Finite Group Databasebeta

← C2×#13124620 #16730416

Subgroups — C2×#13124620 #16730416

Order 3328.

2162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719222C211yesmaximal, characteristic, complemented
2C2×#41×Dic13C211yesmaximal, characteristic
3#13124620C2116yesmaximal, direct product factor
4C2×#11718457C211yesmaximal, characteristic, complemented
5C2×#11718460C211yesmaximal, characteristic, complemented
6C2×#11718455C211yesmaximal, characteristic, complemented
7C2×#11718452C211yesmaximal, characteristic, complemented
8C2×#11718424C211yesmaximal, characteristic, complemented
9C2×#11718427C211yesmaximal, characteristic, complemented
10C2×#11718422C211yesmaximal, characteristic, complemented
11C2×#11718420C211yesmaximal, characteristic, complemented
12C2×#11718767C211yesmaximal, characteristic, complemented
13C2×#11718659C211yesmaximal, characteristic, complemented
14C22×#88054C211yesmaximal, characteristic, complemented
15C2×#11718894C211yesmaximal, characteristic
16C2×C13×#416C211yesmaximal, characteristic
17C22×C13×#41C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×C13×#117C2211yescharacteristic
20#41×Dic13—24no—
21#41×Dic13C2218yes—
22C2×Q8×Dic13C2211yescharacteristic
23C2×Q8×Dic13C2211yescharacteristic
24C2×D4×Dic13—21no—
25C2×D4×Dic13—21no—
26C2×D4×Dic13C2211yescharacteristic
27C2×D4×Dic13C2211yescharacteristic
28C2×#88180—21no—
29C2×#88180C2211yescharacteristic
30C2×#88180C2211yescharacteristic
31C22×C4×Dic13—21no—
32C22×C4×Dic13C2211yescharacteristic
33C23×#1055C2211yescharacteristic
34#11719222—24no—
35#11719222C2218yescomplemented
36C2×#88144C2211yescharacteristic
37C2×#88144C2211yescharacteristic
38C2×#88142C2211yescharacteristic
39C2×#88142C2211yescharacteristic
40C2×#88132—21no—
41C2×#88132—21no—
42C2×C4×Dic26—21no—
43C2×C4×Dic26—21no—
44C13×#416C2218yes—
45C2×C13×#103C2211yescharacteristic
46C2×C13×#103C2211yescharacteristic
47C2×C13×#102C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49#11718894C2218yes—
50C2×#88075C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88072C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54#11718767C2218yescomplemented
55C2×#88058C2211yescharacteristic
56C2×#88058C2211yescharacteristic
57C2×#88057C2211yescharacteristic
58C2×#88057C2211yescharacteristic
59C2×#88054C2211yescharacteristic
60C2×#88054C2211yescharacteristic
61C2×#88054C2211yescharacteristic
62C2×#88054C2211yescharacteristic
63C2×#88054C2218yescomplemented
64#11718659C2218yescomplemented
65C2×#88048C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88047C2211yescharacteristic
68C2×#88047C2211yescharacteristic
69#11718460C2218yescomplemented
70#11718457C2218yescomplemented
71#11718455C2218yescomplemented
72#11718452C2218yescomplemented
73#11718427C2218yescomplemented
74#11718424C2218yescomplemented
