteristic, complemented
11C2×#11718616C212yesmaximal
12C2×C13×#399C211yesmaximal, characteristic, complemented
13C25×D13C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C23×Dic26C2211yescharacteristic, complemented
17C22×C13×C4⋊C4C2211yescharacteristic, complemented
18C22×C13×C4⋊C4C2212yescomplemented
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2212yes—
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2212yes—
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2212yes—
28C22×#6103C2212yes—
29C22×C4⋊Dic13C2212yescomplemented
30C22×#6101C2212yescomplemented
31C22×#6101C2212yescomplemented
32C2×#88151—28no—
33C2×#88151C2218yescomplemented
34C2×C22⋊C4×D13—28no—
35C2×C22⋊C4×D13C2218yes—
36C13×#399C2218yescomplemented
37C2×C13×#95C2211yescharacteristic, complemented
38C2×#88071C2211yescharacteristic, complemented
39C2×#88071C2212yescomplemented
40C2×#88071C2212yescomplemented
41#11718655C22116yescomplemented
42#11718653C2218yescomplemented
43#11718650C22116yescomplemented
44#11718616C22116yes—
45#11718609C22116yescomplemented
46#11718608C2218yescomplemented
47#11718334C2218yescomplemented
48#11718328C2218yescomplemented
49C25×C13C2311yescharacteristic
50C24×D13—24no—
51C24×D13—24no—
52C24×D13—44no—
53C24×D13—44no—
54C24×D13Q818yescomplemented
55C24×D13C2311yescharacteristic
56C24×D13C2311yescharacteristic
57C24×D13C2314yes—
58C23×C4×C13C2312yes—
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13C2312yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2312yes—
65C23×Dic13C2311yescharacteristic
66C22×C4×D13—24no—
67C22×C4×D13—44no—
68C22×C4×D13—44no—
69C22×C4×D13D418yes—
70C22×C4×D13C2314yes—
71C22×C4×D13C2314yes—
72C22×Dic26—24no—
73C22×Dic26—44no—
74C22×Dic26C2314yescomplemented
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4—44no—
77C2×C13×C4⋊C4C2314yescomplemented
78C2×C13×C4⋊C4C2318yescomplemented
79C2×C13×C22⋊C4—24no—
80C2×C13×C22⋊C4—44no—
81C2×C13×C22⋊C4C2314yes—
82C2×C13×C22⋊C4C2318yes—
83C2×C22⋊Dic13—24no—
84C2×C22⋊Dic13—44no—
85C2×C22⋊Dic13C2314yes—
86C2×C22⋊Dic13C2318yes—
87C2×#6103—28no—
88C2×#6103—28no—
89C2×#6103—24no—
90C2×#6103—24no—
91C2×#6103—44no—
92C2×#6103—44no—
93C2×#6103C2314yes—
94C2×#6103C2314yes—
95C2×#6103C2318yes—
96C2×#6103C2318yes—
97C2×#6103C2318yes—
98C2×#6103C2318yes—
99C2×C4⋊Dic13—28no—
100C2×C4⋊Dic13C2318yescomplemented
101C2×#6101—44no—
102C2×#6101—44no—
103C2×#6101C2318yescomplemented
104C2×#6101C2318yescomplemented
105#88151—232no—
106C22⋊C4×D13—232no—
107C13×#95C2314yescomplemented
108#88071C2314yescomplemented
109#88071C2318yescomplemented
110#88071C2318yescomplemented
111C2×#2626—131nomaximal, Sylow
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—24no—
115C24×C13—24no—
116C24×C13C2×Q814yes—
117C24×C13C2412yes—
118C24×C13C2411yescharacteristic
