Finite Group Databasebeta

← C2×#13127634 #16742625

Subgroups — C2×#13127634 #16742625

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719274C211yesmaximal, characteristic
2C2×#11719426C211yesmaximal, characteristic
3#13127634C2116yesmaximal, direct product factor
4C2×#11718743C211yesmaximal, characteristic
5C2×#11718458C211yesmaximal, characteristic
6C2×#11718453C211yesmaximal, characteristic
7C2×#11718457C211yesmaximal, characteristic
8C2×#11718490C211yesmaximal, characteristic
9C2×#11718452C211yesmaximal, characteristic
10C2×#11718843C211yesmaximal, characteristic
11C2×#11718843C211yesmaximal, characteristic
12C2×#11718489C211yesmaximal, characteristic
13C2×#11718845C211yesmaximal, characteristic
14C2×#11718691C211yesmaximal, characteristic
15C2×Q16×Dic13C211yesmaximal, characteristic
16C2×C13×#462C211yesmaximal, characteristic
17C22×C13×Q16C2211yescharacteristic
18C22×C13×Q16C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×Q8×Dic13C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23C2×Q8×Dic13C2211yescharacteristic
24C2×Q8×Dic13C2211yescharacteristic
25C2×#88198C2211yescharacteristic
26C2×#88198C2211yescharacteristic
27C22×#6107C2211yescharacteristic
28#11719426—24no—
29#11719426C2218yes—
30#11719274—24no—
31#11719274C2218yes—
32C2×#88144—21no—
33C2×#88144—21no—
34C2×#88144C2211yescharacteristic
35C2×#88143—21no—
36C2×#88143—21no—
37C2×#88142—21no—
38C2×#88142C2211yescharacteristic
39C2×#88141—21no—
40C2×#88124—21no—
41C2×#88124C2211yescharacteristic
42C2×C4×Dic26—21no—
43C2×C4×Dic26C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C13×#462C2218yes—
46C2×C13×C4⋊C8C2211yescharacteristic
47C2×C13×#103C2211yescharacteristic
48C2×C13×#103C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88075C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88075C2211yescharacteristic
54#11718845C2218yes—
55Q16×Dic13C2218yes—
56#11718843C2218yes—
57#11718843C2218yes—
58C2×#88058C2211yescharacteristic
59C2×#88057C2211yescharacteristic
60C2×#88056C2211yescharacteristic
61C2×#88056C2211yescharacteristic
62C2×#88055C2211yescharacteristic
63C2×#88054C2211yescharacteristic
64C2×#88054C2211yescharacteristic
65C2×C8×Dic13C2211yescharacteristic
66#11718743C2218yes—
67#11718691C2218yes—
68C2×#88050C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88043C2211yescharacteristic
71#11718490C2218yes—
72#11718489C2218yes—
73#11718458C2218yes—
74#11718457C2218yes—
75#11718453C2218yes—
76#11718452C2218yes—
77C22×Q8×C13C2311yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C22×Q8×C13C2311yescharacteristic
80C22×Dic26—21no—
81C22×Dic26D411yescharacteristic
82C22×Dic26C2311yescharacteristic
83C2×C13×Q16—24no—
84C2×C13×Q16—24no—
85C2×C13×Q16C2314yes—
86C2×C13×Q16C2314yes—
87C22×C8×C13C2311yescharacteristic
88C22×C8×C13C2311yescharacteristic
89C13×C4⋊Q8—22no—
