Finite Group Databasebeta

← C2×#13127736 #16743397

Subgroups — C2×#13127736 #16743397

Order 3328.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719244C211yesmaximal, characteristic, complemented
2C2×D4×Dic26C211yesmaximal, characteristic, complemented
3#13127736C2116yesmaximal, direct product factor
4C2×#11718363C211yesmaximal, characteristic, complemented
5C2×#11718517C211yesmaximal, characteristic, complemented
6C2×#11718516C211yesmaximal, characteristic, complemented
7C2×#11718670C211yesmaximal, characteristic, complemented
8C2×#11718427C211yesmaximal, characteristic, complemented
9C2×#11718669C211yesmaximal, characteristic, complemented
10C2×#11718422C211yesmaximal, characteristic, complemented
11C2×#11718422C211yesmaximal, characteristic, complemented
12C2×#11718420C211yesmaximal, characteristic, complemented
13C2×#11718362C211yesmaximal, characteristic, complemented
14C2×#11718813C211yesmaximal, characteristic
15C2×D8×Dic13C211yesmaximal, characteristic
16C2×C13×#442C211yesmaximal, characteristic
17C23×Dic26—21no—
18C22×C13×D8C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C2×D4×Dic13C2211yescharacteristic
22C2×D4×Dic13C2211yescharacteristic
23C2×D4×Dic13C2211yescharacteristic
24C2×D4×Dic13C2211yescharacteristic
25C2×#88178—21no—
26C2×#88178—21no—
27C22×#6101—21no—
28#11719244—24no—
29#11719244C2218yescomplemented
30D4×Dic26—24no—
31D4×Dic26C2218yescomplemented
32C2×#88144C2211yescharacteristic
33C2×#88142C2211yescharacteristic
34C2×#88142C2211yescharacteristic
35C2×#88142C2211yescharacteristic
36C2×#88132—21no—
37C2×#88132—21no—
38C2×#88132—21no—
39C2×#88132—21no—
40C2×#88124C2211yescharacteristic
41C2×#88123C2211yescharacteristic
42C2×C4×Dic26C2211yescharacteristic
43C13×#442C2218yes—
44C2×C13×#106C2211yescharacteristic
45C2×C13×#102C2211yescharacteristic
46C2×C13×#102C2211yescharacteristic
47C2×C13×#97C2211yescharacteristic
48C2×#88072C2211yescharacteristic
49C2×#88072C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52#11718813C2218yes—
53D8×Dic13C2218yes—
54C2×#88058C2211yescharacteristic
55C2×#88058C2211yescharacteristic
56C2×#88057C2211yescharacteristic
57C2×#88057C2211yescharacteristic
58C2×#88055C2211yescharacteristic
59C2×#88054C2211yescharacteristic
60C2×#88054C2211yescharacteristic
61C2×C8×Dic13C2211yescharacteristic
62#11718670C2218yescomplemented
63#11718669C2218yescomplemented
64C2×#88048C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88047C2211yescharacteristic
68C2×C4⋊#1055C2211yescharacteristic
69#11718517C2218yescomplemented
70#11718516C2218yescomplemented
71#11718427C2218yescomplemented
72#11718422C2218yescomplemented
73#11718422C2218yescomplemented
74#11718420C2218yescomplemented
75#11718363C2218yescomplemented
76#11718362C2218yescomplemented
77C22×D4×C13C2311yescharacteristic
