Finite Group Databasebeta

← C2×#13124617 #16730413

Subgroups — C2×#13124617 #16730413

Order 3328.

2162 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic, complemented
2C2×C4×#6129C211yesmaximal, characteristic
3#13124617C2116yesmaximal, direct product factor
4C2×#11718538C212yesmaximal, complemented
5C2×#11718511C211yesmaximal, characteristic, complemented
6C2×#11718755C211yesmaximal, characteristic, complemented
7C2×#11718427C212yesmaximal, complemented
8C2×#11718669C211yesmaximal, characteristic, complemented
9C2×#11718541C212yesmaximal, complemented
10C2×D13×C4⋊C8C211yesmaximal, characteristic, complemented
11C2×#11718433C212yesmaximal
12C2×C13×#474C211yesmaximal, characteristic, complemented
13C22×#6129C2211yescharacteristic
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C13C2211yescharacteristic
16C2×#88200—21no—
17C2×Q8×Dic13—21no—
18C2×D4×Dic13C2211yescharacteristic
19C2×C4×C22⋊D13—21no—
20C22×C4×Dic13—21no—
21C22×C8×D13C2212yes—
22#11719433—24no—
23#11719433C2218yescomplemented
24C4×#6129—24no—
25C4×#6129C2218yes—
26C2×#88151—21no—
27C2×#88146C2212yes—
28C2×#88146C2211yescharacteristic
29C2×#88144C2212yes—
30C2×#88141—21no—
31C2×#88141C2211yescharacteristic
32C2×#88135—21no—
33C2×#88131—21no—
34C2×C42×D13C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C2×C4×Dic26C2211yescharacteristic
37C13×#474C2218yescomplemented
38C2×C13×#107C2212yes—
39C2×C13×C4⋊C8C2211yescharacteristic
40C2×C13×#102C2212yes—
41C2×#88072C2212yes—
42C2×#88058C2212yes—
43C2×#88056C2212yes—
44C2×#88054C2212yes—
45#11718755C2218yescomplemented
46#11718669C2218yescomplemented
47C2×#88050C2212yes—
48C2×#88048C2212yes—
49C2×#88048C2212yes—
50C2×C4⋊#1055C2211yescharacteristic
51#11718541C22116yescomplemented
52#11718538C22116yescomplemented
53#11718511C2218yescomplemented
54D13×C4⋊C8C2218yescomplemented
55#11718433C22116yes—
56#11718427C22116yescomplemented
57C22×Q8×C13—21no—
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C22×C22⋊D13—21no—
61C23×Dic13—21no—
62C23×Dic13—21no—
63C2×#6129—22no—
64C2×#6129—24no—
65C2×#6129Q818yescomplemented
66C2×#6129C2314yes—
67C22×C4×D13D411yescharacteristic
68C22×C4×D13D411yescharacteristic
69C22×C4×D13C2311yescharacteristic
70C22×Dic26—21no—
71C22×Dic26C2311yescharacteristic
72C22×C8×C13C2312yes—
73C13×C4⋊Q8—22no—
74C13×C4⋊Q8C2314yes—
75C4×D4×C13—22no—
76C4×D4×C13C2314yes—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2312yes—
80C2×C13×C22⋊C4—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C22⋊Dic13—21no—
83#88200—28no—
84Q8×Dic13—28no—
85D4×Dic13—22no—
86D4×Dic13C2314yes—
87C4×C22⋊D13—28no—
88C2×#6103—21no—
89C2×#6103—22no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2312yes—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—22no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—22no—
101C2×C4×Dic13—28no—
102C2×C4×Dic13D411yescharacteristic
103C2×C4×Dic13D411yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C22×#1055C2312yes—
106C2×C8×D13—28no—
107C2×C8×D13C2318yes—
108#88151—28no—
109#88146—24no—
110#88146—22no—
111#88146C2318yes—
112#88146C2314yes—
113#88144—24no—
114#88144C2318yes—
115#88141—28no—
116#88141—22no—
117#88141C2314yes—
118#88135—28no—
119#88131—28no—
120C42×D13D414yes—
121C42×D13C2314yes—
122#88123—22no—
123#88123C2314yes—
124C4×Dic26—22no—
125C4×Dic26C2314yes—
126C13×#107C2318yes—
