Finite Group Databasebeta

← C2×#13124699 #16730513

Subgroups — C2×#13124699 #16730513

Order 3328.

2094 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×#11719394C211yesmaximal, characteristic, complemented
2C2×#11719251C211yesmaximal, characteristic
3#13124699C2116yesmaximal, direct product factor
4C2×#11718538C211yesmaximal, characteristic, complemented
5C2×#11718724C211yesmaximal, characteristic, complemented
6C2×#11718512C211yesmaximal, characteristic, complemented
7C2×#11718515C211yesmaximal, characteristic, complemented
8C2×#11718424C211yesmaximal, characteristic, complemented
9C2×#11718669C211yesmaximal, characteristic, complemented
10C2×#11718422C211yesmaximal, characteristic, complemented
11C2×#11718542C211yesmaximal, characteristic, complemented
12C2×D13×#106C211yesmaximal, characteristic, complemented
13C2×#11718500C211yesmaximal, characteristic, complemented
14C2×#11718432C211yesmaximal, characteristic
15C2×#11718433C211yesmaximal, characteristic
16C2×C13×#478C211yesmaximal, characteristic, complemented
17C22×#6129C2211yescharacteristic
18C2×C13×#125C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C2×D4×Dic13C2211yescharacteristic
21C2×C4×C22⋊D13—21no—
22C22×#6101—21no—
23C22×#6094C2211yescharacteristic
24C22×C8×D13C2211yescharacteristic
25#11719394—24no—
26#11719394C2218yescomplemented
27#11719251—24no—
28#11719251C2218yes—
29C2×#88151—21no—
30C2×#88150—21no—
31C2×#88146C2211yescharacteristic
32C2×C4⋊C4×D13C2211yescharacteristic
33C2×C4⋊C4×D13C2211yescharacteristic
34C2×#88144C2211yescharacteristic
35C2×#88143—21no—
36C2×#88142—21no—
37C2×#88142C2211yescharacteristic
38C2×#88141C2211yescharacteristic
39C2×#88135—21no—
40C2×#88131—21no—
41C2×#88126C2211yescharacteristic
42C2×#88123C2211yescharacteristic
43C2×C4×Dic26C2211yescharacteristic
44C13×#478C2218yescomplemented
45C2×C13×#107C2211yescharacteristic
46C2×C13×#106C2211yescharacteristic
47C2×C13×C4⋊C8C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49C2×C13×#102C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88057C2211yescharacteristic
53C2×#88057C2211yescharacteristic
54C2×#88056C2211yescharacteristic
55C2×#88056C2211yescharacteristic
56C2×#88054C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58#11718724C2218yescomplemented
59#11718669C2218yescomplemented
60C2×#88050C2211yescharacteristic
61C2×#88050C2211yescharacteristic
62C2×#88048C2211yescharacteristic
63C2×#88048C2211yescharacteristic
64C2×#88048C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×C4⋊#1055C2211yescharacteristic
67#11718542C2218yescomplemented
68#11718538C2218yescomplemented
69D13×#106C2218yescomplemented
70#11718515C2218yescomplemented
71#11718512C2218yescomplemented
72#11718500C2218yescomplemented
73#11718433C2218yes—
74#11718432C2218yes—
75#11718424C2218yescomplemented
76#11718422C2218yescomplemented
77C22×D4×C13C2311yescharacteristic
78C23×C4×C13—21no—
79C22×C22⋊D13—21no—
80C23×Dic13—21no—
81C23×Dic13—21no—
82C2×#6129—22no—
83C2×#6129—24no—
84C2×#6129Q818yescomplemented
85C2×#6129C2314yes—
86C22×C4×D13—21no—
87C22×C4×D13—21no—
88C22×C4×D13C2311yescharacteristic
89C22×Dic26—21no—
90C22×Dic26—21no—
91C22×Dic26C2311yescharacteristic
92C22×C8×C13C2311yescharacteristic
93C22×C8×C13C2311yescharacteristic
94C13×#125—22no—
95C13×#125C2314yes—