90C13×C4⋊Q8C2314yes—
91C4×Q8×C13—22no—
92C4×Q8×C13C2314yes—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C42×C13—21no—
98C2×C42×C13C2311yescharacteristic
99Q8×Dic13—22no—
100Q8×Dic13—22no—
101Q8×Dic13—22no—
102Q8×Dic13—22no—
103Q8×Dic13C2314yes—
104Q8×Dic13C2314yes—
105Q8×Dic13C2314yes—
106Q8×Dic13C2314yes—
107#88198—22no—
108#88198—22no—
109#88198C2314yes—
110#88198C2314yes—
111C2×#6107—24no—
112C2×#6107C2314yes—
113C2×C4⋊Dic13—21no—
114C2×C4⋊Dic13—21no—
115C2×C4⋊Dic13—21no—
116C2×C4⋊Dic13—21no—
117C2×C4⋊Dic13—21no—
118C2×C4⋊Dic13D411yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4⋊Dic13C2311yescharacteristic
121C2×C4⋊Dic13C2311yescharacteristic
122C2×#6101—21no—
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101D411yescharacteristic
132C2×#6101D411yescharacteristic
133C2×C4×Dic13—21no—
134C2×C4×Dic13—21no—
135C2×C4×Dic13—21no—
136C2×C4×Dic13—21no—
137C2×C4×Dic13—21no—
138C2×C4×Dic13C2311yescharacteristic
139C2×C4×Dic13C2311yescharacteristic
140C22×#1055C2311yescharacteristic
141C22×#1055C2311yescharacteristic
142#88144—28no—
143#88144—28no—
144#88144—22no—
145#88144C2314yes—
146#88143—28no—
147#88143—28no—
148#88142—28no—
149#88142—22no—
150#88142C2314yes—
151#88141—28no—
152#88124—22no—
153#88124—28no—
154#88124C2314yes—
155C4×Dic26—22no—
156C4×Dic26—28no—
157C4×Dic26D414yes—
158C4×Dic26C2314yes—
159C4×Dic26C2314yes—
160C13×C4⋊C8C2314yes—
161C13×#103C2314yes—
162C13×#103C2314yes—
163#88075C2314yes—
164#88075C2314yes—
165#88075C2314yes—
166#88075C2314yes—
167#88075C2314yes—
168#88058C2314yes—
169#88057C2314yes—
170#88056C2314yes—
171#88056C2314yes—
172#88055C2314yes—
173#88054C2314yes—
174#88054C2314yes—
175C8×Dic13C2314yes—
176#88050C2314yes—
177#88048C2314yes—
178#88043C2314yes—
179C2×#3374—131nomaximal, Sylow
180C2×Q8×C13—21no—
181C2×Q8×C13—21no—
182C2×Q8×C13—21no—
183C2×Q8×C13—22no—
184C2×Q8×C13—22no—
185C2×Q8×C13—22no—
186C2×Q8×C13—22no—
187C2×Q8×C13—22no—
188C2×Q8×C13#4114yes—
189C2×Q8×C13C2412yes—
190C2×Q8×C13C2412yes—
191C2×Q8×C13C2412yes—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2411yescharacteristic
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13C2×D411yescharacteristic
204C22×Dic13C2×D411yescharacteristic
205C22×Dic13C2×D411yescharacteristic
206C22×Dic13C2×D411yescharacteristic
207C2×Dic26—24no—
208C2×Dic26—22no—
209C2×Dic26—22no—
210C2×Dic26—21no—
211C2×Dic26—24no—
212C2×Dic26—44no—
213C2×Dic26C2×D414yes—
214C2×Dic26C2412yes—
215C13×Q16—28no—
216C13×Q16—28no—
217C2×C8×C13—22no—
218C2×C8×C13—22no—
219C2×C8×C13C2412yes—
220C2×C8×C13C2412yes—
221C13×C4⋊C4—24no—
222C13×C4⋊C4—24no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—24no—
225C13×C4⋊C4C2412yes—
226C42×C13—24no—
227C42×C13C2×D412yes—
228C42×C13C2412yes—
229#6107—28no—
230C4⋊Dic13—21no—
231C4⋊Dic13—21no—
232C4⋊Dic13—21no—
