Finite Group Databasebeta

← C2×#13119756 #16034687

Subgroups — C2×#13119756 #16034687

Order 3328.

3614 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C212yesmaximal, complemented
2C22×C4×Dic26C211yesmaximal, characteristic, complemented
3C22×D4×Dic13C211yesmaximal, characteristic
4#13119756C2116yesmaximal, direct product factor
5C2×#11718609C212yesmaximal, complemented
6C2×#11718609C212yesmaximal, complemented
7C2×#11718882C211yesmaximal, characteristic
8C2×#11718646C211yesmaximal, characteristic, complemented
9C2×#11718589C211yesmaximal, characteristic, complemented
10C2×#11718637C211yesmaximal, characteristic, complemented
11C2×#11718603C212yesmaximal, complemented
12C2×C13×#390C211yesmaximal, characteristic
13C23×D4×C13C2211yescharacteristic
14C24×Dic13C2212yes—
15C23×Dic26C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2212yes—
18C22×C13×C22⋊C4C2212yes—
19C22×C42×C13C2211yescharacteristic
20C22×C22⋊Dic13C2212yes—
21C22×C22⋊Dic13C2212yes—
22C22×C22⋊Dic13C2212yes—
23C2×D4×Dic13—28no—
24C2×D4×Dic13C2218yes—
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2212yes—
29C22×#6101C2211yescharacteristic
30C22×#6101C2212yes—
31C22×#6101C2211yescharacteristic
32C22×#6101C2212yes—
33C22×#6101C2212yes—
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C2×#88132—216no—
37C2×#88132C22116yescomplemented
38C2×C4×Dic26—28no—
39C2×C4×Dic26C2218yescomplemented
40C13×#390C2218yes—
41#11718882C2218yes—
42C2×#88071C2212yes—
43C2×#88071C2212yes—
44#11718646C2218yescomplemented
45#11718637C2218yescomplemented
46#11718609C22116yescomplemented
47#11718609C22116yescomplemented
48#11718603C22116yescomplemented
49#11718589C2218yescomplemented
50C25×C13C2312yes—
51C22×D4×C13—24no—
52C22×D4×C13—24no—
53C22×D4×C13Q818yescomplemented
54C22×D4×C13C2314yes—
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×Dic13—28no—
60C23×Dic13—28no—
61C23×Dic13—28no—
62C23×Dic13C2318yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2312yes—
65C23×Dic13C2312yes—
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C22×Dic26—24no—
70C22×Dic26—24no—
71C22×Dic26D418yescomplemented
72C22×Dic26C2314yes—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4C2314yes—
75C2×C13×C22⋊C4—28no—
76C2×C13×C22⋊C4—44no—
77C2×C13×C22⋊C4C2318yes—
78C2×C13×C22⋊C4C2318yes—
79C2×C42×C13—24no—
80C2×C42×C13C2314yes—
81C2×C22⋊Dic13—28no—
82C2×C22⋊Dic13—28no—
83C2×C22⋊Dic13—44no—
84C2×C22⋊Dic13C2318yes—
85C2×C22⋊Dic13C2318yes—
86C2×C22⋊Dic13C2318yes—
87D4×Dic13—232no—
88C2×C4⋊Dic13—24no—
89C2×C4⋊Dic13—24no—
90C2×C4⋊Dic13—24no—
91C2×C4⋊Dic13—28no—
92C2×C4⋊Dic13C2314yes—
93C2×C4⋊Dic13C2318yes—
94C2×C4⋊Dic13C2314yes—
95C2×C4⋊Dic13C2314yes—
96C2×#6101—28no—
97C2×#6101—24no—
98C2×#6101—24no—
99C2×#6101—28no—
100C2×#6101—44no—
101C2×#6101C2314yes—
102C2×#6101C2314yes—
103C2×#6101C2318yes—
104C2×#6101C2318yes—
105C2×#6101C2318yes—
106C2×C4×Dic13—24no—
107C2×C4×Dic13D418yes—
108C2×C4×Dic13C2314yes—
109C2×C4×Dic13C2314yes—
110#88132—264no—
111C4×Dic26—232no—
112#88071C2318yes—
113#88071C2318yes—
114C2×#2538—131nomaximal, Sylow
115C24×C13—24no—
116C24×C13—24no—
117C24×C13—24no—
118C24×C13—24no—
119C24×C13—24no—
120C24×C13—24no—
121C24×C13C2×Q818yes—
122C24×C13C2414yes—
123C24×C13C2411yescharacteristic
124C2×D4×C13—232no—
125C2×D4×C13—28no—
126C2×D4×C13—28no—
127C2×D4×C13C2×Q8116yescomplemented
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—24no—
