Finite Group Databasebeta

← C2×#13126100 #16735120

Subgroups — C2×#13126100 #16735120

Order 3328.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719205C211yesmaximal, characteristic
2C2×#11719330C211yesmaximal, characteristic
3#13126100C2116yesmaximal, direct product factor
4C2×#11718517C211yesmaximal, characteristic, complemented
5C2×#11718519C211yesmaximal, characteristic, complemented
6C2×#11718458C211yesmaximal, characteristic, complemented
7C2×#11718453C211yesmaximal, characteristic, complemented
8C2×#11718631C211yesmaximal, characteristic
9C2×#11718384C211yesmaximal, characteristic
10C2×#11718706C211yesmaximal, characteristic
11C2×#11718518C211yesmaximal, characteristic, complemented
12C2×#11718460C211yesmaximal, characteristic, complemented
13C2×#11718455C211yesmaximal, characteristic, complemented
14C2×#11718515C211yesmaximal, characteristic, complemented
15C2×#11718381C211yesmaximal, characteristic
16C2×C13×#483C211yesmaximal, characteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×Q8×Dic13C2211yescharacteristic
20C2×#88198C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C2×#88178—21no—
24C2×#88178—21no—
25C2×#88178C2211yescharacteristic
26#11719330—24no—
27#11719330C2218yes—
28#11719205—24no—
29#11719205C2218yes—
30C2×#88144—21no—
31C2×#88144—21no—
32C2×#88144C2211yescharacteristic
33C2×#88144C2211yescharacteristic
34C2×#88144C2211yescharacteristic
35C2×#88143—21no—
36C2×#88142—21no—
37C2×#88142C2211yescharacteristic
38C2×#88142C2211yescharacteristic
39C2×#88141C2211yescharacteristic
40C2×#88133—21no—
41C2×#88133—21no—
42C13×#483C2218yes—
43C2×C13×#106C2211yescharacteristic
44C2×C13×#106C2211yescharacteristic
45C2×C13×#103C2211yescharacteristic
46C2×C13×#103C2211yescharacteristic
47C2×C13×C22⋊C8C2211yescharacteristic
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×#88058C2211yescharacteristic
52C2×#88057C2211yescharacteristic
53C2×#88056C2211yescharacteristic
54C2×#88056C2211yescharacteristic
55C2×#88055C2211yescharacteristic
56C2×#88054C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718706C2218yes—
60#11718631C2218yes—
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88048C2211yescharacteristic
64C2×#88047C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×#88047C2211yescharacteristic
67#11718519C2218yescomplemented
68#11718518C2218yescomplemented
69#11718517C2218yescomplemented
70#11718515C2218yescomplemented
71#11718460C2218yescomplemented
72#11718458C2218yescomplemented
73#11718455C2218yescomplemented
74#11718453C2218yescomplemented
75#11718384C2218yes—
76#11718381C2218yes—
77C22×Q8×C13C2311yescharacteristic
78C23×C4×C13—21no—
79C23×C4×C13C2311yescharacteristic
80C22×Dic26—21no—
81C22×Dic26—21no—
82C22×Dic26C2311yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8C2314yes—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4C2311yescharacteristic
91C2×C13×C4⋊C4C2311yescharacteristic