119C23×D13—24no—
120C23×D13—24no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—24no—
124C23×D13—24no—
125C23×D13—232no—
126C23×D13—28no—
127C23×D13—28no—
128C23×D13—432no—
129C23×D13—48no—
130C23×D13—48no—
131C23×D13—416no—
132C23×D13—416no—
133C23×D13—432no—
134C23×D13C2×D414yes—
135C23×D13C2×Q814yes—
136C23×D13C2×Q814yes—
137C23×D13C2×Q8116yescomplemented
138C23×D13#4114yes—
139C23×D13C2412yes—
140C23×D13C2412yes—
141C22×C4×C13—24no—
142C22×C4×C13—24no—
143C22×C4×C13—22no—
144C22×C4×C13—24no—
145C22×C4×C13—24no—
146C22×C4×C13—24no—
147C22×C4×C13—24no—
148C22×C4×C13—24no—
149C22×C4×C13—24no—
150C22×C4×C13C2×D414yes—
151C22×C4×C13C2412yes—
152C22×C4×C13C2414yes—
153C22×C4×C13C2414yes—
154C22×C4×C13C2412yes—
155C22×Dic13—24no—
156C22×Dic13—24no—
157C22×Dic13—22no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13—24no—
163C22×Dic13—24no—
164C22×Dic13C2×D414yes—
165C22×Dic13C2414yes—
166C22×Dic13C2412yes—
167C22×Dic13C2414yes—
168C22×Dic13C2412yes—
169C2×C4×D13—28no—
170C2×C4×D13—416no—
171C2×C4×D13—48no—
172C2×C4×D13—48no—
173C2×C4×D13—416no—
174C2×C4×D13C2×D4116yes—
175C2×Dic26—28no—
176C2×Dic26—48no—
177C2×Dic26—416no—
178C13×C4⋊C4—28no—
179C13×C4⋊C4—48no—
180C13×C22⋊C4—28no—
181C13×C22⋊C4—48no—
182C22⋊Dic13—28no—
183C22⋊Dic13—48no—
184#6103—216no—
185#6103—216no—
186#6103—28no—
187#6103—28no—
188#6103—48no—
189#6103—48no—
190C4⋊Dic13—216no—
191#6101—48no—
192#6101—48no—
193C22×C22⋊Q8—131no—
194C23×C22⋊C4—131no—
195#2626—1316no—
196C2×#399—131no—
197C2×#399D1311yescharacteristic, complemented
198C2×#396—132no—
199C2×#396—132no—
200C2×#393—131no—
201C2×#393—131no—
202C2×#385—132no—
203C2×#380—131no—
204C2×#379—132no—
205C23×C13—28no—
206C23×C13—216no—
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—24no—
210C23×C13—24no—
211C23×C13—44no—
212C23×C13—44no—
213C23×C13—48no—
214C23×C13C22×D412yes—
215C23×C13C22×Q814yes—
216C23×C13C22×Q812yes—
217C23×C13C2×#4112yes—
218C23×C13H(5,𝔽2)14yes—
219C23×C13H(5,𝔽2)14yes—
220C23×C13C2511yescharacteristic
221C22×D13—28no—
222C22×D13—28no—
223C22×D13—216no—
224C22×D13—216no—
225C22×D13—24no—
226C22×D13—24no—
227C22×D13—28no—
228C22×D13—216no—
229C22×D13—22no—
230C22×D13—22no—
231C22×D13—24no—
232C22×D13—24no—
233C22×D13—232no—
234C22×D13—432no—
235C22×D13—4128no—
236C22×D13—416no—
237C22×D13—416no—
238C22×D13—432no—
239C22×D13—44no—
240C22×D13—44no—
241C22×D13—48no—
242C22×D13C22⋊Q8116yes—
243C22×D13C22×D414yes—
244C22×D13C22×Q814yes—
245C22×D13C22×Q814yes—
246C22×D13C2×#4114yes—
247C2×C4×C13—28no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—22no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—24no—
256C2×C4×C13—24no—
257C2×C4×C13—44no—
258C2×C4×C13—48no—
259C2×C4×C13—48no—
260C2×C4×C13C22×D414yes—