96C4×D4×C13—22no—
97C4×D4×C13C2314yes—
98C2×C13×C4⋊C4—21no—
99C2×C13×C4⋊C4—21no—
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C22⋊C4—21no—
104C2×C42×C13C2311yescharacteristic
105C2×C22⋊Dic13—21no—
106D4×Dic13—22no—
107D4×Dic13C2314yes—
108C4×C22⋊D13—28no—
109C2×#6103—21no—
110C2×#6103D411yescharacteristic
111C2×#6103D411yescharacteristic
112C2×C4⋊Dic13—21no—
113C2×C4⋊Dic13—21no—
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116C2×C4⋊Dic13C2311yescharacteristic
117C2×#6101—21no—
118C2×#6101—21no—
119C2×#6101—21no—
120C2×#6101—21no—
121C2×#6101—21no—
122C2×#6101—21no—
123C2×#6101—28no—
124C2×#6101D411yescharacteristic
125C2×#6101D411yescharacteristic
126C2×C4×Dic13—21no—
127C2×C4×Dic13—21no—
128C2×C4×Dic13—21no—
129C2×C4×Dic13C2311yescharacteristic
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C2×#6094—24no—
133C2×#6094C2314yes—
134C2×C8×D13—24no—
135C2×C8×D13C2314yes—
136#88151—28no—
137#88150—28no—
138#88146—22no—
139#88146C2314yes—
140C4⋊C4×D13—22no—
141C4⋊C4×D13—22no—
142C4⋊C4×D13C2314yes—
143C4⋊C4×D13C2314yes—
144#88144—22no—
145#88144C2314yes—
146#88143—28no—
147#88142—28no—
148#88142—22no—
149#88142C2314yes—
150#88141—22no—
151#88141C2314yes—
152#88135—28no—
153#88131—28no—
154#88126D414yes—
155#88126C2314yes—
156#88123—22no—
157#88123C2314yes—
158C4×Dic26—22no—
159C4×Dic26C2314yes—
160C13×#107C2314yes—
161C13×#106C2314yes—
162C13×C4⋊C8C2314yes—
163C13×#102C2314yes—
164C13×#102C2314yes—
165#88072C2314yes—
166#88072C2314yes—
167#88057C2314yes—
168#88057C2314yes—
169#88056C2314yes—
170#88056C2314yes—
171#88054C2314yes—
172#88054C2314yes—
173#88050C2314yes—
174#88050C2314yes—
175#88048C2314yes—
176#88048C2314yes—
177#88048C2314yes—
178#88047C2314yes—
179C4⋊#1055C2314yes—
180C2×#3084—131nomaximal, Sylow
181C24×C13—21no—
182C23×D13C2×D411yescharacteristic
183C2×D4×C13—21no—
184C2×D4×C13—22no—
185C2×D4×C13C2×Q814yes—
186C2×D4×C13C2412yes—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—24no—
191C22×C4×C13—82no—
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2×D411yescharacteristic
194C22×C4×C13C2411yescharacteristic
195C2×C22⋊D13—28no—
196C2×C22⋊D13—24no—
197C22×Dic13—21no—
198C22×Dic13—28no—
199C22×Dic13—24no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—24no—
204C22×Dic13—82no—
205C22×Dic13C2×D411yescharacteristic
206C22×Dic13C2×D411yescharacteristic
207C22×Dic13C2×D411yescharacteristic
208#6129—216no—
209#6129—28no—
210#6129C2×Q8116yescomplemented
211C2×C4×D13—24no—
212C2×C4×D13—24no—
213C2×C4×D13—82no—
214C2×C4×D13—82no—
215C2×C4×D13C2×D412yes—
216C2×C4×D13C2×Q814yes—
217C2×C4×D13#4114yes—
218C2×C4×D13C2412yes—
219C2×Dic26—21no—
220C2×Dic26—22no—
221C2×Dic26—24no—
222C2×Dic26—24no—
223C2×Dic26—82no—
224C2×Dic26—82no—
225C2×Dic26C2×Q814yes—
226C2×Dic26C2412yes—
227C2×C8×C13—22no—
228C2×C8×C13—22no—
229C2×C8×C13C2412yes—
230C2×C8×C13C2412yes—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—21no—
233C13×C4⋊C4—24no—
234C13×C4⋊C4—24no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4C2412yes—
237C13×C4⋊C4C2412yes—
238C13×C4⋊C4C2412yes—
239C13×C22⋊C4—24no—
240C42×C13C2×D412yes—
241C42×C13C2412yes—
242C22⋊Dic13—24no—
243#6103—24no—
244#6103C2×D414yes—
245#6103C2×D414yes—
246C4⋊Dic13—21no—
247C4⋊Dic13—21no—
248C4⋊Dic13—21no—
249C4⋊Dic13—24no—
250C4⋊Dic13—24no—
251C4⋊Dic13C2412yes—