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2314yes—
94C2×C13×C22⋊C4—21no—
95C2×C22⋊Dic13—21no—
96C2×C22⋊Dic13—21no—
97C2×C22⋊Dic13D411yescharacteristic
98C2×C22⋊Dic13D411yescharacteristic
99Q8×Dic13—22no—
100Q8×Dic13C2314yes—
101#88198—22no—
102#88198C2314yes—
103#88180—22no—
104#88180D414yes—
105#88180C2314yes—
106#88180C2314yes—
107C2×C4⋊Dic13—21no—
108C2×C4⋊Dic13—21no—
109C2×C4⋊Dic13—21no—
110C2×C4⋊Dic13—21no—
111C2×C4⋊Dic13D411yescharacteristic
112C2×C4⋊Dic13D411yescharacteristic
113C2×C4⋊Dic13C2311yescharacteristic
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116#88178—22no—
117#88178—28no—
118#88178—28no—
119#88178C2314yes—
120C2×#6101—21no—
121C2×#6101—21no—
122C2×#6101—21no—
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101—21no—
129C2×C4×Dic13—21no—
130C2×C4×Dic13—21no—
131C2×C4×Dic13—21no—
132C2×C4×Dic13C2311yescharacteristic
133C2×C4×Dic13C2311yescharacteristic
134C22×#1055C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136#88144—28no—
137#88144—28no—
138#88144—22no—
139#88144—22no—
140#88144—22no—
141#88144C2314yes—
142#88144C2314yes—
143#88144C2314yes—
144#88143—28no—
145#88142—28no—
146#88142—22no—
147#88142—22no—
148#88142C2314yes—
149#88142C2314yes—
150#88141—22no—
151#88141C2314yes—
152#88133—28no—
153#88133—28no—
154C13×#106C2314yes—
155C13×#106C2314yes—
156C13×#103C2314yes—
157C13×#103C2314yes—
158C13×C22⋊C8C2314yes—
159#88075C2314yes—
160#88075C2314yes—
161C22⋊#1055C2314yes—
162#88058C2314yes—
163#88057C2314yes—
164#88056C2314yes—
165#88056C2314yes—
166#88055C2314yes—
167#88054C2314yes—
168#88054C2314yes—
169C8×Dic13C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88048C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176C2×#3242—131nomaximal, Sylow
177C24×C13C2×D411yescharacteristic
178C2×Q8×C13—21no—
179C2×Q8×C13—22no—
180C2×Q8×C13—22no—
181C2×Q8×C13C2412yes—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—24no—
189C22×C4×C13—82no—
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2411yescharacteristic
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13C2×D411yescharacteristic
199C22×Dic13C2×D411yescharacteristic
200C22×Dic13C2×D411yescharacteristic
201C22×Dic13C2×D411yescharacteristic
202C2×Dic26—22no—
203C2×Dic26—22no—
204C2×Dic26—21no—
205C2×Dic26—24no—
206C2×Dic26—24no—
207C2×Dic26—82no—
208C2×Dic26—82no—
209C2×Dic26C2412yes—
210C2×C8×C13—22no—
211C2×C8×C13—22no—
212C2×C8×C13C2412yes—
213C2×C8×C13C2412yes—
214C13×C4⋊C4—21no—
215C13×C4⋊C4—24no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—24no—
219C13×C4⋊C4C2412yes—
220C13×C4⋊C4C2412yes—
221C13×C4⋊C4C2412yes—
222C13×C22⋊C4—24no—
223C22⋊Dic13—24no—
224C22⋊Dic13—24no—
225C22⋊Dic13C2×D414yes—
226C22⋊Dic13C2×D414yes—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229C4⋊Dic13—21no—
230C4⋊Dic13—24no—
231C4⋊Dic13—24no—
232C4⋊Dic13—24no—
233C4⋊Dic13—24no—
234C4⋊Dic13C2×D414yes—
235C4⋊Dic13C2×D414yes—
236C4⋊Dic13C2412yes—
237C4⋊Dic13C2412yes—