132C22×C4×C13—24no—
133C22×C4×C13—24no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13C2×D414yes—
137C22×C4×C13C2×D414yes—
138C22×C4×C13C2×Q814yes—
139C22×C4×C13#4114yes—
140C22×C4×C13C2412yes—
141C22×C4×C13C2414yes—
142C22×C4×C13C2412yes—
143C22×C4×C13C2412yes—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—24no—
150C22×Dic13—24no—
151C22×Dic13—24no—
152C22×Dic13—24no—
153C22×Dic13—24no—
154C22×Dic13—24no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—216no—
158C22×Dic13—216no—
159C22×Dic13—216no—
160C22×Dic13—432no—
161C22×Dic13C2×D414yes—
162C22×Dic13C2×D414yes—
163C22×Dic13C2×D414yes—
164C22×Dic13C2×D414yes—
165C22×Dic13#4114yes—
166C22×Dic13C2412yes—
167C22×Dic13C2414yes—
168C22×Dic13C2414yes—
169C22×Dic13C2412yes—
170C22×Dic13C2412yes—
171C22×Dic13C2412yes—
172C2×Dic26—232no—
173C2×Dic26—28no—
174C2×Dic26—28no—
175C2×Dic26C2×D4116yescomplemented
176C13×C4⋊C4—28no—
177C13×C22⋊C4—216no—
178C13×C22⋊C4—48no—
179C42×C13—28no—
180C22⋊Dic13—216no—
181C22⋊Dic13—216no—
182C22⋊Dic13—48no—
183C4⋊Dic13—28no—
184C4⋊Dic13—28no—
185C4⋊Dic13—28no—
186C4⋊Dic13—216no—
187#6101—216no—
188#6101—28no—
189#6101—28no—
190#6101—216no—
191#6101—48no—
192C4×Dic13—28no—
193C4×Dic13C2×D4116yes—
194C22×C22⋊Q8—132no—
195C22×C4×Q8—131no—
196C22×C4×D4—131no—
197#2538—1316no—
198C2×#396—132no—
199C2×#396—132no—
200C2×#390—131no—
201C2×#390D1311yescharacteristic
202C2×#389—131no—
203C2×#389—131no—
204C2×#384—131no—
205C2×#380—132no—
206C23×C13—216no—
207C23×C13—216no—
208C23×C13—216no—
209C23×C13—24no—
210C23×C13—24no—
211C23×C13—24no—
212C23×C13—24no—
213C23×C13—24no—
214C23×C13—24no—
215C23×C13—48no—
216C23×C13—48no—
217C23×C13—48no—
218C23×C13—48no—
219C23×C13C22×D412yes—
220C23×C13C22×D412yes—
221C23×C13C22×Q818yes—
222C23×C13C22×Q812yes—
223C23×C13C2×#4112yes—
224C23×C13C2×#4112yes—
225C23×C13H(5,𝔽2)12yes—
226C23×C132−1+412yes—
227C23×C13C2511yescharacteristic
228D4×C13—232no—
229C2×C4×C13—28no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—44no—
239C2×C4×C13—48no—
240C2×C4×C13C22⋊Q8116yescomplemented
241C2×C4×C13C22×D414yes—
242C2×C4×C13C22×D414yes—
243C2×C4×C13C22×Q814yes—
244C2×C4×C13C2×#4114yes—
245C2×Dic13—28no—
246C2×Dic13—28no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—24no—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—48no—
261C2×Dic13—44no—
262C2×Dic13—48no—
263C2×Dic13—432no—
264C2×Dic13#121116yes—
265C2×Dic13C22×D414yes—
266C2×Dic13C22×D414yes—
267C2×Dic13C22×D414yes—
268C2×Dic13C22×D414yes—
269C2×Dic13C2×#4114yes—
270Dic26—232no—
271C23×Q8—131no—
272C23×D4C2×D1311yescharacteristic
273C24×C4—132no—
274C2×C22⋊Q8—1316no—
275C2×C22⋊Q8—2616no—
276C2×C4×Q8—138no—
277C2×C4×Q8—268no—
278C2×C4×D4—138no—
279C2×C4×D4—268no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—131no—
283C22×C4⋊C4—132no—
284C22×C4⋊C4—131no—
285C22×C4⋊C4—132no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—131no—
288C22×C4⋊C4—132no—
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C22⋊C4—132no—
291C22×C22⋊C4—132no—
292C22×C22⋊C4—132no—
293C22×C22⋊C4C2×D1312yes—
294C22×C22⋊C4C2×D1312yes—
295C22×C42—131no—
296C22×C42—131no—
297C22×C42C2×D1311yescharacteristic
298#396—1316no—
299#396—1316no—
300#390—138no—
301#390C2×D1318yes—
302#389—138no—
303#389—138no—
304#384—138no—
305#380—1316no—
306C2×#95—132no—
307C2×#95—132no—
308C22×C13—28no—
309C22×C13—28no—
310C22×C13—28no—
311C22×C13—44no—
312C22×C13—44no—