127C13×C4⋊C8C2314yes—
128C13×#102C2318yes—
129#88072C2318yes—
130#88058C2318yes—
131#88056C2318yes—
132#88054C2318yes—
133#88050C2318yes—
134#88048C2318yes—
135#88048C2318yes—
136C4⋊#1055C2314yes—
137C2×#3076—131nomaximal, Sylow
138C24×C13—21no—
139C23×D13C2×D411yescharacteristic
140C2×Q8×C13—24no—
141C2×Q8×C13—44no—
142C2×D4×C13—21no—
143C2×D4×C13—22no—
144C2×D4×C13C2×Q814yes—
145C2×D4×C13C2412yes—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13—24no—
149C22×C4×C13—44no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C2×C22⋊D13—28no—
154C2×C22⋊D13—24no—
155C22×Dic13—21no—
156C22×Dic13—28no—
157C22×Dic13—24no—
158C22×Dic13—21no—
159C22×Dic13—22no—
160C22×Dic13—24no—
161C22×Dic13—44no—
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165#6129—216no—
166#6129—28no—
167#6129C2×Q8116yescomplemented
168C2×C4×D13—24no—
169C2×C4×D13—42no—
170C2×C4×D13C2×D414yes—
171C2×C4×D13C2×D414yes—
172C2×C4×D13C2×D412yes—
173C2×C4×D13C2×Q814yes—
174C2×C4×D13#4114yes—
175C2×C4×D13C2412yes—
176C2×Dic26—21no—
177C2×Dic26—22no—
178C2×Dic26—24no—
179C2×Dic26—44no—
180C2×Dic26C2×Q814yes—
181C2×Dic26C2412yes—
182C2×C8×C13—24no—
183C2×C8×C13C2414yes—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4C2414yes—
188C13×C4⋊C4C2412yes—
189C13×C22⋊C4—24no—
190C42×C13C2×D412yes—
191C42×C13C2412yes—
192C22⋊Dic13—24no—
193#6103—24no—
194#6103—28no—
195C4⋊Dic13—21no—
196C4⋊Dic13—22no—
197C4⋊Dic13—24no—
198C4⋊Dic13—28no—
199C4⋊Dic13C2414yes—
200C4⋊Dic13C2412yes—
201#6101—24no—
202#6101—24no—
203#6101—28no—
204C4×Dic13—24no—
205C4×Dic13—24no—
206C4×Dic13—24no—
207C4×Dic13—28no—
208C4×Dic13C2×D412yes—
209C4×Dic13C2×D414yes—
210C4×Dic13C2×D414yes—
211C4×Dic13C2412yes—
212C2×#1055—24no—
213C2×#1055C2414yes—
214C8×D13—216no—
215C2×#533—131no—
216C2×C4×#41—131no—
217#3076—1316no—
218C2×#479—132no—
219C2×#477—131no—
220C2×#475—131no—
221C2×#478—132no—
222C2×#476—131no—
223C2×#474D1311yescharacteristic, complemented
224C2×#427—132no—
225C22×C4⋊C8—131no—
226C2×#416—132no—
227C23×C13—24no—
228C23×C13—22no—
229C23×C13—42no—
230C23×C13—42no—
231C23×C13C22×D411yescharacteristic
232C22×D13—22no—
233C22×D13—22no—
234C22×D13C22⋊Q814yes—
235C22×D13C22×D412yes—
236Q8×C13—48no—
237D4×C13—24no—
238D4×C13—22no—
239D4×C13C22×Q814yes—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—42no—
244C2×C4×C13—44no—
245C2×C4×C13—48no—
246C2×C4×C13#13514yes—
247C2×C4×C13C22×D412yes—
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C22×D412yes—
250C2×C4×C13C22×Q812yes—
251C2×C4×C13C2×#4112yes—
252C2×C4×C13C2511yescharacteristic
253C22⋊D13—216no—
254C2×Dic13—24no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—216no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—48no—
262C2×Dic13—44no—
263C2×Dic13—42no—
264C2×Dic13C22⋊Q814yes—
265C2×Dic13C22×D412yes—
266C2×Dic13C22×D412yes—
267C2×Dic13C22×D412yes—
268C4×D13—28no—
269C4×D13—44no—
270C4×D13C22⋊Q818yes—
271C4×D13C22×Q814yes—
272C4×D13C2×#4114yes—
273Dic26—24no—
274Dic26—22no—
275Dic26—48no—
276Dic26C22×Q814yes—
277C8×C13—24no—
278#1055—24no—
279C22×#41—131no—
280C23×C8—132no—
281#533—138no—
282#533—264no—
283C2×C4⋊Q8—131no—
284C2×C4⋊Q8C2×D1311yescharacteristic
285C2×#125—132no—
286C2×C22⋊Q8—261no—
287C2×C22⋊Q8—261no—
288C4×#41—138no—
289C4×#41—264no—
290C2×C4×Q8—131no—
291C2×C4×Q8—131no—
292C2×C4×Q8—261no—
293C2×C4×Q8—261no—
294C2×C4×D4—131no—