233C4⋊Dic13—24no—
234C4⋊Dic13—24no—
235C4⋊Dic13—24no—
236C4⋊Dic13—24no—
237C4⋊Dic13—24no—
238C4⋊Dic13C2×D414yes—
239C4⋊Dic13C2412yes—
240C4⋊Dic13C2412yes—
241C4⋊Dic13C2412yes—
242#6101—24no—
243#6101—24no—
244#6101—24no—
245#6101—24no—
246#6101—24no—
247#6101—24no—
248#6101—24no—
249#6101—24no—
250#6101—24no—
251#6101C2×D414yes—
252#6101C2×D414yes—
253C4×Dic13—24no—
254C4×Dic13—24no—
255C4×Dic13—24no—
256C4×Dic13—24no—
257C4×Dic13—24no—
258C4×Dic13C2×D412yes—
259C4×Dic13C2×D412yes—
260C4×Dic13C2412yes—
261C4×Dic13C2412yes—
262C2×#1055—22no—
263C2×#1055—22no—
264C2×#1055C2412yes—
265C2×#1055C2412yes—
266C2×#557—131no—
267C2×#557—131no—
268#3374—1316no—
269C2×#491—131no—
270C2×#491—131no—
271C2×#487—131no—
272C2×#479—131no—
273C2×#479—131no—
274C2×#475—131no—
275C2×#462—131no—
276C2×#462—131no—
277C2×#462D1311yescharacteristic
278C2×#446—131no—
279C2×#441—131no—
280C2×#441—131no—
281C2×C4×Q16—131no—
282C23×C13C22×D411yescharacteristic
283Q8×C13—24no—
284Q8×C13—22no—
285Q8×C13—22no—
286Q8×C13—22no—
287Q8×C13—22no—
288Q8×C13—22no—
289Q8×C13—42no—
290Q8×C13—42no—
291Q8×C13C2×#4114yes—
292C2×C4×C13—24no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13C22×D412yes—
303C2×C4×C13C22×D412yes—
304C2×C4×C13C22×D411yescharacteristic
305C2×C4×C13C2×#4112yes—
306C2×C4×C132−1+412yes—
307C2×C4×C13C2511yescharacteristic
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—42no—
316C2×Dic13—42no—
317C2×Dic13—42no—
318C2×Dic13—42no—
319C2×Dic13#13714yes—
320C2×Dic13C22×D412yes—
321C2×Dic13C22×D412yes—
322C2×Dic13C22×D412yes—
323C2×Dic13C22×D412yes—
324Dic26—28no—
325Dic26—22no—
326Dic26—22no—
327Dic26—42no—
328Dic26—48no—
329C8×C13—22no—
330C8×C13—22no—
331#1055—22no—
332#1055—22no—
333C22×Q16—131no—
334C22×Q16C2×D1311yescharacteristic
335C22×Q16C2×D1311yescharacteristic
336#557—138no—
337#557—138no—
338#557—264no—
339#557—264no—
340C2×C4⋊Q8—131no—
341C2×C4⋊Q8—131no—
342C2×C4⋊Q8—131no—
343C2×C4⋊Q8—261no—
344C2×C4⋊Q8C2×D1311yescharacteristic
345C2×#125—131no—
346C2×#125—131no—
347C2×#125—261no—
348C2×#125—261no—
349C2×#125—261no—
350C2×#125—261no—
351C2×#125—261no—
352C2×C4×Q8—131no—
353C2×C4×Q8—131no—
354C2×C4×Q8—131no—
355C2×C4×Q8—131no—
356C2×C4×Q8—131no—
357C2×C4×Q8—131no—
358C2×C4×Q8—261no—
359C2×C4×Q8—261no—
360C2×C4×Q8C2×D1311yescharacteristic
361#491—138no—
362#491—138no—
363#487—138no—
364#479—138no—
365#479—138no—
366#475—138no—
367#462—138no—
368#462—138no—
369#462C2×D1318yes—
370#446—138no—
371#441—138no—
372#441—138no—
373C4×Q16—138no—
374C2×#107—131no—
375C2×#106—131no—
376C2×#106—131no—
377C2×C4⋊C8—131no—
378C2×C4⋊C8—131no—
379C2×C4⋊C8C2×D1311yescharacteristic
380C2×#103—131no—
381C2×#103—131no—
382C2×#103—131no—
383C2×#103—131no—
384C2×#103—131no—
385C2×#103—131no—
386C2×#103—131no—
387C2×#103—131no—
388C2×#103C2×D1311yescharacteristic