75#11718422C2218yescomplemented
76#11718420C2218yescomplemented
77C2×C13×#41—22no—
78C2×C13×#41—24no—
79C2×C13×#41Q818yescomplemented
80C2×C13×#41C2314yes—
81C22×Q8×C13C2311yescharacteristic
82C22×D4×C13—21no—
83C22×D4×C13C2311yescharacteristic
84C23×C4×C13—21no—
85C23×C4×C13C2311yescharacteristic
86C23×Dic13—21no—
87C23×Dic13—21no—
88C23×Dic13D411yescharacteristic
89C23×Dic13D411yescharacteristic
90C22×Dic26—21no—
91C22×Dic26—21no—
92C22×C8×C13—24no—
93C22×C8×C13C2311yescharacteristic
94C22×C8×C13C2311yescharacteristic
95C22×C8×C13C2314yes—
96C13×#117—22no—
97C13×#117C2314yes—
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C13×C22⋊C4—21no—
101C2×C42×C13—21no—
102C2×C22⋊Dic13—21no—
103C2×C22⋊Dic13—21no—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13—21no—
106Q8×Dic13—22no—
107Q8×Dic13—22no—
108Q8×Dic13C2314yes—
109Q8×Dic13C2314yes—
110D4×Dic13—28no—
111D4×Dic13—28no—
112D4×Dic13—22no—
113D4×Dic13—22no—
114D4×Dic13C2314yes—
115D4×Dic13C2314yes—
116#88180—22no—
117#88180—22no—
118#88180—28no—
119#88180C2314yes—
120#88180C2314yes—
121C2×C4⋊Dic13—21no—
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13—21no—
124C2×C4⋊Dic13—21no—
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2311yescharacteristic
128C2×C4⋊Dic13C2311yescharacteristic
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101—21no—
133C2×C4×Dic13—21no—
134C2×C4×Dic13—21no—
135C2×C4×Dic13—21no—
136C2×C4×Dic13—21no—
137C2×C4×Dic13—28no—
138C2×C4×Dic13D411yescharacteristic
139C2×C4×Dic13D411yescharacteristic
140C2×C4×Dic13D414yes—
141C2×C4×Dic13C2311yescharacteristic
142C2×C4×Dic13C2311yescharacteristic
143C2×C4×Dic13C2314yes—
144C22×#1055—24no—
145C22×#1055C2314yes—
146C22×#1055C2311yescharacteristic
147C22×#1055C2311yescharacteristic
148#88144—22no—
149#88144—22no—
150#88144C2314yes—
151#88144C2314yes—
152#88142—22no—
153#88142—22no—
154#88142C2314yes—
155#88142C2314yes—
156#88132—28no—
157#88132—28no—
158C4×Dic26—28no—
159C4×Dic26—28no—
160C13×#103C2314yes—
161C13×#103C2314yes—
162C13×#102C2314yes—
163C13×#102C2314yes—
164#88075C2314yes—
165#88075C2314yes—
166#88072C2314yes—
167#88072C2314yes—
168#88058C2314yes—
169#88058C2314yes—
170#88057C2314yes—
171#88057C2314yes—
172#88054C2314yes—
173#88054C2314yes—
174#88054C2314yes—
175#88054C2314yes—
176#88048C2314yes—
177#88048C2314yes—
178#88047C2314yes—
179#88047C2314yes—
180C2×#3076—131nomaximal, Sylow
181C24×C13—21no—
182C24×C13C2×D411yescharacteristic
183C13×#41—216no—
184C13×#41—28no—
185C13×#41C2×Q8116yescomplemented
186C2×Q8×C13—21no—
187C2×Q8×C13—22no—
188C2×Q8×C13C2×Q814yes—
189C2×Q8×C13C2412yes—
190C2×D4×C13—28no—
191C2×D4×C13—24no—
192C2×D4×C13—21no—
193C2×D4×C13—22no—
194C2×D4×C13C2×Q814yes—
195C2×D4×C13C2412yes—
196C22×C4×C13—21no—
197C22×C4×C13—28no—
198C22×C4×C13—24no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×Q814yes—