295C2×C4×D4—261no—
296C2×C4×D4—261no—
297C2×C4×D4C2×D1311yescharacteristic
298C2×#117—132no—
299C2×#117—131no—
300C2×#117—261no—
301C22×C42—131no—
302C22×C42—261no—
303#479—1316no—
304#478—1316no—
305#477—138no—
306#476—138no—
307#475—138no—
308#474C2×D1318yescomplemented
309#427—1316no—
310C2×#107—132no—
311C2×#107C2×D1312yes—
312C2×#106—132no—
313C2×#106—132no—
314C2×C4⋊C8—132no—
315C2×C4⋊C8—131no—
316C2×C4⋊C8—138no—
317C2×C4⋊C8C2×D1311yescharacteristic
318#416—1316no—
319C2×#103—132no—
320C2×#103—132no—
321C2×#102—132no—
322C2×#102C2×D1312yes—
323C22×C13—24no—
324C22×C13—48no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13C2×C22⋊Q812yes—
328C22×C13C2×#13512yes—
329C22×C13#57512yes—
330C22×C13C23×D411yescharacteristic
331C2×D13—28no—
332C2×D13—22no—
333C2×D13—22no—
334C2×D13C2×C22⋊Q814yes—
335C4×C13—22no—
336C4×C13—42no—
337C4×C13—44no—
338C4×C13C2×C22⋊Q812yes—
339C4×C13C2×#13514yes—
340C4×C13C23×Q811yescharacteristic
341C4×C13C22×#4111yescharacteristic
342Dic13—24no—
343Dic13—22no—
344Dic13—22no—
345Dic13—44no—
346Dic13—42no—
347Dic13C2×C22⋊Q814yes—
348C2×#41—138no—
349C2×#41—134no—
350C2×#41—262no—
351C2×#41—264no—
352C22×Q8—21no—
353C22×Q8—131no—
354C22×Q8—261no—
355C22×D4—261no—
356C22×D4C22×D1311yescharacteristic
357C23×C4—21no—
358C23×C4—131no—
359C23×C4—131no—
360C23×C4—131no—
361C23×C4—261no—
362C23×C4—261no—
363C22×C8—132no—
364C22×C8—138no—
365C22×C8—268no—
366C22×C8C22×D1312yes—
367C4⋊Q8—22no—
368C4⋊Q8—134no—
369C4⋊Q8—262no—
370C4⋊Q8C22×D1314yes—
371#125—138no—
372#125—264no—
373C22⋊Q8—268no—
374C22⋊Q8—268no—
375C4×Q8—134no—
376C4×Q8—134no—
377C4×Q8—262no—
378C4×Q8—268no—
379C4×Q8—268no—
380C4×Q8—262no—
381C4×D4—22no—
382C4×D4—134no—
383C4×D4—262no—
384C4×D4—268no—
385C4×D4—268no—
386C4×D4C22×D1314yes—
387#117—134no—
388#117—138no—
389#117—268no—
390#117—262no—
391#117—264no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—132no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—262no—
397C2×C4⋊C4—262no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C4⋊C4C22×D1312yes—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4—262no—
405C2×C22⋊C4—261no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—134no—
410C2×C42—134no—
411C2×C42—268no—
412C2×C42—261no—
413C2×C42—262no—
414C2×C42—261no—
415C2×C42—261no—
416C2×C42C22×D1311yescharacteristic
417#107—138no—
418#107C22×D1318yes—
419#106—138no—
420#106—138no—
421C4⋊C8—138no—
422C4⋊C8—134no—
423C4⋊C8C22×D1314yes—
424#103—138no—
425#103—138no—
426#102—138no—
427#102C22×D1318yes—
428C2×C13—44no—
429C2×C13#307614yescomplemented
430C2×C13C22×C22⋊Q811yescharacteristic
431C2×C13C22×#13511yescharacteristic
432C2×C13C2×#57511yescharacteristic
433D13—24no—
434C24—21no—
435C24—131no—
436#41—1316no—
437#41—2616no—
438#41—268no—
439C2×Q8—24no—
440C2×Q8—44no—
441C2×Q8—134no—
442C2×Q8—132no—
443C2×Q8—261no—
444C2×Q8—264no—
445C2×Q8—262no—
446C2×Q8—524no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—264no—
450C2×D4—268no—
451C2×D4Q8×D1314yes—
452C2×D4C23×D1312yes—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—44no—
457C22×C4—131no—
458C22×C4—132no—
459C22×C4—134no—
460C22×C4—134no—
461C22×C4—132no—
462C22×C4—131no—
463C22×C4—131no—
464C22×C4—134no—
465C22×C4—134no—
466C22×C4—264no—
467C22×C4—268no—
468C22×C4—264no—
469C22×C4—261no—
470C22×C4—264no—
471C22×C4—261no—
472C22×C4—262no—