78C22×D4×C13C2311yescharacteristic
79C23×C4×C13—21no—
80C23×C4×C13—21no—
81C23×Dic13—21no—
82C23×Dic13—21no—
83C23×Dic13—21no—
84C23×Dic13—21no—
85C22×Dic26—21no—
86C22×Dic26—21no—
87C22×Dic26—21no—
88C22×Dic26—21no—
89C22×Dic26—28no—
90C22×Dic26—48no—
91C22×Dic26D411yescharacteristic
92C2×C13×D8Q818yescomplemented
93C2×C13×D8C2314yes—
94C22×C8×C13C2311yescharacteristic
95C22×C8×C13C2311yescharacteristic
96C4×D4×C13—22no—
97C4×D4×C13—22no—
98C4×D4×C13C2314yes—
99C4×D4×C13C2314yes—
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4—21no—
104C2×C42×C13C2311yescharacteristic
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107C2×C22⋊Dic13—21no—
108C2×C22⋊Dic13—21no—
109D4×Dic13—22no—
110D4×Dic13—22no—
111D4×Dic13—22no—
112D4×Dic13—22no—
113D4×Dic13C2314yes—
114D4×Dic13C2314yes—
115D4×Dic13C2314yes—
116D4×Dic13C2314yes—
117C2×C4⋊Dic13—21no—
118C2×C4⋊Dic13—21no—
119C2×C4⋊Dic13D411yescharacteristic
120C2×C4⋊Dic13C2311yescharacteristic
121C2×C4⋊Dic13C2311yescharacteristic
122C2×C4⋊Dic13C2311yescharacteristic
123C2×C4⋊Dic13C2311yescharacteristic
124#88178—28no—
125#88178—28no—
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101—28no—
133C2×#6101D411yescharacteristic
134C2×#6101D411yescharacteristic
135C2×C4×Dic13C2311yescharacteristic
136C2×C4×Dic13C2311yescharacteristic
137C22×#1055C2311yescharacteristic
138C22×#1055C2311yescharacteristic
139#88144—22no—
140#88144C2314yes—
141#88142—22no—
142#88142—22no—
143#88142—22no—
144#88142C2314yes—
145#88142C2314yes—
146#88142C2314yes—
147#88132—28no—
148#88132—28no—
149#88132—28no—
150#88132—28no—
151#88124—22no—
152#88124C2314yes—
153#88123—22no—
154#88123C2314yes—
155C4×Dic26D414yes—
156C4×Dic26C2314yes—
157C13×#106C2314yes—
158C13×#102C2314yes—
159C13×#102C2314yes—
160C13×#97C2314yes—
161#88072C2314yes—
162#88072C2314yes—
163#88072C2314yes—
164#88072C2314yes—
165#88058C2314yes—
166#88058C2314yes—
167#88057C2314yes—
168#88057C2314yes—
169#88055C2314yes—
170#88054C2314yes—
171#88054C2314yes—
172C8×Dic13C2314yes—
173#88048C2314yes—
174#88048C2314yes—
175#88048C2314yes—
176#88047C2314yes—
177C4⋊#1055C2314yes—
178C2×#3384—131nomaximal, Sylow
179C24×C13—21no—
180C24×C13—21no—
181C2×D4×C13—21no—
182C2×D4×C13—21no—
183C2×D4×C13—22no—
184C2×D4×C13—22no—
185C2×D4×C13C2×Q814yes—
186C2×D4×C13C2×Q814yescomplemented
187C2×D4×C13C2412yes—
188C2×D4×C13C2412yes—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—24no—
192C22×C4×C13—24no—
193C22×C4×C13—44no—
194C22×C4×C13—82no—
195C22×C4×C13C2×D411yescharacteristic
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2411yescharacteristic
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—24no—
203C22×Dic13—24no—
204C22×Dic13—24no—
205C22×Dic13—24no—
206C22×Dic13—44no—
207C22×Dic13—44no—
208C22×Dic13—44no—
209C22×Dic13—82no—