252C4⋊Dic13C2412yes—
253C4⋊Dic13C2412yes—
254#6101—24no—
255#6101—24no—
256#6101—24no—
257#6101—24no—
258#6101—24no—
259#6101—24no—
260#6101C2×D414yes—
261#6101C2×D414yes—
262C4×Dic13—24no—
263C4×Dic13—24no—
264C4×Dic13—24no—
265C4×Dic13C2×D412yes—
266C4×Dic13C2412yes—
267C2×#1055—22no—
268C2×#1055—22no—
269C2×#1055C2412yes—
270C2×#1055C2412yes—
271#6094—28no—
272C8×D13—28no—
273C2×#544—131no—
274C2×#520—131no—
275#3084—1316no—
276C2×#479—131no—
277C2×#479—131no—
278C2×#475—131no—
279C2×#475—131no—
280C2×#478—131no—
281C2×#478D1311yescharacteristic, complemented
282C2×#476—131no—
283C2×#476—131no—
284C2×#428—131no—
285C22×#106—131no—
286C2×#424—131no—
287C2×#417—131no—
288C2×#416—131no—
289C23×C13—24no—
290C23×C13—22no—
291C23×C13—42no—
292C23×C13—42no—
293C23×C13C22×D411yescharacteristic
294C22×D13—22no—
295C22×D13—22no—
296C22×D13C22⋊Q814yes—
297C22×D13C22×D412yes—
298D4×C13—24no—
299D4×C13—22no—
300D4×C13C22×Q814yes—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—84no—
310C2×C4×C13C22×D412yes—
311C2×C4×C13C22×D412yes—
312C2×C4×C13C22×D411yescharacteristic
313C2×C4×C13C22×Q812yes—
314C2×C4×C13C2×#4112yes—
315C2×C4×C13C2511yescharacteristic
316C22⋊D13—216no—
317C2×Dic13—24no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—216no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—84no—
329C2×Dic13C22⋊Q814yes—
330C2×Dic13C22×D412yes—
331C2×Dic13C22×D412yes—
332C2×Dic13C22×D412yes—
333C4×D13—84no—
334C4×D13—84no—
335C4×D13C22⋊Q818yes—
336C4×D13C22×Q814yes—
337C4×D13C2×#4114yes—
338Dic26—24no—
339Dic26—22no—
340Dic26—84no—
341Dic26—84no—
342Dic26C22×Q814yes—
343C8×C13—22no—
344C8×C13—22no—
345#1055—22no—
346#1055—22no—
347C22×#41—131no—
348C22×M16—131no—
349C23×C8—131no—
350#544—138no—
351#544—264no—
352C2×C4⋊Q8—131no—
353C2×C4⋊Q8—131no—
354C2×C4⋊Q8—261no—
355C2×#125—131no—
356C2×#125—261no—
357C2×#125C2×D1311yescharacteristic
358C2×C22⋊Q8—261no—
359C2×C22⋊Q8—261no—
360#520—138no—
361#520—264no—
362C2×C4×Q8—131no—
363C2×C4×Q8—131no—
364C2×C4×D4—131no—
365C2×C4×D4—261no—
366C2×C4×D4—261no—
367C2×C4×D4C2×D1311yescharacteristic
368C2×#117—131no—
369C2×#117—131no—
370C2×#117—261no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—261no—
374#479—138no—
375#479—138no—
376#478—138no—
377#478C2×D1318yescomplemented
378#476—138no—
379#476—138no—
380#475—138no—
381#475—138no—
382#428—138no—
383C2×#107—131no—
384C2×#107C2×D1311yescharacteristic
385C2×#106—131no—
386C2×#106—131no—
387C2×#106—131no—
388C2×#106—131no—
389C2×#106—131no—
390C2×#106—138no—
391C2×#106C2×D1311yescharacteristic
392#424—138no—
393C2×C4⋊C8—131no—
394C2×C4⋊C8—131no—
395C2×C4⋊C8—131no—
396C2×C4⋊C8C2×D1311yescharacteristic
397#417—138no—
398#416—138no—
399C2×#103—131no—
400C2×#103—131no—
401C2×#103—131no—
402C2×#103—131no—
403C2×#102—131no—
404C2×#102—131no—
405C2×#102C2×D1311yescharacteristic
406C2×#102C2×D1311yescharacteristic
407C22×C13—24no—
408C22×C13—48no—
409C22×C13—42no—
410C22×C13—42no—
411C22×C13C2×C22⋊Q812yes—
412C22×C13#57712yes—
413C22×C13#57712yes—
414C22×C13C23×D411yescharacteristic
415C2×D13—28no—
416C2×D13—22no—
417C2×D13—22no—
418C2×D13C2×C22⋊Q814yes—
419C4×C13—22no—
420C4×C13—22no—
421C4×C13—42no—
422C4×C13—42no—
423C4×C13—42no—
424C4×C13C2×C22⋊Q812yes—
425C4×C13C23×Q811yescharacteristic
426C4×C13C22×#4111yescharacteristic