261C2×Dic13—28no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—22no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—24no—
271C2×Dic13—48no—
272C2×Dic13—44no—
273C2×Dic13—48no—
274C2×Dic13C22×D414yes—
275C4×D13—416no—
276C4×D13—416no—
277Dic26—416no—
278C26—131no—
279C23×Q8—131no—
280C24×C4—131no—
281C24×C4—131no—
282C2×C22⋊Q8—138no—
283C2×C22⋊Q8—268no—
284C22×C4⋊C4—132no—
285C22×C4⋊C4—132no—
286C22×C4⋊C4—132no—
287C22×C4⋊C4C2×D1311yescharacteristic, complemented
288C22×C4⋊C4C2×D1312yescomplemented
289C22×C22⋊C4—131no—
290C22×C22⋊C4—131no—
291C22×C22⋊C4—131no—
292C22×C22⋊C4—132no—
293C22×C22⋊C4—132no—
294C22×C22⋊C4—132no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4—132no—
297C22×C22⋊C4—138no—
298C22×C22⋊C4—268no—
299C22×C22⋊C4C2×D1311yescharacteristic
300C22×C22⋊C4C2×D1312yes—
301#399—138no—
302#399C2×D1318yescomplemented
303#396—1316no—
304#396—1316no—
305#393—138no—
306#393—138no—
307#385—1316no—
308#380—138no—
309#379—1316no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—131no—
313C2×#95C2×D1311yescharacteristic, complemented
314C22×C13—24no—
315C22×C13—28no—
316C22×C13—416no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—44no—
320C22×C13C2×C22⋊Q814yes—
321C22×C13#53414yes—
322C22×C13#53514yes—
323C22×C13#53818yes—
324C22×C13#54318yes—
325C22×C13C23×D411yescharacteristic
326C22×C13C23×Q811yescharacteristic
327C22×C13C22×#4111yescharacteristic
328C22×C13C2×H(5,𝔽2)12yes—
329C22×C13C2×H(5,𝔽2)12yes—
330C2×D13—232no—
331C2×D13—24no—
332C2×D13—24no—
333C2×D13—28no—
334C2×D13—28no—
335C2×D13—24no—
336C2×D13—28no—
337C2×D13—464no—
338C2×D13—416no—
339C2×D13—42no—
340C2×D13—42no—
341C2×D13—44no—
342C2×D13C2×C22⋊Q818yes—
343C4×C13—24no—
344C4×C13—42no—
345C4×C13—44no—
346C4×C13—44no—
347Dic13—24no—
348Dic13—44no—
349Dic13—42no—
350Dic13—44no—
351C25—131no—
352C25—131no—
353C25—138no—
354C25—134no—
355C25—264no—
356C25—264no—
357C25—524no—
358C25—524no—
359C25C22×D1311yescharacteristic
360C22×Q8—134no—
361C22×Q8—264no—
362C22×Q8—524no—
363C23×C4—131no—
364C23×C4—138no—
365C23×C4—134no—
366C23×C4—132no—
367C23×C4—132no—
368C23×C4—131no—
369C23×C4—134no—
370C23×C4—264no—
371C23×C4—524no—
372C23×C4—524no—
373C23×C4C22×D1312yes—
374C23×C4C22×D1312yes—
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1311yescharacteristic
377C22⋊Q8—2632no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—138no—
381C2×C4⋊C4—138no—
382C2×C4⋊C4—138no—
383C2×C4⋊C4—268no—
384C2×C4⋊C4—524no—
385C2×C4⋊C4—524no—
386C2×C4⋊C4C22×D1314yescomplemented
387C2×C4⋊C4C22×D1318yescomplemented
388C2×C22⋊C4—24no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—134no—
391C2×C22⋊C4—134no—
392C2×C22⋊C4—134no—
393C2×C22⋊C4—138no—
394C2×C22⋊C4—138no—
395C2×C22⋊C4—138no—
396C2×C22⋊C4—138no—
397C2×C22⋊C4—138no—
398C2×C22⋊C4—2632no—
399C2×C22⋊C4—264no—
400C2×C22⋊C4—268no—
401C2×C22⋊C4—268no—