210C22×Dic13C2×D411yescharacteristic
211C22×Dic13C2×D411yescharacteristic
212C22×Dic13C2×D411yescharacteristic
213C22×Dic13C2×D411yescharacteristic
214C2×Dic26—24no—
215C2×Dic26—24no—
216C2×Dic26—24no—
217C2×Dic26—24no—
218C2×Dic26—24no—
219C2×Dic26—432no—
220C2×Dic26—44no—
221C2×Dic26—44no—
222C2×Dic26—44no—
223C2×Dic26—82no—
224C2×Dic26C2×D414yes—
225C13×D8C2×Q8116yescomplemented
226C2×C8×C13—22no—
227C2×C8×C13C2×Q814yescomplemented
228C2×C8×C13C2412yes—
229C2×C8×C13C2412yes—
230C13×C4⋊C4—21no—
231C13×C4⋊C4—21no—
232C13×C4⋊C4C2412yes—
233C13×C4⋊C4C2412yes—
234C13×C22⋊C4—24no—
235C13×C22⋊C4—24no—
236C42×C13C2×D412yes—
237C42×C13C2412yes—
238C22⋊Dic13—24no—
239C22⋊Dic13—24no—
240C22⋊Dic13—24no—
241C22⋊Dic13—24no—
242C4⋊Dic13—21no—
243C4⋊Dic13—21no—
244C4⋊Dic13—24no—
245C4⋊Dic13—21no—
246C4⋊Dic13—21no—
247C4⋊Dic13—24no—
248C4⋊Dic13C2×D414yes—
249C4⋊Dic13C2412yes—
250C4⋊Dic13C2412yes—
251C4⋊Dic13C2412yes—
252C4⋊Dic13C2412yes—
253#6101—24no—
254#6101—24no—
255#6101—24no—
256#6101—24no—
257#6101—24no—
258#6101—24no—
259#6101C2×D414yes—
260#6101C2×D414yes—
261C4×Dic13C2×D412yes—
262C4×Dic13C2×D412yes—
263C4×Dic13C2412yes—
264C4×Dic13C2412yes—
265C2×#1055—22no—
266C2×#1055—22no—
267C2×#1055C2412yes—
268C2×#1055C2412yes—
269C2×#554—131no—
270C2×D4×Q8—131no—
271#3384—1316no—
272C2×#501—131no—
273C2×#501—131no—
274C2×#498—131no—
275C2×#478—131no—
276C2×#478—131no—
277C2×#476—131no—
278C2×#476—131no—
279C2×#476—131no—
280C2×#474—131no—
281C2×#446—131no—
282C2×#442—131no—
283C2×#442D1311yescharacteristic
284C2×C4×D8—131no—
285C23×C13—24no—
286C23×C13—24no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—42no—
290C23×C13—42no—
291C23×C13—42no—
292C23×C13—42no—
293C23×C13C22×D411yescharacteristic
294D4×C13—24no—
295D4×C13—24no—
296D4×C13—22no—
297D4×C13—22no—
298D4×C13C22×Q814yes—
299D4×C13C22×Q814yescomplemented
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—48no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—84no—
308C2×C4×C13C22×D412yes—
309C2×C4×C13C22×D412yes—
310C2×C4×C13C22×D411yescharacteristic
311C2×C4×C13C22×Q812yes—
312C2×C4×C132−1+412yes—
313C2×C4×C13C2511yescharacteristic
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—48no—
322C2×Dic13—42no—
323C2×Dic13—42no—
324C2×Dic13—42no—
325C2×Dic13—42no—
326C2×Dic13—48no—
327C2×Dic13—48no—
328C2×Dic13—84no—
329C2×Dic13AGL(1,ℤ/8)14yes—
330C2×Dic13C22×D412yes—
331C2×Dic13C22×D412yes—
332C2×Dic13C22×D412yes—
333C2×Dic13C22×D412yes—
334Dic26—28no—
335Dic26—48no—
336Dic26—48no—
337Dic26—48no—
338Dic26—84no—
339C8×C13—22no—
340C8×C13C22×Q814yescomplemented
341#1055—22no—
342#1055—22no—
343C23×Q8—261no—
344C22×D8C2×D1311yescharacteristic
345#554—138no—
346#554—264no—
347D4×Q8—138no—
348D4×Q8—264no—
349C2×C4⋊Q8—131no—
350C2×C4⋊Q8—131no—
351C2×C4⋊Q8—131no—