427Dic13—24no—
428Dic13—22no—
429Dic13—22no—
430Dic13—42no—
431Dic13—42no—
432Dic13—42no—
433Dic13C2×C22⋊Q814yes—
434C2×#41—138no—
435C2×#41—134no—
436C2×#41—262no—
437C2×#41—264no—
438C22×Q8—131no—
439C22×Q8—261no—
440C22×Q8—261no—
441C22×D4—261no—
442C22×D4C22×D1311yescharacteristic
443C23×C4—21no—
444C23×C4—131no—
445C23×C4—261no—
446C23×C4—261no—
447C23×C4—261no—
448C23×C4—261no—
449C2×M16—134no—
450C2×M16—264no—
451C22×C8—131no—
452C22×C8—131no—
453C22×C8—134no—
454C22×C8—264no—
455C22×C8C22×D1311yescharacteristic
456C22×C8C22×D1311yescharacteristic
457C4⋊Q8—134no—
458C4⋊Q8—134no—
459C4⋊Q8—262no—
460C4⋊Q8—268no—
461C4⋊Q8—262no—
462#125—22no—
463#125—134no—
464#125—262no—
465#125—268no—
466#125C22×D1314yes—
467C22⋊Q8—268no—
468C22⋊Q8—268no—
469C4×Q8—134no—
470C4×Q8—134no—
471C4×Q8—262no—
472C4×Q8—262no—
473C4×D4—22no—
474C4×D4—134no—
475C4×D4—262no—
476C4×D4—268no—
477C4×D4—268no—
478C4×D4C22×D1314yes—
479#117—134no—
480#117—134no—
481#117—134no—
482#117—268no—
483#117—262no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—131no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—131no—
491C2×C4⋊C4—134no—
492C2×C4⋊C4—134no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—262no—
495C2×C4⋊C4—268no—
496C2×C4⋊C4—261no—
497C2×C4⋊C4—261no—
498C2×C4⋊C4—261no—
499C2×C4⋊C4—261no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4C22×D1311yescharacteristic
505C2×C4⋊C4C22×D1311yescharacteristic
506C2×C4⋊C4C22×D1311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—131no—
509C2×C22⋊C4—131no—
510C2×C22⋊C4—261no—
511C2×C22⋊C4—261no—
512C2×C42—131no—
513C2×C42—261no—
514C2×C42—261no—
515C2×C42—261no—
516C2×C42C22×D1311yescharacteristic
517#107—134no—
518#107C22×D1314yes—
519#106—134no—
520#106—134no—
521#106—134no—
522#106—134no—
523#106—134no—
524#106C22×D1314yes—
525C4⋊C8—134no—
526C4⋊C8—134no—
527C4⋊C8—134no—
528C4⋊C8C22×D1314yes—
529#103—134no—
530#103—134no—
531#103—134no—
532#103—134no—
533#102—134no—
534#102—134no—
535#102C22×D1314yes—
536#102C22×D1314yes—
537C2×C13—44no—
538C2×C13#308414yescomplemented
539C2×C13C22×C22⋊Q811yescharacteristic
540C2×C13C2×#57711yescharacteristic
541C2×C13C2×#57711yescharacteristic
542D13—24no—
543C24—21no—
544C24—131no—
545#41—1316no—
546#41—2616no—
547#41—268no—
548C2×Q8—134no—
549C2×Q8—132no—
550C2×Q8—264no—
551C2×Q8—261no—
552C2×Q8—264no—
553C2×Q8—262no—
554C2×Q8—1042no—
555C2×Q8—1042no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—264no—
559C2×D4—268no—
560C2×D4Q8×D1314yes—
561C2×D4C23×D1312yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—131no—
568C22×C4—132no—
569C22×C4—134no—
570C22×C4—134no—
571C22×C4—132no—
572C22×C4—131no—
573C22×C4—131no—
574C22×C4—264no—
575C22×C4—264no—
576C22×C4—264no—
577C22×C4—268no—
578C22×C4—264no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—1042no—
584C22×C4—1042no—
585C22×C4—1042no—
586C22×C4D4×D1311yescharacteristic
587C22×C4D4×D1311yescharacteristic
588C22×C4C23×D1311yescharacteristic
589M16—268no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—132no—
593C2×C8—132no—
594C2×C8—268no—
595C2×C8—262no—
596C2×C8—262no—
597C2×C8C23×D1312yes—
598C2×C8C23×D1312yes—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—134no—
605C4⋊C4—134no—
606C4⋊C4—132no—
607C4⋊C4—132no—
608C4⋊C4—132no—
609C4⋊C4—264no—