238C4⋊Dic13C2412yes—
239#6101—24no—
240#6101—24no—
241#6101—24no—
242#6101—24no—
243#6101—24no—
244#6101—24no—
245#6101—24no—
246#6101—24no—
247#6101—24no—
248C4×Dic13—24no—
249C4×Dic13—24no—
250C4×Dic13—24no—
251C4×Dic13C2×D412yes—
252C4×Dic13C2×D412yes—
253C4×Dic13C2412yes—
254C4×Dic13C2412yes—
255C2×#1055—22no—
256C2×#1055—22no—
257C2×#1055C2412yes—
258C2×#1055C2412yes—
259C2×#544—131no—
260C2×#541—131no—
261#3242—1316no—
262C2×#501—131no—
263C2×#499—131no—
264C2×#491—131no—
265C2×#487—131no—
266C2×#484—131no—
267C2×#485—131no—
268C2×#485—131no—
269C2×#483D1311yescharacteristic
270C2×#479—131no—
271C2×#479—131no—
272C2×#477—131no—
273C2×#475—131no—
274C2×#433—131no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13C22×D412yes—
279C23×C13C22×D411yescharacteristic
280Q8×C13—22no—
281Q8×C13—22no—
282Q8×C13—42no—
283C2×C4×C13—22no—
284C2×C4×C13—24no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—84no—
296C2×C4×C13C22×D412yes—
297C2×C4×C13C22×D411yescharacteristic
298C2×C4×C132−1+412yes—
299C2×C4×C132−1+412yes—
300C2×C4×C13C2511yescharacteristic
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—42no—
310C2×Dic13—42no—
311C2×Dic13—42no—
312C2×Dic13—42no—
313C2×Dic13C22×D412yes—
314C2×Dic13C22×D412yes—
315C2×Dic13C22×D412yes—
316C2×Dic13C22×D412yes—
317Dic26—22no—
318Dic26—22no—
319Dic26—42no—
320Dic26—84no—
321Dic26—84no—
322C8×C13—22no—
323C8×C13—22no—
324#1055—22no—
325#1055—22no—
326#544—138no—
327#544—264no—
328#541—138no—
329#541—264no—
330C2×C4⋊Q8—131no—
331C2×C4⋊Q8—131no—
332C2×C4⋊Q8—131no—
333C2×C4⋊Q8—261no—
334C2×#126—261no—
335C2×#126—261no—
336C2×#125—131no—
337C2×#125—131no—
338C2×#125—131no—
339C2×#125—261no—
340C2×#125—261no—
341C2×#125—261no—
342C2×C22⋊Q8—131no—
343C2×C22⋊Q8—261no—
344C2×C22⋊Q8—261no—
345C2×C22⋊Q8C2×D1311yescharacteristic
346C2×C4×Q8—131no—
347C2×C4×Q8—131no—
348C2×#117—131no—
349C2×#117—131no—
350C22×C4⋊C4C2×D1311yescharacteristic
351#501—138no—
352#499—138no—
353#491—138no—
354#487—138no—
355#485—138no—
356#485—138no—
357#484—138no—
358#483C2×D1318yes—
359#479—138no—
360#479—138no—
361#477—138no—
362#475—138no—
363#433—138no—
364C2×#107—131no—
365C2×#107—131no—
366C2×#107—131no—
367C2×#107—131no—
368C2×#106—131no—
369C2×#106—131no—
370C2×#106C2×D1311yescharacteristic
371C2×#106C2×D1311yescharacteristic
372C2×C4⋊C8—131no—
373C2×C4⋊C8—131no—
374C2×#103—131no—
375C2×#103—131no—
376C2×#103—131no—
377C2×#103—131no—
378C2×#103—131no—
379C2×#103—131no—
380C2×#103C2×D1311yescharacteristic
381C2×#103C2×D1311yescharacteristic
382C2×C22⋊C8—131no—
383C2×C22⋊C8C2×D1311yescharacteristic
384C2×#97—131no—
385C2×C4×C8—131no—
386C22×C13—22no—
387C22×C13—22no—
388C22×C13—22no—
389C22×C13—44no—
390C22×C13#53612yes—
391C22×C13#57712yes—
392C22×C13#57812yes—
393C22×C13C23×D411yescharacteristic
394C4×C13—22no—
395C4×C13—42no—
396C4×C13—42no—
397C4×C13—42no—
398C4×C13—42no—
399C4×C13#53612yes—
400C4×C13C2×2−1+411yescharacteristic