204C22×C4×C13#4114yes—
205C22×C4×C13C2411yescharacteristic
206C22×C4×C13C2412yes—
207C22×Dic13—24no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—24no—
213C22×Dic13—24no—
214C22×Dic13—42no—
215C22×Dic13—44no—
216C22×Dic13—44no—
217C22×Dic13C2×D414yes—
218C22×Dic13C2×D411yescharacteristic
219C22×Dic13C2×D411yescharacteristic
220C22×Dic13C2×D411yescharacteristic
221C22×Dic13C2×D414yes—
222C22×Dic13C2×D411yescharacteristic
223C2×Dic26—24no—
224C2×Dic26—24no—
225C2×Dic26—44no—
226C2×Dic26—44no—
227C2×C8×C13—22no—
228C2×C8×C13—22no—
229C2×C8×C13—28no—
230C2×C8×C13C2412yes—
231C2×C8×C13C2412yes—
232C13×C4⋊C4—21no—
233C13×C4⋊C4—21no—
234C13×C4⋊C4C2412yes—
235C13×C4⋊C4C2412yes—
236C13×C22⋊C4—24no—
237C42×C13—24no—
238C22⋊Dic13—24no—
239C22⋊Dic13—24no—
240C22⋊Dic13—24no—
241C22⋊Dic13—24no—
242C4⋊Dic13—21no—
243C4⋊Dic13—21no—
244C4⋊Dic13—21no—
245C4⋊Dic13—21no—
246C4⋊Dic13—24no—
247C4⋊Dic13—24no—
248C4⋊Dic13—24no—
249C4⋊Dic13—24no—
250C4⋊Dic13C2412yes—
251C4⋊Dic13C2412yes—
252C4⋊Dic13C2412yes—
253C4⋊Dic13C2412yes—
254#6101—24no—
255#6101—24no—
256#6101—24no—
257#6101—24no—
258C4×Dic13—24no—
259C4×Dic13—24no—
260C4×Dic13—24no—
261C4×Dic13—24no—
262C4×Dic13C2×D414yes—
263C4×Dic13C2×D414yes—
264C4×Dic13C2×D412yes—
265C4×Dic13C2×D412yes—
266C4×Dic13C2412yes—
267C4×Dic13C2412yes—
268C2×#1055—22no—
269C2×#1055—22no—
270C2×#1055—28no—
271C2×#1055C2412yes—
272C2×#1055C2412yes—
273C2×#533—131no—
274C2×C4×#41—131no—
275#3076—1316no—
276C2×#479—131no—
277C2×#479—131no—
278C2×#477—131no—
279C2×#475—131no—
280C2×#478—131no—
281C2×#478—131no—
282C2×#476—131no—
283C2×#474—131no—
284C2×#427—131no—
285C2×#427—131no—
286C22×C4⋊C8—131no—
287C2×#416—131no—
288C2×#416D1311yescharacteristic
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—24no—
292C23×C13—22no—
293C23×C13—42no—
294C23×C13—42no—
295C23×C13C22⋊Q814yes—
296C23×C13C22×D412yes—
297C23×C13C22×D411yescharacteristic
298Q8×C13—24no—
299Q8×C13—22no—
300Q8×C13C22×Q814yes—
301D4×C13—216no—
302D4×C13—24no—
303D4×C13—22no—
304D4×C13C22×Q814yes—
305C2×C4×C13—24no—
306C2×C4×C13—22no—
307C2×C4×C13—216no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13C22⋊Q814yes—
313C2×C4×C13C22⋊Q818yes—
314C2×C4×C13C22×D412yes—
315C2×C4×C13C22×D411yescharacteristic
316C2×C4×C13C22×Q812yes—
317C2×C4×C13C22×Q814yes—
318C2×C4×C13C2×#4112yes—
319C2×C4×C13C2×#4114yes—
320C2×C4×C13C2511yescharacteristic
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—28no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—44no—
330C2×Dic13—48no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—48no—
336C2×Dic13#13514yes—
337C2×Dic13C22×D412yes—
338C2×Dic13C22×D412yes—
339C2×Dic13C22×D412yes—
340C2×Dic13C22×D412yes—
341Dic26—48no—
342Dic26—48no—
343C8×C13—22no—
344C8×C13—22no—
345#1055—22no—
346#1055—22no—
347C22×#41C2×D1311yescharacteristic