389C2×#103C2×D1311yescharacteristic
390C2×#97—131no—
391C2×#97—131no—
392C2×C4×C8—131no—
393C22×C13#54812yes—
394C22×C13C2×#13712yes—
395C22×C13#57812yes—
396C22×C13C23×D411yescharacteristic
397C4×C13—24no—
398C4×C13—22no—
399C4×C13—22no—
400C4×C13—42no—
401C4×C13—42no—
402C4×C13—42no—
403C4×C13#54812yes—
404C4×C13C22×#4111yescharacteristic
405C4×C13C2×2−1+411yescharacteristic
406Dic13—22no—
407Dic13—22no—
408Dic13—22no—
409Dic13—42no—
410Dic13—42no—
411Dic13—42no—
412Dic13—42no—
413Dic13C2×#13714yes—
414C22×Q8—131no—
415C22×Q8—131no—
416C22×Q8—261no—
417C22×Q8C22×D1311yescharacteristic
418C22×Q8C22×D1311yescharacteristic
419C22×Q8C22×D1311yescharacteristic
420C2×Q16—24no—
421C2×Q16—24no—
422C2×Q16—134no—
423C2×Q16—264no—
424C2×Q16C22×D1314yes—
425C2×Q16C22×D1314yes—
426C22×C8—131no—
427C22×C8—131no—
428C22×C8C22×D1311yescharacteristic
429C22×C8C22×D1311yescharacteristic
430C4⋊Q8—22no—
431C4⋊Q8—134no—
432C4⋊Q8—134no—
433C4⋊Q8—134no—
434C4⋊Q8—262no—
435C4⋊Q8—262no—
436C4⋊Q8—262no—
437C4⋊Q8—268no—
438C4⋊Q8C22×D1314yes—
439#125—134no—
440#125—134no—
441#125—268no—
442#125—262no—
443#125—268no—
444#125—268no—
445#125—268no—
446#125—268no—
447#125—262no—
448C4×Q8—22no—
449C4×Q8—134no—
450C4×Q8—134no—
451C4×Q8—134no—
452C4×Q8—134no—
453C4×Q8—134no—
454C4×Q8—134no—
455C4×Q8—134no—
456C4×Q8—268no—
457C4×Q8—262no—
458C4×Q8—262no—
459C4×Q8—262no—
460C4×Q8—262no—
461C4×Q8—268no—
462C4×Q8—262no—
463C4×Q8C22×D1314yes—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—131no—
471C2×C4⋊C4—131no—
472C2×C4⋊C4—131no—
473C2×C4⋊C4—261no—
474C2×C4⋊C4—261no—
475C2×C4⋊C4—261no—
476C2×C4⋊C4—261no—
477C2×C4⋊C4—261no—
478C2×C4⋊C4—261no—
479C2×C4⋊C4—261no—
480C2×C4⋊C4—261no—
481C2×C4⋊C4—261no—
482C2×C4⋊C4—261no—
483C2×C4⋊C4—261no—
484C2×C4⋊C4—261no—
485C2×C4⋊C4—261no—
486C2×C4⋊C4—261no—
487C2×C4⋊C4C22×D1311yescharacteristic
488C2×C42—21no—
489C2×C42—131no—
490C2×C42—131no—
491C2×C42—261no—
492C2×C42—261no—
493C2×C42—261no—
494C2×C42—261no—
495C2×C42—261no—
496C2×C42C22×D1311yescharacteristic
497#107—134no—
498#106—134no—
499#106—134no—
500C4⋊C8—134no—
501C4⋊C8—134no—
502C4⋊C8C22×D1314yes—
503#103—134no—
504#103—134no—
505#103—134no—
506#103—134no—
507#103—134no—
508#103—134no—
509#103—134no—
510#103—134no—
511#103C22×D1314yes—
512#103C22×D1314yes—
513#97—134no—
514#97—134no—
515C4×C8—134no—
516C2×C13#337414yescomplemented
517C2×C13C2×#54811yescharacteristic
518C2×C13C22×#13711yescharacteristic
519C2×C13C2×#57811yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—134no—
529C2×Q8—132no—
530C2×Q8—264no—
531C2×Q8—264no—
532C2×Q8—261no—
533C2×Q8—262no—
534C2×Q8—262no—
535C2×Q8—524no—
536C2×Q8#612914yes—
537C2×Q8C23×D1312yes—
538C2×Q8C23×D1312yes—
539C2×Q8C23×D1312yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—131no—
545C22×C4—131no—
546C22×C4—131no—
547C22×C4—131no—