610C4⋊C4—264no—
611C4⋊C4—264no—
612C4⋊C4—264no—
613C4⋊C4—264no—
614C4⋊C4—264no—
615C4⋊C4—261no—
616C4⋊C4—261no—
617C4⋊C4—261no—
618C4⋊C4—264no—
619C4⋊C4—264no—
620C4⋊C4C23×D1312yes—
621C4⋊C4C23×D1312yes—
622C4⋊C4C23×D1312yes—
623C22⋊C4—24no—
624C22⋊C4—134no—
625C22⋊C4—134no—
626C22⋊C4—264no—
627C22⋊C4—264no—
628C42—132no—
629C42—132no—
630C42—264no—
631C42—264no—
632C42—264no—
633C42D4×D1312yes—
634C42C23×D1312yes—
635C13C2×#308411yescharacteristic, complemented, Sylow
636C23—24no—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—134no—
641C23—132no—
642C23—262no—
643C23—262no—
644C23C2×D4×D1311yescharacteristic
645Q8—134no—
646Q8—264no—
647Q8—262no—
648Q8—1044no—
649Q8—1044no—
650D4—24no—
651D4—22no—
652D4—2616no—
653D4C2×Q8×D1314yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—134no—
664C2×C4—132no—
665C2×C4—138no—
666C2×C4—134no—
667C2×C4—134no—
668C2×C4—132no—
669C2×C4—132no—
670C2×C4—2616no—
671C2×C4—262no—
672C2×C4—262no—
673C2×C4—264no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—522no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4—1044no—
682C2×C4—1044no—
683C2×C4—1044no—
684C2×C4C2×D4×D1312yes—
685C2×C4C2×D4×D1312yes—
686C2×C4C2×D4×D1311yescharacteristic
687C2×C4C2×Q8×D1312yes—
688C2×C4#41×D1312yes—
689C2×C4C24×D1311yescharacteristic
690C8—22no—
691C8—22no—
692C8—262no—
693C8—262no—
694C22—24no—
695C22—48no—
696C22—42no—
697C22—42no—
698C22—134no—
699C22—268no—
700C22—262no—
701C22—262no—
702C22D13×C22⋊Q812yes—
703C22#1171947512yes—
704C22#1171948012yes—
705C22C22×D4×D1311yescharacteristic
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—134no—
712C4—262no—
713C4—262no—
714C4—264no—
715C4—522no—
716C4—522no—
717C4—522no—
718C4D13×C22⋊Q812yes—
719C4C22×Q8×D1311yescharacteristic
720C4C2×#41×D1311yescharacteristic
721C2—44no—
722C2—264no—
723C2#1312469914yesdirect product factor
724C2C2×D13×C22⋊Q811yescharacteristic
725C2C2×#1171947511yescharacteristic
726C2C2×#1171948011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#478C2
socleC23×C13C22×D4
prime radicalC22×#6129C22
hypercenterC2×#478D13
hypocenterC13C2×#3084
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#11719394C2semidirect
3. #13124699C2direct (N × H)
4. C2×#11718538C2semidirect
5. C2×#11718724C2semidirect
6. C2×#11718512C2semidirect
7. C2×#11718515C2semidirect
8. C2×#11718424C2semidirect
9. C2×#11718669C2semidirect
10. C2×#11718422C2semidirect
11. C2×#11718542C2semidirect
12. C2×D13×#106C2semidirect
13. C2×#11718500C2semidirect
16. C2×C13×#478C2semidirect
26. #11719394C22semidirect
44. C13×#478C22semidirect
58. #11718724C22semidirect
59. #11718669C22semidirect
67. #11718542C22semidirect
68. #11718538C22semidirect
69. D13×#106C22semidirect
70. #11718515C22semidirect
71. #11718512C22semidirect
72. #11718500C22semidirect
75. #11718424C22semidirect
76. #11718422C22semidirect
84. C2×#6129Q8semidirect
210. #6129C2×Q8semidirect
281. C2×#478D13semidirect
377. #478C2×D13semidirect
538. C2×C13#3084semidirect
635. C13C2×#3084semidirect
723. C2#13124699direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193942
C2×#117192512
#131246992
C2×#117185382
C2×#117187242
C2×#117185122
C2×#117185152
C2×#117184242
C2×#117186692
C2×#117184222
C2×#117185422
C2×D13×#1062
C2×#117185002
C2×#117184322
C2×#117184332
C2×C13×#4782
C2×#308413