401C4×C13C2×2−1+411yescharacteristic
402Dic13—22no—
403Dic13—22no—
404Dic13—22no—
405Dic13—22no—
406Dic13—42no—
407Dic13—42no—
408Dic13—42no—
409Dic13—42no—
410C22×Q8—131no—
411C22×Q8—261no—
412C22×Q8—261no—
413C22×Q8C22×D1311yescharacteristic
414C23×C4—21no—
415C23×C4C22×D1311yescharacteristic
416C22×C8—131no—
417C22×C8—131no—
418C22×C8C22×D1311yescharacteristic
419C22×C8C22×D1311yescharacteristic
420C4⋊Q8—134no—
421C4⋊Q8—134no—
422C4⋊Q8—134no—
423C4⋊Q8—262no—
424C4⋊Q8—262no—
425C4⋊Q8—262no—
426C4⋊Q8—268no—
427#126—268no—
428#126—268no—
429#125—134no—
430#125—134no—
431#125—134no—
432#125—262no—
433#125—262no—
434#125—262no—
435#125—268no—
436#125—268no—
437#125—268no—
438C22⋊Q8—22no—
439C22⋊Q8—134no—
440C22⋊Q8—268no—
441C22⋊Q8—268no—
442C22⋊Q8—262no—
443C22⋊Q8C22×D1314yes—
444C4×Q8—134no—
445C4×Q8—134no—
446C4×Q8—262no—
447C4×Q8—262no—
448#117—134no—
449#117—134no—
450#117—134no—
451#117—262no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—131no—
456C2×C4⋊C4—131no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—261no—
461C2×C4⋊C4—261no—
462C2×C4⋊C4—261no—
463C2×C4⋊C4—261no—
464C2×C4⋊C4—261no—
465C2×C4⋊C4—261no—
466C2×C4⋊C4—261no—
467C2×C4⋊C4—261no—
468C2×C4⋊C4—261no—
469C2×C4⋊C4—261no—
470C2×C4⋊C4—261no—
471C2×C4⋊C4—261no—
472C2×C4⋊C4—261no—
473C2×C4⋊C4C22×D1311yescharacteristic
474C2×C4⋊C4C22×D1311yescharacteristic
475C2×C4⋊C4C22×D1314yes—
476C2×C4⋊C4C22×D1311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—131no—
479C2×C22⋊C4—131no—
480C2×C22⋊C4—261no—
481C2×C22⋊C4—261no—
482C2×C42—131no—
483C2×C42—131no—
484C2×C42—261no—
485C2×C42—261no—
486C2×C42—261no—
487#107—134no—
488#107—134no—
489#107—134no—
490#107—134no—
491#106—134no—
492#106—134no—
493#106C22×D1314yes—
494#106C22×D1314yes—
495C4⋊C8—134no—
496C4⋊C8—134no—
497#103—134no—
498#103—134no—
499#103—134no—
500#103—134no—
501#103—134no—
502#103—134no—
503#103C22×D1314yes—
504#103C22×D1314yes—
505C22⋊C8—134no—
506C22⋊C8C22×D1314yes—
507#97—134no—
508C4×C8—134no—
509C2×C13—42no—
510C2×C13#324214yescomplemented
511C2×C13C2×#53611yescharacteristic
512C2×C13C2×#57711yescharacteristic
513C2×C13C2×#57811yescharacteristic
514C24D4×D1311yescharacteristic
515C2×Q8—21no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—132no—
519C2×Q8—264no—
520C2×Q8—264no—
521C2×Q8—261no—
522C2×Q8—262no—
523C2×Q8—262no—
524C2×Q8—1042no—
525C2×Q8—1042no—
526C2×Q8C23×D1312yes—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—24no—
534C22×C4—82no—
535C22×C4—131no—
536C22×C4—131no—
537C22×C4—131no—
538C22×C4—131no—
539C22×C4—261no—
540C22×C4—261no—
541C22×C4—261no—
542C22×C4—261no—
543C22×C4D4×D1312yes—
544C22×C4D4×D1311yescharacteristic
545C22×C4C23×D1312yes—
546C22×C4C23×D1311yescharacteristic
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—132no—
550C2×C8—132no—
551C2×C8—262no—
552C2×C8—262no—
553C2×C8C23×D1312yes—
554C2×C8C23×D1312yes—
555C4⋊C4—24no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—134no—