548C22×C4—261no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4D4×D1311yescharacteristic
553C22×C4D4×D1311yescharacteristic
554C22×C4C23×D1311yescharacteristic
555Q16—28no—
556Q16—28no—
557Q16—268no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—132no—
561C2×C8—132no—
562C2×C8—262no—
563C2×C8—262no—
564C2×C8C23×D1312yes—
565C2×C8C23×D1312yes—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—21no—
570C4⋊C4—134no—
571C4⋊C4—134no—
572C4⋊C4—134no—
573C4⋊C4—132no—
574C4⋊C4—132no—
575C4⋊C4—132no—
576C4⋊C4—264no—
577C4⋊C4—264no—
578C4⋊C4—264no—
579C4⋊C4—264no—
580C4⋊C4—264no—
581C4⋊C4—264no—
582C4⋊C4—264no—
583C4⋊C4—264no—
584C4⋊C4—264no—
585C4⋊C4—264no—
586C4⋊C4—264no—
587C4⋊C4—261no—
588C4⋊C4—261no—
589C4⋊C4—261no—
590C4⋊C4—264no—
591C4⋊C4—264no—
592C4⋊C4—264no—
593C4⋊C4C23×D1312yes—
594C42—24no—
595C42—132no—
596C42—132no—
597C42—132no—
598C42—132no—
599C42—264no—
600C42—264no—
601C42—264no—
602C42—264no—
603C42—264no—
604C42D4×D1312yes—
605C42C23×D1312yes—
606C13C2×#337411yescharacteristic, complemented, Sylow
607C23C2×D4×D1311yescharacteristic
608Q8—24no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—42no—
615Q8—42no—
616Q8—268no—
617Q8—262no—
618Q8—262no—
619Q8—528no—
620Q8—522no—
621Q8C2×#612914yes—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—134no—
633C2×C4—132no—
634C2×C4—132no—
635C2×C4—132no—
636C2×C4—132no—
637C2×C4—262no—
638C2×C4—262no—
639C2×C4—262no—
640C2×C4—262no—
641C2×C4—262no—
642C2×C4—262no—
643C2×C4—262no—
644C2×C4—522no—
645C2×C4—522no—
646C2×C4—522no—
647C2×C4—522no—
648C2×C4C2×D4×D1312yes—
649C2×C4C2×D4×D1312yes—
650C2×C4C2×D4×D1311yescharacteristic
651C2×C4C2×#612912yes—
652C2×C4#8825712yes—
653C2×C4C24×D1311yescharacteristic
654C8—22no—
655C8—22no—
656C8—262no—
657C8—262no—
658C22#1171930312yes—
659C22#1171947112yes—
660C22D13×#13712yes—
661C22C22×D4×D1311yescharacteristic
662C4—22no—
663C4—24no—
664C4—22no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—134no—
669C4—262no—
670C4—262no—
671C4—262no—
672C4—522no—
673C4—522no—
674C4—522no—
675C4—522no—
676C4#1171930312yes—
677C4C22×#612911yescharacteristic
678C4C2×#8825711yescharacteristic
679C2#1312763414yesdirect product factor
680C2C2×#1171930311yescharacteristic
681C2C2×D13×#13711yescharacteristic
682C2C2×#1171947111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#462C2
socle, prime radicalC23×C13C22×D4
hypercenterC2×#462D13
hypocenterC13C2×#3374
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13127634C2direct (N × H)
516. C2×C13#3374semidirect
606. C13C2×#3374semidirect
679. C2#13127634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192742
C2×#117194262
#131276342
C2×#117187432
C2×#117184582
C2×#117184532
C2×#117184572
C2×#117184902
C2×#117184522
C2×#117188432
C2×#117184892
C2×#117188452
C2×#117186912
C2×Q16×Dic132
C2×C13×#4622
C2×#337413