352C2×C4⋊Q8—131no—
353C2×#125—131no—
354C2×#125—131no—
355C2×C22⋊Q8—261no—
356C2×C22⋊Q8—261no—
357C2×C22⋊Q8—261no—
358C2×C22⋊Q8—261no—
359C2×C22⋊Q8—261no—
360C2×C22⋊Q8—261no—
361C2×C4×Q8—131no—
362C2×C4×D4—131no—
363C2×C4×D4—131no—
364C2×C4×D4—131no—
365C2×C4×D4—131no—
366C2×C4×D4C2×D1311yescharacteristic
367C2×C4×D4C2×D1311yescharacteristic
368C22×C4⋊C4—261no—
369#501—138no—
370#501—138no—
371#498—138no—
372#478—138no—
373#478—138no—
374#476—138no—
375#476—138no—
376#476—138no—
377#474—138no—
378#446—138no—
379#442—138no—
380#442C2×D1318yes—
381C4×D8—138no—
382C2×#107—131no—
383C2×#107—131no—
384C2×#107—131no—
385C2×#106—131no—
386C2×#106—131no—
387C2×#106—131no—
388C2×#106—131no—
389C2×#106—131no—
390C2×#106C2×D1311yescharacteristic
391C2×C4⋊C8—131no—
392C2×C4⋊C8—131no—
393C2×C4⋊C8—131no—
394C2×#102—131no—
395C2×#102—131no—
396C2×#102—131no—
397C2×#102—131no—
398C2×#102C2×D1311yescharacteristic
399C2×#102C2×D1311yescharacteristic
400C2×#97—131no—
401C2×#97C2×D1311yescharacteristic
402C2×C4×C8—131no—
403C22×C13—24no—
404C22×C13—24no—
405C22×C13—48no—
406C22×C13—48no—
407C22×C13—42no—
408C22×C13—42no—
409C22×C13—42no—
410C22×C13—42no—
411C22×C13D4×Q812yes—
412C22×C13C2×AGL(1,ℤ/8)12yes—
413C22×C13#57712yes—
414C22×C13C23×D411yescharacteristic
415C4×C13—22no—
416C4×C13—22no—
417C4×C13—42no—
418C4×C13—42no—
419C4×C13D4×Q812yes—
420C4×C13C23×Q811yescharacteristic
421C4×C13C2×2−1+411yescharacteristic
422Dic13—22no—
423Dic13—22no—
424Dic13—22no—
425Dic13—42no—
426Dic13—42no—
427Dic13—42no—
428Dic13—42no—
429Dic13C2×AGL(1,ℤ/8)14yes—
430C22×Q8—131no—
431C22×Q8—261no—
432C22×Q8—261no—
433C22×Q8—261no—
434C22×Q8—268no—
435C22×Q8—261no—
436C22×Q8—528no—
437C22×D4C22×D1311yescharacteristic
438C22×D4C22×D1311yescharacteristic
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—261no—
442C23×C4—261no—
443C23×C4—261no—
444C23×C4—261no—
445C2×D8Dic2618yescomplemented
446C2×D8C22×D1314yes—
447C22×C8—131no—
448C22×C8—131no—
449C22×C8C22×D1311yescharacteristic
450C22×C8C22×D1311yescharacteristic
451C4⋊Q8—134no—
452C4⋊Q8—134no—
453C4⋊Q8—134no—
454C4⋊Q8—134no—
455C4⋊Q8—262no—
456C4⋊Q8—262no—
457C4⋊Q8—262no—
458C4⋊Q8—262no—
459#125—134no—
460#125—134no—
461#125—262no—
462#125—262no—
463C22⋊Q8—268no—
464C22⋊Q8—268no—
465C22⋊Q8—268no—
466C22⋊Q8—268no—
467C22⋊Q8—268no—
468C22⋊Q8—268no—
469C4×Q8—134no—
470C4×Q8—134no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—134no—
474C4×D4—134no—
475C4×D4—134no—
476C4×D4—134no—
477C4×D4—262no—
478C4×D4—262no—
479C4×D4—262no—
480C4×D4—262no—
481C4×D4C22×D1314yes—
482C4×D4C22×D1314yes—
483C2×C4⋊C4—131no—
484C2×C4⋊C4—131no—
485C2×C4⋊C4—131no—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—131no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—268no—
491C2×C4⋊C4—261no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4—261no—