348C23×C8—131no—
349C23×C8C2×D1311yescharacteristic
350#533—138no—
351#533—264no—
352C2×C4⋊Q8—131no—
353C2×C4⋊Q8—131no—
354C2×#125—131no—
355C2×#125—131no—
356C2×C22⋊Q8—261no—
357C2×C22⋊Q8—261no—
358C4×#41—138no—
359C4×#41—264no—
360C2×C4×Q8—131no—
361C2×C4×Q8—131no—
362C2×C4×Q8—261no—
363C2×C4×Q8—261no—
364C2×C4×D4—131no—
365C2×C4×D4—131no—
366C2×C4×D4—261no—
367C2×C4×D4—261no—
368C2×#117—131no—
369C2×#117—131no—
370C2×#117—261no—
371C2×#117C2×D1311yescharacteristic
372C22×C42—131no—
373C22×C42—261no—
374#479—138no—
375#479—138no—
376#478—138no—
377#478—138no—
378#477—138no—
379#476—138no—
380#475—138no—
381#474—138no—
382#427—138no—
383#427—138no—
384C2×#107—131no—
385C2×#107—131no—
386C2×#107—131no—
387C2×#107—131no—
388C2×#106—131no—
389C2×#106—131no—
390C2×#106—131no—
391C2×#106—131no—
392C2×C4⋊C8—131no—
393C2×C4⋊C8—131no—
394C2×C4⋊C8—131no—
395C2×C4⋊C8—131no—
396C2×C4⋊C8—138no—
397#416—138no—
398#416C2×D1318yes—
399C2×#103—131no—
400C2×#103—131no—
401C2×#103C2×D1311yescharacteristic
402C2×#103C2×D1311yescharacteristic
403C2×#102—131no—
404C2×#102—131no—
405C2×#102C2×D1311yescharacteristic
406C2×#102C2×D1311yescharacteristic
407C22×C13—28no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—24no—
411C22×C13—48no—
412C22×C13—42no—
413C22×C13—42no—
414C22×C13C2×C22⋊Q814yes—
415C22×C13C2×C22⋊Q812yes—
416C22×C13C2×#13512yes—
417C22×C13#57512yes—
418C22×C13C23×D411yescharacteristic
419C4×C13—24no—
420C4×C13—42no—
421C4×C13—42no—
422C4×C13C2×C22⋊Q814yes—
423C4×C13C2×C22⋊Q812yes—
424C4×C13C23×Q811yescharacteristic
425C4×C13C22×#4111yescharacteristic
426Dic13—22no—
427Dic13—22no—
428Dic13—22no—
429Dic13—42no—
430Dic13—42no—
431Dic13—42no—
432Dic13—42no—
433Dic13C2×#13514yes—
434C2×#41—22no—
435C2×#41—24no—
436C2×#41Dic2618yescomplemented
437C2×#41C22×D1314yes—
438C22×Q8—261no—
439C22×Q8—261no—
440C22×Q8C22×D1311yescharacteristic
441C22×D4—21no—
442C22×D4C22×D1311yescharacteristic
443C23×C4—21no—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4—261no—
447C23×C4—261no—
448C23×C4C22×D1311yescharacteristic
449C22×C8—24no—
450C22×C8—131no—
451C22×C8—131no—
452C22×C8—134no—
453C22×C8—264no—
454C22×C8C22×D1311yescharacteristic
455C22×C8C22×D1311yescharacteristic
456C22×C8C22×D1314yes—
457C4⋊Q8—134no—
458C4⋊Q8—134no—
459C4⋊Q8—262no—
460C4⋊Q8—262no—
461#125—134no—
462#125—134no—
463#125—262no—
464#125—262no—
465C22⋊Q8—268no—
466C22⋊Q8—268no—
467C4×Q8—134no—
468C4×Q8—134no—
469C4×Q8—268no—
470C4×Q8—268no—
471C4×Q8—262no—
472C4×Q8—262no—
473C4×D4—134no—
474C4×D4—134no—
475C4×D4—262no—
476C4×D4—262no—
477C4×D4—268no—
478C4×D4—268no—
479#117—22no—
480#117—134no—
481#117—134no—
482#117—268no—
483#117—262no—
484#117—262no—
485#117C22×D1314yes—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—131no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—261no—