561C4⋊C4—134no—
562C4⋊C4—132no—
563C4⋊C4—132no—
564C4⋊C4—132no—
565C4⋊C4—264no—
566C4⋊C4—264no—
567C4⋊C4—264no—
568C4⋊C4—264no—
569C4⋊C4—264no—
570C4⋊C4—264no—
571C4⋊C4—264no—
572C4⋊C4—264no—
573C4⋊C4—264no—
574C4⋊C4—264no—
575C4⋊C4—264no—
576C4⋊C4—264no—
577C4⋊C4—261no—
578C4⋊C4—261no—
579C4⋊C4—261no—
580C4⋊C4—264no—
581C4⋊C4C23×D1312yes—
582C4⋊C4C23×D1312yes—
583C4⋊C4C23×D1312yes—
584C22⋊C4—24no—
585C22⋊C4—134no—
586C22⋊C4—134no—
587C22⋊C4—264no—
588C22⋊C4—264no—
589C42—132no—
590C42—132no—
591C42—132no—
592C42—132no—
593C42—264no—
594C42—264no—
595C42—264no—
596C13C2×#324211yescharacteristic, complemented, Sylow
597C23—22no—
598C23—22no—
599C23—22no—
600C23C2×D4×D1312yes—
601C23C2×D4×D1311yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—42no—
605Q8—262no—
606Q8—262no—
607Q8—522no—
608Q8—1044no—
609Q8—1044no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—84no—
623C2×C4—132no—
624C2×C4—132no—
625C2×C4—132no—
626C2×C4—132no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—262no—
630C2×C4—262no—
631C2×C4—262no—
632C2×C4—262no—
633C2×C4—262no—
634C2×C4—262no—
635C2×C4—522no—
636C2×C4—522no—
637C2×C4—522no—
638C2×C4—522no—
639C2×C4C2×D4×D1312yes—
640C2×C4C2×D4×D1311yescharacteristic
641C2×C4#8825712yes—
642C2×C4#8825712yes—
643C2×C4C24×D1311yescharacteristic
644C8—22no—
645C8—22no—
646C8—262no—
647C8—262no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22#1171935312yes—
653C22#1171946712yes—
654C22#1171948412yes—
655C22C22×D4×D1311yescharacteristic
656C4—22no—
657C4—42no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—262no—
662C4—262no—
663C4—262no—
664C4—262no—
665C4—522no—
666C4—522no—
667C4—522no—
668C4—522no—
669C4#1171935312yes—
670C4C2×#8825711yescharacteristic
671C4C2×#8825711yescharacteristic
672C2—42no—
673C2#1312610014yesdirect product factor
674C2C2×#1171935311yescharacteristic
675C2C2×#1171946711yescharacteristic
676C2C2×#1171948411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#483C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#483D13
hypocenterC13C2×#3242
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #13126100C2direct (N × H)
4. C2×#11718517C2semidirect
5. C2×#11718519C2semidirect
6. C2×#11718458C2semidirect
7. C2×#11718453C2semidirect
11. C2×#11718518C2semidirect
12. C2×#11718460C2semidirect
13. C2×#11718455C2semidirect
14. C2×#11718515C2semidirect
67. #11718519C22semidirect
68. #11718518C22semidirect
69. #11718517C22semidirect
70. #11718515C22semidirect
71. #11718460C22semidirect
72. #11718458C22semidirect
73. #11718455C22semidirect
74. #11718453C22semidirect
510. C2×C13#3242semidirect
596. C13C2×#3242semidirect
673. C2#13126100direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192052
C2×#117193302
#131261002
C2×#117185172
C2×#117185192
C2×#117184582
C2×#117184532
C2×#117186312
C2×#117183842
C2×#117187062
C2×#117185182
C2×#117184602
C2×#117184552
C2×#117185152
C2×#117183812
C2×C13×#4832
C2×#324213