495C2×C4⋊C4—261no—
496C2×C4⋊C4—261no—
497C2×C4⋊C4—261no—
498C2×C4⋊C4—261no—
499C2×C4⋊C4C22×D1311yescharacteristic
500C2×C4⋊C4C22×D1311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—261no—
504C2×C22⋊C4—261no—
505C2×C22⋊C4—261no—
506C2×C22⋊C4—261no—
507C2×C42—131no—
508C2×C42—131no—
509C2×C42C22×D1311yescharacteristic
510#107—134no—
511#107—134no—
512#107—134no—
513#106—134no—
514#106—134no—
515#106—134no—
516#106—134no—
517#106—134no—
518#106C22×D1314yes—
519C4⋊C8—134no—
520C4⋊C8—134no—
521C4⋊C8—134no—
522#102—134no—
523#102—134no—
524#102—134no—
525#102—134no—
526#102C22×D1314yes—
527#102C22×D1314yes—
528#97—134no—
529#97C22×D1314yes—
530C4×C8—134no—
531C2×C13—44no—
532C2×C13—44no—
533C2×C13#338414yescomplemented
534C2×C13C2×D4×Q811yescharacteristic
535C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
536C2×C13C2×#57711yescharacteristic
537C24—21no—
538C24—21no—
539C2×Q8—134no—
540C2×Q8—264no—
541C2×Q8—264no—
542C2×Q8—264no—
543C2×Q8—264no—
544C2×Q8—264no—
545C2×Q8—524no—
546C2×Q8—524no—
547C2×Q8—524no—
548C2×Q8—5232no—
549C2×Q8—1042no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4C2×Dic2614yes—
555C2×D4C2×Dic2614yescomplemented
556C2×D4C23×D1312yes—
557C2×D4C23×D1312yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—44no—
563C22×C4—82no—
564C22×C4—131no—
565C22×C4—131no—
566C22×C4—131no—
567C22×C4—131no—
568C22×C4—264no—
569C22×C4—264no—
570C22×C4—264no—
571C22×C4—264no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—524no—
577C22×C4—524no—
578C22×C4—524no—
579C22×C4—1042no—
580C22×C4D4×D1311yescharacteristic
581C22×C4D4×D1311yescharacteristic
582C22×C4C23×D1311yescharacteristic
583D8C2×Dic26116yescomplemented
584C2×C8—22no—
585C2×C8—132no—
586C2×C8—132no—
587C2×C8—262no—
588C2×C8—262no—
589C2×C8C2×Dic2614yescomplemented
590C2×C8C23×D1312yes—
591C2×C8C23×D1312yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—134no—
595C4⋊C4—134no—
596C4⋊C4—134no—
597C4⋊C4—132no—
598C4⋊C4—132no—
599C4⋊C4—132no—
600C4⋊C4—132no—
601C4⋊C4—264no—
602C4⋊C4—264no—
603C4⋊C4—264no—
604C4⋊C4—264no—
605C4⋊C4—264no—
606C4⋊C4—261no—
607C4⋊C4—261no—
608C4⋊C4—261no—
609C4⋊C4—261no—
610C4⋊C4—264no—
611C4⋊C4—264no—
612C4⋊C4—264no—
613C4⋊C4C23×D1312yes—
614C4⋊C4C23×D1312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—264no—
618C22⋊C4—264no—
619C22⋊C4—264no—
620C22⋊C4—264no—
621C42—132no—
622C42—132no—
623C42—132no—
624C42—132no—
625C42D4×D1312yes—
626C42C23×D1312yes—
627C13C2×#338411yescharacteristic, complemented, Sylow
628C23—24no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23C2×D4×D1311yescharacteristic
637Q8—268no—
638Q8—528no—
639Q8—528no—
640Q8—528no—
641Q8—1044no—
642D4—24no—
643D4—24no—
644D4—22no—
645D4—22no—
646D4C22×Dic2614yes—
647D4C22×Dic2614yescomplemented