402C2×C22⋊C4—264no—
403C2×C22⋊C4—264no—
404C2×C22⋊C4—524no—
405C2×C22⋊C4—524no—
406C2×C22⋊C4—524no—
407C2×C22⋊C4C22×D1314yes—
408C2×C22⋊C4C22×D1318yes—
409#95—134no—
410#95—138no—
411#95—138no—
412#95C22×D1314yescomplemented
413C2×C13—44no—
414C2×C13#262618yescomplemented
415C2×C13C22×C22⋊Q811yescharacteristic
416C2×C13C2×#53411yescharacteristic
417C2×C13C2×#53511yescharacteristic
418C2×C13C2×#53812yes—
419C2×C13C2×#54312yes—
420D13—28no—
421D13—44no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—24no—
426C24—134no—
427C24—134no—
428C24—134no—
429C24—132no—
430C24—134no—
431C24—132no—
432C24—1316no—
433C24—268no—
434C24—2632no—
435C24—268no—
436C24—264no—
437C24—264no—
438C24—262no—
439C24—264no—
440C24—262no—
441C24—264no—
442C24—5232no—
443C24—528no—
444C24—528no—
445C24—5216no—
446C24—5232no—
447C24—5216no—
448C24Q8×D1314yes—
449C24C23×D1312yes—
450C24C23×D1311yescharacteristic
451C2×Q8—268no—
452C2×Q8—528no—
453C2×Q8—5216no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—134no—
464C22×C4—132no—
465C22×C4—1316no—
466C22×C4—134no—
467C22×C4—134no—
468C22×C4—132no—
469C22×C4—268no—
470C22×C4—264no—
471C22×C4—262no—
472C22×C4—264no—
473C22×C4—264no—
474C22×C4—264no—
475C22×C4—264no—
476C22×C4—264no—
477C22×C4—264no—
478C22×C4—264no—
479C22×C4—5216no—
480C22×C4—528no—
481C22×C4—528no—
482C22×C4—5216no—
483C22×C4D4×D1314yes—
484C22×C4C23×D1312yes—
485C22×C4C23×D1314yes—
486C22×C4C23×D1314yes—
487C22×C4C23×D1312yes—
488C4⋊C4—28no—
489C4⋊C4—48no—
490C4⋊C4—2616no—
491C4⋊C4—528no—
492C4⋊C4—528no—
493C22⋊C4—28no—
494C22⋊C4—48no—
495C22⋊C4—268no—
496C22⋊C4—2616no—
497C22⋊C4—2616no—
498C22⋊C4—268no—
499C22⋊C4—268no—
500C22⋊C4—528no—
501C22⋊C4—528no—
502C22⋊C4—528no—
503C13C2×#262611yescharacteristic, complemented, Sylow
504C23—28no—
505C23—216no—
506C23—22no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—44no—
511C23—48no—
512C23—44no—
513C23—1316no—
514C23—134no—
515C23—134no—
516C23—134no—
517C23—134no—
518C23—2632no—
519C23—2616no—
520C23—268no—
521C23—2616no—
522C23—264no—
523C23—264no—
524C23—268no—
525C23—268no—
526C23—2616no—
527C23—262no—
528C23—264no—
529C23—262no—
530C23—264no—
531C23—5232no—
532C23—52128no—
533C23—5216no—
534C23—5216no—
535C23—5232no—
536C23—524no—
537C23—528no—
538C23—524no—
539C23C2×D4×D1312yes—
540C23#8825114yes—
541C23C2×Q8×D1314yes—
542C23C2×Q8×D1312yes—
543C23#41×D1312yes—
544C23#8825614yes—
545C23C24×D1311yescharacteristic
546Q8—5216no—
547C2×C4—28no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—48no—
558C2×C4—44no—
559C2×C4—48no—
560C2×C4—134no—
561C2×C4—268no—
562C2×C4—264no—
563C2×C4—262no—
564C2×C4—264no—
565C2×C4—264no—
566C2×C4—264no—
567C2×C4—264no—
568C2×C4—264no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—5216no—
572C2×C4—5216no—
573C2×C4—528no—