313C22×C13—44no—
314C22×C13—44no—
315C22×C13—432no—
316C22×C13C2×#12114yes—
317C22×C13C2×C22⋊Q814yes—
318C22×C13#53714yes—
319C22×C13D4×Q814yes—
320C22×C13#55014yes—
321C22×C13#55414yes—
322C22×C13#55614yes—
323C22×C13C23×D411yescharacteristic
324C22×C13C23×D411yescharacteristic
325C22×C13C23×Q811yescharacteristic
326C22×C13C22×#4111yescharacteristic
327C22×C13C22×#4111yescharacteristic
328C22×C13C2×H(5,𝔽2)11yescharacteristic
329C22×C13C2×2−1+411yescharacteristic
330C4×C13—24no—
331C4×C13—42no—
332C4×C13—44no—
333C4×C13C2×C22⋊Q818yescomplemented
334Dic13—24no—
335Dic13—24no—
336Dic13—44no—
337Dic13—42no—
338Dic13—44no—
339Dic13C2×#12118yes—
340C25C22×D1312yes—
341C22×Q8—138no—
342C22×Q8—134no—
343C22×Q8—264no—
344C22×Q8—264no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4Dic2618yescomplemented
348C22×D4C22×D1314yes—
349C23×C4—131no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—138no—
353C23×C4—132no—
354C23×C4—131no—
355C23×C4—132no—
356C23×C4—268no—
357C23×C4—268no—
358C23×C4—268no—
359C23×C4C22×D1312yes—
360C23×C4C22×D1311yescharacteristic
361C23×C4C22×D1311yescharacteristic
362C23×C4C22×D1311yescharacteristic
363C22⋊Q8—2664no—
364C4×Q8—2632no—
365C4×D4—2632no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—134no—
368C2×C4⋊C4—134no—
369C2×C4⋊C4—134no—
370C2×C4⋊C4—134no—
371C2×C4⋊C4—138no—
372C2×C4⋊C4—138no—
373C2×C4⋊C4—138no—
374C2×C4⋊C4—134no—
375C2×C4⋊C4—138no—
376C2×C4⋊C4—264no—
377C2×C4⋊C4—264no—
378C2×C4⋊C4—264no—
379C2×C4⋊C4—268no—
380C2×C4⋊C4—268no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—268no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—524no—
385C2×C4⋊C4C22×D1314yes—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—138no—
389C2×C22⋊C4—138no—
390C2×C22⋊C4—138no—
391C2×C22⋊C4—268no—
392C2×C22⋊C4—268no—
393C2×C22⋊C4—524no—
394C2×C22⋊C4C22×D1318yes—
395C2×C22⋊C4C22×D1318yes—
396C2×C42—24no—
397C2×C42—138no—
398C2×C42—134no—
399C2×C42—134no—
400C2×C42—264no—
401C2×C42C22×D1314yes—
402#95—138no—
403#95—138no—
404C2×C13—48no—
405C2×C13#253818yescomplemented
406C2×C13C22×#12111yescharacteristic
407C2×C13C22×C22⋊Q811yescharacteristic
408C2×C13C2×#53711yescharacteristic
409C2×C13C2×D4×Q811yescharacteristic
410C2×C13C2×#55011yescharacteristic
411C2×C13C2×#55411yescharacteristic
412C2×C13C2×#55611yescharacteristic
413C24—24no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24C2×Dic2618yes—
420C24C23×D1314yes—
421C24C23×D1311yescharacteristic
422C2×Q8—1316no—
423C2×Q8—268no—
424C2×Q8—2632no—
425C2×Q8—268no—
426C2×D4—232no—
427C2×D4—28no—
428C2×D4—28no—
429C2×D4C2×Dic26116yescomplemented
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—134no—
439C22×C4—134no—
440C22×C4—134no—
441C22×C4—132no—
442C22×C4—134no—
443C22×C4—134no—
444C22×C4—132no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—134no—
448C22×C4—134no—
449C22×C4—2616no—
450C22×C4—2616no—
451C22×C4—2616no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—264no—
458C22×C4—264no—
459C22×C4—264no—
460C22×C4—264no—
461C22×C4—262no—
462C22×C4—264no—
463C22×C4—264no—
464C22×C4—262no—
465C22×C4—5232no—
466C22×C4C2×Dic2614yes—
467C22×C4D4×D1314yes—
468C22×C4D4×D1314yes—
469C22×C4#612914yes—
470C22×C4C23×D1312yes—
471C22×C4C23×D1314yes—
472C22×C4C23×D1312yes—
473C22×C4C23×D1312yes—
474C4⋊C4—28no—
475C4⋊C4—268no—
476C4⋊C4—268no—
477C4⋊C4—268no—
478C4⋊C4—2616no—
479C4⋊C4—2616no—
480C4⋊C4—268no—