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⋊C4C22×D1311yescharacteristic
499C2×C4⋊C4C22×D1311yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—261no—
502C2×C22⋊C4—261no—
503C2×C22⋊C4—261no—
504C2×C22⋊C4—261no—
505C2×C42—21no—
506C2×C42—134no—
507C2×C42—131no—
508C2×C42—131no—
509C2×C42—131no—
510C2×C42—131no—
511C2×C42—134no—
512C2×C42—268no—
513C2×C42—261no—
514C2×C42—261no—
515C2×C42—261no—
516C2×C42—261no—
517#107—134no—
518#107—134no—
519#107—134no—
520#107—134no—
521#106—134no—
522#106—134no—
523#106—134no—
524#106—134no—
525C4⋊C8—134no—
526C4⋊C8—134no—
527C4⋊C8—134no—
528C4⋊C8—134no—
529#103—134no—
530#103—134no—
531#103C22×D1314yes—
532#103C22×D1314yes—
533#102—134no—
534#102—134no—
535#102C22×D1314yes—
536#102C22×D1314yes—
537C2×C13—24no—
538C2×C13—44no—
539C2×C13#307614yescomplemented
540C2×C13C22×C22⋊Q811yescharacteristic
541C2×C13C22×#13511yescharacteristic
542C2×C13C2×#57511yescharacteristic
543C24—21no—
544C24D4×D1311yescharacteristic
545#41—216no—
546#41—28no—
547#41C2×Dic26116yescomplemented
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—264no—
551C2×Q8—264no—
552C2×Q8—524no—
553C2×Q8—524no—
554C2×Q8C2×Dic2614yes—
555C2×Q8C23×D1312yes—
556C2×D4—28no—
557C2×D4—24no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4C2×Dic2614yes—
561C2×D4C23×D1312yes—
562C22×C4—21no—
563C22×C4—28no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—131no—
568C22×C4—131no—
569C22×C4—131no—
570C22×C4—131no—
571C22×C4—134no—
572C22×C4—134no—
573C22×C4—264no—
574C22×C4—264no—
575C22×C4—264no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—524no—
581C22×C4—522no—
582C22×C4—524no—
583C22×C4C2×Dic2614yes—
584C22×C4D4×D1312yes—
585C22×C4D4×D1311yescharacteristic
586C22×C4#612914yes—
587C22×C4C23×D1311yescharacteristic
588C22×C4C23×D1312yes—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—28no—
592C2×C8—132no—
593C2×C8—132no—
594C2×C8—262no—
595C2×C8—262no—
596C2×C8—268no—
597C2×C8C23×D1312yes—
598C2×C8C23×D1312yes—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—132no—
602C4⋊C4—132no—
603C4⋊C4—132no—
604C4⋊C4—132no—
605C4⋊C4—264no—
606C4⋊C4—264no—
607C4⋊C4—264no—
608C4⋊C4—264no—
609C4⋊C4—264no—
610C4⋊C4—264no—
611C4⋊C4—264no—
612C4⋊C4—264no—
613C4⋊C4—261no—
614C4⋊C4—261no—
615C4⋊C4—261no—
616C4⋊C4—261no—
617C4⋊C4C23×D1312yes—
618C4⋊C4C23×D1312yes—
619C22⋊C4—24no—
620C22⋊C4—264no—
621C22⋊C4—264no—
622C22⋊C4—264no—
623C22⋊C4—264no—
624C42—24no—
625C42—134no—
626C42—134no—
627C42—132no—
628C42—132no—
629C42—132no—
630C42—132no—
631C42—264no—
632C42—264no—
633C42—264no—
634C42—264no—
635C13C2×#307611yescharacteristic, complemented, Sylow
636C23—22no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—42no—
641C23—42no—
642C23#8813214yes—
643C23C2×D4×D1312yes—
644C23C2×D4×D1311yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—528no—