574C2×C4—528no—
575C2×C4—524no—
576C2×C4C2×D4×D1314yes—
577C22—28no—
578C22—24no—
579C22—416no—
580C22—42no—
581C22—42no—
582C22—44no—
583C22—138no—
584C22—268no—
585C22—2632no—
586C22—264no—
587C22—264no—
588C22—268no—
589C22—268no—
590C22—264no—
591C22—5264no—
592C22—5216no—
593C22—522no—
594C22—522no—
595C22—524no—
596C22D13×C22⋊Q814yes—
597C22#1171933918yes—
598C22#1171935814yes—
599C22#1171936218yes—
600C22#1171942014yes—
601C22C22×D4×D1311yescharacteristic
602C22C2×#8825112yes—
603C22C22×Q8×D1311yescharacteristic
604C22C2×#41×D1311yescharacteristic
605C22C2×#8825612yes—
606C4—24no—
607C4—44no—
608C4—42no—
609C4—44no—
610C4—264no—
611C4—524no—
612C4—522no—
613C4—524no—
614C2—44no—
615C2—268no—
616C2—524no—
617C2#1312064218yesdirect product factor
618C2C2×D13×C22⋊Q811yescharacteristic
619C2C2×#1171935811yescharacteristic
620C2C2×#1171942011yescharacteristic
621C2C2×#1171936212yes—
622C2C2×#1171933912yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#399C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#399D13
hypocenterC13C2×#2626
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#88151C2semidirect
3. #13120642C2direct (N × H)
4. C2×#11718653C2semidirect
5. C2×#11718609C2semidirect
6. C2×#11718655C2semidirect
7. C2×#11718334C2semidirect
8. C2×#11718608C2semidirect
9. C2×#11718650C2semidirect
10. C2×#11718328C2semidirect
12. C2×C13×#399C2semidirect
16. C23×Dic26C22semidirect
17. C22×C13×C4⋊C4C22semidirect
18. C22×C13×C4⋊C4C22semidirect
29. C22×C4⋊Dic13C22semidirect
30. C22×#6101C22semidirect
31. C22×#6101C22semidirect
33. C2×#88151C22semidirect
36. C13×#399C22semidirect
37. C2×C13×#95C22semidirect
38. C2×#88071C22semidirect
39. C2×#88071C22semidirect
40. C2×#88071C22semidirect
41. #11718655C22semidirect
42. #11718653C22semidirect
43. #11718650C22semidirect
45. #11718609C22semidirect
46. #11718608C22semidirect
47. #11718334C22semidirect
48. #11718328C22semidirect
54. C24×D13Q8semidirect
74. C22×Dic26C23semidirect
77. C2×C13×C4⋊C4C23semidirect
78. C2×C13×C4⋊C4C23semidirect
100. C2×C4⋊Dic13C23semidirect
103. C2×#6101C23semidirect
104. C2×#6101C23semidirect
107. C13×#95C23semidirect
108. #88071C23semidirect
109. #88071C23semidirect
110. #88071C23semidirect
137. C23×D13C2×Q8semidirect
197. C2×#399D13semidirect
287. C22×C4⋊C4C2×D13semidirect
288. C22×C4⋊C4C2×D13semidirect
302. #399C2×D13semidirect
313. C2×#95C2×D13semidirect
386. C2×C4⋊C4C22×D13semidirect
387. C2×C4⋊C4C22×D13semidirect
412. #95C22×D13semidirect
414. C2×C13#2626semidirect
503. C13C2×#2626semidirect
617. C2#13120642direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881512
C22×C22⋊C4×D132
#131206422
C2×#117186532
C2×#117186092
C2×#117186552
C2×#117183342
C2×#117186082
C2×#117186502
C2×#117183282
C2×#117186162
C2×C13×#3992
C2×#262613