481C4⋊C4—2616no—
482C4⋊C4—268no—
483C4⋊C4—528no—
484C22⋊C4—216no—
485C22⋊C4—48no—
486C22⋊C4—2616no—
487C22⋊C4—2616no—
488C22⋊C4—528no—
489C42—28no—
490C42—1316no—
491C42—268no—
492C13C2×#253811yescharacteristic, complemented, Sylow
493C23—216no—
494C23—216no—
495C23—216no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—48no—
503C23—48no—
504C23—48no—
505C23—48no—
506C23C22×Dic2618yes—
507C23C22×Dic2612yes—
508C23C2×D4×D1312yes—
509C23C2×D4×D1312yes—
510C23C2×#612912yes—
511C23#8825112yes—
512C23#41×D1312yes—
513C23#8825712yes—
514C23C24×D1311yescharacteristic
515Q8—2632no—
516D4—232no—
517C2×C4—28no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—48no—
528C2×C4—1316no—
529C2×C4—134no—
530C2×C4—134no—
531C2×C4—134no—
532C2×C4—134no—
533C2×C4—134no—
534C2×C4—268no—
535C2×C4—268no—
536C2×C4—262no—
537C2×C4—262no—
538C2×C4—262no—
539C2×C4—262no—
540C2×C4—262no—
541C2×C4—264no—
542C2×C4—264no—
543C2×C4—264no—
544C2×C4—264no—
545C2×C4—262no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—262no—
549C2×C4—5232no—
550C2×C4—528no—
551C2×C4—524no—
552C2×C4—528no—
553C2×C4#88132116yescomplemented
554C2×C4C22×Dic2614yes—
555C2×C4C2×D4×D1314yes—
556C2×C4C2×D4×D1314yes—
557C2×C4C2×#612914yes—
558C22—28no—
559C22—28no—
560C22—28no—
561C22—432no—
562C22—44no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22C2×#8813214yes—
567C22D4×Dic2614yes—
568C22#1171924414yes—
569C22D13×#12114yes—
570C22#1171931314yes—
571C22#1171937614yes—
572C22#1171942314yes—
573C22C23×Dic2611yescharacteristic
574C22C22×D4×D1311yescharacteristic
575C22C22×D4×D1311yescharacteristic
576C22C22×#612911yescharacteristic
577C22C2×#8825111yescharacteristic
578C22C2×#41×D1311yescharacteristic
579C22C2×#8825711yescharacteristic
580C4—24no—
581C4—44no—
582C4—42no—
583C4—138no—
584C4—264no—
585C4—264no—
586C4—524no—
587C4—524no—
588C4—522no—
589C4C2×#8813218yescomplemented
590C2—48no—
591C2#1311975618yesdirect product factor
592C2C2×D13×#12111yescharacteristic
593C2C22×#8813211yescharacteristic
594C2C2×#1171931311yescharacteristic
595C2C2×D4×Dic2611yescharacteristic
596C2C2×#1171942311yescharacteristic
597C2C2×#1171924411yescharacteristic
598C2C2×#1171937611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#390C2
socleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13C2×#2538
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#88132C2semidirect
2. C22×C4×Dic26C2semidirect
4. #13119756C2direct (N × H)
5. C2×#11718609C2semidirect
6. C2×#11718609C2semidirect
8. C2×#11718646C2semidirect
9. C2×#11718589C2semidirect
10. C2×#11718637C2semidirect
11. C2×#11718603C2semidirect
37. C2×#88132C22semidirect
39. C2×C4×Dic26C22semidirect
44. #11718646C22semidirect
45. #11718637C22semidirect
46. #11718609C22semidirect
47. #11718609C22semidirect
48. #11718603C22semidirect
49. #11718589C22semidirect
53. C22×D4×C13Q8semidirect
71. C22×Dic26D4semidirect
127. C2×D4×C13C2×Q8semidirect
175. C2×Dic26C2×D4semidirect
240. C2×C4×C13C22⋊Q8semidirect
333. C4×C13C2×C22⋊Q8semidirect
347. C22×D4Dic26semidirect
405. C2×C13#2538semidirect
429. C2×D4C2×Dic26semidirect
492. C13C2×#2538semidirect
553. C2×C4#88132semidirect
589. C4C2×#88132semidirect
591. C2#13119756direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881322
C22×C4×Dic262
C22×D4×Dic132
#131197562
C2×#117186092
C2×#117188822
C2×#117186462
C2×#117185892
C2×#117186372
C2×#117186032
C2×C13×#3902
C2×#253813