473C22×C4—522no—
474C22×C4—524no—
475C22×C4D4×D1311yescharacteristic
476C22×C4D4×D1311yescharacteristic
477C22×C4C23×D1311yescharacteristic
478C2×C8—24no—
479C2×C8—134no—
480C2×C8—2616no—
481C2×C8—264no—
482C2×C8C23×D1314yes—
483C4⋊C4—24no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—134no—
487C4⋊C4—132no—
488C4⋊C4—264no—
489C4⋊C4—268no—
490C4⋊C4—268no—
491C4⋊C4—261no—
492C4⋊C4—262no—
493C4⋊C4—264no—
494C4⋊C4—264no—
495C4⋊C4C23×D1314yes—
496C4⋊C4C23×D1312yes—
497C22⋊C4—24no—
498C22⋊C4—264no—
499C22⋊C4—268no—
500C22⋊C4—264no—
501C42—134no—
502C42—134no—
503C42—132no—
504C42—132no—
505C42—264no—
506C42—264no—
507C42—268no—
508C42—264no—
509C42D4×D1312yes—
510C42C23×D1312yes—
511C13C2×#307611yescharacteristic, complemented, Sylow
512C23—24no—
513C23—22no—
514C23—42no—
515C23—42no—
516C23—134no—
517C23—132no—
518C23—262no—
519C23—262no—
520C23C2×D4×D1311yescharacteristic
521Q8—48no—
522Q8—134no—
523Q8—264no—
524Q8—262no—
525Q8—528no—
526D4—24no—
527D4—22no—
528D4—2616no—
529D4C2×Q8×D1314yes—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—48no—
536C2×C4—134no—
537C2×C4—132no—
538C2×C4—138no—
539C2×C4—134no—
540C2×C4—134no—
541C2×C4—132no—
542C2×C4—132no—
543C2×C4—2616no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—264no—
547C2×C4—262no—
548C2×C4—268no—
549C2×C4—262no—
550C2×C4—264no—
551C2×C4—524no—
552C2×C4—528no—
553C2×C4—522no—
554C2×C4—524no—
555C2×C4#8816614yes—
556C2×C4C2×D4×D1312yes—
557C2×C4C2×D4×D1312yes—
558C2×C4C2×D4×D1311yescharacteristic
559C2×C4C2×Q8×D1312yes—
560C2×C4#41×D1312yes—
561C2×C4C24×D1311yescharacteristic
562C8—24no—
563C8—264no—
564C22—24no—
565C22—48no—
566C22—42no—
567C22—42no—
568C22—134no—
569C22—268no—
570C22—262no—
571C22—262no—
572C22D13×C22⋊Q812yes—
573C22C2×#8816612yes—
574C22#1171948212yes—
575C22C22×D4×D1311yescharacteristic
576C4—22no—
577C4—42no—
578C4—44no—
579C4—134no—
580C4—262no—
581C4—262no—
582C4—264no—
583C4—522no—
584C4—524no—
585C4D13×C22⋊Q812yes—
586C4C2×#8816614yes—
587C4C22×Q8×D1311yescharacteristic
588C4C2×#41×D1311yescharacteristic
589C2—44no—
590C2—264no—
591C2#1312461714yesdirect product factor
592C2C2×D13×C22⋊Q811yescharacteristic
593C2C22×#8816611yescharacteristic
594C2C2×#1171948211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#474C2
socleC23×C13C22×D4
prime radicalC22×#6129C22
hypercenterC2×#474D13
hypocenterC13C2×#3076
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#11719433C2semidirect
3. #13124617C2direct (N × H)
4. C2×#11718538C2semidirect
5. C2×#11718511C2semidirect
6. C2×#11718755C2semidirect
7. C2×#11718427C2semidirect
8. C2×#11718669C2semidirect
9. C2×#11718541C2semidirect
10. C2×D13×C4⋊C8C2semidirect
12. C2×C13×#474C2semidirect
23. #11719433C22semidirect
37. C13×#474C22semidirect
45. #11718755C22semidirect
46. #11718669C22semidirect
51. #11718541C22semidirect
52. #11718538C22semidirect
53. #11718511C22semidirect
54. D13×C4⋊C8C22semidirect
56. #11718427C22semidirect
65. C2×#6129Q8semidirect
167. #6129C2×Q8semidirect
223. C2×#474D13semidirect
308. #474C2×D13semidirect
429. C2×C13#3076semidirect
511. C13C2×#3076semidirect
591. C2#13124617direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194332
C2×C4×#61292
#131246172
C2×#117185382
C2×#117185112
C2×#117187552
C2×#117184272
C2×#117186692
C2×#117185412
C2×D13×C4⋊C82
C2×#117184332
C2×C13×#4742
C2×#307613