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—84no—
656C2×C4—134no—
657C2×C4—132no—
658C2×C4—132no—
659C2×C4—132no—
660C2×C4—132no—
661C2×C4—262no—
662C2×C4—262no—
663C2×C4—262no—
664C2×C4—262no—
665C2×C4—262no—
666C2×C4—262no—
667C2×C4—262no—
668C2×C4—528no—
669C2×C4—528no—
670C2×C4—528no—
671C2×C4—522no—
672C2×C4—522no—
673C2×C4—522no—
674C2×C4—522no—
675C2×C4—1044no—
676C2×C4C22×Dic2612yes—
677C2×C4C2×D4×D1312yes—
678C2×C4C2×D4×D1312yes—
679C2×C4C2×D4×D1311yescharacteristic
680C2×C4#8825712yes—
681C2×C4C24×D1311yescharacteristic
682C8—22no—
683C8—262no—
684C8—262no—
685C8C22×Dic2614yescomplemented
686C22—24no—
687C22—24no—
688C22—48no—
689C22—48no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22D4×Dic2612yes—
695C22D13×AGL(1,ℤ/8)12yes—
696C22#1171948012yes—
697C22C22×D4×D1311yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—134no—
703C4—262no—
704C4—262no—
705C4—262no—
706C4—522no—
707C4—522no—
708C4—522no—
709C4—522no—
710C4D4×Dic2612yes—
711C4C23×Dic2611yescharacteristic
712C4C2×#8825711yescharacteristic
713C2—44no—
714C2—44no—
715C2#1312773614yesdirect product factor
716C2C2×D4×Dic2611yescharacteristic
717C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
718C2C2×#1171948011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#442C2
socleC23×C13C22×D4
prime radicalC22×C13×D8C22
hypercenterC2×#442D13
hypocenterC13C2×#3384
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#11719244C2semidirect
2. C2×D4×Dic26C2semidirect
3. #13127736C2direct (N × H)
4. C2×#11718363C2semidirect
5. C2×#11718517C2semidirect
6. C2×#11718516C2semidirect
7. C2×#11718670C2semidirect
8. C2×#11718427C2semidirect
9. C2×#11718669C2semidirect
10. C2×#11718422C2semidirect
11. C2×#11718422C2semidirect
12. C2×#11718420C2semidirect
13. C2×#11718362C2semidirect
29. #11719244C22semidirect
31. D4×Dic26C22semidirect
62. #11718670C22semidirect
63. #11718669C22semidirect
69. #11718517C22semidirect
70. #11718516C22semidirect
71. #11718427C22semidirect
72. #11718422C22semidirect
73. #11718422C22semidirect
74. #11718420C22semidirect
75. #11718363C22semidirect
76. #11718362C22semidirect
92. C2×C13×D8Q8semidirect
186. C2×D4×C13C2×Q8semidirect
225. C13×D8C2×Q8semidirect
227. C2×C8×C13C2×Q8semidirect
299. D4×C13C22×Q8semidirect
340. C8×C13C22×Q8semidirect
445. C2×D8Dic26semidirect
533. C2×C13#3384semidirect
555. C2×D4C2×Dic26semidirect
583. D8C2×Dic26semidirect
589. C2×C8C2×Dic26semidirect
627. C13C2×#3384semidirect
647. D4C22×Dic26semidirect
685. C8C22×Dic26semidirect
715. C2#13127736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192442
C2×D4×Dic262
#131277362
C2×#117183632
C2×#117185172
C2×#117185162
C2×#117186702
C2×#117184272
C2×#117186692
C2×#117184222
C2×#117184202
C2×#117183622
C2×#117188132
C2×D8×Dic132
C2×C13×#4422
C2×#338413