648Q8—528no—
649Q8C22×Dic2614yes—
650D4—216no—
651D4—24no—
652D4—22no—
653D4C22×Dic2614yes—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—216no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—134no—
662C2×C4—132no—
663C2×C4—132no—
664C2×C4—132no—
665C2×C4—132no—
666C2×C4—268no—
667C2×C4—262no—
668C2×C4—262no—
669C2×C4—262no—
670C2×C4—262no—
671C2×C4—262no—
672C2×C4—262no—
673C2×C4—262no—
674C2×C4—528no—
675C2×C4—524no—
676C2×C4—528no—
677C2×C4—522no—
678C2×C4—522no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4#8813214yes—
682C2×C4#8813218yes—
683C2×C4C22×Dic2612yes—
684C2×C4C22×Dic2614yes—
685C2×C4C2×D4×D1312yes—
686C2×C4C2×D4×D1311yescharacteristic
687C2×C4C2×#612912yes—
688C2×C4C2×#612914yes—
689C2×C4C24×D1311yescharacteristic
690C8—22no—
691C8—22no—
692C8—262no—
693C8—262no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—48no—
699C22—42no—
700C22—42no—
701C22C2×#8813214yes—
702C22C2×#8813212yes—
703C22D13×#13512yes—
704C22#1171947312yes—
705C22C22×D4×D1311yescharacteristic
706C4—24no—
707C4—42no—
708C4—42no—
709C4—134no—
710C4—262no—
711C4—262no—
712C4—262no—
713C4—522no—
714C4—522no—
715C4—522no—
716C4—522no—
717C4C2×#8813214yes—
718C4C2×#8813212yes—
719C4C23×Dic2611yescharacteristic
720C4C22×#612911yescharacteristic
721C2—24no—
722C2—44no—
723C2#1312462014yesdirect product factor
724C2C22×#8813211yescharacteristic
725C2C2×D13×#13511yescharacteristic
726C2C2×#1171947311yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#416C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenterC2×#416D13
hypocenterC13C2×#3076
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#11719222C2semidirect
3. #13124620C2direct (N × H)
4. C2×#11718457C2semidirect
5. C2×#11718460C2semidirect
6. C2×#11718455C2semidirect
7. C2×#11718452C2semidirect
8. C2×#11718424C2semidirect
9. C2×#11718427C2semidirect
10. C2×#11718422C2semidirect
11. C2×#11718420C2semidirect
12. C2×#11718767C2semidirect
13. C2×#11718659C2semidirect
14. C22×#88054C2semidirect
35. #11719222C22semidirect
54. #11718767C22semidirect
63. C2×#88054C22semidirect
64. #11718659C22semidirect
69. #11718460C22semidirect
70. #11718457C22semidirect
71. #11718455C22semidirect
72. #11718452C22semidirect
73. #11718427C22semidirect
74. #11718424C22semidirect
75. #11718422C22semidirect
76. #11718420C22semidirect
79. C2×C13×#41Q8semidirect
185. C13×#41C2×Q8semidirect
436. C2×#41Dic26semidirect
539. C2×C13#3076semidirect
547. #41C2×Dic26semidirect
635. C13C2×#3076semidirect
723. C2#13124620direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192222
C2×#41×Dic132
#131246202
C2×#117184572
C2×#117184602
C2×#117184552
C2×#117184522
C2×#117184242
C2×#117184272
C2×#117184222
C2×#117184202
C2×#117187672
C2×#117186592
C22×#880542
C2×#117188942
C2×C13×#4162
C2×#307613